From 86a683de264404f8bd26a2c924dc3fc45c5ddb64 Mon Sep 17 00:00:00 2001
From: ianchb <i@4t.pw>
Date: Sun, 12 Apr 2026 21:19:14 +0800
Subject: [PATCH] Replace legacy ABEGPU stack with ABE_CUDA backend

---
 AMSS_NCKU_Input.py                |    4 +-
 AMSS_NCKU_Program.py              |    2 +-
 AMSS_NCKU_source/bssn_gpu.cu      | 2908 -----------
 AMSS_NCKU_source/bssn_gpu.h       |   73 -
 AMSS_NCKU_source/bssn_gpu_class.C | 7790 -----------------------------
 AMSS_NCKU_source/bssn_gpu_class.h |  210 -
 AMSS_NCKU_source/bssn_rhs_cuda.cu | 2565 ++++++++++
 AMSS_NCKU_source/bssn_rhs_cuda.h  |   36 +
 AMSS_NCKU_source/bssn_step_gpu.C  | 1942 -------
 AMSS_NCKU_source/makefile         |  163 +-
 AMSS_NCKU_source/makefile.inc     |    4 +
 generate_macrodef.py              |    2 +-
 makefile_and_run.py               |    4 +-
 13 files changed, 2707 insertions(+), 12996 deletions(-)
 delete mode 100644 AMSS_NCKU_source/bssn_gpu.cu
 delete mode 100644 AMSS_NCKU_source/bssn_gpu.h
 delete mode 100644 AMSS_NCKU_source/bssn_gpu_class.C
 delete mode 100644 AMSS_NCKU_source/bssn_gpu_class.h
 create mode 100644 AMSS_NCKU_source/bssn_rhs_cuda.cu
 create mode 100644 AMSS_NCKU_source/bssn_rhs_cuda.h
 delete mode 100644 AMSS_NCKU_source/bssn_step_gpu.C

diff --git a/AMSS_NCKU_Input.py b/AMSS_NCKU_Input.py
index fe25a50..67e7c1c 100755
--- a/AMSS_NCKU_Input.py
+++ b/AMSS_NCKU_Input.py
@@ -16,9 +16,9 @@ import numpy
 File_directory   = "GW150914"                    ## output file directory
 Output_directory = "binary_output"               ## binary data file directory
                                                  ## The file directory name should not be too long
-MPI_processes    = 64                             ## number of mpi processes used in the simulation
+MPI_processes    = 8                             ## number of mpi processes used in the simulation
 
-GPU_Calculation  = "no"                          ## Use GPU or not 
+GPU_Calculation  = "yes"                          ## Use GPU or not 
                                                  ## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)
 CPU_Part         = 1.0
 GPU_Part         = 0.0
diff --git a/AMSS_NCKU_Program.py b/AMSS_NCKU_Program.py
index 2d777cd..9ba512e 100755
--- a/AMSS_NCKU_Program.py
+++ b/AMSS_NCKU_Program.py
@@ -258,7 +258,7 @@ print()
 if (input_data.GPU_Calculation == "no"):
     ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABE")
 elif (input_data.GPU_Calculation == "yes"):
-    ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABEGPU")
+    ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABE_CUDA")
 
 if not os.path.exists( ABE_file ):
     print(                                                                                                  )
diff --git a/AMSS_NCKU_source/bssn_gpu.cu b/AMSS_NCKU_source/bssn_gpu.cu
deleted file mode 100644
index e67ae18..0000000
--- a/AMSS_NCKU_source/bssn_gpu.cu
+++ /dev/null
@@ -1,2908 +0,0 @@
-// includes, system
-#include <stdlib.h>
-#include <stdio.h>
-#include <string.h>
-#include <math.h>
-#include <iostream>
-#include <sys/time.h>
-#include <cuda.h>
-//#include "cutil.h"
-#include <nvrtc.h>
-#include <cuda_runtime.h>
-using namespace std;
-
-//includes, bssn
-#include "gpu_mem.h"
-#include "bssn_gpu.h"
-#ifdef RESULT_CHECK
-#include <fstream>
-#endif
-
-void compare_result_gpu(int ftag1,double * datac,int data_num){
-	double * data = (double*)malloc(sizeof(double)*data_num);
-	cudaMemcpy(data, datac, data_num * sizeof(double), cudaMemcpyDeviceToHost);
-	compare_result(ftag1,data,data_num);
-	free(data);
-}
-
-__global__ void test_const_address(double * testd){
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	if(_t == 0)
-		testd[0] = F1o3;
-}
-
-__global__ void enforce_ga(double * trA){
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	//int ps; //TOTRY: i,j,k; double value;
-	
-	while(_t < _3D_SIZE[0])
-	{
-		  M_ gxx[_t] = M_ dxx[_t] + 1;
-		  M_ gyy[_t] = M_ dyy[_t] + 1;
-		  M_ gzz[_t] = M_ dzz[_t] + 1;
-		// for M_ g;
-		  M_ gupzz[_t] =  M_ gxx[_t] * M_ gyy[_t] * M_ gzz[_t] + M_ gxy[_t] * M_ gyz[_t] * M_ gxz[_t] + M_ gxz[_t] * M_ gxy[_t] * M_ gyz[_t] - 
-		           M_ gxz[_t] * M_ gyy[_t] * M_ gxz[_t] - M_ gxy[_t] * M_ gxy[_t] * M_ gzz[_t] - M_ gxx[_t] * M_ gyz[_t] * M_ gyz[_t]; 
-		
-		  M_ gupzz[_t] = 1.0 / pow( M_ gupzz[_t] , F1o3 ) ;
-		  
-		  M_ gxx[_t] = M_ gxx[_t] * M_ gupzz[_t]; 
-		  M_ gxy[_t] = M_ gxy[_t] * M_ gupzz[_t]; 
-		  M_ gxz[_t] = M_ gxz[_t] * M_ gupzz[_t]; 
-		  M_ gyy[_t] = M_ gyy[_t] * M_ gupzz[_t]; 
-		  M_ gyz[_t] = M_ gyz[_t] * M_ gupzz[_t]; 
-		  M_ gzz[_t] = M_ gzz[_t] * M_ gupzz[_t]; 
-		
-		  M_ dxx[_t] = M_ gxx[_t] - 1;
-		  M_ dyy[_t] = M_ gyy[_t] - 1;
-		  M_ dzz[_t] = M_ gzz[_t] - 1;
-		// for A  ;
-		
-		  M_ gupxx[_t] =   ( M_ gyy[_t] * M_ gzz[_t] - M_ gyz[_t] * M_ gyz[_t] );
-		  M_ gupxy[_t] = - ( M_ gxy[_t] * M_ gzz[_t] - M_ gyz[_t] * M_ gxz[_t] );
-		  M_ gupxz[_t] =   ( M_ gxy[_t] * M_ gyz[_t] - M_ gyy[_t] * M_ gxz[_t] );
-		  M_ gupyy[_t] =   ( M_ gxx[_t] * M_ gzz[_t] - M_ gxz[_t] * M_ gxz[_t] );
-		  M_ gupyz[_t] = - ( M_ gxx[_t] * M_ gyz[_t] - M_ gxy[_t] * M_ gxz[_t] );
-		  M_ gupzz[_t] =   ( M_ gxx[_t] * M_ gyy[_t] - M_ gxy[_t] * M_ gxy[_t] );
-		
-		  trA[_t] =         M_ gupxx[_t] *M_ Axx[_t] + M_ gupyy[_t] * M_ Ayy[_t] + M_ gupzz[_t] * M_ Azz[_t] 
-		       + 2 * (M_ gupxy[_t] *M_ Axy[_t] + M_ gupxz[_t] *M_ Axz[_t] + M_ gupyz[_t] * M_ Ayz[_t]);
-		
-		  M_ Axx[_t] = M_ Axx[_t] - F1o3 * M_ gxx[_t] * trA[_t];
-		  M_ Axy[_t] = M_ Axy[_t] - F1o3 * M_ gxy[_t] * trA[_t];
-		  M_ Axz[_t] = M_ Axz[_t] - F1o3 * M_ gxz[_t] * trA[_t];
-		  M_ Ayy[_t] = M_ Ayy[_t] - F1o3 * M_ gyy[_t] * trA[_t];
-		  M_ Ayz[_t] = M_ Ayz[_t] - F1o3 * M_ gyz[_t] * trA[_t];
-		  M_ Azz[_t] = M_ Azz[_t] - F1o3 * M_ gzz[_t] * trA[_t];
-		//-------------------
-		_t += STEP_SIZE;
-	}
-}
-
-inline void sub_enforce_ga(int matrix_size){
-	double * trA = M_ chin1;
-	enforce_ga<<<GRID_DIM,BLOCK_DIM>>>(trA);
-	cudaMemset(trA,0,matrix_size * sizeof(double));
-	cudaThreadSynchronize(); 
-	
-	//cudaMemset(Mh_ gupxx,0,matrix_size * sizeof(double));
-	//trA gxx,gyy,gzz gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
-	
-}
-__device__ volatile unsigned int global_count = 0;
-__global__ void test_init_matrix(){
-	int tid = blockIdx.x*blockDim.x+threadIdx.x;
-	int curr = tid;
-	while(curr < _3D_SIZE[2])
-	{
-		metac.fh[curr] = 0;
-	  	curr += STEP_SIZE;
-	}
-	curr = tid;
-	while(curr < _3D_SIZE[0])
-	{
-		metac.betaxx[curr] = 0;
-		metac.betaxy[curr] = 0;
-		metac.betaxz[curr] = 0;
-	  	curr += STEP_SIZE;
-	}
-}
-__global__ void init_matrix(double * mat){
-	int tid = blockIdx.x*blockDim.x+threadIdx.x;
-	int curr = tid;
-	while(curr < _3D_SIZE[0])
-	{
-		mat[curr] = 0;
-	  	curr += STEP_SIZE;
-	}
-}
-__global__ void init_3_matrixs(double * mat1,double* mat2,double *mat3){
-	int tid = blockIdx.x*blockDim.x+threadIdx.x;
-	int curr = tid;
-	while(curr < _3D_SIZE[0])
-	{
-		mat1[curr] = 0;
-		mat2[curr] = 0;
-		mat3[curr] = 0;
-	  	curr += STEP_SIZE;
-	}
-}
-__global__ void init_matrix_fh(double * mat){
-	int tid = blockIdx.x*blockDim.x+threadIdx.x;
-	int curr = tid;
-	while(curr < _3D_SIZE[2])
-	{
-		mat[curr] = 0;
-	  	curr += STEP_SIZE;
-	}
-}
-
-
-__global__ void sub_symmetry_bd_partF(int ord, double * func, double *funcc)
-{
-	int curr = blockIdx.x*blockDim.x+threadIdx.x;
-	int ps; //TOTRY: i,j,k; double value;
-	
-	while(curr < _3D_SIZE[0])
-	{
-		int k = curr / _2D_SIZE[0];
-		ps = curr - (_2D_SIZE[0] * k); //TOTRY: = curr % _2D_SIZE[0];
-		int j = ps / ex_c[0];
-		int i = ps  - (j * ex_c[0]);  //= ps % ex_c[0];
-		
-		funcc[i+ ord + (ord +j)* _1D_SIZE[ord] + (k + ord) * _2D_SIZE[ord]] = func[curr];
-	
-		curr += STEP_SIZE;
-	}
-	
-}
-
-#ifdef Vertex
-__global__ void sub_symmetry_bd_partI(int ord, double * func, double * funcc,double S1){
-	//for i
-	int curr = blockIdx.x*blockDim.x+threadIdx.x;
-	int ps;
-	int m;
-	while(curr < (ex_c[1]+ord)*(ex_c[2]+ord) ){
-		m =  ord * 2;
-		ps = curr * _1D_SIZE[ord];
-		for(int i = 0;i < ord; ++i){
-			funcc[ps] = funcc [ps + m] * S1;
-			ps ++;
-			m -= 2;
-		}
-		curr+= STEP_SIZE;
-	}
-	__syncthreads();
-}
-__global__ void sub_symmetry_bd_partJ(int ord,double * func, double * funcc,double S2){
-	//for j
-	int curr = blockIdx.x*blockDim.x+threadIdx.x;
-	int ps;
-	int m;
-	
-	while(curr < (ex_c[0]+ord)*(ex_c[2]+ord))
-	{
-		m = 2 * ord;
-		ps = (curr/_1D_SIZE[ord])*_2D_SIZE[ord] + (curr % _1D_SIZE[ord]);
-		for(int i = 0;i<ord;++i){
-			funcc[ps] = funcc[ps + _1D_SIZE[ord] * m]* S2;
-			ps += _1D_SIZE[ord];
-			m -= 2;
-		}
-		curr+=STEP_SIZE;
-	}
-}
-__global__ void sub_symmetry_bd_partK(int ord,double * func, double * funcc,double S3){
-	//for k
-	int curr = blockIdx.x*blockDim.x+threadIdx.x;
-	int m ;
-	while(curr < _2D_SIZE[ord]){
-		m = ord * 2;
-		for(int i = 0;i < ord;++i){
-			funcc[curr] = funcc[curr + _2D_SIZE[ord] * m] * S3;
-			curr += _2D_SIZE[ord];
-			m -= 2;
-		}
-		curr+= STEP_SIZE;
-	}
-	
-	//TOTALLY use only 1 cycle
-	/*curr = tid + _2D_SIZE[2];
-	while(curr < 2 * _2D_SIZE[2]){
-		funcc[curr] = funcc [curr + _2D_SIZE[2]*2] * SoA[3];
-		curr+= STEP_SIZE;
-	}*/
-
-}
-
-#else //ifdef Vertex
-#ifdef Cell
-__global__ void sub_symmetry_bd_partI(int ord, double * func, double * funcc,double S1){
-	//for i
-	int curr = blockIdx.x*blockDim.x+threadIdx.x;
-	int ps;
-	int m;
-	while(curr < (ex_c[1]+ord)*(ex_c[2]+ord) ){
-		m =  ord * 2 - 1;  //changed from "m =  ord * 2"
-		ps = curr * _1D_SIZE[ord];
-		for(int i = 0;i < ord; ++i){
-			funcc[ps] = funcc [ps + m] * S1;
-			ps ++;
-			m -= 2;
-		}
-		curr+= STEP_SIZE;
-	}
-	__syncthreads();
-}
-
-__global__ void sub_symmetry_bd_partJ(int ord,double * func, double * funcc,double S2){
-	//for j
-	int curr = blockIdx.x*blockDim.x+threadIdx.x;
-	int ps;
-	int m;
-	
-	while(curr < (ex_c[0]+ord)*(ex_c[2]+ord))
-	{
-		m = 2 * ord - 1;
-		ps = (curr/_1D_SIZE[ord])*_2D_SIZE[ord] + (curr % _1D_SIZE[ord]);
-		for(int i = 0;i<ord;++i){
-			funcc[ps] = funcc[ps + _1D_SIZE[ord] * m]* S2;
-			ps += _1D_SIZE[ord];
-			m -= 2;
-		}
-		curr+=STEP_SIZE;
-	}
-}
-
-__global__ void sub_symmetry_bd_partK(int ord,double * func, double * funcc,double S3){
-	//for k
-	int curr = blockIdx.x*blockDim.x+threadIdx.x;
-	int m ;
-	while(curr < _2D_SIZE[ord]){
-		m = ord * 2 - 1;
-		for(int i = 0;i < ord;++i){
-			funcc[curr] = funcc[curr + _2D_SIZE[ord] * m] * S3;
-			curr += _2D_SIZE[ord];
-			m -= 2;
-		}
-		curr+= STEP_SIZE;
-	}
-}
-#endif //ifdef Cell
-#endif //ifdef Vertex
-inline void sub_symmetry_bd(int ord,double * func, double * funcc,double * SoA){
-	sub_symmetry_bd_partF<<<GRID_DIM,BLOCK_DIM>>>(ord,func,funcc);
-	cudaThreadSynchronize();
-	sub_symmetry_bd_partI<<<GRID_DIM,BLOCK_DIM>>>(ord,func,funcc,SoA[0]);
-	cudaThreadSynchronize();
-	sub_symmetry_bd_partJ<<<GRID_DIM,BLOCK_DIM>>>(ord,func,funcc,SoA[1]);
-	cudaThreadSynchronize();
-	sub_symmetry_bd_partK<<<GRID_DIM,BLOCK_DIM>>>(ord,func,funcc,SoA[2]);
-	cudaThreadSynchronize();
-}
-
-
-__global__ void sub_fdderivs_part1(double * f,double *fh,double *fxx,double *fxy,double *fxz,double *fyy,double *fyz,double *fzz)
- {	
-	int curr = blockIdx.x*blockDim.x+threadIdx.x;
-	int ps; //TOTRY: i,j,k; double value;
-	
-	while(curr < _3D_SIZE[0])
-	{
-		int k = curr / _2D_SIZE[0];
-		ps = curr - (_2D_SIZE[0] * k); //TOTRY: = curr % _2D_SIZE[0];
-		int j = ps / ex_c[0];
-		int i = ps  - (j * ex_c[0]);
-		
-		if(k == ex_c[2]-1 || i == ex_c[0]-1 || j == ex_c[1]-1){
-			curr += STEP_SIZE;	
-			continue;
-		}
-		else
-		{
-			//xx
-			if(i+2 <= ijk_max[0] && i-2 >= ijk_min[0]){
-				fxx[curr] = Fdxdx*(-_FH2_(i,(j+2),(k+2))+16*_FH2_((i+1),(j+2),(k+2))-30*_FH2_((i+2),(j+2),(k+2)) 
-			            -_FH2_((i+4),(j+2),(k+2))+16*_FH2_((i+3),(j+2),(k+2))		);
-							
-			}
-			else if(i+1 <= ijk_max[0] && i-1 >= ijk_min[0]){
-				fxx[curr] = Sdxdx*(_FH2_((i+1),(j+2),(k+2))-2*_FH2_((i+2),(j+2),(k+2)) 
-			            +_FH2_(i+3,(j+2),(k+2))              );
-			}
-			//zz--
-			if(k+2 <= ijk_max[2] && k-2 >= ijk_min[2]){
-				fzz[curr] = Fdzdz * (-_FH2_((i+2),(j+2),k) + 16 *_FH2_((i+2),(j+2),(k+1))- 30*_FH2_((i+2),(j+2),(k+2)) 
-		            -_FH2_((i+2),(j+2),(k+4))+ 16*_FH2_((i+2),(j+2),(k+3))              );
-			}
-			else if(k+1 <= ijk_max[2] && k-1 >= ijk_min[2]){
-				fzz[curr] = Sdzdz*(_FH2_((i+2),(j+2),(k+1))- 2 * _FH2_((i+2),(j+2),(k+2)) 
-			            + _FH2_((i+2),(j+2),(k+3))              );
-			}
-
-			//yy--
-			if(j+2 <= ijk_max[1] && j-2 >= ijk_min[1]){
-			    fyy[curr] = Fdydy*(-_FH2_((i+2),j,(k+2))+16*_FH2_((i+2),(j+1),(k+2))-30*_FH2_((i+2),(j+2),(k+2)) 
-			            -_FH2_((i+2),(j+4),(k+2))+16*_FH2_((i+2),(j+3),(k+2))              );
-			}
-			else if(j+1 <= ijk_max[1] && j-1 >= ijk_min[1]){
-				fyy[curr] = Sdydy*(_FH2_((i+2),(j+1),(k+2))-2*_FH2_((i+2),(j+2),(k+2)) 
-			            +_FH2_((i+2),(j+3),(k+2))              );
-			}
-
-			
-			
-			//xy
-		    if(i+2 <= ijk_max[0] && i-2 >= ijk_min[0] && j+2 <= ijk_max[1] && j-2 >= ijk_min[1])	
-		   		fxy[curr] = Fdxdy*((_FH2_(i,j,(k+2))-8*_FH2_((i+1),j,(k+2))+8*_FH2_((i+3),j,(k+2))-_FH2_((i+4),j,(k+2))) 
-		                       -8 *(_FH2_(i,(j+1),(k+2))-8*_FH2_((i+1),(j+1),(k+2))+8*_FH2_((i+3),(j+1),(k+2))-_FH2_((i+4),(j+1),(k+2)))  
-		                       +8 *(_FH2_(i,(j+3),(k+2))-8*_FH2_((i+1),(j+3),(k+2))+8*_FH2_((i+3),(j+3),(k+2))-_FH2_((i+4),(j+3),(k+2)))  
-		                       -    (_FH2_(i,(j+4),(k+2))-8*_FH2_((i+1),(j+4),(k+2))+8*_FH2_((i+3),(j+4),(k+2))-_FH2_((i+4),(j+4),(k+2))));
-
-		   	else if(i+1 <= ijk_max[0] && i-1 >= ijk_min[0] && j+1 <= ijk_max[1] && j-1 >= ijk_min[1])
-		                
-		   		fxy[curr] = Sdxdy*(_FH2_((i+1),(j+1),(k+2))-_FH2_((i+3),(j+1),(k+2))-_FH2_((i+1),(j+3),(k+2))+_FH2_((i+3),(j+3),(k+2)));
-			//xz
-		    if(i+2 <= ijk_max[0] && i-2 >= ijk_min[0] && k+2 <= ijk_max[2] && k-2 >= ijk_min[2])
-		   		fxz[curr] = Fdxdz*(     (_FH2_(i,(j+2),k)-8*_FH2_((i+1),(j+2),k)+8*_FH2_((i+3),(j+2),k)-_FH2_((i+4),(j+2),k)) 
-		                       -8 *(_FH2_(i,(j+2),(k+1))-8*_FH2_((i+1),(j+2),(k+1))+8*_FH2_((i+3),(j+2),(k+1))-_FH2_((i+4),(j+2),(k+1))) 
-		                       +8 *(_FH2_(i,(j+2),(k+3))-8*_FH2_((i+1),(j+2),(k+3))+8*_FH2_((i+3),(j+2),(k+3))-_FH2_((i+4),(j+2),(k+3)))  
-		                       -    (_FH2_(i,(j+2),(k+4))-8*_FH2_((i+1),(j+2),(k+4))+8*_FH2_((i+3),(j+2),(k+4))-_FH2_((i+4),(j+2),(k+4))));
-		                       
-			else if(i+1 <= ijk_max[0] && i-1 >= ijk_min[0] && k+1 <= ijk_max[2] && k-1 >= ijk_min[2])
-					fxz[curr] = Sdxdz*(_FH2_((i+1),(j+2),(k+1))-_FH2_((i+3),(j+2),(k+1))-_FH2_((i+1),(j+2),(k+3))+_FH2_((i+3),(j+2),(k+3)));
-			//yz
-			if(j+2 <= ijk_max[1] && j-2 >= ijk_min[1] && k+2 <= ijk_max[2] && k-2 >= ijk_min[2])
-					fyz[curr] = Fdydz*(     (_FH2_((i+2),j,k)-8*_FH2_((i+2),(j+1),k)+8*_FH2_((i+2),(j+3),k)-_FH2_((i+2),(j+4),k))  
-		                       -8 *(_FH2_((i+2),j,(k+1))-8*_FH2_((i+2),(j+1),(k+1))+8*_FH2_((i+2),(j+3),(k+1))-_FH2_((i+2),(j+4),(k+1)))  
-		                       +8 *(_FH2_((i+2),j,(k+3))-8*_FH2_((i+2),(j+1),(k+3))+8*_FH2_((i+2),(j+3),(k+3))-_FH2_((i+2),(j+4),(k+3)))  
-		                       -    (_FH2_((i+2),j,(k+4))-8*_FH2_((i+2),(j+1),(k+4))+8*_FH2_((i+2),(j+3),(k+4))-_FH2_((i+2),(j+4),(k+4))));
-		                       
-			else if(j+1 <= ijk_max[1] && j-1 >= ijk_min[1] && k+1 <= ijk_max[2] && k-1 >= ijk_min[2])
-					fyz[curr] = Sdydz*(_FH2_((i+2),(j+1),(k+1))-_FH2_((i+2),(j+3),(k+1))-_FH2_((i+2),(j+1),(k+3))+_FH2_((i+2),(j+3),(k+3)));
-			
-			curr += STEP_SIZE;
-		}
-	}
- 	
- 	__syncthreads();
- }
-
-inline void sub_fdderivs(double * f,double *fh,double *fxx,double *fxy,double *fxz,double *fyy,double *fyz,double *fzz,double* SoA)
-{
-	sub_symmetry_bd(2,f,fh,SoA);
-	cudaMemset(fxx,0,_3D_SIZE[0] * sizeof(double));
-	cudaMemset(fxy,0,_3D_SIZE[0] * sizeof(double));
-	cudaMemset(fxz,0,_3D_SIZE[0] * sizeof(double));
-	cudaMemset(fyy,0,_3D_SIZE[0] * sizeof(double));
-	cudaMemset(fyz,0,_3D_SIZE[0] * sizeof(double));
-	cudaMemset(fzz,0,_3D_SIZE[0] * sizeof(double));
-	cudaThreadSynchronize(); 
-	sub_fdderivs_part1<<<GRID_DIM,BLOCK_DIM>>>(f,fh,fxx,fxy,fxz,fyy,fyz,fzz);
-	cudaThreadSynchronize(); 
-}
-
-__global__ void sub_fderivs_part1(double * f,double * fh,double *fx,double *fy,double *fz  )
- {	
-	int curr = blockIdx.x*blockDim.x+threadIdx.x;
-	int ps; //TOTRY: i,j,k; double value;
-	
-	while(curr < _3D_SIZE[0])
-	{
-		int k = curr / _2D_SIZE[0];
-		ps = curr - (_2D_SIZE[0] * k); //TOTRY: = curr % _2D_SIZE[0];
-		int j = ps / ex_c[0];
-		int i = ps  - (j * ex_c[0]);
-		
-		if(k == ex_c[2]-1 || i == ex_c[0]-1 || j == ex_c[1]-1){
-			curr += STEP_SIZE;	
-			continue;
-		}
-		
-			//X--
-			if(i+2 <= ijk_max[0] && i-2 >= ijk_min[0])
-				fx[curr] = d12dxyz[0]*(fh[i+(j+2)*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]] - 
-								8*fh[i+1+(j+2)*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]]	+
-								8*fh[i+3+(j+2)*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]]	-
-								fh[i+4+(j+2)*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]]	);
-							
-			else if(i+1 <= ijk_max[0] && i-1 >= ijk_min[0])
-				fx[curr] = d2dxyz[0]*(-fh[i+1+(j+2)*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]]	+
-								fh[i+3+(j+2)*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]]	);
-			//Y--
-			if(j+2 <= ijk_max[1] && j-2 >= ijk_min[1])
-	      		fy[curr]=d12dxyz[1]*(fh[i+2+j*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]]-
-	      						8*fh[i+2+(j+1)*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]]	+
-	      						8*fh[i+2+(j+3)*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]]	-
-	      						fh[i+2+(j+4)*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]]);
-	      						
-	    	else if(j+1 <= ijk_max[1] && j-1 >= ijk_min[1])
-	     		fy[curr]=d2dxyz[1]*(-fh[i+2+(j+1)*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]]		+
-	     						fh[i+2+(j+3)*_1D_SIZE[2]+(k+2)*_2D_SIZE[2]]);
-	     	//Z--
-      
-	     	if(k+2 <= ijk_max[2] && k-2 >= ijk_min[2])
-	      	   fz[curr]=d12dxyz[2]*(	fh[i+2+(j+2)*_1D_SIZE[2]+k    *_2D_SIZE[2]]		-
-	      						 8*		fh[i+2+(j+2)*_1D_SIZE[2]+(k+1)*_2D_SIZE[2]]		+
-	      						 8*		fh[i+2+(j+2)*_1D_SIZE[2]+(k+3)*_2D_SIZE[2]]		-
-	      								fh[i+2+(j+2)*_1D_SIZE[2]+(k+4)*_2D_SIZE[2]]);
-	      					
-	    	else if(k+1 <= ijk_max[2] && k-1 >= ijk_min[2])
-	      		fz[curr]=d2dxyz[2]*(-fh[i+2+(j+2)*_1D_SIZE[2]+(k+1)*_2D_SIZE[2]]+
-	      						fh[i+2+(j+2)*_1D_SIZE[2]+(k+3)*_2D_SIZE[2]]);
-      
-			curr += STEP_SIZE;
-		
-	}
- }
- 
-inline void sub_fderivs(double * f,double * fh,double *fx,double *fy,double *fz,double * SoA)
-{
-	sub_symmetry_bd(2,f,fh,SoA);
-	
-	cudaMemset(fx,0,_3D_SIZE[0] * sizeof(double));
-	cudaMemset(fy,0,_3D_SIZE[0] * sizeof(double));
-	cudaMemset(fz,0,_3D_SIZE[0] * sizeof(double));
-	
-	cudaThreadSynchronize(); 
-	sub_fderivs_part1<<<GRID_DIM,BLOCK_DIM>>>(f,fh,fx,fy,fz);
-	cudaThreadSynchronize();
-}
-
-__global__ void computeRicci_part1(double * dst)
-{
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	while(_t < _3D_SIZE[0])
-	{	
-		dst[_t] = M_ gupxx [_t]* M_ fxx [_t]+ M_ gupyy[_t]* M_ fyy[_t]+ M_ gupzz[_t]* M_ fzz[_t]+ 
-         ( M_ gupxy[_t]* M_ fxy[_t]+ M_ gupxz[_t]* M_ fxz[_t]+ M_ gupyz[_t]* M_ fyz[_t]) * 2;
-	
-		_t += STEP_SIZE;
-	}
-}
-
- inline void computeRicci(double * src,double* dst,double * SoA, Meta* meta)
-{
-	sub_fdderivs(src,Mh_ fh,Mh_ fxx,Mh_ fxy,Mh_ fxz,Mh_ fyy,Mh_ fyz,Mh_ fzz,SoA);
-	cudaThreadSynchronize();
-	computeRicci_part1<<<GRID_DIM,BLOCK_DIM>>>(dst);
-	cudaThreadSynchronize();
-	
-}/*Exception*/
-
-__global__ void sub_kodis_part1(double *f,double *fh,double *f_rhs)
-{
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	int ps; //TOTRY: i,j,k; double value;
-	double inc_f_rhs;
-	while(_t < _3D_SIZE[0])
-	{
-		int k = _t / _2D_SIZE[0];
-		ps = _t - (_2D_SIZE[0] * k); //TOTRY: = curr % _2D_SIZE[0];
-		int j = ps / ex_c[0];
-		int i = ps  - (j * ex_c[0]);
-		
-		if(k == ex_c[2]-1 && i == ex_c[0]-1 && j == ex_c[1]-1){
-			_t += STEP_SIZE;
-			continue;
-		}
-
-		if(i-3 >= ijk_min3[0] && i+3 <= ijk_max[0] && 
-		    j-3 >= ijk_min3[1] && j+3 <= ijk_max[1] && 
-		    k-3 >= ijk_min3[2] && k+3 <= ijk_max[2])
-		{ 
-		// x direction
-		   inc_f_rhs =  		( (_FH3_(i,(j+3),(k+3))+_FH3_((i+6),(j+3),(k+3))) - 
-		                6*(_FH3_((i+1),(j+3),(k+3))+_FH3_((i+5),(j+3),(k+3))) + 
-		                15*(_FH3_((i+2),(j+3),(k+3))+_FH3_((i+4),(j+3),(k+3))) - 
-		                20* _FH3_((i+3),(j+3),(k+3))          ) /dX;
-		                
-       					
-		// y direction
-
-	   		inc_f_rhs +=		(  (_FH3_((i+3),j,(k+3))+_FH3_((i+3),(j+6),(k+3))) - 
-		                6*(_FH3_((i+3),(j+1),(k+3))+_FH3_((i+3),(j+5),(k+3))) + 
-		                15*(_FH3_((i+3),(j+2),(k+3))+_FH3_((i+3),(j+4),(k+3))) - 
-		                20* _FH3_((i+3),(j+3),(k+3))             )/dY;
-		                
-		// z direction
-					
-		   	inc_f_rhs +=		 ( (_FH3_((i+3),(j+3),k)+_FH3_((i+3),(j+3),(k+6))) - 
-		            6*(_FH3_((i+3),(j+3),(k+1))+_FH3_((i+3),(j+3),(k+5))) + 
-		            15*(_FH3_((i+3),(j+3),(k+2))+_FH3_((i+3),(j+3),(k+4))) - 
-		            20* _FH3_((i+3),(j+3),(k+3))             )/dZ;
-		   inc_f_rhs *= eps_c;
-		   inc_f_rhs /= 64;         
-		   f_rhs[_t] += inc_f_rhs;  //be careful the mark is "+=" not "==" !
-		}
-	   
-		_t += STEP_SIZE;
-	}
-}
-
-inline void sub_kodis(double *f,double *fh,double *f_rhs,double *SoA)
-{
-	sub_symmetry_bd(3,f,fh,SoA);
-	cudaThreadSynchronize();
-	sub_kodis_part1<<<GRID_DIM,BLOCK_DIM>>>(f,fh,f_rhs);
-	cudaThreadSynchronize();
-}
- 
-__global__ void  sub_lopsided_part1(double *f,double* fh,double *f_rhs,double *Sfx,double *Sfy,double *Sfz)
-{
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	int ps; //TOTRY: i,j,k; double value;
-	
-	while(_t < _3D_SIZE[0])
-	{
-		int k = _t / _2D_SIZE[0];
-		ps = _t - (_2D_SIZE[0] * k); //TOTRY: = curr % _2D_SIZE[0];
-		int j = ps / ex_c[0];
-		int i = ps  - (j * ex_c[0]);
-		
-		if(k < ex_c[2]-1 && i < ex_c[0]-1 && j < ex_c[1]-1){
-			// x direction   
-		    if(Sfx[_t] >= 0 && i+3 <= ijk_max[0] && i-1 >= ijk_min2[0])
-		     f_rhs[_t]=f_rhs[_t]+                                                   
-		                  Sfx[_t]*d12dxyz[0]*(-3*_FH3_((i+2),(j+3),(k+3))-10*_FH3_((i+3),(j+3),(k+3))+18*_FH3_((i+4),(j+3),(k+3)) 
-		                                    -6*_FH3_((i+5),(j+3),(k+3))+    _FH3_((i+6),(j+3),(k+3)));
-
-		     else if(Sfx[_t] <= 0 && i-3 >= ijk_min2[0] && i+1 <= ijk_max[0])
-		     f_rhs[_t]=f_rhs[_t]-                                                   
-		                  Sfx[_t]*d12dxyz[0]*(-3*_FH3_((i+4),(j+3),(k+3))-10*_FH3_((i+3),(j+3),(k+3))+18*_FH3_((i+2),(j+3),(k+3)) 
-		                                    -6*_FH3_((i+1),(j+3),(k+3))+    _FH3_(i,(j+3),(k+3)));
-
-		     else if(i+2 <= ijk_max[0] && i-2 >= ijk_min2[0])
-
-
-		     f_rhs[_t]=f_rhs[_t]+                                                           
-		                  Sfx[_t]*d12dxyz[0]*(_FH3_((i+1),(j+3),(k+3))-8*_FH3_((i+2),(j+3),(k+3))+8*_FH3_((i+4),(j+3),(k+3))-_FH3_((i+5),(j+3),(k+3)));
-
-		     else if(i+1 <= ijk_max[0] && i-1 >= ijk_min2[0])
-
-		     f_rhs[_t]=f_rhs[_t] + Sfx[_t]*d2dxyz[0]*(-_FH3_((i+2),(j+3),(k+3))+_FH3_((i+4),(j+3),(k+3)));
-
-
-			// y direction   
-		    if(Sfy[_t] >= 0 && j+3 <= ijk_max[1] && j-1 >= ijk_min2[1])
-
-		     f_rhs[_t]=f_rhs[_t]+                                                   
-		                  Sfy[_t]*d12dxyz[1]*(-3*_FH3_((i+3),(j+2),(k+3))-10*_FH3_((i+3),(j+3),(k+3))+18*_FH3_((i+3),(j+4),(k+3)) 
-		                                    -6*_FH3_((i+3),(j+5),(k+3))+    _FH3_((i+3),(j+6),(k+3)));
-
-		    else if(Sfy[_t] <= 0 && j-3 >= ijk_min2[1] && j+1 <= ijk_max[1])
-		     f_rhs[_t]=f_rhs[_t]-                                                   
-		                  Sfy[_t]*d12dxyz[1]*(-3*_FH3_((i+3),(j+4),(k+3))-10*_FH3_((i+3),(j+3),(k+3))+18*_FH3_((i+3),(j+2),(k+3)) 
-		                                    -6*_FH3_((i+3),(j+1),(k+3))+    _FH3_((i+3),j,(k+3)));
-
-		    else if(j+2 <= ijk_max[1] && j-2 >= ijk_min2[1])
-
-		     f_rhs[_t]=f_rhs[_t]+                                                            
-		                  Sfy[_t]*d12dxyz[1]*(_FH3_((i+3),(j+1),(k+3))-8*_FH3_((i+3),(j+2),(k+3))+8*_FH3_((i+3),(j+4),(k+3))-_FH3_((i+3),(j+5),(k+3)));
-
-		    else if(j+1 <= ijk_max[1] && j-1 >= ijk_min2[1])
-
-		     f_rhs[_t]=f_rhs[_t] + Sfy[_t]*d2dxyz[1]*(-_FH3_((i+3),(j+2),(k+3))+_FH3_((i+3),(j+4),(k+3)));
-		     
-
-			// z direction   
-		    if(Sfz[_t] >= 0 && k+3 <= ijk_max[2] && k-1 >= ijk_min2[2])
-			//         v
-			// D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
-			//  i     12dx       i-v      i      i+v     i+2v    i+3v
-		     f_rhs[_t]=f_rhs[_t]+                                                   
-		                  Sfz[_t]*d12dxyz[2]*(-3*_FH3_((i+3),(j+3),(k+2))-10*_FH3_((i+3),(j+3),(k+3))+18*_FH3_((i+3),(j+3),(k+4)) 
-		                                    -6*_FH3_((i+3),(j+3),(k+5))+    _FH3_((i+3),(j+3),(k+6)));
-
-		    else if(Sfz[_t] <= 0 && k-3 >= ijk_min2[2] && k+1 <= ijk_max[2])
-		     f_rhs[_t]=f_rhs[_t]-                                                   
-		                  Sfz[_t]*d12dxyz[2]*(-3*_FH3_((i+3),(j+3),(k+4))-10*_FH3_((i+3),(j+3),(k+3))+18*_FH3_((i+3),(j+3),(k+2)) 
-		                                    -6*_FH3_((i+3),(j+3),(k+1))+    _FH3_((i+3),(j+3),k));
-
-		     else if(k+2 <= ijk_max[2] && k-2 >= ijk_min2[2])
-
-		     f_rhs[_t]=f_rhs[_t]+                                                            
-		                  Sfz[_t]*d12dxyz[2]*(_FH3_((i+3),(j+3),(k+1))-8*_FH3_((i+3),(j+3),(k+2))+8*_FH3_((i+3),(j+3),(k+4))-_FH3_((i+3),(j+3),(k+5)));
-
-		     else if(k+1 <= ijk_max[2] && k-1 >= ijk_min2[2])
-
-		     f_rhs[_t]=f_rhs[_t]+Sfz[_t]*d2dxyz[2]*(-_FH3_((i+3),(j+3),(k+2))+_FH3_((i+3),(j+3),(k+4)));
-		}
-		//-------------------
-		_t += STEP_SIZE;
-	}
-}
-
-
-inline void  sub_lopsided(double *f,double*fh,double *f_rhs,double *Sfx,double *Sfy,double *Sfz,double *SoA){
-	sub_symmetry_bd(3,f,fh,SoA);
-	cudaThreadSynchronize(); 
-	sub_lopsided_part1<<<GRID_DIM,BLOCK_DIM>>>(f,fh,f_rhs,Sfx,Sfy,Sfz);
-	cudaThreadSynchronize(); 
-}
-
-__global__ void compute_rhs_bssn_part1() 
-{
-	int tid = blockIdx.x*blockDim.x+threadIdx.x;
-	int curr = tid;
-	while(curr < _3D_SIZE[0])
-	{
-		metac.alpn1[curr] = metac.Lap[curr] + 1; 
-	  	metac.chin1[curr] = metac.chi[curr] + 1;
-	  	metac.gxx[curr] = metac.dxx[curr] + 1;
-	  	metac.gyy[curr] = metac.dyy[curr] + 1;
-	  	metac.gzz[curr] = metac.dzz[curr] + 1;
-	  	
-	  	curr += STEP_SIZE;
-	}
-}
-
-__global__ void compute_rhs_bssn_part2() 
-{
-	//__shared__ int judge = 1;
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	while(_t < _3D_SIZE[0])
-	{
-
-		M_ div_beta[_t] = M_ betaxx[_t] + M_ betayy[_t] + M_ betazz[_t];
-		M_ chi_rhs[_t] = F2o3 *M_ chin1[_t]*( M_ alpn1[_t] * M_ trK[_t] - M_ div_beta[_t] ); //rhs[_t] for M_ chi
-
-		M_ gxx_rhs[_t] = - 2 * M_ alpn1[_t] * M_ Axx[_t]   -  F2o3 * M_ gxx[_t]* M_ div_beta[_t]        + 
-		            2 *(  M_ gxx[_t]* M_ betaxx[_t]+   M_ gxy[_t]* M_ betayx[_t]+   M_ gxz[_t]* M_ betazx[_t]);
-		M_ gyy_rhs[_t] = - 2 * M_ alpn1[_t] * M_ Ayy[_t]   -  F2o3 * M_ gyy[_t]* M_ div_beta[_t]        + 
-		            2 *(  M_ gxy[_t]* M_ betaxy[_t]+   M_ gyy[_t]* M_ betayy[_t]+   M_ gyz[_t]* M_ betazy[_t]);
-
-		M_ gzz_rhs[_t] = - 2 * M_ alpn1[_t] * M_ Azz[_t]   -  F2o3 * M_ gzz[_t]* M_ div_beta[_t]        + 
-		            2 *(  M_ gxz[_t]* M_ betaxz[_t]+   M_ gyz[_t]* M_ betayz[_t]+   M_ gzz[_t]* M_ betazz[_t]);
-
-		M_ gxy_rhs[_t] = - 2 * M_ alpn1[_t] * M_ Axy[_t]   +  F1o3 * M_ gxy[_t]   * M_ div_beta[_t]     + 
-		                    M_ gxx[_t]* M_ betaxy[_t]                 +   M_ gxz[_t]* M_ betazy[_t]+ 
-		                                    M_ gyy[_t]* M_ betayx[_t]+   M_ gyz[_t]* M_ betazx[_t]  
-		                                                -   M_ gxy[_t]* M_ betazz[_t];
-
-		M_ gyz_rhs[_t] = - 2 * M_ alpn1[_t] * M_ Ayz[_t]   +  F1o3 * M_ gyz[_t]   * M_ div_beta[_t]     + 
-		                    M_ gxy[_t]* M_ betaxz[_t]+   M_ gyy[_t]* M_ betayz[_t]                 + 
-		                    M_ gxz[_t]* M_ betaxy[_t]                 +   M_ gzz[_t]* M_ betazy[_t]  
-		                                                -   M_ gyz[_t]* M_ betaxx[_t];
-
-		M_ gxz_rhs[_t] = - 2 * M_ alpn1[_t] * M_ Axz[_t]   +  F1o3 * M_ gxz[_t]   * M_ div_beta[_t]     + 
-		                    M_ gxx[_t]* M_ betaxz[_t]+   M_ gxy[_t]* M_ betayz[_t]                 + 
-		                                    M_ gyz[_t]* M_ betayx[_t]+   M_ gzz[_t]* M_ betazx[_t]  
-		                                                -   M_ gxz[_t]* M_ betayy[_t];    //rhs[_t] for gij
-
-		// invert tilted metric
-		M_ gupzz[_t]=  M_ gxx[_t]* M_ gyy[_t]* M_ gzz[_t]+ M_ gxy[_t]* M_ gyz[_t]* M_ gxz[_t]+ M_ gxz[_t]* M_ gxy[_t]* M_ gyz[_t]- 
-		        M_ gxz[_t]* M_ gyy[_t]* M_ gxz[_t]- M_ gxy[_t]* M_ gxy[_t]* M_ gzz[_t]- M_ gxx[_t]* M_ gyz[_t]* M_ gyz[_t];
-		M_ gupxx[_t]=   ( M_ gyy[_t]* M_ gzz[_t]- M_ gyz[_t]* M_ gyz[_t]) / M_ gupzz[_t];
-		M_ gupxy[_t]= - ( M_ gxy[_t]* M_ gzz[_t]- M_ gyz[_t]* M_ gxz[_t]) / M_ gupzz[_t];
-		M_ gupxz[_t]=   ( M_ gxy[_t]* M_ gyz[_t]- M_ gyy[_t]* M_ gxz[_t]) / M_ gupzz[_t];
-		M_ gupyy[_t]=   ( M_ gxx[_t]* M_ gzz[_t]- M_ gxz[_t]* M_ gxz[_t]) / M_ gupzz[_t];
-		M_ gupyz[_t]= - ( M_ gxx[_t]* M_ gyz[_t]- M_ gxy[_t]* M_ gxz[_t]) / M_ gupzz[_t];
-		M_ gupzz[_t]=   ( M_ gxx[_t]* M_ gyy[_t]- M_ gxy[_t]* M_ gxy[_t]) / M_ gupzz[_t];
-		//if(threadIdx.x == 0){
-		//	judge = co_c;
-		//}
-		//__syncthreads();
-
-		if(co_c == 0)
-		{
-		// M_ Gam^i_Res = M_ Gam^i + M_ gup^ij_,j
-		M_ Gmx_Res[_t] = M_ Gamx[_t] - (M_ gupxx[_t]*(M_ gupxx[_t]*M_ gxxx[_t]+M_ gupxy[_t]*M_ gxyx[_t]+M_ gupxz[_t]*M_ gxzx[_t])
-		                +M_ gupxy[_t]*(M_ gupxx[_t]*M_ gxyx[_t]+M_ gupxy[_t]*M_ gyyx[_t]+M_ gupxz[_t]*M_ gyzx[_t])
-		                +M_ gupxz[_t]*(M_ gupxx[_t]*M_ gxzx[_t]+M_ gupxy[_t]*M_ gyzx[_t]+M_ gupxz[_t]*M_ gzzx[_t])
-		                +M_ gupxx[_t]*(M_ gupxy[_t]*M_ gxxy[_t]+M_ gupyy[_t]*M_ gxyy[_t]+M_ gupyz[_t]*M_ gxzy[_t])
-		                +M_ gupxy[_t]*(M_ gupxy[_t]*M_ gxyy[_t]+M_ gupyy[_t]*M_ gyyy[_t]+M_ gupyz[_t]*M_ gyzy[_t])
-		                +M_ gupxz[_t]*(M_ gupxy[_t]*M_ gxzy[_t]+M_ gupyy[_t]*M_ gyzy[_t]+M_ gupyz[_t]*M_ gzzy[_t])
-		                +M_ gupxx[_t]*(M_ gupxz[_t]*M_ gxxz[_t]+M_ gupyz[_t]*M_ gxyz[_t]+M_ gupzz[_t]*M_ gxzz[_t])
-		                +M_ gupxy[_t]*(M_ gupxz[_t]*M_ gxyz[_t]+M_ gupyz[_t]*M_ gyyz[_t]+M_ gupzz[_t]*M_ gyzz[_t])
-		                +M_ gupxz[_t]*(M_ gupxz[_t]*M_ gxzz[_t]+M_ gupyz[_t]*M_ gyzz[_t]+M_ gupzz[_t]*M_ gzzz[_t]));
-		M_ Gmy_Res[_t] = M_ Gamy[_t] - (M_ gupxx[_t]*(M_ gupxy[_t]*M_ gxxx[_t]+M_ gupyy[_t]*M_ gxyx[_t]+M_ gupyz[_t]*M_ gxzx[_t])
-		                +M_ gupxy[_t]*(M_ gupxy[_t]*M_ gxyx[_t]+M_ gupyy[_t]*M_ gyyx[_t]+M_ gupyz[_t]*M_ gyzx[_t])
-		                +M_ gupxz[_t]*(M_ gupxy[_t]*M_ gxzx[_t]+M_ gupyy[_t]*M_ gyzx[_t]+M_ gupyz[_t]*M_ gzzx[_t])
-		                +M_ gupxy[_t]*(M_ gupxy[_t]*M_ gxxy[_t]+M_ gupyy[_t]*M_ gxyy[_t]+M_ gupyz[_t]*M_ gxzy[_t])
-		                +M_ gupyy[_t]*(M_ gupxy[_t]*M_ gxyy[_t]+M_ gupyy[_t]*M_ gyyy[_t]+M_ gupyz[_t]*M_ gyzy[_t])
-		                +M_ gupyz[_t]*(M_ gupxy[_t]*M_ gxzy[_t]+M_ gupyy[_t]*M_ gyzy[_t]+M_ gupyz[_t]*M_ gzzy[_t])
-		                +M_ gupxy[_t]*(M_ gupxz[_t]*M_ gxxz[_t]+M_ gupyz[_t]*M_ gxyz[_t]+M_ gupzz[_t]*M_ gxzz[_t])
-		                +M_ gupyy[_t]*(M_ gupxz[_t]*M_ gxyz[_t]+M_ gupyz[_t]*M_ gyyz[_t]+M_ gupzz[_t]*M_ gyzz[_t])
-		                +M_ gupyz[_t]*(M_ gupxz[_t]*M_ gxzz[_t]+M_ gupyz[_t]*M_ gyzz[_t]+M_ gupzz[_t]*M_ gzzz[_t]));
-		M_ Gmz_Res[_t] = M_ Gamz[_t] - (M_ gupxx[_t]*(M_ gupxz[_t]*M_ gxxx[_t]+M_ gupyz[_t]*M_ gxyx[_t]+M_ gupzz[_t]*M_ gxzx[_t])
-		                +M_ gupxy[_t]*(M_ gupxz[_t]*M_ gxyx[_t]+M_ gupyz[_t]*M_ gyyx[_t]+M_ gupzz[_t]*M_ gyzx[_t])
-		                +M_ gupxz[_t]*(M_ gupxz[_t]*M_ gxzx[_t]+M_ gupyz[_t]*M_ gyzx[_t]+M_ gupzz[_t]*M_ gzzx[_t])
-		                +M_ gupxy[_t]*(M_ gupxz[_t]*M_ gxxy[_t]+M_ gupyz[_t]*M_ gxyy[_t]+M_ gupzz[_t]*M_ gxzy[_t])
-		                +M_ gupyy[_t]*(M_ gupxz[_t]*M_ gxyy[_t]+M_ gupyz[_t]*M_ gyyy[_t]+M_ gupzz[_t]*M_ gyzy[_t])
-		                +M_ gupyz[_t]*(M_ gupxz[_t]*M_ gxzy[_t]+M_ gupyz[_t]*M_ gyzy[_t]+M_ gupzz[_t]*M_ gzzy[_t])
-		                +M_ gupxz[_t]*(M_ gupxz[_t]*M_ gxxz[_t]+M_ gupyz[_t]*M_ gxyz[_t]+M_ gupzz[_t]*M_ gxzz[_t])
-		                +M_ gupyz[_t]*(M_ gupxz[_t]*M_ gxyz[_t]+M_ gupyz[_t]*M_ gyyz[_t]+M_ gupzz[_t]*M_ gyzz[_t])
-		                +M_ gupzz[_t]*(M_ gupxz[_t]*M_ gxzz[_t]+M_ gupyz[_t]*M_ gyzz[_t]+M_ gupzz[_t]*M_ gzzz[_t]));
-		}//if(co == 0)
-
-		// second kind of connection
-		M_ Gamxxx[_t]=HALF*( M_ gupxx[_t]*M_ gxxx[_t]+ M_ gupxy[_t]*(2*M_ gxyx[_t]- M_ gxxy[_t]) + M_ gupxz[_t]*(2*M_ gxzx[_t]- M_ gxxz[_t]));
-		M_ Gamyxx[_t]=HALF*( M_ gupxy[_t]*M_ gxxx[_t]+ M_ gupyy[_t]*(2*M_ gxyx[_t]- M_ gxxy[_t]) + M_ gupyz[_t]*(2*M_ gxzx[_t]- M_ gxxz[_t]));
-		M_ Gamzxx[_t]=HALF*( M_ gupxz[_t]*M_ gxxx[_t]+ M_ gupyz[_t]*(2*M_ gxyx[_t]- M_ gxxy[_t]) + M_ gupzz[_t]*(2*M_ gxzx[_t]- M_ gxxz[_t]));
-
-		M_ Gamxyy[_t]=HALF*( M_ gupxx[_t]*(2*M_ gxyy[_t]- M_ gyyx[_t]) + M_ gupxy[_t]*M_ gyyy[_t]+ M_ gupxz[_t]*(2*M_ gyzy[_t]- M_ gyyz[_t]));
-		M_ Gamyyy[_t]=HALF*( M_ gupxy[_t]*(2*M_ gxyy[_t]- M_ gyyx[_t]) + M_ gupyy[_t]*M_ gyyy[_t]+ M_ gupyz[_t]*(2*M_ gyzy[_t]- M_ gyyz[_t]));
-		M_ Gamzyy[_t]=HALF*( M_ gupxz[_t]*(2*M_ gxyy[_t]- M_ gyyx[_t]) + M_ gupyz[_t]*M_ gyyy[_t]+ M_ gupzz[_t]*(2*M_ gyzy[_t]- M_ gyyz[_t]));
-
-		M_ Gamxzz[_t]=HALF*( M_ gupxx[_t]*(2*M_ gxzz[_t]- M_ gzzx[_t]) + M_ gupxy[_t]*(2*M_ gyzz[_t]- M_ gzzy[_t]) + M_ gupxz[_t]*M_ gzzz[_t]);
-		M_ Gamyzz[_t]=HALF*( M_ gupxy[_t]*(2*M_ gxzz[_t]- M_ gzzx[_t]) + M_ gupyy[_t]*(2*M_ gyzz[_t]- M_ gzzy[_t]) + M_ gupyz[_t]*M_ gzzz[_t]);
-		M_ Gamzzz[_t]=HALF*( M_ gupxz[_t]*(2*M_ gxzz[_t]- M_ gzzx[_t]) + M_ gupyz[_t]*(2*M_ gyzz[_t]- M_ gzzy[_t]) + M_ gupzz[_t]*M_ gzzz[_t]);
-
-		M_ Gamxxy[_t]=HALF*( M_ gupxx[_t]*M_ gxxy[_t]+ M_ gupxy[_t]*M_ gyyx[_t]+ M_ gupxz[_t]*( M_ gxzy[_t]+ M_ gyzx[_t]- M_ gxyz[_t]) );
-		M_ Gamyxy[_t]=HALF*( M_ gupxy[_t]*M_ gxxy[_t]+ M_ gupyy[_t]*M_ gyyx[_t]+ M_ gupyz[_t]*( M_ gxzy[_t]+ M_ gyzx[_t]- M_ gxyz[_t]) );
-		M_ Gamzxy[_t]=HALF*( M_ gupxz[_t]*M_ gxxy[_t]+ M_ gupyz[_t]*M_ gyyx[_t]+ M_ gupzz[_t]*( M_ gxzy[_t]+ M_ gyzx[_t]- M_ gxyz[_t]) );
-
-		M_ Gamxxz[_t]=HALF*( M_ gupxx[_t]*M_ gxxz[_t]+ M_ gupxy[_t]*( M_ gxyz[_t]+ M_ gyzx[_t]- M_ gxzy[_t]) + M_ gupxz[_t]*M_ gzzx[_t]);
-		M_ Gamyxz[_t]=HALF*( M_ gupxy[_t]*M_ gxxz[_t]+ M_ gupyy[_t]*( M_ gxyz[_t]+ M_ gyzx[_t]- M_ gxzy[_t]) + M_ gupyz[_t]*M_ gzzx[_t]);
-		M_ Gamzxz[_t]=HALF*( M_ gupxz[_t]*M_ gxxz[_t]+ M_ gupyz[_t]*( M_ gxyz[_t]+ M_ gyzx[_t]- M_ gxzy[_t]) + M_ gupzz[_t]*M_ gzzx[_t]);
-
-		M_ Gamxyz[_t]=HALF*( M_ gupxx[_t]*( M_ gxyz[_t]+ M_ gxzy[_t]- M_ gyzx[_t]) + M_ gupxy[_t]*M_ gyyz[_t]+ M_ gupxz[_t]*M_ gzzy[_t]);
-		M_ Gamyyz[_t]=HALF*( M_ gupxy[_t]*( M_ gxyz[_t]+ M_ gxzy[_t]- M_ gyzx[_t]) + M_ gupyy[_t]*M_ gyyz[_t]+ M_ gupyz[_t]*M_ gzzy[_t]);
-		M_ Gamzyz[_t]=HALF*( M_ gupxz[_t]*( M_ gxyz[_t]+ M_ gxzy[_t]- M_ gyzx[_t]) + M_ gupyz[_t]*M_ gyyz[_t]+ M_ gupzz[_t]*M_ gzzy[_t]);
-		// Raise indices of \tilde A_{ij} and store in R_ij
-
-		M_ Rxx[_t]=    M_ gupxx[_t]* M_ gupxx[_t]* M_ Axx[_t]+ M_ gupxy[_t]* M_ gupxy[_t]* M_ Ayy[_t]+ M_ gupxz[_t]* M_ gupxz[_t]* M_ Azz[_t]+ 
-		    2*(M_ gupxx[_t]* M_ gupxy[_t]* M_ Axy[_t]+ M_ gupxx[_t]* M_ gupxz[_t]* M_ Axz[_t]+ M_ gupxy[_t]* M_ gupxz[_t]* M_ Ayz[_t]);
-
-		M_ Ryy[_t]=    M_ gupxy[_t]* M_ gupxy[_t]* M_ Axx[_t]+ M_ gupyy[_t]* M_ gupyy[_t]* M_ Ayy[_t]+ M_ gupyz[_t]* M_ gupyz[_t]* M_ Azz[_t]+ 
-		    2*(M_ gupxy[_t]* M_ gupyy[_t]* M_ Axy[_t]+ M_ gupxy[_t]* M_ gupyz[_t]* M_ Axz[_t]+ M_ gupyy[_t]* M_ gupyz[_t]* M_ Ayz[_t]);
-
-		M_ Rzz[_t]=    M_ gupxz[_t]* M_ gupxz[_t]* M_ Axx[_t]+ M_ gupyz[_t]* M_ gupyz[_t]* M_ Ayy[_t]+ M_ gupzz[_t]* M_ gupzz[_t]* M_ Azz[_t]+ 
-		    2*(M_ gupxz[_t]* M_ gupyz[_t]* M_ Axy[_t]+ M_ gupxz[_t]* M_ gupzz[_t]* M_ Axz[_t]+ M_ gupyz[_t]* M_ gupzz[_t]* M_ Ayz[_t]);
-
-		M_ Rxy[_t]=    M_ gupxx[_t]* M_ gupxy[_t]* M_ Axx[_t]+ M_ gupxy[_t]* M_ gupyy[_t]* M_ Ayy[_t]+ M_ gupxz[_t]* M_ gupyz[_t]* M_ Azz[_t]+ 
-		        (M_ gupxx[_t]* M_ gupyy[_t]      + M_ gupxy[_t]* M_ gupxy[_t])* M_ Axy[_t]                      + 
-		        (M_ gupxx[_t]* M_ gupyz[_t]      + M_ gupxz[_t]* M_ gupxy[_t])* M_ Axz[_t]                      + 
-		        (M_ gupxy[_t]* M_ gupyz[_t]      + M_ gupxz[_t]* M_ gupyy[_t])* M_ Ayz[_t];
-
-		M_ Rxz[_t]=    M_ gupxx[_t]* M_ gupxz[_t]* M_ Axx[_t]+ M_ gupxy[_t]* M_ gupyz[_t]* M_ Ayy[_t]+ M_ gupxz[_t]* M_ gupzz[_t]* M_ Azz[_t]+ 
-		        (M_ gupxx[_t]* M_ gupyz[_t]      + M_ gupxy[_t]* M_ gupxz[_t])* M_ Axy[_t]                      + 
-		        (M_ gupxx[_t]* M_ gupzz[_t]      + M_ gupxz[_t]* M_ gupxz[_t])* M_ Axz[_t]                      + 
-		        (M_ gupxy[_t]* M_ gupzz[_t]      + M_ gupxz[_t]* M_ gupyz[_t])* M_ Ayz[_t];
-
-		M_ Ryz[_t]=    M_ gupxy[_t]* M_ gupxz[_t]* M_ Axx[_t]+ M_ gupyy[_t]* M_ gupyz[_t]* M_ Ayy[_t]+ M_ gupyz[_t]* M_ gupzz[_t]* M_ Azz[_t]+ 
-		        (M_ gupxy[_t]* M_ gupyz[_t]      + M_ gupyy[_t]* M_ gupxz[_t])* M_ Axy[_t]                      + 
-		        (M_ gupxy[_t]* M_ gupzz[_t]      + M_ gupyz[_t]* M_ gupxz[_t])* M_ Axz[_t]                      + 
-		        (M_ gupyy[_t]* M_ gupzz[_t]      + M_ gupyz[_t]* M_ gupyz[_t])* M_ Ayz[_t];
-
-		// Right hand side for M_ Gam^i without shift terms...
-
-		M_ Gamx_rhs[_t] = - 2 * (   M_ Lapx[_t] * M_ Rxx[_t]+   M_ Lapy[_t] * M_ Rxy[_t]+   M_ Lapz[_t] * M_ Rxz[_t]) + 
-		    2 * M_ alpn1[_t] * (                                                
-		    -F3o2/M_ chin1[_t] * (   M_ chix[_t] * M_ Rxx[_t]+   M_ chiy[_t] * M_ Rxy[_t]+   M_ chiz[_t] * M_ Rxz[_t]) - 
-		            M_ gupxx[_t]* (   F2o3 * M_ Kx[_t]  +  8 * PI * M_ Sx[_t]            ) - 
-		            M_ gupxy[_t]* (   F2o3 * M_ Ky[_t]  +  8 * PI * M_ Sy[_t]           ) - 
-		            M_ gupxz[_t]* (   F2o3 * M_ Kz[_t]  +  8 * PI * M_ Sz[_t]            ) + 
-		                    M_ Gamxxx[_t]* M_ Rxx[_t]+ M_ Gamxyy[_t]* M_ Ryy[_t]+ M_ Gamxzz[_t]* M_ Rzz[_t]  + 
-		            2 * ( M_ Gamxxy[_t]* M_ Rxy[_t]+ M_ Gamxxz[_t]* M_ Rxz[_t]+ M_ Gamxyz[_t]* M_ Ryz[_t]) );
-
-		M_ Gamy_rhs[_t] = - 2 * (   M_ Lapx[_t] * M_ Rxy[_t]+   M_ Lapy[_t] * M_ Ryy[_t]+   M_ Lapz[_t] * M_ Ryz[_t]) + 
-		    2 * M_ alpn1[_t] * (                                                
-		    -F3o2/M_ chin1[_t] * (   M_ chix[_t] * M_ Rxy[_t]+  M_ chiy[_t] * M_ Ryy[_t]+    M_ chiz[_t] * M_ Ryz[_t]) - 
-		            M_ gupxy[_t]* (   F2o3 * M_ Kx[_t]  +  8 * PI * M_ Sx[_t]            ) - 
-		            M_ gupyy[_t]* (   F2o3 * M_ Ky[_t]  +  8 * PI * M_ Sy[_t]            ) - 
-		            M_ gupyz[_t]* (   F2o3 * M_ Kz [_t] +  8 * PI * M_ Sz[_t]            ) + 
-		                    M_ Gamyxx[_t]* M_ Rxx[_t]+ M_ Gamyyy[_t]* M_ Ryy[_t]+ M_ Gamyzz[_t]* M_ Rzz[_t]  + 
-		            2 * ( M_ Gamyxy[_t]* M_ Rxy[_t]+ M_ Gamyxz[_t]* M_ Rxz[_t]+ M_ Gamyyz[_t]* M_ Ryz[_t]) );
-
-		M_ Gamz_rhs[_t] = - 2 * (   M_ Lapx[_t] * M_ Rxz[_t]+   M_ Lapy[_t] * M_ Ryz[_t]+   M_ Lapz[_t] * M_ Rzz[_t]) + 
-		    2 * M_ alpn1[_t] * (                                                
-		    -F3o2/M_ chin1[_t] * (   M_ chix[_t] * M_ Rxz[_t]+  M_ chiy[_t] * M_ Ryz[_t]+    M_ chiz[_t] * M_ Rzz[_t]) - 
-		            M_ gupxz[_t]* (   F2o3 * M_ Kx[_t]  +  8 * PI * M_ Sx[_t]            ) - 
-		            M_ gupyz[_t]* (   F2o3 * M_ Ky[_t]  +  8 * PI * M_ Sy[_t]            ) - 
-		            M_ gupzz[_t]* (   F2o3 * M_ Kz[_t]  +  8 * PI * M_ Sz[_t]           ) + 
-		                    M_ Gamzxx[_t]* M_ Rxx[_t]+ M_ Gamzyy[_t]* M_ Ryy[_t]+ M_ Gamzzz[_t]* M_ Rzz[_t]  + 
-		            2 * ( M_ Gamzxy[_t]* M_ Rxy[_t]+ M_ Gamzxz[_t]* M_ Rxz[_t]+ M_ Gamzyz[_t]* M_ Ryz[_t]) );
-			
-		_t += STEP_SIZE;
-	}
-}
-
-__global__ void compute_rhs_bssn_part3() 
-{
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	while(_t < _3D_SIZE[0])
-	{
-		M_ fxx [_t]= M_ gxxx[_t]+ M_ gxyy[_t]+ M_ gxzz[_t];
-		M_ fxy[_t]= M_ gxyx[_t]+ M_ gyyy[_t]+ M_ gyzz[_t];
-		M_ fxz[_t]= M_ gxzx[_t]+ M_ gyzy[_t]+ M_ gzzz[_t];
-
-		M_ Gamxa[_t]=       M_ gupxx [_t]* M_ Gamxxx [_t]+ M_ gupyy[_t]* M_ Gamxyy[_t]+ M_ gupzz[_t]* M_ Gamxzz[_t]+ 
-		    2*( M_ gupxy[_t]* M_ Gamxxy[_t]+ M_ gupxz[_t]* M_ Gamxxz[_t]+ M_ gupyz[_t]* M_ Gamxyz[_t]);
-		M_ Gamya[_t]=       M_ gupxx [_t]* M_ Gamyxx [_t]+ M_ gupyy[_t]* M_ Gamyyy[_t]+ M_ gupzz[_t]* M_ Gamyzz[_t]+ 
-		    2*( M_ gupxy[_t]* M_ Gamyxy[_t]+ M_ gupxz[_t]* M_ Gamyxz[_t]+ M_ gupyz[_t]* M_ Gamyyz[_t]);
-		M_ Gamza[_t]=       M_ gupxx [_t]* M_ Gamzxx [_t]+ M_ gupyy[_t]* M_ Gamzyy[_t]+ M_ gupzz[_t]* M_ Gamzzz[_t]+ 
-		    2*( M_ gupxy[_t]* M_ Gamzxy[_t]+ M_ gupxz[_t]* M_ Gamzxz[_t]+ M_ gupyz[_t]* M_ Gamzyz[_t]);
-
-
-
-		M_ Gamx_rhs[_t] =  M_ Gamx_rhs[_t] +  F2o3 *  M_ Gamxa[_t]* M_ div_beta[_t]       - 
-		                M_ Gamxa[_t]* M_ betaxx [_t]- M_ Gamya[_t]* M_ betaxy[_t]- M_ Gamza[_t]* M_ betaxz[_t] + 
-		        F1o3 * (M_ gupxx [_t]* M_ fxx [_t]   + M_ gupxy[_t]* M_ fxy[_t]   + M_ gupxz[_t]* M_ fxz[_t]   ) + 
-		                M_ gupxx [_t]* M_ gxxx [_t]  + M_ gupyy[_t]* M_ gyyx [_t]  + M_ gupzz[_t]* M_ gzzx [_t]   + 
-		        2 * (M_ gupxy[_t]* M_ gxyx [_t]  + M_ gupxz[_t]* M_ gxzx [_t]  + M_ gupyz[_t]* M_ gyzx [_t] );
-
-		M_ Gamy_rhs[_t] =               M_ Gamy_rhs[_t] +  F2o3 *  M_ Gamya[_t]* M_ div_beta[_t]       - 
-		                M_ Gamxa[_t]* M_ betayx [_t]- M_ Gamya[_t]* M_ betayy[_t]- M_ Gamza[_t]* M_ betayz[_t] + 
-		        F1o3 * (M_ gupxy[_t]* M_ fxx [_t]   + M_ gupyy[_t]* M_ fxy[_t]   + M_ gupyz[_t]* M_ fxz[_t]   ) + 
-		                M_ gupxx [_t]* M_ gxxy[_t]  + M_ gupyy[_t]* M_ gyyy[_t]  + M_ gupzz[_t]* M_ gzzy[_t]   + 
-		        2 * (M_ gupxy[_t]* M_ gxyy[_t]  + M_ gupxz[_t]* M_ gxzy[_t]  + M_ gupyz[_t]* M_ gyzy[_t] );
-
-		M_ Gamz_rhs[_t] =               M_ Gamz_rhs[_t] +  F2o3 *  M_ Gamza[_t]* M_ div_beta[_t]       - 
-		                M_ Gamxa[_t]* M_ betazx [_t]- M_ Gamya[_t]* M_ betazy[_t]- M_ Gamza[_t]* M_ betazz[_t] + 
-		        F1o3 * (M_ gupxz[_t]* M_ fxx [_t]   + M_ gupyz[_t]* M_ fxy[_t]   + M_ gupzz[_t]* M_ fxz[_t]   ) + 
-		                M_ gupxx [_t]* M_ gxxz[_t]  + M_ gupyy[_t]* M_ gyyz[_t]  + M_ gupzz[_t]* M_ gzzz[_t]   + 
-		        2 * (M_ gupxy[_t]* M_ gxyz[_t]  + M_ gupxz[_t]* M_ gxzz[_t]  + M_ gupyz[_t]* M_ gyzz[_t] )  ;  //rhs M_ for M_ Gam^i
-
-		//first kind of connection stored in M_ gij,k
-		M_ gxxx [_t]= M_ gxx [_t]* M_ Gamxxx [_t]+ M_ gxy[_t]* M_ Gamyxx [_t]+ M_ gxz[_t]* M_ Gamzxx[_t];
-		M_ gxyx [_t]= M_ gxx [_t]* M_ Gamxxy[_t]+ M_ gxy[_t]* M_ Gamyxy[_t]+ M_ gxz[_t]* M_ Gamzxy[_t];
-		M_ gxzx [_t]= M_ gxx [_t]* M_ Gamxxz[_t]+ M_ gxy[_t]* M_ Gamyxz[_t]+ M_ gxz[_t]* M_ Gamzxz[_t];
-		M_ gyyx [_t]= M_ gxx [_t]* M_ Gamxyy[_t]+ M_ gxy[_t]* M_ Gamyyy[_t]+ M_ gxz[_t]* M_ Gamzyy[_t];
-		M_ gyzx [_t]= M_ gxx [_t]* M_ Gamxyz[_t]+ M_ gxy[_t]* M_ Gamyyz[_t]+ M_ gxz[_t]* M_ Gamzyz[_t];
-		M_ gzzx [_t]= M_ gxx [_t]* M_ Gamxzz[_t]+ M_ gxy[_t]* M_ Gamyzz[_t]+ M_ gxz[_t]* M_ Gamzzz[_t];
-		M_ gxxy[_t]= M_ gxy[_t]* M_ Gamxxx [_t]+ M_ gyy[_t]* M_ Gamyxx [_t]+ M_ gyz[_t]* M_ Gamzxx[_t];
-		M_ gxyy[_t]= M_ gxy[_t]* M_ Gamxxy[_t]+ M_ gyy[_t]* M_ Gamyxy[_t]+ M_ gyz[_t]* M_ Gamzxy[_t];
-		M_ gxzy[_t]= M_ gxy[_t]* M_ Gamxxz[_t]+ M_ gyy[_t]* M_ Gamyxz[_t]+ M_ gyz[_t]* M_ Gamzxz[_t];
-		M_ gyyy[_t]= M_ gxy[_t]* M_ Gamxyy[_t]+ M_ gyy[_t]* M_ Gamyyy[_t]+ M_ gyz[_t]* M_ Gamzyy[_t];
-		M_ gyzy[_t]= M_ gxy[_t]* M_ Gamxyz[_t]+ M_ gyy[_t]* M_ Gamyyz[_t]+ M_ gyz[_t]* M_ Gamzyz[_t];
-		M_ gzzy[_t]= M_ gxy[_t]* M_ Gamxzz[_t]+ M_ gyy[_t]* M_ Gamyzz[_t]+ M_ gyz[_t]* M_ Gamzzz[_t];
-		M_ gxxz[_t]= M_ gxz[_t]* M_ Gamxxx [_t]+ M_ gyz[_t]* M_ Gamyxx [_t]+ M_ gzz[_t]* M_ Gamzxx[_t];
-		M_ gxyz[_t]= M_ gxz[_t]* M_ Gamxxy[_t]+ M_ gyz[_t]* M_ Gamyxy[_t]+ M_ gzz[_t]* M_ Gamzxy[_t];
-		M_ gxzz[_t]= M_ gxz[_t]* M_ Gamxxz[_t]+ M_ gyz[_t]* M_ Gamyxz[_t]+ M_ gzz[_t]* M_ Gamzxz[_t];
-		M_ gyyz[_t]= M_ gxz[_t]* M_ Gamxyy[_t]+ M_ gyz[_t]* M_ Gamyyy[_t]+ M_ gzz[_t]* M_ Gamzyy[_t];
-		M_ gyzz[_t]= M_ gxz[_t]* M_ Gamxyz[_t]+ M_ gyz[_t]* M_ Gamyyz[_t]+ M_ gzz[_t]* M_ Gamzyz[_t];
-		M_ gzzz[_t]= M_ gxz[_t]* M_ Gamxzz[_t]+ M_ gyz[_t]* M_ Gamyzz[_t]+ M_ gzz[_t]* M_ Gamzzz[_t];
-		
-	  	
-	  	_t += STEP_SIZE;
-	}
-}
-
-__global__ void compute_rhs_bssn_part4() 
-{
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	while(_t < _3D_SIZE[0])
-	{
-		M_ Rxx [_t]=     - HALF *M_ Rxx [_t]                                  + 
-		        M_ gxx [_t]* M_ Gamxx[_t] +M_ gxy[_t]* M_ Gamyx [_t]  +   M_ gxz[_t]* M_ Gamzx [_t]+ 
-		        M_ Gamxa[_t]*M_ gxxx [_t]+  M_ Gamya[_t]*M_ gxyx [_t]+  M_ Gamza[_t]*M_ gxzx [_t] + 
-		M_ gupxx [_t]*(                                                  
-		    2*(M_ Gamxxx [_t]*M_ gxxx [_t]+ M_ Gamyxx [_t]*M_ gxyx [_t]+ M_ Gamzxx [_t]*M_ gxzx[_t]) + 
-		        M_ Gamxxx [_t]*M_ gxxx [_t]+ M_ Gamyxx [_t]*M_ gxxy[_t]+ M_ Gamzxx [_t]*M_ gxxz[_t])+ 
-		M_ gupxy[_t]*(                                                  
-		    2*(M_ Gamxxx [_t]*M_ gxyx [_t]+ M_ Gamyxx [_t]*M_ gyyx [_t]+ M_ Gamzxx [_t]*M_ gyzx [_t] + 
-		        M_ Gamxxy[_t]*M_ gxxx [_t]+ M_ Gamyxy[_t]*M_ gxyx [_t]+ M_ Gamzxy[_t]*M_ gxzx[_t]) + 
-		        M_ Gamxxy[_t]*M_ gxxx [_t]+ M_ Gamyxy[_t]*M_ gxxy[_t]+ M_ Gamzxy[_t]*M_ gxxz[_t] + 
-		        M_ Gamxxx [_t]*M_ gxyx [_t]+ M_ Gamyxx [_t]*M_ gxyy[_t]+ M_ Gamzxx [_t]*M_ gxyz[_t])+ 
-		M_ gupxz[_t]*(                                                  
-		    2*(M_ Gamxxx [_t]*M_ gxzx [_t]+ M_ Gamyxx [_t]*M_ gyzx [_t]+ M_ Gamzxx [_t]*M_ gzzx [_t] + 
-		        M_ Gamxxz[_t]*M_ gxxx [_t]+ M_ Gamyxz[_t]*M_ gxyx [_t]+ M_ Gamzxz[_t]*M_ gxzx[_t]) + 
-		        M_ Gamxxz[_t]*M_ gxxx [_t]+ M_ Gamyxz[_t]*M_ gxxy[_t]+ M_ Gamzxz[_t]*M_ gxxz[_t] + 
-		        M_ Gamxxx [_t]*M_ gxzx [_t]+ M_ Gamyxx [_t]*M_ gxzy[_t]+ M_ Gamzxx [_t]*M_ gxzz[_t])+ 
-		M_ gupyy[_t]*(                                                  
-		    2*(M_ Gamxxy[_t]*M_ gxyx [_t]+ M_ Gamyxy[_t]*M_ gyyx [_t]+ M_ Gamzxy[_t]*M_ gyzx[_t]) + 
-		        M_ Gamxxy[_t]*M_ gxyx [_t]+ M_ Gamyxy[_t]*M_ gxyy[_t]+ M_ Gamzxy[_t]*M_ gxyz[_t])+ 
-		M_ gupyz[_t]*(                                                  
-		    2*(M_ Gamxxy[_t]*M_ gxzx [_t]+ M_ Gamyxy[_t]*M_ gyzx [_t]+ M_ Gamzxy[_t]*M_ gzzx [_t] + 
-		        M_ Gamxxz[_t]*M_ gxyx [_t]+ M_ Gamyxz[_t]*M_ gyyx [_t]+ M_ Gamzxz[_t]*M_ gyzx[_t]) + 
-		        M_ Gamxxz[_t]*M_ gxyx [_t]+ M_ Gamyxz[_t]*M_ gxyy[_t]+ M_ Gamzxz[_t]*M_ gxyz[_t] + 
-		        M_ Gamxxy[_t]*M_ gxzx [_t]+ M_ Gamyxy[_t]*M_ gxzy[_t]+ M_ Gamzxy[_t]*M_ gxzz[_t])+ 
-		M_ gupzz[_t]*(                                                  
-		    2*(M_ Gamxxz[_t]*M_ gxzx [_t]+ M_ Gamyxz[_t]*M_ gyzx [_t]+ M_ Gamzxz[_t]*M_ gzzx[_t]) + 
-		        M_ Gamxxz[_t]*M_ gxzx [_t]+ M_ Gamyxz[_t]*M_ gxzy[_t]+ M_ Gamzxz[_t]*M_ gxzz[_t]);
-
-		M_ Ryy[_t]=     - HALF *M_ Ryy[_t]                                  + 
-		            M_ gxy[_t]* M_ Gamxy[_t]+ M_ gyy[_t]* M_ Gamyy[_t] + M_ gyz[_t]* M_ Gamzy[_t]  + 
-		            M_ Gamxa[_t]*M_ gxyy[_t]+  M_ Gamya[_t]*M_ gyyy[_t]+  M_ Gamza[_t]*M_ gyzy[_t] + 
-		M_ gupxx [_t]*(                                                  
-		    2*(M_ Gamxxy[_t]*M_ gxxy[_t]+ M_ Gamyxy[_t]*M_ gxyy[_t]+ M_ Gamzxy[_t]*M_ gxzy[_t]) + 
-		        M_ Gamxxy[_t]*M_ gxyx [_t]+ M_ Gamyxy[_t]*M_ gxyy[_t]+ M_ Gamzxy[_t]*M_ gxyz[_t])+ 
-		M_ gupxy[_t]*(                                                  
-		    2*(M_ Gamxxy[_t]*M_ gxyy[_t]+ M_ Gamyxy[_t]*M_ gyyy[_t]+ M_ Gamzxy[_t]*M_ gyzy[_t] + 
-		        M_ Gamxyy[_t]*M_ gxxy[_t]+ M_ Gamyyy[_t]*M_ gxyy[_t]+ M_ Gamzyy[_t]*M_ gxzy[_t]) + 
-		        M_ Gamxyy[_t]*M_ gxyx [_t]+ M_ Gamyyy[_t]*M_ gxyy[_t]+ M_ Gamzyy[_t]*M_ gxyz[_t] + 
-		        M_ Gamxxy[_t]*M_ gyyx [_t]+ M_ Gamyxy[_t]*M_ gyyy[_t]+ M_ Gamzxy[_t]*M_ gyyz[_t])+ 
-		M_ gupxz[_t]*(                                                  
-		    2*(M_ Gamxxy[_t]*M_ gxzy[_t]+ M_ Gamyxy[_t]*M_ gyzy[_t]+ M_ Gamzxy[_t]*M_ gzzy[_t] + 
-		        M_ Gamxyz[_t]*M_ gxxy[_t]+ M_ Gamyyz[_t]*M_ gxyy[_t]+ M_ Gamzyz[_t]*M_ gxzy[_t]) + 
-		        M_ Gamxyz[_t]*M_ gxyx [_t]+ M_ Gamyyz[_t]*M_ gxyy[_t]+ M_ Gamzyz[_t]*M_ gxyz[_t] + 
-		        M_ Gamxxy[_t]*M_ gyzx [_t]+ M_ Gamyxy[_t]*M_ gyzy[_t]+ M_ Gamzxy[_t]*M_ gyzz[_t])+ 
-		M_ gupyy[_t]*(                                                  
-		    2*(M_ Gamxyy[_t]*M_ gxyy[_t]+ M_ Gamyyy[_t]*M_ gyyy[_t]+ M_ Gamzyy[_t]*M_ gyzy[_t]) + 
-		        M_ Gamxyy[_t]*M_ gyyx [_t]+ M_ Gamyyy[_t]*M_ gyyy[_t]+ M_ Gamzyy[_t]*M_ gyyz[_t])+ 
-		M_ gupyz[_t]*(                                                  
-		    2*(M_ Gamxyy[_t]*M_ gxzy[_t]+ M_ Gamyyy[_t]*M_ gyzy[_t]+ M_ Gamzyy[_t]*M_ gzzy[_t] + 
-		        M_ Gamxyz[_t]*M_ gxyy[_t]+ M_ Gamyyz[_t]*M_ gyyy[_t]+ M_ Gamzyz[_t]*M_ gyzy[_t]) + 
-		        M_ Gamxyz[_t]*M_ gyyx [_t]+ M_ Gamyyz[_t]*M_ gyyy[_t]+ M_ Gamzyz[_t]*M_ gyyz[_t] + 
-		        M_ Gamxyy[_t]*M_ gyzx [_t]+ M_ Gamyyy[_t]*M_ gyzy[_t]+ M_ Gamzyy[_t]*M_ gyzz[_t])+ 
-		M_ gupzz[_t]*(                                                  
-		    2*(M_ Gamxyz[_t]*M_ gxzy[_t]+ M_ Gamyyz[_t]*M_ gyzy[_t]+ M_ Gamzyz[_t]*M_ gzzy[_t]) + 
-		        M_ Gamxyz[_t]*M_ gyzx [_t]+ M_ Gamyyz[_t]*M_ gyzy[_t]+ M_ Gamzyz[_t]*M_ gyzz[_t]);
-
-		M_ Rzz[_t]=     - HALF *M_ Rzz[_t]                                  + 
-		            M_ gxz[_t]* M_ Gamxz[_t] +M_ gyz[_t]* M_ Gamyz[_t] +   M_ gzz[_t]* M_ Gamzz[_t] + 
-		            M_ Gamxa[_t]*M_ gxzz[_t]+  M_ Gamya[_t]*M_ gyzz[_t]+  M_ Gamza[_t]*M_ gzzz[_t] + 
-		M_ gupxx [_t]*(                                                  
-		    2*(M_ Gamxxz[_t]*M_ gxxz[_t]+ M_ Gamyxz[_t]*M_ gxyz[_t]+ M_ Gamzxz[_t]*M_ gxzz[_t]) + 
-		        M_ Gamxxz[_t]*M_ gxzx [_t]+ M_ Gamyxz[_t]*M_ gxzy[_t]+ M_ Gamzxz[_t]*M_ gxzz[_t])+ 
-		M_ gupxy[_t]*(                                                  
-		    2*(M_ Gamxxz[_t]*M_ gxyz[_t]+ M_ Gamyxz[_t]*M_ gyyz[_t]+ M_ Gamzxz[_t]*M_ gyzz[_t] + 
-		        M_ Gamxyz[_t]*M_ gxxz[_t]+ M_ Gamyyz[_t]*M_ gxyz[_t]+ M_ Gamzyz[_t]*M_ gxzz[_t]) + 
-		        M_ Gamxyz[_t]*M_ gxzx [_t]+ M_ Gamyyz[_t]*M_ gxzy[_t]+ M_ Gamzyz[_t]*M_ gxzz[_t] + 
-		        M_ Gamxxz[_t]*M_ gyzx [_t]+ M_ Gamyxz[_t]*M_ gyzy[_t]+ M_ Gamzxz[_t]*M_ gyzz[_t])+ 
-		M_ gupxz[_t]*(                                                  
-		    2*(M_ Gamxxz[_t]*M_ gxzz[_t]+ M_ Gamyxz[_t]*M_ gyzz[_t]+ M_ Gamzxz[_t]*M_ gzzz[_t] + 
-		        M_ Gamxzz[_t]*M_ gxxz[_t]+ M_ Gamyzz[_t]*M_ gxyz[_t]+ M_ Gamzzz[_t]*M_ gxzz[_t]) + 
-		        M_ Gamxzz[_t]*M_ gxzx [_t]+ M_ Gamyzz[_t]*M_ gxzy[_t]+ M_ Gamzzz[_t]*M_ gxzz[_t] + 
-		        M_ Gamxxz[_t]*M_ gzzx [_t]+ M_ Gamyxz[_t]*M_ gzzy[_t]+ M_ Gamzxz[_t]*M_ gzzz[_t])+ 
-		M_ gupyy[_t]*(                                                  
-		    2*(M_ Gamxyz[_t]*M_ gxyz[_t]+ M_ Gamyyz[_t]*M_ gyyz[_t]+ M_ Gamzyz[_t]*M_ gyzz[_t]) + 
-		        M_ Gamxyz[_t]*M_ gyzx [_t]+ M_ Gamyyz[_t]*M_ gyzy[_t]+ M_ Gamzyz[_t]*M_ gyzz[_t])+ 
-		M_ gupyz[_t]*(                                                  
-		    2*(M_ Gamxyz[_t]*M_ gxzz[_t]+ M_ Gamyyz[_t]*M_ gyzz[_t]+ M_ Gamzyz[_t]*M_ gzzz[_t] + 
-		        M_ Gamxzz[_t]*M_ gxyz[_t]+ M_ Gamyzz[_t]*M_ gyyz[_t]+ M_ Gamzzz[_t]*M_ gyzz[_t]) + 
-		        M_ Gamxzz[_t]*M_ gyzx [_t]+ M_ Gamyzz[_t]*M_ gyzy[_t]+ M_ Gamzzz[_t]*M_ gyzz[_t] + 
-		        M_ Gamxyz[_t]*M_ gzzx [_t]+ M_ Gamyyz[_t]*M_ gzzy[_t]+ M_ Gamzyz[_t]*M_ gzzz[_t])+ 
-		M_ gupzz[_t]*(                                                  
-		    2*(M_ Gamxzz[_t]*M_ gxzz[_t]+ M_ Gamyzz[_t]*M_ gyzz[_t]+ M_ Gamzzz[_t]*M_ gzzz[_t]) + 
-		        M_ Gamxzz[_t]*M_ gzzx [_t]+ M_ Gamyzz[_t]*M_ gzzy[_t]+ M_ Gamzzz[_t]*M_ gzzz[_t]);
-
-		M_ Rxy[_t]= HALF*(     -M_ Rxy[_t]                                  + 
-		            M_ gxx [_t]* M_ Gamxy[_t]+   M_ gxy[_t]* M_ Gamyy[_t]+M_ gxz[_t]* M_ Gamzy[_t] + 
-		            M_ gxy[_t]* M_ Gamxx [_t]+   M_ gyy[_t]* M_ Gamyx [_t]+M_ gyz[_t]* M_ Gamzx [_t] + 
-		            M_ Gamxa[_t]*M_ gxyx [_t]+  M_ Gamya[_t]*M_ gyyx [_t]+  M_ Gamza[_t]*M_ gyzx [_t] + 
-		            M_ Gamxa[_t]*M_ gxxy[_t]+  M_ Gamya[_t]*M_ gxyy[_t]+  M_ Gamza[_t]*M_ gxzy[_t])+ 
-		M_ gupxx [_t]*(                                                  
-		        M_ Gamxxx [_t]*M_ gxxy[_t]+ M_ Gamyxx [_t]*M_ gxyy[_t]+ M_ Gamzxx [_t]*M_ gxzy[_t] + 
-		        M_ Gamxxy[_t]*M_ gxxx [_t]+ M_ Gamyxy[_t]*M_ gxyx [_t]+ M_ Gamzxy[_t]*M_ gxzx [_t] + 
-		        M_ Gamxxx [_t]*M_ gxyx [_t]+ M_ Gamyxx [_t]*M_ gxyy[_t]+ M_ Gamzxx [_t]*M_ gxyz[_t])+ 
-		M_ gupxy[_t]*(                                                  
-		        M_ Gamxxx [_t]*M_ gxyy[_t]+ M_ Gamyxx [_t]*M_ gyyy[_t]+ M_ Gamzxx [_t]*M_ gyzy[_t] + 
-		        M_ Gamxxy[_t]*M_ gxyx [_t]+ M_ Gamyxy[_t]*M_ gyyx [_t]+ M_ Gamzxy[_t]*M_ gyzx [_t] + 
-		        M_ Gamxxy[_t]*M_ gxyx [_t]+ M_ Gamyxy[_t]*M_ gxyy[_t]+ M_ Gamzxy[_t]*M_ gxyz[_t] + 
-		        M_ Gamxxy[_t]*M_ gxxy[_t]+ M_ Gamyxy[_t]*M_ gxyy[_t]+ M_ Gamzxy[_t]*M_ gxzy[_t] + 
-		        M_ Gamxyy[_t]*M_ gxxx [_t]+ M_ Gamyyy[_t]*M_ gxyx [_t]+ M_ Gamzyy[_t]*M_ gxzx [_t] + 
-		        M_ Gamxxx [_t]*M_ gyyx [_t]+ M_ Gamyxx [_t]*M_ gyyy[_t]+ M_ Gamzxx [_t]*M_ gyyz[_t])+ 
-		M_ gupxz[_t]*(                                                  
-		        M_ Gamxxx [_t]*M_ gxzy[_t]+ M_ Gamyxx [_t]*M_ gyzy[_t]+ M_ Gamzxx [_t]*M_ gzzy[_t] + 
-		        M_ Gamxxy[_t]*M_ gxzx [_t]+ M_ Gamyxy[_t]*M_ gyzx [_t]+ M_ Gamzxy[_t]*M_ gzzx [_t] + 
-		        M_ Gamxxz[_t]*M_ gxyx [_t]+ M_ Gamyxz[_t]*M_ gxyy[_t]+ M_ Gamzxz[_t]*M_ gxyz[_t] + 
-		        M_ Gamxxz[_t]*M_ gxxy[_t]+ M_ Gamyxz[_t]*M_ gxyy[_t]+ M_ Gamzxz[_t]*M_ gxzy[_t] + 
-		        M_ Gamxyz[_t]*M_ gxxx [_t]+ M_ Gamyyz[_t]*M_ gxyx [_t]+ M_ Gamzyz[_t]*M_ gxzx [_t] + 
-		        M_ Gamxxx [_t]*M_ gyzx [_t]+ M_ Gamyxx [_t]*M_ gyzy[_t]+ M_ Gamzxx [_t]*M_ gyzz[_t])+ 
-		M_ gupyy[_t]*(                                                  
-		        M_ Gamxxy[_t]*M_ gxyy[_t]+ M_ Gamyxy[_t]*M_ gyyy[_t]+ M_ Gamzxy[_t]*M_ gyzy[_t] + 
-		        M_ Gamxyy[_t]*M_ gxyx [_t]+ M_ Gamyyy[_t]*M_ gyyx [_t]+ M_ Gamzyy[_t]*M_ gyzx [_t] + 
-		        M_ Gamxxy[_t]*M_ gyyx [_t]+ M_ Gamyxy[_t]*M_ gyyy[_t]+ M_ Gamzxy[_t]*M_ gyyz[_t])+ 
-		M_ gupyz[_t]*(                                                  
-		        M_ Gamxxy[_t]*M_ gxzy[_t]+ M_ Gamyxy[_t]*M_ gyzy[_t]+ M_ Gamzxy[_t]*M_ gzzy[_t] + 
-		        M_ Gamxyy[_t]*M_ gxzx [_t]+ M_ Gamyyy[_t]*M_ gyzx [_t]+ M_ Gamzyy[_t]*M_ gzzx [_t] + 
-		        M_ Gamxxz[_t]*M_ gyyx [_t]+ M_ Gamyxz[_t]*M_ gyyy[_t]+ M_ Gamzxz[_t]*M_ gyyz[_t] + 
-		        M_ Gamxxz[_t]*M_ gxyy[_t]+ M_ Gamyxz[_t]*M_ gyyy[_t]+ M_ Gamzxz[_t]*M_ gyzy[_t] + 
-		        M_ Gamxyz[_t]*M_ gxyx [_t]+ M_ Gamyyz[_t]*M_ gyyx [_t]+ M_ Gamzyz[_t]*M_ gyzx [_t] + 
-		        M_ Gamxxy[_t]*M_ gyzx [_t]+ M_ Gamyxy[_t]*M_ gyzy[_t]+ M_ Gamzxy[_t]*M_ gyzz[_t])+ 
-		M_ gupzz[_t]*(                                                  
-		        M_ Gamxxz[_t]*M_ gxzy[_t]+ M_ Gamyxz[_t]*M_ gyzy[_t]+ M_ Gamzxz[_t]*M_ gzzy[_t] + 
-		        M_ Gamxyz[_t]*M_ gxzx [_t]+ M_ Gamyyz[_t]*M_ gyzx [_t]+ M_ Gamzyz[_t]*M_ gzzx [_t] + 
-		        M_ Gamxxz[_t]*M_ gyzx [_t]+ M_ Gamyxz[_t]*M_ gyzy[_t]+ M_ Gamzxz[_t]*M_ gyzz[_t]);
-
-		M_ Rxz[_t]= HALF*(     -M_ Rxz[_t]                                  + 
-		            M_ gxx [_t]* M_ Gamxz[_t]+ M_ gxy[_t]* M_ Gamyz[_t]+M_ gxz[_t]* M_ Gamzz[_t]   + 
-		            M_ gxz[_t]* M_ Gamxx [_t]+ M_ gyz[_t]* M_ Gamyx [_t]+M_ gzz[_t]* M_ Gamzx [_t]   + 
-		            M_ Gamxa[_t]*M_ gxzx [_t]+  M_ Gamya[_t]*M_ gyzx [_t]+  M_ Gamza[_t]*M_ gzzx [_t] + 
-		            M_ Gamxa[_t]*M_ gxxz[_t]+  M_ Gamya[_t]*M_ gxyz[_t]+  M_ Gamza[_t]*M_ gxzz[_t])+ 
-		M_ gupxx [_t]*(                                                  
-		        M_ Gamxxx [_t]*M_ gxxz[_t]+ M_ Gamyxx [_t]*M_ gxyz[_t]+ M_ Gamzxx [_t]*M_ gxzz[_t] + 
-		        M_ Gamxxz[_t]*M_ gxxx [_t]+ M_ Gamyxz[_t]*M_ gxyx [_t]+ M_ Gamzxz[_t]*M_ gxzx [_t] + 
-		        M_ Gamxxx [_t]*M_ gxzx [_t]+ M_ Gamyxx [_t]*M_ gxzy[_t]+ M_ Gamzxx [_t]*M_ gxzz[_t])+ 
-		M_ gupxy[_t]*(                                                  
-		        M_ Gamxxx [_t]*M_ gxyz[_t]+ M_ Gamyxx [_t]*M_ gyyz[_t]+ M_ Gamzxx [_t]*M_ gyzz[_t] + 
-		        M_ Gamxxz[_t]*M_ gxyx [_t]+ M_ Gamyxz[_t]*M_ gyyx [_t]+ M_ Gamzxz[_t]*M_ gyzx [_t] + 
-		        M_ Gamxxy[_t]*M_ gxzx [_t]+ M_ Gamyxy[_t]*M_ gxzy[_t]+ M_ Gamzxy[_t]*M_ gxzz[_t] + 
-		        M_ Gamxxy[_t]*M_ gxxz[_t]+ M_ Gamyxy[_t]*M_ gxyz[_t]+ M_ Gamzxy[_t]*M_ gxzz[_t] + 
-		        M_ Gamxyz[_t]*M_ gxxx [_t]+ M_ Gamyyz[_t]*M_ gxyx [_t]+ M_ Gamzyz[_t]*M_ gxzx [_t] + 
-		        M_ Gamxxx [_t]*M_ gyzx [_t]+ M_ Gamyxx [_t]*M_ gyzy[_t]+ M_ Gamzxx [_t]*M_ gyzz[_t])+ 
-		M_ gupxz[_t]*(                                                  
-		        M_ Gamxxx [_t]*M_ gxzz[_t]+ M_ Gamyxx [_t]*M_ gyzz[_t]+ M_ Gamzxx [_t]*M_ gzzz[_t] + 
-		        M_ Gamxxz[_t]*M_ gxzx [_t]+ M_ Gamyxz[_t]*M_ gyzx [_t]+ M_ Gamzxz[_t]*M_ gzzx [_t] + 
-		        M_ Gamxxz[_t]*M_ gxzx [_t]+ M_ Gamyxz[_t]*M_ gxzy[_t]+ M_ Gamzxz[_t]*M_ gxzz[_t] + 
-		        M_ Gamxxz[_t]*M_ gxxz[_t]+ M_ Gamyxz[_t]*M_ gxyz[_t]+ M_ Gamzxz[_t]*M_ gxzz[_t] + 
-		        M_ Gamxzz[_t]*M_ gxxx [_t]+ M_ Gamyzz[_t]*M_ gxyx [_t]+ M_ Gamzzz[_t]*M_ gxzx [_t] + 
-		        M_ Gamxxx [_t]*M_ gzzx [_t]+ M_ Gamyxx [_t]*M_ gzzy[_t]+ M_ Gamzxx [_t]*M_ gzzz[_t])+ 
-		M_ gupyy[_t]*(                                                  
-		        M_ Gamxxy[_t]*M_ gxyz[_t]+ M_ Gamyxy[_t]*M_ gyyz[_t]+ M_ Gamzxy[_t]*M_ gyzz[_t] + 
-		        M_ Gamxyz[_t]*M_ gxyx [_t]+ M_ Gamyyz[_t]*M_ gyyx [_t]+ M_ Gamzyz[_t]*M_ gyzx [_t] + 
-		        M_ Gamxxy[_t]*M_ gyzx [_t]+ M_ Gamyxy[_t]*M_ gyzy[_t]+ M_ Gamzxy[_t]*M_ gyzz[_t])+ 
-		M_ gupyz[_t]*(                                                  
-		        M_ Gamxxy[_t]*M_ gxzz[_t]+ M_ Gamyxy[_t]*M_ gyzz[_t]+ M_ Gamzxy[_t]*M_ gzzz[_t] + 
-		        M_ Gamxyz[_t]*M_ gxzx [_t]+ M_ Gamyyz[_t]*M_ gyzx [_t]+ M_ Gamzyz[_t]*M_ gzzx [_t] + 
-		        M_ Gamxxz[_t]*M_ gyzx [_t]+ M_ Gamyxz[_t]*M_ gyzy[_t]+ M_ Gamzxz[_t]*M_ gyzz[_t] + 
-		        M_ Gamxxz[_t]*M_ gxyz[_t]+ M_ Gamyxz[_t]*M_ gyyz[_t]+ M_ Gamzxz[_t]*M_ gyzz[_t] + 
-		        M_ Gamxzz[_t]*M_ gxyx [_t]+ M_ Gamyzz[_t]*M_ gyyx [_t]+ M_ Gamzzz[_t]*M_ gyzx [_t] + 
-		        M_ Gamxxy[_t]*M_ gzzx [_t]+ M_ Gamyxy[_t]*M_ gzzy[_t]+ M_ Gamzxy[_t]*M_ gzzz[_t])+ 
-		M_ gupzz[_t]*(                                                  
-		        M_ Gamxxz[_t]*M_ gxzz[_t]+ M_ Gamyxz[_t]*M_ gyzz[_t]+ M_ Gamzxz[_t]*M_ gzzz[_t] + 
-		        M_ Gamxzz[_t]*M_ gxzx [_t]+ M_ Gamyzz[_t]*M_ gyzx [_t]+ M_ Gamzzz[_t]*M_ gzzx [_t] + 
-		        M_ Gamxxz[_t]*M_ gzzx [_t]+ M_ Gamyxz[_t]*M_ gzzy[_t]+ M_ Gamzxz[_t]*M_ gzzz[_t]);
-
-		M_ Ryz[_t]= HALF*(     -M_ Ryz[_t]                                  + 
-		            M_ gxy[_t]* M_ Gamxz[_t]+M_ gyy[_t]* M_ Gamyz[_t]+M_ gyz[_t]* M_ Gamzz[_t]    + 
-		            M_ gxz[_t]* M_ Gamxy[_t]+M_ gyz[_t]* M_ Gamyy[_t]+M_ gzz[_t]* M_ Gamzy[_t]    + 
-		            M_ Gamxa[_t]*M_ gxzy[_t]+  M_ Gamya[_t]*M_ gyzy[_t]+  M_ Gamza[_t]*M_ gzzy[_t] + 
-		            M_ Gamxa[_t]*M_ gxyz[_t]+  M_ Gamya[_t]*M_ gyyz[_t]+  M_ Gamza[_t]*M_ gyzz[_t])+ 
-		M_ gupxx [_t]*(                                                  
-		        M_ Gamxxy[_t]*M_ gxxz[_t]+ M_ Gamyxy[_t]*M_ gxyz[_t]+ M_ Gamzxy[_t]*M_ gxzz[_t] + 
-		        M_ Gamxxz[_t]*M_ gxxy[_t]+ M_ Gamyxz[_t]*M_ gxyy[_t]+ M_ Gamzxz[_t]*M_ gxzy[_t] + 
-		        M_ Gamxxy[_t]*M_ gxzx [_t]+ M_ Gamyxy[_t]*M_ gxzy[_t]+ M_ Gamzxy[_t]*M_ gxzz[_t])+ 
-		M_ gupxy[_t]*(                                                  
-		        M_ Gamxxy[_t]*M_ gxyz[_t]+ M_ Gamyxy[_t]*M_ gyyz[_t]+ M_ Gamzxy[_t]*M_ gyzz[_t] + 
-		        M_ Gamxxz[_t]*M_ gxyy[_t]+ M_ Gamyxz[_t]*M_ gyyy[_t]+ M_ Gamzxz[_t]*M_ gyzy[_t] + 
-		        M_ Gamxyy[_t]*M_ gxzx [_t]+ M_ Gamyyy[_t]*M_ gxzy[_t]+ M_ Gamzyy[_t]*M_ gxzz[_t] + 
-		        M_ Gamxyy[_t]*M_ gxxz[_t]+ M_ Gamyyy[_t]*M_ gxyz[_t]+ M_ Gamzyy[_t]*M_ gxzz[_t] + 
-		        M_ Gamxyz[_t]*M_ gxxy[_t]+ M_ Gamyyz[_t]*M_ gxyy[_t]+ M_ Gamzyz[_t]*M_ gxzy[_t] + 
-		        M_ Gamxxy[_t]*M_ gyzx [_t]+ M_ Gamyxy[_t]*M_ gyzy[_t]+ M_ Gamzxy[_t]*M_ gyzz[_t])+ 
-		M_ gupxz[_t]*(                                                  
-		        M_ Gamxxy[_t]*M_ gxzz[_t]+ M_ Gamyxy[_t]*M_ gyzz[_t]+ M_ Gamzxy[_t]*M_ gzzz[_t] + 
-		        M_ Gamxxz[_t]*M_ gxzy[_t]+ M_ Gamyxz[_t]*M_ gyzy[_t]+ M_ Gamzxz[_t]*M_ gzzy[_t] + 
-		        M_ Gamxyz[_t]*M_ gxzx [_t]+ M_ Gamyyz[_t]*M_ gxzy[_t]+ M_ Gamzyz[_t]*M_ gxzz[_t] + 
-		        M_ Gamxyz[_t]*M_ gxxz[_t]+ M_ Gamyyz[_t]*M_ gxyz[_t]+ M_ Gamzyz[_t]*M_ gxzz[_t] + 
-		        M_ Gamxzz[_t]*M_ gxxy[_t]+ M_ Gamyzz[_t]*M_ gxyy[_t]+ M_ Gamzzz[_t]*M_ gxzy[_t] + 
-		        M_ Gamxxy[_t]*M_ gzzx [_t]+ M_ Gamyxy[_t]*M_ gzzy[_t]+ M_ Gamzxy[_t]*M_ gzzz[_t])+ 
-		M_ gupyy[_t]*(                                                  
-		        M_ Gamxyy[_t]*M_ gxyz[_t]+ M_ Gamyyy[_t]*M_ gyyz[_t]+ M_ Gamzyy[_t]*M_ gyzz[_t] + 
-		        M_ Gamxyz[_t]*M_ gxyy[_t]+ M_ Gamyyz[_t]*M_ gyyy[_t]+ M_ Gamzyz[_t]*M_ gyzy[_t] + 
-		        M_ Gamxyy[_t]*M_ gyzx [_t]+ M_ Gamyyy[_t]*M_ gyzy[_t]+ M_ Gamzyy[_t]*M_ gyzz[_t])+ 
-		M_ gupyz[_t]*(                                                  
-		        M_ Gamxyy[_t]*M_ gxzz[_t]+ M_ Gamyyy[_t]*M_ gyzz[_t]+ M_ Gamzyy[_t]*M_ gzzz[_t] + 
-		        M_ Gamxyz[_t]*M_ gxzy[_t]+ M_ Gamyyz[_t]*M_ gyzy[_t]+ M_ Gamzyz[_t]*M_ gzzy[_t] + 
-		        M_ Gamxyz[_t]*M_ gyzx [_t]+ M_ Gamyyz[_t]*M_ gyzy[_t]+ M_ Gamzyz[_t]*M_ gyzz[_t] + 
-		        M_ Gamxyz[_t]*M_ gxyz[_t]+ M_ Gamyyz[_t]*M_ gyyz[_t]+ M_ Gamzyz[_t]*M_ gyzz[_t] + 
-		        M_ Gamxzz[_t]*M_ gxyy[_t]+ M_ Gamyzz[_t]*M_ gyyy[_t]+ M_ Gamzzz[_t]*M_ gyzy[_t] + 
-		        M_ Gamxyy[_t]*M_ gzzx [_t]+ M_ Gamyyy[_t]*M_ gzzy[_t]+ M_ Gamzyy[_t]*M_ gzzz[_t])+ 
-		M_ gupzz[_t]*(                                                  
-		        M_ Gamxyz[_t]*M_ gxzz[_t]+ M_ Gamyyz[_t]*M_ gyzz[_t]+ M_ Gamzyz[_t]*M_ gzzz[_t] + 
-		        M_ Gamxzz[_t]*M_ gxzy[_t]+ M_ Gamyzz[_t]*M_ gyzy[_t]+ M_ Gamzzz[_t]*M_ gzzy[_t] + 
-		        M_ Gamxyz[_t]*M_ gzzx [_t]+ M_ Gamyyz[_t]*M_ gzzy[_t]+ M_ Gamzyz[_t]*M_ gzzz[_t]);
-
-		_t += STEP_SIZE;
-	}
-}
-__global__ void compute_rhs_bssn_part5() 
-{
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	while(_t < _3D_SIZE[0])
-	{
-		M_ fxx [_t]=M_ fxx [_t]- M_ Gamxxx [_t]* M_ chix [_t]- M_ Gamyxx [_t]* M_ chiy[_t]- M_ Gamzxx [_t]* M_ chiz[_t];
-		M_ fxy[_t]=M_ fxy[_t]- M_ Gamxxy[_t]* M_ chix [_t]- M_ Gamyxy[_t]* M_ chiy[_t]- M_ Gamzxy[_t]* M_ chiz[_t];
-		M_ fxz[_t]=M_ fxz[_t]- M_ Gamxxz[_t]* M_ chix [_t]- M_ Gamyxz[_t]* M_ chiy[_t]- M_ Gamzxz[_t]* M_ chiz[_t];
-		M_ fyy[_t]=M_ fyy[_t]- M_ Gamxyy[_t]* M_ chix [_t]- M_ Gamyyy[_t]* M_ chiy[_t]- M_ Gamzyy[_t]* M_ chiz[_t];
-		M_ fyz[_t]=M_ fyz[_t]- M_ Gamxyz[_t]* M_ chix [_t]- M_ Gamyyz[_t]* M_ chiy[_t]- M_ Gamzyz[_t]* M_ chiz[_t];
-		M_ fzz[_t]=M_ fzz[_t]- M_ Gamxzz[_t]* M_ chix [_t]- M_ Gamyzz[_t]* M_ chiy[_t]- M_ Gamzzz[_t]* M_ chiz[_t];
-		// M_ Store D^l D_l M_ chi - 3/(2*M_ chi) D^l M_ chi D_l M_ chi inM_ f[_t]
-
-		M_ f[_t] =       M_ gupxx [_t]* (M_ fxx [_t]- F3o2/M_ chin1[_t] * M_ chix [_t]* M_ chix [_t]) + 
-		        M_ gupyy[_t]* (M_ fyy[_t]- F3o2/M_ chin1[_t] * M_ chiy[_t]* M_ chiy[_t]) + 
-		        M_ gupzz[_t]* (M_ fzz[_t]- F3o2/M_ chin1[_t] * M_ chiz[_t]* M_ chiz[_t]) + 
-		    2 *M_ gupxy[_t]* (M_ fxy[_t]- F3o2/M_ chin1[_t] * M_ chix [_t]* M_ chiy[_t]) + 
-		    2 *M_ gupxz[_t]* (M_ fxz[_t]- F3o2/M_ chin1[_t] * M_ chix [_t]* M_ chiz[_t]) + 
-		    2 *M_ gupyz[_t]* (M_ fyz[_t]- F3o2/M_ chin1[_t] * M_ chiy[_t]* M_ chiz[_t]);
-		// M_ Add M_ chi part toM_ Ricci tensor:
-
-		M_ Rxx [_t]=M_ Rxx [_t]+ (M_ fxx [_t]- M_ chix[_t]*M_ chix[_t]/M_ chin1[_t]/2 +M_ gxx [_t]*M_ f[_t])/M_ chin1[_t]/2;
-		M_ Ryy[_t]=M_ Ryy[_t]+ (M_ fyy[_t]- M_ chiy[_t]*M_ chiy[_t]/M_ chin1[_t]/2 +M_ gyy[_t]*M_ f[_t])/M_ chin1[_t]/2;
-		M_ Rzz[_t]=M_ Rzz[_t]+ (M_ fzz[_t]- M_ chiz[_t]*M_ chiz[_t]/M_ chin1[_t]/2 +M_ gzz[_t]*M_ f[_t])/M_ chin1[_t]/2;
-		M_ Rxy[_t]=M_ Rxy[_t]+ (M_ fxy[_t]- M_ chix[_t]*M_ chiy[_t]/M_ chin1[_t]/2 +M_ gxy[_t]*M_ f[_t])/M_ chin1[_t]/2;
-		M_ Rxz[_t]=M_ Rxz[_t]+ (M_ fxz[_t]- M_ chix[_t]*M_ chiz[_t]/M_ chin1[_t]/2 +M_ gxz[_t]*M_ f[_t])/M_ chin1[_t]/2;
-		M_ Ryz[_t]=M_ Ryz[_t]+ (M_ fyz[_t]- M_ chiy[_t]*M_ chiz[_t]/M_ chin1[_t]/2 +M_ gyz[_t]*M_ f[_t])/M_ chin1[_t]/2;
-		
-			
-		_t += STEP_SIZE;
-	}
-}
-
-__global__ void compute_rhs_bssn_part6() 
-{
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	while(_t < _3D_SIZE[0])
-	{
-		M_ gxxx [_t]= (M_ gupxx [_t]* M_ chix [_t]+M_ gupxy[_t]* M_ chiy[_t]+M_ gupxz[_t]* M_ chiz[_t])/M_ chin1[_t];
-		M_ gxxy[_t]= (M_ gupxy[_t]* M_ chix [_t]+M_ gupyy[_t]* M_ chiy[_t]+M_ gupyz[_t]* M_ chiz[_t])/M_ chin1[_t];
-		M_ gxxz[_t]= (M_ gupxz[_t]* M_ chix [_t]+M_ gupyz[_t]* M_ chiy[_t]+M_ gupzz[_t]* M_ chiz[_t])/M_ chin1[_t];
-		// nowM_ get physical second kind of connection
-		M_ Gamxxx [_t]= M_ Gamxxx [_t]- ( (M_ chix [_t]+ M_ chix[_t])/M_ chin1[_t] -M_ gxx [_t]*M_ gxxx [_t])*HALF;
-		M_ Gamyxx [_t]= M_ Gamyxx [_t]- (                     -M_ gxx [_t]*M_ gxxy[_t])*HALF;
-		M_ Gamzxx [_t]= M_ Gamzxx [_t]- (                     -M_ gxx [_t]*M_ gxxz[_t])*HALF;
-		M_ Gamxyy[_t]= M_ Gamxyy[_t]- (                     -M_ gyy[_t]*M_ gxxx [_t])*HALF;
-		M_ Gamyyy[_t]= M_ Gamyyy[_t]- ( (M_ chiy[_t]+ M_ chiy[_t])/M_ chin1[_t] -M_ gyy[_t]*M_ gxxy[_t])*HALF;
-		M_ Gamzyy[_t]= M_ Gamzyy[_t]- (                     -M_ gyy[_t]*M_ gxxz[_t])*HALF;
-		M_ Gamxzz[_t]= M_ Gamxzz[_t]- (                     -M_ gzz[_t]*M_ gxxx [_t])*HALF;
-		M_ Gamyzz[_t]= M_ Gamyzz[_t]- (                     -M_ gzz[_t]*M_ gxxy[_t])*HALF;
-		M_ Gamzzz[_t]= M_ Gamzzz[_t]- ( (M_ chiz[_t]+ M_ chiz[_t])/M_ chin1[_t] -M_ gzz[_t]*M_ gxxz[_t])*HALF;
-		M_ Gamxxy[_t]= M_ Gamxxy[_t]- (  M_ chiy[_t]       /M_ chin1[_t] -M_ gxy[_t]*M_ gxxx [_t])*HALF;
-		M_ Gamyxy[_t]= M_ Gamyxy[_t]- (         M_ chix [_t]/M_ chin1[_t] -M_ gxy[_t]*M_ gxxy[_t])*HALF;
-		M_ Gamzxy[_t]= M_ Gamzxy[_t]- (                     -M_ gxy[_t]*M_ gxxz[_t])*HALF;
-		M_ Gamxxz[_t]= M_ Gamxxz[_t]- (  M_ chiz[_t]       /M_ chin1[_t] -M_ gxz[_t]*M_ gxxx [_t])*HALF;
-		M_ Gamyxz[_t]= M_ Gamyxz[_t]- (                     -M_ gxz[_t]*M_ gxxy[_t])*HALF;
-		M_ Gamzxz[_t]= M_ Gamzxz[_t]- (         M_ chix [_t]/M_ chin1[_t] -M_ gxz[_t]*M_ gxxz[_t])*HALF;
-		M_ Gamxyz[_t]= M_ Gamxyz[_t]- (                     -M_ gyz[_t]*M_ gxxx [_t])*HALF;
-		M_ Gamyyz[_t]= M_ Gamyyz[_t]- (  M_ chiz[_t]       /M_ chin1[_t] -M_ gyz[_t]*M_ gxxy[_t])*HALF;
-		M_ Gamzyz[_t]= M_ Gamzyz[_t]- (         M_ chiy[_t]/M_ chin1[_t] -M_ gyz[_t]*M_ gxxz[_t])*HALF;
-
-		M_ fxx [_t]=M_ fxx [_t]- M_ Gamxxx[_t]*M_ Lapx [_t]- M_ Gamyxx[_t]*M_ Lapy[_t]- M_ Gamzxx[_t]*M_ Lapz[_t];
-		M_ fyy[_t]=M_ fyy[_t]- M_ Gamxyy[_t]*M_ Lapx [_t]- M_ Gamyyy[_t]*M_ Lapy[_t]- M_ Gamzyy[_t]*M_ Lapz[_t];
-		M_ fzz[_t]=M_ fzz[_t]- M_ Gamxzz[_t]*M_ Lapx [_t]- M_ Gamyzz[_t]*M_ Lapy[_t]- M_ Gamzzz[_t]*M_ Lapz[_t];
-		M_ fxy[_t]=M_ fxy[_t]- M_ Gamxxy[_t]*M_ Lapx [_t]- M_ Gamyxy[_t]*M_ Lapy[_t]- M_ Gamzxy[_t]*M_ Lapz[_t];
-		M_ fxz[_t]=M_ fxz[_t]- M_ Gamxxz[_t]*M_ Lapx [_t]- M_ Gamyxz[_t]*M_ Lapy[_t]- M_ Gamzxz[_t]*M_ Lapz[_t];
-		M_ fyz[_t]=M_ fyz[_t]- M_ Gamxyz[_t]*M_ Lapx [_t]- M_ Gamyyz[_t]*M_ Lapy[_t]- M_ Gamzyz[_t]*M_ Lapz[_t];
-
-		// store D^i D_i Lap in M_ trK_rhs[_t] upto M_ chi
-		M_ trK_rhs[_t] =   M_ gupxx [_t]*M_ fxx [_t]+M_ gupyy[_t]*M_ fyy[_t]+M_ gupzz[_t]*M_ fzz[_t]+ 
-		2* (M_ gupxy[_t]*M_ fxy[_t]+M_ gupxz[_t]*M_ fxz[_t]+M_ gupyz[_t]*M_ fyz[_t]);
-		// M_ Add lapse and M_ S_ij parts toM_ Ricci tensor:
-		
-		//follow bam code
-		M_ S[_t] =  M_ chin1[_t] * ( M_ gupxx[_t] * M_ Sxx[_t] + M_ gupyy[_t] * M_ Syy[_t] + M_ gupzz[_t] * M_ Szz[_t] + 
-
-     2 * ( M_ gupxy[_t] * M_ Sxy[_t] + M_ gupxz[_t] * M_ Sxz[_t] + M_ gupyz[_t] * M_ Syz[_t] ) );
-     
-
-M_  f[_t] = F2o3 * M_ trK[_t] * M_ trK[_t] -(
-
-       M_ gupxx[_t] * ( 
-
-       M_ gupxx[_t] * M_ Axx[_t] * M_ Axx[_t] + M_ gupyy[_t] * M_ Axy[_t] * M_ Axy[_t] + M_ gupzz[_t] * M_ Axz[_t] * M_ Axz[_t] + 
-
-       2 * (M_ gupxy[_t] * M_ Axx[_t] * M_ Axy[_t] + M_ gupxz[_t] * M_ Axx[_t] * M_ Axz[_t] + M_ gupyz[_t] * M_ Axy[_t] * M_ Axz[_t]) ) + 
-
-       M_ gupyy[_t] * ( 
-
-       M_ gupxx[_t] * M_ Axy[_t] * M_ Axy[_t] + M_ gupyy[_t] * M_ Ayy[_t] * M_ Ayy[_t] + M_ gupzz[_t] * M_ Ayz[_t] * M_ Ayz[_t] + 
-
-       2 * (M_ gupxy[_t] * M_ Axy[_t] * M_ Ayy[_t] + M_ gupxz[_t] * M_ Axy[_t] * M_ Ayz[_t] + M_ gupyz[_t] * M_ Ayy[_t] * M_ Ayz[_t]) ) + 
-
-       M_ gupzz[_t] * ( 
-
-       M_ gupxx[_t] * M_ Axz[_t] * M_ Axz[_t] + M_ gupyy[_t] * M_ Ayz[_t] * M_ Ayz[_t] + M_ gupzz[_t] * M_ Azz[_t] * M_ Azz[_t] + 
-
-       2 * (M_ gupxy[_t] * M_ Axz[_t] * M_ Ayz[_t] + M_ gupxz[_t] * M_ Axz[_t] * M_ Azz[_t] + M_ gupyz[_t] * M_ Ayz[_t] * M_ Azz[_t]) ) + 
-
-       2 * ( 
-
-       M_ gupxy[_t] * ( 
-
-       M_ gupxx[_t] * M_ Axx[_t] * M_ Axy[_t] + M_ gupyy[_t] * M_ Axy[_t] * M_ Ayy[_t] + M_ gupzz[_t] * M_ Axz[_t] * M_ Ayz[_t] + 
-
-       M_ gupxy[_t] * (M_ Axx[_t] * M_ Ayy[_t] + M_ Axy[_t] * M_ Axy[_t]) + 
-
-       M_ gupxz[_t] * (M_ Axx[_t] * M_ Ayz[_t] + M_ Axz[_t] * M_ Axy[_t]) + 
-
-       M_ gupyz[_t] * (M_ Axy[_t] * M_ Ayz[_t] + M_ Axz[_t] * M_ Ayy[_t]) ) + 
-
-       M_ gupxz[_t] * ( 
-
-       M_ gupxx[_t] * M_ Axx[_t] * M_ Axz[_t] + M_ gupyy[_t] * M_ Axy[_t] * M_ Ayz[_t] + M_ gupzz[_t] * M_ Axz[_t] * M_ Azz[_t] + 
-
-       M_ gupxy[_t] * (M_ Axx[_t] * M_ Ayz[_t] + M_ Axy[_t] * M_ Axz[_t]) + 
-
-       M_ gupxz[_t] * (M_ Axx[_t] * M_ Azz[_t] + M_ Axz[_t] * M_ Axz[_t]) + 
-
-       M_ gupyz[_t] * (M_ Axy[_t] * M_ Azz[_t] + M_ Axz[_t] * M_ Ayz[_t]) ) + 
-
-       M_ gupyz[_t] * ( 
-
-       M_ gupxx[_t] * M_ Axy[_t] * M_ Axz[_t] + M_ gupyy[_t] * M_ Ayy[_t] * M_ Ayz[_t] + M_ gupzz[_t] * M_ Ayz[_t] * M_ Azz[_t] + 
-
-       M_ gupxy[_t] * (M_ Axy[_t] * M_ Ayz[_t] + M_ Ayy[_t] * M_ Axz[_t]) + 
-
-       M_ gupxz[_t] * (M_ Axy[_t] * M_ Azz[_t] + M_ Ayz[_t] * M_ Axz[_t]) + 
-
-       M_ gupyz[_t] * (M_ Ayy[_t] * M_ Azz[_t] + M_ Ayz[_t] * M_ Ayz[_t]) ) )) -16 * PI * M_ rho[_t] + 8 * PI * M_ S[_t];
-       
-
-  M_ f[_t] = - F1o3 *(  M_ gupxx[_t] * M_ fxx[_t] + M_ gupyy[_t] * M_ fyy[_t] + M_ gupzz[_t] * M_ fzz[_t] + 
-
-        2* ( M_ gupxy[_t] * M_ fxy[_t] + M_ gupxz[_t] * M_ fxz[_t] + M_ gupyz[_t] * M_ fyz[_t] ) + M_ alpn1[_t] / M_ chin1[_t] * M_ f[_t]);
-
-  
-
-  M_ fxx[_t] = M_ alpn1[_t] * (M_ Rxx[_t] - 8 * PI * M_ Sxx[_t]) - M_ fxx[_t];
-
-  M_ fxy[_t] = M_ alpn1[_t] * (M_ Rxy[_t] - 8 * PI * M_ Sxy[_t]) - M_ fxy[_t];
-
-  M_ fxz[_t] = M_ alpn1[_t] * (M_ Rxz[_t] - 8 * PI * M_ Sxz[_t]) - M_ fxz[_t];
-
-  M_ fyy[_t] = M_ alpn1[_t] * (M_ Ryy[_t] - 8 * PI * M_ Syy[_t]) - M_ fyy[_t];
-
-  M_ fyz[_t] = M_ alpn1[_t] * (M_ Ryz[_t] - 8 * PI * M_ Syz[_t]) - M_ fyz[_t];
-
-  M_ fzz[_t] = M_ alpn1[_t] * (M_ Rzz[_t] - 8 * PI * M_ Szz[_t]) - M_ fzz[_t];
-		/*
-		M_ fxx [_t]= M_ alpn1[_t]* (M_ Rxx [_t]- 8 * PI * M_ Sxx[_t]) -M_ fxx[_t];
-		M_ fxy[_t]= M_ alpn1[_t]* (M_ Rxy[_t]- 8 * PI * M_ Sxy[_t]) -M_ fxy[_t];
-		M_ fxz[_t]= M_ alpn1[_t]* (M_ Rxz[_t]- 8 * PI * M_ Sxz[_t]) -M_ fxz[_t];
-		M_ fyy[_t]= M_ alpn1[_t]* (M_ Ryy[_t]- 8 * PI * M_ Syy[_t]) -M_ fyy[_t];
-		M_ fyz[_t]= M_ alpn1[_t]* (M_ Ryz[_t]- 8 * PI * M_ Syz[_t]) -M_ fyz[_t];
-		M_ fzz[_t]= M_ alpn1[_t]* (M_ Rzz[_t]- 8 * PI * M_ Szz[_t]) -M_ fzz[_t];
-
-		// Compute trace-free part (note: M_ chi^-1 and M_ chi cancel//):
-
-		M_ f[_t] = F1o3 *( M_ gupxx [_t]*M_ fxx [_t]+M_ gupyy[_t]*M_ fyy[_t]+M_ gupzz[_t]*M_ fzz[_t]+ 
-		2* (M_ gupxy[_t]*M_ fxy[_t]+M_ gupxz[_t]*M_ fxz[_t]+M_ gupyz[_t]*M_ fyz[_t]) );
-		*/
-		M_ Axx_rhs[_t] =M_ fxx [_t]-M_ gxx [_t]*M_ f[_t];
-		M_ Ayy_rhs[_t] =M_ fyy[_t]-M_ gyy[_t]*M_ f[_t];
-		M_ Azz_rhs[_t] =M_ fzz[_t]-M_ gzz[_t]*M_ f[_t];
-		M_ Axy_rhs[_t] =M_ fxy[_t]-M_ gxy[_t]*M_ f[_t];
-		M_ Axz_rhs[_t] =M_ fxz[_t]-M_ gxz[_t]*M_ f[_t];
-		M_ Ayz_rhs[_t] =M_ fyz[_t]-M_ gyz[_t]*M_ f[_t];
-
-		// Now: store M_ A_il M_ A^l_j intoM_ fij:
-
-		M_ fxx [_t]=      M_ gupxx [_t]* M_ Axx [_t]* M_ Axx [_t]+M_ gupyy[_t]* M_ Axy[_t]* M_ Axy[_t]+M_ gupzz[_t]* M_ Axz[_t]* M_ Axz[_t]+ 
-		2 * (M_ gupxy[_t]* M_ Axx [_t]* M_ Axy[_t]+M_ gupxz[_t]* M_ Axx [_t]* M_ Axz[_t]+M_ gupyz[_t]* M_ Axy[_t]* M_ Axz[_t]);
-
-		M_ fyy[_t]=      M_ gupxx [_t]* M_ Axy[_t]* M_ Axy[_t]+M_ gupyy[_t]* M_ Ayy[_t]* M_ Ayy[_t]+M_ gupzz[_t]* M_ Ayz[_t]* M_ Ayz[_t]+ 
-		2 * (M_ gupxy[_t]* M_ Axy[_t]* M_ Ayy[_t]+M_ gupxz[_t]* M_ Axy[_t]* M_ Ayz[_t]+M_ gupyz[_t]* M_ Ayy[_t]* M_ Ayz[_t]);
-
-		M_ fzz[_t]=      M_ gupxx [_t]* M_ Axz[_t]* M_ Axz[_t]+M_ gupyy[_t]* M_ Ayz[_t]* M_ Ayz[_t]+M_ gupzz[_t]* M_ Azz[_t]* M_ Azz[_t]+ 
-		2 * (M_ gupxy[_t]* M_ Axz[_t]* M_ Ayz[_t]+M_ gupxz[_t]* M_ Axz[_t]* M_ Azz[_t]+M_ gupyz[_t]* M_ Ayz[_t]* M_ Azz[_t]);
-
-		M_ fxy[_t]=      M_ gupxx [_t]* M_ Axx [_t]* M_ Axy[_t]+M_ gupyy[_t]* M_ Axy[_t]* M_ Ayy[_t]+M_ gupzz[_t]* M_ Axz[_t]* M_ Ayz[_t]+ 
-		        M_ gupxy[_t]*(M_ Axx [_t]* M_ Ayy[_t]+ M_ Axy[_t]* M_ Axy[_t])                            + 
-		        M_ gupxz[_t]*(M_ Axx [_t]* M_ Ayz[_t]+ M_ Axz[_t]* M_ Axy[_t])                            + 
-		        M_ gupyz[_t]*(M_ Axy[_t]* M_ Ayz[_t]+ M_ Axz[_t]* M_ Ayy[_t]);
-		M_ fxz[_t]=      M_ gupxx [_t]* M_ Axx [_t]* M_ Axz[_t]+M_ gupyy[_t]* M_ Axy[_t]* M_ Ayz[_t]+M_ gupzz[_t]* M_ Axz[_t]* M_ Azz[_t]+ 
-		        M_ gupxy[_t]*(M_ Axx [_t]* M_ Ayz[_t]+ M_ Axy[_t]* M_ Axz[_t])                            + 
-		        M_ gupxz[_t]*(M_ Axx [_t]* M_ Azz[_t]+ M_ Axz[_t]* M_ Axz[_t])                            + 
-		        M_ gupyz[_t]*(M_ Axy[_t]* M_ Azz[_t]+ M_ Axz[_t]* M_ Ayz[_t]);
-		M_ fyz[_t]=      M_ gupxx [_t]* M_ Axy[_t]* M_ Axz[_t]+M_ gupyy[_t]* M_ Ayy[_t]* M_ Ayz[_t]+M_ gupzz[_t]* M_ Ayz[_t]* M_ Azz[_t]+ 
-		        M_ gupxy[_t]*(M_ Axy[_t]* M_ Ayz[_t]+ M_ Ayy[_t]* M_ Axz[_t])                            + 
-		        M_ gupxz[_t]*(M_ Axy[_t]* M_ Azz[_t]+ M_ Ayz[_t]* M_ Axz[_t])                            + 
-		        M_ gupyz[_t]*(M_ Ayy[_t]* M_ Azz[_t]+ M_ Ayz[_t]* M_ Ayz[_t]);
-
-		M_ f[_t] = M_ chin1[_t];
-		// store D^i D_i Lap in M_ trK_rhs[_t]
-		M_ trK_rhs[_t] =M_ f[_t]*M_ trK_rhs[_t];
-		    
-		M_ Axx_rhs[_t] =          M_ f[_t] * M_ Axx_rhs[_t]+ M_ alpn1[_t]* (M_ trK[_t]* M_ Axx [_t]- 2 *M_ fxx[_t])  + 
-		    2 * (  M_ Axx [_t]* M_ betaxx [_t]+   M_ Axy[_t]* M_ betayx [_t]+   M_ Axz[_t]* M_ betazx [_t])- 
-		        F2o3 * M_ Axx [_t]* M_ div_beta[_t];
-
-		M_ Ayy_rhs[_t] =          M_ f[_t] * M_ Ayy_rhs[_t]+ M_ alpn1[_t]* (M_ trK[_t]* M_ Ayy[_t]- 2 *M_ fyy[_t])  + 
-		    2 * (  M_ Axy[_t]* M_ betaxy[_t]+   M_ Ayy[_t]* M_ betayy[_t]+   M_ Ayz[_t]* M_ betazy[_t])- 
-		        F2o3 * M_ Ayy[_t]* M_ div_beta[_t];
-
-		M_ Azz_rhs[_t] =          M_ f[_t] * M_ Azz_rhs[_t]+ M_ alpn1[_t]* (M_ trK[_t]* M_ Azz[_t]- 2 *M_ fzz[_t])  + 
-		    2 * (  M_ Axz[_t]* M_ betaxz[_t]+   M_ Ayz[_t]* M_ betayz[_t]+   M_ Azz[_t]* M_ betazz[_t])- 
-		        F2o3 * M_ Azz[_t]* M_ div_beta[_t];
-
-		M_ Axy_rhs[_t] =          M_ f[_t] * M_ Axy_rhs[_t]+ M_ alpn1[_t]*( M_ trK[_t]* M_ Axy[_t] - 2 *M_ fxy[_t])+ 
-		            M_ Axx [_t]* M_ betaxy[_t]                 +   M_ Axz[_t]* M_ betazy[_t] + 
-		                                M_ Ayy[_t]* M_ betayx [_t]+   M_ Ayz[_t]* M_ betazx [_t] + 
-		        F1o3 * M_ Axy[_t]* M_ div_beta[_t]               -   M_ Axy[_t]* M_ betazz[_t];
-
-		M_ Ayz_rhs[_t] =          M_ f[_t] * M_ Ayz_rhs[_t]+ M_ alpn1[_t]*( M_ trK[_t]* M_ Ayz[_t] - 2 *M_ fyz[_t])+ 
-		            M_ Axy[_t]* M_ betaxz[_t]+   M_ Ayy[_t]* M_ betayz[_t]                  + 
-		            M_ Axz[_t]* M_ betaxy[_t]                 +   M_ Azz[_t]* M_ betazy[_t] + 
-		        F1o3 * M_ Ayz[_t]* M_ div_beta[_t]               -   M_ Ayz[_t]* M_ betaxx[_t];
-
-		M_ Axz_rhs[_t] =          M_ f[_t] * M_ Axz_rhs[_t]+ M_ alpn1[_t]*( M_ trK[_t]* M_ Axz[_t] - 2 *M_ fxz[_t])+ 
-		            M_ Axx [_t]* M_ betaxz[_t]+   M_ Axy[_t]* M_ betayz[_t]                  + 
-		                                M_ Ayz[_t]* M_ betayx [_t]+   M_ Azz[_t]* M_ betazx [_t] + 
-		        F1o3 * M_ Axz[_t]* M_ div_beta[_t]               -   M_ Axz[_t]* M_ betayy[_t]  ;   //rhsM_ for M_ Aij
-
-		// Compute trace of M_ S_ij
-
-		M_ S[_t] = M_ f[_t] * (M_ gupxx [_t]* M_ Sxx [_t]+M_ gupyy[_t]* M_ Syy[_t]+M_ gupzz[_t]* M_ Szz[_t]+ 
-		2 * (M_ gupxy[_t]* M_ Sxy[_t]+M_ gupxz[_t]* M_ Sxz[_t]+M_ gupyz[_t]* M_ Syz[_t]) );
-
-		M_ trK_rhs[_t] = - M_ trK_rhs[_t] + M_ alpn1[_t]*( F1o3 * M_ trK[_t]* M_ trK[_t]        + 
-		        M_ gupxx [_t]*M_ fxx [_t]+M_ gupyy[_t]*M_ fyy[_t]+M_ gupzz[_t]*M_ fzz[_t]  + 
-		2 * (M_ gupxy[_t]*M_ fxy[_t]+M_ gupxz[_t]*M_ fxz[_t]+M_ gupyz[_t]*M_ fyz[_t]) + 
-		4 * PI * ( M_ rho[_t] + M_ S[_t] )) ;                               //rhsM_ for M_ trK[_t]
-
-		////////M_ gauge variable part
-
-		M_ Lap_rhs[_t] = -2*M_ alpn1[_t] * M_ trK[_t];
-		
-#if (GAUGE == 0)
-		M_ betax_rhs[_t] =0.75*M_ dtSfx[_t];
-		M_ betay_rhs[_t] =0.75*M_ dtSfy[_t];
-		M_ betaz_rhs[_t] =0.75*M_ dtSfz[_t];
-
-		M_ dtSfx_rhs[_t] = M_ Gamx_rhs[_t] -2*M_ dtSfx[_t];
-		M_ dtSfy_rhs[_t] = M_ Gamy_rhs[_t] -2*M_ dtSfy[_t];
-		M_ dtSfz_rhs[_t] = M_ Gamz_rhs[_t] -2*M_ dtSfz[_t];
-		
-#elif (GAUGE == 1)
-		M_ betax_rhs[_t] =M_ Gamx[_t] - 2 * M_ betax[_t] ;
-
-  		M_ betay_rhs[_t] =M_ Gamy[_t] - 2 * M_ betay[_t] ;
-
-  		M_ betaz_rhs[_t] =M_ Gamz[_t] - 2 * M_ betaz[_t] ;
-
-		M_ dtSfx_rhs[_t] = 0;
-		M_ dtSfy_rhs[_t] = 0;
-		M_ dtSfz_rhs[_t] = 0;
-		
-#elif (GAUGE == 2 || GAUGE == 3)
-
-  M_ betax_rhs[_t] = 0.75* M_ dtSfx[_t];
-
-  M_ betay_rhs[_t] = 0.75* M_ dtSfy[_t];
-
-  M_ betaz_rhs[_t] = 0.75* M_ dtSfz[_t];
-  	
-#elif (GAUGE == 6)
-		if(BHN==2)
-		{
-			int k = _t / _2D_SIZE[0];
-			int ps = _t - (_2D_SIZE[0] * k); //TOTRY: = curr % _2D_SIZE[0];
-			int j = ps / ex_c[0];
-			int i = ps  - (j * ex_c[0]);
-			
-			r1 = ( pow2((Porg[0]-X[i]))+ pow2((Porg[1]-Y[j]))+ pow2((Porg[2]-Z[k])) ) / 
-
-          		( pow2((Porg[0]-Porg[3]))+ pow2((Porg[1]-Porg[4])) + pow2((Porg[2]-Porg[5])) );
-          
-
-		    r2 = ( pow2((Porg[3]-X[i])) + pow2((Porg[4]-Y[j])) + pow2((Porg[5]-Z[k])) )/ 
-
-		          ( pow2((Porg[0]-Porg[3])) + pow2((Porg[1]-Porg[4])) + pow2((Porg[2]-Porg[5])) );
-          
-
-     		reta[i+ j*_1D_SIZE[0]+ k*_2D_SIZE[0] ] = A + C1/(1 + 12 * r1) + C2/(1 + 12 *r2);
-		}//BHN == 2
-		
-		M_ betax_rhs[_t] = 0.75*M_ dtSfx[_t];
-
-		M_ betay_rhs[_t] = 0.75*M_ dtSfy[_t];
-
-		M_ betaz_rhs[_t] = 0.75*M_ dtSfz[_t];
-
-
-
-		M_ dtSfx_rhs[_t] = M_ Gamx_rhs[_t] - M_ reta[_t] * M_ dtSfx[_t];
-
-		M_ dtSfy_rhs[_t] = M_ Gamy_rhs[_t] - M_ reta[_t] * M_ dtSfy[_t];
-
-		M_ dtSfz_rhs[_t] = M_ Gamz_rhs[_t] - M_ reta[_t] * M_ dtSfz[_t];
-		
-#elif (GAUGE == 7)
-		if(BHN==2){
-			int k = _t / _2D_SIZE[0];
-			int ps = _t - (_2D_SIZE[0] * k); //TOTRY: = curr % _2D_SIZE[0];
-			int j = ps / ex_c[0];
-			int i = ps  - (j * ex_c[0]);
-			
-			r1 = ( pow2((Porg[0]-X[i])) + pow2((Porg[1]-Y[j])) + pow2((Porg[2]-Z[k])) )/ 
-
-          		( pow2((Porg[0]-Porg[3])) + pow2((Porg[1]-Porg[4])) + pow2((Porg[2]-Porg[5])) );
-          
-
-		    r2 = ( pow2((Porg[3]-X[i])) + pow2((Porg[4]-Y[j])) + pow2((Porg[5]-Z[k])) )/ 
-
-		          ( pow2((Porg[0]-Porg[3])) + pow2((Porg[1]-Porg[4])) + pow2((Porg[2]-Porg[5])) );
-		          
-
-		    M_ reta[_t][i+ j*_1D_SIZE[0]+ k*_2D_SIZE[0] ] = A + C1* exp(-12 *r1) + C2*exp(- 12*r2);
-		}//BHN ==2
-		
-		M_ betax_rhs[_t] = 0.75*M_ dtSfx[_t];
-
-		M_ betay_rhs[_t] = 0.75*M_ dtSfy[_t];
-
-		M_ betaz_rhs[_t] = 0.75*M_ dtSfz[_t];
-
-
-
-		M_ dtSfx_rhs[_t] = M_ Gamx_rhs[_t] - M_ reta[_t]*M_ dtSfx[_t];
-
-		M_ dtSfy_rhs[_t] = M_ Gamy_rhs[_t] - M_ reta[_t]*M_ dtSfy[_t];
-
-		M_ dtSfz_rhs[_t] = M_ Gamz_rhs[_t] - M_ reta[_t]*M_ dtSfz[_t];
-
-#endif  //if (GAUGE == ?)
-
-		_t += STEP_SIZE;
-	}
-}	
-
-__global__ void compute_rhs_bssn_part6_gauge() 
-{	
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	while(_t < _3D_SIZE[0])
-	{
-#if (GAUGE == 2)
-	M_ reta[_t] =  M_ gupxx[_t] *  M_ dtSfx_rhs[_t] *  M_ dtSfx_rhs[_t] +  M_ gupyy[_t] *  M_ dtSfy_rhs[_t] *  M_ dtSfy_rhs[_t] +  M_ gupzz[_t] *  M_ dtSfz_rhs[_t] *  M_ dtSfz_rhs[_t] + 
-
-       2 * ( M_ gupxy[_t] *  M_ dtSfx_rhs[_t] *  M_ dtSfy_rhs[_t] +  M_ gupxz[_t] *  M_ dtSfx_rhs[_t] *  M_ dtSfz_rhs[_t] +  M_ gupyz[_t] *  M_ dtSfy_rhs[_t] *  M_ dtSfz_rhs[_t]);
-       
-
-   M_ reta[_t] = 1.13 / 2 * sqrt( M_ reta[_t]/M_ chin1[_t])/ pow2( ( 1-sqrt(M_ chin1[_t]) ) );
-  
-
-   M_ dtSfx_rhs[_t] =  M_ Gamx_rhs[_t] -  M_ reta[_t]* M_ dtSfx[_t];
-
-   M_ dtSfy_rhs[_t] =  M_ Gamy_rhs[_t] -  M_ reta[_t]* M_ dtSfy[_t];
-
-   M_ dtSfz_rhs[_t] =  M_ Gamz_rhs[_t] -  M_ reta[_t]* M_ dtSfz[_t];
-
-#elif (GAUGE == 3)
-	M_ reta[_t] =  M_ gupxx[_t] *  M_ dtSfx_rhs[_t] *  M_ dtSfx_rhs[_t] +  M_ gupyy[_t] *  M_ dtSfy_rhs[_t] *  M_ dtSfy_rhs[_t]
-					 +  M_ gupzz[_t] *  M_ dtSfz_rhs[_t] *  M_ dtSfz_rhs[_t] + 
-
-       				2 * ( M_ gupxy[_t] *  M_ dtSfx_rhs[_t] *  M_ dtSfy_rhs[_t] +  
-       				M_ gupxz[_t] *  M_ dtSfx_rhs[_t] *  M_ dtSfz_rhs[_t] +  
-       				M_ gupyz[_t] *  M_ dtSfy_rhs[_t] *  M_ dtSfz_rhs[_t]);
-       
-
-	M_ reta[_t] = 1.13/2 * sqrt( M_ reta[_t]/ M_ chin1[_t])/ pow2((1-M_ chin1[_t]));
-
-	M_ dtSfx_rhs[_t] =  M_ Gamx_rhs[_t] -  M_ reta[_t]* M_ dtSfx[_t];
-
-	M_ dtSfy_rhs[_t] =  M_ Gamy_rhs[_t] -  M_ reta[_t]* M_ dtSfy[_t];
-
-	M_ dtSfz_rhs[_t] =  M_ Gamz_rhs[_t] -  M_ reta[_t]* M_ dtSfz[_t];
-	
-#elif (GAUGE == 4)
-	M_ reta[_t] =  M_ gupxx[_t] *  M_ dtSfx_rhs[_t] *  M_ dtSfx_rhs[_t] +  M_ gupyy[_t] *  M_ dtSfy_rhs[_t] *
-				  M_ dtSfy_rhs[_t] +  M_ gupzz[_t] *  M_ dtSfz_rhs[_t] *  M_ dtSfz_rhs[_t] + 
-
-       				2 * ( M_ gupxy[_t] *  M_ dtSfx_rhs[_t] *  M_ dtSfy_rhs[_t] +  M_ gupxz[_t] *  
-       				M_ dtSfx_rhs[_t] *  M_ dtSfz_rhs[_t] +  M_ gupyz[_t] *  M_ dtSfy_rhs[_t] *  M_ dtSfz_rhs[_t]);
-       
-
-	M_ reta[_t] = 1.13 / 2 * sqrt( M_ reta[_t]/M_ chin1[_t])/ pow( (1-sqrt(M_ chin1[_t])));
-
-
-	M_ betax_rhs[_t] = 0.75* M_ Gamx[_t] -  M_ reta[_t]*M_ betax[_t];
-
-	M_ betay_rhs[_t] = 0.75* M_ Gamy[_t] -  M_ reta[_t]*M_ betay[_t];
-
-	M_ betaz_rhs[_t] = 0.75* M_ Gamz[_t] -  M_ reta[_t]*M_ betaz[_t];
-	
-#elif (GAUGE == 5)
-	M_ reta[_t] =  M_ gupxx[_t] *  M_ dtSfx_rhs[_t] *  M_ dtSfx_rhs[_t] +  M_ gupyy[_t] *  M_ dtSfy_rhs[_t] *  M_ dtSfy_rhs[_t] +  M_ gupzz[_t] *  M_ dtSfz_rhs[_t] *  M_ dtSfz_rhs[_t] + 
-
-       2 * ( M_ gupxy[_t] *  M_ dtSfx_rhs[_t] *  M_ dtSfy_rhs[_t] +  M_ gupxz[_t] *  M_ dtSfx_rhs[_t] *  M_ dtSfz_rhs[_t] +  M_ gupyz[_t] *  M_ dtSfy_rhs[_t] *  M_ dtSfz_rhs[_t]);
-       
-
-	M_ reta[_t] = 1.13 / 2 * sqrt( M_ reta[_t]/M_ chin1)/ pow( (1-M_ chin1[_t]) );
-
-	M_ betax_rhs[_t] = 0.75* M_ Gamx[_t] -  M_ reta[_t]*M_ betax[_t];
-
-	M_ betay_rhs[_t] = 0.75* M_ Gamy[_t] -  M_ reta[_t]*M_ betay[_t];
-
-	M_ betaz_rhs[_t] = 0.75* M_ Gamz[_t] -  M_ reta[_t]*M_ betaz[_t];
-
-
-
-	M_ dtSfx_rhs[_t] = 0;
-
-	M_ dtSfy_rhs[_t] = 0;
-
-	M_ dtSfz_rhs[_t] = 0;
-#endif
-		_t += STEP_SIZE;
-	}
-}
-__global__ void compute_rhs_bssn_part7() 
-{
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	while(_t < _3D_SIZE[0])
-	{
-		M_ ham_Res[_t] =   M_ gupxx [_t]* M_ Rxx [_t]+ M_ gupyy[_t]* M_ Ryy[_t]+ M_ gupzz[_t]* M_ Rzz[_t]+ 
-						2* ( M_ gupxy[_t]* M_ Rxy[_t]+ M_ gupxz[_t]* M_ Rxz[_t]+ M_ gupyz[_t]* M_ Ryz[_t]);
-
-		M_ ham_Res[_t] = M_ chin1[_t]*M_ ham_Res[_t] + F2o3 * M_ trK[_t] * M_ trK[_t] -(
-					M_ gupxx [_t]* ( 
-					M_ gupxx [_t]* M_ Axx [_t]* M_ Axx [_t]+ M_ gupyy[_t]* M_ Axy[_t]* M_ Axy[_t]+ M_ gupzz[_t]* M_ Axz[_t]* M_ Axz[_t]+ 
-					2 * (M_ gupxy[_t]* M_ Axx [_t]* M_ Axy[_t]+ M_ gupxz[_t]* M_ Axx [_t]* M_ Axz[_t]+ M_ gupyz[_t]* M_ Axy[_t]* M_ Axz[_t]) ) + 
-					M_ gupyy[_t]* ( 
-					M_ gupxx [_t]* M_ Axy[_t]* M_ Axy[_t]+ M_ gupyy[_t]* M_ Ayy[_t]* M_ Ayy[_t]+ M_ gupzz[_t]* M_ Ayz[_t]* M_ Ayz[_t]+ 
-					2 * (M_ gupxy[_t]* M_ Axy[_t]* M_ Ayy[_t]+ M_ gupxz[_t]* M_ Axy[_t]* M_ Ayz[_t]+ M_ gupyz[_t]* M_ Ayy[_t]* M_ Ayz[_t]) ) + 
-					M_ gupzz[_t]* ( 
-					M_ gupxx [_t]* M_ Axz[_t]* M_ Axz[_t]+ M_ gupyy[_t]* M_ Ayz[_t]* M_ Ayz[_t]+ M_ gupzz[_t]* M_ Azz[_t]* M_ Azz[_t]+ 
-					2 * (M_ gupxy[_t]* M_ Axz[_t]* M_ Ayz[_t]+ M_ gupxz[_t]* M_ Axz[_t]* M_ Azz[_t]+ M_ gupyz[_t]* M_ Ayz[_t]* M_ Azz[_t]) ) + 
-					2 * ( 
-					M_ gupxy[_t]* ( 
-					M_ gupxx [_t]* M_ Axx [_t]* M_ Axy[_t]+ M_ gupyy[_t]* M_ Axy[_t]* M_ Ayy[_t]+ M_ gupzz[_t]* M_ Axz[_t]* M_ Ayz[_t]+ 
-					M_ gupxy[_t]* (M_ Axx [_t]* M_ Ayy[_t]+ M_ Axy[_t]* M_ Axy[_t]) + 
-					M_ gupxz[_t]* (M_ Axx [_t]* M_ Ayz[_t]+ M_ Axz[_t]* M_ Axy[_t]) + 
-					M_ gupyz[_t]* (M_ Axy[_t]* M_ Ayz[_t]+ M_ Axz[_t]* M_ Ayy[_t]) ) + 
-					M_ gupxz[_t]* ( 
-					M_ gupxx [_t]* M_ Axx [_t]* M_ Axz[_t]+ M_ gupyy[_t]* M_ Axy[_t]* M_ Ayz[_t]+ M_ gupzz[_t]* M_ Axz[_t]* M_ Azz[_t]+ 
-					M_ gupxy[_t]* (M_ Axx [_t]* M_ Ayz[_t]+ M_ Axy[_t]* M_ Axz[_t]) + 
-					M_ gupxz[_t]* (M_ Axx [_t]* M_ Azz[_t]+ M_ Axz[_t]* M_ Axz[_t]) + 
-					M_ gupyz[_t]* (M_ Axy[_t]* M_ Azz[_t]+ M_ Axz[_t]* M_ Ayz[_t]) ) + 
-					M_ gupyz[_t]* ( 
-					M_ gupxx [_t]* M_ Axy[_t]* M_ Axz[_t]+ M_ gupyy[_t]* M_ Ayy[_t]* M_ Ayz[_t]+ M_ gupzz[_t]* M_ Ayz[_t]* M_ Azz[_t]+ 
-					M_ gupxy[_t]* (M_ Axy[_t]* M_ Ayz[_t]+ M_ Ayy[_t]* M_ Axz[_t]) + 
-					M_ gupxz[_t]* (M_ Axy[_t]* M_ Azz[_t]+ M_ Ayz[_t]* M_ Axz[_t]) + 
-					M_ gupyz[_t]* (M_ Ayy[_t]* M_ Azz[_t]+ M_ Ayz[_t]* M_ Ayz[_t]) ) ))- 16 * PI * M_ rho[_t];
-		
-		_t += STEP_SIZE;
-	}
-}
-__global__ void compute_rhs_bssn_part8() 
-{
-	int _t = blockIdx.x*blockDim.x+threadIdx.x;
-	while(_t < _3D_SIZE[0])
-	{
-		M_ gxxx [_t]= M_ gxxx [_t]- (  M_ Gamxxx [_t]* M_ Axx [_t]+ M_ Gamyxx [_t]* M_ Axy[_t]+ M_ Gamzxx [_t]* M_ Axz[_t]
-		                + M_ Gamxxx [_t]* M_ Axx [_t]+ M_ Gamyxx [_t]* M_ Axy[_t]+ M_ Gamzxx [_t]* M_ Axz[_t]) - M_ chix[_t]*M_ Axx[_t]/M_ chin1[_t];
-		                
-		M_ gxyx [_t]= M_ gxyx [_t]- (  M_ Gamxxy[_t]* M_ Axx [_t]+ M_ Gamyxy[_t]* M_ Axy[_t]+ M_ Gamzxy[_t]* M_ Axz[_t]
-		                + M_ Gamxxx [_t]* M_ Axy[_t]+ M_ Gamyxx [_t]* M_ Ayy[_t]+ M_ Gamzxx [_t]* M_ Ayz[_t]) - M_ chix[_t]*M_ Axy[_t]/M_ chin1[_t];
-		                
-		M_ gxzx [_t]= M_ gxzx [_t]- (  M_ Gamxxz[_t]* M_ Axx [_t]+ M_ Gamyxz[_t]* M_ Axy[_t]+ M_ Gamzxz[_t]* M_ Axz[_t]
-		                + M_ Gamxxx [_t]* M_ Axz[_t]+ M_ Gamyxx [_t]* M_ Ayz[_t]+ M_ Gamzxx [_t]* M_ Azz[_t]) - M_ chix[_t]*M_ Axz[_t]/M_ chin1[_t];
-		                
-		M_ gyyx [_t]= M_ gyyx [_t]- (  M_ Gamxxy[_t]* M_ Axy[_t]+ M_ Gamyxy[_t]* M_ Ayy[_t]+ M_ Gamzxy[_t]* M_ Ayz[_t]
-		                + M_ Gamxxy[_t]* M_ Axy[_t]+ M_ Gamyxy[_t]* M_ Ayy[_t]+ M_ Gamzxy[_t]* M_ Ayz[_t]) - M_ chix[_t]*M_ Ayy[_t]/M_ chin1[_t];
-		                
-		M_ gyzx [_t]= M_ gyzx [_t]- (  M_ Gamxxz[_t]* M_ Axy[_t]+ M_ Gamyxz[_t]* M_ Ayy[_t]+ M_ Gamzxz[_t]* M_ Ayz[_t]
-		                + M_ Gamxxy[_t]* M_ Axz[_t]+ M_ Gamyxy[_t]* M_ Ayz[_t]+ M_ Gamzxy[_t]* M_ Azz[_t]) - M_ chix[_t]*M_ Ayz[_t]/M_ chin1[_t];
-		                
-		M_ gzzx [_t]= M_ gzzx [_t]- (  M_ Gamxxz[_t]* M_ Axz[_t]+ M_ Gamyxz[_t]* M_ Ayz[_t]+ M_ Gamzxz[_t]* M_ Azz[_t]
-		                + M_ Gamxxz[_t]* M_ Axz[_t]+ M_ Gamyxz[_t]* M_ Ayz[_t]+ M_ Gamzxz[_t]* M_ Azz[_t]) - M_ chix[_t]*M_ Azz[_t]/M_ chin1[_t];
-		                
-		M_ gxxy[_t]= M_ gxxy[_t]- (  M_ Gamxxy[_t]* M_ Axx [_t]+ M_ Gamyxy[_t]* M_ Axy[_t]+ M_ Gamzxy[_t]* M_ Axz[_t]
-		                + M_ Gamxxy[_t]* M_ Axx [_t]+ M_ Gamyxy[_t]* M_ Axy[_t]+ M_ Gamzxy[_t]* M_ Axz[_t]) - M_ chiy[_t]*M_ Axx[_t]/M_ chin1[_t];
-		                
-		M_ gxyy[_t]= M_ gxyy[_t]- (  M_ Gamxyy[_t]* M_ Axx [_t]+ M_ Gamyyy[_t]* M_ Axy[_t]+ M_ Gamzyy[_t]* M_ Axz[_t]
-		                + M_ Gamxxy[_t]* M_ Axy[_t]+ M_ Gamyxy[_t]* M_ Ayy[_t]+ M_ Gamzxy[_t]* M_ Ayz[_t]) - M_ chiy[_t]*M_ Axy[_t]/M_ chin1[_t];
-		                
-		M_ gxzy[_t]= M_ gxzy[_t]- (  M_ Gamxyz[_t]* M_ Axx [_t]+ M_ Gamyyz[_t]* M_ Axy[_t]+ M_ Gamzyz[_t]* M_ Axz[_t]
-		                + M_ Gamxxy[_t]* M_ Axz[_t]+ M_ Gamyxy[_t]* M_ Ayz[_t]+ M_ Gamzxy[_t]* M_ Azz[_t]) - M_ chiy[_t]*M_ Axz[_t]/M_ chin1[_t];
-		                
-		M_ gyyy[_t]= M_ gyyy[_t]- (  M_ Gamxyy[_t]* M_ Axy[_t]+ M_ Gamyyy[_t]* M_ Ayy[_t]+ M_ Gamzyy[_t]* M_ Ayz[_t]
-		                + M_ Gamxyy[_t]* M_ Axy[_t]+ M_ Gamyyy[_t]* M_ Ayy[_t]+ M_ Gamzyy[_t]* M_ Ayz[_t]) - M_ chiy[_t]*M_ Ayy[_t]/M_ chin1[_t];
-		                
-		M_ gyzy[_t]= M_ gyzy[_t]- (  M_ Gamxyz[_t]* M_ Axy[_t]+ M_ Gamyyz[_t]* M_ Ayy[_t]+ M_ Gamzyz[_t]* M_ Ayz[_t]
-		                + M_ Gamxyy[_t]* M_ Axz[_t]+ M_ Gamyyy[_t]* M_ Ayz[_t]+ M_ Gamzyy[_t]* M_ Azz[_t]) - M_ chiy[_t]*M_ Ayz[_t]/M_ chin1[_t];
-		                
-		M_ gzzy[_t]= M_ gzzy[_t]- (  M_ Gamxyz[_t]* M_ Axz[_t]+ M_ Gamyyz[_t]* M_ Ayz[_t]+ M_ Gamzyz[_t]* M_ Azz[_t]
-		                + M_ Gamxyz[_t]* M_ Axz[_t]+ M_ Gamyyz[_t]* M_ Ayz[_t]+ M_ Gamzyz[_t]* M_ Azz[_t]) - M_ chiy[_t]*M_ Azz[_t]/M_ chin1[_t];
-		                
-		M_ gxxz[_t]= M_ gxxz[_t]- (  M_ Gamxxz[_t]* M_ Axx [_t]+ M_ Gamyxz[_t]* M_ Axy[_t]+ M_ Gamzxz[_t]* M_ Axz[_t]
-		                + M_ Gamxxz[_t]* M_ Axx [_t]+ M_ Gamyxz[_t]* M_ Axy[_t]+ M_ Gamzxz[_t]* M_ Axz[_t]) - M_ chiz[_t]*M_ Axx[_t]/M_ chin1[_t];
-		                
-		M_ gxyz[_t]= M_ gxyz[_t]- (  M_ Gamxyz[_t]* M_ Axx [_t]+ M_ Gamyyz[_t]* M_ Axy[_t]+ M_ Gamzyz[_t]* M_ Axz[_t]
-		                + M_ Gamxxz[_t]* M_ Axy[_t]+ M_ Gamyxz[_t]* M_ Ayy[_t]+ M_ Gamzxz[_t]* M_ Ayz[_t]) - M_ chiz[_t]*M_ Axy[_t]/M_ chin1[_t];
-		                
-		M_ gxzz[_t]= M_ gxzz[_t]- (  M_ Gamxzz[_t]* M_ Axx [_t]+ M_ Gamyzz[_t]* M_ Axy[_t]+ M_ Gamzzz[_t]* M_ Axz[_t]
-		                + M_ Gamxxz[_t]* M_ Axz[_t]+ M_ Gamyxz[_t]* M_ Ayz[_t]+ M_ Gamzxz[_t]* M_ Azz[_t]) - M_ chiz[_t]*M_ Axz[_t]/M_ chin1[_t];
-		                
-		M_ gyyz[_t]= M_ gyyz[_t]- (  M_ Gamxyz[_t]* M_ Axy[_t]+ M_ Gamyyz[_t]* M_ Ayy[_t]+ M_ Gamzyz[_t]* M_ Ayz[_t]
-		                + M_ Gamxyz[_t]* M_ Axy[_t]+ M_ Gamyyz[_t]* M_ Ayy[_t]+ M_ Gamzyz[_t]* M_ Ayz[_t]) - M_ chiz[_t]*M_ Ayy[_t]/M_ chin1[_t];
-		                
-		M_ gyzz[_t]= M_ gyzz[_t]- (  M_ Gamxzz[_t]* M_ Axy[_t]+ M_ Gamyzz[_t]* M_ Ayy[_t]+ M_ Gamzzz[_t]* M_ Ayz[_t]
-		                + M_ Gamxyz[_t]* M_ Axz[_t]+ M_ Gamyyz[_t]* M_ Ayz[_t]+ M_ Gamzyz[_t]* M_ Azz[_t]) - M_ chiz[_t]*M_ Ayz[_t]/M_ chin1[_t];
-		                
-		M_ gzzz[_t]= M_ gzzz[_t]- (  M_ Gamxzz[_t]* M_ Axz[_t]+ M_ Gamyzz[_t]* M_ Ayz[_t]+ M_ Gamzzz[_t]* M_ Azz[_t]
-		                + M_ Gamxzz[_t]* M_ Axz[_t]+ M_ Gamyzz[_t]* M_ Ayz[_t]+ M_ Gamzzz[_t]* M_ Azz[_t]) - M_ chiz[_t]*M_ Azz[_t]/M_ chin1[_t];
-		                
-		M_ movx_Res[_t] = M_ gupxx[_t]*M_ gxxx [_t]+ M_ gupyy[_t]*M_ gxyy[_t]+ M_ gupzz[_t]*M_ gxzz[_t]
-		        +M_ gupxy[_t]*M_ gxyx [_t]+ M_ gupxz[_t]*M_ gxzx [_t]+ M_ gupyz[_t]*M_ gxzy[_t]
-		        +M_ gupxy[_t]*M_ gxxy[_t]+ M_ gupxz[_t]*M_ gxxz[_t]+ M_ gupyz[_t]*M_ gxyz[_t];
-		M_ movy_Res[_t] = M_ gupxx[_t]*M_ gxyx [_t]+ M_ gupyy[_t]*M_ gyyy[_t]+ M_ gupzz[_t]*M_ gyzz[_t]
-		        +M_ gupxy[_t]*M_ gyyx [_t]+ M_ gupxz[_t]*M_ gyzx [_t]+ M_ gupyz[_t]*M_ gyzy[_t]
-		        +M_ gupxy[_t]*M_ gxyy[_t]+ M_ gupxz[_t]*M_ gxyz[_t]+ M_ gupyz[_t]*M_ gyyz[_t];
-		        
-		M_ movz_Res[_t] = M_ gupxx[_t]*M_ gxzx [_t]+ M_ gupyy[_t]*M_ gyzy[_t]+ M_ gupzz[_t]*M_ gzzz[_t]
-		        +M_ gupxy[_t]*M_ gyzx [_t]+ M_ gupxz[_t]*M_ gzzx [_t]+ M_ gupyz[_t]*M_ gzzy[_t]
-		        +M_ gupxy[_t]*M_ gxzy[_t]+ M_ gupxz[_t]*M_ gxzz[_t]+ M_ gupyz[_t]*M_ gyzz[_t];
-
-		M_ movx_Res[_t] = M_ movx_Res[_t] - F2o3*M_ Kx [_t]- 8*PI*M_ Sx[_t];
-		M_ movy_Res[_t] = M_ movy_Res[_t] - F2o3*M_ Ky[_t]- 8*PI*M_ Sy[_t];
-		M_ movz_Res[_t] = M_ movz_Res[_t] - F2o3*M_ Kz[_t]- 8*PI*M_ Sz[_t];
-		
-		_t += STEP_SIZE;
-	}
-}
-
-
-
-__global__ void device_test(double * result, double * Xt){	
-	/*result[0] = MAXSIZE;
-	result[1] = STEP;
-	result[2] = ex_c[0];
-	result[3] = ex_c[1];
-	result[4] = ex_c[2];
-	result[5] = Xt[0];
-	result[6] = Xt[1];
-	result[7] = metac.X[0];
-	result[8] = metac.X[1];	*/
-	
-	result[0] = metac.gzz[0];
-	result[1] = metac.gzz[1];
-	result[2] = metac.gzz[2];
-	result[3] = metac.gyy[0];
-	result[4] = metac.gyy[1];
-	result[5] = metac.gyy[2];
-	result[6] = _3D_SIZE[0];
-	result[7] = STEP_SIZE;
-	result[8] = blockDim.x * gridDim.x;
-}
-
-void destroy_meta(Meta *meta)
-{
-	/*
-	if(Mh_ X) CUDA_SAFE_CALL(cudaFree(Mh_ X));
-	if(Mh_ Y) CUDA_SAFE_CALL(cudaFree(Mh_ Y));
-	if(Mh_ Z) CUDA_SAFE_CALL(cudaFree(Mh_ Z));
-	if(Mh_ chi) CUDA_SAFE_CALL(cudaFree(Mh_ chi));
-	if(Mh_ dxx) CUDA_SAFE_CALL(cudaFree(Mh_ dxx));
-	if(Mh_ dyy) CUDA_SAFE_CALL(cudaFree(Mh_ dyy));
-	if(Mh_ dzz) CUDA_SAFE_CALL(cudaFree(Mh_ dzz));
-	if(Mh_ trK) CUDA_SAFE_CALL(cudaFree(Mh_ trK));
-	if(Mh_ gxy) CUDA_SAFE_CALL(cudaFree(Mh_ gxy));
-	if(Mh_ gxz) CUDA_SAFE_CALL(cudaFree(Mh_ gxz));
-	if(Mh_ gyz) CUDA_SAFE_CALL(cudaFree(Mh_ gyz));
-	if(Mh_ Axx) CUDA_SAFE_CALL(cudaFree(Mh_ Axx));
-	if(Mh_ Axy) CUDA_SAFE_CALL(cudaFree(Mh_ Axy));
-	if(Mh_ Axz) CUDA_SAFE_CALL(cudaFree(Mh_ Axz));
-	if(Mh_ Ayz) CUDA_SAFE_CALL(cudaFree(Mh_ Ayz));
-	if(Mh_ Ayy) CUDA_SAFE_CALL(cudaFree(Mh_ Ayy));
-	if(Mh_ Azz) CUDA_SAFE_CALL(cudaFree(Mh_ Azz));
-	if(Mh_ Gamx) CUDA_SAFE_CALL(cudaFree(Mh_ Gamx));
-	if(Mh_ Gamy) CUDA_SAFE_CALL(cudaFree(Mh_ Gamy));
-	if(Mh_ Gamz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamz));
-	if(Mh_ Lap) CUDA_SAFE_CALL(cudaFree(Mh_ Lap));
-	if(Mh_ betax) CUDA_SAFE_CALL(cudaFree(Mh_ betax));
-	if(Mh_ betay) CUDA_SAFE_CALL(cudaFree(Mh_ betay));
-	if(Mh_ betaz) CUDA_SAFE_CALL(cudaFree(Mh_ betaz));
-	if(Mh_ dtSfx) CUDA_SAFE_CALL(cudaFree(Mh_ dtSfx));
-	if(Mh_ dtSfy) CUDA_SAFE_CALL(cudaFree(Mh_ dtSfy));
-	if(Mh_ dtSfz) CUDA_SAFE_CALL(cudaFree(Mh_ dtSfz));
-	if(Mh_ chi_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ chi_rhs));
-	if(Mh_ trK_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ trK_rhs));
-	if(Mh_ gxy_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ gxy_rhs));
-	if(Mh_ gxz_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ gxz_rhs));
-	if(Mh_ gyz_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ gyz_rhs));
-	if(Mh_ Axx_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ Axx_rhs));
-	if(Mh_ Axy_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ Axy_rhs));
-	if(Mh_ Axz_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ Axz_rhs));
-	if(Mh_ Ayz_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ Ayz_rhs));
-	if(Mh_ Ayy_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ Ayy_rhs));
-	if(Mh_ Azz_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ Azz_rhs));
-	if(Mh_ Gamx_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ Gamx_rhs));
-	if(Mh_ Gamy_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ Gamy_rhs));
-	if(Mh_ Gamz_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ Gamz_rhs));
-	if(Mh_ Lap_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ Lap_rhs));
-	if(Mh_ betax_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ betax_rhs));
-	if(Mh_ betay_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ betay_rhs));  
-	if(Mh_ betaz_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ betaz_rhs));
-	if(Mh_ dtSfx_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ dtSfx_rhs));
-	if(Mh_ dtSfy_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ dtSfy_rhs));
-	if(Mh_ dtSfz_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ dtSfz_rhs));
-	if(Mh_ rho) CUDA_SAFE_CALL(cudaFree(Mh_ rho));
-	if(Mh_ Sx) CUDA_SAFE_CALL(cudaFree(Mh_ Sx));
-	if(Mh_ Sy) CUDA_SAFE_CALL(cudaFree(Mh_ Sy));
-	if(Mh_ Sz) CUDA_SAFE_CALL(cudaFree(Mh_ Sz));
-	if(Mh_ Sxx) CUDA_SAFE_CALL(cudaFree(Mh_ Sxx));
-	if(Mh_ Sxy) CUDA_SAFE_CALL(cudaFree(Mh_ Sxy));
-	if(Mh_ Sxz) CUDA_SAFE_CALL(cudaFree(Mh_ Sxz));
-	if(Mh_ Syz) CUDA_SAFE_CALL(cudaFree(Mh_ Syz));
-	if(Mh_ Syy) CUDA_SAFE_CALL(cudaFree(Mh_ Syy));
-	if(Mh_ Szz) CUDA_SAFE_CALL(cudaFree(Mh_ Szz));
-	if(Mh_ Gamxxx) CUDA_SAFE_CALL(cudaFree(Mh_ Gamxxx));
-	if(Mh_ Gamxxy) CUDA_SAFE_CALL(cudaFree(Mh_ Gamxxy));
-	if(Mh_ Gamxxz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamxxz));
-	if(Mh_ Gamxyy) CUDA_SAFE_CALL(cudaFree(Mh_ Gamxyy));
-	if(Mh_ Gamxyz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamxyz));
-	if(Mh_ Gamxzz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamxzz));
-	if(Mh_ Gamyxx) CUDA_SAFE_CALL(cudaFree(Mh_ Gamyxx));
-	if(Mh_ Gamyxy) CUDA_SAFE_CALL(cudaFree(Mh_ Gamyxy));
-	if(Mh_ Gamyxz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamyxz));
-	if(Mh_ Gamyyy) CUDA_SAFE_CALL(cudaFree(Mh_ Gamyyy));
-	if(Mh_ Gamyyz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamyyz));
-	if(Mh_ Gamyzz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamyzz));
-	if(Mh_ Gamzxx) CUDA_SAFE_CALL(cudaFree(Mh_ Gamzxx));
-	if(Mh_ Gamzxy) CUDA_SAFE_CALL(cudaFree(Mh_ Gamzxy));
-	if(Mh_ Gamzxz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamzxz));
-	if(Mh_ Gamzyz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamzyz));
-	if(Mh_ Gamzyy) CUDA_SAFE_CALL(cudaFree(Mh_ Gamzyy));
-	if(Mh_ Gamzzz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamzzz));
-	if(Mh_ Rxx) CUDA_SAFE_CALL(cudaFree(Mh_ Rxx));
-	if(Mh_ Rxy) CUDA_SAFE_CALL(cudaFree(Mh_ Rxy));
-	if(Mh_ Rxz) CUDA_SAFE_CALL(cudaFree(Mh_ Rxz));
-	if(Mh_ Ryy) CUDA_SAFE_CALL(cudaFree(Mh_ Ryy));
-	if(Mh_ Ryz) CUDA_SAFE_CALL(cudaFree(Mh_ Ryz));
-	if(Mh_ Rzz) CUDA_SAFE_CALL(cudaFree(Mh_ Rzz));
-	if(Mh_ ham_Res) CUDA_SAFE_CALL(cudaFree(Mh_ ham_Res));
-	if(Mh_ movx_Res) CUDA_SAFE_CALL(cudaFree(Mh_ movx_Res));
-	if(Mh_ movy_Res) CUDA_SAFE_CALL(cudaFree(Mh_ movy_Res));
-	if(Mh_ movz_Res) CUDA_SAFE_CALL(cudaFree(Mh_ movz_Res));
-	if(Mh_ Gmx_Res) CUDA_SAFE_CALL(cudaFree(Mh_ Gmx_Res));
-	if(Mh_ Gmy_Res) CUDA_SAFE_CALL(cudaFree(Mh_ Gmy_Res));
-	if(Mh_ Gmz_Res) CUDA_SAFE_CALL(cudaFree(Mh_ Gmz_Res));
-	if(Mh_ gxx) CUDA_SAFE_CALL(cudaFree(Mh_ gxx));
-	if(Mh_ gyy) CUDA_SAFE_CALL(cudaFree(Mh_ gyy));
-	if(Mh_ gzz) CUDA_SAFE_CALL(cudaFree(Mh_ gzz));
-	if(Mh_ chix) CUDA_SAFE_CALL(cudaFree(Mh_ chix));
-	if(Mh_ chiy) CUDA_SAFE_CALL(cudaFree(Mh_ chiy));
-	if(Mh_ chiz) CUDA_SAFE_CALL(cudaFree(Mh_ chiz));
-	if(Mh_ gxxx) CUDA_SAFE_CALL(cudaFree(Mh_ gxxx));
-	if(Mh_ gxyx) CUDA_SAFE_CALL(cudaFree(Mh_ gxyx));
-	if(Mh_ gxzx) CUDA_SAFE_CALL(cudaFree(Mh_ gxzx));
-	if(Mh_ gyyx) CUDA_SAFE_CALL(cudaFree(Mh_ gyyx));
-	if(Mh_ gyzx) CUDA_SAFE_CALL(cudaFree(Mh_ gyzx));
-	if(Mh_ gzzx) CUDA_SAFE_CALL(cudaFree(Mh_ gzzx));
-	if(Mh_ gxxy) CUDA_SAFE_CALL(cudaFree(Mh_ gxxy));
-	if(Mh_ gxyy) CUDA_SAFE_CALL(cudaFree(Mh_ gxyy));
-	if(Mh_ gxzy) CUDA_SAFE_CALL(cudaFree(Mh_ gxzy));
-	if(Mh_ gyyy) CUDA_SAFE_CALL(cudaFree(Mh_ gyyy));
-	if(Mh_ gyzy) CUDA_SAFE_CALL(cudaFree(Mh_ gyzy));
-	if(Mh_ gzzy) CUDA_SAFE_CALL(cudaFree(Mh_ gzzy));
-	if(Mh_ gxxz) CUDA_SAFE_CALL(cudaFree(Mh_ gxxz));
-	if(Mh_ gxyz) CUDA_SAFE_CALL(cudaFree(Mh_ gxyz));
-	if(Mh_ gxzz) CUDA_SAFE_CALL(cudaFree(Mh_ gxzz));
-	if(Mh_ gyyz) CUDA_SAFE_CALL(cudaFree(Mh_ gyyz));
-	if(Mh_ gyzz) CUDA_SAFE_CALL(cudaFree(Mh_ gyzz));
-	if(Mh_ gzzz) CUDA_SAFE_CALL(cudaFree(Mh_ gzzz));
-	if(Mh_ Lapx) CUDA_SAFE_CALL(cudaFree(Mh_ Lapx));
-	if(Mh_ Lapy) CUDA_SAFE_CALL(cudaFree(Mh_ Lapy));
-	if(Mh_ Lapz) CUDA_SAFE_CALL(cudaFree(Mh_ Lapz));
-	if(Mh_ betaxx) CUDA_SAFE_CALL(cudaFree(Mh_ betaxx));
-	if(Mh_ betaxy) CUDA_SAFE_CALL(cudaFree(Mh_ betaxy));
-	if(Mh_ betaxz) CUDA_SAFE_CALL(cudaFree(Mh_ betaxz));
-	if(Mh_ betayy) CUDA_SAFE_CALL(cudaFree(Mh_ betayy));
-	if(Mh_ betayz) CUDA_SAFE_CALL(cudaFree(Mh_ betayz));
-	if(Mh_ betazz) CUDA_SAFE_CALL(cudaFree(Mh_ betazz));
-	if(Mh_ betayx) CUDA_SAFE_CALL(cudaFree(Mh_ betayx));
-	if(Mh_ betazy) CUDA_SAFE_CALL(cudaFree(Mh_ betazy));
-	if(Mh_ betazx) CUDA_SAFE_CALL(cudaFree(Mh_ betazx));
-	if(Mh_ Kx) CUDA_SAFE_CALL(cudaFree(Mh_ Kx));
-	if(Mh_ Ky) CUDA_SAFE_CALL(cudaFree(Mh_ Ky));
-	if(Mh_ Kz) CUDA_SAFE_CALL(cudaFree(Mh_ Kz));
-	if(Mh_ Gamxx) CUDA_SAFE_CALL(cudaFree(Mh_ Gamxx));
-	if(Mh_ Gamxy) CUDA_SAFE_CALL(cudaFree(Mh_ Gamxy));
-	if(Mh_ Gamxz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamxz));
-	if(Mh_ Gamyy) CUDA_SAFE_CALL(cudaFree(Mh_ Gamyy));
-	if(Mh_ Gamyz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamyz));
-	if(Mh_ Gamzz) CUDA_SAFE_CALL(cudaFree(Mh_ Gamzz));
-	if(Mh_ Gamyx) CUDA_SAFE_CALL(cudaFree(Mh_ Gamyx));
-	if(Mh_ Gamzy) CUDA_SAFE_CALL(cudaFree(Mh_ Gamzy));
-	if(Mh_ Gamzx) CUDA_SAFE_CALL(cudaFree(Mh_ Gamzx));
-	if(Mh_ div_beta) CUDA_SAFE_CALL(cudaFree(Mh_ div_beta));
-	if(Mh_ S) CUDA_SAFE_CALL(cudaFree(Mh_ S));
-	if(Mh_ f) CUDA_SAFE_CALL(cudaFree(Mh_ f));
-	if(Mh_ fxx) CUDA_SAFE_CALL(cudaFree(Mh_ fxx));
-	if(Mh_ fxy) CUDA_SAFE_CALL(cudaFree(Mh_ fxy));
-	if(Mh_ fxz) CUDA_SAFE_CALL(cudaFree(Mh_ fxz));
-	if(Mh_ fyy) CUDA_SAFE_CALL(cudaFree(Mh_ fyy));
-	if(Mh_ fyz) CUDA_SAFE_CALL(cudaFree(Mh_ fyz));
-	if(Mh_ fzz) CUDA_SAFE_CALL(cudaFree(Mh_ fzz));
-	if(Mh_ gupxx) CUDA_SAFE_CALL(cudaFree(Mh_ gupxx));
-	if(Mh_ gupxy) CUDA_SAFE_CALL(cudaFree(Mh_ gupxy));
-	if(Mh_ gupxz) CUDA_SAFE_CALL(cudaFree(Mh_ gupxz));
-	if(Mh_ gupyy) CUDA_SAFE_CALL(cudaFree(Mh_ gupyy));
-	if(Mh_ gupyz) CUDA_SAFE_CALL(cudaFree(Mh_ gupyz));
-	if(Mh_ gupzz) CUDA_SAFE_CALL(cudaFree(Mh_ gupzz));
-	if(Mh_ Gamxa) CUDA_SAFE_CALL(cudaFree(Mh_ Gamxa));
-	if(Mh_ Gamya) CUDA_SAFE_CALL(cudaFree(Mh_ Gamya));
-	if(Mh_ Gamza) CUDA_SAFE_CALL(cudaFree(Mh_ Gamza));
-	if(Mh_ alpn1) CUDA_SAFE_CALL(cudaFree(Mh_ alpn1));
-	if(Mh_ chin1) CUDA_SAFE_CALL(cudaFree(Mh_ chin1));
-	if(Mh_ fh) CUDA_SAFE_CALL(cudaFree(Mh_ fh));
-	if(Mh_ fh2) CUDA_SAFE_CALL(cudaFree(Mh_ fh2));
-	if(Mh_ gxx_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ gxx_rhs));
-	if(Mh_ gyy_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ gyy_rhs));
-	if(Mh_ gzz_rhs) CUDA_SAFE_CALL(cudaFree(Mh_ gzz_rhs));
-	*/
-	
-	if(Mh_ X) cudaFree(Mh_ X);
-	if(Mh_ Y) cudaFree(Mh_ Y);
-	if(Mh_ Z) cudaFree(Mh_ Z);
-	if(Mh_ chi) cudaFree(Mh_ chi);
-	if(Mh_ dxx) cudaFree(Mh_ dxx);
-	if(Mh_ dyy) cudaFree(Mh_ dyy);
-	if(Mh_ dzz) cudaFree(Mh_ dzz);
-	if(Mh_ trK) cudaFree(Mh_ trK);
-	if(Mh_ gxy) cudaFree(Mh_ gxy);
-	if(Mh_ gxz) cudaFree(Mh_ gxz);
-	if(Mh_ gyz) cudaFree(Mh_ gyz);
-	if(Mh_ Axx) cudaFree(Mh_ Axx);
-	if(Mh_ Axy) cudaFree(Mh_ Axy);
-	if(Mh_ Axz) cudaFree(Mh_ Axz);
-	if(Mh_ Ayz) cudaFree(Mh_ Ayz);
-	if(Mh_ Ayy) cudaFree(Mh_ Ayy);
-	if(Mh_ Azz) cudaFree(Mh_ Azz);
-	if(Mh_ Gamx) cudaFree(Mh_ Gamx);
-	if(Mh_ Gamy) cudaFree(Mh_ Gamy);
-	if(Mh_ Gamz) cudaFree(Mh_ Gamz);
-	if(Mh_ Lap) cudaFree(Mh_ Lap);
-	if(Mh_ betax) cudaFree(Mh_ betax);
-	if(Mh_ betay) cudaFree(Mh_ betay);
-	if(Mh_ betaz) cudaFree(Mh_ betaz);
-	if(Mh_ dtSfx) cudaFree(Mh_ dtSfx);
-	if(Mh_ dtSfy) cudaFree(Mh_ dtSfy);
-	if(Mh_ dtSfz) cudaFree(Mh_ dtSfz);
-	if(Mh_ chi_rhs) cudaFree(Mh_ chi_rhs);
-	if(Mh_ trK_rhs) cudaFree(Mh_ trK_rhs);
-	if(Mh_ gxy_rhs) cudaFree(Mh_ gxy_rhs);
-	if(Mh_ gxz_rhs) cudaFree(Mh_ gxz_rhs);
-	if(Mh_ gyz_rhs) cudaFree(Mh_ gyz_rhs);
-	if(Mh_ Axx_rhs) cudaFree(Mh_ Axx_rhs);
-	if(Mh_ Axy_rhs) cudaFree(Mh_ Axy_rhs);
-	if(Mh_ Axz_rhs) cudaFree(Mh_ Axz_rhs);
-	if(Mh_ Ayz_rhs) cudaFree(Mh_ Ayz_rhs);
-	if(Mh_ Ayy_rhs) cudaFree(Mh_ Ayy_rhs);
-	if(Mh_ Azz_rhs) cudaFree(Mh_ Azz_rhs);
-	if(Mh_ Gamx_rhs) cudaFree(Mh_ Gamx_rhs);
-	if(Mh_ Gamy_rhs) cudaFree(Mh_ Gamy_rhs);
-	if(Mh_ Gamz_rhs) cudaFree(Mh_ Gamz_rhs);
-	if(Mh_ Lap_rhs) cudaFree(Mh_ Lap_rhs);
-	if(Mh_ betax_rhs) cudaFree(Mh_ betax_rhs);
-	if(Mh_ betay_rhs) cudaFree(Mh_ betay_rhs);  
-	if(Mh_ betaz_rhs) cudaFree(Mh_ betaz_rhs);
-	if(Mh_ dtSfx_rhs) cudaFree(Mh_ dtSfx_rhs);
-	if(Mh_ dtSfy_rhs) cudaFree(Mh_ dtSfy_rhs);
-	if(Mh_ dtSfz_rhs) cudaFree(Mh_ dtSfz_rhs);
-	if(Mh_ rho) cudaFree(Mh_ rho);
-	if(Mh_ Sx) cudaFree(Mh_ Sx);
-	if(Mh_ Sy) cudaFree(Mh_ Sy);
-	if(Mh_ Sz) cudaFree(Mh_ Sz);
-	if(Mh_ Sxx) cudaFree(Mh_ Sxx);
-	if(Mh_ Sxy) cudaFree(Mh_ Sxy);
-	if(Mh_ Sxz) cudaFree(Mh_ Sxz);
-	if(Mh_ Syz) cudaFree(Mh_ Syz);
-	if(Mh_ Syy) cudaFree(Mh_ Syy);
-	if(Mh_ Szz) cudaFree(Mh_ Szz);
-	if(Mh_ Gamxxx) cudaFree(Mh_ Gamxxx);
-	if(Mh_ Gamxxy) cudaFree(Mh_ Gamxxy);
-	if(Mh_ Gamxxz) cudaFree(Mh_ Gamxxz);
-	if(Mh_ Gamxyy) cudaFree(Mh_ Gamxyy);
-	if(Mh_ Gamxyz) cudaFree(Mh_ Gamxyz);
-	if(Mh_ Gamxzz) cudaFree(Mh_ Gamxzz);
-	if(Mh_ Gamyxx) cudaFree(Mh_ Gamyxx);
-	if(Mh_ Gamyxy) cudaFree(Mh_ Gamyxy);
-	if(Mh_ Gamyxz) cudaFree(Mh_ Gamyxz);
-	if(Mh_ Gamyyy) cudaFree(Mh_ Gamyyy);
-	if(Mh_ Gamyyz) cudaFree(Mh_ Gamyyz);
-	if(Mh_ Gamyzz) cudaFree(Mh_ Gamyzz);
-	if(Mh_ Gamzxx) cudaFree(Mh_ Gamzxx);
-	if(Mh_ Gamzxy) cudaFree(Mh_ Gamzxy);
-	if(Mh_ Gamzxz) cudaFree(Mh_ Gamzxz);
-	if(Mh_ Gamzyz) cudaFree(Mh_ Gamzyz);
-	if(Mh_ Gamzyy) cudaFree(Mh_ Gamzyy);
-	if(Mh_ Gamzzz) cudaFree(Mh_ Gamzzz);
-	if(Mh_ Rxx) cudaFree(Mh_ Rxx);
-	if(Mh_ Rxy) cudaFree(Mh_ Rxy);
-	if(Mh_ Rxz) cudaFree(Mh_ Rxz);
-	if(Mh_ Ryy) cudaFree(Mh_ Ryy);
-	if(Mh_ Ryz) cudaFree(Mh_ Ryz);
-	if(Mh_ Rzz) cudaFree(Mh_ Rzz);
-	if(Mh_ ham_Res) cudaFree(Mh_ ham_Res);
-	if(Mh_ movx_Res) cudaFree(Mh_ movx_Res);
-	if(Mh_ movy_Res) cudaFree(Mh_ movy_Res);
-	if(Mh_ movz_Res) cudaFree(Mh_ movz_Res);
-	if(Mh_ Gmx_Res) cudaFree(Mh_ Gmx_Res);
-	if(Mh_ Gmy_Res) cudaFree(Mh_ Gmy_Res);
-	if(Mh_ Gmz_Res) cudaFree(Mh_ Gmz_Res);
-	if(Mh_ gxx) cudaFree(Mh_ gxx);
-	if(Mh_ gyy) cudaFree(Mh_ gyy);
-	if(Mh_ gzz) cudaFree(Mh_ gzz);
-	if(Mh_ chix) cudaFree(Mh_ chix);
-	if(Mh_ chiy) cudaFree(Mh_ chiy);
-	if(Mh_ chiz) cudaFree(Mh_ chiz);
-	if(Mh_ gxxx) cudaFree(Mh_ gxxx);
-	if(Mh_ gxyx) cudaFree(Mh_ gxyx);
-	if(Mh_ gxzx) cudaFree(Mh_ gxzx);
-	if(Mh_ gyyx) cudaFree(Mh_ gyyx);
-	if(Mh_ gyzx) cudaFree(Mh_ gyzx);
-	if(Mh_ gzzx) cudaFree(Mh_ gzzx);
-	if(Mh_ gxxy) cudaFree(Mh_ gxxy);
-	if(Mh_ gxyy) cudaFree(Mh_ gxyy);
-	if(Mh_ gxzy) cudaFree(Mh_ gxzy);
-	if(Mh_ gyyy) cudaFree(Mh_ gyyy);
-	if(Mh_ gyzy) cudaFree(Mh_ gyzy);
-	if(Mh_ gzzy) cudaFree(Mh_ gzzy);
-	if(Mh_ gxxz) cudaFree(Mh_ gxxz);
-	if(Mh_ gxyz) cudaFree(Mh_ gxyz);
-	if(Mh_ gxzz) cudaFree(Mh_ gxzz);
-	if(Mh_ gyyz) cudaFree(Mh_ gyyz);
-	if(Mh_ gyzz) cudaFree(Mh_ gyzz);
-	if(Mh_ gzzz) cudaFree(Mh_ gzzz);
-	if(Mh_ Lapx) cudaFree(Mh_ Lapx);
-	if(Mh_ Lapy) cudaFree(Mh_ Lapy);
-	if(Mh_ Lapz) cudaFree(Mh_ Lapz);
-	if(Mh_ betaxx) cudaFree(Mh_ betaxx);
-	if(Mh_ betaxy) cudaFree(Mh_ betaxy);
-	if(Mh_ betaxz) cudaFree(Mh_ betaxz);
-	if(Mh_ betayy) cudaFree(Mh_ betayy);
-	if(Mh_ betayz) cudaFree(Mh_ betayz);
-	if(Mh_ betazz) cudaFree(Mh_ betazz);
-	if(Mh_ betayx) cudaFree(Mh_ betayx);
-	if(Mh_ betazy) cudaFree(Mh_ betazy);
-	if(Mh_ betazx) cudaFree(Mh_ betazx);
-	if(Mh_ Kx) cudaFree(Mh_ Kx);
-	if(Mh_ Ky) cudaFree(Mh_ Ky);
-	if(Mh_ Kz) cudaFree(Mh_ Kz);
-	if(Mh_ Gamxx) cudaFree(Mh_ Gamxx);
-	if(Mh_ Gamxy) cudaFree(Mh_ Gamxy);
-	if(Mh_ Gamxz) cudaFree(Mh_ Gamxz);
-	if(Mh_ Gamyy) cudaFree(Mh_ Gamyy);
-	if(Mh_ Gamyz) cudaFree(Mh_ Gamyz);
-	if(Mh_ Gamzz) cudaFree(Mh_ Gamzz);
-	if(Mh_ Gamyx) cudaFree(Mh_ Gamyx);
-	if(Mh_ Gamzy) cudaFree(Mh_ Gamzy);
-	if(Mh_ Gamzx) cudaFree(Mh_ Gamzx);
-	if(Mh_ div_beta) cudaFree(Mh_ div_beta);
-	if(Mh_ S) cudaFree(Mh_ S);
-	if(Mh_ f) cudaFree(Mh_ f);
-	if(Mh_ fxx) cudaFree(Mh_ fxx);
-	if(Mh_ fxy) cudaFree(Mh_ fxy);
-	if(Mh_ fxz) cudaFree(Mh_ fxz);
-	if(Mh_ fyy) cudaFree(Mh_ fyy);
-	if(Mh_ fyz) cudaFree(Mh_ fyz);
-	if(Mh_ fzz) cudaFree(Mh_ fzz);
-	if(Mh_ gupxx) cudaFree(Mh_ gupxx);
-	if(Mh_ gupxy) cudaFree(Mh_ gupxy);
-	if(Mh_ gupxz) cudaFree(Mh_ gupxz);
-	if(Mh_ gupyy) cudaFree(Mh_ gupyy);
-	if(Mh_ gupyz) cudaFree(Mh_ gupyz);
-	if(Mh_ gupzz) cudaFree(Mh_ gupzz);
-	if(Mh_ Gamxa) cudaFree(Mh_ Gamxa);
-	if(Mh_ Gamya) cudaFree(Mh_ Gamya);
-	if(Mh_ Gamza) cudaFree(Mh_ Gamza);
-	if(Mh_ alpn1) cudaFree(Mh_ alpn1);
-	if(Mh_ chin1) cudaFree(Mh_ chin1);
-	if(Mh_ fh) cudaFree(Mh_ fh);
-	if(Mh_ fh2) cudaFree(Mh_ fh2);
-	if(Mh_ gxx_rhs) cudaFree(Mh_ gxx_rhs);
-	if(Mh_ gyy_rhs) cudaFree(Mh_ gyy_rhs);
-	if(Mh_ gzz_rhs) cudaFree(Mh_ gzz_rhs);
-	
-#if (GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
-	// if(Mh_ reta) CUDA_SAFE_CALL(cudaFree(Mh_ reta));
-	if(Mh_ reta) cudaFree(Mh_ reta);
-
-#endif
-	
-	//if(Mh_ other_int) cudaFree(Mh_ other_int);
-	//if(Mh_ other_double) cudaFree(Mh_ other_double);
-	//cout<<"Address of meta:"<<&meta<<endl;
-	
-	/*if(meta){
-		cout<<"Free gpu meta."<<endl;
-		free(meta);
-	}*/
-}
-
-/*void fetch_data(Meta *meta, int matrix_size)
-{
-	
-
-}*/
-
-int gpu_rhs(int calledby, int mpi_rank, int *ex, double &T,double *X, double *Y, double *Z,                                     
-               double *chi, double *  trK ,                                             
-               double *dxx , double *  gxy    ,double *gxz ,double * dyy,double *gyz,double *dzz,     
-               double *Axx ,   double *Axy ,  double * Axz ,  double * Ayy ,  double * Ayz , double * Azz,     
-               double *Gamx ,  double *Gamy ,  double *Gamz ,                                  
-               double *Lap ,  double *betax ,  double *betay ,  double *betaz ,                       
-               double *dtSfx,  double *dtSfy ,  double *dtSfz ,                                  
-               double *chi_rhs, double *  trK_rhs,                                             
-               double *gxx_rhs,  double * gxy_rhs,  double * gxz_rhs,  double * gyy_rhs,   double *gyz_rhs,  double * gzz_rhs, 
-               double *Axx_rhs, double *  Axy_rhs,  double * Axz_rhs,  double * Ayy_rhs,   double *Ayz_rhs,   double *Azz_rhs, 
-           	   double *Gamx_rhs, double * Gamy_rhs, double * Gamz_rhs,                                 
-               double *Lap_rhs,  double *betax_rhs, double * betay_rhs, double * betaz_rhs,                    
-               double *dtSfx_rhs, double * dtSfy_rhs, double * dtSfz_rhs,                              
-               double *rho,double *Sx,double *Sy,double *Sz,double *Sxx,
-               double *Sxy,double *Sxz,double *Syy,double *Syz,double *Szz,                           
-               double *Gamxxx,double *Gamxxy,double *Gamxxz,double *Gamxyy,double *Gamxyz,double *Gamxzz,                      
-               double *Gamyxx,double *Gamyxy,double *Gamyxz,double *Gamyyy,double *Gamyyz,double *Gamyzz,                      
-               double *Gamzxx,double *Gamzxy,double *Gamzxz,double *Gamzyy,double *Gamzyz,double *Gamzzz,                      
-               double *Rxx,double *Rxy,double *Rxz,double *Ryy,double *Ryz,double *Rzz,                                        
-               double *ham_Res, double *movx_Res, double *movy_Res,double * movz_Res, 
-               double * Gmx_Res, double *Gmy_Res,double * Gmz_Res ,
-               int & Symmetry,int &Lev, double &eps, int &co)
-{
-	//#1------------init gpu meta data---------------------
-	//cout<<"init GPU meta data\n";
-
-#ifdef DEVICE_ID  
-  	// which device to use
-  	cudaSetDevice(DEVICE_ID);
-#endif
-
-#ifdef DEVICE_ID_BY_PID
-	pid_t pid = getpid();
-	cudaSetDevice(pid % 2);
-	cout<<"My pid= "<<pid<<endl;
-#endif
-
-#ifdef DEVICE_ID_BY_MPI_RANK
-	cudaSetDevice(mpi_rank % 2);
-#endif
-
-#ifdef TIMING  
-  struct timeval tvStart, tvEnd;
-  struct timeval tv1, tv2;
-  gettimeofday(&tvStart, NULL );
-  gettimeofday(&tv1, NULL );
-#endif
-
-	//int dim = 3;
-	int matrix_size = ex[0] * ex[1] * ex[2];
-	Meta met;
-	Meta * meta = &met;
-	
-	/*
-	//#1--------------------init_gpu_meta(meta,matrix_size)---------------------------
-
-	//1.1 inout
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ X), ex[0] * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Y), ex[1] * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Z), ex[2] * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ chi), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ dxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ dyy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ dzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ trK), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gyz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Axx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Axy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Axz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Ayz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Ayy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Azz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Lap), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betax), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betay), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betaz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ dtSfx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ dtSfy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ dtSfz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ chi_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ trK_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxx_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxy_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gyy_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxz_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gyz_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gzz_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Axx_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Axy_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Axz_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Ayz_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Ayy_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Azz_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamx_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamy_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamz_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Lap_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betax_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betay_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betaz_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ dtSfx_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ dtSfy_rhs), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ dtSfz_rhs), matrix_size * sizeof(double)));
-
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ rho), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Sx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Sy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Sz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Sxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Sxy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Sxz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Syz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Syy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Szz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamxxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamxxy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamxxz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamxyy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamxyz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamxzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamyxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamyxy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamyxz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamyyy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamyyz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamyzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamzxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamzxy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamzxz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamzyz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamzyy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamzzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Rxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Rxy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Rxz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Ryy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Ryz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Rzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ ham_Res), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ movx_Res), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ movy_Res), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ movz_Res), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gmx_Res), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gmy_Res), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gmz_Res), matrix_size * sizeof(double)));
-
-	//1.2 local Data
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gyy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ chix), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ chiy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ chiz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxyx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxzx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gyyx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gyzx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gzzx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxxy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxyy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxzy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gyyy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gyzy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gzzy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxxz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxyz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gxzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gyyz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gyzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gzzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Lapx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Lapy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Lapz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betaxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betaxy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betaxz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betayy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betayz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betazz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betayx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betazy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ betazx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Kx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Ky), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Kz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamxy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamxz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamyy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamyz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamyx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamzy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamzx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ div_beta), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ S), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ f), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ fxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ fxy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ fxz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ fyy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ fyz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ fzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gupxx), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gupxy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gupxz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gupyy), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gupyz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ gupzz), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamxa), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamya), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ Gamza), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ alpn1), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ chin1), matrix_size * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ fh), (ex[0]+2)*(ex[1]+2)*(ex[2]+2) * sizeof(double)));
-	CUDA_SAFE_CALL(cudaMalloc((void**)&(Mh_ fh2), (ex[0]+3)*(ex[1]+3)*(ex[2]+3) * sizeof(double)));
-	*/
-	
-	//#1--------------------init_gpu_meta(meta,matrix_size)---------------------------
-
-	//1.1 inout
-	cudaMalloc((void**)&(Mh_ X), ex[0] * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Y), ex[1] * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Z), ex[2] * sizeof(double));
-	cudaMalloc((void**)&(Mh_ chi), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ dxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ dyy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ dzz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ trK), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gyz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Axx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Axy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Axz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Ayz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Ayy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Azz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Lap), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betax), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betay), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betaz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ dtSfx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ dtSfy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ dtSfz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ chi_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ trK_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxx_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxy_rhs), matrix_size * sizeof(double));
-
-	cudaMalloc((void**)&(Mh_ gyy_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxz_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gyz_rhs), matrix_size * sizeof(double));
-
-	cudaMalloc((void**)&(Mh_ gzz_rhs), matrix_size * sizeof(double));
-
-	cudaMalloc((void**)&(Mh_ Axx_rhs), matrix_size * sizeof(double));
-
-	cudaMalloc((void**)&(Mh_ Axy_rhs), matrix_size * sizeof(double));
-
-	cudaMalloc((void**)&(Mh_ Axz_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Ayz_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Ayy_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Azz_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamx_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamy_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamz_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Lap_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betax_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betay_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betaz_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ dtSfx_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ dtSfy_rhs), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ dtSfz_rhs), matrix_size * sizeof(double));
-
-	cudaMalloc((void**)&(Mh_ rho), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Sx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Sy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Sz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Sxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Sxy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Sxz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Syz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Syy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Szz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamxxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamxxy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamxxz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamxyy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamxyz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamxzz), matrix_size * sizeof(double));
-
-	cudaMalloc((void**)&(Mh_ Gamyxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamyxy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamyxz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamyyy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamyyz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamyzz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamzxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamzxy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamzxz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamzyz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamzyy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamzzz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Rxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Rxy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Rxz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Ryy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Ryz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Rzz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ ham_Res), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ movx_Res), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ movy_Res), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ movz_Res), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gmx_Res), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gmy_Res), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gmz_Res), matrix_size * sizeof(double));
-
-
-	//1.2 local Data
-	cudaMalloc((void**)&(Mh_ gxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gyy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gzz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ chix), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ chiy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ chiz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxyx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxzx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gyyx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gyzx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gzzx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxxy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxyy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxzy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gyyy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gyzy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gzzy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxxz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxyz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gxzz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gyyz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gyzz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gzzz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Lapx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Lapy), matrix_size * sizeof(double));
-
-	cudaMalloc((void**)&(Mh_ Lapz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betaxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betaxy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betaxz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betayy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betayz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betazz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betayx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betazy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ betazx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Kx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Ky), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Kz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamxy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamxz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamyy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamyz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamzz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamyx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamzy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamzx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ div_beta), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ S), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ f), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ fxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ fxy), matrix_size * sizeof(double));
-
-	cudaMalloc((void**)&(Mh_ fxz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ fyy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ fyz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ fzz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gupxx), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gupxy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gupxz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gupyy), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gupyz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ gupzz), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamxa), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamya), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ Gamza), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ alpn1), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ chin1), matrix_size * sizeof(double));
-	cudaMalloc((void**)&(Mh_ fh), (ex[0]+2)*(ex[1]+2)*(ex[2]+2) * sizeof(double));
-	cudaMalloc((void**)&(Mh_ fh2), (ex[0]+3)*(ex[1]+3)*(ex[2]+3) * sizeof(double));
-	
-	#if (GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
-
-  		cudaMalloc((void**)&(Mh_ reta), matrix_size * sizeof(double));
-
-	#endif
-	  
-//2 ----------------Copy Data to Device------------------
-	cudaMemcpy(Mh_ X, X, ex[0] * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Y, Y, ex[1] * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Z, Z, ex[2] * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ chi, chi, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ dxx, dxx, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ dyy, dyy, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ dzz, dzz, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ trK, trK, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ gxy, gxy, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ gxz, gxz, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ gyz, gyz, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Axx, Axx, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Axy, Axy, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Axz, Axz, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Ayz, Ayz, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Ayy, Ayy, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Azz, Azz, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Gamx, Gamx, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Gamy, Gamy, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Gamz, Gamz, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ betax, betax, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ betay, betay, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ betaz, betaz, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ Lap, Lap, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ dtSfx, dtSfx, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ dtSfy, dtSfy, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemcpy(Mh_ dtSfz, dtSfz, matrix_size * sizeof(double), cudaMemcpyHostToDevice);
-	cudaMemset(Mh_ rho,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Sxx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Sxy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Sxz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Syz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Syy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Szz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Sx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Sy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Sz,0,matrix_size * sizeof(double));
-
-	//init local var
-	cudaMemset(Mh_ gxx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gyy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gzz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ chix,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ chiy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ chiz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gxxx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gxyx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gxzx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gyyx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gyzx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gzzx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gxxy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gxyy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gxzy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gyyy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gyzy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gzzy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gxxz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gxyz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gxzz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gyyz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gyzz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gzzz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Lapx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Lapy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Lapz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ betaxx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ betaxy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ betaxz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ betayy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ betayz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ betazz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ betayx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ betazy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ betazx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Kx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Ky,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Kz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamxx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamxy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamxz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamyy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamyz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamzz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamyx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamzy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamzx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ div_beta,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ S,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ f,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ fxx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ fxy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ fxz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ fyy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ fyz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ fzz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gupxx,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gupxy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gupxz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gupyy,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gupyz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ gupzz,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamxa,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamya,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ Gamza,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ alpn1,0,matrix_size * sizeof(double));
-	cudaMemset(Mh_ chin1,0,matrix_size * sizeof(double));
-	
-	
-	double sss[3] = {1,1,1};
-	double aas[3] = {-1,-1,1};
-	double asa[3] = {-1,1,-1};
-	double saa[3] = {1,-1,-1};
-	double ass[3] = {-1,1,1};
-	double sas[3] = {1,-1,1};
-	double ssa[3] = {1,1,-1};
-
-//3 --------------------Init constant memory---------------------
-#if (GAUGE == 6 || GAUGE == 7)
-	int BHN_h;
-
-	double Porg_h[9];
-
-	double Mass_h[3];
-//call getpbh(BHN,Porg,Mass)
-#ifdef fortran1
-
-	getpbh
-
-#endif	
-
-#ifdef fortran2
-
-	GETPBH
-
-#endif
-
-#ifdef fortran3
-
-	getpbh_
-
-#endif
-	(BHN_h,double Porg_h,double Mass_h);
-	
-	cudaMemcpyToSymbol(BHN,&BHN_h, sizeof(int));
-	cudaMemcpyToSymbol(Porg,&Porg_h,9 * sizeof(double));
-	cudaMemcpyToSymbol(Mass,&Mass_h,3 * sizeof(double));
-	
-	double tmp_con = Mass[0] + Mass[1]; //t = M
-	cudaMemcpyToSymbol(M, &tmp_con, sizeof(double));
-	tmp_con = 2 / tmp_con;  //t = A
-	cudaMemcpyToSymbol(A, &tmp_con, sizeof(double));
-	
-	double tmp_con2 = 1/Mass[0] - tmp_con;
-	cudaMemcpyToSymbol(C1, &tmp_con2, sizeof(double));
-	double tmp_con2 = 1/Mass[1] - tmp_con;
-	cudaMemcpyToSymbol(C2, &tmp_con2, sizeof(double));
-		
-
-#endif//if (GAUGE == 6 || GAUGE == 7)
-//3.1-----for compute_rhs_bssn---------
-	//cout<<"Size of Meta:"<<sizeof(Meta)<<endl;
-	cudaMemcpyToSymbol(metac,meta, sizeof(Meta));
-	cudaMemcpyToSymbol(ex_c,ex, 3*sizeof(int));
-	cudaMemcpyToSymbol(T_c,&T, sizeof(double));
-	cudaMemcpyToSymbol(Symmetry_c,&Symmetry, sizeof(int));
-	cudaMemcpyToSymbol(Lev_c,&Lev, sizeof(int));
-	cudaMemcpyToSymbol(co_c,&co, sizeof(int));
-	cudaMemcpyToSymbol(eps_c,&eps, sizeof(double));
-	
-	double F1o3h  = 1.0;	F1o3h /= 3.0;
-	double F2o3h  = 2.0;	F2o3h /= 3.0;
-	double F1o6h  = 1.0;	F1o6h /= 6.0;
-	double PIh = M_PI;
-	int step = GRID_DIM * BLOCK_DIM;
-	double dXh = X[1] - X[0];
-	double dYh = Y[1] - Y[0];
-	double dZh = Z[1] - Z[0];
-	
-	cudaMemcpyToSymbol(F1o3,&F1o3h, sizeof(double));
-	cudaMemcpyToSymbol(F2o3,&F2o3h, sizeof(double));
-	cudaMemcpyToSymbol(F1o6,&F1o6h, sizeof(double));
-	cudaMemcpyToSymbol(PI,&PIh, sizeof(double));
-	cudaMemcpyToSymbol(STEP_SIZE,&step, sizeof(int));
-	cudaMemcpyToSymbol(dX,&dXh, sizeof(double));
-	cudaMemcpyToSymbol(dY,&dYh, sizeof(double));
-	cudaMemcpyToSymbol(dZ,&dZh, sizeof(double));
-	
-	int _1d_size[4];
-	int _2d_size[4];
-	int _3d_size[4];
-	for(int i = 0;i<4;++i){
-		_1d_size[i] = ex[0] + i;
-		_2d_size[i] = _1d_size[i] * (ex[1]+i);
-		_3d_size[i] = _2d_size[i] * (ex[2]+i);
-		//cout<<_1d_size[i]<<' '<<_2d_size[i]<<' '<<_3d_size[i]<<endl;
-	}
-	cudaMemcpyToSymbol(_1D_SIZE,_1d_size, 4*sizeof(int));
-	cudaMemcpyToSymbol(_2D_SIZE,_2d_size, 4*sizeof(int));
-	cudaMemcpyToSymbol(_3D_SIZE,_3d_size, 4*sizeof(int));
-
-	
-//3.2--------for fderivs------------
-	int ijkmax_h[3] = {ex[0]-1,ex[1]-1,ex[2]-1};
-	int ijkmin_h[3] = {0,0,0};
-	int ijkmin2_h[3] = {0,0,0};
-	int ijkmin3_h[3] = {0,0,0};
-	
-	double abs[3] = {X[0],Y[0],Z[0]};
-	for(int i = 0;i<3;++i){
-		if(abs[i] < 0) abs[i] = -abs[i]; 
-	}
-  	if(Symmetry > 1 && abs[0] < dXh) {ijkmin_h[0] = -2; ijkmin2_h[0] = -3;}
-  	if(Symmetry > 1 && abs[1] < dYh) {ijkmin_h[1] = -2; ijkmin2_h[1] = -3;}
-  	if(Symmetry > 0 && abs[2] < dZh) {ijkmin_h[2] = -2; ijkmin2_h[2] = -3;}
-  	
-  	if(Symmetry > 2 && abs[0] < dXh) {ijkmin3_h[0] = -3;}
-  	if(Symmetry > 2 && abs[1] < dYh) {ijkmin3_h[1] = -3;}
-  	if(Symmetry > 0 && abs[2] < dZh) {ijkmin3_h[2] = -3;}
-  	
-  	cudaMemcpyToSymbol(ijk_max,ijkmax_h,3*sizeof(int));
-  	cudaMemcpyToSymbol(ijk_min,ijkmin_h,3*sizeof(int));
-  	cudaMemcpyToSymbol(ijk_min2,ijkmin2_h,3*sizeof(int));
-  	cudaMemcpyToSymbol(ijk_min3,ijkmin3_h,3*sizeof(int));
-	
-	double d12dxyz_h[3] = {1.0,1.0,1.0};
-	double d2dxyz_h[3] = {1.0,1.0,1.0};
-	d12dxyz_h[0] /= 12; d12dxyz_h[1] /= 12; d12dxyz_h[2] /= 12;
-	d12dxyz_h[0] /= dXh; d12dxyz_h[1] /= dYh; d12dxyz_h[2] /= dZh;
-	d2dxyz_h[0] /= 2; d2dxyz_h[1] /= 2; d2dxyz_h[2] /= 2;
-	d2dxyz_h[0] /= dXh; d2dxyz_h[1] /= dYh; d2dxyz_h[2] /= dZh;
-	
-	cudaMemcpyToSymbol(d12dxyz,d12dxyz_h,3*sizeof(double));
-	cudaMemcpyToSymbol(d2dxyz,d2dxyz_h,3*sizeof(double));
-	
-//3.3--------for fdderivs------------
-	double Sdxdxh =  1.0 /( dXh * dXh ); 
-	double Sdydyh =  1.0 /( dYh * dYh );
-	double Sdzdzh =  1.0 /( dZh * dZh );
-	double Fdxdxh = 1.0 / 12.0 /( dXh * dXh );
-	double Fdydyh = 1.0 / 12.0 /( dYh * dYh );
-	double Fdzdzh = 1.0 / 12.0 /( dZh * dZh );
-	double Sdxdyh = 1.0/4.0 /( dXh * dYh );
-	double Sdxdzh = 1.0/4.0 /( dXh * dZh );
-	double Sdydzh = 1.0/4.0 /( dYh * dZh );
-	double Fdxdyh = 1.0/144.0 /( dXh * dYh );
-	double Fdxdzh = 1.0/144.0 /( dXh * dZh );
-	double Fdydzh = 1.0/144.0 /( dYh * dZh );
-	cudaMemcpyToSymbol(Sdxdx,&Sdxdxh,sizeof(double));
-	cudaMemcpyToSymbol(Sdydy,&Sdydyh,sizeof(double));
-	cudaMemcpyToSymbol(Sdzdz,&Sdzdzh,sizeof(double));
-	cudaMemcpyToSymbol(Sdxdy,&Sdxdyh,sizeof(double));
-	cudaMemcpyToSymbol(Sdxdz,&Sdxdzh,sizeof(double));
-	cudaMemcpyToSymbol(Sdydz,&Sdydzh,sizeof(double));
-	cudaMemcpyToSymbol(Fdxdx,&Fdxdxh,sizeof(double));
-	cudaMemcpyToSymbol(Fdydy,&Fdydyh,sizeof(double));
-	cudaMemcpyToSymbol(Fdzdz,&Fdzdzh,sizeof(double));
-	cudaMemcpyToSymbol(Fdxdy,&Fdxdyh,sizeof(double));
-	cudaMemcpyToSymbol(Fdxdz,&Fdxdzh,sizeof(double));
-	cudaMemcpyToSymbol(Fdydz,&Fdydzh,sizeof(double));
-
-//3.4---------for lopsided---------------------------
-
-
-#ifdef TIMING1
-	cudaThreadSynchronize();
-	gettimeofday(&tv2, NULL);
-   	cout<<"TIME USED"<<TimeBetween(tv1, tv2)<<endl; 
-#endif	
-	//cout<<"GPU meta data ready.\n";
-	
-	cudaThreadSynchronize();
-
-//--------------test constant memory address & value--------------
-/*	double rank = mpi_rank;
-	cudaMemcpyToSymbol(F1o3,&rank, sizeof(double));
-	double ctest1 = -1;
-	double * ctest = &ctest1;
-	double * ctest_d;
-	cudaMalloc((void**)&ctest_d,sizeof(double));
-	test_const_address<<<1,1>>>(ctest_d);
-	cudaMemcpy(ctest, ctest_d, sizeof(double), cudaMemcpyDeviceToHost);
-	cout<<"My rank is: "<<rank<<" "<<"const value is: "<<ctest[0]<<" const Address is:"<<&F1o3<<endl;
-	cudaFree(ctest_d);
-*/
-//-------------get device info-------------------------------------
-/*	int deviceCount; cudaGetDeviceCount(&deviceCount);
-	cout<<"myrank is: "<<mpi_rank<<" deviceCount is:"<<deviceCount<<endl;
-*/
-//#4-----------------------calculate------------------------------
-	//4.0------enforce_ga---------
-	//sub_enforce_ga(matrix_size);
-	//4.1-----compute rhs---------
-	compute_rhs_bssn_part1<<<GRID_DIM,BLOCK_DIM>>>();
-	cudaThreadSynchronize();
-
-	sub_fderivs(Mh_ betax,Mh_ fh,Mh_ betaxx,Mh_ betaxy,Mh_ betaxz,ass);
-	sub_fderivs(Mh_ betay,Mh_ fh,Mh_ betayx,Mh_ betayy,Mh_ betayz,sas);
-	sub_fderivs(Mh_ betaz,Mh_ fh,Mh_ betazx,Mh_ betazy,Mh_ betazz,ssa);
-	sub_fderivs(Mh_ chi,Mh_ fh,Mh_ chix,Mh_ chiy,Mh_ chiz, sss);
-	sub_fderivs(Mh_ Lap,Mh_ fh,Mh_ Lapx,Mh_ Lapy,Mh_ Lapz, sss);
-	sub_fderivs(Mh_ trK,Mh_ fh,Mh_ Kx,Mh_ Ky,Mh_ Kz, sss);
-	sub_fderivs(Mh_ dxx,Mh_ fh,Mh_ gxxx,Mh_ gxxy,Mh_ gxxz, sss);
-	sub_fderivs(Mh_ dyy,Mh_ fh,Mh_ gyyx,Mh_ gyyy,Mh_ gyyz, sss);
-	sub_fderivs(Mh_ dzz,Mh_ fh,Mh_ gzzx,Mh_ gzzy,Mh_ gzzz, sss);
-	sub_fderivs(Mh_ gxy,Mh_ fh,Mh_ gxyx,Mh_ gxyy,Mh_ gxyz, aas);
-	sub_fderivs(Mh_ gxz,Mh_ fh,Mh_ gxzx,Mh_ gxzy,Mh_ gxzz, asa);
-	sub_fderivs(Mh_ gyz,Mh_ fh,Mh_ gyzx,Mh_ gyzy,Mh_ gyzz, saa);
-  	
-  	compute_rhs_bssn_part2<<<GRID_DIM,BLOCK_DIM>>>();
-	cudaThreadSynchronize();
-	
-	sub_fdderivs(Mh_ betax,Mh_ fh,Mh_ gxxx,Mh_ gxyx,Mh_ gxzx,Mh_ gyyx,Mh_ gyzx,Mh_ gzzx,ass);
-	sub_fdderivs(Mh_ betay,Mh_ fh,Mh_ gxxy,Mh_ gxyy,Mh_ gxzy,Mh_ gyyy,Mh_ gyzy,Mh_ gzzy,sas);
-	sub_fdderivs(Mh_ betaz,Mh_ fh,Mh_ gxxz,Mh_ gxyz,Mh_ gxzz,Mh_ gyyz,Mh_ gyzz,Mh_ gzzz,ssa);        
-	sub_fderivs( Mh_ Gamx, Mh_ fh,Mh_ Gamxx, Mh_ Gamxy, Mh_ Gamxz,ass);
-	sub_fderivs( Mh_ Gamy, Mh_ fh,Mh_ Gamyx, Mh_ Gamyy, Mh_ Gamyz,sas);
-	sub_fderivs( Mh_ Gamz, Mh_ fh,Mh_ Gamzx, Mh_ Gamzy, Mh_ Gamzz,ssa);
-	
-	compute_rhs_bssn_part3<<<GRID_DIM,BLOCK_DIM>>>();
-	cudaThreadSynchronize();
-	
-	computeRicci(Mh_ dxx,Mh_ Rxx,sss, meta);
-	computeRicci(Mh_ dyy,Mh_ Ryy,sss, meta);
-	computeRicci(Mh_ dzz,Mh_ Rzz,sss, meta);
-	computeRicci(Mh_ gxy,Mh_ Rxy,aas, meta);
-	computeRicci(Mh_ gxz,Mh_ Rxz,asa, meta);
-	computeRicci(Mh_ gyz,Mh_ Ryz,saa, meta);
-	
-	cudaThreadSynchronize();
-	
-	compute_rhs_bssn_part4<<<GRID_DIM,BLOCK_DIM>>>();
-	cudaThreadSynchronize();
-	
-	sub_fdderivs(Mh_ chi,Mh_ fh,Mh_ fxx,Mh_ fxy,Mh_ fxz,Mh_ fyy,Mh_ fyz,Mh_ fzz,sss);
-	
-	compute_rhs_bssn_part5<<<GRID_DIM,BLOCK_DIM>>>();
-	cudaThreadSynchronize();
-	
-	sub_fdderivs(Mh_ Lap,Mh_ fh,Mh_ fxx,Mh_ fxy,Mh_ fxz,Mh_ fyy,Mh_ fyz,Mh_ fzz,sss);
-	
-	compute_rhs_bssn_part6<<<GRID_DIM,BLOCK_DIM>>>();
-	cudaThreadSynchronize();
-	
-#if (GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5)
-	sub_fderivs(Mh_ chi,Mh_ fh, Mh_ dtSfx_rhs, Mh_ dtSfy_rhs, Mh_ dtSfz_rhs,sss);
-	compute_rhs_bssn_part6_gauge<<<GRID_DIM,BLOCK_DIM>>>();
-#endif	
-
-	sub_lopsided(Mh_ gxx,Mh_ fh2,Mh_ gxx_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sss);
-	sub_lopsided(Mh_ gxy,Mh_ fh2,Mh_ gxy_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,aas);
-	sub_lopsided(Mh_ gxz,Mh_ fh2,Mh_ gxz_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,asa);
-	sub_lopsided(Mh_ gyy,Mh_ fh2,Mh_ gyy_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sss);
-	sub_lopsided(Mh_ gyz,Mh_ fh2,Mh_ gyz_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,saa);
-	sub_lopsided(Mh_ gzz,Mh_ fh2,Mh_ gzz_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sss);
-	sub_lopsided(Mh_ Axx,Mh_ fh2,Mh_ Axx_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sss);
-	sub_lopsided(Mh_ Axy,Mh_ fh2,Mh_ Axy_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,aas);
-	sub_lopsided(Mh_ Axz,Mh_ fh2,Mh_ Axz_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,asa);
-	sub_lopsided(Mh_ Ayy,Mh_ fh2,Mh_ Ayy_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sss);
-	sub_lopsided(Mh_ Ayz,Mh_ fh2,Mh_ Ayz_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,saa);
-	sub_lopsided(Mh_ Azz,Mh_ fh2,Mh_ Azz_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sss);
-	sub_lopsided(Mh_ chi,Mh_ fh2,Mh_ chi_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sss);
-	sub_lopsided(Mh_ trK,Mh_ fh2,Mh_ trK_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sss);
-	sub_lopsided(Mh_ Gamx,Mh_ fh2,Mh_ Gamx_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,ass);
-	sub_lopsided(Mh_ Gamy,Mh_ fh2,Mh_ Gamy_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sas);
-	sub_lopsided(Mh_ Gamz,Mh_ fh2,Mh_ Gamz_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,ssa);
-	sub_lopsided(Mh_ Lap,Mh_ fh2,Mh_ Lap_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sss);
-	
-#if (GAUGE == 0 || GAUGE == 1 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
-
-  	sub_lopsided(Mh_ betax,Mh_ fh2,Mh_ betax_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,ass);
-	sub_lopsided(Mh_ betay,Mh_ fh2,Mh_ betay_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sas);
-	sub_lopsided(Mh_ betaz,Mh_ fh2,Mh_ betaz_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,ssa);
-
-#endif
-#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)	
-	sub_lopsided(Mh_ dtSfx,Mh_ fh2,Mh_ dtSfx_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,ass);
-	sub_lopsided(Mh_ dtSfy,Mh_ fh2,Mh_ dtSfy_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,sas);
-	sub_lopsided(Mh_ dtSfz,Mh_ fh2,Mh_ dtSfz_rhs,Mh_ betax,Mh_ betay,Mh_ betaz,ssa);
-#endif	
-	if(eps > 0){
-		sub_kodis(Mh_ chi,Mh_ fh2, Mh_ chi_rhs,sss);
-		sub_kodis(Mh_ trK,Mh_ fh2, Mh_ trK_rhs,sss);
-		sub_kodis(Mh_ dxx,Mh_ fh2, Mh_ gxx_rhs,sss);
-		sub_kodis(Mh_ gxy,Mh_ fh2, Mh_ gxy_rhs,aas);
-		sub_kodis(Mh_ gxz,Mh_ fh2, Mh_ gxz_rhs,asa);
-		sub_kodis(Mh_ dyy,Mh_ fh2, Mh_ gyy_rhs,sss);
-		sub_kodis(Mh_ gyz,Mh_ fh2, Mh_ gyz_rhs,saa);
-		sub_kodis(Mh_ dzz,Mh_ fh2, Mh_ gzz_rhs,sss);
-		sub_kodis(Mh_ Axx,Mh_ fh2, Mh_ Axx_rhs,sss);
-		sub_kodis(Mh_ Axy,Mh_ fh2, Mh_ Axy_rhs,aas);
-		sub_kodis(Mh_ Axz,Mh_ fh2, Mh_ Axz_rhs,asa);
-		sub_kodis(Mh_ Ayy,Mh_ fh2, Mh_ Ayy_rhs,sss);
-		sub_kodis(Mh_ Ayz,Mh_ fh2, Mh_ Ayz_rhs,saa);
-		sub_kodis(Mh_ Azz,Mh_ fh2, Mh_ Azz_rhs,sss);
-		sub_kodis(Mh_ Gamx,Mh_ fh2, Mh_ Gamx_rhs,ass);
-		sub_kodis(Mh_ Gamy,Mh_ fh2, Mh_ Gamy_rhs,sas);
-		sub_kodis(Mh_ Gamz,Mh_ fh2, Mh_ Gamz_rhs,ssa);
-		
-		sub_kodis(Mh_ Lap,Mh_ fh2, Mh_ Lap_rhs,sss);
-		sub_kodis(Mh_ betax,Mh_ fh2, Mh_ betax_rhs,ass);
-		sub_kodis(Mh_ betay,Mh_ fh2, Mh_ betay_rhs,sas);
-		sub_kodis(Mh_ betaz,Mh_ fh2, Mh_ betaz_rhs,ssa);
-		
-#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)		
-		sub_kodis(Mh_ dtSfx,Mh_ fh2, Mh_ dtSfx_rhs,ass);
-		sub_kodis(Mh_ dtSfy,Mh_ fh2, Mh_ dtSfy_rhs,sas);
-		sub_kodis(Mh_ dtSfz,Mh_ fh2, Mh_ dtSfz_rhs,ssa);
-#endif
-
-	}
-	
-	if(co == 0){
-		compute_rhs_bssn_part7<<<GRID_DIM,BLOCK_DIM>>>();
-		cudaThreadSynchronize();
-
-		sub_fderivs(Mh_ Axx,Mh_ fh,Mh_ gxxx,Mh_ gxxy,Mh_ gxxz,sss);
-		sub_fderivs(Mh_ Axy,Mh_ fh,Mh_ gxyx,Mh_ gxyy,Mh_ gxyz,aas);
-		sub_fderivs(Mh_ Axz,Mh_ fh,Mh_ gxzx,Mh_ gxzy,Mh_ gxzz,asa);
-		sub_fderivs(Mh_ Ayy,Mh_ fh,Mh_ gyyx,Mh_ gyyy,Mh_ gyyz,sss);
-		sub_fderivs(Mh_ Ayz,Mh_ fh,Mh_ gyzx,Mh_ gyzy,Mh_ gyzz,saa);
-		sub_fderivs(Mh_ Azz,Mh_ fh,Mh_ gzzx,Mh_ gzzy,Mh_ gzzz,sss);
-		compute_rhs_bssn_part8<<<GRID_DIM,BLOCK_DIM>>>();
-		cudaThreadSynchronize();
-	}
-
-#if (ABV == 1)
-	cout<<"TODO: bssn_gpu.cu::2373 (ABV == 1)"<<endl;
-#endif
-//5---------------------------get result----------------------------
-	/*cudaMemcpy(chi, Mh_ chi, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-	cudaMemcpy(dxx, Mh_ dxx, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-	cudaMemcpy(dyy, Mh_ dyy, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-	cudaMemcpy(dzz, Mh_ dzz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-	cudaMemcpy(Lap, Mh_ Lap, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-	cudaMemcpy(betax, Mh_ betax, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-	cudaMemcpy(betay, Mh_ betay, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-	cudaMemcpy(betaz, Mh_ betaz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);*/
-	if(calledby == CALLED_BY_STEP)
-	{	
-		cudaMemcpy(chi_rhs, Mh_ chi_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(trK_rhs, Mh_ trK_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(gxx_rhs, Mh_ gxx_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(gxy_rhs, Mh_ gxy_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(gxz_rhs, Mh_ gxz_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(gyy_rhs, Mh_ gyy_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(gyz_rhs, Mh_ gyz_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(gzz_rhs, Mh_ gzz_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Axx_rhs, Mh_ Axx_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Axy_rhs, Mh_ Axy_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Axz_rhs, Mh_ Axz_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Ayy_rhs, Mh_ Ayy_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Ayz_rhs, Mh_ Ayz_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Azz_rhs, Mh_ Azz_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamx_rhs, Mh_ Gamx_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamy_rhs, Mh_ Gamy_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamz_rhs, Mh_ Gamz_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Lap_rhs, Mh_ Lap_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(betax_rhs, Mh_ betax_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(betay_rhs, Mh_ betay_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(betaz_rhs, Mh_ betaz_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(dtSfx_rhs, Mh_ dtSfx_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(dtSfy_rhs, Mh_ dtSfy_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(dtSfz_rhs, Mh_ dtSfz_rhs, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-	}
-	else if(calledby == CALLED_BY_CONSTRAINT)
-	{
-		cudaMemcpy(Gamxxx, Mh_ Gamxxx, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamxxy, Mh_ Gamxxy, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamxxz, Mh_ Gamxxz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamxyy, Mh_ Gamxyy, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamxyz, Mh_ Gamxyz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamxzz, Mh_ Gamxzz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamyxx, Mh_ Gamyxx, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamyxy, Mh_ Gamyxy, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamyxz, Mh_ Gamyxz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamyyy, Mh_ Gamyyy, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamyyz, Mh_ Gamyyz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamyzz, Mh_ Gamyzz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamzxx, Mh_ Gamzxx, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamzxy, Mh_ Gamzxy, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamzxz, Mh_ Gamzxz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamzyy, Mh_ Gamzyy, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamzyz, Mh_ Gamzyz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gamzzz, Mh_ Gamzzz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Rxx, Mh_ Rxx, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Rxy, Mh_ Rxy, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Rxz, Mh_ Rxz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Ryy, Mh_ Ryy, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Ryz, Mh_ Ryz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Rzz, Mh_ Rzz, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(ham_Res, Mh_ ham_Res, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(movx_Res, Mh_ movx_Res, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(movy_Res, Mh_ movy_Res, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(movz_Res, Mh_ movz_Res, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gmx_Res, Mh_ Gmx_Res, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gmy_Res, Mh_ Gmy_Res, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-		cudaMemcpy(Gmz_Res, Mh_ Gmz_Res, matrix_size * sizeof(double), cudaMemcpyDeviceToHost);
-	}
-
-//-----------------------------------------------------
-//-------------------FOR GPU TEST----------------------
-//-----------------------------------------------------
-#ifdef TIMING
-	cudaThreadSynchronize();
-	gettimeofday(&tv2, NULL);
-   	cout<<"MPI rank is: "<<mpi_rank<<" GPU TIME is"<<TimeBetween(tv1, tv2)<<" (s)."<<endl; 
-#endif
-
-
-	destroy_meta(meta);
-
-	
-	return 0;//TODO return
-}
diff --git a/AMSS_NCKU_source/bssn_gpu.h b/AMSS_NCKU_source/bssn_gpu.h
deleted file mode 100644
index 37d91d1..0000000
--- a/AMSS_NCKU_source/bssn_gpu.h
+++ /dev/null
@@ -1,73 +0,0 @@
-
-#ifndef BSSN_GPU_H_
-#define BSSN_GPU_H_
-#include "bssn_macro.h"
-#include "macrodef.fh"
-
-#define DEVICE_ID 0
-// #define DEVICE_ID_BY_MPI_RANK
-#define GRID_DIM 256
-#define BLOCK_DIM 128
-
-#define _FH2_(i, j, k) fh[(i) + (j) * _1D_SIZE[2] + (k) * _2D_SIZE[2]]
-#define _FH3_(i, j, k) fh[(i) + (j) * _1D_SIZE[3] + (k) * _2D_SIZE[3]]
-#define pow2(x) ((x) * (x))
-#define TimeBetween(a, b) ((b.tv_sec - a.tv_sec) + (b.tv_usec - a.tv_usec) / 1000000.0f)
-#define M_ metac.
-#define Mh_ meta->
-#define Ms_ metassc.
-#define Msh_ metass->
-
-// #define TIMING
-
-#define RHS_SS_PARA int calledby, int mpi_rank, int *ex, double &T, double *crho, double *sigma, double *R, double *X, double *Y, double *Z, double *drhodx, double *drhody, double *drhodz, double *dsigmadx, double *dsigmady, double *dsigmadz, double *dRdx, double *dRdy, double *dRdz, double *drhodxx, double *drhodxy, double *drhodxz, double *drhodyy, double *drhodyz, double *drhodzz, double *dsigmadxx, double *dsigmadxy, double *dsigmadxz, double *dsigmadyy, double *dsigmadyz, double *dsigmadzz, double *dRdxx, double *dRdxy, double *dRdxz, double *dRdyy, double *dRdyz, double *dRdzz, double *chi, double *trK, double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz, double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz, double *Gamx, double *Gamy, double *Gamz, double *Lap, double *betax, double *betay, double *betaz, double *dtSfx, double *dtSfy, double *dtSfz, double *chi_rhs, double *trK_rhs, double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs, double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs, double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs, double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs, double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs, double *rho, double *Sx, double *Sy, double *Sz, double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz, double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz, double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz, double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz, double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz, double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res, double *Gmx_Res, double *Gmy_Res, double *Gmz_Res, int &Symmetry, int &Lev, double &eps, int &sst, int &co
-
-/**  main function */
-int gpu_rhs(int calledby, int mpi_rank, int *ex, double &T,
-            double *X, double *Y, double *Z,
-
-            double *chi, double *trK,
-
-            double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
-
-            double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
-
-            double *Gamx, double *Gamy, double *Gamz,
-
-            double *Lap, double *betax, double *betay, double *betaz,
-
-            double *dtSfx, double *dtSfy, double *dtSfz,
-
-            double *chi_rhs, double *trK_rhs,
-
-            double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
-
-            double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
-
-            double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
-
-            double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
-
-            double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
-
-            double *rho, double *Sx, double *Sy, double *Sz, double *Sxx,
-            double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
-
-            double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
-
-            double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
-
-            double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
-
-            double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
-
-            double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
-            double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
-            int &Symmetry, int &Lev, double &eps, int &co);
-
-int gpu_rhs_ss(RHS_SS_PARA);
-
-/** Init GPU side data in GPUMeta. */
-// void init_fluid_meta_gpu(GPUMeta *gpu_meta);
-
-#endif
diff --git a/AMSS_NCKU_source/bssn_gpu_class.C b/AMSS_NCKU_source/bssn_gpu_class.C
deleted file mode 100644
index f6d5170..0000000
--- a/AMSS_NCKU_source/bssn_gpu_class.C
+++ /dev/null
@@ -1,7790 +0,0 @@
-
-#ifdef newc
-#include <sstream>
-#include <cstdio>
-using namespace std;
-#else
-#include <stdio.h>
-#endif
-
-#include "macrodef.h"
-#include "misc.h"
-#include <time.h>
-#include "Ansorg.h"
-#include "fmisc.h"
-#include "Parallel.h"
-#include "bssn_gpu_class.h"
-#include "bssn_rhs.h"
-#include "initial_puncture.h"
-#include "enforce_algebra.h"
-#include "rungekutta4_rout.h"
-#include "sommerfeld_rout.h"
-#include "getnp4.h"
-#include "shellfunctions.h"
-
-#ifdef With_AHF
-#include "derivatives.h"
-#include "myglobal.h"
-#endif
-
-#include "perf.h"
-#include "derivatives.h"
-#include "ricci_gamma.h"
-
-// include GPU files
-#include "bssn_gpu.h"
-
-//================================================================================================
-
-// Define bssn_gpu_class
-
-//================================================================================================
-
-bssn_class::bssn_class(double Couranti, double StartTimei, double TotalTimei, 
-                       double DumpTimei, double d2DumpTimei, double CheckTimei, double AnasTimei,
-                       int Symmetryi, int checkruni, char *checkfilenamei, 
-                       double numepssi, double numepsbi, double numepshi,
-                       int a_levi, int maxli, int decni, double maxrexi, double drexi) 
-                       : Courant(Couranti), StartTime(StartTimei), TotalTime(TotalTimei), 
-                         DumpTime(DumpTimei), d2DumpTime(d2DumpTimei), CheckTime(CheckTimei), AnasTime(AnasTimei),
-                         Symmetry(Symmetryi), checkrun(checkruni), numepss(numepssi), numepsb(numepsbi), numepsh(numepshi),
-#ifdef With_AHF
-                         xc(0), yc(0), zc(0), xr(0), yr(0), zr(0), trigger(0), dTT(0), dumpid(0),
-#endif
-                         a_lev(a_levi), maxl(maxli), decn(decni), maxrex(maxrexi), drex(drexi),
-                         CheckPoint(0)
-{
-  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-
-  // setup Monitors
-  {
-    stringstream a_stream;
-    a_stream.setf(ios::left);
-    a_stream << "# Error log information";
-    ErrorMonitor = new monitor("Error.log", myrank, a_stream.str());
-    ErrorMonitor->print_message("Warning: we always assume intput parameter in cell center style.");
-
-    a_stream.clear();
-    a_stream.str("");
-    a_stream << setw(15) << "# time";
-    char str[50];
-    for (int pl = 2; pl < maxl + 1; pl++)
-      for (int pm = -pl; pm < pl + 1; pm++)
-      {
-        sprintf(str, "R%02dm%03d", pl, pm);
-        a_stream << setw(16) << str;
-        sprintf(str, "I%02dm%03d", pl, pm);
-        a_stream << setw(16) << str;
-      }
-    Psi4Monitor = new monitor("bssn_psi4.dat", myrank, a_stream.str());
-
-    a_stream.clear();
-    a_stream.str("");
-    a_stream << setw(15) << "# time";
-    BHMonitor = new monitor("bssn_BH.dat", myrank, a_stream.str());
-
-    a_stream.clear();
-    a_stream.str("");
-    a_stream << setw(15) << "# time ADMmass ADMPx ADMPy ADMPz ADMSx ADMSy ADMSz";
-    MAPMonitor = new monitor("bssn_ADMQs.dat", myrank, a_stream.str());
-
-    a_stream.clear();
-    a_stream.str("");
-    a_stream << setw(15) << "# time Ham Px Py Pz Gx Gy Gz";
-    ConVMonitor = new monitor("bssn_constraint.dat", myrank, a_stream.str());
-  }
-  // setup sphere integration engine
-  Waveshell = new surface_integral(Symmetry);
-
-  trfls = 0;
-  chitiny = 0;
-  // read parameter from file
-  {
-    char filename[50];
-    strcpy(filename, "input.par");
-    const int LEN = 256;
-    char pline[LEN];
-    string str, sgrp, skey, sval;
-    int sind;
-    ifstream inf(filename, ifstream::in);
-    if (!inf.good() && myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "Can not open parameter file " << filename 
-                              << " for inputing information of black holes" << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-
-    for (int i = 1; inf.good(); i++)
-    {
-      inf.getline(pline, LEN);
-      str = pline;
-
-      int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-      if (status == -1)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "error reading parameter file " << filename 
-                                << " in line " << i << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-      else if (status == 0)
-        continue;
-
-      if (sgrp == "BSSN" && skey == "chitiny")
-        chitiny = atof(sval.c_str());
-      else if (sgrp == "BSSN" && skey == "time refinement start from level")
-        trfls = atoi(sval.c_str());
-#ifdef With_AHF
-      else if (sgrp == "AHF" && skey == "AHfindevery")
-        AHfindevery = atoi(sval.c_str());
-      else if (sgrp == "AHF" && skey == "AHdumptime")
-        AHdumptime = atof(sval.c_str());
-#endif
-    }
-    inf.close();
-  }
-  if (myrank == 0)
-  {
-    // echo information of lower bound of chi
-    cout << "chitiny = " << chitiny << endl;
-    cout << "time refinement start from level #" << trfls << endl;
-#ifdef With_AHF
-    cout << "parameters for AHF:" << endl;
-    cout << "AHfindevery = " << AHfindevery << endl;
-    cout << "AHdumptime = " << AHdumptime << endl;
-#endif
-  }
-
-  chitiny = chitiny - 1; // because we have subtracted one from chi
-
-  strcpy(checkfilename, checkfilenamei);
-
-  ngfs = 0;
-  phio = new var("phio", ngfs++, 1, 1, 1);
-  trKo = new var("trKo", ngfs++, 1, 1, 1);
-  gxxo = new var("gxxo", ngfs++, 1, 1, 1);
-  gxyo = new var("gxyo", ngfs++, -1, -1, 1);
-  gxzo = new var("gxzo", ngfs++, -1, 1, -1);
-  gyyo = new var("gyyo", ngfs++, 1, 1, 1);
-  gyzo = new var("gyzo", ngfs++, 1, -1, -1);
-  gzzo = new var("gzzo", ngfs++, 1, 1, 1);
-  Axxo = new var("Axxo", ngfs++, 1, 1, 1);
-  Axyo = new var("Axyo", ngfs++, -1, -1, 1);
-  Axzo = new var("Axzo", ngfs++, -1, 1, -1);
-  Ayyo = new var("Ayyo", ngfs++, 1, 1, 1);
-  Ayzo = new var("Ayzo", ngfs++, 1, -1, -1);
-  Azzo = new var("Azzo", ngfs++, 1, 1, 1);
-  Gmxo = new var("Gmxo", ngfs++, -1, 1, 1);
-  Gmyo = new var("Gmyo", ngfs++, 1, -1, 1);
-  Gmzo = new var("Gmzo", ngfs++, 1, 1, -1);
-  Lapo = new var("Lapo", ngfs++, 1, 1, 1);
-  Sfxo = new var("Sfxo", ngfs++, -1, 1, 1);
-  Sfyo = new var("Sfyo", ngfs++, 1, -1, 1);
-  Sfzo = new var("Sfzo", ngfs++, 1, 1, -1);
-  dtSfxo = new var("dtSfxo", ngfs++, -1, 1, 1);
-  dtSfyo = new var("dtSfyo", ngfs++, 1, -1, 1);
-  dtSfzo = new var("dtSfzo", ngfs++, 1, 1, -1);
-
-  phi0 = new var("phi0", ngfs++, 1, 1, 1);
-  trK0 = new var("trK0", ngfs++, 1, 1, 1);
-  gxx0 = new var("gxx0", ngfs++, 1, 1, 1);
-  gxy0 = new var("gxy0", ngfs++, -1, -1, 1);
-  gxz0 = new var("gxz0", ngfs++, -1, 1, -1);
-  gyy0 = new var("gyy0", ngfs++, 1, 1, 1);
-  gyz0 = new var("gyz0", ngfs++, 1, -1, -1);
-  gzz0 = new var("gzz0", ngfs++, 1, 1, 1);
-  Axx0 = new var("Axx0", ngfs++, 1, 1, 1);
-  Axy0 = new var("Axy0", ngfs++, -1, -1, 1);
-  Axz0 = new var("Axz0", ngfs++, -1, 1, -1);
-  Ayy0 = new var("Ayy0", ngfs++, 1, 1, 1);
-  Ayz0 = new var("Ayz0", ngfs++, 1, -1, -1);
-  Azz0 = new var("Azz0", ngfs++, 1, 1, 1);
-  Gmx0 = new var("Gmx0", ngfs++, -1, 1, 1);
-  Gmy0 = new var("Gmy0", ngfs++, 1, -1, 1);
-  Gmz0 = new var("Gmz0", ngfs++, 1, 1, -1);
-  Lap0 = new var("Lap0", ngfs++, 1, 1, 1);
-  Sfx0 = new var("Sfx0", ngfs++, -1, 1, 1);
-  Sfy0 = new var("Sfy0", ngfs++, 1, -1, 1);
-  Sfz0 = new var("Sfz0", ngfs++, 1, 1, -1);
-  dtSfx0 = new var("dtSfx0", ngfs++, -1, 1, 1);
-  dtSfy0 = new var("dtSfy0", ngfs++, 1, -1, 1);
-  dtSfz0 = new var("dtSfz0", ngfs++, 1, 1, -1);
-
-  phi = new var("phi", ngfs++, 1, 1, 1);
-  trK = new var("trK", ngfs++, 1, 1, 1);
-  gxx = new var("gxx", ngfs++, 1, 1, 1);
-  gxy = new var("gxy", ngfs++, -1, -1, 1);
-  gxz = new var("gxz", ngfs++, -1, 1, -1);
-  gyy = new var("gyy", ngfs++, 1, 1, 1);
-  gyz = new var("gyz", ngfs++, 1, -1, -1);
-  gzz = new var("gzz", ngfs++, 1, 1, 1);
-  Axx = new var("Axx", ngfs++, 1, 1, 1);
-  Axy = new var("Axy", ngfs++, -1, -1, 1);
-  Axz = new var("Axz", ngfs++, -1, 1, -1);
-  Ayy = new var("Ayy", ngfs++, 1, 1, 1);
-  Ayz = new var("Ayz", ngfs++, 1, -1, -1);
-  Azz = new var("Azz", ngfs++, 1, 1, 1);
-  Gmx = new var("Gmx", ngfs++, -1, 1, 1);
-  Gmy = new var("Gmy", ngfs++, 1, -1, 1);
-  Gmz = new var("Gmz", ngfs++, 1, 1, -1);
-  Lap = new var("Lap", ngfs++, 1, 1, 1);
-  Sfx = new var("Sfx", ngfs++, -1, 1, 1);
-  Sfy = new var("Sfy", ngfs++, 1, -1, 1);
-  Sfz = new var("Sfz", ngfs++, 1, 1, -1);
-  dtSfx = new var("dtSfx", ngfs++, -1, 1, 1);
-  dtSfy = new var("dtSfy", ngfs++, 1, -1, 1);
-  dtSfz = new var("dtSfz", ngfs++, 1, 1, -1);
-
-  phi1 = new var("phi1", ngfs++, 1, 1, 1);
-  trK1 = new var("trK1", ngfs++, 1, 1, 1);
-  gxx1 = new var("gxx1", ngfs++, 1, 1, 1);
-  gxy1 = new var("gxy1", ngfs++, -1, -1, 1);
-  gxz1 = new var("gxz1", ngfs++, -1, 1, -1);
-  gyy1 = new var("gyy1", ngfs++, 1, 1, 1);
-  gyz1 = new var("gyz1", ngfs++, 1, -1, -1);
-  gzz1 = new var("gzz1", ngfs++, 1, 1, 1);
-  Axx1 = new var("Axx1", ngfs++, 1, 1, 1);
-  Axy1 = new var("Axy1", ngfs++, -1, -1, 1);
-  Axz1 = new var("Axz1", ngfs++, -1, 1, -1);
-  Ayy1 = new var("Ayy1", ngfs++, 1, 1, 1);
-  Ayz1 = new var("Ayz1", ngfs++, 1, -1, -1);
-  Azz1 = new var("Azz1", ngfs++, 1, 1, 1);
-  Gmx1 = new var("Gmx1", ngfs++, -1, 1, 1);
-  Gmy1 = new var("Gmy1", ngfs++, 1, -1, 1);
-  Gmz1 = new var("Gmz1", ngfs++, 1, 1, -1);
-  Lap1 = new var("Lap1", ngfs++, 1, 1, 1);
-  Sfx1 = new var("Sfx1", ngfs++, -1, 1, 1);
-  Sfy1 = new var("Sfy1", ngfs++, 1, -1, 1);
-  Sfz1 = new var("Sfz1", ngfs++, 1, 1, -1);
-  dtSfx1 = new var("dtSfx1", ngfs++, -1, 1, 1);
-  dtSfy1 = new var("dtSfy1", ngfs++, 1, -1, 1);
-  dtSfz1 = new var("dtSfz1", ngfs++, 1, 1, -1);
-
-  phi_rhs = new var("phi_rhs", ngfs++, 1, 1, 1);
-  trK_rhs = new var("trK_rhs", ngfs++, 1, 1, 1);
-  gxx_rhs = new var("gxx_rhs", ngfs++, 1, 1, 1);
-  gxy_rhs = new var("gxy_rhs", ngfs++, -1, -1, 1);
-  gxz_rhs = new var("gxz_rhs", ngfs++, -1, 1, -1);
-  gyy_rhs = new var("gyy_rhs", ngfs++, 1, 1, 1);
-  gyz_rhs = new var("gyz_rhs", ngfs++, 1, -1, -1);
-  gzz_rhs = new var("gzz_rhs", ngfs++, 1, 1, 1);
-  Axx_rhs = new var("Axx_rhs", ngfs++, 1, 1, 1);
-  Axy_rhs = new var("Axy_rhs", ngfs++, -1, -1, 1);
-  Axz_rhs = new var("Axz_rhs", ngfs++, -1, 1, -1);
-  Ayy_rhs = new var("Ayy_rhs", ngfs++, 1, 1, 1);
-  Ayz_rhs = new var("Ayz_rhs", ngfs++, 1, -1, -1);
-  Azz_rhs = new var("Azz_rhs", ngfs++, 1, 1, 1);
-  Gmx_rhs = new var("Gmx_rhs", ngfs++, -1, 1, 1);
-  Gmy_rhs = new var("Gmy_rhs", ngfs++, 1, -1, 1);
-  Gmz_rhs = new var("Gmz_rhs", ngfs++, 1, 1, -1);
-  Lap_rhs = new var("Lap_rhs", ngfs++, 1, 1, 1);
-  Sfx_rhs = new var("Sfx_rhs", ngfs++, -1, 1, 1);
-  Sfy_rhs = new var("Sfy_rhs", ngfs++, 1, -1, 1);
-  Sfz_rhs = new var("Sfz_rhs", ngfs++, 1, 1, -1);
-  dtSfx_rhs = new var("dtSfx_rhs", ngfs++, -1, 1, 1);
-  dtSfy_rhs = new var("dtSfy_rhs", ngfs++, 1, -1, 1);
-  dtSfz_rhs = new var("dtSfz_rhs", ngfs++, 1, 1, -1);
-
-  rho = new var("rho", ngfs++, 1, 1, 1);
-  Sx = new var("Sx", ngfs++, -1, 1, 1);
-  Sy = new var("Sy", ngfs++, 1, -1, 1);
-  Sz = new var("Sz", ngfs++, 1, 1, -1);
-  Sxx = new var("Sxx", ngfs++, 1, 1, 1);
-  Sxy = new var("Sxy", ngfs++, -1, -1, 1);
-  Sxz = new var("Sxz", ngfs++, -1, 1, -1);
-  Syy = new var("Syy", ngfs++, 1, 1, 1);
-  Syz = new var("Syz", ngfs++, 1, -1, -1);
-  Szz = new var("Szz", ngfs++, 1, 1, 1);
-
-  Gamxxx = new var("Gamxxx", ngfs++, -1, 1, 1);
-  Gamxxy = new var("Gamxxy", ngfs++, 1, -1, 1);
-  Gamxxz = new var("Gamxxz", ngfs++, 1, 1, -1);
-  Gamxyy = new var("Gamxyy", ngfs++, -1, 1, 1);
-  Gamxyz = new var("Gamxyz", ngfs++, -1, -1, -1);
-  Gamxzz = new var("Gamxzz", ngfs++, -1, 1, 1);
-  Gamyxx = new var("Gamyxx", ngfs++, 1, -1, 1);
-  Gamyxy = new var("Gamyxy", ngfs++, -1, 1, 1);
-  Gamyxz = new var("Gamyxz", ngfs++, -1, -1, -1);
-  Gamyyy = new var("Gamyyy", ngfs++, 1, -1, 1);
-  Gamyyz = new var("Gamyyz", ngfs++, 1, 1, -1);
-  Gamyzz = new var("Gamyzz", ngfs++, 1, -1, 1);
-  Gamzxx = new var("Gamzxx", ngfs++, 1, 1, -1);
-  Gamzxy = new var("Gamzxy", ngfs++, -1, -1, -1);
-  Gamzxz = new var("Gamzxz", ngfs++, -1, 1, 1);
-  Gamzyy = new var("Gamzyy", ngfs++, 1, 1, -1);
-  Gamzyz = new var("Gamzyz", ngfs++, 1, -1, 1);
-  Gamzzz = new var("Gamzzz", ngfs++, 1, 1, -1);
-
-  Rxx = new var("Rxx", ngfs++, 1, 1, 1);
-  Rxy = new var("Rxy", ngfs++, -1, -1, 1);
-  Rxz = new var("Rxz", ngfs++, -1, 1, -1);
-  Ryy = new var("Ryy", ngfs++, 1, 1, 1);
-  Ryz = new var("Ryz", ngfs++, 1, -1, -1);
-  Rzz = new var("Rzz", ngfs++, 1, 1, 1);
-
-  // refer to PRD, 77, 024027 (2008)
-  Rpsi4 = new var("Rpsi4", ngfs++, 1, 1, 1);
-  Ipsi4 = new var("Ipsi4", ngfs++, -1, -1, -1);
-  t1Rpsi4 = new var("t1Rpsi4", ngfs++, 1, 1, 1);
-  t1Ipsi4 = new var("t1Ipsi4", ngfs++, -1, -1, -1);
-  t2Rpsi4 = new var("t2Rpsi4", ngfs++, 1, 1, 1);
-  t2Ipsi4 = new var("t2Ipsi4", ngfs++, -1, -1, -1);
-
-  // constraint violation monitor variables
-  Cons_Ham = new var("Cons_Ham", ngfs++, 1, 1, 1);
-  Cons_Px = new var("Cons_Px", ngfs++, -1, 1, 1);
-  Cons_Py = new var("Cons_Py", ngfs++, 1, -1, 1);
-  Cons_Pz = new var("Cons_Pz", ngfs++, 1, 1, -1);
-  Cons_Gx = new var("Cons_Gx", ngfs++, -1, 1, 1);
-  Cons_Gy = new var("Cons_Gy", ngfs++, 1, -1, 1);
-  Cons_Gz = new var("Cons_Gz", ngfs++, 1, 1, -1);
-
-#ifdef Point_Psi4
-  phix = new var("phix", ngfs++, -1, 1, 1);
-  phiy = new var("phiy", ngfs++, 1, -1, 1);
-  phiz = new var("phiz", ngfs++, 1, 1, -1);
-  trKx = new var("trKx", ngfs++, -1, 1, 1);
-  trKy = new var("trKy", ngfs++, 1, -1, 1);
-  trKz = new var("trKz", ngfs++, 1, 1, -1);
-  Axxx = new var("Axxx", ngfs++, -1, 1, 1);
-  Axxy = new var("Axxy", ngfs++, 1, -1, 1);
-  Axxz = new var("Axxz", ngfs++, 1, 1, -1);
-  Axyx = new var("Axyx", ngfs++, 1, -1, 1);
-  Axyy = new var("Axyy", ngfs++, -1, 1, 1);
-  Axyz = new var("Axyz", ngfs++, -1, -1, -1);
-  Axzx = new var("Axzx", ngfs++, 1, 1, -1);
-  Axzy = new var("Axzy", ngfs++, -1, -1, -1);
-  Axzz = new var("Axzz", ngfs++, -1, 1, 1);
-  Ayyx = new var("Ayyx", ngfs++, -1, 1, 1);
-  Ayyy = new var("Ayyy", ngfs++, 1, -1, 1);
-  Ayyz = new var("Ayyz", ngfs++, 1, 1, -1);
-  Ayzx = new var("Ayzx", ngfs++, -1, -1, -1);
-  Ayzy = new var("Ayzy", ngfs++, 1, 1, -1);
-  Ayzz = new var("Ayzz", ngfs++, 1, -1, 1);
-  Azzx = new var("Azzx", ngfs++, -1, 1, 1);
-  Azzy = new var("Azzy", ngfs++, 1, -1, 1);
-  Azzz = new var("Azzz", ngfs++, 1, 1, -1);
-#endif
-
-  // specific properspeed for 1+log slice
-  {
-    const double vl = sqrt(2);
-    trKo->setpropspeed(vl);
-    trK0->setpropspeed(vl);
-    trK->setpropspeed(vl);
-    trK1->setpropspeed(vl);
-    trK_rhs->setpropspeed(vl);
-
-    phio->setpropspeed(vl);
-    phi0->setpropspeed(vl);
-    phi->setpropspeed(vl);
-    phi1->setpropspeed(vl);
-    phi_rhs->setpropspeed(vl);
-
-    Lapo->setpropspeed(vl);
-    Lap0->setpropspeed(vl);
-    Lap->setpropspeed(vl);
-    Lap1->setpropspeed(vl);
-    Lap_rhs->setpropspeed(vl);
-  }
-
-  OldStateList = new MyList<var>(phio);
-  OldStateList->insert(trKo);
-  OldStateList->insert(gxxo);
-  OldStateList->insert(gxyo);
-  OldStateList->insert(gxzo);
-  OldStateList->insert(gyyo);
-  OldStateList->insert(gyzo);
-  OldStateList->insert(gzzo);
-  OldStateList->insert(Axxo);
-  OldStateList->insert(Axyo);
-  OldStateList->insert(Axzo);
-  OldStateList->insert(Ayyo);
-  OldStateList->insert(Ayzo);
-  OldStateList->insert(Azzo);
-  OldStateList->insert(Gmxo);
-  OldStateList->insert(Gmyo);
-  OldStateList->insert(Gmzo);
-  OldStateList->insert(Lapo);
-  OldStateList->insert(Sfxo);
-  OldStateList->insert(Sfyo);
-  OldStateList->insert(Sfzo);
-  OldStateList->insert(dtSfxo);
-  OldStateList->insert(dtSfyo);
-  OldStateList->insert(dtSfzo);
-
-  StateList = new MyList<var>(phi0);
-  StateList->insert(trK0);
-  StateList->insert(gxx0);
-  StateList->insert(gxy0);
-  StateList->insert(gxz0);
-  StateList->insert(gyy0);
-  StateList->insert(gyz0);
-  StateList->insert(gzz0);
-  StateList->insert(Axx0);
-  StateList->insert(Axy0);
-  StateList->insert(Axz0);
-  StateList->insert(Ayy0);
-  StateList->insert(Ayz0);
-  StateList->insert(Azz0);
-  StateList->insert(Gmx0);
-  StateList->insert(Gmy0);
-  StateList->insert(Gmz0);
-  StateList->insert(Lap0);
-  StateList->insert(Sfx0);
-  StateList->insert(Sfy0);
-  StateList->insert(Sfz0);
-  StateList->insert(dtSfx0);
-  StateList->insert(dtSfy0);
-  StateList->insert(dtSfz0);
-
-  RHSList = new MyList<var>(phi_rhs);
-  RHSList->insert(trK_rhs);
-  RHSList->insert(gxx_rhs);
-  RHSList->insert(gxy_rhs);
-  RHSList->insert(gxz_rhs);
-  RHSList->insert(gyy_rhs);
-  RHSList->insert(gyz_rhs);
-  RHSList->insert(gzz_rhs);
-  RHSList->insert(Axx_rhs);
-  RHSList->insert(Axy_rhs);
-  RHSList->insert(Axz_rhs);
-  RHSList->insert(Ayy_rhs);
-  RHSList->insert(Ayz_rhs);
-  RHSList->insert(Azz_rhs);
-  RHSList->insert(Gmx_rhs);
-  RHSList->insert(Gmy_rhs);
-  RHSList->insert(Gmz_rhs);
-  RHSList->insert(Lap_rhs);
-  RHSList->insert(Sfx_rhs);
-  RHSList->insert(Sfy_rhs);
-  RHSList->insert(Sfz_rhs);
-  RHSList->insert(dtSfx_rhs);
-  RHSList->insert(dtSfy_rhs);
-  RHSList->insert(dtSfz_rhs);
-
-  SynchList_pre = new MyList<var>(phi);
-  SynchList_pre->insert(trK);
-  SynchList_pre->insert(gxx);
-  SynchList_pre->insert(gxy);
-  SynchList_pre->insert(gxz);
-  SynchList_pre->insert(gyy);
-  SynchList_pre->insert(gyz);
-  SynchList_pre->insert(gzz);
-  SynchList_pre->insert(Axx);
-  SynchList_pre->insert(Axy);
-  SynchList_pre->insert(Axz);
-  SynchList_pre->insert(Ayy);
-  SynchList_pre->insert(Ayz);
-  SynchList_pre->insert(Azz);
-  SynchList_pre->insert(Gmx);
-  SynchList_pre->insert(Gmy);
-  SynchList_pre->insert(Gmz);
-  SynchList_pre->insert(Lap);
-  SynchList_pre->insert(Sfx);
-  SynchList_pre->insert(Sfy);
-  SynchList_pre->insert(Sfz);
-  SynchList_pre->insert(dtSfx);
-  SynchList_pre->insert(dtSfy);
-  SynchList_pre->insert(dtSfz);
-
-  SynchList_cor = new MyList<var>(phi1);
-  SynchList_cor->insert(trK1);
-  SynchList_cor->insert(gxx1);
-  SynchList_cor->insert(gxy1);
-  SynchList_cor->insert(gxz1);
-  SynchList_cor->insert(gyy1);
-  SynchList_cor->insert(gyz1);
-  SynchList_cor->insert(gzz1);
-  SynchList_cor->insert(Axx1);
-  SynchList_cor->insert(Axy1);
-  SynchList_cor->insert(Axz1);
-  SynchList_cor->insert(Ayy1);
-  SynchList_cor->insert(Ayz1);
-  SynchList_cor->insert(Azz1);
-  SynchList_cor->insert(Gmx1);
-  SynchList_cor->insert(Gmy1);
-  SynchList_cor->insert(Gmz1);
-  SynchList_cor->insert(Lap1);
-  SynchList_cor->insert(Sfx1);
-  SynchList_cor->insert(Sfy1);
-  SynchList_cor->insert(Sfz1);
-  SynchList_cor->insert(dtSfx1);
-  SynchList_cor->insert(dtSfy1);
-  SynchList_cor->insert(dtSfz1);
-
-  DumpList = new MyList<var>(phi0);
-  DumpList->insert(trK0);
-  DumpList->insert(gxx0);
-  DumpList->insert(gxy0);
-  DumpList->insert(gxz0);
-  DumpList->insert(gyy0);
-  DumpList->insert(gyz0);
-  DumpList->insert(gzz0);
-  // DumpList->insert(Axx0);
-  // DumpList->insert(Axy0);
-  // DumpList->insert(Axz0);
-  // DumpList->insert(Ayy0);
-  // DumpList->insert(Ayz0);
-  // DumpList->insert(Azz0);
-  // DumpList->insert(Gmx0);
-  // DumpList->insert(Gmy0);
-  // DumpList->insert(Gmz0);
-  DumpList->insert(Lap0);
-  // DumpList->insert(Sfx0);
-  // DumpList->insert(Sfy0);
-  // DumpList->insert(Sfz0);
-  // DumpList->insert(dtSfx0);
-  // DumpList->insert(dtSfy0);
-  // DumpList->insert(dtSfz0);
-  DumpList->insert(Rpsi4);
-  DumpList->insert(Ipsi4);
-  DumpList->insert(Cons_Ham);
-  DumpList->insert(Cons_Px);
-  DumpList->insert(Cons_Py);
-  DumpList->insert(Cons_Pz);
-  // DumpList->insert(Cons_Gx);
-  // DumpList->insert(Cons_Gy);
-  // DumpList->insert(Cons_Gz);
-
-  ConstraintList = new MyList<var>(Cons_Ham);
-  ConstraintList->insert(Cons_Px);
-  ConstraintList->insert(Cons_Py);
-  ConstraintList->insert(Cons_Pz);
-  ConstraintList->insert(Cons_Gx);
-  ConstraintList->insert(Cons_Gy);
-  ConstraintList->insert(Cons_Gz);
-#ifdef With_AHF
-  // setup kinds of var list
-  // List for AparentHorizonFinderDirect
-  // special attension is payed to symmetry type
-  // gij   gij,x   gij,y   gij,z
-  AHList = new MyList<var>(gxx0);
-  AHList->insert(Gamxxx);
-  AHList->insert(Gamyxx);
-  AHList->insert(Gamzxx);
-  AHList->insert(gxy0);
-  AHList->insert(Gamxxy);
-  AHList->insert(Gamyxy);
-  AHList->insert(Gamzxy);
-  AHList->insert(gxz0);
-  AHList->insert(Gamxxz);
-  AHList->insert(Gamyxz);
-  AHList->insert(Gamzxz);
-  AHList->insert(gyy0);
-  AHList->insert(Gamxyy);
-  AHList->insert(Gamyyy);
-  AHList->insert(Gamzyy);
-  AHList->insert(gyz0);
-  AHList->insert(Gamxyz);
-  AHList->insert(Gamyyz);
-  AHList->insert(Gamzyz);
-  AHList->insert(gzz0);
-  AHList->insert(Gamxzz);
-  AHList->insert(Gamyzz);
-  AHList->insert(Gamzzz);
-  // phi  phi,x  phi,y  phi,z
-  AHList->insert(phi0);
-  AHList->insert(dtSfx_rhs);
-  AHList->insert(dtSfy_rhs);
-  AHList->insert(dtSfz_rhs);
-  // Aij
-  AHList->insert(Axx0);
-  AHList->insert(Axy0);
-  AHList->insert(Axz0);
-  AHList->insert(Ayy0);
-  AHList->insert(Ayz0);
-  AHList->insert(Azz0);
-  // trK
-  AHList->insert(trK0);
-  // gij,x  gij,y  gij,z
-  AHDList = new MyList<var>(Gamxxx);
-  AHDList->insert(Gamyxx);
-  AHDList->insert(Gamzxx);
-  AHDList->insert(Gamxxy);
-  AHDList->insert(Gamyxy);
-  AHDList->insert(Gamzxy);
-  AHDList->insert(Gamxxz);
-  AHDList->insert(Gamyxz);
-  AHDList->insert(Gamzxz);
-  AHDList->insert(Gamxyy);
-  AHDList->insert(Gamyyy);
-  AHDList->insert(Gamzyy);
-  AHDList->insert(Gamxyz);
-  AHDList->insert(Gamyyz);
-  AHDList->insert(Gamzyz);
-  AHDList->insert(Gamxzz);
-  AHDList->insert(Gamyzz);
-  AHDList->insert(Gamzzz);
-  // phi,x  phi,y  phi,z
-  AHDList->insert(dtSfx_rhs);
-  AHDList->insert(dtSfy_rhs);
-  AHDList->insert(dtSfz_rhs);
-
-  GaugeList = new MyList<var>(Lap0);
-  GaugeList->insert(Sfx0);
-  GaugeList->insert(Sfy0);
-  GaugeList->insert(Sfz0);
-#endif
-
-  CheckPoint = new checkpoint(checkrun, checkfilename, myrank);
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function initializes the class
-
-//================================================================================================
-
-void bssn_class::Initialize()
-{
-  if (myrank == 0)
-    cout << "you have setted " << ngfs << " grid functions." << endl;
-
-  CheckPoint->addvariablelist(StateList);
-  CheckPoint->addvariablelist(OldStateList);
-
-  GH = new cgh(0, ngfs, Symmetry, "input.par", checkrun, ErrorMonitor);
-  if (checkrun)
-    CheckPoint->readcheck_cgh(PhysTime, GH, myrank, nprocs, Symmetry);
-  else
-    GH->compose_cgh(nprocs);
-
-#ifdef WithShell
-  SH = new ShellPatch(0, ngfs, "input.par", Symmetry, myrank, ErrorMonitor);
-  SH->matchcheck(GH->PatL[0]);
-  SH->compose_sh(nprocs);
-  //   SH->compose_shr(nprocs);  //sh is faster than shr
-  SH->setupcordtrans();
-  SH->Dump_xyz(0, 0, 1);
-  SH->setupintintstuff(nprocs, GH->PatL[0], Symmetry);
-
-  if (checkrun)
-    CheckPoint->readcheck_sh(SH, myrank);
-#else
-  SH = 0;
-#endif
-
-  double h = GH->PatL[0]->data->blb->data->getdX(0);
-  for (int i = 1; i < dim; i++)
-    h = Mymin(h, GH->PatL[0]->data->blb->data->getdX(i));
-  dT = Courant * h;
-
-  if (checkrun)
-  {
-    CheckPoint->read_Black_Hole_position(BH_num_input, BH_num, Porg0, Pmom, Spin, Mass, Porgbr, Porg, Porg1, Porg_rhs);
-  }
-  else
-  {
-    PhysTime = StartTime;
-    Setup_Black_Hole_position();
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// Destructor: free allocated variables
-
-//================================================================================================
-
-bssn_class::~bssn_class()
-{
-#ifdef With_AHF
-  AHList->clearList();
-  AHDList->clearList();
-  GaugeList->clearList();
-  if (lastahdumpid)
-    delete[] lastahdumpid;
-  if (findeveryl)
-    delete[] findeveryl;
-
-  if (xc)
-  {
-    delete[] xc;
-    delete[] yc;
-    delete[] zc;
-    delete[] xr;
-    delete[] yr;
-    delete[] zr;
-    delete[] trigger;
-    delete[] dumpid;
-    delete[] dTT;
-  }
-
-  AHFinderDirect::AHFinderDirect_cleanup();
-#endif
-
-  StateList->clearList();
-  RHSList->clearList();
-  OldStateList->clearList();
-  SynchList_pre->clearList();
-  SynchList_cor->clearList();
-  DumpList->clearList();
-  ConstraintList->clearList();
-
-  delete phio;
-  delete trKo;
-  delete gxxo;
-  delete gxyo;
-  delete gxzo;
-  delete gyyo;
-  delete gyzo;
-  delete gzzo;
-  delete Axxo;
-  delete Axyo;
-  delete Axzo;
-  delete Ayyo;
-  delete Ayzo;
-  delete Azzo;
-  delete Gmxo;
-  delete Gmyo;
-  delete Gmzo;
-  delete Lapo;
-  delete Sfxo;
-  delete Sfyo;
-  delete Sfzo;
-  delete dtSfxo;
-  delete dtSfyo;
-  delete dtSfzo;
-
-  delete phi0;
-  delete trK0;
-  delete gxx0;
-  delete gxy0;
-  delete gxz0;
-  delete gyy0;
-  delete gyz0;
-  delete gzz0;
-  delete Axx0;
-  delete Axy0;
-  delete Axz0;
-  delete Ayy0;
-  delete Ayz0;
-  delete Azz0;
-  delete Gmx0;
-  delete Gmy0;
-  delete Gmz0;
-  delete Lap0;
-  delete Sfx0;
-  delete Sfy0;
-  delete Sfz0;
-  delete dtSfx0;
-  delete dtSfy0;
-  delete dtSfz0;
-
-  delete phi;
-  delete trK;
-  delete gxx;
-  delete gxy;
-  delete gxz;
-  delete gyy;
-  delete gyz;
-  delete gzz;
-  delete Axx;
-  delete Axy;
-  delete Axz;
-  delete Ayy;
-  delete Ayz;
-  delete Azz;
-  delete Gmx;
-  delete Gmy;
-  delete Gmz;
-  delete Lap;
-  delete Sfx;
-  delete Sfy;
-  delete Sfz;
-  delete dtSfx;
-  delete dtSfy;
-  delete dtSfz;
-
-  delete phi1;
-  delete trK1;
-  delete gxx1;
-  delete gxy1;
-  delete gxz1;
-  delete gyy1;
-  delete gyz1;
-  delete gzz1;
-  delete Axx1;
-  delete Axy1;
-  delete Axz1;
-  delete Ayy1;
-  delete Ayz1;
-  delete Azz1;
-  delete Gmx1;
-  delete Gmy1;
-  delete Gmz1;
-  delete Lap1;
-  delete Sfx1;
-  delete Sfy1;
-  delete Sfz1;
-  delete dtSfx1;
-  delete dtSfy1;
-  delete dtSfz1;
-
-  delete phi_rhs;
-  delete trK_rhs;
-  delete gxx_rhs;
-  delete gxy_rhs;
-  delete gxz_rhs;
-  delete gyy_rhs;
-  delete gyz_rhs;
-  delete gzz_rhs;
-  delete Axx_rhs;
-  delete Axy_rhs;
-  delete Axz_rhs;
-  delete Ayy_rhs;
-  delete Ayz_rhs;
-  delete Azz_rhs;
-  delete Gmx_rhs;
-  delete Gmy_rhs;
-  delete Gmz_rhs;
-  delete Lap_rhs;
-  delete Sfx_rhs;
-  delete Sfy_rhs;
-  delete Sfz_rhs;
-  delete dtSfx_rhs;
-  delete dtSfy_rhs;
-  delete dtSfz_rhs;
-
-  delete rho;
-  delete Sx;
-  delete Sy;
-  delete Sz;
-  delete Sxx;
-  delete Sxy;
-  delete Sxz;
-  delete Syy;
-  delete Syz;
-  delete Szz;
-
-  delete Gamxxx;
-  delete Gamxxy;
-  delete Gamxxz;
-  delete Gamxyy;
-  delete Gamxyz;
-  delete Gamxzz;
-  delete Gamyxx;
-  delete Gamyxy;
-  delete Gamyxz;
-  delete Gamyyy;
-  delete Gamyyz;
-  delete Gamyzz;
-  delete Gamzxx;
-  delete Gamzxy;
-  delete Gamzxz;
-  delete Gamzyy;
-  delete Gamzyz;
-  delete Gamzzz;
-
-  delete Rxx;
-  delete Rxy;
-  delete Rxz;
-  delete Ryy;
-  delete Ryz;
-  delete Rzz;
-
-  delete Rpsi4;
-  delete Ipsi4;
-  delete t1Rpsi4;
-  delete t1Ipsi4;
-  delete t2Rpsi4;
-  delete t2Ipsi4;
-
-  delete Cons_Ham;
-  delete Cons_Px;
-  delete Cons_Py;
-  delete Cons_Pz;
-  delete Cons_Gx;
-  delete Cons_Gy;
-  delete Cons_Gz;
-
-#ifdef Point_Psi4
-  delete phix;
-  delete phiy;
-  delete phiz;
-  delete trKx;
-  delete trKy;
-  delete trKz;
-  delete Axxx;
-  delete Axxy;
-  delete Axxz;
-  delete Axyx;
-  delete Axyy;
-  delete Axyz;
-  delete Axzx;
-  delete Axzy;
-  delete Axzz;
-  delete Ayyx;
-  delete Ayyy;
-  delete Ayyz;
-  delete Ayzx;
-  delete Ayzy;
-  delete Ayzz;
-  delete Azzx;
-  delete Azzy;
-  delete Azzz;
-#endif
-
-  delete GH;
-#ifdef WithShell
-  delete SH;
-#endif
-
-  for (int i = 0; i < BH_num; i++)
-  {
-    delete[] Porg0[i];
-    delete[] Porgbr[i];
-    delete[] Porg[i];
-    delete[] Porg1[i];
-    delete[] Porg_rhs[i];
-  }
-
-  delete[] Porg0;
-  delete[] Porgbr;
-  delete[] Porg;
-  delete[] Porg1;
-  delete[] Porg_rhs;
-
-  delete[] Mass;
-  delete[] Spin;
-  delete[] Pmom;
-
-  delete ErrorMonitor;
-  delete Psi4Monitor;
-  delete BHMonitor;
-  delete MAPMonitor;
-  delete ConVMonitor;
-  delete Waveshell;
-
-  delete CheckPoint;
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function computes initial data using Lousto's analytic formulas
-
-//================================================================================================
-
-void bssn_class::Setup_Initial_Data_Lousto()
-{
-  if (!checkrun)
-  {
-    if (myrank == 0)
-      cout << "Setup initial data with Lousto's analytical formula." << endl;
-    char filename[50];
-    strcpy(filename, "input.par");
-    int BH_NM;
-    double *Porg_here, *Pmom_here, *Spin_here, *Mass_here;
-    // read parameter from file
-    {
-      const int LEN = 256;
-      char pline[LEN];
-      string str, sgrp, skey, sval;
-      int sind;
-      ifstream inf(filename, ifstream::in);
-      if (!inf.good() && myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "Can not open parameter file " << filename 
-                                << " for inputing information of black holes" << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-
-      for (int i = 1; inf.good(); i++)
-      {
-        inf.getline(pline, LEN);
-        str = pline;
-
-        int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-        if (status == -1)
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << "error reading parameter file " << filename << " in line " << i << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        else if (status == 0)
-          continue;
-
-        if (sgrp == "BSSN" && skey == "BH_num")
-        {
-          BH_NM = atoi(sval.c_str());
-          break;
-        }
-      }
-      inf.close();
-    }
-
-    Porg_here = new double[3 * BH_NM];
-    Pmom_here = new double[3 * BH_NM];
-    Spin_here = new double[3 * BH_NM];
-    Mass_here = new double[BH_NM];
-    // read parameter from file
-    {
-      const int LEN = 256;
-      char pline[LEN];
-      string str, sgrp, skey, sval;
-      int sind;
-      ifstream inf(filename, ifstream::in);
-      if (!inf.good() && myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "Can not open parameter file " << filename
-                                << " for inputing information of black holes" << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-
-      for (int i = 1; inf.good(); i++)
-      {
-        inf.getline(pline, LEN);
-        str = pline;
-
-        int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-        if (status == -1)
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << "error reading parameter file " << filename << " in line " << i << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        else if (status == 0)
-          continue;
-
-        if (sgrp == "BSSN" && sind < BH_NM)
-        {
-          if (skey == "Mass")
-            Mass_here[sind] = atof(sval.c_str());
-          else if (skey == "Porgx")
-            Porg_here[sind * 3] = atof(sval.c_str());
-          else if (skey == "Porgy")
-            Porg_here[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Porgz")
-            Porg_here[sind * 3 + 2] = atof(sval.c_str());
-          else if (skey == "Spinx")
-            Spin_here[sind * 3] = atof(sval.c_str());
-          else if (skey == "Spiny")
-            Spin_here[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Spinz")
-            Spin_here[sind * 3 + 2] = atof(sval.c_str());
-          else if (skey == "Pmomx")
-            Pmom_here[sind * 3] = atof(sval.c_str());
-          else if (skey == "Pmomy")
-            Pmom_here[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Pmomz")
-            Pmom_here[sind * 3 + 2] = atof(sval.c_str());
-        }
-      }
-      inf.close();
-    }
-    // set initial data
-    for (int lev = 0; lev < GH->levels; lev++)
-    {
-      MyList<Patch> *Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BL = Pp->data->blb;
-        while (BL)
-        {
-          Block *cg = BL->data;
-          if (myrank == cg->rank)
-          {
-            // Use Lousto's analytic formulas to compute initial data
-            f_get_lousto_nbhs(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                              cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                              cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                              cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                              cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                              cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                              cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                              cg->fgfs[Lap0->sgfn], 
-                              cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                              cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn], 
-                              Mass_here, Porg_here, Pmom_here, Spin_here, BH_NM);
-          }
-          if (BL == Pp->data->ble)
-            break;
-          BL = BL->next;
-        }
-        Pp = Pp->next;
-      }
-    }
-    // dump read_in initial data
-    for (int lev = 0; lev < GH->levels; lev++)
-      Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT);
-#ifdef WithShell
-    // ShellPatch part
-    MyList<ss_patch> *Pp = SH->PatL;
-    while (Pp)
-    {
-      MyList<Block> *BL = Pp->data->blb;
-      while (BL)
-      {
-        Block *cg = BL->data;
-        if (myrank == cg->rank)
-        {
-          f_get_initial_nbhs_sh(cg->shape, 
-                                cg->fgfs[Pp->data->fngfs + ShellPatch::gx], 
-                                cg->fgfs[Pp->data->fngfs + ShellPatch::gy],
-                                cg->fgfs[Pp->data->fngfs + ShellPatch::gz],
-                                cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                                cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                                cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                                cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                                cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                                cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                                cg->fgfs[Lap0->sgfn], 
-                                cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                                cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn], 
-                                Mass_here, Porg_here, Pmom_here, Spin_here, BH_NM);
-        }
-        if (BL == Pp->data->ble)
-          break;
-        BL = BL->next;
-      }
-      Pp = Pp->next;
-    }
-    // dump read_in initial data
-    SH->Dump_Data(StateList, 0, PhysTime, dT);
-#endif
-
-    delete[] Porg_here;
-    delete[] Mass_here;
-    delete[] Pmom_here;
-    delete[] Spin_here;
-    //   SH->Synch(GH->PatL[0],StateList,Symmetry);
-    //   exit(0);
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function computes initial data using analytic formulas by Prof. Cao
-
-//================================================================================================
-
-void bssn_class::Setup_Initial_Data_Cao()
-{
-  if (!checkrun)
-  {
-    if (myrank == 0)
-      cout << "Setup initial data with Cao's analytical formula." << endl;
-    char filename[50];
-    strcpy(filename, "input.par");
-    int BH_NM;
-    double *Porg_here, *Pmom_here, *Spin_here, *Mass_here;
-    // read parameter from file
-    {
-      const int LEN = 256;
-      char pline[LEN];
-      string str, sgrp, skey, sval;
-      int sind;
-      ifstream inf(filename, ifstream::in);
-      if (!inf.good() && myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "Can not open parameter file " << filename 
-                                << " for inputing information of black holes" << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-
-      for (int i = 1; inf.good(); i++)
-      {
-        inf.getline(pline, LEN);
-        str = pline;
-
-        int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-        if (status == -1)
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << "error reading parameter file " << filename << " in line " << i << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        else if (status == 0)
-          continue;
-
-        if (sgrp == "BSSN" && skey == "BH_num")
-        {
-          BH_NM = atoi(sval.c_str());
-          break;
-        }
-      }
-      inf.close();
-    }
-
-    Porg_here = new double[3 * BH_NM];
-    Pmom_here = new double[3 * BH_NM];
-    Spin_here = new double[3 * BH_NM];
-    Mass_here = new double[BH_NM];
-    // read parameter from file
-    {
-      const int LEN = 256;
-      char pline[LEN];
-      string str, sgrp, skey, sval;
-      int sind;
-      ifstream inf(filename, ifstream::in);
-      if (!inf.good() && myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "Can not open parameter file " << filename
-                                << " for inputing information of black holes" << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-
-      for (int i = 1; inf.good(); i++)
-      {
-        inf.getline(pline, LEN);
-        str = pline;
-
-        int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-        if (status == -1)
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << "error reading parameter file " << filename << " in line " << i << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        else if (status == 0)
-          continue;
-
-        if (sgrp == "BSSN" && sind < BH_NM)
-        {
-          if (skey == "Mass")
-            Mass_here[sind] = atof(sval.c_str());
-          else if (skey == "Porgx")
-            Porg_here[sind * 3] = atof(sval.c_str());
-          else if (skey == "Porgy")
-            Porg_here[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Porgz")
-            Porg_here[sind * 3 + 2] = atof(sval.c_str());
-          else if (skey == "Spinx")
-            Spin_here[sind * 3] = atof(sval.c_str());
-          else if (skey == "Spiny")
-            Spin_here[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Spinz")
-            Spin_here[sind * 3 + 2] = atof(sval.c_str());
-          else if (skey == "Pmomx")
-            Pmom_here[sind * 3] = atof(sval.c_str());
-          else if (skey == "Pmomy")
-            Pmom_here[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Pmomz")
-            Pmom_here[sind * 3 + 2] = atof(sval.c_str());
-        }
-      }
-      inf.close();
-    }
-    // set initial data
-    for (int lev = 0; lev < GH->levels; lev++)
-    {
-      MyList<Patch> *Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BL = Pp->data->blb;
-        while (BL)
-        {
-          Block *cg = BL->data;
-          if (myrank == cg->rank)
-          {
-            // Use Prof. Cao's analytic formulas to compute initial data
-            f_get_initial_nbhs(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                               cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                               cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                               cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                               cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                               cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                               cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                               cg->fgfs[Lap0->sgfn], 
-                               cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                               cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn], 
-                               Mass_here, Porg_here, Pmom_here, Spin_here, BH_NM);
-          }
-          if (BL == Pp->data->ble)
-            break;
-          BL = BL->next;
-        }
-        Pp = Pp->next;
-      }
-    }
-    // dump read_in initial data
-    for (int lev = 0; lev < GH->levels; lev++)
-      Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT);
-#ifdef WithShell
-    // ShellPatch part
-    MyList<ss_patch> *Pp = SH->PatL;
-    while (Pp)
-    {
-      MyList<Block> *BL = Pp->data->blb;
-      while (BL)
-      {
-        Block *cg = BL->data;
-        if (myrank == cg->rank)
-        {
-          f_get_initial_nbhs_sh(cg->shape, 
-                                cg->fgfs[Pp->data->fngfs + ShellPatch::gx], 
-                                cg->fgfs[Pp->data->fngfs + ShellPatch::gy],
-                                cg->fgfs[Pp->data->fngfs + ShellPatch::gz],
-                                cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                                cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                                cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                                cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                                cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                                cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                                cg->fgfs[Lap0->sgfn], 
-                                cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                                cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn], 
-                                Mass_here, Porg_here, Pmom_here, Spin_here, BH_NM);
-        }
-        if (BL == Pp->data->ble)
-          break;
-        BL = BL->next;
-      }
-      Pp = Pp->next;
-    }
-    // dump read_in initial data
-    SH->Dump_Data(StateList, 0, PhysTime, dT);
-#endif
-
-    delete[] Porg_here;
-    delete[] Mass_here;
-    delete[] Pmom_here;
-    delete[] Spin_here;
-    //   SH->Synch(GH->PatL[0],StateList,Symmetry);
-    //   exit(0);
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function computes Kerr-Schild initial data analytically
-
-//================================================================================================
-
-void bssn_class::Setup_KerrSchild()
-{
-  if (!checkrun)
-  {
-    // set initial data
-    for (int lev = 0; lev < GH->levels; lev++)
-    {
-      MyList<Patch> *Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BL = Pp->data->blb;
-        while (BL)
-        {
-          Block *cg = BL->data;
-          if (myrank == cg->rank)
-          {
-            f_get_initial_kerrschild(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                     cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                                     cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                                     cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                                     cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                                     cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                                     cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                                     cg->fgfs[Lap0->sgfn], 
-                                     cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                                     cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn]);
-          }
-          if (BL == Pp->data->ble)
-            break;
-          BL = BL->next;
-        }
-        Pp = Pp->next;
-      }
-    }
-#ifdef WithShell
-    // ShellPatch part
-    MyList<ss_patch> *Pp = SH->PatL;
-    while (Pp)
-    {
-      int lev = 0, fngfs = Pp->data->fngfs;
-
-      MyList<Block> *BL = Pp->data->blb;
-      while (BL)
-      {
-        Block *cg = BL->data;
-        if (myrank == cg->rank)
-        {
-          f_get_initial_kerrschild_ss(cg->shape, 
-                                      cg->fgfs[Pp->data->fngfs + ShellPatch::gx], 
-                                      cg->fgfs[Pp->data->fngfs + ShellPatch::gy],
-                                      cg->fgfs[Pp->data->fngfs + ShellPatch::gz],
-                                      cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                                      cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                                      cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                                      cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                                      cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                                      cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                                      cg->fgfs[Lap0->sgfn], 
-                                      cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                                      cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn]);
-          /*
-               f_fderivs_shc(cg->shape,
-                             cg->fgfs[phi0->sgfn],
-                             cg->fgfs[Sfx_rhs->sgfn],cg->fgfs[Sfy_rhs->sgfn],cg->fgfs[Sfz_rhs->sgfn],
-                             cg->X[0],cg->X[1],cg->X[2],
-                             phi0->SoA[0],phi0->SoA[1],phi0->SoA[2],
-                             Symmetry,lev,Pp->data->sst,
-                             cg->fgfs[fngfs+ShellPatch::drhodx],
-                             cg->fgfs[fngfs+ShellPatch::drhody],
-                             cg->fgfs[fngfs+ShellPatch::drhodz],
-                             cg->fgfs[fngfs+ShellPatch::dsigmadx],
-                             cg->fgfs[fngfs+ShellPatch::dsigmady],
-                             cg->fgfs[fngfs+ShellPatch::dsigmadz],
-                             cg->fgfs[fngfs+ShellPatch::dRdx],
-                             cg->fgfs[fngfs+ShellPatch::dRdy],
-                             cg->fgfs[fngfs+ShellPatch::dRdz]);
-               f_fdderivs_shc(cg->shape,cg->fgfs[phi0->sgfn],
-                              cg->fgfs[Axx_rhs->sgfn],cg->fgfs[Axy_rhs->sgfn],cg->fgfs[Axz_rhs->sgfn],
-                              cg->fgfs[Ayy_rhs->sgfn],cg->fgfs[Ayz_rhs->sgfn],cg->fgfs[Azz_rhs->sgfn],
-                              cg->X[0],cg->X[1],cg->X[2],
-                              phi0->SoA[0],phi0->SoA[1],phi0->SoA[2],
-                              Symmetry,lev,Pp->data->sst,
-                              cg->fgfs[fngfs+ShellPatch::drhodx],
-                              cg->fgfs[fngfs+ShellPatch::drhody],
-                              cg->fgfs[fngfs+ShellPatch::drhodz],
-                              cg->fgfs[fngfs+ShellPatch::dsigmadx],
-                              cg->fgfs[fngfs+ShellPatch::dsigmady],
-                              cg->fgfs[fngfs+ShellPatch::dsigmadz],
-                              cg->fgfs[fngfs+ShellPatch::dRdx],
-                              cg->fgfs[fngfs+ShellPatch::dRdy],
-                              cg->fgfs[fngfs+ShellPatch::dRdz],
-                              cg->fgfs[fngfs+ShellPatch::drhodxx],
-                              cg->fgfs[fngfs+ShellPatch::drhodxy],
-                              cg->fgfs[fngfs+ShellPatch::drhodxz],
-                              cg->fgfs[fngfs+ShellPatch::drhodyy],
-                              cg->fgfs[fngfs+ShellPatch::drhodyz],
-                              cg->fgfs[fngfs+ShellPatch::drhodzz],
-                              cg->fgfs[fngfs+ShellPatch::dsigmadxx],
-                              cg->fgfs[fngfs+ShellPatch::dsigmadxy],
-                              cg->fgfs[fngfs+ShellPatch::dsigmadxz],
-                              cg->fgfs[fngfs+ShellPatch::dsigmadyy],
-                              cg->fgfs[fngfs+ShellPatch::dsigmadyz],
-                              cg->fgfs[fngfs+ShellPatch::dsigmadzz],
-                              cg->fgfs[fngfs+ShellPatch::dRdxx],
-                              cg->fgfs[fngfs+ShellPatch::dRdxy],
-                              cg->fgfs[fngfs+ShellPatch::dRdxz],
-                              cg->fgfs[fngfs+ShellPatch::dRdyy],
-                              cg->fgfs[fngfs+ShellPatch::dRdyz],
-                              cg->fgfs[fngfs+ShellPatch::dRdzz]);
-          */
-        }
-        if (BL == Pp->data->ble)
-          break;
-        BL = BL->next;
-      }
-      Pp = Pp->next;
-    }
-#endif
-
-    // dump read_in initial data
-    //   SH->Synch(GH->PatL[0],StateList,Symmetry);
-    //   for(int lev=0;lev<GH->levels;lev++) Parallel::Dump_Data(GH->PatL[lev],StateList,0,PhysTime,dT);
-    //   SH->Dump_Data(StateList,0,PhysTime,dT);
-    //   exit(0);
-
-    /*
-       {
-             MyList<var> * DG_List=new MyList<var>(Sfx_rhs);
-             DG_List->insert(Sfy_rhs); DG_List->insert(Sfz_rhs);
-             DG_List->insert(Axx_rhs); DG_List->insert(Axy_rhs); DG_List->insert(Axz_rhs);
-             DG_List->insert(Ayy_rhs); DG_List->insert(Ayz_rhs); DG_List->insert(Azz_rhs);
-             SH->Synch(DG_List,Symmetry);
-             SH->Dump_Data(DG_List,0,PhysTime,dT);
-             DG_List->clearList();
-             exit(0);
-       }
-    */
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function reads initial data produced by Pablo Galaviz's Olliptic program
-
-//================================================================================================
-
-//|----------------------------------------------------------------------------
-//  read ASCII file with the style of Pablo
-//|----------------------------------------------------------------------------
-bool bssn_class::read_Pablo_file(int *ext, double *datain, char *filename)
-{
-  int nx = ext[0], ny = ext[1], nz = ext[2];
-  int i, j, k;
-  double x, y, z;
-  //|--->open in put file
-  ifstream infile;
-  infile.open(filename);
-  if (!infile)
-  {
-    cout << "bssn_class: read_Pablo_file can't open " << filename << " for input." << endl;
-    return false;
-  }
-  for (k = 0; k < nz; k++)
-    for (j = 0; j < ny; j++)
-      for (i = 0; i < nx; i++)
-      {
-        infile >> x >> y >> z >> datain[i + j * nx + k * nx * ny];
-      }
-
-  infile.close();
-
-  return true;
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function writes initial data for Pablo Galaviz's Olliptic program
-
-//================================================================================================
-
-//|----------------------------------------------------------------------------
-//  write ASCII file with the style of Pablo
-//|----------------------------------------------------------------------------
-void bssn_class::write_Pablo_file(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
-                                  char *filename)
-{
-  int nx = ext[0], ny = ext[1], nz = ext[2];
-  int i, j, k;
-  double *X, *Y, *Z;
-  X = new double[nx];
-  Y = new double[ny];
-  Z = new double[nz];
-  double dX, dY, dZ;
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-  dX = (xmax - xmin) / (nx - 1);
-  for (i = 0; i < nx; i++)
-    X[i] = xmin + i * dX;
-  dY = (ymax - ymin) / (ny - 1);
-  for (j = 0; j < ny; j++)
-    Y[j] = ymin + j * dY;
-  dZ = (zmax - zmin) / (nz - 1);
-  for (k = 0; k < nz; k++)
-    Z[k] = zmin + k * dZ;
-#else
-#ifdef Cell
-  dX = (xmax - xmin) / nx;
-  for (i = 0; i < nx; i++)
-    X[i] = xmin + (i + 0.5) * dX;
-  dY = (ymax - ymin) / ny;
-  for (j = 0; j < ny; j++)
-    Y[j] = ymin + (j + 0.5) * dY;
-  dZ = (zmax - zmin) / nz;
-  for (k = 0; k < nz; k++)
-    Z[k] = zmin + (k + 0.5) * dZ;
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-  //|--->open out put file
-  ofstream outfile;
-  outfile.open(filename);
-  if (!outfile)
-  {
-    cout << "bssn=_class: write_Pablo_file can't open " << filename << " for output." << endl;
-    MPI_Abort(MPI_COMM_WORLD, 1);
-  }
-  outfile.setf(ios::scientific, ios::floatfield);
-  outfile.precision(16);
-  for (k = 0; k < nz; k++)
-    for (j = 0; j < ny; j++)
-      for (i = 0; i < nx; i++)
-      {
-        outfile << X[i] << " " << Y[j] << " " << Z[k] << " "
-                << 0 << endl;
-      }
-  outfile.close();
-
-  delete[] X;
-  delete[] Y;
-  delete[] Z;
-}
-
-//================================================================================================
-
-
-
-
-//================================================================================================
-
-// This member function reads TwoPuncture initial data produced by the Ansorg solver
-
-//================================================================================================
-
-// Read initial data solved by Ansorg, PRD 70, 064011 (2004)
-
-void bssn_class::Read_Ansorg()
-{
-  if (!checkrun)
-  {
-    if (myrank == 0)
-      cout << "Read initial data from Ansorg's solver,"
-           << " please be sure the input parameters for black holes are puncture parameters!!" << endl;
-    char filename[50];
-    strcpy(filename, "input.par");
-    int BH_NM;
-    double *Porg_here, *Pmom_here, *Spin_here, *Mass_here;
-    // read parameter from file
-    {
-      const int LEN = 256;
-      char pline[LEN];
-      string str, sgrp, skey, sval;
-      int sind;
-      ifstream inf(filename, ifstream::in);
-      if (!inf.good() && myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "Can not open parameter file " << filename 
-                                << " for inputing information of black holes" << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-
-      for (int i = 1; inf.good(); i++)
-      {
-        inf.getline(pline, LEN);
-        str = pline;
-
-        int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-        if (status == -1)
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << "error reading parameter file " << filename << " in line " << i << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        else if (status == 0)
-          continue;
-
-        if (sgrp == "BSSN" && skey == "BH_num")
-        {
-          BH_NM = atoi(sval.c_str());
-          break;
-        }
-      }
-      inf.close();
-    }
-
-    Porg_here = new double[3 * BH_NM];
-    Pmom_here = new double[3 * BH_NM];
-    Spin_here = new double[3 * BH_NM];
-    Mass_here = new double[BH_NM];
-    // read parameter from file
-    {
-      const int LEN = 256;
-      char pline[LEN];
-      string str, sgrp, skey, sval;
-      int sind;
-      ifstream inf(filename, ifstream::in);
-      if (!inf.good() && myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "Can not open parameter file " << filename
-                                << " for inputing information of black holes" << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-
-      for (int i = 1; inf.good(); i++)
-      {
-        inf.getline(pline, LEN);
-        str = pline;
-
-        int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-        if (status == -1)
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << "error reading parameter file " << filename << " in line " << i << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        else if (status == 0)
-          continue;
-
-        if (sgrp == "BSSN" && sind < BH_NM)
-        {
-          if (skey == "Mass")
-            Mass_here[sind] = atof(sval.c_str());
-          else if (skey == "Porgx")
-            Porg_here[sind * 3] = atof(sval.c_str());
-          else if (skey == "Porgy")
-            Porg_here[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Porgz")
-            Porg_here[sind * 3 + 2] = atof(sval.c_str());
-          else if (skey == "Spinx")
-            Spin_here[sind * 3] = atof(sval.c_str());
-          else if (skey == "Spiny")
-            Spin_here[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Spinz")
-            Spin_here[sind * 3 + 2] = atof(sval.c_str());
-          else if (skey == "Pmomx")
-            Pmom_here[sind * 3] = atof(sval.c_str());
-          else if (skey == "Pmomy")
-            Pmom_here[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Pmomz")
-            Pmom_here[sind * 3 + 2] = atof(sval.c_str());
-        }
-      }
-      inf.close();
-    }
-
-    int order = 6;
-    Ansorg read_ansorg("Ansorg.psid", order);
-    // set initial data
-    for (int lev = 0; lev < GH->levels; lev++)
-    {
-      MyList<Patch> *Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BL = Pp->data->blb;
-        while (BL)
-        {
-          Block *cg = BL->data;
-          if (myrank == cg->rank)
-          {
-            for (int k = 0; k < cg->shape[2]; k++)
-              for (int j = 0; j < cg->shape[1]; j++)
-                for (int i = 0; i < cg->shape[0]; i++)
-                  cg->fgfs[phi0->sgfn][i + j * cg->shape[0] + k * cg->shape[0] * cg->shape[1]] =
-                      read_ansorg.ps_u_at_xyz(cg->X[0][i], cg->X[1][j], cg->X[2][k]);
-
-            f_get_ansorg_nbhs(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                              cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                              cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                              cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                              cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                              cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                              cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                              cg->fgfs[Lap0->sgfn], 
-                              cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                              cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                              Mass_here, Porg_here, Pmom_here, Spin_here, BH_NM);
-          }
-          if (BL == Pp->data->ble)
-            break;
-          BL = BL->next;
-        }
-        Pp = Pp->next;
-      }
-    }
-#ifdef WithShell
-    // ShellPatch part
-    MyList<ss_patch> *Pp = SH->PatL;
-    while (Pp)
-    {
-      MyList<Block> *BL = Pp->data->blb;
-      while (BL)
-      {
-        Block *cg = BL->data;
-        if (myrank == cg->rank)
-        {
-          for (int k = 0; k < cg->shape[2]; k++)
-            for (int j = 0; j < cg->shape[1]; j++)
-              for (int i = 0; i < cg->shape[0]; i++)
-                cg->fgfs[phi0->sgfn][i + j * cg->shape[0] + k * cg->shape[0] * cg->shape[1]] =
-                    read_ansorg.ps_u_at_xyz(cg->fgfs[Pp->data->fngfs + ShellPatch::gx][i + j * cg->shape[0] + k * cg->shape[0] * cg->shape[1]],
-                                            cg->fgfs[Pp->data->fngfs + ShellPatch::gy][i + j * cg->shape[0] + k * cg->shape[0] * cg->shape[1]],
-                                            cg->fgfs[Pp->data->fngfs + ShellPatch::gz][i + j * cg->shape[0] + k * cg->shape[0] * cg->shape[1]]);
-
-          f_get_ansorg_nbhs_ss(cg->shape, 
-                               cg->fgfs[Pp->data->fngfs + ShellPatch::gx], 
-                               cg->fgfs[Pp->data->fngfs + ShellPatch::gy],
-                               cg->fgfs[Pp->data->fngfs + ShellPatch::gz],
-                               cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                               cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                               cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                               cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                               cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                               cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                               cg->fgfs[Lap0->sgfn], 
-                               cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                               cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                               Mass_here, Porg_here, Pmom_here, Spin_here, BH_NM);
-#if 0
-// for check fderivs_sh
-            f_fderivs_sh(cg->shape,cg->fgfs[Ayz0->sgfn],
-			 cg->fgfs[Sfx0->sgfn],cg->fgfs[Sfy0->sgfn],cg->fgfs[Sfz0->sgfn],
-                         cg->X[0],cg->X[1],cg->X[2],
-                         Ayz0->SoA[0],Ayz0->SoA[1],Ayz0->SoA[2],
-                         Symmetry,Pp->data->sst,Pp->data->sst);
-#endif
-#if 0
-// for check fderivs_shc
-            int fngfs = Pp->data->fngfs;
-            f_fderivs_shc(cg->shape,cg->fgfs[Ayz0->sgfn],
-			  cg->fgfs[Sfx0->sgfn],cg->fgfs[Sfy0->sgfn],cg->fgfs[Sfz0->sgfn],
-                          cg->X[0],cg->X[1],cg->X[2],
-                          Ayz0->SoA[0],Ayz0->SoA[1],Ayz0->SoA[2],
-                          Symmetry,Pp->data->sst,Pp->data->sst,
-                          cg->fgfs[fngfs+ShellPatch::drhodx],
-                          cg->fgfs[fngfs+ShellPatch::drhody],
-                          cg->fgfs[fngfs+ShellPatch::drhodz],
-                          cg->fgfs[fngfs+ShellPatch::dsigmadx],
-                          cg->fgfs[fngfs+ShellPatch::dsigmady],
-                          cg->fgfs[fngfs+ShellPatch::dsigmadz],
-                          cg->fgfs[fngfs+ShellPatch::dRdx],
-                          cg->fgfs[fngfs+ShellPatch::dRdy],
-                          cg->fgfs[fngfs+ShellPatch::dRdz]);
-#endif
-        }
-        if (BL == Pp->data->ble)
-          break;
-        BL = BL->next;
-      }
-      Pp = Pp->next;
-    }
-#endif
-
-    delete[] Porg_here;
-    delete[] Mass_here;
-    delete[] Pmom_here;
-    delete[] Spin_here;
-
-    Compute_Constraint();
-    // dump read_in initial data
-    for (int lev = 0; lev < GH->levels; lev++)
-      Parallel::Dump_Data(GH->PatL[lev], DumpList, 0, PhysTime, dT);
-#ifdef WithShell
-    SH->Dump_Data(DumpList, 0, PhysTime, dT);
-#endif
-    //   if(myrank==0) MPI_Abort(MPI_COMM_WORLD,1);
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function sets up the time evolution for the entire process
-
-//================================================================================================
-
-void bssn_class::Evolve(int Steps)
-{
-
-  clock_t prev_clock, curr_clock;
-  double LastDump = 0.0, LastCheck = 0.0, Last2dDump = 0.0;
-  LastAnas = 0;
-#if 0
-//initial checkpoint for special uasge
-     {
-       CheckPoint->write_Black_Hole_position(BH_num_input,BH_num,Porg0,Porgbr,Mass);
-       CheckPoint->writecheck_cgh(PhysTime,GH);
-#ifdef WithShell   
-       CheckPoint->writecheck_sh(PhysTime,SH);
-#endif
-       CheckPoint->write_bssn(LastDump,Last2dDump,LastAnas);
-       misc::tillherecheck("complete initialization preparation"); // we need synchronization here
-       if(myrank==0) MPI_Abort(MPI_COMM_WORLD,1);
-     }
-#endif
-
-  double beg_time;
-  beg_time = MPI_Wtime();
-// added by yangquan
-#ifdef USE_GPU
-#ifdef USE_GPU_DIVIDE
-  // new code considering different partition for cpu and gpu
-  {
-    MyList<Patch> *Pp = GH->PatL[0];
-    bool fg = true;
-    while (fg && Pp)
-    {
-      MyList<Block> *BP = Pp->data->blb;
-      while (fg && BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-          use_gpu = cg->cgpu;
-          fg = false;
-          break;
-        }
-        if (BP == Pp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      Pp = Pp->next;
-    }
-  }
-#else
-  // old yangquan code
-  use_gpu = 0;
-  if (myrank % 2 == 1)
-    use_gpu = 1;
-#endif
-#endif
-
-  // for step 0 constraint interpolation
-  Interp_Constraint(true);
-
-#ifdef With_AHF
-  // setup apparent horizon finder direct of thornburg
-  {
-    HN_num = BH_num;
-    for (int ia = 0; ia < BH_num; ia++)
-      for (int ib = ia + 1; ib < BH_num; ib++)
-        HN_num++;
-
-    AHFinderDirect::AHFinderDirect_setup(AHList, GaugeList,
-                                         this,
-                                         Symmetry, HN_num, &PhysTime);
-
-    lastahdumpid = new int[HN_num];
-    findeveryl = new int[HN_num];
-    xc = new double[HN_num];
-    yc = new double[HN_num];
-    zc = new double[HN_num];
-    xr = new double[HN_num];
-    yr = new double[HN_num];
-    zr = new double[HN_num];
-    dTT = new double[HN_num];
-    trigger = new bool[HN_num];
-    dumpid = new int[HN_num];
-
-    for (int ihn = 0; ihn < HN_num; ihn++)
-    {
-      lastahdumpid[ihn] = 0;
-      findeveryl[ihn] = AHfindevery;
-    }
-  }
-#endif
-
-  if (checkrun)
-    CheckPoint->read_bssn(LastDump, Last2dDump, LastAnas);
-
-  double dT_mon = dT * pow(0.5, Mymax(0, trfls));
-  /*
-  #ifdef With_AHF
-  //initial apparent horizon finding
-      {
-         double gam;
-         double massmin=Mass[0];
-         for(int ihn=1;ihn<BH_num;ihn++) massmin=Mymin(massmin,Mass[ihn]);
-
-         for(int ihn=0;ihn<BH_num;ihn++)
-         {
-           xc[ihn] = Porg0[ihn][0];
-           yc[ihn] = Porg0[ihn][1];
-           zc[ihn] = Porg0[ihn][2];
-           gam = fabs(Pmom[ihn*3])/(Mass[ihn]);
-           gam = sqrt(1-gam*gam);
-           xr[ihn] = Mass[ihn]*gam;
-           gam = fabs(Pmom[ihn*3+1])/(Mass[ihn]);
-           gam = sqrt(1-gam*gam);
-           yr[ihn] = Mass[ihn]*gam;
-           gam = fabs(Pmom[ihn*3+2])/(Mass[ihn]);
-           gam = sqrt(1-gam*gam);
-           zr[ihn] = Mass[ihn]*gam;
-           findeveryl[ihn] = findeveryl[ihn]*(Mymax(int(Mass[ihn]/massmin),1));
-         }
-         int ihn = BH_num;
-         for(int ia=0;ia<BH_num;ia++)
-           for(int ib=ia+1;ib<BH_num;ib++)
-           {
-             xc[ihn] = (Porg0[ia][0] + Porg0[ib][0])/2;
-             yc[ihn] = (Porg0[ia][1] + Porg0[ib][1])/2;
-             zc[ihn] = (Porg0[ia][2] + Porg0[ib][2])/2;
-             xr[ihn] = yr[ihn] = zr[ihn] = (Mass[ia])+(Mass[ib]);
-             findeveryl[ihn] = findeveryl[ihn]*(int(xr[ihn]/Mass[0]));
-
-             ihn++;
-           }
-
-         AHFinderDirect::AHFinderDirect_enforcefind(HN_num,xc,yc,zc,xr,yr,zr);  
-         // note rhs has been used as temp storage space
-
-         delete[] xc; delete[] yc; delete[] zc; delete[] xr; delete[] yr; delete[] zr;
-      }
-  #endif
-  */
-  perf bssn_perf;
-  size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
-
-  for (int lev = 0; lev < GH->levels; lev++)
-    GH->Lt[lev] = PhysTime;
-
-  GH->settrfls(trfls);
-
-  for (int ncount = 1; ncount < Steps + 1; ncount++)
-  {
-    cout << "Before Step: " << ncount << " My Rank: " << myrank 
-         << " takes " << MPI_Wtime() - beg_time << " seconds!" << endl;
-    beg_time = MPI_Wtime();
-#if (PSTR == 0)
-    RecursiveStep(0);
-#elif (PSTR == 1)
-    // data analysis part
-    // Warning NOTE: the variables1 are used as temp storege room
-    AnalysisStuff(a_lev, dT_mon);
-    ParallelStep();
-#endif
-    cout << "After Step: " << ncount << " My Rank: " << myrank 
-         << " takes " << MPI_Wtime() - beg_time << " seconds!" << endl;
-    beg_time = MPI_Wtime();
-
-    //     misc::tillherecheck("before Constraint_Out");
-
-    Constraint_Out(); // this will affect the Dump_List
-
-    LastDump += dT_mon;
-    Last2dDump += dT_mon;
-    LastCheck += dT_mon;
-
-    if (LastDump >= DumpTime)
-    {
-      //       misc::tillherecheck("before Dump_Data");
-
-      for (int lev = 0; lev < GH->levels; lev++)
-        Parallel::Dump_Data(GH->PatL[lev], DumpList, 0, PhysTime, dT_mon);
-#ifdef WithShell
-      SH->Dump_Data(DumpList, 0, PhysTime, dT_mon);
-#endif
-
-      LastDump = 0;
-
-      if (myrank == 0)
-      {
-        cout << "Dump done." << endl;
-      }
-    }
-
-    if (Last2dDump >= d2DumpTime)
-    {
-      //       misc::tillherecheck("before 2dDump_Data");
-
-      for (int lev = 0; lev < GH->levels; lev++)
-        Parallel::d2Dump_Data(GH->PatL[lev], DumpList, 0, PhysTime, dT_mon);
-
-      Last2dDump = 0;
-
-      if (myrank == 0)
-      {
-        cout << "2dDump done." << endl;
-      }
-    }
-
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "Timestep # " << ncount << ": integrating to time: " << PhysTime << endl;
-      cout << "used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-    }
-
-    if (PhysTime >= TotalTime)
-      break;
-
-#if (REGLEV == 1)
-    GH->Regrid(Symmetry, BH_num, Porgbr, Porg0,
-               SynchList_cor, OldStateList, StateList, SynchList_pre,
-               fgt(PhysTime - dT_mon, StartTime, dT_mon / 2), ErrorMonitor);
-#endif
-
-#if (REGLEV == 0 && PSTR == 1)
-//     GH->Regrid_fake(Symmetry,BH_num,Porgbr,Porg0,
-//		SynchList_cor,OldStateList,StateList,SynchList_pre,
-//		fgt(PhysTime-dT_mon,StartTime,dT_mon/2),ErrorMonitor);
-#endif
-
-    bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
-                          &peak_min, &peak_avg, &peak_max, nprocs);
-    if (myrank == 0)
-      printf("Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
-             "peak %0.4lg/%0.4lg/%0.4lgMB\n",
-             (double)current_min / (1024.0 * 1024.0),
-             (double)current_avg / (1024.0 * 1024.0),
-             (double)current_max / (1024.0 * 1024.0),
-             (double)peak_min / (1024.0 * 1024.0),
-             (double)peak_avg / (1024.0 * 1024.0),
-             (double)peak_max / (1024.0 * 1024.0));
-
-    if (LastCheck >= CheckTime)
-    {
-      LastCheck = 0;
-
-      CheckPoint->write_Black_Hole_position(BH_num_input, BH_num, Porg0, Porgbr, Mass);
-      CheckPoint->writecheck_cgh(PhysTime, GH);
-      CheckPoint->writecheck_sh(PhysTime, SH);
-      CheckPoint->write_bssn(LastDump, Last2dDump, LastAnas);
-    }
-  }
-  /*
-  #ifdef With_AHF
-  // final apparent horizon finding
-      {
-         double gam;
-         for(int ihn=0;ihn<BH_num;ihn++)
-         {
-      xc[ihn] = Porg0[ihn][0];
-      yc[ihn] = Porg0[ihn][1];
-      zc[ihn] = Porg0[ihn][2];
-      gam = fabs(Pmom[ihn*3]  )/(Mass[ihn]);
-      gam = sqrt(1-gam*gam);
-      xr[ihn] = Mass[ihn]*gam;
-      gam = fabs(Pmom[ihn*3+1])/(Mass[ihn]);
-      gam = sqrt(1-gam*gam);
-      yr[ihn] = Mass[ihn]*gam;
-      gam = fabs(Pmom[ihn*3+2])/(Mass[ihn]);
-      gam = sqrt(1-gam*gam);
-      zr[ihn] = Mass[ihn]*gam;
-         }
-         int ihn = BH_num;
-         for(int ia=0;ia<BH_num;ia++)
-      for(int ib=ia+1;ib<BH_num;ib++)
-      {
-           xc[ihn] = (Porg0[ia][0] + Porg0[ib][0])/2;
-           yc[ihn] = (Porg0[ia][1] + Porg0[ib][1])/2;
-           zc[ihn] = (Porg0[ia][2] + Porg0[ib][2])/2;
-           xr[ihn] = yr[ihn] = zr[ihn] = (Mass[ia])+(Mass[ib]);
-
-           ihn++;
-      }
-
-         AHFinderDirect::AHFinderDirect_enforcefind(HN_num,xc,yc,zc,xr,yr,zr);  // note rhs has been used as temp storage space
-
-         delete[] xc; delete[] yc; delete[] zc; delete[] xr; delete[] yr; delete[] zr;
-      }
-  #endif
-  */
-}
-
-//================================================================================================
-
-
-
-
-//================================================================================================
-
-// This member function sets up recursive time evolution across different grid levels
-
-//================================================================================================
-
-void bssn_class::RecursiveStep(int lev)
-{
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-
-  int NoIterations = 1, YN;
-  if (lev <= trfls)
-    NoIterations = 1;
-  else
-    NoIterations = 2;
-
-  for (int i = 0; i < NoIterations; i++)
-  {
-    //     if(myrank==0) cout<<"level now = "<<lev<<" NoIteration = "<<i<<endl;
-    YN = (i == NoIterations - 1) ? 1 : 0; // 1: same time level for coarse level and fine level
-
-// added by yangquan
-#ifdef USE_GPU
-    if (use_gpu == 1)
-      Step_GPU(lev, YN);
-    else
-      Step(lev, YN);
-#else
-    Step(lev, YN);
-#endif
-
-#if (AGM == 2)
-    if (GH->levels == 1)
-    {
-      Enforce_algcon(lev, 0);
-    }
-#endif
-
-    GH->Lt[lev] += dT_lev;
-
-    if (lev < GH->levels - 1)
-    {
-      int lf = lev + 1;
-      RecursiveStep(lf);
-    }
-    else
-      PhysTime += dT * pow(0.5, lev);
-
-#if (AGM == 2)
-    if (lev > 0)
-    {
-      Enforce_algcon(lev, 0);
-      if (YN == 1)
-        Enforce_algcon(lev - 1, 0);
-    }
-#endif
-
-#if (RPS == 1)
-    // mesh refinement boundary part
-    //
-    // till here the PhysTime has updated dT_lev
-    RestrictProlong(lev, YN, fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), StateList, OldStateList, SynchList_cor);
-    // RestrictProlong(lev,YN,false,StateList,OldStateList,SynchList_cor);
-
-#ifdef WithShell
-    if (lev == 0)
-    {
-      clock_t prev_clock, curr_clock;
-      if (myrank == 0)
-        curr_clock = clock();
-      SH->CS_Inter(StateList, Symmetry);
-      if (myrank == 0)
-      {
-        prev_clock = curr_clock;
-        curr_clock = clock();
-        cout << "CS_Inter used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-      }
-    }
-#endif
-
-#endif
-
-    //     Parallel::Dump_Data(GH->PatL[lev],StateList,0,PhysTime,dT_lev);
-  }
-
-#if 0
-    if(lev>0) Parallel::Restrict_after(GH->PatL[lev-1],GH->PatL[lev],StateList,StateList,Symmetry);
-#endif
-
-#if (REGLEV == 0)
-  GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
-                      SynchList_cor, OldStateList, StateList, SynchList_pre,
-                      fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
-#endif
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// ParallelStep performs time evolution across multiple grid levels (includes parallel execution)
-// This section applies only when PSTR == 1
-
-//================================================================================================
-
-#if (PSTR == 1)
-void bssn_class::ParallelStep()
-{
-  //  stringstream a_stream;
-  //  a_stream.setf(ios::left);
-
-  double *tporg, *tporgo;
-  tporg = new double[3 * BH_num];
-  tporgo = new double[3 * BH_num];
-
-  int lev = GH->mylev;
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-  double dT_levp1 = dT * pow(0.5, Mymax(lev + 1, trfls));
-  double dT_levm1 = dT * pow(0.5, Mymax(lev - 1, trfls));
-
-  int NoIterations = 1, YN;
-  if (lev <= trfls)
-    NoIterations = 1;
-  else
-    NoIterations = int(pow(2.0, lev - trfls));
-
-  for (int i = 0; i < NoIterations; i++)
-  {
-    //     if(myrank==GH->start_rank[lev]) cout<<"level now = "<<lev<<" NoIteration = "<<i<<endl;
-
-    if (NoIterations == 1)
-      YN = 1;
-    else if (i % 2 == 0)
-      YN = 0;
-    else
-      YN = 1; // 1: same time level for coarse level and fine level
-
-      //     a_stream<<lev<<": before calling Step";
-      //     misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-
-      // Step(lev,YN);
-#ifdef USE_GPU
-    if (use_gpu == 1)
-      Step_GPU(lev, YN);
-    else
-      Step(lev, YN);
-#else
-    Step(lev, YN);
-#endif
-
-      //     a_stream.clear();
-      //     a_stream.str("");
-      //     a_stream<<lev<<": after calling Step";
-      //     misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-
-#if (AGM == 2)
-    if (GH->levels == 1)
-    {
-      Enforce_algcon(lev, 0);
-    }
-#endif
-
-    GH->Lt[lev] += dT_lev;
-
-    PhysTime += dT_lev;
-
-#if (AGM == 2)
-    if (lev > 0)
-    {
-      Enforce_algcon(lev, 0);
-      if (YN == 1)
-        Enforce_algcon(lev - 1, 0);
-    }
-#endif
-
-#if (RPS == 1)
-    // mesh refinement boundary part
-    //
-    // till here the PhysTime has updated dT_lev
-    //   a_stream.clear();
-    //   a_stream.str("");
-    //   a_stream<<lev<<": before RestrictProlong";
-    //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-    if (lev < GH->levels - 1)
-    {
-      if (lev + 1 <= trfls)
-      {
-        //	RestrictProlong_aux(lev,1,fgt(PhysTime-dT_lev,StartTime,dT_levp1/2),StateList,OldStateList,SynchList_cor);
-        RestrictProlong(lev + 1, 1, fgt(PhysTime - dT_lev, StartTime, dT_levp1 / 2), StateList, OldStateList, SynchList_cor);
-      }
-      else
-      {
-        //        if(myrank==GH->start_rank[lev]) cout<<GH->mylev<<", "<<YN<<endl;
-        //        misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"between RestrictProlong");
-
-        //	RestrictProlong_aux(lev,0,fgt(PhysTime-dT_lev,StartTime,dT_levp1/2),StateList,OldStateList,SynchList_cor);
-        //	RestrictProlong_aux(lev,1,fgt(PhysTime-dT_levp1,StartTime,dT_levp1/2),StateList,OldStateList,SynchList_cor);
-        RestrictProlong(lev + 1, 0, fgt(PhysTime - dT_lev, StartTime, dT_levp1 / 2), StateList, OldStateList, SynchList_cor);
-        RestrictProlong(lev + 1, 1, fgt(PhysTime - dT_levp1, StartTime, dT_levp1 / 2), StateList, OldStateList, SynchList_cor);
-      }
-    }
-
-    //   if(myrank==GH->start_rank[lev]) cout<<GH->mylev<<", "<<YN<<endl;
-    //   a_stream.clear();
-    //   a_stream.str("");
-    //   a_stream<<lev<<": between RestrictProlong";
-    //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-
-    RestrictProlong(lev, YN, fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), StateList, OldStateList, SynchList_cor);
-    // RestrictProlong(lev,YN,false,StateList,OldStateList,SynchList_cor);
-
-//   if(myrank==GH->start_rank[lev]) cout<<GH->mylev<<endl;
-//   a_stream.clear();
-//   a_stream.str("");
-//   a_stream<<lev<<": after RestrictProlong";
-//   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-#endif
-
-    //     Parallel::Dump_Data(GH->PatL[lev],StateList,0,PhysTime,dT_lev);
-
-    {
-      MPI_Status status;
-      // receive
-      if (lev < GH->levels - 1)
-      {
-        if (myrank == GH->start_rank[lev])
-        {
-          MPI_Recv(tporgo, 3 * BH_num, MPI_DOUBLE, GH->start_rank[lev + 1], 1, MPI_COMM_WORLD, &status);
-          //	 cout<<tporgo[0]<<","<<tporgo[1]<<","<<tporgo[2]<<endl;
-        }
-        else
-          for (int i = 0; i < 3 * BH_num; i++)
-            tporgo[i] = 0;
-        MPI_Allreduce(tporgo, tporg, 3 * BH_num, MPI_DOUBLE, MPI_SUM, GH->Commlev[lev]);
-
-        for (int i = 0; i < BH_num; i++)
-          for (int j = 0; j < 3; j++)
-            Porg0[i][j] = tporg[3 * i + j];
-
-        //      if(myrank==GH->start_rank[lev]) cout<<Porg0[0][0]<<","<<Porg0[0][1]<<","<<Porg0[0][2]<<endl;
-      }
-      // send
-      if (lev > 0 && YN == 1 && myrank == GH->start_rank[lev])
-      {
-        for (int i = 0; i < BH_num; i++)
-          for (int j = 0; j < 3; j++)
-            tporg[3 * i + j] = Porg0[i][j];
-
-        MPI_Send(tporg, 3 * BH_num, MPI_DOUBLE, GH->start_rank[lev - 1], 1, MPI_COMM_WORLD);
-      }
-
-      //   a_stream.clear();
-      //   a_stream.str("");
-      //   a_stream<<lev<<": after PBH Sync";
-      //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-    }
-#if (REGLEV == 0)
-    // for higher level
-    if (lev < GH->levels - 1)
-    {
-      if (lev + 1 >= GH->movls)
-      {
-        //	       GH->Regrid_Onelevel_aux(lev,Symmetry,BH_num,Porgbr,Porg0,
-        GH->Regrid_Onelevel(lev + 1, Symmetry, BH_num, Porgbr, Porg0,
-                            SynchList_cor, OldStateList, StateList, SynchList_pre,
-                            fgt(PhysTime - dT_levp1, StartTime, dT_levp1 / 2), ErrorMonitor);
-
-        //               a_stream.clear();
-        //               a_stream.str("");
-        //               a_stream<<lev<<": after calling GH->Regrid_Onelevel_aux for higher level";
-        //               misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-      }
-    }
-
-    // for this level
-    if (YN == 1)
-    {
-      GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
-                          SynchList_cor, OldStateList, StateList, SynchList_pre,
-                          fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
-
-      //               a_stream.clear();
-      //               a_stream.str("");
-      //               a_stream<<lev<<": after calling GH->Regrid_Onelevel";
-      //               misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-    }
-
-    // for lower level
-    if (lev - 1 >= GH->movls)
-    {
-      if (lev - 1 <= trfls)
-      {
-        if (YN == 1)
-        {
-          //	   GH->Regrid_Onelevel_aux(lev-2,Symmetry,BH_num,Porgbr,Porg0,
-          GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
-                              SynchList_cor, OldStateList, StateList, SynchList_pre,
-                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor);
-
-          //               a_stream.clear();
-          //               a_stream.str("");
-          //               a_stream<<lev<<": after calling GH->Regrid_Onelevel_aux for lower level";
-          //               misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-        }
-      }
-      else
-      {
-        if (i % 4 == 3)
-        {
-          //	   GH->Regrid_Onelevel_aux(lev-2,Symmetry,BH_num,Porgbr,Porg0,
-          GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
-                              SynchList_cor, OldStateList, StateList, SynchList_pre,
-                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor);
-
-          //               a_stream.clear();
-          //               a_stream.str("");
-          //               a_stream<<lev<<": after calling GH->Regrid_Onelevel_aux for lower level";
-          //               misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-        }
-      }
-    }
-#endif
-  }
-
-#ifdef WithShell
-  SHStep();
-  //               a_stream.clear();
-  //               a_stream.str("");
-  //               a_stream<<lev<<": after calling SHStep";
-  //               misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-
-#if (RPS == 1)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->CS_Inter(StateList, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "CS_Inter used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-    }
-    //               a_stream.clear();
-    //               a_stream.str("");
-    //               a_stream<<lev<<": after calling shell cartisian sync";
-    //               misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],a_stream.str());
-  }
-#endif
-
-#endif
-
-#if 0
-    if(lev>0) Parallel::Restrict_after(GH->PatL[lev-1],GH->PatL[lev],StateList,StateList,Symmetry);
-#endif
-
-  delete[] tporg;
-  delete[] tporgo;
-}
-#endif
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function configures the single-step time evolution for each grid level
-// during the time evolution process.
-// For the case PSTR == 0
-
-//================================================================================================
-
-#if (PSTR == 0)
-#if 1
-void bssn_class::Step(int lev, int YN)
-{
-  setpbh(BH_num, Porg0, Mass, BH_num_input);
-
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-
-// new code 2013-2-15, zjcao
-#if (MAPBH == 1)
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      for (int ith = 0; ith < 3; ith++)
-        Porg1[ithBH][ith] = Porg0[ithBH][ith] + Porg_rhs[ithBH][ith] * dT_lev;
-      if (Symmetry > 0)
-        Porg1[ithBH][2] = fabs(Porg1[ithBH][2]);
-      if (Symmetry == 2)
-      {
-        Porg1[ithBH][0] = fabs(Porg1[ithBH][0]);
-        Porg1[ithBH][1] = fabs(Porg1[ithBH][1]);
-      }
-      if (!finite(Porg1[ithBH][0]) || !finite(Porg1[ithBH][1]) || !finite(Porg1[ithBH][2]))
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "predictor step finds NaN for BH's position from ("
-                                << Porg0[ithBH][0] << "," << Porg0[ithBH][1] << "," << Porg0[ithBH][2] << ")" << endl;
-
-        MyList<var> *DG_List = new MyList<var>(Sfx0);
-        DG_List->insert(Sfx0);
-        DG_List->insert(Sfy0);
-        DG_List->insert(Sfz0);
-        Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-        DG_List->clearList();
-      }
-    }
-  }
-
-  // data analysis part
-  // Warning NOTE: the variables1 are used as temp storege room
-  if (lev == a_lev)
-  {
-    AnalysisStuff(lev, dT_lev);
-  }
-#endif
-
-#ifdef With_AHF
-  AH_Step_Find(lev, dT_lev);
-#endif
-  bool BB = fgt(PhysTime, StartTime, dT_lev / 2);
-  double ndeps = numepss;
-  if (lev < GH->movls)
-    ndeps = numepsb;
-  double TRK4 = PhysTime;
-  int iter_count = 0; // count RK4 substeps
-  int pre = 0, cor = 1;
-  int ERROR = 0;
-
-  MyList<ss_patch> *sPp;
-  // Predictor
-  MyList<Patch> *Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-#if (AGM == 0)
-        f_enforce_ga(cg->shape,
-                     cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                     cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                     cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                     cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-        if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                               cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                               cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                               cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                               cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                               cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                               cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                               cg->fgfs[Lap0->sgfn], 
-                               cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                               cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                               cg->fgfs[phi_rhs->sgfn], cg->fgfs[trK_rhs->sgfn],
-                               cg->fgfs[gxx_rhs->sgfn], cg->fgfs[gxy_rhs->sgfn], cg->fgfs[gxz_rhs->sgfn],
-                               cg->fgfs[gyy_rhs->sgfn], cg->fgfs[gyz_rhs->sgfn], cg->fgfs[gzz_rhs->sgfn],
-                               cg->fgfs[Axx_rhs->sgfn], cg->fgfs[Axy_rhs->sgfn], cg->fgfs[Axz_rhs->sgfn],
-                               cg->fgfs[Ayy_rhs->sgfn], cg->fgfs[Ayz_rhs->sgfn], cg->fgfs[Azz_rhs->sgfn],
-                               cg->fgfs[Gmx_rhs->sgfn], cg->fgfs[Gmy_rhs->sgfn], cg->fgfs[Gmz_rhs->sgfn],
-                               cg->fgfs[Lap_rhs->sgfn], 
-                               cg->fgfs[Sfx_rhs->sgfn], cg->fgfs[Sfy_rhs->sgfn], cg->fgfs[Sfz_rhs->sgfn],
-                               cg->fgfs[dtSfx_rhs->sgfn], cg->fgfs[dtSfy_rhs->sgfn], cg->fgfs[dtSfz_rhs->sgfn],
-                               cg->fgfs[rho->sgfn], cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                               cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                               cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                               cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                               cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                               cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                               cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                               cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                               cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                               cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                               cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                               cg->fgfs[Cons_Ham->sgfn],
-                               cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                               cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                               Symmetry, lev, ndeps, pre))
-        {
-          cout << "find NaN in domain: (" 
-               << cg->bbox[0] << ":" << cg->bbox[3] << "," 
-               << cg->bbox[1] << ":" << cg->bbox[4] << ","
-               << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-          ERROR = 1;
-        }
-
-        // rk4 substep and boundary
-        {
-          MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; 
-          // we do not check the correspondence here
-          
-          while (varl0)
-          {
-#if (SommerType == 0)
-#ifndef WithShell
-            if (lev == 0) // sommerfeld indeed
-              f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                   Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                   Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                   cg->fgfs[varlrhs->data->sgfn],
-                                   cg->fgfs[varl0->data->sgfn], 
-                                   varl0->data->propspeed, varl0->data->SoA,
-                                   Symmetry);
-
-#endif
-#endif
-            f_rungekutta4_rout(cg->shape, dT_lev, 
-                               cg->fgfs[varl0->data->sgfn], 
-                               cg->fgfs[varl->data->sgfn], 
-                               cg->fgfs[varlrhs->data->sgfn],
-                               iter_count);
-#ifndef WithShell
-            if (lev > 0) // fix BD point
-#endif
-              f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                dT_lev, 
-                                cg->fgfs[phi0->sgfn],
-                                cg->fgfs[Lap0->sgfn], 
-                                cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], 
-                                varl0->data->SoA,
-                                Symmetry, cor);
-
-#if (SommerType == 1)
-#warning "shell part still bam type"
-            if (lev == 0) // Shibata type sommerfeld
-              f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                dT_lev, 
-                                cg->fgfs[phi0->sgfn],
-                                cg->fgfs[Lap0->sgfn], 
-                                cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], 
-                                varl0->data->SoA,
-                                Symmetry, pre);
-#endif
-
-            varl0 = varl0->next;
-            varl = varl->next;
-            varlrhs = varlrhs->next;
-          }
-        }
-        f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
-#ifdef WithShell
-  // evolve Shell Patches
-  if (lev == 0)
-  {
-    sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      int fngfs = sPp->data->fngfs;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-#if (AGM == 0)
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                       cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                       cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                       cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-          if (f_compute_rhs_bssn_ss(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                    cg->fgfs[fngfs + ShellPatch::gx], 
-                                    cg->fgfs[fngfs + ShellPatch::gy], 
-                                    cg->fgfs[fngfs + ShellPatch::gz],
-                                    cg->fgfs[fngfs + ShellPatch::drhodx], 
-                                    cg->fgfs[fngfs + ShellPatch::drhody], 
-                                    cg->fgfs[fngfs + ShellPatch::drhodz],
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                                    cg->fgfs[fngfs + ShellPatch::dRdx], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdy], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdz],
-                                    cg->fgfs[fngfs + ShellPatch::drhodxx], 
-                                    cg->fgfs[fngfs + ShellPatch::drhodxy], 
-                                    cg->fgfs[fngfs + ShellPatch::drhodxz],
-                                    cg->fgfs[fngfs + ShellPatch::drhodyy], 
-                                    cg->fgfs[fngfs + ShellPatch::drhodyz], 
-                                    cg->fgfs[fngfs + ShellPatch::drhodzz],
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadxx], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadxy], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadxz],
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadyy], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadyz], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadzz],
-                                    cg->fgfs[fngfs + ShellPatch::dRdxx], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdxy], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdxz],
-                                    cg->fgfs[fngfs + ShellPatch::dRdyy], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdyz], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdzz],
-                                    cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                                    cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                                    cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                                    cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                                    cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                                    cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                                    cg->fgfs[Lap0->sgfn], 
-                                    cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                                    cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                                    cg->fgfs[phi_rhs->sgfn], cg->fgfs[trK_rhs->sgfn],
-                                    cg->fgfs[gxx_rhs->sgfn], cg->fgfs[gxy_rhs->sgfn], cg->fgfs[gxz_rhs->sgfn],
-                                    cg->fgfs[gyy_rhs->sgfn], cg->fgfs[gyz_rhs->sgfn], cg->fgfs[gzz_rhs->sgfn],
-                                    cg->fgfs[Axx_rhs->sgfn], cg->fgfs[Axy_rhs->sgfn], cg->fgfs[Axz_rhs->sgfn],
-                                    cg->fgfs[Ayy_rhs->sgfn], cg->fgfs[Ayz_rhs->sgfn], cg->fgfs[Azz_rhs->sgfn],
-                                    cg->fgfs[Gmx_rhs->sgfn], cg->fgfs[Gmy_rhs->sgfn], cg->fgfs[Gmz_rhs->sgfn],
-                                    cg->fgfs[Lap_rhs->sgfn], 
-                                    cg->fgfs[Sfx_rhs->sgfn], cg->fgfs[Sfy_rhs->sgfn], cg->fgfs[Sfz_rhs->sgfn],
-                                    cg->fgfs[dtSfx_rhs->sgfn], cg->fgfs[dtSfy_rhs->sgfn], cg->fgfs[dtSfz_rhs->sgfn],
-                                    cg->fgfs[rho->sgfn], cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                                    cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                                    cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                                    cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                                    cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                                    cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                                    cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                                    cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                                    cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                                    cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                                    cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                                    cg->fgfs[Cons_Ham->sgfn],
-                                    cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                                    cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                                    Symmetry, lev, numepsh, sPp->data->sst, pre))
-          {
-            cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" 
-                 << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                 << cg->bbox[1] << ":" << cg->bbox[4] << "," 
-                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-            ERROR = 1;
-          }
-
-          // rk4 substep and boundary
-          {
-            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; 
-            // we do not check the correspondence here
-            
-            while (varl0)
-            {
-              // sommerfeld indeed for outter boudary while fix BD for inner boundary
-              f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                      sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], 
-                                      sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                      cg->fgfs[varlrhs->data->sgfn],
-                                      cg->fgfs[varl0->data->sgfn], 
-                                      varl0->data->propspeed, varl0->data->SoA,
-                                      Symmetry);
-
-              f_rungekutta4_rout(cg->shape, dT_lev, 
-                                 cg->fgfs[varl0->data->sgfn], 
-                                 cg->fgfs[varl->data->sgfn], 
-                                 cg->fgfs[varlrhs->data->sgfn],
-                                 iter_count);
-
-              varl0 = varl0->next;
-              varl = varl->next;
-              varlrhs = varlrhs->next;
-            }
-          }
-          f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-        }
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-#if 0 
-// check rhs    
-  {
-         SH->Dump_Data(RHSList,0,PhysTime,dT_lev);
-         if(myrank == 0)
-	 {
-            cout<<"check rhs"<<endl;
-	    MPI_Abort(MPI_COMM_WORLD,1);
-	 }
-  }
-#endif
-  }
-
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-
-  if (ERROR)
-  {
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-#endif
-
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "Shell stuff synchronization used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-    }
-  }
-#endif
-
-#if (MAPBH == 0)
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][0], Porg[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][1], Porg[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][2], Porg[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-      if (Symmetry > 0)
-        Porg[ithBH][2] = fabs(Porg[ithBH][2]);
-      if (Symmetry == 2)
-      {
-        Porg[ithBH][0] = fabs(Porg[ithBH][0]);
-        Porg[ithBH][1] = fabs(Porg[ithBH][1]);
-      }
-      if (!finite(Porg[ithBH][0]) || !finite(Porg[ithBH][1]) || !finite(Porg[ithBH][2]))
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "predictor step finds NaN for BH's position from ("
-                                << Porg0[ithBH][0] << "," << Porg0[ithBH][1] << "," << Porg0[ithBH][2] 
-                                << ")" << endl;
-
-        MyList<var> *DG_List = new MyList<var>(Sfx0);
-        DG_List->insert(Sfx0);
-        DG_List->insert(Sfy0);
-        DG_List->insert(Sfz0);
-        Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-        DG_List->clearList();
-      }
-    }
-  }
-  // data analysis part
-  // Warning NOTE: the variables1 are used as temp storege room
-  if (lev == a_lev)
-  {
-    AnalysisStuff(lev, dT_lev);
-  }
-#endif
-
-  // corrector
-  for (iter_count = 1; iter_count < 4; iter_count++)
-  {
-    // for RK4: t0, t0+dt/2, t0+dt/2, t0+dt;
-    if (iter_count == 1 || iter_count == 3)
-      TRK4 += dT_lev / 2;
-    Pp = GH->PatL[lev];
-    while (Pp)
-    {
-      MyList<Block> *BP = Pp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-#if (AGM == 0)
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                       cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                       cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                       cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-          if (iter_count == 3)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                         cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                         cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-          if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                 cg->fgfs[phi->sgfn], cg->fgfs[trK->sgfn],
-                                 cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                                 cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                                 cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                                 cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn],
-                                 cg->fgfs[Gmx->sgfn], cg->fgfs[Gmy->sgfn], cg->fgfs[Gmz->sgfn],
-                                 cg->fgfs[Lap->sgfn], 
-                                 cg->fgfs[Sfx->sgfn], cg->fgfs[Sfy->sgfn], cg->fgfs[Sfz->sgfn],
-                                 cg->fgfs[dtSfx->sgfn], cg->fgfs[dtSfy->sgfn], cg->fgfs[dtSfz->sgfn],
-                                 cg->fgfs[phi1->sgfn], cg->fgfs[trK1->sgfn],
-                                 cg->fgfs[gxx1->sgfn], cg->fgfs[gxy1->sgfn], cg->fgfs[gxz1->sgfn],
-                                 cg->fgfs[gyy1->sgfn], cg->fgfs[gyz1->sgfn], cg->fgfs[gzz1->sgfn],
-                                 cg->fgfs[Axx1->sgfn], cg->fgfs[Axy1->sgfn], cg->fgfs[Axz1->sgfn],
-                                 cg->fgfs[Ayy1->sgfn], cg->fgfs[Ayz1->sgfn], cg->fgfs[Azz1->sgfn],
-                                 cg->fgfs[Gmx1->sgfn], cg->fgfs[Gmy1->sgfn], cg->fgfs[Gmz1->sgfn],
-                                 cg->fgfs[Lap1->sgfn], 
-                                 cg->fgfs[Sfx1->sgfn], cg->fgfs[Sfy1->sgfn], cg->fgfs[Sfz1->sgfn],
-                                 cg->fgfs[dtSfx1->sgfn], cg->fgfs[dtSfy1->sgfn], cg->fgfs[dtSfz1->sgfn],
-                                 cg->fgfs[rho->sgfn], 
-                                 cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                                 cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                                 cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                                 cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                                 cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                                 cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                                 cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                                 cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                                 cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                                 cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                                 cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                                 cg->fgfs[Cons_Ham->sgfn],
-                                 cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                                 cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                                 Symmetry, lev, ndeps, cor))
-          {
-            cout << "find NaN in domain: (" 
-                 << cg->bbox[0] << ":" << cg->bbox[3] << "," 
-                 << cg->bbox[1] << ":" << cg->bbox[4] << ","
-                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-            ERROR = 1;
-          }
-          // rk4 substep and boundary
-          {
-            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; 
-            // we do not check the correspondence here
-            
-            while (varl0)
-            {
-#if (SommerType == 0)
-#ifndef WithShell
-              if (lev == 0) // sommerfeld indeed
-                f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                     Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                     Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                     cg->fgfs[varl1->data->sgfn],
-                                     cg->fgfs[varl->data->sgfn], 
-                                     varl0->data->propspeed, varl0->data->SoA,
-                                     Symmetry);
-#endif
-#endif
-              f_rungekutta4_rout(cg->shape, dT_lev, 
-                                 cg->fgfs[varl0->data->sgfn], 
-                                 cg->fgfs[varl1->data->sgfn], 
-                                 cg->fgfs[varlrhs->data->sgfn],
-                                 iter_count);
-
-#ifndef WithShell
-              if (lev > 0) // fix BD point
-#endif
-                f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                  Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                  Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                  dT_lev, 
-                                  cg->fgfs[phi0->sgfn],
-                                  cg->fgfs[Lap0->sgfn], 
-                                  cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], 
-                                  varl0->data->SoA,
-                                  Symmetry, cor);
-
-#if (SommerType == 1)
-              if (lev == 1) // shibata type sommerfeld
-                f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                  Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                  Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                  dT_lev, 
-                                  cg->fgfs[phi0->sgfn],
-                                  cg->fgfs[Lap0->sgfn], 
-                                  cg->fgfs[varl->data->sgfn], cg->fgfs[varl1->data->sgfn], 
-                                  varl0->data->SoA,
-                                  Symmetry, cor);
-#endif
-
-              varl0 = varl0->next;
-              varl = varl->next;
-              varl1 = varl1->next;
-              varlrhs = varlrhs->next;
-            }
-          }
-          f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-        }
-        if (BP == Pp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      Pp = Pp->next;
-    }
-
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime 
-                                << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
-#ifdef WithShell
-    // evolve Shell Patches
-    if (lev == 0)
-    {
-      sPp = SH->PatL;
-      while (sPp)
-      {
-        MyList<Block> *BP = sPp->data->blb;
-        int fngfs = sPp->data->fngfs;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          if (myrank == cg->rank)
-          {
-#if (AGM == 0)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                         cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                         cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-            if (iter_count == 3)
-              f_enforce_ga(cg->shape,
-                           cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                           cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                           cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                           cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-            if (f_compute_rhs_bssn_ss(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                      cg->fgfs[fngfs + ShellPatch::gx], 
-                                      cg->fgfs[fngfs + ShellPatch::gy], 
-                                      cg->fgfs[fngfs + ShellPatch::gz],
-                                      cg->fgfs[fngfs + ShellPatch::drhodx], 
-                                      cg->fgfs[fngfs + ShellPatch::drhody], 
-                                      cg->fgfs[fngfs + ShellPatch::drhodz],
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                                      cg->fgfs[fngfs + ShellPatch::dRdx], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdy], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdz],
-                                      cg->fgfs[fngfs + ShellPatch::drhodxx], 
-                                      cg->fgfs[fngfs + ShellPatch::drhodxy], 
-                                      cg->fgfs[fngfs + ShellPatch::drhodxz],
-                                      cg->fgfs[fngfs + ShellPatch::drhodyy], 
-                                      cg->fgfs[fngfs + ShellPatch::drhodyz], 
-                                      cg->fgfs[fngfs + ShellPatch::drhodzz],
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadxx], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadxy], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadxz],
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadyy], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadyz], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadzz],
-                                      cg->fgfs[fngfs + ShellPatch::dRdxx], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdxy], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdxz],
-                                      cg->fgfs[fngfs + ShellPatch::dRdyy], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdyz], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdzz],
-                                      cg->fgfs[phi->sgfn], cg->fgfs[trK->sgfn],
-                                      cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                                      cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                                      cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                                      cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn],
-                                      cg->fgfs[Gmx->sgfn], cg->fgfs[Gmy->sgfn], cg->fgfs[Gmz->sgfn],
-                                      cg->fgfs[Lap->sgfn], 
-                                      cg->fgfs[Sfx->sgfn], cg->fgfs[Sfy->sgfn], cg->fgfs[Sfz->sgfn],
-                                      cg->fgfs[dtSfx->sgfn], cg->fgfs[dtSfy->sgfn], cg->fgfs[dtSfz->sgfn],
-                                      cg->fgfs[phi1->sgfn], cg->fgfs[trK1->sgfn],
-                                      cg->fgfs[gxx1->sgfn], cg->fgfs[gxy1->sgfn], cg->fgfs[gxz1->sgfn],
-                                      cg->fgfs[gyy1->sgfn], cg->fgfs[gyz1->sgfn], cg->fgfs[gzz1->sgfn],
-                                      cg->fgfs[Axx1->sgfn], cg->fgfs[Axy1->sgfn], cg->fgfs[Axz1->sgfn],
-                                      cg->fgfs[Ayy1->sgfn], cg->fgfs[Ayz1->sgfn], cg->fgfs[Azz1->sgfn],
-                                      cg->fgfs[Gmx1->sgfn], cg->fgfs[Gmy1->sgfn], cg->fgfs[Gmz1->sgfn],
-                                      cg->fgfs[Lap1->sgfn], 
-                                      cg->fgfs[Sfx1->sgfn], cg->fgfs[Sfy1->sgfn], cg->fgfs[Sfz1->sgfn],
-                                      cg->fgfs[dtSfx1->sgfn], cg->fgfs[dtSfy1->sgfn], cg->fgfs[dtSfz1->sgfn],
-                                      cg->fgfs[rho->sgfn], 
-                                      cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                                      cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                                      cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                                      cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                                      cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                                      cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                                      cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                                      cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                                      cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                                      cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                                      cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                                      cg->fgfs[Cons_Ham->sgfn],
-                                      cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                                      cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                                      Symmetry, lev, numepsh, sPp->data->sst, cor))
-            {
-              cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" 
-                   << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                   << cg->bbox[1] << ":" << cg->bbox[4] << "," 
-                   << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-              ERROR = 1;
-            }
-            // rk4 substep and boundary
-            {
-              MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; 
-              // we do not check the correspondence here
-              
-              while (varl0)
-              {
-                // sommerfeld indeed for outter boudary while fix BD for inner boundary
-                f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                        sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], 
-                                        sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                        cg->fgfs[varl1->data->sgfn],
-                                        cg->fgfs[varl->data->sgfn], 
-                                        varl0->data->propspeed, varl0->data->SoA,
-                                        Symmetry);
-
-                f_rungekutta4_rout(cg->shape, dT_lev, 
-                                   cg->fgfs[varl0->data->sgfn], 
-                                   cg->fgfs[varl1->data->sgfn], 
-                                   cg->fgfs[varlrhs->data->sgfn],
-                                   iter_count);
-
-                varl0 = varl0->next;
-                varl = varl->next;
-                varl1 = varl1->next;
-                varlrhs = varlrhs->next;
-              }
-            }
-            f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-          }
-          if (BP == sPp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        sPp = sPp->next;
-      }
-    }
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-#endif
-
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-
-#ifdef WithShell
-    if (lev == 0)
-    {
-      clock_t prev_clock, curr_clock;
-      if (myrank == 0)
-        curr_clock = clock();
-      SH->Synch(SynchList_cor, Symmetry);
-      if (myrank == 0)
-      {
-        prev_clock = curr_clock;
-        curr_clock = clock();
-        cout << "Shell stuff synchronization used " 
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-             << " seconds!" << endl;
-      }
-    }
-#endif
-
-#if (MAPBH == 0)
-    // for black hole position
-    if (BH_num > 0 && lev == GH->levels - 1)
-    {
-      compute_Porg_rhs(Porg, Porg1, Sfx, Sfy, Sfz, lev);
-      for (int ithBH = 0; ithBH < BH_num; ithBH++)
-      {
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][0], Porg1[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][1], Porg1[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][2], Porg1[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-        if (Symmetry > 0)
-          Porg1[ithBH][2] = fabs(Porg1[ithBH][2]);
-        if (Symmetry == 2)
-        {
-          Porg1[ithBH][0] = fabs(Porg1[ithBH][0]);
-          Porg1[ithBH][1] = fabs(Porg1[ithBH][1]);
-        }
-        if (!finite(Porg1[ithBH][0]) || !finite(Porg1[ithBH][1]) || !finite(Porg1[ithBH][2]))
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << iter_count << " corrector step finds NaN for BH's position from ("
-                                  << Porg[ithBH][0] << "," << Porg[ithBH][1] << "," << Porg[ithBH][2] 
-                                  << ")" << endl;
-
-          MyList<var> *DG_List = new MyList<var>(Sfx0);
-          DG_List->insert(Sfx0);
-          DG_List->insert(Sfy0);
-          DG_List->insert(Sfz0);
-          Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-          DG_List->clearList();
-        }
-      }
-    }
-#endif
-
-    // swap time level
-    if (iter_count < 3)
-    {
-      Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BP = Pp->data->blb;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          cg->swapList(SynchList_pre, SynchList_cor, myrank);
-          if (BP == Pp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        Pp = Pp->next;
-      }
-#ifdef WithShell
-      if (lev == 0)
-      {
-        sPp = SH->PatL;
-        while (sPp)
-        {
-          MyList<Block> *BP = sPp->data->blb;
-          while (BP)
-          {
-            Block *cg = BP->data;
-            cg->swapList(SynchList_pre, SynchList_cor, myrank);
-            if (BP == sPp->data->ble)
-              break;
-            BP = BP->next;
-          }
-          sPp = sPp->next;
-        }
-      }
-#endif
-
-#if (MAPBH == 0)
-      // for black hole position
-      if (BH_num > 0 && lev == GH->levels - 1)
-      {
-        for (int ithBH = 0; ithBH < BH_num; ithBH++)
-        {
-          Porg[ithBH][0] = Porg1[ithBH][0];
-          Porg[ithBH][1] = Porg1[ithBH][1];
-          Porg[ithBH][2] = Porg1[ithBH][2];
-        }
-      }
-#endif
-    }
-  }
-#if (RPS == 0)
-  // mesh refinement boundary part
-  RestrictProlong(lev, YN, BB);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->CS_Inter(SynchList_cor, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "CS_Inter used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds!" << endl;
-    }
-  }
-#endif
-
-#endif
-  // note the data structure before update
-  // SynchList_cor 1   -----------
-  //
-  // StateList     0   -----------
-  //
-  // OldStateList  old -----------
-  // update
-  Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      cg->swapList(StateList, SynchList_cor, myrank);
-      cg->swapList(OldStateList, SynchList_cor, myrank);
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-#ifdef WithShell
-  if (lev == 0)
-  {
-    sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        cg->swapList(StateList, SynchList_cor, myrank);
-        cg->swapList(OldStateList, SynchList_cor, myrank);
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-#if 0
-// check StateList   
-  {
-         SH->Dump_Data(StateList,0,PhysTime,dT_lev);
-         if(myrank == 0)
-	 {
-            cout<<"check StateList"<<endl;
-	    MPI_Abort(MPI_COMM_WORLD,1);
-	 }
-  }
-#endif
-  }
-#endif
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      Porg0[ithBH][0] = Porg1[ithBH][0];
-      Porg0[ithBH][1] = Porg1[ithBH][1];
-      Porg0[ithBH][2] = Porg1[ithBH][2];
-    }
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function sets up the single-step time evolution for each grid level (alternate version)
-
-//================================================================================================
-
-#else // #if 1 (comment may be incorrect; should be #if 0)
-// ICN for bam comparison
-void bssn_class::Step(int lev, int YN)
-{
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-#ifdef With_AHF
-  AH_Step_Find(lev, dT_lev);
-#endif
-  bool BB = fgt(PhysTime, StartTime, dT_lev / 2);
-  double ndeps = numepss;
-  if (lev < GH->movls)
-    ndeps = numepsb;
-  double TRK4 = PhysTime;
-  int iter_count = 0; // count RK4 substeps
-  int pre = 0, cor = 1;
-  int ERROR = 0;
-
-  MyList<ss_patch> *sPp;
-  // Predictor
-  MyList<Patch> *Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-#if (AGM == 0)
-        f_enforce_ga(cg->shape,
-                     cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                     cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                     cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                     cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-        if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                               cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                               cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                               cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                               cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                               cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                               cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                               cg->fgfs[Lap0->sgfn], 
-                               cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                               cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                               cg->fgfs[phi_rhs->sgfn], cg->fgfs[trK_rhs->sgfn],
-                               cg->fgfs[gxx_rhs->sgfn], cg->fgfs[gxy_rhs->sgfn], cg->fgfs[gxz_rhs->sgfn],
-                               cg->fgfs[gyy_rhs->sgfn], cg->fgfs[gyz_rhs->sgfn], cg->fgfs[gzz_rhs->sgfn],
-                               cg->fgfs[Axx_rhs->sgfn], cg->fgfs[Axy_rhs->sgfn], cg->fgfs[Axz_rhs->sgfn],
-                               cg->fgfs[Ayy_rhs->sgfn], cg->fgfs[Ayz_rhs->sgfn], cg->fgfs[Azz_rhs->sgfn],
-                               cg->fgfs[Gmx_rhs->sgfn], cg->fgfs[Gmy_rhs->sgfn], cg->fgfs[Gmz_rhs->sgfn],
-                               cg->fgfs[Lap_rhs->sgfn], 
-                               cg->fgfs[Sfx_rhs->sgfn], cg->fgfs[Sfy_rhs->sgfn], cg->fgfs[Sfz_rhs->sgfn],
-                               cg->fgfs[dtSfx_rhs->sgfn], cg->fgfs[dtSfy_rhs->sgfn], cg->fgfs[dtSfz_rhs->sgfn],
-                               cg->fgfs[rho->sgfn], cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                               cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                               cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                               cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                               cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                               cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                               cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                               cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                               cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                               cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                               cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                               cg->fgfs[Cons_Ham->sgfn],
-                               cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                               cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                               Symmetry, lev, ndeps, pre))
-        {
-          cout << "find NaN in domain: (" 
-               << cg->bbox[0] << ":" << cg->bbox[3] << "," 
-               << cg->bbox[1] << ":" << cg->bbox[4] << ","
-               << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-          ERROR = 1;
-        }
-
-        // rk4 substep and boundary
-        {
-          MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; 
-          // we do not check the correspondence here
-          
-          while (varl0)
-          {
-#ifndef WithShell
-            if (lev == 0) // sommerfeld indeed
-              f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                   Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                   Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                   cg->fgfs[varlrhs->data->sgfn],
-                                   cg->fgfs[varl0->data->sgfn], 
-                                   varl0->data->propspeed, varl0->data->SoA,
-                                   Symmetry);
-
-#endif
-            f_icn_rout(cg->shape, dT_lev, 
-                       cg->fgfs[varl0->data->sgfn], 
-                       cg->fgfs[varl->data->sgfn], 
-                       cg->fgfs[varlrhs->data->sgfn],
-                       iter_count);
-#ifndef WithShell
-            if (lev > 0) // fix BD point
-#endif
-              f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                dT_lev, cg->fgfs[phi0->sgfn],
-                                cg->fgfs[Lap0->sgfn], 
-                                cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], 
-                                varl0->data->SoA,
-                                Symmetry, cor);
-
-            varl0 = varl0->next;
-            varl = varl->next;
-            varlrhs = varlrhs->next;
-          }
-        }
-        f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime 
-                              << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
-#ifdef WithShell
-  // evolve Shell Patches
-  if (lev == 0)
-  {
-    sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      int fngfs = sPp->data->fngfs;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-#if (AGM == 0)
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                       cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                       cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                       cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-          if (f_compute_rhs_bssn_ss(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                    cg->fgfs[fngfs + ShellPatch::gx], 
-                                    cg->fgfs[fngfs + ShellPatch::gy], 
-                                    cg->fgfs[fngfs + ShellPatch::gz],
-                                    cg->fgfs[fngfs + ShellPatch::drhodx], 
-                                    cg->fgfs[fngfs + ShellPatch::drhody], 
-                                    cg->fgfs[fngfs + ShellPatch::drhodz],
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                                    cg->fgfs[fngfs + ShellPatch::dRdx], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdy], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdz],
-                                    cg->fgfs[fngfs + ShellPatch::drhodxx], 
-                                    cg->fgfs[fngfs + ShellPatch::drhodxy], 
-                                    cg->fgfs[fngfs + ShellPatch::drhodxz],
-                                    cg->fgfs[fngfs + ShellPatch::drhodyy], 
-                                    cg->fgfs[fngfs + ShellPatch::drhodyz], 
-                                    cg->fgfs[fngfs + ShellPatch::drhodzz],
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadxx], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadxy], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadxz],
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadyy], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadyz], 
-                                    cg->fgfs[fngfs + ShellPatch::dsigmadzz],
-                                    cg->fgfs[fngfs + ShellPatch::dRdxx], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdxy], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdxz],
-                                    cg->fgfs[fngfs + ShellPatch::dRdyy], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdyz], 
-                                    cg->fgfs[fngfs + ShellPatch::dRdzz],
-                                    cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                                    cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                                    cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                                    cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                                    cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                                    cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                                    cg->fgfs[Lap0->sgfn], 
-                                    cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                                    cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                                    cg->fgfs[phi_rhs->sgfn], cg->fgfs[trK_rhs->sgfn],
-                                    cg->fgfs[gxx_rhs->sgfn], cg->fgfs[gxy_rhs->sgfn], cg->fgfs[gxz_rhs->sgfn],
-                                    cg->fgfs[gyy_rhs->sgfn], cg->fgfs[gyz_rhs->sgfn], cg->fgfs[gzz_rhs->sgfn],
-                                    cg->fgfs[Axx_rhs->sgfn], cg->fgfs[Axy_rhs->sgfn], cg->fgfs[Axz_rhs->sgfn],
-                                    cg->fgfs[Ayy_rhs->sgfn], cg->fgfs[Ayz_rhs->sgfn], cg->fgfs[Azz_rhs->sgfn],
-                                    cg->fgfs[Gmx_rhs->sgfn], cg->fgfs[Gmy_rhs->sgfn], cg->fgfs[Gmz_rhs->sgfn],
-                                    cg->fgfs[Lap_rhs->sgfn], 
-                                    cg->fgfs[Sfx_rhs->sgfn], cg->fgfs[Sfy_rhs->sgfn], cg->fgfs[Sfz_rhs->sgfn],
-                                    cg->fgfs[dtSfx_rhs->sgfn], cg->fgfs[dtSfy_rhs->sgfn], cg->fgfs[dtSfz_rhs->sgfn],
-                                    cg->fgfs[rho->sgfn], cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                                    cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                                    cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                                    cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                                    cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                                    cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                                    cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                                    cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                                    cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                                    cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                                    cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                                    cg->fgfs[Cons_Ham->sgfn],
-                                    cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                                    cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                                    Symmetry, lev, numepsh, sPp->data->sst, pre))
-          {
-            cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" 
-                 << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                 << cg->bbox[1] << ":" << cg->bbox[4] << "," 
-                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-            ERROR = 1;
-          }
-
-          // rk4 substep and boundary
-          {
-            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; 
-            // we do not check the correspondence here
-            
-            while (varl0)
-            {
-              // sommerfeld indeed for outter boudary while fix BD for inner boundary
-              f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                      sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], 
-                                      sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                      cg->fgfs[varlrhs->data->sgfn],
-                                      cg->fgfs[varl0->data->sgfn], 
-                                      varl0->data->propspeed, varl0->data->SoA,
-                                      Symmetry);
-
-              f_icn_rout(cg->shape, dT_lev, 
-                         cg->fgfs[varl0->data->sgfn], 
-                         cg->fgfs[varl->data->sgfn], 
-                         cg->fgfs[varlrhs->data->sgfn],
-                         iter_count);
-
-              varl0 = varl0->next;
-              varl = varl->next;
-              varlrhs = varlrhs->next;
-            }
-          }
-          f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-        }
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-#if 0 
-// check rhs    
-  {
-         SH->Dump_Data(RHSList,0,PhysTime,dT_lev);
-         if(myrank == 0)
-	 {
-            cout<<"check rhs"<<endl;
-	    MPI_Abort(MPI_COMM_WORLD,1);
-	 }
-  }
-#endif
-  }
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-  if (ERROR)
-  {
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-#endif
-
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "Shell stuff synchronization used " 
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds!" << endl;
-    }
-  }
-#endif
-
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      f_icn_scalar(dT_lev, Porg0[ithBH][0], Porg[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-      f_icn_scalar(dT_lev, Porg0[ithBH][1], Porg[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-      f_icn_scalar(dT_lev, Porg0[ithBH][2], Porg[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-      if (Symmetry > 0)
-        Porg[ithBH][2] = fabs(Porg[ithBH][2]);
-      if (Symmetry == 2)
-      {
-        Porg[ithBH][0] = fabs(Porg[ithBH][0]);
-        Porg[ithBH][1] = fabs(Porg[ithBH][1]);
-      }
-      if (!finite(Porg[ithBH][0]) || !finite(Porg[ithBH][1]) || !finite(Porg[ithBH][2]))
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "predictor step finds NaN for BH's position from ("
-                                << Porg0[ithBH][0] << "," << Porg0[ithBH][1] << "," << Porg0[ithBH][2] 
-                                << ")" << endl;
-
-        MyList<var> *DG_List = new MyList<var>(Sfx0);
-        DG_List->insert(Sfx0);
-        DG_List->insert(Sfy0);
-        DG_List->insert(Sfz0);
-        Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-        DG_List->clearList();
-      }
-    }
-  }
-  // data analysis part
-  // Warning NOTE: the variables1 are used as temp storege room
-  if (lev == a_lev)
-  {
-    AnalysisStuff(lev, dT_lev);
-  }
-  // corrector
-  for (iter_count = 1; iter_count < 3; iter_count++)
-  {
-    Pp = GH->PatL[lev];
-    while (Pp)
-    {
-      MyList<Block> *BP = Pp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-#if (AGM == 0)
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                       cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                       cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                       cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-          if (iter_count == 3)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                         cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                         cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-          if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                 cg->fgfs[phi->sgfn], cg->fgfs[trK->sgfn],
-                                 cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                                 cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                                 cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                                 cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn],
-                                 cg->fgfs[Gmx->sgfn], cg->fgfs[Gmy->sgfn], cg->fgfs[Gmz->sgfn],
-                                 cg->fgfs[Lap->sgfn], 
-                                 cg->fgfs[Sfx->sgfn], cg->fgfs[Sfy->sgfn], cg->fgfs[Sfz->sgfn],
-                                 cg->fgfs[dtSfx->sgfn], cg->fgfs[dtSfy->sgfn], cg->fgfs[dtSfz->sgfn],
-                                 cg->fgfs[phi1->sgfn], cg->fgfs[trK1->sgfn],
-                                 cg->fgfs[gxx1->sgfn], cg->fgfs[gxy1->sgfn], cg->fgfs[gxz1->sgfn],
-                                 cg->fgfs[gyy1->sgfn], cg->fgfs[gyz1->sgfn], cg->fgfs[gzz1->sgfn],
-                                 cg->fgfs[Axx1->sgfn], cg->fgfs[Axy1->sgfn], cg->fgfs[Axz1->sgfn],
-                                 cg->fgfs[Ayy1->sgfn], cg->fgfs[Ayz1->sgfn], cg->fgfs[Azz1->sgfn],
-                                 cg->fgfs[Gmx1->sgfn], cg->fgfs[Gmy1->sgfn], cg->fgfs[Gmz1->sgfn],
-                                 cg->fgfs[Lap1->sgfn], 
-                                 cg->fgfs[Sfx1->sgfn], cg->fgfs[Sfy1->sgfn], cg->fgfs[Sfz1->sgfn],
-                                 cg->fgfs[dtSfx1->sgfn], cg->fgfs[dtSfy1->sgfn], cg->fgfs[dtSfz1->sgfn],
-                                 cg->fgfs[rho->sgfn], cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                                 cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                                 cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                                 cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                                 cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                                 cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                                 cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                                 cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                                 cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                                 cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                                 cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                                 cg->fgfs[Cons_Ham->sgfn],
-                                 cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                                 cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                                 Symmetry, lev, ndeps, cor))
-          {
-            cout << "find NaN in domain: (" 
-                 << cg->bbox[0] << ":" << cg->bbox[3] << "," 
-                 << cg->bbox[1] << ":" << cg->bbox[4] << ","
-                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-            ERROR = 1;
-          }
-          // rk4 substep and boundary
-          {
-            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; 
-            // we do not check the correspondence here
-            
-            while (varl0)
-            {
-#ifndef WithShell
-              if (lev == 0) // sommerfeld indeed
-                f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                     Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                     Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                     cg->fgfs[varl1->data->sgfn],
-                                     cg->fgfs[varl->data->sgfn], 
-                                     varl0->data->propspeed, varl0->data->SoA,
-                                     Symmetry);
-#endif
-              f_icn_rout(cg->shape, dT_lev, 
-                         cg->fgfs[varl0->data->sgfn], 
-                         cg->fgfs[varl1->data->sgfn], 
-                         cg->fgfs[varlrhs->data->sgfn],
-                         iter_count);
-
-#ifndef WithShell
-              if (lev > 0) // fix BD point
-#endif
-                f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                  Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                  Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                  dT_lev, 
-                                  cg->fgfs[phi0->sgfn],
-                                  cg->fgfs[Lap0->sgfn], 
-                                  cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], 
-                                  varl0->data->SoA,
-                                  Symmetry, cor);
-
-              varl0 = varl0->next;
-              varl = varl->next;
-              varl1 = varl1->next;
-              varlrhs = varlrhs->next;
-            }
-          }
-          f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-        }
-        if (BP == Pp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      Pp = Pp->next;
-    }
-
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime 
-                                << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
-#ifdef WithShell
-    // evolve Shell Patches
-    if (lev == 0)
-    {
-      sPp = SH->PatL;
-      while (sPp)
-      {
-        MyList<Block> *BP = sPp->data->blb;
-        int fngfs = sPp->data->fngfs;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          if (myrank == cg->rank)
-          {
-#if (AGM == 0)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                         cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                         cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-            if (iter_count == 3)
-              f_enforce_ga(cg->shape,
-                           cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                           cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                           cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                           cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-            if (f_compute_rhs_bssn_ss(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                      cg->fgfs[fngfs + ShellPatch::gx], 
-                                      cg->fgfs[fngfs + ShellPatch::gy], 
-                                      cg->fgfs[fngfs + ShellPatch::gz],
-                                      cg->fgfs[fngfs + ShellPatch::drhodx], 
-                                      cg->fgfs[fngfs + ShellPatch::drhody], 
-                                      cg->fgfs[fngfs + ShellPatch::drhodz],
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                                      cg->fgfs[fngfs + ShellPatch::dRdx], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdy], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdz],
-                                      cg->fgfs[fngfs + ShellPatch::drhodxx], 
-                                      cg->fgfs[fngfs + ShellPatch::drhodxy], 
-                                      cg->fgfs[fngfs + ShellPatch::drhodxz],
-                                      cg->fgfs[fngfs + ShellPatch::drhodyy], 
-                                      cg->fgfs[fngfs + ShellPatch::drhodyz], 
-                                      cg->fgfs[fngfs + ShellPatch::drhodzz],
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadxx], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadxy], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadxz],
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadyy], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadyz], 
-                                      cg->fgfs[fngfs + ShellPatch::dsigmadzz],
-                                      cg->fgfs[fngfs + ShellPatch::dRdxx], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdxy], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdxz],
-                                      cg->fgfs[fngfs + ShellPatch::dRdyy], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdyz], 
-                                      cg->fgfs[fngfs + ShellPatch::dRdzz],
-                                      cg->fgfs[phi->sgfn], cg->fgfs[trK->sgfn],
-                                      cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                                      cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                                      cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                                      cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn],
-                                      cg->fgfs[Gmx->sgfn], cg->fgfs[Gmy->sgfn], cg->fgfs[Gmz->sgfn],
-                                      cg->fgfs[Lap->sgfn], 
-                                      cg->fgfs[Sfx->sgfn], cg->fgfs[Sfy->sgfn], cg->fgfs[Sfz->sgfn],
-                                      cg->fgfs[dtSfx->sgfn], cg->fgfs[dtSfy->sgfn], cg->fgfs[dtSfz->sgfn],
-                                      cg->fgfs[phi1->sgfn], cg->fgfs[trK1->sgfn],
-                                      cg->fgfs[gxx1->sgfn], cg->fgfs[gxy1->sgfn], cg->fgfs[gxz1->sgfn],
-                                      cg->fgfs[gyy1->sgfn], cg->fgfs[gyz1->sgfn], cg->fgfs[gzz1->sgfn],
-                                      cg->fgfs[Axx1->sgfn], cg->fgfs[Axy1->sgfn], cg->fgfs[Axz1->sgfn],
-                                      cg->fgfs[Ayy1->sgfn], cg->fgfs[Ayz1->sgfn], cg->fgfs[Azz1->sgfn],
-                                      cg->fgfs[Gmx1->sgfn], cg->fgfs[Gmy1->sgfn], cg->fgfs[Gmz1->sgfn],
-                                      cg->fgfs[Lap1->sgfn], 
-                                      cg->fgfs[Sfx1->sgfn], cg->fgfs[Sfy1->sgfn], cg->fgfs[Sfz1->sgfn],
-                                      cg->fgfs[dtSfx1->sgfn], cg->fgfs[dtSfy1->sgfn], cg->fgfs[dtSfz1->sgfn],
-                                      cg->fgfs[rho->sgfn], 
-                                      cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                                      cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                                      cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                                      cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                                      cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                                      cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                                      cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                                      cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                                      cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                                      cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                                      cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                                      cg->fgfs[Cons_Ham->sgfn],
-                                      cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                                      cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                                      Symmetry, lev, numepsh, sPp->data->sst, cor))
-            {
-              cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" 
-                   << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                   << cg->bbox[1] << ":" << cg->bbox[4] << "," 
-                   << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-              ERROR = 1;
-            }
-            // rk4 substep and boundary
-            {
-              MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; 
-              // we do not check the correspondence here
-              
-              while (varl0)
-              {
-                // sommerfeld indeed for outter boudary while fix BD for inner boundary
-                f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                        sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], 
-                                        sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                        cg->fgfs[varl1->data->sgfn],
-                                        cg->fgfs[varl->data->sgfn], 
-                                        varl0->data->propspeed, varl0->data->SoA,
-                                        Symmetry);
-
-                f_rungekutta4_rout(cg->shape, dT_lev, 
-                                   cg->fgfs[varl0->data->sgfn], 
-                                   cg->fgfs[varl1->data->sgfn], 
-                                   cg->fgfs[varlrhs->data->sgfn],
-                                   iter_count);
-
-                varl0 = varl0->next;
-                varl = varl->next;
-                varl1 = varl1->next;
-                varlrhs = varlrhs->next;
-              }
-            }
-            f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-          }
-          if (BP == sPp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        sPp = sPp->next;
-      }
-    }
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-#endif
-
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-
-#ifdef WithShell
-    if (lev == 0)
-    {
-      clock_t prev_clock, curr_clock;
-      if (myrank == 0)
-        curr_clock = clock();
-      SH->Synch(SynchList_cor, Symmetry);
-      if (myrank == 0)
-      {
-        prev_clock = curr_clock;
-        curr_clock = clock();
-        cout << "Shell stuff synchronization used " 
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-             << " seconds!" << endl;
-      }
-    }
-#endif
-    // for black hole position
-    if (BH_num > 0 && lev == GH->levels - 1)
-    {
-      compute_Porg_rhs(Porg, Porg1, Sfx, Sfy, Sfz, lev);
-      for (int ithBH = 0; ithBH < BH_num; ithBH++)
-      {
-        f_icn_scalar(dT_lev, Porg0[ithBH][0], Porg1[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-        f_icn_scalar(dT_lev, Porg0[ithBH][1], Porg1[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-        f_icn_scalar(dT_lev, Porg0[ithBH][2], Porg1[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-        if (Symmetry > 0)
-          Porg1[ithBH][2] = fabs(Porg1[ithBH][2]);
-        if (Symmetry == 2)
-        {
-          Porg1[ithBH][0] = fabs(Porg1[ithBH][0]);
-          Porg1[ithBH][1] = fabs(Porg1[ithBH][1]);
-        }
-        if (!finite(Porg1[ithBH][0]) || !finite(Porg1[ithBH][1]) || !finite(Porg1[ithBH][2]))
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << iter_count << " corrector step finds NaN for BH's position from ("
-                                  << Porg[ithBH][0] << "," << Porg[ithBH][1] << "," << Porg[ithBH][2] 
-                                  << ")" << endl;
-
-          MyList<var> *DG_List = new MyList<var>(Sfx0);
-          DG_List->insert(Sfx0);
-          DG_List->insert(Sfy0);
-          DG_List->insert(Sfz0);
-          Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-          DG_List->clearList();
-        }
-      }
-    }
-    // swap time level
-    if (iter_count < 3)
-    {
-      Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BP = Pp->data->blb;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          cg->swapList(SynchList_pre, SynchList_cor, myrank);
-          if (BP == Pp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        Pp = Pp->next;
-      }
-#ifdef WithShell
-      if (lev == 0)
-      {
-        sPp = SH->PatL;
-        while (sPp)
-        {
-          MyList<Block> *BP = sPp->data->blb;
-          while (BP)
-          {
-            Block *cg = BP->data;
-            cg->swapList(SynchList_pre, SynchList_cor, myrank);
-            if (BP == sPp->data->ble)
-              break;
-            BP = BP->next;
-          }
-          sPp = sPp->next;
-        }
-      }
-#endif
-      // for black hole position
-      if (BH_num > 0 && lev == GH->levels - 1)
-      {
-        for (int ithBH = 0; ithBH < BH_num; ithBH++)
-        {
-          Porg[ithBH][0] = Porg1[ithBH][0];
-          Porg[ithBH][1] = Porg1[ithBH][1];
-          Porg[ithBH][2] = Porg1[ithBH][2];
-        }
-      }
-    }
-  }
-#if (RPS == 0)
-  // mesh refinement boundary part
-  RestrictProlong(lev, YN, BB);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->CS_Inter(SynchList_cor, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "CS_Inter used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds!" << endl;
-    }
-  }
-#endif
-
-#endif
-  // note the data structure before update
-  // SynchList_cor 1   -----------
-  //
-  // StateList     0   -----------
-  //
-  // OldStateList  old -----------
-  // update
-  Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      cg->swapList(StateList, SynchList_cor, myrank);
-      cg->swapList(OldStateList, SynchList_cor, myrank);
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-#ifdef WithShell
-  if (lev == 0)
-  {
-    sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        cg->swapList(StateList, SynchList_cor, myrank);
-        cg->swapList(OldStateList, SynchList_cor, myrank);
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-#if 0
-// check StateList   
-  {
-         SH->Dump_Data(StateList,0,PhysTime,dT_lev);
-         if(myrank == 0)
-	 {
-            cout<<"check StateList"<<endl;
-	    MPI_Abort(MPI_COMM_WORLD,1);
-	 }
-  }
-#endif
-  }
-#endif
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      Porg0[ithBH][0] = Porg1[ithBH][0];
-      Porg0[ithBH][1] = Porg1[ithBH][1];
-      Porg0[ithBH][2] = Porg1[ithBH][2];
-    }
-  }
-}
-#endif
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function sets up the single-step time evolution for each grid level
-// For the case PSTR == 1
-
-//================================================================================================
-
-#elif (PSTR == 1)
-void bssn_class::Step(int lev, int YN)
-{
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"start Step");
-
-  setpbh(BH_num, Porg0, Mass, BH_num_input);
-
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-
-// new code 2013-2-15, zjcao
-#if (MAPBH == 1)
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      for (int ith = 0; ith < 3; ith++)
-        Porg1[ithBH][ith] = Porg0[ithBH][ith] + Porg_rhs[ithBH][ith] * dT_lev;
-      if (Symmetry > 0)
-        Porg1[ithBH][2] = fabs(Porg1[ithBH][2]);
-      if (Symmetry == 2)
-      {
-        Porg1[ithBH][0] = fabs(Porg1[ithBH][0]);
-        Porg1[ithBH][1] = fabs(Porg1[ithBH][1]);
-      }
-      if (!finite(Porg1[ithBH][0]) || !finite(Porg1[ithBH][1]) || !finite(Porg1[ithBH][2]))
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "predictor step finds NaN for BH's position from ("
-                                << Porg0[ithBH][0] << "," << Porg0[ithBH][1] << "," << Porg0[ithBH][2] 
-                                << ")" << endl;
-
-        MyList<var> *DG_List = new MyList<var>(Sfx0);
-        DG_List->insert(Sfx0);
-        DG_List->insert(Sfy0);
-        DG_List->insert(Sfz0);
-        Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-        DG_List->clearList();
-      }
-    }
-  }
-#endif //(MAPBH == 1)
-
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor");
-
-#ifdef With_AHF
-  AH_Step_Find(lev, dT_lev);
-#endif
-  bool BB = fgt(PhysTime, StartTime, dT_lev / 2);
-  double ndeps = numepss;
-  if (lev < GH->movls)
-    ndeps = numepsb;
-  double TRK4 = PhysTime;
-  int iter_count = 0; // count RK4 substeps
-  int pre = 0, cor = 1;
-  int ERROR = 0;
-
-  MyList<ss_patch> *sPp;
-  // Predictor
-  MyList<Patch> *Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-#if (AGM == 0)
-        f_enforce_ga(cg->shape,
-                     cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                     cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                     cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                     cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-        if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                               cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                               cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                               cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                               cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                               cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                               cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                               cg->fgfs[Lap0->sgfn], 
-                               cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                               cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                               cg->fgfs[phi_rhs->sgfn], cg->fgfs[trK_rhs->sgfn],
-                               cg->fgfs[gxx_rhs->sgfn], cg->fgfs[gxy_rhs->sgfn], cg->fgfs[gxz_rhs->sgfn],
-                               cg->fgfs[gyy_rhs->sgfn], cg->fgfs[gyz_rhs->sgfn], cg->fgfs[gzz_rhs->sgfn],
-                               cg->fgfs[Axx_rhs->sgfn], cg->fgfs[Axy_rhs->sgfn], cg->fgfs[Axz_rhs->sgfn],
-                               cg->fgfs[Ayy_rhs->sgfn], cg->fgfs[Ayz_rhs->sgfn], cg->fgfs[Azz_rhs->sgfn],
-                               cg->fgfs[Gmx_rhs->sgfn], cg->fgfs[Gmy_rhs->sgfn], cg->fgfs[Gmz_rhs->sgfn],
-                               cg->fgfs[Lap_rhs->sgfn], 
-                               cg->fgfs[Sfx_rhs->sgfn], cg->fgfs[Sfy_rhs->sgfn], cg->fgfs[Sfz_rhs->sgfn],
-                               cg->fgfs[dtSfx_rhs->sgfn], cg->fgfs[dtSfy_rhs->sgfn], cg->fgfs[dtSfz_rhs->sgfn],
-                               cg->fgfs[rho->sgfn], cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                               cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                               cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                               cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                               cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                               cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                               cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                               cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                               cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                               cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                               cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                               cg->fgfs[Cons_Ham->sgfn],
-                               cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                               cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                               Symmetry, lev, ndeps, pre))
-        {
-          cout << "find NaN in domain: (" 
-               << cg->bbox[0] << ":" << cg->bbox[3] << "," 
-               << cg->bbox[1] << ":" << cg->bbox[4] << ","
-               << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-          ERROR = 1;
-        }
-
-        // rk4 substep and boundary
-        {
-          MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; 
-          // we do not check the correspondence here
-          
-          while (varl0)
-          {
-#if (SommerType == 0)
-#ifndef WithShell
-            if (lev == 0) // sommerfeld indeed
-              f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                   Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                   Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                   cg->fgfs[varlrhs->data->sgfn],
-                                   cg->fgfs[varl0->data->sgfn], 
-                                   varl0->data->propspeed, varl0->data->SoA,
-                                   Symmetry);
-
-#endif
-#endif
-            f_rungekutta4_rout(cg->shape, dT_lev, 
-                               cg->fgfs[varl0->data->sgfn], 
-                               cg->fgfs[varl->data->sgfn], 
-                               cg->fgfs[varlrhs->data->sgfn],
-                               iter_count);
-#ifndef WithShell
-            if (lev > 0) // fix BD point
-#endif
-              f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                dT_lev, 
-                                cg->fgfs[phi0->sgfn],
-                                cg->fgfs[Lap0->sgfn], 
-                                cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], 
-                                varl0->data->SoA,
-                                Symmetry, cor);
-
-#if (SommerType == 1)
-#warning "shell part still bam type"
-            if (lev == 0) // Shibata type sommerfeld
-              f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                dT_lev, 
-                                cg->fgfs[phi0->sgfn],
-                                cg->fgfs[Lap0->sgfn], 
-                                cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], 
-                                varl0->data->SoA,
-                                Symmetry, pre);
-#endif
-
-            varl0 = varl0->next;
-            varl = varl->next;
-            varlrhs = varlrhs->next;
-          }
-        }
-        f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Predictor rhs calculation");
-
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
-  }
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime 
-                              << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor sync");
-
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-
-#if (MAPBH == 0)
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][0], Porg[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][1], Porg[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][2], Porg[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-      if (Symmetry > 0)
-        Porg[ithBH][2] = fabs(Porg[ithBH][2]);
-      if (Symmetry == 2)
-      {
-        Porg[ithBH][0] = fabs(Porg[ithBH][0]);
-        Porg[ithBH][1] = fabs(Porg[ithBH][1]);
-      }
-      if (!finite(Porg[ithBH][0]) || !finite(Porg[ithBH][1]) || !finite(Porg[ithBH][2]))
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "predictor step finds NaN for BH's position from ("
-                                << Porg0[ithBH][0] << "," << Porg0[ithBH][1] << "," << Porg0[ithBH][2] 
-                                << ")" << endl;
-
-        MyList<var> *DG_List = new MyList<var>(Sfx0);
-        DG_List->insert(Sfx0);
-        DG_List->insert(Sfy0);
-        DG_List->insert(Sfz0);
-        Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-        DG_List->clearList();
-      }
-    }
-  }
-#endif
-
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector");
-
-  // corrector
-  for (iter_count = 1; iter_count < 4; iter_count++)
-  {
-    //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"head of Corrector");
-
-    // for RK4: t0, t0+dt/2, t0+dt/2, t0+dt;
-    if (iter_count == 1 || iter_count == 3)
-      TRK4 += dT_lev / 2;
-    Pp = GH->PatL[lev];
-    while (Pp)
-    {
-      MyList<Block> *BP = Pp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-#if (AGM == 0)
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                       cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                       cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                       cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-          if (iter_count == 3)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                         cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                         cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-          if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                 cg->fgfs[phi->sgfn], cg->fgfs[trK->sgfn],
-                                 cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                                 cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                                 cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                                 cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn],
-                                 cg->fgfs[Gmx->sgfn], cg->fgfs[Gmy->sgfn], cg->fgfs[Gmz->sgfn],
-                                 cg->fgfs[Lap->sgfn], 
-                                 cg->fgfs[Sfx->sgfn], cg->fgfs[Sfy->sgfn], cg->fgfs[Sfz->sgfn],
-                                 cg->fgfs[dtSfx->sgfn], cg->fgfs[dtSfy->sgfn], cg->fgfs[dtSfz->sgfn],
-                                 cg->fgfs[phi1->sgfn], cg->fgfs[trK1->sgfn],
-                                 cg->fgfs[gxx1->sgfn], cg->fgfs[gxy1->sgfn], cg->fgfs[gxz1->sgfn],
-                                 cg->fgfs[gyy1->sgfn], cg->fgfs[gyz1->sgfn], cg->fgfs[gzz1->sgfn],
-                                 cg->fgfs[Axx1->sgfn], cg->fgfs[Axy1->sgfn], cg->fgfs[Axz1->sgfn],
-                                 cg->fgfs[Ayy1->sgfn], cg->fgfs[Ayz1->sgfn], cg->fgfs[Azz1->sgfn],
-                                 cg->fgfs[Gmx1->sgfn], cg->fgfs[Gmy1->sgfn], cg->fgfs[Gmz1->sgfn],
-                                 cg->fgfs[Lap1->sgfn], 
-                                 cg->fgfs[Sfx1->sgfn], cg->fgfs[Sfy1->sgfn], cg->fgfs[Sfz1->sgfn],
-                                 cg->fgfs[dtSfx1->sgfn], cg->fgfs[dtSfy1->sgfn], cg->fgfs[dtSfz1->sgfn],
-                                 cg->fgfs[rho->sgfn], 
-                                 cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                                 cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                                 cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                                 cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                                 cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                                 cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                                 cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                                 cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                                 cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                                 cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                                 cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                                 cg->fgfs[Cons_Ham->sgfn],
-                                 cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                                 cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                                 Symmetry, lev, ndeps, cor))
-          {
-            cout << "find NaN in domain: (" 
-                 << cg->bbox[0] << ":" << cg->bbox[3] << "," 
-                 << cg->bbox[1] << ":" << cg->bbox[4] << ","
-                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-            ERROR = 1;
-          }
-          // rk4 substep and boundary
-          {
-            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; 
-            // we do not check the correspondence here
-            
-            while (varl0)
-            {
-#if (SommerType == 0)
-#ifndef WithShell
-              if (lev == 0) // sommerfeld indeed
-                f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                     Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                     Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                     cg->fgfs[varl1->data->sgfn],
-                                     cg->fgfs[varl->data->sgfn], 
-                                     varl0->data->propspeed, varl0->data->SoA,
-                                     Symmetry);
-#endif
-#endif
-              f_rungekutta4_rout(cg->shape, dT_lev, 
-                                 cg->fgfs[varl0->data->sgfn], 
-                                 cg->fgfs[varl1->data->sgfn], 
-                                 cg->fgfs[varlrhs->data->sgfn],
-                                 iter_count);
-
-#ifndef WithShell
-              if (lev > 0) // fix BD point
-#endif
-                f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                  Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                  Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                  dT_lev, 
-                                  cg->fgfs[phi0->sgfn],
-                                  cg->fgfs[Lap0->sgfn], 
-                                  cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], 
-                                  varl0->data->SoA,
-                                  Symmetry, cor);
-
-#if (SommerType == 1)
-              if (lev == 1) // shibata type sommerfeld
-                f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                  Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], 
-                                  Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                  dT_lev, 
-                                  cg->fgfs[phi0->sgfn],
-                                  cg->fgfs[Lap0->sgfn], 
-                                  cg->fgfs[varl->data->sgfn], cg->fgfs[varl1->data->sgfn], 
-                                  varl0->data->SoA,
-                                  Symmetry, cor);
-#endif
-
-              varl0 = varl0->next;
-              varl = varl->next;
-              varl1 = varl1->next;
-              varlrhs = varlrhs->next;
-            }
-          }
-          f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-        }
-        if (BP == Pp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      Pp = Pp->next;
-    }
-
-    //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector error check");
-
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
-    }
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector sync");
-
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector sync");
-
-#if (MAPBH == 0)
-    // for black hole position
-    if (BH_num > 0 && lev == GH->levels - 1)
-    {
-      compute_Porg_rhs(Porg, Porg1, Sfx, Sfy, Sfz, lev);
-      for (int ithBH = 0; ithBH < BH_num; ithBH++)
-      {
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][0], Porg1[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][1], Porg1[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][2], Porg1[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-        if (Symmetry > 0)
-          Porg1[ithBH][2] = fabs(Porg1[ithBH][2]);
-        if (Symmetry == 2)
-        {
-          Porg1[ithBH][0] = fabs(Porg1[ithBH][0]);
-          Porg1[ithBH][1] = fabs(Porg1[ithBH][1]);
-        }
-        if (!finite(Porg1[ithBH][0]) || !finite(Porg1[ithBH][1]) || !finite(Porg1[ithBH][2]))
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << iter_count << " corrector step finds NaN for BH's position from ("
-                                  << Porg[ithBH][0] << "," << Porg[ithBH][1] << "," << Porg[ithBH][2] 
-                                  << ")" << endl;
-
-          MyList<var> *DG_List = new MyList<var>(Sfx0);
-          DG_List->insert(Sfx0);
-          DG_List->insert(Sfy0);
-          DG_List->insert(Sfz0);
-          Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-          DG_List->clearList();
-        }
-      }
-    }
-//    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector of black hole position");
-#endif
-
-    // swap time level
-    if (iter_count < 3)
-    {
-      Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BP = Pp->data->blb;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          cg->swapList(SynchList_pre, SynchList_cor, myrank);
-          if (BP == Pp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        Pp = Pp->next;
-      }
-      //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after pre cor swap");
-
-#if (MAPBH == 0)
-      // for black hole position
-      if (BH_num > 0 && lev == GH->levels - 1)
-      {
-        for (int ithBH = 0; ithBH < BH_num; ithBH++)
-        {
-          Porg[ithBH][0] = Porg1[ithBH][0];
-          Porg[ithBH][1] = Porg1[ithBH][1];
-          Porg[ithBH][2] = Porg1[ithBH][2];
-        }
-      }
-#endif
-    }
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"tail of corrector");
-  }
-#if (RPS == 0)
-  // mesh refinement boundary part
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before RestrictProlong");
-  RestrictProlong(lev, YN, BB);
-#endif
-  // note the data structure before update
-  // SynchList_cor 1   -----------
-  //
-  // StateList     0   -----------
-  //
-  // OldStateList  old -----------
-  // update
-  Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      cg->swapList(StateList, SynchList_cor, myrank);
-      cg->swapList(OldStateList, SynchList_cor, myrank);
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      Porg0[ithBH][0] = Porg1[ithBH][0];
-      Porg0[ithBH][1] = Porg1[ithBH][1];
-      Porg0[ithBH][2] = Porg1[ithBH][2];
-      // if(myrank==GH->start_rank[lev]) 
-      //     cout<<Porg0[ithBH][0]<<","<<Porg0[ithBH][1]<<","<<Porg0[ithBH][2]<<endl;
-    }
-  }
-
-  //     if(myrank==GH->start_rank[lev]) cout<<GH->mylev<<endl;
-  //     misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"complet GH Step");
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function sets up the single-step time evolution for the spherical shell
-// grid part during the time evolution process
-
-//================================================================================================
-
-#ifdef WithShell
-void bssn_class::SHStep()
-{
-  int lev = 0;
-  // #if (PSTR == 1)
-  //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"start Step");
-  // #endif
-
-  setpbh(BH_num, Porg0, Mass, BH_num_input);
-
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-
-  // #if (PSTR == 1)
-  //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor");
-  // #endif
-
-#ifdef With_AHF
-  AH_Step_Find(lev, dT_lev);
-#endif
-  bool BB = fgt(PhysTime, StartTime, dT_lev / 2);
-  double ndeps = numepss;
-  if (lev < GH->movls)
-    ndeps = numepsb;
-  double TRK4 = PhysTime;
-  int iter_count = 0; // count RK4 substeps
-  int pre = 0, cor = 1;
-  int ERROR = 0;
-
-  MyList<ss_patch> *sPp;
-  // Predictor
-  sPp = SH->PatL;
-  while (sPp)
-  {
-    MyList<Block> *BP = sPp->data->blb;
-    int fngfs = sPp->data->fngfs;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-#if (AGM == 0)
-        f_enforce_ga(cg->shape,
-                     cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                     cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                     cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                     cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-#ifdef USE_GPU
-        if (use_gpu == 1)
-        {
-
-          if (gpu_rhs_ss(CALLED_BY_STEP, myrank, RHS_PARA_CALLED_FIRST_TIME))
-
-          {
-
-            cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" 
-                 << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                 << cg->bbox[1] << ":" << cg->bbox[4] << "," 
-                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-
-            ERROR = 1;
-          }
-        }
-        else
-        {
-          if (f_compute_rhs_bssn_ss(RHS_PARA_CALLED_FIRST_TIME))
-
-          {
-
-            cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" 
-                 << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                 << cg->bbox[1] << ":" << cg->bbox[4] << "," 
-                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-
-            ERROR = 1;
-          }
-        }
-
-#else
-        if (f_compute_rhs_bssn_ss(RHS_PARA_CALLED_FIRST_TIME))
-
-        {
-
-          cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" 
-               << cg->bbox[0] << ":" << cg->bbox[3] << ","
-               << cg->bbox[1] << ":" << cg->bbox[4] << "," 
-               << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-
-          ERROR = 1;
-        }
-#endif // USE_GPU
-
-        // rk4 substep and boundary
-        {
-          MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; 
-          // we do not check the correspondence here
-          
-          while (varl0)
-          {
-            // sommerfeld indeed for outter boudary while fix BD for inner boundary
-            f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                    sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], 
-                                    sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                    cg->fgfs[varlrhs->data->sgfn],
-                                    cg->fgfs[varl0->data->sgfn], 
-                                    varl0->data->propspeed, varl0->data->SoA,
-                                    Symmetry);
-
-            f_rungekutta4_rout(cg->shape, dT_lev, 
-                               cg->fgfs[varl0->data->sgfn], 
-                               cg->fgfs[varl->data->sgfn], 
-                               cg->fgfs[varlrhs->data->sgfn],
-                               iter_count);
-
-            varl0 = varl0->next;
-            varl = varl->next;
-            varlrhs = varlrhs->next;
-          }
-        }
-        f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-      }
-      if (BP == sPp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    sPp = sPp->next;
-  }
-
-#if (PSTR == 1)
-//   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor's error check");
-#endif
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-
-  if (ERROR)
-  {
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "Shell stuff synchronization used " 
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds!" << endl;
-    }
-  }
-
-  // corrector
-  for (iter_count = 1; iter_count < 4; iter_count++)
-  {
-    // for RK4: t0, t0+dt/2, t0+dt/2, t0+dt;
-    if (iter_count == 1 || iter_count == 3)
-      TRK4 += dT_lev / 2;
-
-    {
-      sPp = SH->PatL;
-      while (sPp)
-      {
-        MyList<Block> *BP = sPp->data->blb;
-        int fngfs = sPp->data->fngfs;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          if (myrank == cg->rank)
-          {
-#if (AGM == 0)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                         cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                         cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-            if (iter_count == 3)
-              f_enforce_ga(cg->shape,
-                           cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                           cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                           cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                           cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-#ifdef USE_GPU
-            if (use_gpu == 1)
-            {
-
-             if(gpu_rhs_ss(CALLED_BY_STEP,myrank,RHS_PARA_CALLED_THEN)
-
-		     {
-                cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" 
-                     << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                     << cg->bbox[1] << ":" << cg->bbox[4] << "," 
-                     << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-
-                ERROR = 1;
-
-		     }
-            }
-            else
-            {
-              if (f_compute_rhs_bssn_ss(RHS_PARA_CALLED_THEN))
-
-              {
-
-                cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" 
-                     << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                     << cg->bbox[1] << ":" << cg->bbox[4] << "," 
-                     << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-
-                ERROR = 1;
-              }
-            }
-
-#else
-            if (f_compute_rhs_bssn_ss(RHS_PARA_CALLED_THEN))
-
-            {
-
-              cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" 
-                   << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                   << cg->bbox[1] << ":" << cg->bbox[4] << "," 
-                   << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-
-              ERROR = 1;
-            }
-#endif // USE_GPU
-       // rk4 substep and boundary
-            {
-              MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; 
-              // we do not check the correspondence here
-              
-              while (varl0)
-              {
-                // sommerfeld indeed for outter boudary while fix BD for inner boundary
-                f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                        sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], 
-                                        sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                        cg->fgfs[varl1->data->sgfn],
-                                        cg->fgfs[varl->data->sgfn], 
-                                        varl0->data->propspeed, varl0->data->SoA,
-                                        Symmetry);
-
-                f_rungekutta4_rout(cg->shape, dT_lev, 
-                                   cg->fgfs[varl0->data->sgfn], 
-                                   cg->fgfs[varl1->data->sgfn], 
-                                   cg->fgfs[varlrhs->data->sgfn],
-                                   iter_count);
-
-                varl0 = varl0->next;
-                varl = varl->next;
-                varl1 = varl1->next;
-                varlrhs = varlrhs->next;
-              }
-            }
-            f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-          }
-          if (BP == sPp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        sPp = sPp->next;
-      }
-    }
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
-    {
-      clock_t prev_clock, curr_clock;
-      if (myrank == 0)
-        curr_clock = clock();
-      SH->Synch(SynchList_cor, Symmetry);
-      if (myrank == 0)
-      {
-        prev_clock = curr_clock;
-        curr_clock = clock();
-        cout << "Shell stuff synchronization used " 
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-             << " seconds!" << endl;
-      }
-    }
-
-    sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        cg->swapList(SynchList_pre, SynchList_cor, myrank);
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-  }
-#if (RPS == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->CS_Inter(SynchList_cor, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "CS_Inter used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds!" << endl;
-    }
-  }
-#endif
-  // note the data structure before update
-  // SynchList_cor 1   -----------
-  //
-  // StateList     0   -----------
-  //
-  // OldStateList  old -----------
-  // update
-  sPp = SH->PatL;
-  while (sPp)
-  {
-    MyList<Block> *BP = sPp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      cg->swapList(StateList, SynchList_cor, myrank);
-      cg->swapList(OldStateList, SynchList_cor, myrank);
-      if (BP == sPp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    sPp = sPp->next;
-  }
-}
-#endif
-#endif // withshell
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// 0: do not use mixing two levels data for OutBD; 1: do use
-
-#define MIXOUTB 0
-void bssn_class::RestrictProlong(int lev, int YN, bool BB,
-                                 MyList<var> *SL, MyList<var> *OL, MyList<var> *corL)
-// we assume
-// StateList      1   -----------
-//
-// OldStateList   0   -----------
-//
-// SynchList_cor  old -----------
-{
-#if (PSTR == 1)
-//  stringstream a_stream;
-//  a_stream.setf(ios::left);
-#endif
-
-  if (lev > 0)
-  {
-    MyList<Patch> *Pp, *Ppc;
-    if (lev > trfls && YN == 0) // time refinement levels and for intermediat time level
-    {
-      Pp = GH->PatL[lev - 1];
-      while (Pp)
-      {
-        if (BB)
-          Parallel::prepare_inter_time_level(Pp->data, SL, OL, corL,
-                                             SynchList_pre, 0); // use SynchList_pre as temporal storage space
-        else
-          Parallel::prepare_inter_time_level(Pp->data, SL, OL,
-                                             SynchList_pre, 0); // use SynchList_pre as temporal storage space
-
-#if (PSTR == 1)
-//	 Pp->data->checkPatch(0,GH->start_rank[GH->mylev]);
-#endif
-        Pp = Pp->next;
-      }
-
-#if (PSTR == 1)
-//       Pp=GH->PatL[lev];
-//       while(Pp)
-//       {
-//	 Pp->data->checkPatch(0,GH->start_rank[GH->mylev]);
-//	 Pp=Pp->next;
-//       }
-
-//       a_stream.clear();
-//       a_stream.str("");
-//       a_stream<<GH->mylev<<": 0 before Restrict";
-//       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
-#endif
-
-#if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry);
-#elif (RPB == 1)
-      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SynchList_pre,Symmetry);
-      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
-#endif
-
-#if (PSTR == 1)
-//       a_stream.clear();
-//       a_stream.str("");
-//       a_stream<<GH->mylev<<": 0 after Restrict";
-//       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
-#endif
-
-      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
-
-#if (PSTR == 1)
-//       a_stream.clear();
-//       a_stream.str("");
-//       a_stream<<GH->mylev<<": 0 after Sync";
-//       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
-#endif
-
-#if (RPB == 0)
-      Ppc = GH->PatL[lev - 1];
-      while (Ppc)
-      {
-        Pp = GH->PatL[lev];
-        while (Pp)
-        {
-#if (MIXOUTB == 0)
-          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
-#elif (MIXOUTB == 1)
-          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
-#endif
-          Pp = Pp->next;
-        }
-        Ppc = Ppc->next;
-      }
-#elif (RPB == 1)
-      //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SL,Symmetry);
-      Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, GH->bdsul[lev], Symmetry);
-#endif
-
-#if (PSTR == 1)
-//       a_stream.clear();
-//       a_stream.str("");
-//       a_stream<<GH->mylev<<": 0 after OutBdLow2Hi";
-//       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
-#endif
-    }
-    else // no time refinement levels and for all same time levels
-    {
-
-#if (PSTR == 1)
-//       a_stream.clear();
-//       a_stream.str("");
-//       a_stream<<GH->mylev<<": 1 before Restrict";
-//       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
-#endif
-
-#if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
-#elif (RPB == 1)
-      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
-      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
-#endif
-
-#if (PSTR == 1)
-//       a_stream.clear();
-//       a_stream.str("");
-//       a_stream<<GH->mylev<<": 1 before Sync";
-//       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
-#endif
-
-      Parallel::Sync(GH->PatL[lev - 1], SL, Symmetry);
-
-#if (PSTR == 1)
-//       a_stream.clear();
-//       a_stream.str("");
-//       a_stream<<GH->mylev<<": 1 after Sync";
-//       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
-#endif
-
-#if (RPB == 0)
-      Ppc = GH->PatL[lev - 1];
-      while (Ppc)
-      {
-        Pp = GH->PatL[lev];
-        while (Pp)
-        {
-#if (MIXOUTB == 0)
-          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SL, SL, Symmetry);
-#elif (MIXOUTB == 1)
-          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SL, SL, Symmetry);
-#endif
-          Pp = Pp->next;
-        }
-        Ppc = Ppc->next;
-      }
-#elif (RPB == 1)
-      //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
-      Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->bdsul[lev], Symmetry);
-#endif
-
-#if (PSTR == 1)
-//       a_stream.clear();
-//       a_stream.str("");
-//       a_stream<<GH->mylev<<": 1 after OutBdLow2Hi";
-//       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
-#endif
-    }
-
-    Parallel::Sync(GH->PatL[lev], SL, Symmetry);
-
-#if (PSTR == 1)
-//    a_stream.clear();
-//    a_stream.str("");
-//    a_stream<<GH->mylev<<": after Sync";
-//    misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
-#endif
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// auxiliary operation, input lev means original lev-1
-
-void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
-                                     MyList<var> *SL, MyList<var> *OL, MyList<var> *corL)
-// we assume
-// StateList      1   -----------
-//
-// OldStateList   0   -----------
-//
-// SynchList_cor  old -----------
-{
-  //  misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"starting RestrictProlong_aux");
-
-  if (lev >= GH->levels - 1)
-    return;
-  lev = lev + 1;
-
-  if (lev > 0)
-  {
-    MyList<Patch> *Pp, *Ppc;
-    if (lev > trfls && YN == 0) // time refinement levels and for intermediat time level
-    {
-      Pp = GH->PatL[lev - 1];
-      while (Pp)
-      {
-        if (BB)
-          Parallel::prepare_inter_time_level(Pp->data, SL, OL, corL,
-                                             SynchList_pre, 0); // use SynchList_pre as temporal storage space
-        else
-          Parallel::prepare_inter_time_level(Pp->data, SL, OL,
-                                             SynchList_pre, 0); // use SynchList_pre as temporal storage space
-        Pp = Pp->next;
-      }
-
-#if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry);
-#elif (RPB == 1)
-      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SynchList_pre,Symmetry);
-      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
-#endif
-
-      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
-
-#if (RPB == 0)
-      Ppc = GH->PatL[lev - 1];
-      while (Ppc)
-      {
-        Pp = GH->PatL[lev];
-        while (Pp)
-        {
-#if (MIXOUTB == 0)
-          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
-#elif (MIXOUTB == 1)
-          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
-#endif
-          Pp = Pp->next;
-        }
-        Ppc = Ppc->next;
-      }
-#elif (RPB == 1)
-      //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SL,Symmetry);
-      Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, GH->bdsul[lev], Symmetry);
-#endif
-    }
-    else // no time refinement levels and for all same time levels
-    {
-#if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
-#elif (RPB == 1)
-      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
-      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
-#endif
-
-      Parallel::Sync(GH->PatL[lev - 1], SL, Symmetry);
-
-#if (RPB == 0)
-      Ppc = GH->PatL[lev - 1];
-      while (Ppc)
-      {
-        Pp = GH->PatL[lev];
-        while (Pp)
-        {
-#if (MIXOUTB == 0)
-          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SL, SL, Symmetry);
-#elif (MIXOUTB == 1)
-          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SL, SL, Symmetry);
-#endif
-          Pp = Pp->next;
-        }
-        Ppc = Ppc->next;
-      }
-#elif (RPB == 1)
-      //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
-      Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->bdsul[lev], Symmetry);
-#endif
-    }
-
-    Parallel::Sync(GH->PatL[lev], SL, Symmetry);
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-void bssn_class::RestrictProlong(int lev, int YN, bool BB)
-{
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-  // we assume  for fine
-  // SynchList_cor 1   -----------
-  //
-  // StateList     0   -----------
-  //
-  // OldStateList  old -----------
-  //            for coarse
-  // StateList      1   -----------
-  //
-  // OldStateList   0   -----------
-  //
-  // SynchList_cor  old -----------
-  if (lev > 0)
-  {
-    MyList<Patch> *Pp, *Ppc;
-    if (lev > trfls && YN == 0) // time refinement levels and for intermediat time level
-    {
-      if (myrank == 0)
-        cout << "/=: " << GH->Lt[lev - 1] << "," << GH->Lt[lev] + dT_lev << endl;
-      Pp = GH->PatL[lev - 1];
-      while (Pp)
-      {
-        if (BB)
-          Parallel::prepare_inter_time_level(Pp->data, StateList, OldStateList, SynchList_cor,
-                                             SynchList_pre, 0); // use SynchList_pre as temporal storage space
-        else
-          Parallel::prepare_inter_time_level(Pp->data, StateList, OldStateList,
-                                             SynchList_pre, 0); // use SynchList_pre as temporal storage space
-        Pp = Pp->next;
-      }
-
-#if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, Symmetry);
-#elif (RPB == 1)
-      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_cor,SynchList_pre,Symmetry);
-      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, GH->rsul[lev], Symmetry);
-#endif
-
-      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
-
-#if (RPB == 0)
-      Ppc = GH->PatL[lev - 1];
-      while (Ppc)
-      {
-        Pp = GH->PatL[lev];
-        while (Pp)
-        {
-#if (MIXOUTB == 0)
-          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
-#elif (MIXOUTB == 1)
-          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
-#endif
-          Pp = Pp->next;
-        }
-        Ppc = Ppc->next;
-      }
-#elif (RPB == 1)
-      //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SynchList_cor,Symmetry);
-      Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, GH->bdsul[lev], Symmetry);
-#endif
-    }
-    else // no time refinement levels and for all same time levels
-    {
-      if (myrank == 0)
-        cout << "===: " << GH->Lt[lev - 1] << "," << GH->Lt[lev] + dT_lev << endl;
-#if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
-#elif (RPB == 1)
-      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_cor,StateList,Symmetry);
-      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, GH->rsul[lev], Symmetry);
-#endif
-
-      Parallel::Sync(GH->PatL[lev - 1], StateList, Symmetry);
-
-#if (RPB == 0)
-      Ppc = GH->PatL[lev - 1];
-      while (Ppc)
-      {
-        Pp = GH->PatL[lev];
-        while (Pp)
-        {
-#if (MIXOUTB == 0)
-          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
-#elif (MIXOUTB == 1)
-          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
-#endif
-          Pp = Pp->next;
-        }
-        Ppc = Ppc->next;
-      }
-#elif (RPB == 1)
-      //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],StateList,SynchList_cor,Symmetry);
-      Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, GH->bdsul[lev], Symmetry);
-#endif
-    }
-
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
-{
-  if (lev > 0)
-  {
-    MyList<Patch> *Pp, *Ppc;
-    if (lev > trfls && YN == 0) // time refinement levels and for intermediat time level
-    {
-      Pp = GH->PatL[lev - 1];
-      while (Pp)
-      {
-        if (BB)
-          Parallel::prepare_inter_time_level(Pp->data, StateList, OldStateList, SynchList_cor,
-                                             SynchList_pre, 0); // use SynchList_pre as temporal storage space
-        else
-          Parallel::prepare_inter_time_level(Pp->data, StateList, OldStateList,
-                                             SynchList_pre, 0); // use SynchList_pre as temporal storage space
-        Pp = Pp->next;
-      }
-
-#if (RPB == 0)
-      Ppc = GH->PatL[lev - 1];
-      while (Ppc)
-      {
-        Pp = GH->PatL[lev];
-        while (Pp)
-        {
-#if (MIXOUTB == 0)
-          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
-#elif (MIXOUTB == 1)
-          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
-#endif
-          Pp = Pp->next;
-        }
-        Ppc = Ppc->next;
-      }
-#elif (RPB == 1)
-      //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SynchList_cor,Symmetry);
-      Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, GH->bdsul[lev], Symmetry);
-#endif
-    }
-    else // no time refinement levels and for all same time levels
-    {
-#if (RPB == 0)
-      Ppc = GH->PatL[lev - 1];
-      while (Ppc)
-      {
-        Pp = GH->PatL[lev];
-        while (Pp)
-        {
-#if (MIXOUTB == 0)
-          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
-#elif (MIXOUTB == 1)
-          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
-#endif
-          Pp = Pp->next;
-        }
-        Ppc = Ppc->next;
-      }
-#elif (RPB == 1)
-      //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],StateList,SynchList_cor,Symmetry);
-      Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, GH->bdsul[lev], Symmetry);
-#endif
-
-#if 0
-#if (RPB == 0)
-       Parallel::Restrict(GH->PatL[lev-1],GH->PatL[lev],SynchList_cor,StateList,Symmetry);
-#elif (RPB == 1)
-//       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_cor,StateList,Symmetry);
-       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_cor,StateList,GH->rsul[lev],Symmetry);
-#endif
-#else
-      Parallel::Restrict_after(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
-#endif
-      Parallel::Sync(GH->PatL[lev - 1], StateList, Symmetry);
-    }
-
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-  }
-}
-#undef MIXOUTB
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function computes the gravitational radiation scalar Psi4
-
-//================================================================================================
-
-void bssn_class::Compute_Psi4(int lev)
-{
-  MyList<var> *DG_List = new MyList<var>(Rpsi4);
-  DG_List->insert(Ipsi4);
-
-#if 0 // test showes this operation does not help    
-for(int ilev = GH->levels-1;ilev>=lev;ilev--)
-{
-  MyList<Patch> *Pp=GH->PatL[ilev];
-#else
-  MyList<Patch> *Pp = GH->PatL[lev];
-#endif
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-#if (Psi4type == 0)
-        if (0) // if Gamma^i_jk and R_ij can be reused from the rhs calculation
-          f_ricci_gamma(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                        cg->fgfs[phi0->sgfn],
-                        cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                        cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                        cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                        cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                        cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                        cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                        cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                        cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                        cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                        cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                        cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                        Symmetry);
-        // the input arguments Gamma^i_jk and R_ij do not need synch, because we do not need to derivate them
-        f_getnp4(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                 cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                 cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                 cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                 cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                 cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                 cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                 cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                 cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                 cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                 cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                 cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                 cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                 cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                 cg->fgfs[Rpsi4->sgfn], cg->fgfs[Ipsi4->sgfn],
-                 Symmetry);
-#elif (Psi4type == 1)
-        f_getnp4old(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                    cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                    cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                    cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                    cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                    cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                    cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                    cg->fgfs[Lap0->sgfn], 
-                    cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                    cg->fgfs[Rpsi4->sgfn], cg->fgfs[Ipsi4->sgfn],
-                    Symmetry);
-#else
-#error "not recognized Psi4type"
-#endif
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-
-#if 0  
-    Parallel::Sync(GH->PatL[ilev],DG_List,Symmetry);
-}
-// because of double level data change, you can not do this in above loop
-// prolong restrict Psi4
-for(int ilev=GH->levels-1;ilev>lev;ilev--)
-    RestrictProlong(ilev,1,false,DG_List,DG_List,DG_List);
-#else
-  Parallel::Sync(GH->PatL[lev], DG_List, Symmetry);
-#endif
-
-#ifdef WithShell
-  // ShellPatch part
-  if (lev == 0)
-  {
-    MyList<ss_patch> *Pp = SH->PatL;
-    while (Pp)
-    {
-      MyList<Block> *BL = Pp->data->blb;
-      int fngfs = Pp->data->fngfs;
-      while (BL)
-      {
-        Block *cg = BL->data;
-        if (myrank == cg->rank)
-        {
-#if (Psi4type == 0)
-          if (0) // if Gamma^i_jk and R_ij can be reused from the rhs calculation
-            f_ricci_gamma_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                             cg->fgfs[fngfs + ShellPatch::gx], 
-                             cg->fgfs[fngfs + ShellPatch::gy], 
-                             cg->fgfs[fngfs + ShellPatch::gz],
-                             cg->fgfs[fngfs + ShellPatch::drhodx], 
-                             cg->fgfs[fngfs + ShellPatch::drhody], 
-                             cg->fgfs[fngfs + ShellPatch::drhodz],
-                             cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                             cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                             cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                             cg->fgfs[fngfs + ShellPatch::dRdx], 
-                             cg->fgfs[fngfs + ShellPatch::dRdy], 
-                             cg->fgfs[fngfs + ShellPatch::dRdz],
-                             cg->fgfs[fngfs + ShellPatch::drhodxx], 
-                             cg->fgfs[fngfs + ShellPatch::drhodxy], 
-                             cg->fgfs[fngfs + ShellPatch::drhodxz],
-                             cg->fgfs[fngfs + ShellPatch::drhodyy], 
-                             cg->fgfs[fngfs + ShellPatch::drhodyz], 
-                             cg->fgfs[fngfs + ShellPatch::drhodzz],
-                             cg->fgfs[fngfs + ShellPatch::dsigmadxx], 
-                             cg->fgfs[fngfs + ShellPatch::dsigmadxy], 
-                             cg->fgfs[fngfs + ShellPatch::dsigmadxz],
-                             cg->fgfs[fngfs + ShellPatch::dsigmadyy], 
-                             cg->fgfs[fngfs + ShellPatch::dsigmadyz], 
-                             cg->fgfs[fngfs + ShellPatch::dsigmadzz],
-                             cg->fgfs[fngfs + ShellPatch::dRdxx], 
-                             cg->fgfs[fngfs + ShellPatch::dRdxy], 
-                             cg->fgfs[fngfs + ShellPatch::dRdxz],
-                             cg->fgfs[fngfs + ShellPatch::dRdyy], 
-                             cg->fgfs[fngfs + ShellPatch::dRdyz], 
-                             cg->fgfs[fngfs + ShellPatch::dRdzz],
-                             cg->fgfs[phi0->sgfn],
-                             cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                             cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                             cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                             cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                             cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                             cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                             cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                             cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                             cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                             cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                             cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                             Symmetry, lev, Pp->data->sst);
-
-          f_getnp4_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                      cg->fgfs[fngfs + ShellPatch::gx], 
-                      cg->fgfs[fngfs + ShellPatch::gy], 
-                      cg->fgfs[fngfs + ShellPatch::gz],
-                      cg->fgfs[fngfs + ShellPatch::drhodx], 
-                      cg->fgfs[fngfs + ShellPatch::drhody], 
-                      cg->fgfs[fngfs + ShellPatch::drhodz],
-                      cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                      cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                      cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                      cg->fgfs[fngfs + ShellPatch::dRdx], 
-                      cg->fgfs[fngfs + ShellPatch::dRdy], 
-                      cg->fgfs[fngfs + ShellPatch::dRdz],
-                      cg->fgfs[fngfs + ShellPatch::drhodxx], 
-                      cg->fgfs[fngfs + ShellPatch::drhodxy], 
-                      cg->fgfs[fngfs + ShellPatch::drhodxz],
-                      cg->fgfs[fngfs + ShellPatch::drhodyy], 
-                      cg->fgfs[fngfs + ShellPatch::drhodyz], 
-                      cg->fgfs[fngfs + ShellPatch::drhodzz],
-                      cg->fgfs[fngfs + ShellPatch::dsigmadxx], 
-                      cg->fgfs[fngfs + ShellPatch::dsigmadxy], 
-                      cg->fgfs[fngfs + ShellPatch::dsigmadxz],
-                      cg->fgfs[fngfs + ShellPatch::dsigmadyy], 
-                      cg->fgfs[fngfs + ShellPatch::dsigmadyz], 
-                      cg->fgfs[fngfs + ShellPatch::dsigmadzz],
-                      cg->fgfs[fngfs + ShellPatch::dRdxx], 
-                      cg->fgfs[fngfs + ShellPatch::dRdxy], 
-                      cg->fgfs[fngfs + ShellPatch::dRdxz],
-                      cg->fgfs[fngfs + ShellPatch::dRdyy], 
-                      cg->fgfs[fngfs + ShellPatch::dRdyz], 
-                      cg->fgfs[fngfs + ShellPatch::dRdzz],
-                      cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                      cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                      cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                      cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                      cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                      cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                      cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                      cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                      cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                      cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                      cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                      cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                      cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                      cg->fgfs[Rpsi4->sgfn], cg->fgfs[Ipsi4->sgfn],
-                      Symmetry, Pp->data->sst);
-#elif (Psi4type == 1)
-          f_getnp4old_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                         cg->fgfs[fngfs + ShellPatch::gx], 
-                         cg->fgfs[fngfs + ShellPatch::gy], 
-                         cg->fgfs[fngfs + ShellPatch::gz],
-                         cg->fgfs[fngfs + ShellPatch::drhodx], 
-                         cg->fgfs[fngfs + ShellPatch::drhody], 
-                         cg->fgfs[fngfs + ShellPatch::drhodz],
-                         cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                         cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                         cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                         cg->fgfs[fngfs + ShellPatch::dRdx], 
-                         cg->fgfs[fngfs + ShellPatch::dRdy], 
-                         cg->fgfs[fngfs + ShellPatch::dRdz],
-                         cg->fgfs[fngfs + ShellPatch::drhodxx], 
-                         cg->fgfs[fngfs + ShellPatch::drhodxy], 
-                         cg->fgfs[fngfs + ShellPatch::drhodxz],
-                         cg->fgfs[fngfs + ShellPatch::drhodyy], 
-                         cg->fgfs[fngfs + ShellPatch::drhodyz], 
-                         cg->fgfs[fngfs + ShellPatch::drhodzz],
-                         cg->fgfs[fngfs + ShellPatch::dsigmadxx], 
-                         cg->fgfs[fngfs + ShellPatch::dsigmadxy], 
-                         cg->fgfs[fngfs + ShellPatch::dsigmadxz],
-                         cg->fgfs[fngfs + ShellPatch::dsigmadyy], 
-                         cg->fgfs[fngfs + ShellPatch::dsigmadyz], 
-                         cg->fgfs[fngfs + ShellPatch::dsigmadzz],
-                         cg->fgfs[fngfs + ShellPatch::dRdxx], 
-                         cg->fgfs[fngfs + ShellPatch::dRdxy], 
-                         cg->fgfs[fngfs + ShellPatch::dRdxz],
-                         cg->fgfs[fngfs + ShellPatch::dRdyy], 
-                         cg->fgfs[fngfs + ShellPatch::dRdyz], 
-                         cg->fgfs[fngfs + ShellPatch::dRdzz],
-                         cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                         cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                         cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                         cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                         cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                         cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                         cg->fgfs[Lap0->sgfn], 
-                         cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                         cg->fgfs[Rpsi4->sgfn], cg->fgfs[Ipsi4->sgfn],
-                         Symmetry, Pp->data->sst);
-#else
-#error "not recognized Psi4type"
-#endif
-        }
-        if (BL == Pp->data->ble)
-          break;
-        BL = BL->next;
-      }
-      Pp = Pp->next;
-    }
-
-    SH->Synch(DG_List, Symmetry);
-#if 0     
-// interpolate Psi4
-     SH->CS_Inter(DG_List,Symmetry);
-#endif
-  }
-#endif
-
-  DG_List->clearList();
-
-  //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"end of Compute_Psi4");
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function sets the puncture positions of black holes at the initial time
-
-//================================================================================================
-
-void bssn_class::Setup_Black_Hole_position()
-{
-  char filename[50];
-  strcpy(filename, "input.par");
-  // read parameter from file
-  {
-    const int LEN = 256;
-    char pline[LEN];
-    string str, sgrp, skey, sval;
-    int sind;
-    ifstream inf(filename, ifstream::in);
-    if (!inf.good() && myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "Can not open parameter file " << filename 
-                              << " for inputing information of black holes" << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-
-    for (int i = 1; inf.good(); i++)
-    {
-      inf.getline(pline, LEN);
-      str = pline;
-
-      int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-      if (status == -1)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "error reading parameter file " << filename 
-                                << " in line " << i << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-      else if (status == 0)
-        continue;
-
-      if (sgrp == "BSSN" && skey == "BH_num")
-      {
-        BH_num_input = BH_num = atoi(sval.c_str());
-        break;
-      }
-    }
-    inf.close();
-  }
-  // set up the data for black holes
-  // these arrays will be deleted when bssn_class is deleted
-  Pmom = new double[3 * BH_num];
-  Spin = new double[3 * BH_num];
-  Mass = new double[BH_num];
-  Porg0 = new double *[BH_num];
-  Porgbr = new double *[BH_num];
-  Porg = new double *[BH_num];
-  Porg1 = new double *[BH_num];
-  Porg_rhs = new double *[BH_num];
-  for (int i = 0; i < BH_num; i++)
-  {
-    Porg0[i] = new double[3];
-    Porgbr[i] = new double[3];
-    Porg[i] = new double[3];
-    Porg1[i] = new double[3];
-    Porg_rhs[i] = new double[3];
-  }
-  // read parameter from file
-  {
-    const int LEN = 256;
-    char pline[LEN];
-    string str, sgrp, skey, sval;
-    int sind;
-    ifstream inf(filename, ifstream::in);
-    if (!inf.good() && myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "Can not open parameter file " << filename
-                              << " for inputing information of black holes" << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-
-    for (int i = 1; inf.good(); i++)
-    {
-      inf.getline(pline, LEN);
-      str = pline;
-
-      int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-      if (status == -1)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "error reading parameter file " << filename 
-                                << " in line " << i << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-      else if (status == 0)
-        continue;
-
-      if (sgrp == "BSSN" && sind < BH_num)
-      {
-        if (skey == "Mass")
-          Mass[sind] = atof(sval.c_str());
-        else if (skey == "Porgx")
-          Porg0[sind][0] = atof(sval.c_str());
-        else if (skey == "Porgy")
-          Porg0[sind][1] = atof(sval.c_str());
-        else if (skey == "Porgz")
-          Porg0[sind][2] = atof(sval.c_str());
-        else if (skey == "Spinx")
-          Spin[sind * 3] = atof(sval.c_str());
-        else if (skey == "Spiny")
-          Spin[sind * 3 + 1] = atof(sval.c_str());
-        else if (skey == "Spinz")
-          Spin[sind * 3 + 2] = atof(sval.c_str());
-        else if (skey == "Pmomx")
-          Pmom[sind * 3] = atof(sval.c_str());
-        else if (skey == "Pmomy")
-          Pmom[sind * 3 + 1] = atof(sval.c_str());
-        else if (skey == "Pmomz")
-          Pmom[sind * 3 + 2] = atof(sval.c_str());
-      }
-    }
-    inf.close();
-  }
-  // echo information of Black holes
-  if (myrank == 0)
-  {
-    cout << "initial information of " << BH_num << " Black Hole(s)" << endl;
-    cout << setw(16) << "Mass"
-         << setw(16) << "x"
-         << setw(16) << "y"
-         << setw(16) << "z"
-         << setw(16) << "Px"
-         << setw(16) << "Py"
-         << setw(16) << "Pz"
-         << setw(16) << "Sx"
-         << setw(16) << "Sy"
-         << setw(16) << "Sz" << endl;
-    for (int i = 0; i < BH_num; i++)
-    {
-      cout << setw(16) << Mass[i]
-           << setw(16) << Porg0[i][0]
-           << setw(16) << Porg0[i][1]
-           << setw(16) << Porg0[i][2]
-           << setw(16) << Pmom[i * 3]
-           << setw(16) << Pmom[i * 3 + 1]
-           << setw(16) << Pmom[i * 3 + 2]
-           << setw(16) << Spin[i * 3]
-           << setw(16) << Spin[i * 3 + 1]
-           << setw(16) << Spin[i * 3 + 2] << endl;
-    }
-  }
-
-  int maxl = 1;
-  int levels;
-  int *grids;
-  double bbox[6];
-  // read parameter from file
-  {
-    const int LEN = 256;
-    char pline[LEN];
-    string str, sgrp, skey, sval;
-    int sind1, sind2, sind3;
-    ifstream inf(filename, ifstream::in);
-    if (!inf.good() && myrank == 0)
-    {
-      cout << "bssn_class::Setup_Black_Hole_position: Can not open parameter file " << filename 
-           << " for inputing information of black holes" << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-
-    for (int i = 1; inf.good(); i++)
-    {
-      inf.getline(pline, LEN);
-      str = pline;
-
-      int status = misc::parse_parts(str, sgrp, skey, sval, sind1);
-      if (status == -1)
-      {
-        cout << "error reading parameter file " << filename << " in line " << i << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-      else if (status == 0)
-        continue;
-
-      if (sgrp == "cgh" && skey == "levels")
-      {
-        levels = atoi(sval.c_str());
-        break;
-      }
-    }
-    inf.close();
-  }
-  grids = new int[levels];
-  // read parameter from file
-  {
-    const int LEN = 256;
-    char pline[LEN];
-    string str, sgrp, skey, sval;
-    int sind1, sind2, sind3;
-    ifstream inf(filename, ifstream::in);
-    if (!inf.good() && myrank == 0)
-    {
-      cout << "bssn_class::Setup_Black_Hole_position: Can not open parameter file " << filename 
-           << " for inputing information of black holes" << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-
-    for (int i = 1; inf.good(); i++)
-    {
-      inf.getline(pline, LEN);
-      str = pline;
-
-      int status = misc::parse_parts(str, sgrp, skey, sval, sind1, sind2, sind3);
-      if (status == -1)
-      {
-        cout << "error reading parameter file " << filename << " in line " << i << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-      else if (status == 0)
-        continue;
-
-      if (sgrp == "cgh" && skey == "grids" && sind1 < levels)
-        grids[sind1] = atoi(sval.c_str());
-      if (sgrp == "cgh" && skey == "bbox" && sind1 == 0 && sind2 == 0)
-        bbox[sind3] = atof(sval.c_str());
-    }
-    inf.close();
-  }
-  for (int i = 0; i < levels; i++)
-    if (maxl < grids[i])
-      maxl = grids[i];
-
-  delete[] grids;
-
-  if (BH_num > maxl)
-  {
-    int BH_numc = BH_num;
-    for (int i = 0; i < BH_num; i++)
-      if (Porg0[i][0] < bbox[0] || Porg0[i][0] > bbox[3] ||
-          Porg0[i][1] < bbox[1] || Porg0[i][1] > bbox[4] ||
-          Porg0[i][2] < bbox[2] || Porg0[i][2] > bbox[5])
-      {
-        delete[] Porg0[i];
-        Porg0[i] = 0;
-        BH_numc--;
-      }
-
-    if (BH_num > BH_numc)
-    {
-      maxl = BH_numc;
-      int bhi;
-      double *tmp;
-
-      tmp = Pmom;
-      Pmom = new double[3 * maxl];
-      bhi = 0;
-      for (int i = 0; i < BH_num; i++)
-        if (Porg0[i])
-        {
-          for (int j = 0; j < 3; j++)
-            Pmom[3 * bhi + j] = tmp[3 * i + j];
-          bhi++;
-        }
-      delete[] tmp;
-
-      tmp = Spin;
-      Spin = new double[3 * maxl];
-      bhi = 0;
-      for (int i = 0; i < BH_num; i++)
-        if (Porg0[i])
-        {
-          for (int j = 0; j < 3; j++)
-            Spin[3 * bhi + j] = tmp[3 * i + j];
-          bhi++;
-        }
-      delete[] tmp;
-
-      tmp = Mass;
-      Mass = new double[3 * maxl];
-      bhi = 0;
-      for (int i = 0; i < BH_num; i++)
-        if (Porg0[i])
-        {
-          Mass[bhi] = tmp[i];
-          bhi++;
-        }
-      delete[] tmp;
-
-      double **ttmp;
-      ttmp = Porg0;
-      Porg0 = new double *[maxl];
-      bhi = 0;
-      for (int i = 0; i < BH_num; i++)
-        if (ttmp[i])
-        {
-          Porg0[bhi] = ttmp[i];
-          bhi++;
-        }
-      delete[] ttmp;
-
-      for (int i = 0; i < BH_num; i++)
-      {
-        delete[] Porgbr[i];
-        delete[] Porg[i];
-        delete[] Porg1[i];
-        delete[] Porg_rhs[i];
-      }
-      delete[] Porgbr;
-      delete[] Porg;
-      delete[] Porg1;
-      delete[] Porg_rhs;
-
-      BH_num = maxl;
-
-      Porgbr = new double *[BH_num];
-      Porg = new double *[BH_num];
-      Porg1 = new double *[BH_num];
-      Porg_rhs = new double *[BH_num];
-
-      for (int i = 0; i < BH_num; i++)
-      {
-        Porgbr[i] = new double[3];
-        Porg[i] = new double[3];
-        Porg1[i] = new double[3];
-        Porg_rhs[i] = new double[3];
-      }
-    }
-  }
-
-  for (int i = 0; i < BH_num; i++)
-  {
-    for (int j = 0; j < dim; j++)
-      Porgbr[i][j] = Porg0[i][j];
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function computes black hole positions
-
-//================================================================================================
-
-#if 0
-// old code 
-
-void bssn_class::compute_Porg_rhs(double **BH_PS,double **BH_RHS,var *forx,var *fory,var *forz,int lev)
-{
-  const int InList = 3;
-
-  MyList<var> * DG_List=new MyList<var>(forx);
-  DG_List->insert(fory); DG_List->insert(forz);
-
-  int n;
-  double *x1,*y1,*z1;
-  double *shellf;
-  shellf=new double[3*BH_num];
-  double *pox[3];
-  for(int i=0;i<3;i++) pox[i] = new double[BH_num];
-  for( n = 0; n < BH_num; n++)
-  {
-    pox[0][n] = BH_PS[n][0];
-    pox[1][n] = BH_PS[n][1];
-    pox[2][n] = BH_PS[n][2];
-  }
-
-  if(!Parallel::PatList_Interp_Points(GH->PatL[lev],DG_List,BH_num,pox,shellf,Symmetry))
-  {
-	  ErrorMonitor->outfile<<"fail to find black holes at t = "<<PhysTime<<endl;
-          for( n = 0; n < BH_num; n++) 
-              ErrorMonitor->outfile<<"(x,y,z) = ("<<pox[0][n]<<","<<pox[1][n]<<","<<pox[2][n]<<")"<<endl;
-  }
-  
-  for( n = 0; n < BH_num; n++)
-  {
-    BH_RHS[n][0]=-shellf[3*n  ];
-    BH_RHS[n][1]=-shellf[3*n+1];
-    BH_RHS[n][2]=-shellf[3*n+2];
-  }
-   
-  DG_List->clearList();
-  delete[] shellf;
-  for(int i=0;i<3;i++) delete[] pox[i];
-}
-
-#else
-
-// new code considering diferent levels for different black hole
-
-void bssn_class::compute_Porg_rhs(double **BH_PS, double **BH_RHS, var *forx, var *fory, var *forz, int ilev)
-{
-  const int InList = 3;
-
-  MyList<var> *DG_List = new MyList<var>(forx);
-  DG_List->insert(fory);
-  DG_List->insert(forz);
-
-  double *x1, *y1, *z1;
-  double *shellf;
-  shellf = new double[3];
-  double *pox[3];
-  for (int i = 0; i < 3; i++)
-    pox[i] = new double[1];
-
-  for (int n = 0; n < BH_num; n++)
-  {
-    pox[0][0] = BH_PS[n][0];
-    pox[1][0] = BH_PS[n][1];
-    pox[2][0] = BH_PS[n][2];
-
-    int lev = ilev;
-
-#if (PSTR == 0)
-    while (!Parallel::PatList_Interp_Points(GH->PatL[lev], DG_List, 1, pox, shellf, Symmetry))
-#elif (PSTR == 1)
-    while (!Parallel::PatList_Interp_Points(GH->PatL[lev], DG_List, 1, pox, shellf, Symmetry, GH->Commlev[lev]))
-#endif
-    {
-      lev--;
-      if (lev < 0)
-      {
-        ErrorMonitor->outfile << "fail to find black holes at t = " << PhysTime << endl;
-        for (n = 0; n < BH_num; n++)
-          ErrorMonitor->outfile << "(x,y,z) = (" << pox[0][n] << "," << pox[1][n] << "," << pox[2][n] << ")" << endl;
-        break;
-      }
-    }
-
-    if (lev >= 0)
-    {
-      BH_RHS[n][0] = -shellf[0];
-      BH_RHS[n][1] = -shellf[1];
-      BH_RHS[n][2] = -shellf[2];
-    }
-  }
-
-  DG_List->clearList();
-  delete[] shellf;
-  for (int i = 0; i < 3; i++)
-    delete[] pox[i];
-}
-#endif
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function computes gravitational-wave related data
-
-//================================================================================================
-
-void bssn_class::AnalysisStuff(int lev, double dT_lev)
-{
-  LastAnas += dT_lev;
-
-  if (LastAnas >= AnasTime)
-  {
-#ifdef Point_Psi4
-#error "not support parallel levels yet"
-    // Gam_ijk and R_ij have been calculated in Interp_Constraint()
-    double SYM = 1, ANT = -1;
-    for (int levh = lev; levh < GH->levels; levh++)
-    {
-      MyList<Patch> *Pp = GH->PatL[levh];
-      while (Pp)
-      {
-        MyList<Block> *BP = Pp->data->blb;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          if (myrank == cg->rank)
-          {
-            f_fderivs(cg->shape, cg->fgfs[phi0->sgfn], 
-                      cg->fgfs[phix->sgfn], cg->fgfs[phiy->sgfn], cg->fgfs[phiz->sgfn],
-                      cg->X[0], cg->X[1], cg->X[2], 
-                      SYM, SYM, SYM, Symmetry, levh);
-            f_fderivs(cg->shape, cg->fgfs[trK0->sgfn], 
-                      cg->fgfs[trKx->sgfn], cg->fgfs[trKy->sgfn], cg->fgfs[trKz->sgfn],
-                      cg->X[0], cg->X[1], cg->X[2], 
-                      SYM, SYM, SYM, Symmetry, levh);
-            f_fderivs(cg->shape, cg->fgfs[Axx0->sgfn], 
-                      cg->fgfs[Axxx->sgfn], cg->fgfs[Axxy->sgfn], cg->fgfs[Axxz->sgfn],
-                      cg->X[0], cg->X[1], cg->X[2], 
-                      SYM, SYM, SYM, Symmetry, levh);
-            f_fderivs(cg->shape, cg->fgfs[Axy0->sgfn], 
-                      cg->fgfs[Axyx->sgfn], cg->fgfs[Axyy->sgfn], cg->fgfs[Axyz->sgfn],
-                      cg->X[0], cg->X[1], cg->X[2], 
-                      ANT, ANT, SYM, Symmetry, levh);
-            f_fderivs(cg->shape, cg->fgfs[Axz0->sgfn], 
-                      cg->fgfs[Axzx->sgfn], cg->fgfs[Axzy->sgfn], cg->fgfs[Axzz->sgfn],
-                      cg->X[0], cg->X[1], cg->X[2], 
-                      ANT, SYM, ANT, Symmetry, levh);
-            f_fderivs(cg->shape, cg->fgfs[Ayy0->sgfn], 
-                      cg->fgfs[Ayyx->sgfn], cg->fgfs[Ayyy->sgfn], cg->fgfs[Ayyz->sgfn],
-                      cg->X[0], cg->X[1], cg->X[2], 
-                      SYM, SYM, SYM, Symmetry, levh);
-            f_fderivs(cg->shape, cg->fgfs[Ayz0->sgfn], 
-                      cg->fgfs[Ayzx->sgfn], cg->fgfs[Ayzy->sgfn], cg->fgfs[Ayzz->sgfn],
-                      cg->X[0], cg->X[1], cg->X[2], 
-                      SYM, ANT, ANT, Symmetry, levh);
-            f_fderivs(cg->shape, cg->fgfs[Azz0->sgfn], 
-                      cg->fgfs[Azzx->sgfn], cg->fgfs[Azzy->sgfn], cg->fgfs[Azzz->sgfn],
-                      cg->X[0], cg->X[1], cg->X[2], 
-                      SYM, SYM, SYM, Symmetry, levh);
-          }
-          if (BP == Pp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        Pp = Pp->next;
-      }
-
-#ifdef WithShell
-      // ShellPatch part
-      if (lev == 0)
-      {
-        MyList<ss_patch> *Pp = SH->PatL;
-        while (Pp)
-        {
-          MyList<Block> *BL = Pp->data->blb;
-          int fngfs = Pp->data->fngfs;
-          while (BL)
-          {
-            Block *cg = BL->data;
-            if (myrank == cg->rank)
-            {
-              f_fderivs_shc(cg->shape, cg->fgfs[phi0->sgfn], 
-                            cg->fgfs[phix->sgfn], cg->fgfs[phiy->sgfn], cg->fgfs[phiz->sgfn],
-                            cg->X[0], cg->X[1], cg->X[2],
-                            phi0->SoA[0], phi0->SoA[1], phi0->SoA[2], 
-                            Symmetry, levh, Pp->data->sst,
-                            cg->fgfs[fngfs + ShellPatch::drhodx], 
-                            cg->fgfs[fngfs + ShellPatch::drhody], 
-                            cg->fgfs[fngfs + ShellPatch::drhodz],
-                            cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                            cg->fgfs[fngfs + ShellPatch::dRdx], 
-                            cg->fgfs[fngfs + ShellPatch::dRdy], 
-                            cg->fgfs[fngfs + ShellPatch::dRdz]);
-              f_fderivs_shc(cg->shape, cg->fgfs[trK0->sgfn], 
-                            cg->fgfs[trKx->sgfn], cg->fgfs[trKy->sgfn], cg->fgfs[trKz->sgfn],
-                            cg->X[0], cg->X[1], cg->X[2],
-                            trK0->SoA[0], trK0->SoA[1], trK0->SoA[2], 
-                            Symmetry, levh, Pp->data->sst,
-                            cg->fgfs[fngfs + ShellPatch::drhodx], 
-                            cg->fgfs[fngfs + ShellPatch::drhody], 
-                            cg->fgfs[fngfs + ShellPatch::drhodz],
-                            cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                            cg->fgfs[fngfs + ShellPatch::dRdx], 
-                            cg->fgfs[fngfs + ShellPatch::dRdy], 
-                            cg->fgfs[fngfs + ShellPatch::dRdz]);
-              f_fderivs_shc(cg->shape, cg->fgfs[Axx0->sgfn], 
-                            cg->fgfs[Axxx->sgfn], cg->fgfs[Axxy->sgfn], cg->fgfs[Axxz->sgfn],
-                            cg->X[0], cg->X[1], cg->X[2],
-                            Axx0->SoA[0], Axx0->SoA[1], Axx0->SoA[2], 
-                            Symmetry, levh, Pp->data->sst,
-                            cg->fgfs[fngfs + ShellPatch::drhodx], 
-                            cg->fgfs[fngfs + ShellPatch::drhody], 
-                            cg->fgfs[fngfs + ShellPatch::drhodz],
-                            cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                            cg->fgfs[fngfs + ShellPatch::dRdx], 
-                            cg->fgfs[fngfs + ShellPatch::dRdy], 
-                            cg->fgfs[fngfs + ShellPatch::dRdz]);
-              f_fderivs_shc(cg->shape, cg->fgfs[Axy0->sgfn], 
-                            cg->fgfs[Axyx->sgfn], cg->fgfs[Axyy->sgfn], cg->fgfs[Axyz->sgfn],
-                            cg->X[0], cg->X[1], cg->X[2],
-                            Axy0->SoA[0], Axy0->SoA[1], Axy0->SoA[2], 
-                            Symmetry, levh, Pp->data->sst,
-                            cg->fgfs[fngfs + ShellPatch::drhodx], 
-                            cg->fgfs[fngfs + ShellPatch::drhody], 
-                            cg->fgfs[fngfs + ShellPatch::drhodz],
-                            cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                            cg->fgfs[fngfs + ShellPatch::dRdx], 
-                            cg->fgfs[fngfs + ShellPatch::dRdy], 
-                            cg->fgfs[fngfs + ShellPatch::dRdz]);
-              f_fderivs_shc(cg->shape, cg->fgfs[Axz0->sgfn], 
-                            cg->fgfs[Axzx->sgfn], cg->fgfs[Axzy->sgfn], cg->fgfs[Axzz->sgfn],
-                            cg->X[0], cg->X[1], cg->X[2],
-                            Axz0->SoA[0], Axz0->SoA[1], Axz0->SoA[2], 
-                            Symmetry, levh, Pp->data->sst,
-                            cg->fgfs[fngfs + ShellPatch::drhodx], 
-                            cg->fgfs[fngfs + ShellPatch::drhody], 
-                            cg->fgfs[fngfs + ShellPatch::drhodz],
-                            cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                            cg->fgfs[fngfs + ShellPatch::dRdx], 
-                            cg->fgfs[fngfs + ShellPatch::dRdy], 
-                            cg->fgfs[fngfs + ShellPatch::dRdz]);
-              f_fderivs_shc(cg->shape, cg->fgfs[Ayy0->sgfn], 
-                            cg->fgfs[Ayyx->sgfn], cg->fgfs[Ayyy->sgfn], cg->fgfs[Ayyz->sgfn],
-                            cg->X[0], cg->X[1], cg->X[2],
-                            Ayy0->SoA[0], Ayy0->SoA[1], Ayy0->SoA[2], 
-                            Symmetry, levh, Pp->data->sst,
-                            cg->fgfs[fngfs + ShellPatch::drhodx], 
-                            cg->fgfs[fngfs + ShellPatch::drhody], 
-                            cg->fgfs[fngfs + ShellPatch::drhodz],
-                            cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                            cg->fgfs[fngfs + ShellPatch::dRdx], 
-                            cg->fgfs[fngfs + ShellPatch::dRdy], 
-                            cg->fgfs[fngfs + ShellPatch::dRdz]);
-              f_fderivs_shc(cg->shape, cg->fgfs[Ayz0->sgfn], 
-                            cg->fgfs[Ayzx->sgfn], cg->fgfs[Ayzy->sgfn], cg->fgfs[Ayzz->sgfn],
-                            cg->X[0], cg->X[1], cg->X[2],
-                            Ayz0->SoA[0], Ayz0->SoA[1], Ayz0->SoA[2], 
-                            Symmetry, levh, Pp->data->sst,
-                            cg->fgfs[fngfs + ShellPatch::drhodx], 
-                            cg->fgfs[fngfs + ShellPatch::drhody], 
-                            cg->fgfs[fngfs + ShellPatch::drhodz],
-                            cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                            cg->fgfs[fngfs + ShellPatch::dRdx], 
-                            cg->fgfs[fngfs + ShellPatch::dRdy], 
-                            cg->fgfs[fngfs + ShellPatch::dRdz]);
-              f_fderivs_shc(cg->shape, cg->fgfs[Azz0->sgfn], 
-                            cg->fgfs[Azzx->sgfn], cg->fgfs[Azzy->sgfn], cg->fgfs[Azzz->sgfn],
-                            cg->X[0], cg->X[1], cg->X[2],
-                            Azz0->SoA[0], Azz0->SoA[1], Azz0->SoA[2], 
-                            Symmetry, levh, Pp->data->sst,
-                            cg->fgfs[fngfs + ShellPatch::drhodx], 
-                            cg->fgfs[fngfs + ShellPatch::drhody], 
-                            cg->fgfs[fngfs + ShellPatch::drhodz],
-                            cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                            cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                            cg->fgfs[fngfs + ShellPatch::dRdx], 
-                            cg->fgfs[fngfs + ShellPatch::dRdy], 
-                            cg->fgfs[fngfs + ShellPatch::dRdz]);
-            }
-            if (BL == Pp->data->ble)
-              break;
-            BL = BL->next;
-          }
-          Pp = Pp->next;
-        }
-      }
-#endif
-    }
-#else
-    Compute_Psi4(lev);
-#endif
-    double *RP, *IP, *RoutMAP;
-    int NN = 0;
-    for (int pl = 2; pl < maxl + 1; pl++)
-      for (int pm = -pl; pm < pl + 1; pm++)
-        NN++;
-    RP = new double[NN];
-    IP = new double[NN];
-    RoutMAP = new double[7];
-    double Rex = maxrex;
-    for (int i = 0; i < decn; i++)
-    {
-#ifdef Point_Psi4
-      Waveshell->surf_Wave(Rex, GH, SH,
-                           phi, trK,
-                           gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
-                           Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
-                           phix, phiy, phiz,
-                           trKx, trKy, trKz,
-                           Axxx, Axxy, Axxz,
-                           Axyx, Axyy, Axyz,
-                           Axzx, Axzy, Axzz,
-                           Ayyx, Ayyy, Ayyz,
-                           Ayzx, Ayzy, Ayzz,
-                           Azzx, Azzy, Azzz,
-                           Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
-                           Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
-                           Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
-                           Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
-                           2, maxl, NN, RP, IP, ErrorMonitor);
-#ifdef WithShell
-      if (lev > 0 || Rex < GH->bbox[0][0][3])
-      {
-        Waveshell->surf_MassPAng(Rex, lev, GH, phi0, trK0,
-                                 gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
-                                 Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
-                                 Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                                 RoutMAP, ErrorMonitor);
-      }
-      else
-      {
-        Waveshell->surf_MassPAng(Rex, lev, SH, phi0, trK0,
-                                 gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
-                                 Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
-                                 Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                                 RoutMAP, ErrorMonitor);
-      }
-#else
-      Waveshell->surf_MassPAng(Rex, lev, GH, phi0, trK0,
-                               gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
-                               Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
-                               Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                               RoutMAP, ErrorMonitor);
-#endif
-#else
-//        misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before surface integral");
-#ifdef WithShell
-      if (lev > 0 || Rex < GH->bbox[0][0][3])
-      {
-        Waveshell->surf_Wave(Rex, lev, GH, Rpsi4, Ipsi4, 2, maxl, NN, RP, IP, ErrorMonitor);
-        Waveshell->surf_MassPAng(Rex, lev, GH, phi0, trK0,
-                                 gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
-                                 Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
-                                 Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                                 RoutMAP, ErrorMonitor);
-      }
-      else
-      {
-        Waveshell->surf_Wave(Rex, lev, SH, Rpsi4, Ipsi4, 2, maxl, NN, RP, IP, ErrorMonitor);
-        Waveshell->surf_MassPAng(Rex, lev, SH, phi0, trK0,
-                                 gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
-                                 Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
-                                 Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                                 RoutMAP, ErrorMonitor);
-      }
-#else
-#if (PSTR == 0)
-      Waveshell->surf_Wave(Rex, lev, GH, Rpsi4, Ipsi4, 2, maxl, NN, RP, IP, ErrorMonitor);
-      Waveshell->surf_MassPAng(Rex, lev, GH, phi0, trK0,
-                               gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
-                               Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
-                               Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                               RoutMAP, ErrorMonitor);
-#elif (PSTR == 1)
-      Waveshell->surf_Wave(Rex, lev, GH, Rpsi4, Ipsi4, 2, maxl, NN, RP, IP, ErrorMonitor, GH->Commlev[lev]);
-      //        misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after surf_Wave");
-      Waveshell->surf_MassPAng(Rex, lev, GH, phi0, trK0,
-                               gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
-                               Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
-                               Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                               RoutMAP, ErrorMonitor, GH->Commlev[lev]);
-#endif
-#endif
-//        misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"end surface integral");
-#endif
-      if (i == 0)
-      {
-        ADMMass = RoutMAP[0];
-      }
-#if (PSTR == 1)
-      if (GH->start_rank[a_lev] > 0)
-      {
-        MPI_Status status;
-        // receive
-        if (myrank == 0)
-        {
-          MPI_Recv(RP, NN, MPI_DOUBLE, GH->start_rank[a_lev], 1, MPI_COMM_WORLD, &status);
-          MPI_Recv(IP, NN, MPI_DOUBLE, GH->start_rank[a_lev], 2, MPI_COMM_WORLD, &status);
-          MPI_Recv(RoutMAP, 7, MPI_DOUBLE, GH->start_rank[a_lev], 3, MPI_COMM_WORLD, &status);
-        }
-        // send
-        if (myrank == GH->start_rank[a_lev])
-        {
-          MPI_Send(RP, NN, MPI_DOUBLE, 0, 1, MPI_COMM_WORLD);
-          MPI_Send(IP, NN, MPI_DOUBLE, 0, 2, MPI_COMM_WORLD);
-          MPI_Send(RoutMAP, 7, MPI_DOUBLE, 0, 3, MPI_COMM_WORLD);
-        }
-      }
-#endif
-      Psi4Monitor->writefile(PhysTime, NN, RP, IP);
-      MAPMonitor->writefile(PhysTime, 7, RoutMAP);
-      Rex = Rex - drex;
-    }
-    delete[] RP;
-    delete[] IP;
-    delete[] RoutMAP;
-
-    // black hole's position
-    {
-      double *pox;
-      pox = new double[dim * BH_num];
-      for (int bhi = 0; bhi < BH_num; bhi++)
-        for (int i = 0; i < dim; i++)
-          pox[dim * bhi + i] = Porg0[bhi][i];
-      BHMonitor->writefile(PhysTime, dim * BH_num, pox);
-      delete[] pox;
-    }
-
-    LastAnas = 0;
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function computes and outputs constraint violations
-
-//================================================================================================
-
-void bssn_class::Constraint_Out()
-{
-  LastConsOut += dT * pow(0.5, Mymax(0, trfls));
-
-  if (LastConsOut >= AnasTime)
-  // Constraint violation
-  {
-    // recompute least the constraint data lost for moved new grid
-    for (int lev = 0; lev < GH->levels; lev++)
-    {
-      // make sure the data consistent for higher levels
-      if (lev > 0) // if the constrait quantities can be reused from the step rhs calculation
-      {
-        double TRK4 = PhysTime;
-        double ndeps = numepsb;
-        int pre = 0;
-        MyList<Patch> *Pp = GH->PatL[lev];
-        while (Pp)
-        {
-          MyList<Block> *BP = Pp->data->blb;
-          while (BP)
-          {
-            Block *cg = BP->data;
-            if (myrank == cg->rank)
-            {
-// added by yangquan
-#ifdef USE_GPU
-              if (use_gpu == 1)
-                gpu_rhs(CALLED_BY_CONSTRAINT, myrank, RHS_PARA_CALLED_Constraint_Out);
-
-              else
-                f_compute_rhs_bssn(RHS_PARA_CALLED_Constraint_Out);
-#else
-              f_compute_rhs_bssn(RHS_PARA_CALLED_Constraint_Out);
-#endif
-            }
-            if (BP == Pp->data->ble)
-              break;
-            BP = BP->next;
-          }
-          Pp = Pp->next;
-        }
-      }
-      Parallel::Sync(GH->PatL[lev], ConstraintList, Symmetry);
-    }
-#ifdef WithShell
-    if (0) // if the constrait quantities can be reused from the step rhs calculation
-    {
-      MyList<ss_patch> *sPp;
-      sPp = SH->PatL;
-      while (sPp)
-      {
-        double TRK4 = PhysTime;
-        int pre = 0;
-        int lev = 0;
-        MyList<Block> *BP = sPp->data->blb;
-        int fngfs = sPp->data->fngfs;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          if (myrank == cg->rank)
-          {
-#ifdef USE_GPU
-            if (use_gpu == 1)
-
-              gpu_rhs_ss(CALLED_BY_CONSTRAINT, myrank, RHS_PARA_CALLED_Constraint_Out_SS);
-            else
-              f_compute_rhs_bssn_ss(RHS_PARA_CALLED_Constraint_Out_SS);
-#else
-            f_compute_rhs_bssn_ss(RHS_PARA_CALLED_Constraint_Out_SS);
-
-#endif // USE_GPU
-          }
-          if (BP == sPp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        sPp = sPp->next;
-      }
-    }
-    SH->Synch(ConstraintList, Symmetry);
-#endif
-
-    double ConV[7];
-#if (PSTR == 1)
-    double ConV_h[7];
-#endif
-
-#ifdef WithShell
-    ConV[0] = SH->L2Norm(Cons_Ham);
-    ConV[1] = SH->L2Norm(Cons_Px);
-    ConV[2] = SH->L2Norm(Cons_Py);
-    ConV[3] = SH->L2Norm(Cons_Pz);
-    ConV[4] = SH->L2Norm(Cons_Gx);
-    ConV[5] = SH->L2Norm(Cons_Gy);
-    ConV[6] = SH->L2Norm(Cons_Gz);
-    ConVMonitor->writefile(PhysTime, 7, ConV);
-#endif
-    for (int levi = 0; levi < GH->levels; levi++)
-    {
-#if (PSTR == 0)
-      ConV[0] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Ham);
-      ConV[1] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Px);
-      ConV[2] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Py);
-      ConV[3] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Pz);
-      ConV[4] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gx);
-      ConV[5] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gy);
-      ConV[6] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gz);
-#elif (PSTR == 1)
-      ConV[0] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Ham, GH->Commlev[levi]);
-      ConV[1] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Px, GH->Commlev[levi]);
-      ConV[2] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Py, GH->Commlev[levi]);
-      ConV[3] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Pz, GH->Commlev[levi]);
-      ConV[4] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gx, GH->Commlev[levi]);
-      ConV[5] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gy, GH->Commlev[levi]);
-      ConV[6] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gz, GH->Commlev[levi]);
-      //        misc::tillherecheck("before collect data to cpu0");
-      // MPI_ALLREDUCE( sendbuf, recvbuf, count, datatype, op, comm), sendbu and recvbuf must be different
-      if (levi > 0)
-      {
-        if (GH->mylev == levi && myrank == GH->start_rank[levi])
-          for (int i = 0; i < 7; i++)
-            ConV_h[i] = ConV[i];
-        else
-          for (int i = 0; i < 7; i++)
-            ConV_h[i] = 0;
-        MPI_Allreduce(ConV_h, ConV, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-      }
-#endif
-      ConVMonitor->writefile(PhysTime, 7, ConV);
-      /*
-        if(fabs(ConV[0])<0.00001)
-        {
-          MyList<var> * DG_List=new MyList<var>(Cons_Ham);
-                DG_List->insert(Cons_Px); DG_List->insert(Cons_Py); DG_List->insert(Cons_Px);
-                DG_List->insert(Cons_Gx); DG_List->insert(Cons_Gy); DG_List->insert(Cons_Gx);
-          Parallel::Dump_Data(GH->PatL[levi],DG_List,"jiu",0,1);
-          DG_List->clearList();
-          if(myrank==0) MPI_Abort(MPI_COMM_WORLD,1);
-        }
-      */
-    }
-
-    Interp_Constraint(false);
-
-    LastConsOut = 0;
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function computes derivatives required by the apparent-horizon routines
-
-//================================================================================================
-
-#ifdef With_AHF
-void bssn_class::AH_Prepare_derivatives()
-{
-  double SYM = 1.0, ANT = -1.0;
-  int ZEO = 0;
-
-  for (int lev = 0; lev < GH->levels; lev++)
-  {
-    MyList<Patch> *Pp = GH->PatL[lev];
-    while (Pp)
-    {
-      MyList<Block> *BP = Pp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-          f_fderivs(cg->shape, cg->fgfs[phi0->sgfn], 
-                    cg->fgfs[dtSfx_rhs->sgfn], cg->fgfs[dtSfy_rhs->sgfn], cg->fgfs[dtSfz_rhs->sgfn],
-                    cg->X[0], cg->X[1], cg->X[2], 
-                    SYM, SYM, SYM, Symmetry, ZEO);
-          f_fderivs(cg->shape, cg->fgfs[gxx0->sgfn], 
-                    cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamzxx->sgfn],
-                    cg->X[0], cg->X[1], cg->X[2], 
-                    SYM, SYM, SYM, Symmetry, ZEO);
-          f_fderivs(cg->shape, cg->fgfs[gxy0->sgfn], 
-                    cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamzxy->sgfn],
-                    cg->X[0], cg->X[1], cg->X[2], 
-                    ANT, ANT, SYM, Symmetry, ZEO);
-          f_fderivs(cg->shape, cg->fgfs[gxz0->sgfn], 
-                    cg->fgfs[Gamxxz->sgfn], cg->fgfs[Gamyxz->sgfn], cg->fgfs[Gamzxz->sgfn],
-                    cg->X[0], cg->X[1], cg->X[2], 
-                    ANT, SYM, ANT, Symmetry, ZEO);
-          f_fderivs(cg->shape, cg->fgfs[gyy0->sgfn], 
-                    cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamzyy->sgfn],
-                    cg->X[0], cg->X[1], cg->X[2], 
-                    SYM, SYM, SYM, Symmetry, ZEO);
-          f_fderivs(cg->shape, cg->fgfs[gyz0->sgfn], 
-                    cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamzyz->sgfn],
-                    cg->X[0], cg->X[1], cg->X[2], 
-                    SYM, ANT, ANT, Symmetry, ZEO);
-          f_fderivs(cg->shape, cg->fgfs[gzz0->sgfn], 
-                    cg->fgfs[Gamxzz->sgfn], cg->fgfs[Gamyzz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                    cg->X[0], cg->X[1], cg->X[2], 
-                    SYM, SYM, SYM, Symmetry, ZEO);
-        }
-        if (BP == Pp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      Pp = Pp->next;
-    }
-    Parallel::Sync(GH->PatL[lev], AHDList, Symmetry);
-  }
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function interpolates apparent-horizon data
-
-//================================================================================================
-
-bool bssn_class::AH_Interp_Points(MyList<var> *VarList,
-                                  int NN, double **XX,
-                                  double *Shellf, int Symmetryi)
-{
-  MyList<var> *varl;
-  int num_var = 0;
-  varl = VarList;
-  while (varl)
-  {
-    num_var++;
-    varl = varl->next;
-  }
-
-  double pox[3];
-  for (int i = 0; i < NN; i++)
-  {
-    for (int j = 0; j < 3; j++)
-      pox[j] = XX[j][i];
-    int lev = GH->levels - 1;
-    bool notfound = true;
-
-    while (notfound)
-    {
-      if (lev < 0)
-      {
-#ifdef WithShell
-        if (SH->Interp_One_Point(VarList, pox, Shellf + i * num_var, Symmetryi))
-        {
-          return true;
-        }
-        if (myrank == 0)
-          cout << "bssn_class::AH_Interp_Points: point (" 
-               << pox[0] << "," << pox[1] << "," << pox[2] 
-               << ") is out of cgh and shell domain!" << endl;
-#else
-        if (myrank == 0)
-          cout << "bssn_class::AH_Interp_Points: point (" 
-               << pox[0] << "," << pox[1] << "," << pox[2] 
-               << ") is out of cgh domain!" << endl;
-#endif
-        return false;
-      }
-      MyList<Patch> *Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        if (Pp->data->Interp_ONE_Point(VarList, pox, Shellf + i * num_var, Symmetryi))
-        {
-          notfound = false;
-          break;
-        }
-        Pp = Pp->next;
-      }
-      lev--;
-    }
-  }
-  return true;
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function computes the apparent horizon at the current iteration step
-
-//================================================================================================
-
-void bssn_class::AH_Step_Find(int lev, double dT_lev)
-{
-  if ((lev == GH->levels - 1))
-  {
-    int ncount = int(PhysTime / dT_lev);
-    bool tf = false;
-    for (int ihn = 0; ihn < HN_num; ihn++)
-    {
-      if (ncount % findeveryl[ihn] == 0)
-      {
-        tf = true;
-        break;
-      }
-    }
-    if (tf)
-    {
-      clock_t prev_clock, curr_clock;
-      if (myrank == 0)
-        prev_clock = clock();
-      const int cdumpid = int(PhysTime / AHdumptime) + 1;
-      for (int ihn = 0; ihn < HN_num; ihn++)
-        dumpid[ihn] = cdumpid;
-
-      double gam;
-      for (int ihn = 0; ihn < BH_num; ihn++)
-      {
-        xc[ihn] = Porg0[ihn][0];
-        yc[ihn] = Porg0[ihn][1];
-        zc[ihn] = Porg0[ihn][2];
-        gam = fabs(Pmom[ihn * 3]) / (Mass[ihn]);
-        gam = sqrt(1 - gam * gam);
-        xr[ihn] = Mass[ihn] * gam;
-        gam = fabs(Pmom[ihn * 3 + 1]) / (Mass[ihn]);
-        gam = sqrt(1 - gam * gam);
-        yr[ihn] = Mass[ihn] * gam;
-        gam = fabs(Pmom[ihn * 3 + 2]) / (Mass[ihn]);
-        gam = sqrt(1 - gam * gam);
-        zr[ihn] = Mass[ihn] * gam;
-        dTT[ihn] = -1;
-
-        if (ncount % findeveryl[ihn] == 0)
-        {
-          trigger[ihn] = true;
-          dTT[ihn] = findeveryl[ihn] * dT_lev;
-        }
-        else
-          trigger[ihn] = false;
-        if (trigger[ihn] && (dumpid[ihn] > lastahdumpid[ihn]))
-          lastahdumpid[ihn] = dumpid[ihn];
-        else
-          dumpid[ihn] = 0;
-      }
-      int ihn = BH_num;
-      for (int ia = 0; ia < BH_num; ia++)
-        for (int ib = ia + 1; ib < BH_num; ib++)
-        {
-          xc[ihn] = (Porg0[ia][0] + Porg0[ib][0]) / 2;
-          yc[ihn] = (Porg0[ia][1] + Porg0[ib][1]) / 2;
-          zc[ihn] = (Porg0[ia][2] + Porg0[ib][2]) / 2;
-
-          xr[ihn] = yr[ihn] = zr[ihn] = Mass[ia] + Mass[ib];
-
-          dTT[ihn] = -1;
-
-          if (fabs(Porg0[ia][0] - Porg0[ib][0]) < 2 * xr[ihn] &&
-              fabs(Porg0[ia][1] - Porg0[ib][1]) < 2 * xr[ihn] &&
-              fabs(Porg0[ia][2] - Porg0[ib][2]) < 2 * xr[ihn] &&
-              (ncount % findeveryl[ihn] == 0))
-          {
-            trigger[ihn] = true;
-            dTT[ihn] = findeveryl[ihn] * dT_lev;
-          }
-          else
-            trigger[ihn] = false;
-
-          if (trigger[ihn] && (dumpid[ihn] > lastahdumpid[ihn]))
-            lastahdumpid[ihn] = dumpid[ihn];
-          else
-            dumpid[ihn] = 0;
-
-          ihn++;
-        }
-#if (ABEtype == 1)
-      if (PhysTime > 10)
-      {
-        ihn--;
-        trigger[ihn] = true;
-        xr[ihn] = yr[ihn] = zr[ihn] = 50;
-        //	if(myrank==0) for(ihn=0;ihn<HN_num;ihn++) cout<<"trigger#"<<ihn<<": "<<trigger[ihn]<<endl;
-      }
-#endif
-      AHFinderDirect::AHFinderDirect_find_horizons(HN_num, dumpid,
-                                                   xc, yc, zc, xr, yr, zr, trigger, dTT); 
-                                                   // note rhs and Gamijk have been used as temp storage space
-
-      if (myrank == 0)
-      {
-        curr_clock = clock();
-        cout << "Finding horizon used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-             << " seconds!" << endl;
-      }
-    }
-  }
-}
-#endif
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function interpolates constraint data
-
-//================================================================================================
-
-void bssn_class::Interp_Constraint(bool infg)
-{
-  if (infg)
-  {
-    // we do not support a_lev != 0 yet.
-    if (a_lev > 0)
-      return;
-
-    // recompute least the constraint data lost for moved new grid
-    for (int lev = 0; lev < GH->levels; lev++)
-    {
-      // make sure the data consistent for higher levels
-      if (lev > 0) // if the constrait quantities can be reused from the step rhs calculation
-      {
-        double TRK4 = PhysTime;
-        double ndeps = numepsb;
-        int pre = 0;
-        MyList<Patch> *Pp = GH->PatL[lev];
-        while (Pp)
-        {
-          MyList<Block> *BP = Pp->data->blb;
-          while (BP)
-          {
-            Block *cg = BP->data;
-            if (myrank == cg->rank)
-            {
-// added by yangquan
-#ifdef USE_GPU
-              if (use_gpu == 1)
-                gpu_rhs(CALLED_BY_CONSTRAINT, myrank, RHS_PARA_CALLED_Interp_Constraint);
-              else
-                f_compute_rhs_bssn(RHS_PARA_CALLED_Interp_Constraint);
-#else
-              f_compute_rhs_bssn(RHS_PARA_CALLED_Interp_Constraint);
-#endif
-            }
-            if (BP == Pp->data->ble)
-              break;
-            BP = BP->next;
-          }
-          Pp = Pp->next;
-        }
-      }
-      Parallel::Sync(GH->PatL[lev], ConstraintList, Symmetry);
-    }
-#ifdef WithShell
-    if (0) // if the constrait quantities can be reused from the step rhs calculation
-    {
-      MyList<ss_patch> *sPp;
-      sPp = SH->PatL;
-      while (sPp)
-      {
-        double TRK4 = PhysTime;
-        int pre = 0;
-        int lev = 0;
-        MyList<Block> *BP = sPp->data->blb;
-        int fngfs = sPp->data->fngfs;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          if (myrank == cg->rank)
-          {
-#ifdef USE_GPU
-            if (use_gpu == 1)
-
-              gpu_rhs_ss(CALLED_BY_CONSTRAINT, myrank, RHS_PARA_CALLED_Intrp_Constraint_Out_SS);
-            else
-              f_compute_rhs_bssn_ss(RHS_PARA_CALLED_Intrp_Constraint_Out_SS);
-#else
-            f_compute_rhs_bssn_ss(RHS_PARA_CALLED_Intrp_Constraint_Out_SS);
-
-#endif // USE_GPU
-          }
-          if (BP == sPp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        sPp = sPp->next;
-      }
-    }
-    SH->Synch(ConstraintList, Symmetry);
-#endif
-  }
-  //    interpolate
-  double *x1, *y1, *z1;
-  const int n = 1000;
-  double lmax, lmin, dd;
-  lmin = 0;
-#ifdef WithShell
-  lmax = SH->Rrange[1];
-#else
-  lmax = GH->bbox[0][0][4];
-#endif
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-  dd = (lmax - lmin) / (n - 1);
-#else
-#ifdef Cell
-  dd = (lmax - lmin) / n;
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-  x1 = new double[n];
-  y1 = new double[n];
-  z1 = new double[n];
-  for (int i = 0; i < n; i++)
-  {
-    x1[i] = 0;
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-    y1[i] = lmin + i * dd;
-#else
-#ifdef Cell
-    y1[i] = lmin + (i + 0.5) * dd;
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-    z1[i] = 0;
-  }
-
-  int InList = 0;
-
-  MyList<var> *varl = ConstraintList;
-  while (varl)
-  {
-    InList++;
-    varl = varl->next;
-  }
-  double *shellf;
-  shellf = new double[n * InList];
-  for (int i = 0; i < n; i++)
-  {
-    double XX[3];
-    XX[0] = x1[i];
-    XX[1] = y1[i];
-    XX[2] = z1[i];
-    bool fg = GH->Interp_One_Point(ConstraintList, XX, shellf + i * InList, Symmetry);
-#ifdef WithShell
-    if (!fg)
-      fg = SH->Interp_One_Point(ConstraintList, XX, shellf + i * InList, Symmetry);
-#endif
-    if (!fg && myrank == 0)
-    {
-      cout << "bssn_class::Interp_Constraint meets wrong" << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
-  if (myrank == 0)
-  {
-    ofstream outfile;
-    char filename[50];
-    sprintf(filename, "%s/interp_constraint_%05d.dat", ErrorMonitor->out_dir.c_str(), int(PhysTime / dT + 0.5)); 
-    // 0.5 for round off
-    
-    outfile.open(filename);
-    outfile << "#  corrdinate, H_Res, Px_Res, Py_Res, Pz_Res, Gx_Res, Gy_Res, Gz_Res, ...." << endl;
-    for (int i = 0; i < n; i++)
-    {
-      outfile << setw(10) << setprecision(10) << y1[i];
-      for (int j = 0; j < InList; j++)
-        outfile << " " << setw(16) << setprecision(15) << shellf[InList * i + j];
-      outfile << endl;
-    }
-    outfile.close();
-  }
-
-  delete[] shellf;
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function computes constraint violations
-
-//================================================================================================
-
-void bssn_class::Compute_Constraint()
-{
-  double TRK4 = PhysTime;
-  double ndeps = numepsb;
-  int pre = 0;
-  int lev;
-
-  for (lev = 0; lev < GH->levels; lev++)
-  {
-    {
-      MyList<Patch> *Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BP = Pp->data->blb;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          if (myrank == cg->rank)
-          {
-            f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                               cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                               cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                               cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                               cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                               cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                               cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                               cg->fgfs[Lap0->sgfn], 
-                               cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                               cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                               cg->fgfs[phi_rhs->sgfn], cg->fgfs[trK_rhs->sgfn],
-                               cg->fgfs[gxx_rhs->sgfn], cg->fgfs[gxy_rhs->sgfn], cg->fgfs[gxz_rhs->sgfn],
-                               cg->fgfs[gyy_rhs->sgfn], cg->fgfs[gyz_rhs->sgfn], cg->fgfs[gzz_rhs->sgfn],
-                               cg->fgfs[Axx_rhs->sgfn], cg->fgfs[Axy_rhs->sgfn], cg->fgfs[Axz_rhs->sgfn],
-                               cg->fgfs[Ayy_rhs->sgfn], cg->fgfs[Ayz_rhs->sgfn], cg->fgfs[Azz_rhs->sgfn],
-                               cg->fgfs[Gmx_rhs->sgfn], cg->fgfs[Gmy_rhs->sgfn], cg->fgfs[Gmz_rhs->sgfn],
-                               cg->fgfs[Lap_rhs->sgfn], 
-                               cg->fgfs[Sfx_rhs->sgfn], cg->fgfs[Sfy_rhs->sgfn], cg->fgfs[Sfz_rhs->sgfn],
-                               cg->fgfs[dtSfx_rhs->sgfn], cg->fgfs[dtSfy_rhs->sgfn], cg->fgfs[dtSfz_rhs->sgfn],
-                               cg->fgfs[rho->sgfn], cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                               cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                               cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                               cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                               cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                               cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                               cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                               cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                               cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                               cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                               cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                               cg->fgfs[Cons_Ham->sgfn],
-                               cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                               cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                               Symmetry, lev, ndeps, pre);
-          }
-          if (BP == Pp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        Pp = Pp->next;
-      }
-    }
-    Parallel::Sync(GH->PatL[lev], ConstraintList, Symmetry);
-  }
-  // prolong restrict constraint quantities
-  for (lev = GH->levels - 1; lev > 0; lev--)
-    RestrictProlong(lev, 1, false, ConstraintList, ConstraintList, ConstraintList);
-
-#ifdef WithShell
-  lev = 0;
-  {
-    MyList<ss_patch> *sPp;
-    sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      int fngfs = sPp->data->fngfs;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-          f_compute_rhs_bssn_ss(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                cg->fgfs[fngfs + ShellPatch::gx], 
-                                cg->fgfs[fngfs + ShellPatch::gy], 
-                                cg->fgfs[fngfs + ShellPatch::gz],
-                                cg->fgfs[fngfs + ShellPatch::drhodx], 
-                                cg->fgfs[fngfs + ShellPatch::drhody], 
-                                cg->fgfs[fngfs + ShellPatch::drhodz],
-                                cg->fgfs[fngfs + ShellPatch::dsigmadx], 
-                                cg->fgfs[fngfs + ShellPatch::dsigmady], 
-                                cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                                cg->fgfs[fngfs + ShellPatch::dRdx], 
-                                cg->fgfs[fngfs + ShellPatch::dRdy], 
-                                cg->fgfs[fngfs + ShellPatch::dRdz],
-                                cg->fgfs[fngfs + ShellPatch::drhodxx], 
-                                cg->fgfs[fngfs + ShellPatch::drhodxy], 
-                                cg->fgfs[fngfs + ShellPatch::drhodxz],
-                                cg->fgfs[fngfs + ShellPatch::drhodyy], 
-                                cg->fgfs[fngfs + ShellPatch::drhodyz], 
-                                cg->fgfs[fngfs + ShellPatch::drhodzz],
-                                cg->fgfs[fngfs + ShellPatch::dsigmadxx], 
-                                cg->fgfs[fngfs + ShellPatch::dsigmadxy], 
-                                cg->fgfs[fngfs + ShellPatch::dsigmadxz],
-                                cg->fgfs[fngfs + ShellPatch::dsigmadyy], 
-                                cg->fgfs[fngfs + ShellPatch::dsigmadyz], 
-                                cg->fgfs[fngfs + ShellPatch::dsigmadzz],
-                                cg->fgfs[fngfs + ShellPatch::dRdxx], 
-                                cg->fgfs[fngfs + ShellPatch::dRdxy], 
-                                cg->fgfs[fngfs + ShellPatch::dRdxz],
-                                cg->fgfs[fngfs + ShellPatch::dRdyy], 
-                                cg->fgfs[fngfs + ShellPatch::dRdyz], 
-                                cg->fgfs[fngfs + ShellPatch::dRdzz],
-                                cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                                cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                                cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                                cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                                cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
-                                cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                                cg->fgfs[Lap0->sgfn], 
-                                cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                                cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                                cg->fgfs[phi_rhs->sgfn], cg->fgfs[trK_rhs->sgfn],
-                                cg->fgfs[gxx_rhs->sgfn], cg->fgfs[gxy_rhs->sgfn], cg->fgfs[gxz_rhs->sgfn],
-                                cg->fgfs[gyy_rhs->sgfn], cg->fgfs[gyz_rhs->sgfn], cg->fgfs[gzz_rhs->sgfn],
-                                cg->fgfs[Axx_rhs->sgfn], cg->fgfs[Axy_rhs->sgfn], cg->fgfs[Axz_rhs->sgfn],
-                                cg->fgfs[Ayy_rhs->sgfn], cg->fgfs[Ayz_rhs->sgfn], cg->fgfs[Azz_rhs->sgfn],
-                                cg->fgfs[Gmx_rhs->sgfn], cg->fgfs[Gmy_rhs->sgfn], cg->fgfs[Gmz_rhs->sgfn],
-                                cg->fgfs[Lap_rhs->sgfn], 
-                                cg->fgfs[Sfx_rhs->sgfn], cg->fgfs[Sfy_rhs->sgfn], cg->fgfs[Sfz_rhs->sgfn],
-                                cg->fgfs[dtSfx_rhs->sgfn], cg->fgfs[dtSfy_rhs->sgfn], cg->fgfs[dtSfz_rhs->sgfn],
-                                cg->fgfs[rho->sgfn], cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                                cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                                cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                                cg->fgfs[Gamxxx->sgfn], cg->fgfs[Gamxxy->sgfn], cg->fgfs[Gamxxz->sgfn],
-                                cg->fgfs[Gamxyy->sgfn], cg->fgfs[Gamxyz->sgfn], cg->fgfs[Gamxzz->sgfn],
-                                cg->fgfs[Gamyxx->sgfn], cg->fgfs[Gamyxy->sgfn], cg->fgfs[Gamyxz->sgfn],
-                                cg->fgfs[Gamyyy->sgfn], cg->fgfs[Gamyyz->sgfn], cg->fgfs[Gamyzz->sgfn],
-                                cg->fgfs[Gamzxx->sgfn], cg->fgfs[Gamzxy->sgfn], cg->fgfs[Gamzxz->sgfn],
-                                cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
-                                cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
-                                cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                                cg->fgfs[Cons_Ham->sgfn],
-                                cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                                cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                                Symmetry, lev, numepsh, sPp->data->sst, pre);
-        }
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-  }
-  SH->Synch(ConstraintList, Symmetry);
-  // interpolate constraint quantities
-  SH->CS_Inter(ConstraintList, Symmetry);
-#endif
-}
-
-
-void bssn_class::testRestrict()
-{
-  MyList<var> *DG_List = new MyList<var>(phi0);
-  int lev = 0;
-  double ZEO = 0, ONE = 1;
-  MyList<Patch> *Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-        f_set_value(cg->shape, cg->fgfs[phi0->sgfn], ZEO);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-
-  lev = 1;
-  Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-        f_set_value(cg->shape, cg->fgfs[phi0->sgfn], ONE);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-
-  Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], DG_List, DG_List, Symmetry);
-  Parallel::Sync(GH->PatL[lev - 1], DG_List, Symmetry);
-
-  Parallel::Dump_Data(GH->PatL[lev - 1], DG_List, 0, PhysTime, dT);
-  Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT);
-
-  DG_List->clearList();
-  exit(0);
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-void bssn_class::testOutBd()
-{
-  MyList<var> *DG_List = new MyList<var>(phi0);
-  int lev = 1;
-  double ZEO = 0, ONE = 1;
-  MyList<Patch> *Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-        f_set_value(cg->shape, cg->fgfs[phi0->sgfn], ZEO);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-
-  lev = 0;
-  Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-        f_set_value(cg->shape, cg->fgfs[phi0->sgfn], ONE);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-
-  lev = 1;
-  MyList<Patch> *Ppc = GH->PatL[lev - 1];
-  while (Ppc)
-  {
-    Pp = GH->PatL[lev];
-    while (Pp)
-    {
-      Parallel::OutBdLow2Hi(Ppc->data, Pp->data, DG_List, DG_List, Symmetry);
-      Pp = Pp->next;
-    }
-    Ppc = Ppc->next;
-  }
-
-  Parallel::Sync(GH->PatL[lev], DG_List, Symmetry);
-
-  Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT);
-  Parallel::Dump_Data(GH->PatL[lev - 1], DG_List, 0, PhysTime, dT);
-
-  DG_List->clearList();
-  exit(0);
-}
-
-//================================================================================================
-
-
-
-//================================================================================================
-
-// This member function enforces/checks the trace-free condition
-
-//================================================================================================
-
-void bssn_class::Enforce_algcon(int lev, int fg)
-{
-  MyList<Patch> *Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-        if (fg == 0)
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                       cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                       cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                       cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-        else
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                       cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                       cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                       cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    MyList<ss_patch> *sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      int fngfs = sPp->data->fngfs;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-          if (fg == 0)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                         cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                         cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
-                         cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-          else
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                         cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
-                         cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-        }
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-  }
-#endif
-}
-
-// added by yangquan
-void bssn_class::Get_runtime_envirment()
-{
-  // get processor name
-  char pname[MPI_MAX_PROCESSOR_NAME];
-  int resultlen = 0, pcode = 0;
-  MPI_Get_processor_name(pname, &resultlen);
-  cout << "MPI rank: " << myrank << "Processor name:" << pname << endl;
-  for (int i = 0; i < resultlen; ++i)
-  {
-    pcode += ((int)(pname[i]) - 65) * i;
-  }
-
-  /*if(myrank % 2 == 0){
-
-  } */
-}
-
-//================================================================================================
-
diff --git a/AMSS_NCKU_source/bssn_gpu_class.h b/AMSS_NCKU_source/bssn_gpu_class.h
deleted file mode 100644
index 98e844d..0000000
--- a/AMSS_NCKU_source/bssn_gpu_class.h
+++ /dev/null
@@ -1,210 +0,0 @@
-
-#ifndef BSSN_GPU_CLASS_H
-#define BSSN_GPU_CLASS_H
-
-#ifdef newc
-#include <iostream>
-#include <iomanip>
-#include <fstream>
-#include <cstdlib>
-#include <string>
-#include <cmath>
-using namespace std;
-#else
-#include <iostream.h>
-#include <iomanip.h>
-#include <fstream.h>
-#include <stdlib.h>
-#include <string.h>
-#include <math.h>
-#endif
-
-#include <mpi.h>
-
-#include "macrodef.h"
-#include "cgh.h"
-#include "ShellPatch.h"
-#include "misc.h"
-#include "var.h"
-#include "MyList.h"
-#include "monitor.h"
-#include "surface_integral.h"
-#include "checkpoint.h"
-
-// added by yangquan
-#include "bssn_macro.h"
-
-extern void setpbh(int iBHN, double **iPBH, double *iMass, int rBHN);
-
-class bssn_class
-{
-public:
-       // added by yangquan
-       //----------------------
-       int gpu_num_mynode;
-       int cpu_core_num_mynode;
-       int mpi_process_num_mynode;
-       int my_sequence_mynode;
-       int mynode_id;
-       int use_gpu;
-
-       virtual void Step_GPU(int lev, int YN);
-       virtual void Get_runtime_envirment();
-       // virtual void Step_OPENMP(int lev,int YN);
-       //----------------------
-
-       int ngfs;
-       int nprocs, myrank;
-       cgh *GH;
-       ShellPatch *SH;
-       double PhysTime;
-
-       int checkrun;
-       char checkfilename[50];
-       int Steps;
-       double StartTime, TotalTime;
-       double AnasTime, DumpTime, d2DumpTime, CheckTime;
-       double LastAnas, LastConsOut;
-       double Courant;
-       double numepss, numepsb, numepsh;
-       int Symmetry;
-       int maxl, decn;
-       double maxrex, drex;
-       int trfls, a_lev;
-
-       double dT;
-       double chitiny;
-
-       double **Porg0, **Porgbr, **Porg, **Porg1, **Porg_rhs;
-       int BH_num, BH_num_input;
-       double *Mass, *Pmom, *Spin;
-       double ADMMass;
-
-       var *phio, *trKo;
-       var *gxxo, *gxyo, *gxzo, *gyyo, *gyzo, *gzzo;
-       var *Axxo, *Axyo, *Axzo, *Ayyo, *Ayzo, *Azzo;
-       var *Gmxo, *Gmyo, *Gmzo;
-       var *Lapo, *Sfxo, *Sfyo, *Sfzo;
-       var *dtSfxo, *dtSfyo, *dtSfzo;
-
-       var *phi0, *trK0;
-       var *gxx0, *gxy0, *gxz0, *gyy0, *gyz0, *gzz0;
-       var *Axx0, *Axy0, *Axz0, *Ayy0, *Ayz0, *Azz0;
-       var *Gmx0, *Gmy0, *Gmz0;
-       var *Lap0, *Sfx0, *Sfy0, *Sfz0;
-       var *dtSfx0, *dtSfy0, *dtSfz0;
-
-       var *phi, *trK;
-       var *gxx, *gxy, *gxz, *gyy, *gyz, *gzz;
-       var *Axx, *Axy, *Axz, *Ayy, *Ayz, *Azz;
-       var *Gmx, *Gmy, *Gmz;
-       var *Lap, *Sfx, *Sfy, *Sfz;
-       var *dtSfx, *dtSfy, *dtSfz;
-
-       var *phi1, *trK1;
-       var *gxx1, *gxy1, *gxz1, *gyy1, *gyz1, *gzz1;
-       var *Axx1, *Axy1, *Axz1, *Ayy1, *Ayz1, *Azz1;
-       var *Gmx1, *Gmy1, *Gmz1;
-       var *Lap1, *Sfx1, *Sfy1, *Sfz1;
-       var *dtSfx1, *dtSfy1, *dtSfz1;
-
-       var *phi_rhs, *trK_rhs;
-       var *gxx_rhs, *gxy_rhs, *gxz_rhs, *gyy_rhs, *gyz_rhs, *gzz_rhs;
-       var *Axx_rhs, *Axy_rhs, *Axz_rhs, *Ayy_rhs, *Ayz_rhs, *Azz_rhs;
-       var *Gmx_rhs, *Gmy_rhs, *Gmz_rhs;
-       var *Lap_rhs, *Sfx_rhs, *Sfy_rhs, *Sfz_rhs;
-       var *dtSfx_rhs, *dtSfy_rhs, *dtSfz_rhs;
-
-       var *rho, *Sx, *Sy, *Sz, *Sxx, *Sxy, *Sxz, *Syy, *Syz, *Szz;
-
-       var *Gamxxx, *Gamxxy, *Gamxxz, *Gamxyy, *Gamxyz, *Gamxzz;
-       var *Gamyxx, *Gamyxy, *Gamyxz, *Gamyyy, *Gamyyz, *Gamyzz;
-       var *Gamzxx, *Gamzxy, *Gamzxz, *Gamzyy, *Gamzyz, *Gamzzz;
-
-       var *Rxx, *Rxy, *Rxz, *Ryy, *Ryz, *Rzz;
-
-       var *Rpsi4, *Ipsi4;
-       var *t1Rpsi4, *t1Ipsi4, *t2Rpsi4, *t2Ipsi4;
-
-       var *Cons_Ham, *Cons_Px, *Cons_Py, *Cons_Pz, *Cons_Gx, *Cons_Gy, *Cons_Gz;
-
-#ifdef Point_Psi4
-       var *phix, *phiy, *phiz;
-       var *trKx, *trKy, *trKz;
-       var *Axxx, *Axxy, *Axxz;
-       var *Axyx, *Axyy, *Axyz;
-       var *Axzx, *Axzy, *Axzz;
-       var *Ayyx, *Ayyy, *Ayyz;
-       var *Ayzx, *Ayzy, *Ayzz;
-       var *Azzx, *Azzy, *Azzz;
-#endif
-       // FIXME: uc = StateList, up = OldStateList, upp = SynchList_cor; so never touch these three data
-       MyList<var> *StateList, *SynchList_pre, *SynchList_cor, *RHSList;
-       MyList<var> *OldStateList, *DumpList;
-       MyList<var> *ConstraintList;
-
-       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
-       monitor *ConVMonitor;
-       surface_integral *Waveshell;
-       checkpoint *CheckPoint;
-
-public:
-       bssn_class(double Couranti, double StartTimei, double TotalTimei, double DumpTimei, double d2DumpTimei, double CheckTimei, double AnasTimei,
-                  int Symmetryi, int checkruni, char *checkfilenamei, double numepssi, double numepsbi, double numepshi,
-                  int a_levi, int maxli, int decni, double maxrexi, double drexi);
-       ~bssn_class();
-
-       void Evolve(int Steps);
-       void RecursiveStep(int lev);
-#if (PSTR == 1)
-       void ParallelStep();
-       void SHStep();
-#endif
-       void RestrictProlong(int lev, int YN, bool BB, MyList<var> *SL, MyList<var> *OL, MyList<var> *corL);
-       void RestrictProlong_aux(int lev, int YN, bool BB, MyList<var> *SL, MyList<var> *OL, MyList<var> *corL);
-       void RestrictProlong(int lev, int YN, bool BB);
-       void ProlongRestrict(int lev, int YN, bool BB);
-       void Setup_Black_Hole_position();
-       void compute_Porg_rhs(double **BH_PS, double **BH_RHS, var *forx, var *fory, var *forz, int lev);
-       bool read_Pablo_file(int *ext, double *datain, char *filename);
-       void write_Pablo_file(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
-                             char *filename);
-       void AnalysisStuff(int lev, double dT_lev);
-       void Setup_KerrSchild();
-       void Enforce_algcon(int lev, int fg);
-
-       void testRestrict();
-       void testOutBd();
-
-       virtual void Setup_Initial_Data_Lousto();
-       virtual void Setup_Initial_Data_Cao();
-       virtual void Initialize();
-       virtual void Read_Ansorg();
-       virtual void Read_Pablo() {};
-       virtual void Compute_Psi4(int lev);
-       virtual void Step(int lev, int YN);
-       virtual void Interp_Constraint(bool infg);
-       virtual void Constraint_Out();
-       virtual void Compute_Constraint();
-
-#ifdef With_AHF
-protected:
-       MyList<var> *AHList, *AHDList, *GaugeList;
-       int AHfindevery;
-       double AHdumptime;
-       int *lastahdumpid, HN_num; // number of possible horizons
-       int *findeveryl;
-       double *xc, *yc, *zc, *xr, *yr, *zr;
-       bool *trigger;
-       double *dTT;
-       int *dumpid;
-
-public:
-       void AH_Prepare_derivatives();
-       bool AH_Interp_Points(MyList<var> *VarList,
-                             int NN, double **XX,
-                             double *Shellf, int Symmetryi);
-       void AH_Step_Find(int lev, double dT_lev);
-#endif
-};
-#endif /* BSSN_GPU_CLASS_H */
diff --git a/AMSS_NCKU_source/bssn_rhs_cuda.cu b/AMSS_NCKU_source/bssn_rhs_cuda.cu
new file mode 100644
index 0000000..640b1c1
--- /dev/null
+++ b/AMSS_NCKU_source/bssn_rhs_cuda.cu
@@ -0,0 +1,2565 @@
+/*
+ * bssn_rhs_cuda.cu — GPU implementation of f_compute_rhs_bssn
+ *
+ * Drop-in replacement for bssn_rhs_c.C.
+ * Compile with nvcc, link bssn_rhs_cuda.o in place of bssn_rhs_c.o.
+ */
+
+#include <cstdio>
+#include <cstdlib>
+#include <cmath>
+#include <cstring>
+#include <cuda_runtime.h>
+#include "macrodef.h"
+#include "bssn_rhs.h"
+
+/* ------------------------------------------------------------------ */
+/*  Multi-GPU dispatch: distribute ranks across available GPUs          */
+/* ------------------------------------------------------------------ */
+static struct {
+    int  num_gpus;
+    int  my_rank;
+    int  my_local_rank;
+    int  my_device;
+    bool inited;
+} g_dispatch = {0, -1, -1, -1, false};
+
+static int env_to_int(const char *name, int fallback = -1) {
+    const char *v = getenv(name);
+    if (!v || !*v) return fallback;
+    return atoi(v);
+}
+
+static void init_gpu_dispatch() {
+    if (g_dispatch.inited) return;
+    cudaError_t err = cudaGetDeviceCount(&g_dispatch.num_gpus);
+    if (err != cudaSuccess) g_dispatch.num_gpus = 1;
+    if (g_dispatch.num_gpus < 1) g_dispatch.num_gpus = 1;
+
+    /* Get MPI rank from environment (set by mpirun/mpiexec). */
+    g_dispatch.my_rank = env_to_int("PMI_RANK",
+                         env_to_int("OMPI_COMM_WORLD_RANK",
+                         env_to_int("MV2_COMM_WORLD_RANK",
+                         env_to_int("SLURM_PROCID", 0))));
+
+    /* Prefer local rank for per-node GPU mapping (avoids cross-node skew). */
+    g_dispatch.my_local_rank = env_to_int("OMPI_COMM_WORLD_LOCAL_RANK",
+                               env_to_int("MV2_COMM_WORLD_LOCAL_RANK",
+                               env_to_int("MPI_LOCALRANKID",
+                               env_to_int("SLURM_LOCALID", -1))));
+
+    const int rank_for_map = (g_dispatch.my_local_rank >= 0)
+                           ? g_dispatch.my_local_rank : g_dispatch.my_rank;
+    g_dispatch.my_device = rank_for_map % g_dispatch.num_gpus;
+    cudaSetDevice(g_dispatch.my_device);
+
+    if (g_dispatch.my_rank == 0) {
+        printf("[AMSS-GPU] %d GPU(s) detected, device map uses %s rank\n",
+               g_dispatch.num_gpus,
+               (g_dispatch.my_local_rank >= 0) ? "local" : "global");
+    }
+    g_dispatch.inited = true;
+}
+
+/* ------------------------------------------------------------------ */
+/*  Error checking                                                     */
+/* ------------------------------------------------------------------ */
+#define CUDA_CHECK(call) do {                                         \
+    cudaError_t err = (call);                                         \
+    if (err != cudaSuccess) {                                         \
+        fprintf(stderr, "CUDA error %s:%d: %s\n",                    \
+                __FILE__, __LINE__, cudaGetErrorString(err));         \
+        exit(EXIT_FAILURE);                                           \
+    }                                                                 \
+} while(0)
+
+/* ------------------------------------------------------------------ */
+/*  Physical / gauge constants (matching bssn_rhs_c.C)                 */
+/* ------------------------------------------------------------------ */
+static const double PI_VAL  = 3.14159265358979323846;
+static const double FF_VAL  = 0.75;
+static const double ETA_VAL = 2.0;
+
+/* ------------------------------------------------------------------ */
+/*  Constant memory for grid parameters and stencil coefficients       */
+/* ------------------------------------------------------------------ */
+struct GridParams {
+    int    ex[3];          /* nx, ny, nz */
+    int    all;            /* nx*ny*nz   */
+    double dX, dY, dZ;
+    /* fderivs coefficients */
+    double d12dx, d12dy, d12dz;   /* 1/(12*dX) etc */
+    double d2dx,  d2dy,  d2dz;   /* 1/(2*dX)  etc */
+    /* fdderivs coefficients */
+    double Fdxdx, Fdydy, Fdzdz;  /* 1/(12*dX^2) etc */
+    double Sdxdx, Sdydy, Sdzdz;  /* 1/(dX^2)    etc */
+    double Fdxdy, Fdxdz, Fdydz;  /* 1/(144*dX*dY) etc */
+    double Sdxdy, Sdxdz, Sdydz;  /* 1/(4*dX*dY)   etc */
+    /* symmetry bounds (Fortran 1-based) */
+    int iminF, jminF, kminF;
+    int imaxF, jmaxF, kmaxF;
+    /* symmetry bounds for ord=3 (lopsided/kodis) */
+    int iminF3, jminF3, kminF3;
+    int Symmetry;
+    double eps;
+    int co;
+    /* padded sizes */
+    int fh2_nx, fh2_ny, fh2_nz;  /* (nx+2), (ny+2), (nz+2) for ord=2 */
+    int fh3_nx, fh3_ny, fh3_nz;  /* (nx+3), (ny+3), (nz+3) for ord=3 */
+};
+
+__constant__ GridParams d_gp;
+
+/* ------------------------------------------------------------------ */
+/*  Device indexing helpers                                             */
+/* ------------------------------------------------------------------ */
+__device__ __forceinline__ int idx_ex_d(int i0, int j0, int k0) {
+    return i0 + j0 * d_gp.ex[0] + k0 * d_gp.ex[0] * d_gp.ex[1];
+}
+
+/* ord=2 ghost-padded: Fortran index iF -> flat index */
+__device__ __forceinline__ int idx_fh2(int iF, int jF, int kF) {
+    return (iF + 1) + (jF + 1) * d_gp.fh2_nx + (kF + 1) * d_gp.fh2_nx * d_gp.fh2_ny;
+}
+
+/* ord=3 ghost-padded: Fortran index iF -> flat index */
+__device__ __forceinline__ int idx_fh3(int iF, int jF, int kF) {
+    return (iF + 2) + (jF + 2) * d_gp.fh3_nx + (kF + 2) * d_gp.fh3_nx * d_gp.fh3_ny;
+}
+
+/* ------------------------------------------------------------------ */
+/*  GPU buffer management                                              */
+/* ------------------------------------------------------------------ */
+/*
+ * Array slot indices — all arrays live in one big cudaMalloc block.
+ * INPUT arrays (H2D): 39 slots
+ * OUTPUT arrays (D2H): 52 slots
+ * TEMPORARY arrays (GPU-only): ~65 slots
+ * Plus 2 extended arrays for ghost-padded stencils (fh_ord2, fh_ord3)
+ */
+
+/* Total number of "all"-sized slots */
+#define NUM_SLOTS 160
+
+struct GpuBuffers {
+    double *d_mem;          /* single big allocation */
+    double *d_fh2;          /* ghost-padded ord=2: (nx+2)*(ny+2)*(nz+2) */
+    double *d_fh3;          /* ghost-padded ord=3: (nx+3)*(ny+3)*(nz+3) */
+    double *h_stage;        /* host staging buffer for bulk H2D/D2H */
+    bool    h_stage_pinned; /* true if allocated by cudaMallocHost */
+    double *slot[NUM_SLOTS]; /* pointers into d_mem */
+    size_t  cap_all;
+    size_t  cap_fh2_size;
+    size_t  cap_fh3_size;
+    int     prev_nx, prev_ny, prev_nz;
+    bool    initialized;
+};
+
+static GpuBuffers g_buf = {
+    nullptr, nullptr, nullptr, nullptr, false, {},
+    0, 0, 0, 0, 0, 0, false
+};
+
+/* Slot assignments — INPUT (H2D) */
+enum {
+    S_chi=0, S_trK, S_dxx, S_gxy, S_gxz, S_dyy, S_gyz, S_dzz,
+    S_Axx, S_Axy, S_Axz, S_Ayy, S_Ayz, S_Azz,
+    S_Gamx, S_Gamy, S_Gamz,
+    S_Lap, S_betax, S_betay, S_betaz,
+    S_dtSfx, S_dtSfy, S_dtSfz,
+    S_rho, S_Sx, S_Sy, S_Sz,
+    S_Sxx, S_Sxy, S_Sxz, S_Syy, S_Syz, S_Szz,
+    S_X, S_Y, S_Z,                /* coordinate arrays — only nx/ny/nz long */
+    /* 37 input slots so far; X/Y/Z are special-sized */
+
+    /* OUTPUT (D2H) */
+    S_chi_rhs, S_trK_rhs,
+    S_gxx_rhs, S_gxy_rhs, S_gxz_rhs, S_gyy_rhs, S_gyz_rhs, S_gzz_rhs,
+    S_Axx_rhs, S_Axy_rhs, S_Axz_rhs, S_Ayy_rhs, S_Ayz_rhs, S_Azz_rhs,
+    S_Gamx_rhs, S_Gamy_rhs, S_Gamz_rhs,
+    S_Lap_rhs, S_betax_rhs, S_betay_rhs, S_betaz_rhs,
+    S_dtSfx_rhs, S_dtSfy_rhs, S_dtSfz_rhs,
+    S_Gamxxx, S_Gamxxy, S_Gamxxz, S_Gamxyy, S_Gamxyz, S_Gamxzz,
+    S_Gamyxx, S_Gamyxy, S_Gamyxz, S_Gamyyy, S_Gamyyz, S_Gamyzz,
+    S_Gamzxx, S_Gamzxy, S_Gamzxz, S_Gamzyy, S_Gamzyz, S_Gamzzz,
+    S_Rxx, S_Rxy, S_Rxz, S_Ryy, S_Ryz, S_Rzz,
+    S_ham_Res, S_movx_Res, S_movy_Res, S_movz_Res,
+    S_Gmx_Res, S_Gmy_Res, S_Gmz_Res,
+
+    /* TEMPORARY (GPU-only) */
+    S_gxx, S_gyy, S_gzz,          /* physical metric = dxx+1 etc */
+    S_alpn1, S_chin1,
+    S_chix, S_chiy, S_chiz,
+    S_gxxx, S_gxyx, S_gxzx, S_gyyx, S_gyzx, S_gzzx,
+    S_gxxy, S_gxyy, S_gxzy, S_gyyy, S_gyzy, S_gzzy,
+    S_gxxz, S_gxyz, S_gxzz, S_gyyz, S_gyzz, S_gzzz,
+    S_Lapx, S_Lapy, S_Lapz,
+    S_betaxx, S_betaxy, S_betaxz,
+    S_betayx, S_betayy, S_betayz,
+    S_betazx, S_betazy, S_betazz,
+    S_Gamxx, S_Gamxy, S_Gamxz,
+    S_Gamyx, S_Gamyy_t, S_Gamyz_t,
+    S_Gamzx, S_Gamzy, S_Gamzz_t,
+    S_Kx, S_Ky, S_Kz,
+    S_S_arr, S_f_arr,
+    S_fxx, S_fxy, S_fxz, S_fyy, S_fyz, S_fzz,
+    S_Gamxa, S_Gamya, S_Gamza,
+    S_gupxx, S_gupxy, S_gupxz,
+    S_gupyy, S_gupyz, S_gupzz,
+    NUM_USED_SLOTS
+};
+
+static_assert(NUM_USED_SLOTS <= NUM_SLOTS, "Increase NUM_SLOTS");
+
+static const int H2D_INPUT_SLOT_COUNT = (S_Szz - S_chi + 1);
+static const int D2H_BASE_SLOT_COUNT = (S_Rzz - S_chi_rhs + 1);
+static const int D2H_CONSTRAINT_SLOT_COUNT = (S_Gmz_Res - S_ham_Res + 1);
+static const int STAGE_SLOT_COUNT =
+    (H2D_INPUT_SLOT_COUNT > (D2H_BASE_SLOT_COUNT + D2H_CONSTRAINT_SLOT_COUNT))
+        ? H2D_INPUT_SLOT_COUNT
+        : (D2H_BASE_SLOT_COUNT + D2H_CONSTRAINT_SLOT_COUNT);
+
+static void ensure_gpu_buffers(int nx, int ny, int nz) {
+    size_t all = (size_t)nx * ny * nz;
+    size_t fh2_size = (size_t)(nx+2) * (ny+2) * (nz+2);
+    size_t fh3_size = (size_t)(nx+3) * (ny+3) * (nz+3);
+    const bool need_grow = (!g_buf.initialized)
+                        || (all > g_buf.cap_all)
+                        || (fh2_size > g_buf.cap_fh2_size)
+                        || (fh3_size > g_buf.cap_fh3_size);
+
+    if (need_grow) {
+        if (g_buf.d_mem) { cudaFree(g_buf.d_mem); g_buf.d_mem = nullptr; }
+        if (g_buf.d_fh2) { cudaFree(g_buf.d_fh2); g_buf.d_fh2 = nullptr; }
+        if (g_buf.d_fh3) { cudaFree(g_buf.d_fh3); g_buf.d_fh3 = nullptr; }
+        if (g_buf.h_stage) {
+            if (g_buf.h_stage_pinned) cudaFreeHost(g_buf.h_stage);
+            else free(g_buf.h_stage);
+            g_buf.h_stage = nullptr;
+            g_buf.h_stage_pinned = false;
+        }
+
+        CUDA_CHECK(cudaMalloc(&g_buf.d_mem, NUM_USED_SLOTS * all * sizeof(double)));
+        CUDA_CHECK(cudaMalloc(&g_buf.d_fh2, fh2_size * sizeof(double)));
+        CUDA_CHECK(cudaMalloc(&g_buf.d_fh3, fh3_size * sizeof(double)));
+
+        const size_t stage_bytes = (size_t)STAGE_SLOT_COUNT * all * sizeof(double);
+        cudaError_t stage_err = cudaMallocHost((void**)&g_buf.h_stage, stage_bytes);
+        if (stage_err == cudaSuccess) {
+            g_buf.h_stage_pinned = true;
+        } else {
+            g_buf.h_stage = (double *)malloc(stage_bytes);
+            g_buf.h_stage_pinned = false;
+            if (!g_buf.h_stage) {
+                fprintf(stderr, "Host stage allocation failed (%zu bytes)\n", stage_bytes);
+                exit(EXIT_FAILURE);
+            }
+        }
+
+        g_buf.cap_all = all;
+        g_buf.cap_fh2_size = fh2_size;
+        g_buf.cap_fh3_size = fh3_size;
+        g_buf.initialized = true;
+    }
+
+    for (int s = 0; s < NUM_USED_SLOTS; ++s)
+        g_buf.slot[s] = g_buf.d_mem + s * all;
+
+    g_buf.prev_nx = nx;
+    g_buf.prev_ny = ny;
+    g_buf.prev_nz = nz;
+}
+
+/* ================================================================== */
+/*  A. Symmetry boundary kernels (ord=2 and ord=3)                     */
+/* ================================================================== */
+
+/* Step 1: Copy interior into ghost-padded array */
+__global__ void kern_symbd_copy_interior_ord2(const double * __restrict__ func,
+                                               double * __restrict__ fh,
+                                               double SoA0, double SoA1, double SoA2)
+{
+    const int nx = d_gp.ex[0], ny = d_gp.ex[1], nz = d_gp.ex[2];
+    const int fnx = d_gp.fh2_nx, fny = d_gp.fh2_ny;
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < d_gp.all;
+         tid += blockDim.x * gridDim.x)
+    {
+        int i0 = tid % nx;
+        int j0 = (tid / nx) % ny;
+        int k0 = tid / (nx * ny);
+        int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
+        fh[(iF+1) + (jF+1)*fnx + (kF+1)*fnx*fny] = func[tid];
+    }
+}
+
+/* Fused symmetry pack (ord=2): fill full fh from interior func in one pass. */
+__global__ void kern_symbd_pack_ord2(const double * __restrict__ func,
+                                     double * __restrict__ fh,
+                                     double SoA0, double SoA1, double SoA2)
+{
+    const int nx = d_gp.ex[0], ny = d_gp.ex[1];
+    const int fnx = d_gp.fh2_nx, fny = d_gp.fh2_ny, fnz = d_gp.fh2_nz;
+    const int total = fnx * fny * fnz;
+
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < total;
+         tid += blockDim.x * gridDim.x)
+    {
+        int ii = tid % fnx;
+        int jj = (tid / fnx) % fny;
+        int kk = tid / (fnx * fny);
+
+        int iF = ii - 1;   /* -1 .. nx */
+        int jF = jj - 1;   /* -1 .. ny */
+        int kF = kk - 1;   /* -1 .. nz */
+
+        int siF = (iF <= 0) ? (1 - iF) : iF;  /* 1..nx */
+        int sjF = (jF <= 0) ? (1 - jF) : jF;  /* 1..ny */
+        int skF = (kF <= 0) ? (1 - kF) : kF;  /* 1..nz */
+
+        double sign = 1.0;
+        if (iF <= 0) sign *= SoA0;
+        if (jF <= 0) sign *= SoA1;
+        if (kF <= 0) sign *= SoA2;
+
+        int src = (siF - 1) + (sjF - 1) * nx + (skF - 1) * nx * ny;
+        fh[tid] = sign * func[src];
+    }
+}
+
+/* Step 2: Fill i-ghosts (x-direction symmetry) */
+__global__ void kern_symbd_ighost_ord2(double * __restrict__ fh, double SoA0)
+{
+    const int ny = d_gp.ex[1], nz = d_gp.ex[2];
+    const int fnx = d_gp.fh2_nx, fny = d_gp.fh2_ny;
+    /* ord=2: fill iF=0 and iF=-1, i.e. ghost layers ii=0 from ii=2, ii=1 from ii=1 */
+    /* Fortran: do ii=0,ord-1: funcc(-ii,jF,kF) = funcc(ii+1,jF,kF)*SoA[0] */
+    int total = ny * nz;  /* jF=1..ny, kF=1..nz */
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < total * 2;  /* 2 ghost layers */
+         tid += blockDim.x * gridDim.x)
+    {
+        int ii = tid / total;  /* 0 or 1 */
+        int rem = tid % total;
+        int j0 = rem % ny;
+        int k0 = rem / ny;
+        int jF = j0 + 1, kF = k0 + 1;
+        int iF_dst = -ii;     /* 0, -1 */
+        int iF_src = ii + 1;  /* 1, 2  */
+        fh[(iF_dst+1) + (jF+1)*fnx + (kF+1)*fnx*fny] =
+            fh[(iF_src+1) + (jF+1)*fnx + (kF+1)*fnx*fny] * SoA0;
+    }
+}
+
+/* Step 3: Fill j-ghosts (y-direction symmetry) */
+__global__ void kern_symbd_jghost_ord2(double * __restrict__ fh, double SoA1)
+{
+    const int nx = d_gp.ex[0], nz = d_gp.ex[2];
+    const int fnx = d_gp.fh2_nx, fny = d_gp.fh2_ny;
+    /* iF ranges from -1 to nx (i.e. -ord+1 to ex1), total = nx+2 */
+    int irange = nx + 2;
+    int total = irange * nz;
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < total * 2;
+         tid += blockDim.x * gridDim.x)
+    {
+        int jj = tid / total;
+        int rem = tid % total;
+        int ii = rem % irange;
+        int k0 = rem / irange;
+        int iF = ii - 1;  /* -1 .. nx */
+        int kF = k0 + 1;
+        int jF_dst = -jj;
+        int jF_src = jj + 1;
+        fh[(iF+1) + (jF_dst+1)*fnx + (kF+1)*fnx*fny] =
+            fh[(iF+1) + (jF_src+1)*fnx + (kF+1)*fnx*fny] * SoA1;
+    }
+}
+
+/* Step 4: Fill k-ghosts (z-direction symmetry) */
+__global__ void kern_symbd_kghost_ord2(double * __restrict__ fh, double SoA2)
+{
+    const int nx = d_gp.ex[0], ny = d_gp.ex[1];
+    const int fnx = d_gp.fh2_nx, fny = d_gp.fh2_ny;
+    int irange = nx + 2;
+    int jrange = ny + 2;
+    int total = irange * jrange;
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < total * 2;
+         tid += blockDim.x * gridDim.x)
+    {
+        int kk = tid / total;
+        int rem = tid % total;
+        int ii = rem % irange;
+        int jj = rem / irange;
+        int iF = ii - 1;
+        int jF = jj - 1;
+        int kF_dst = -kk;
+        int kF_src = kk + 1;
+        fh[(iF+1) + (jF+1)*fnx + (kF_dst+1)*fnx*fny] =
+            fh[(iF+1) + (jF+1)*fnx + (kF_src+1)*fnx*fny] * SoA2;
+    }
+}
+
+/* ---- ord=3 variants (for lopsided / kodis) ---- */
+
+__global__ void kern_symbd_copy_interior_ord3(const double * __restrict__ func,
+                                               double * __restrict__ fh)
+{
+    const int nx = d_gp.ex[0], ny = d_gp.ex[1], nz = d_gp.ex[2];
+    const int fnx = d_gp.fh3_nx, fny = d_gp.fh3_ny;
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < d_gp.all;
+         tid += blockDim.x * gridDim.x)
+    {
+        int i0 = tid % nx;
+        int j0 = (tid / nx) % ny;
+        int k0 = tid / (nx * ny);
+        int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
+        fh[(iF+2) + (jF+2)*fnx + (kF+2)*fnx*fny] = func[tid];
+    }
+}
+
+/* Fused symmetry pack (ord=3): fill full fh from interior func in one pass. */
+__global__ void kern_symbd_pack_ord3(const double * __restrict__ func,
+                                     double * __restrict__ fh,
+                                     double SoA0, double SoA1, double SoA2)
+{
+    const int nx = d_gp.ex[0], ny = d_gp.ex[1];
+    const int fnx = d_gp.fh3_nx, fny = d_gp.fh3_ny, fnz = d_gp.fh3_nz;
+    const int total = fnx * fny * fnz;
+
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < total;
+         tid += blockDim.x * gridDim.x)
+    {
+        int ii = tid % fnx;
+        int jj = (tid / fnx) % fny;
+        int kk = tid / (fnx * fny);
+
+        int iF = ii - 2;   /* -2 .. nx */
+        int jF = jj - 2;   /* -2 .. ny */
+        int kF = kk - 2;   /* -2 .. nz */
+
+        int siF = (iF <= 0) ? (1 - iF) : iF;  /* 1..nx */
+        int sjF = (jF <= 0) ? (1 - jF) : jF;  /* 1..ny */
+        int skF = (kF <= 0) ? (1 - kF) : kF;  /* 1..nz */
+
+        double sign = 1.0;
+        if (iF <= 0) sign *= SoA0;
+        if (jF <= 0) sign *= SoA1;
+        if (kF <= 0) sign *= SoA2;
+
+        int src = (siF - 1) + (sjF - 1) * nx + (skF - 1) * nx * ny;
+        fh[tid] = sign * func[src];
+    }
+}
+
+__global__ void kern_symbd_ighost_ord3(double * __restrict__ fh, double SoA0)
+{
+    const int ny = d_gp.ex[1], nz = d_gp.ex[2];
+    const int fnx = d_gp.fh3_nx, fny = d_gp.fh3_ny;
+    int total = ny * nz;
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < total * 3;
+         tid += blockDim.x * gridDim.x)
+    {
+        int ii = tid / total;
+        int rem = tid % total;
+        int j0 = rem % ny;
+        int k0 = rem / ny;
+        int jF = j0 + 1, kF = k0 + 1;
+        int iF_dst = -ii;
+        int iF_src = ii + 1;
+        fh[(iF_dst+2) + (jF+2)*fnx + (kF+2)*fnx*fny] =
+            fh[(iF_src+2) + (jF+2)*fnx + (kF+2)*fnx*fny] * SoA0;
+    }
+}
+
+__global__ void kern_symbd_jghost_ord3(double * __restrict__ fh, double SoA1)
+{
+    const int nx = d_gp.ex[0], nz = d_gp.ex[2];
+    const int fnx = d_gp.fh3_nx, fny = d_gp.fh3_ny;
+    int irange = nx + 3;
+    int total = irange * nz;
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < total * 3;
+         tid += blockDim.x * gridDim.x)
+    {
+        int jj = tid / total;
+        int rem = tid % total;
+        int ii = rem % irange;
+        int k0 = rem / irange;
+        int iF = ii - 2;
+        int kF = k0 + 1;
+        int jF_dst = -jj;
+        int jF_src = jj + 1;
+        fh[(iF+2) + (jF_dst+2)*fnx + (kF+2)*fnx*fny] =
+            fh[(iF+2) + (jF_src+2)*fnx + (kF+2)*fnx*fny] * SoA1;
+    }
+}
+
+__global__ void kern_symbd_kghost_ord3(double * __restrict__ fh, double SoA2)
+{
+    const int nx = d_gp.ex[0], ny = d_gp.ex[1];
+    const int fnx = d_gp.fh3_nx, fny = d_gp.fh3_ny;
+    int irange = nx + 3;
+    int jrange = ny + 3;
+    int total = irange * jrange;
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < total * 3;
+         tid += blockDim.x * gridDim.x)
+    {
+        int kk = tid / total;
+        int rem = tid % total;
+        int ii = rem % irange;
+        int jj = rem / irange;
+        int iF = ii - 2;
+        int jF = jj - 2;
+        int kF_dst = -kk;
+        int kF_src = kk + 1;
+        fh[(iF+2) + (jF+2)*fnx + (kF_dst+2)*fnx*fny] =
+            fh[(iF+2) + (jF+2)*fnx + (kF_src+2)*fnx*fny] * SoA2;
+    }
+}
+
+/* ================================================================== */
+/*  B. Stencil kernels                                                 */
+/* ================================================================== */
+
+/* ---- First derivatives (ord=2, 4th/2nd order) ---- */
+__global__ __launch_bounds__(128, 4)
+void kern_fderivs(const double * __restrict__ fh,
+                  double * __restrict__ fx,
+                  double * __restrict__ fy,
+                  double * __restrict__ fz)
+{
+    const int nx = d_gp.ex[0], ny = d_gp.ex[1], nz = d_gp.ex[2];
+    const int imaxF = d_gp.imaxF, jmaxF = d_gp.jmaxF, kmaxF = d_gp.kmaxF;
+    const int iminF = d_gp.iminF, jminF = d_gp.jminF, kminF = d_gp.kminF;
+
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < d_gp.all;
+         tid += blockDim.x * gridDim.x)
+    {
+        int i0 = tid % nx;
+        int j0 = (tid / nx) % ny;
+        int k0 = tid / (nx * ny);
+
+        /* boundary points: leave as zero */
+        if (i0 > nx - 2 || j0 > ny - 2 || k0 > nz - 2) {
+            fx[tid] = 0.0; fy[tid] = 0.0; fz[tid] = 0.0;
+            continue;
+        }
+
+        int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
+
+        if ((iF+2) <= imaxF && (iF-2) >= iminF &&
+            (jF+2) <= jmaxF && (jF-2) >= jminF &&
+            (kF+2) <= kmaxF && (kF-2) >= kminF)
+        {
+            fx[tid] = d_gp.d12dx * (
+                fh[idx_fh2(iF-2,jF,kF)] - 8.0*fh[idx_fh2(iF-1,jF,kF)]
+              + 8.0*fh[idx_fh2(iF+1,jF,kF)] - fh[idx_fh2(iF+2,jF,kF)]);
+            fy[tid] = d_gp.d12dy * (
+                fh[idx_fh2(iF,jF-2,kF)] - 8.0*fh[idx_fh2(iF,jF-1,kF)]
+              + 8.0*fh[idx_fh2(iF,jF+1,kF)] - fh[idx_fh2(iF,jF+2,kF)]);
+            fz[tid] = d_gp.d12dz * (
+                fh[idx_fh2(iF,jF,kF-2)] - 8.0*fh[idx_fh2(iF,jF,kF-1)]
+              + 8.0*fh[idx_fh2(iF,jF,kF+1)] - fh[idx_fh2(iF,jF,kF+2)]);
+        }
+        else if ((iF+1) <= imaxF && (iF-1) >= iminF &&
+                 (jF+1) <= jmaxF && (jF-1) >= jminF &&
+                 (kF+1) <= kmaxF && (kF-1) >= kminF)
+        {
+            fx[tid] = d_gp.d2dx * (
+                -fh[idx_fh2(iF-1,jF,kF)] + fh[idx_fh2(iF+1,jF,kF)]);
+            fy[tid] = d_gp.d2dy * (
+                -fh[idx_fh2(iF,jF-1,kF)] + fh[idx_fh2(iF,jF+1,kF)]);
+            fz[tid] = d_gp.d2dz * (
+                -fh[idx_fh2(iF,jF,kF-1)] + fh[idx_fh2(iF,jF,kF+1)]);
+        }
+        else {
+            fx[tid] = 0.0; fy[tid] = 0.0; fz[tid] = 0.0;
+        }
+    }
+}
+
+/* ---- Second derivatives (ord=2, 4th/2nd order) ---- */
+__global__ __launch_bounds__(128, 4)
+void kern_fdderivs(const double * __restrict__ fh,
+                   double * __restrict__ fxx, double * __restrict__ fxy,
+                   double * __restrict__ fxz, double * __restrict__ fyy,
+                   double * __restrict__ fyz, double * __restrict__ fzz)
+{
+    const int nx = d_gp.ex[0], ny = d_gp.ex[1], nz = d_gp.ex[2];
+    const int imaxF = d_gp.imaxF, jmaxF = d_gp.jmaxF, kmaxF = d_gp.kmaxF;
+    const int iminF = d_gp.iminF, jminF = d_gp.jminF, kminF = d_gp.kminF;
+
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < d_gp.all;
+         tid += blockDim.x * gridDim.x)
+    {
+        int i0 = tid % nx;
+        int j0 = (tid / nx) % ny;
+        int k0 = tid / (nx * ny);
+
+        if (i0 > nx - 2 || j0 > ny - 2 || k0 > nz - 2) {
+            fxx[tid]=0; fxy[tid]=0; fxz[tid]=0;
+            fyy[tid]=0; fyz[tid]=0; fzz[tid]=0;
+            continue;
+        }
+
+        int iF = i0+1, jF = j0+1, kF = k0+1;
+
+        if ((iF+2)<=imaxF && (iF-2)>=iminF &&
+            (jF+2)<=jmaxF && (jF-2)>=jminF &&
+            (kF+2)<=kmaxF && (kF-2)>=kminF)
+        {
+            /* 4th-order diagonal */
+            double c = fh[idx_fh2(iF,jF,kF)];
+            fxx[tid] = d_gp.Fdxdx*(
+                -fh[idx_fh2(iF-2,jF,kF)] + 16.0*fh[idx_fh2(iF-1,jF,kF)]
+                -30.0*c + 16.0*fh[idx_fh2(iF+1,jF,kF)] - fh[idx_fh2(iF+2,jF,kF)]);
+            fyy[tid] = d_gp.Fdydy*(
+                -fh[idx_fh2(iF,jF-2,kF)] + 16.0*fh[idx_fh2(iF,jF-1,kF)]
+                -30.0*c + 16.0*fh[idx_fh2(iF,jF+1,kF)] - fh[idx_fh2(iF,jF+2,kF)]);
+            fzz[tid] = d_gp.Fdzdz*(
+                -fh[idx_fh2(iF,jF,kF-2)] + 16.0*fh[idx_fh2(iF,jF,kF-1)]
+                -30.0*c + 16.0*fh[idx_fh2(iF,jF,kF+1)] - fh[idx_fh2(iF,jF,kF+2)]);
+
+            /* 4th-order cross: fxy */
+            {
+                double t_jm2 = fh[idx_fh2(iF-2,jF-2,kF)] - 8.0*fh[idx_fh2(iF-1,jF-2,kF)]
+                             + 8.0*fh[idx_fh2(iF+1,jF-2,kF)] - fh[idx_fh2(iF+2,jF-2,kF)];
+                double t_jm1 = fh[idx_fh2(iF-2,jF-1,kF)] - 8.0*fh[idx_fh2(iF-1,jF-1,kF)]
+                             + 8.0*fh[idx_fh2(iF+1,jF-1,kF)] - fh[idx_fh2(iF+2,jF-1,kF)];
+                double t_jp1 = fh[idx_fh2(iF-2,jF+1,kF)] - 8.0*fh[idx_fh2(iF-1,jF+1,kF)]
+                             + 8.0*fh[idx_fh2(iF+1,jF+1,kF)] - fh[idx_fh2(iF+2,jF+1,kF)];
+                double t_jp2 = fh[idx_fh2(iF-2,jF+2,kF)] - 8.0*fh[idx_fh2(iF-1,jF+2,kF)]
+                             + 8.0*fh[idx_fh2(iF+1,jF+2,kF)] - fh[idx_fh2(iF+2,jF+2,kF)];
+                fxy[tid] = d_gp.Fdxdy*(t_jm2 - 8.0*t_jm1 + 8.0*t_jp1 - t_jp2);
+            }
+            /* 4th-order cross: fxz */
+            {
+                double t_km2 = fh[idx_fh2(iF-2,jF,kF-2)] - 8.0*fh[idx_fh2(iF-1,jF,kF-2)]
+                             + 8.0*fh[idx_fh2(iF+1,jF,kF-2)] - fh[idx_fh2(iF+2,jF,kF-2)];
+                double t_km1 = fh[idx_fh2(iF-2,jF,kF-1)] - 8.0*fh[idx_fh2(iF-1,jF,kF-1)]
+                             + 8.0*fh[idx_fh2(iF+1,jF,kF-1)] - fh[idx_fh2(iF+2,jF,kF-1)];
+                double t_kp1 = fh[idx_fh2(iF-2,jF,kF+1)] - 8.0*fh[idx_fh2(iF-1,jF,kF+1)]
+                             + 8.0*fh[idx_fh2(iF+1,jF,kF+1)] - fh[idx_fh2(iF+2,jF,kF+1)];
+                double t_kp2 = fh[idx_fh2(iF-2,jF,kF+2)] - 8.0*fh[idx_fh2(iF-1,jF,kF+2)]
+                             + 8.0*fh[idx_fh2(iF+1,jF,kF+2)] - fh[idx_fh2(iF+2,jF,kF+2)];
+                fxz[tid] = d_gp.Fdxdz*(t_km2 - 8.0*t_km1 + 8.0*t_kp1 - t_kp2);
+            }
+            /* 4th-order cross: fyz */
+            {
+                double t_km2 = fh[idx_fh2(iF,jF-2,kF-2)] - 8.0*fh[idx_fh2(iF,jF-1,kF-2)]
+                             + 8.0*fh[idx_fh2(iF,jF+1,kF-2)] - fh[idx_fh2(iF,jF+2,kF-2)];
+                double t_km1 = fh[idx_fh2(iF,jF-2,kF-1)] - 8.0*fh[idx_fh2(iF,jF-1,kF-1)]
+                             + 8.0*fh[idx_fh2(iF,jF+1,kF-1)] - fh[idx_fh2(iF,jF+2,kF-1)];
+                double t_kp1 = fh[idx_fh2(iF,jF-2,kF+1)] - 8.0*fh[idx_fh2(iF,jF-1,kF+1)]
+                             + 8.0*fh[idx_fh2(iF,jF+1,kF+1)] - fh[idx_fh2(iF,jF+2,kF+1)];
+                double t_kp2 = fh[idx_fh2(iF,jF-2,kF+2)] - 8.0*fh[idx_fh2(iF,jF-1,kF+2)]
+                             + 8.0*fh[idx_fh2(iF,jF+1,kF+2)] - fh[idx_fh2(iF,jF+2,kF+2)];
+                fyz[tid] = d_gp.Fdydz*(t_km2 - 8.0*t_km1 + 8.0*t_kp1 - t_kp2);
+            }
+        }
+        else if ((iF+1)<=imaxF && (iF-1)>=iminF &&
+                 (jF+1)<=jmaxF && (jF-1)>=jminF &&
+                 (kF+1)<=kmaxF && (kF-1)>=kminF)
+        {
+            double c = fh[idx_fh2(iF,jF,kF)];
+            fxx[tid] = d_gp.Sdxdx*(fh[idx_fh2(iF-1,jF,kF)] - 2.0*c + fh[idx_fh2(iF+1,jF,kF)]);
+            fyy[tid] = d_gp.Sdydy*(fh[idx_fh2(iF,jF-1,kF)] - 2.0*c + fh[idx_fh2(iF,jF+1,kF)]);
+            fzz[tid] = d_gp.Sdzdz*(fh[idx_fh2(iF,jF,kF-1)] - 2.0*c + fh[idx_fh2(iF,jF,kF+1)]);
+            fxy[tid] = d_gp.Sdxdy*(fh[idx_fh2(iF-1,jF-1,kF)] - fh[idx_fh2(iF+1,jF-1,kF)]
+                                   -fh[idx_fh2(iF-1,jF+1,kF)] + fh[idx_fh2(iF+1,jF+1,kF)]);
+            fxz[tid] = d_gp.Sdxdz*(fh[idx_fh2(iF-1,jF,kF-1)] - fh[idx_fh2(iF+1,jF,kF-1)]
+                                   -fh[idx_fh2(iF-1,jF,kF+1)] + fh[idx_fh2(iF+1,jF,kF+1)]);
+            fyz[tid] = d_gp.Sdydz*(fh[idx_fh2(iF,jF-1,kF-1)] - fh[idx_fh2(iF,jF+1,kF-1)]
+                                   -fh[idx_fh2(iF,jF-1,kF+1)] + fh[idx_fh2(iF,jF+1,kF+1)]);
+        }
+        else {
+            fxx[tid]=0; fxy[tid]=0; fxz[tid]=0;
+            fyy[tid]=0; fyz[tid]=0; fzz[tid]=0;
+        }
+    }
+}
+
+/* ---- Lopsided (upwind advection) kernel ---- */
+__global__ __launch_bounds__(128, 4)
+void kern_lopsided(const double * __restrict__ fh,
+                   double * __restrict__ f_rhs,
+                   const double * __restrict__ Sfx,
+                   const double * __restrict__ Sfy,
+                   const double * __restrict__ Sfz)
+{
+    const int nx = d_gp.ex[0], ny = d_gp.ex[1], nz = d_gp.ex[2];
+    const int iminF = d_gp.iminF3, jminF = d_gp.jminF3, kminF = d_gp.kminF3;
+
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < d_gp.all;
+         tid += blockDim.x * gridDim.x)
+    {
+        int i0 = tid % nx;
+        int j0 = (tid / nx) % ny;
+        int k0 = tid / (nx * ny);
+
+        if (i0 > nx - 2 || j0 > ny - 2 || k0 > nz - 2) continue;
+
+        int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
+        double val = 0.0;
+
+        /* --- x direction --- */
+        double sfx = Sfx[tid];
+        if (sfx > 0.0) {
+            if (i0 <= nx - 4) {
+                val += sfx * d_gp.d12dx * (
+                    -3.0*fh[idx_fh3(iF-1,jF,kF)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF+1,jF,kF)] - 6.0*fh[idx_fh3(iF+2,jF,kF)]
+                    + fh[idx_fh3(iF+3,jF,kF)]);
+            } else if (i0 <= nx - 3) {
+                val += sfx * d_gp.d12dx * (
+                    fh[idx_fh3(iF-2,jF,kF)] - 8.0*fh[idx_fh3(iF-1,jF,kF)]
+                    +8.0*fh[idx_fh3(iF+1,jF,kF)] - fh[idx_fh3(iF+2,jF,kF)]);
+            } else if (i0 <= nx - 2) {
+                val -= sfx * d_gp.d12dx * (
+                    -3.0*fh[idx_fh3(iF+1,jF,kF)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF-1,jF,kF)] - 6.0*fh[idx_fh3(iF-2,jF,kF)]
+                    + fh[idx_fh3(iF-3,jF,kF)]);
+            }
+        } else if (sfx < 0.0) {
+            if ((i0 - 2) >= iminF) {
+                val -= sfx * d_gp.d12dx * (
+                    -3.0*fh[idx_fh3(iF+1,jF,kF)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF-1,jF,kF)] - 6.0*fh[idx_fh3(iF-2,jF,kF)]
+                    + fh[idx_fh3(iF-3,jF,kF)]);
+            } else if ((i0 - 1) >= iminF) {
+                val += sfx * d_gp.d12dx * (
+                    fh[idx_fh3(iF-2,jF,kF)] - 8.0*fh[idx_fh3(iF-1,jF,kF)]
+                    +8.0*fh[idx_fh3(iF+1,jF,kF)] - fh[idx_fh3(iF+2,jF,kF)]);
+            } else if (i0 >= iminF) {
+                val += sfx * d_gp.d12dx * (
+                    -3.0*fh[idx_fh3(iF-1,jF,kF)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF+1,jF,kF)] - 6.0*fh[idx_fh3(iF+2,jF,kF)]
+                    + fh[idx_fh3(iF+3,jF,kF)]);
+            }
+        }
+
+        /* --- y direction --- */
+        double sfy = Sfy[tid];
+        if (sfy > 0.0) {
+            if (j0 <= ny - 4) {
+                val += sfy * d_gp.d12dy * (
+                    -3.0*fh[idx_fh3(iF,jF-1,kF)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF,jF+1,kF)] - 6.0*fh[idx_fh3(iF,jF+2,kF)]
+                    + fh[idx_fh3(iF,jF+3,kF)]);
+            } else if (j0 <= ny - 3) {
+                val += sfy * d_gp.d12dy * (
+                    fh[idx_fh3(iF,jF-2,kF)] - 8.0*fh[idx_fh3(iF,jF-1,kF)]
+                    +8.0*fh[idx_fh3(iF,jF+1,kF)] - fh[idx_fh3(iF,jF+2,kF)]);
+            } else if (j0 <= ny - 2) {
+                val -= sfy * d_gp.d12dy * (
+                    -3.0*fh[idx_fh3(iF,jF+1,kF)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF,jF-1,kF)] - 6.0*fh[idx_fh3(iF,jF-2,kF)]
+                    + fh[idx_fh3(iF,jF-3,kF)]);
+            }
+        } else if (sfy < 0.0) {
+            if ((j0 - 2) >= jminF) {
+                val -= sfy * d_gp.d12dy * (
+                    -3.0*fh[idx_fh3(iF,jF+1,kF)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF,jF-1,kF)] - 6.0*fh[idx_fh3(iF,jF-2,kF)]
+                    + fh[idx_fh3(iF,jF-3,kF)]);
+            } else if ((j0 - 1) >= jminF) {
+                val += sfy * d_gp.d12dy * (
+                    fh[idx_fh3(iF,jF-2,kF)] - 8.0*fh[idx_fh3(iF,jF-1,kF)]
+                    +8.0*fh[idx_fh3(iF,jF+1,kF)] - fh[idx_fh3(iF,jF+2,kF)]);
+            } else if (j0 >= jminF) {
+                val += sfy * d_gp.d12dy * (
+                    -3.0*fh[idx_fh3(iF,jF-1,kF)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF,jF+1,kF)] - 6.0*fh[idx_fh3(iF,jF+2,kF)]
+                    + fh[idx_fh3(iF,jF+3,kF)]);
+            }
+        }
+
+        /* --- z direction --- */
+        double sfz = Sfz[tid];
+        if (sfz > 0.0) {
+            if (k0 <= nz - 4) {
+                val += sfz * d_gp.d12dz * (
+                    -3.0*fh[idx_fh3(iF,jF,kF-1)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF,jF,kF+1)] - 6.0*fh[idx_fh3(iF,jF,kF+2)]
+                    + fh[idx_fh3(iF,jF,kF+3)]);
+            } else if (k0 <= nz - 3) {
+                val += sfz * d_gp.d12dz * (
+                    fh[idx_fh3(iF,jF,kF-2)] - 8.0*fh[idx_fh3(iF,jF,kF-1)]
+                    +8.0*fh[idx_fh3(iF,jF,kF+1)] - fh[idx_fh3(iF,jF,kF+2)]);
+            } else if (k0 <= nz - 2) {
+                val -= sfz * d_gp.d12dz * (
+                    -3.0*fh[idx_fh3(iF,jF,kF+1)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF,jF,kF-1)] - 6.0*fh[idx_fh3(iF,jF,kF-2)]
+                    + fh[idx_fh3(iF,jF,kF-3)]);
+            }
+        } else if (sfz < 0.0) {
+            if ((k0 - 2) >= kminF) {
+                val -= sfz * d_gp.d12dz * (
+                    -3.0*fh[idx_fh3(iF,jF,kF+1)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF,jF,kF-1)] - 6.0*fh[idx_fh3(iF,jF,kF-2)]
+                    + fh[idx_fh3(iF,jF,kF-3)]);
+            } else if ((k0 - 1) >= kminF) {
+                val += sfz * d_gp.d12dz * (
+                    fh[idx_fh3(iF,jF,kF-2)] - 8.0*fh[idx_fh3(iF,jF,kF-1)]
+                    +8.0*fh[idx_fh3(iF,jF,kF+1)] - fh[idx_fh3(iF,jF,kF+2)]);
+            } else if (k0 >= kminF) {
+                val += sfz * d_gp.d12dz * (
+                    -3.0*fh[idx_fh3(iF,jF,kF-1)] - 10.0*fh[idx_fh3(iF,jF,kF)]
+                    +18.0*fh[idx_fh3(iF,jF,kF+1)] - 6.0*fh[idx_fh3(iF,jF,kF+2)]
+                    + fh[idx_fh3(iF,jF,kF+3)]);
+            }
+        }
+
+        f_rhs[tid] += val;
+    }
+}
+
+/* ---- KO dissipation kernel (ord=3, 6th-order) ---- */
+__global__ __launch_bounds__(128, 4)
+void kern_kodis(const double * __restrict__ fh,
+                double * __restrict__ f_rhs,
+                double eps_val)
+{
+    const int nx = d_gp.ex[0], ny = d_gp.ex[1], nz = d_gp.ex[2];
+    const int iminF = d_gp.iminF3, jminF = d_gp.jminF3, kminF = d_gp.kminF3;
+    const int imaxF = d_gp.imaxF, jmaxF = d_gp.jmaxF, kmaxF = d_gp.kmaxF;
+    const double cof = 64.0;
+
+    for (int tid = blockIdx.x * blockDim.x + threadIdx.x;
+         tid < d_gp.all;
+         tid += blockDim.x * gridDim.x)
+    {
+        int i0 = tid % nx;
+        int j0 = (tid / nx) % ny;
+        int k0 = tid / (nx * ny);
+        int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
+
+        if ((iF-3) >= iminF && (iF+3) <= imaxF &&
+            (jF-3) >= jminF && (jF+3) <= jmaxF &&
+            (kF-3) >= kminF && (kF+3) <= kmaxF)
+        {
+            double Dx = (fh[idx_fh3(iF-3,jF,kF)] + fh[idx_fh3(iF+3,jF,kF)])
+                - 6.0*(fh[idx_fh3(iF-2,jF,kF)] + fh[idx_fh3(iF+2,jF,kF)])
+                +15.0*(fh[idx_fh3(iF-1,jF,kF)] + fh[idx_fh3(iF+1,jF,kF)])
+                -20.0* fh[idx_fh3(iF,jF,kF)];
+            Dx /= d_gp.dX;
+
+            double Dy = (fh[idx_fh3(iF,jF-3,kF)] + fh[idx_fh3(iF,jF+3,kF)])
+                - 6.0*(fh[idx_fh3(iF,jF-2,kF)] + fh[idx_fh3(iF,jF+2,kF)])
+                +15.0*(fh[idx_fh3(iF,jF-1,kF)] + fh[idx_fh3(iF,jF+1,kF)])
+                -20.0* fh[idx_fh3(iF,jF,kF)];
+            Dy /= d_gp.dY;
+
+            double Dz = (fh[idx_fh3(iF,jF,kF-3)] + fh[idx_fh3(iF,jF,kF+3)])
+                - 6.0*(fh[idx_fh3(iF,jF,kF-2)] + fh[idx_fh3(iF,jF,kF+2)])
+                +15.0*(fh[idx_fh3(iF,jF,kF-1)] + fh[idx_fh3(iF,jF,kF+1)])
+                -20.0* fh[idx_fh3(iF,jF,kF)];
+            Dz /= d_gp.dZ;
+
+            f_rhs[tid] += (eps_val / cof) * (Dx + Dy + Dz);
+        }
+    }
+}
+
+/* ================================================================== */
+/*  Host wrapper helpers                                               */
+/* ================================================================== */
+static const int BLK = 128;
+static inline int grid(size_t n) {
+    if (n == 0) return 1;
+    size_t g = (n + BLK - 1) / BLK;
+    if (g > 2147483647u) g = 2147483647u;
+    return (int)g;
+}
+
+/* symmetry_bd on GPU for ord=2, then launch fderivs kernel */
+static void gpu_fderivs(double *d_f, double *d_fx, double *d_fy, double *d_fz,
+                        double SoA0, double SoA1, double SoA2, int all)
+{
+    double *fh = g_buf.d_fh2;
+    const size_t nx = (size_t)g_buf.prev_nx;
+    const size_t ny = (size_t)g_buf.prev_ny;
+    const size_t nz = (size_t)g_buf.prev_nz;
+    const size_t w_pack = (nx + 2ull) * (ny + 2ull) * (nz + 2ull);
+
+    kern_symbd_pack_ord2<<<grid(w_pack), BLK>>>(d_f, fh, SoA0, SoA1, SoA2);
+    kern_fderivs<<<grid(all), BLK>>>(fh, d_fx, d_fy, d_fz);
+}
+
+/* symmetry_bd on GPU for ord=2, then launch fdderivs kernel */
+static void gpu_fdderivs(double *d_f,
+                         double *d_fxx, double *d_fxy, double *d_fxz,
+                         double *d_fyy, double *d_fyz, double *d_fzz,
+                         double SoA0, double SoA1, double SoA2, int all)
+{
+    double *fh = g_buf.d_fh2;
+    const size_t nx = (size_t)g_buf.prev_nx;
+    const size_t ny = (size_t)g_buf.prev_ny;
+    const size_t nz = (size_t)g_buf.prev_nz;
+    const size_t w_pack = (nx + 2ull) * (ny + 2ull) * (nz + 2ull);
+
+    kern_symbd_pack_ord2<<<grid(w_pack), BLK>>>(d_f, fh, SoA0, SoA1, SoA2);
+    kern_fdderivs<<<grid(all), BLK>>>(fh, d_fxx, d_fxy, d_fxz, d_fyy, d_fyz, d_fzz);
+}
+
+/* Combined ord=3 advection + KO dissipation.
+ * When advection and KO use the same source field, symmetry packing is shared.
+ * If they differ (e.g. gxx advection + dxx KO), only KO repacks.
+ */
+static void gpu_lopsided_kodis(double *d_f_adv, double *d_f_ko, double *d_f_rhs,
+                               double *d_Sfx, double *d_Sfy, double *d_Sfz,
+                               double SoA0, double SoA1, double SoA2,
+                               double eps_val, int all)
+{
+    double *fh = g_buf.d_fh3;
+    const size_t nx = (size_t)g_buf.prev_nx;
+    const size_t ny = (size_t)g_buf.prev_ny;
+    const size_t nz = (size_t)g_buf.prev_nz;
+    const size_t w_pack = (nx + 3ull) * (ny + 3ull) * (nz + 3ull);
+
+    kern_symbd_pack_ord3<<<grid(w_pack), BLK>>>(d_f_adv, fh, SoA0, SoA1, SoA2);
+    kern_lopsided<<<grid(all), BLK>>>(fh, d_f_rhs, d_Sfx, d_Sfy, d_Sfz);
+
+    if (eps_val > 0.0) {
+        if (d_f_ko != d_f_adv) {
+            kern_symbd_pack_ord3<<<grid(w_pack), BLK>>>(d_f_ko, fh, SoA0, SoA1, SoA2);
+        }
+        kern_kodis<<<grid(all), BLK>>>(fh, d_f_rhs, eps_val);
+    }
+}
+
+/* ================================================================== */
+/*  C. Point-wise computation kernels                                  */
+/* ================================================================== */
+
+/* Phase 1: alpn1, chin1, gxx=dxx+1, gyy=dyy+1, gzz=dzz+1 */
+__global__ void kern_phase1_prep(
+    const double* __restrict__ Lap, const double* __restrict__ chi,
+    const double* __restrict__ dxx, const double* __restrict__ dyy,
+    const double* __restrict__ dzz,
+    double* __restrict__ alpn1, double* __restrict__ chin1,
+    double* __restrict__ gxx, double* __restrict__ gyy, double* __restrict__ gzz)
+{
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        alpn1[i] = Lap[i] + 1.0;
+        chin1[i] = chi[i] + 1.0;
+        gxx[i] = dxx[i] + 1.0;
+        gyy[i] = dyy[i] + 1.0;
+        gzz[i] = dzz[i] + 1.0;
+    }
+}
+
+/* Phase 2a: chi_rhs, gij_rhs */
+__global__ void kern_phase2_metric_rhs(
+    const double* __restrict__ alpn1, const double* __restrict__ chin1,
+    const double* __restrict__ gxx, const double* __restrict__ gxy,
+    const double* __restrict__ gxz, const double* __restrict__ gyy,
+    const double* __restrict__ gyz, const double* __restrict__ gzz,
+    const double* __restrict__ trK,
+    const double* __restrict__ Axx, const double* __restrict__ Axy,
+    const double* __restrict__ Axz, const double* __restrict__ Ayy,
+    const double* __restrict__ Ayz, const double* __restrict__ Azz,
+    const double* __restrict__ betaxx, const double* __restrict__ betaxy,
+    const double* __restrict__ betaxz, const double* __restrict__ betayx,
+    const double* __restrict__ betayy, const double* __restrict__ betayz,
+    const double* __restrict__ betazx, const double* __restrict__ betazy,
+    const double* __restrict__ betazz,
+    double* __restrict__ chi_rhs, double* __restrict__ gxx_rhs,
+    double* __restrict__ gyy_rhs, double* __restrict__ gzz_rhs,
+    double* __restrict__ gxy_rhs, double* __restrict__ gyz_rhs,
+    double* __restrict__ gxz_rhs)
+{
+    const double F2o3 = 2.0/3.0, F1o3 = 1.0/3.0, TWO = 2.0;
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double db = betaxx[i] + betayy[i] + betazz[i];
+        chi_rhs[i] = F2o3 * chin1[i] * (alpn1[i] * trK[i] - db);
+        gxx_rhs[i] = -TWO*alpn1[i]*Axx[i] - F2o3*gxx[i]*db
+            + TWO*(gxx[i]*betaxx[i] + gxy[i]*betayx[i] + gxz[i]*betazx[i]);
+        gyy_rhs[i] = -TWO*alpn1[i]*Ayy[i] - F2o3*gyy[i]*db
+            + TWO*(gxy[i]*betaxy[i] + gyy[i]*betayy[i] + gyz[i]*betazy[i]);
+        gzz_rhs[i] = -TWO*alpn1[i]*Azz[i] - F2o3*gzz[i]*db
+            + TWO*(gxz[i]*betaxz[i] + gyz[i]*betayz[i] + gzz[i]*betazz[i]);
+        gxy_rhs[i] = -TWO*alpn1[i]*Axy[i] + F1o3*gxy[i]*db
+            + gxx[i]*betaxy[i] + gxz[i]*betazy[i] + gyy[i]*betayx[i]
+            + gyz[i]*betazx[i] - gxy[i]*betazz[i];
+        gyz_rhs[i] = -TWO*alpn1[i]*Ayz[i] + F1o3*gyz[i]*db
+            + gxy[i]*betaxz[i] + gyy[i]*betayz[i] + gxz[i]*betaxy[i]
+            + gzz[i]*betazy[i] - gyz[i]*betaxx[i];
+        gxz_rhs[i] = -TWO*alpn1[i]*Axz[i] + F1o3*gxz[i]*db
+            + gxx[i]*betaxz[i] + gxy[i]*betayz[i] + gyz[i]*betayx[i]
+            + gzz[i]*betazx[i] - gxz[i]*betayy[i];
+    }
+}
+
+/* Phase 2b: metric inverse */
+__global__ void kern_phase2_inverse(
+    const double* __restrict__ gxx, const double* __restrict__ gxy,
+    const double* __restrict__ gxz, const double* __restrict__ gyy,
+    const double* __restrict__ gyz, const double* __restrict__ gzz,
+    double* __restrict__ gupxx, double* __restrict__ gupxy,
+    double* __restrict__ gupxz, double* __restrict__ gupyy,
+    double* __restrict__ gupyz, double* __restrict__ gupzz)
+{
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double det = gxx[i]*gyy[i]*gzz[i] + gxy[i]*gyz[i]*gxz[i] + gxz[i]*gxy[i]*gyz[i]
+                   - gxz[i]*gyy[i]*gxz[i] - gxy[i]*gxy[i]*gzz[i] - gxx[i]*gyz[i]*gyz[i];
+        double inv = 1.0 / det;
+        gupxx[i] = (gyy[i]*gzz[i] - gyz[i]*gyz[i]) * inv;
+        gupxy[i] = -(gxy[i]*gzz[i] - gyz[i]*gxz[i]) * inv;
+        gupxz[i] = (gxy[i]*gyz[i] - gyy[i]*gxz[i]) * inv;
+        gupyy[i] = (gxx[i]*gzz[i] - gxz[i]*gxz[i]) * inv;
+        gupyz[i] = -(gxx[i]*gyz[i] - gxy[i]*gxz[i]) * inv;
+        gupzz[i] = (gxx[i]*gyy[i] - gxy[i]*gxy[i]) * inv;
+    }
+}
+
+/* Phase 3: Gamma constraint residuals (co==0 only) */
+__global__ void kern_phase3_gamma_constraint(
+    const double* __restrict__ Gamx, const double* __restrict__ Gamy,
+    const double* __restrict__ Gamz,
+    const double* __restrict__ gupxx, const double* __restrict__ gupxy,
+    const double* __restrict__ gupxz, const double* __restrict__ gupyy,
+    const double* __restrict__ gupyz, const double* __restrict__ gupzz,
+    const double* __restrict__ gxxx, const double* __restrict__ gxyx,
+    const double* __restrict__ gxzx, const double* __restrict__ gyyx,
+    const double* __restrict__ gyzx, const double* __restrict__ gzzx,
+    const double* __restrict__ gxxy, const double* __restrict__ gxyy,
+    const double* __restrict__ gxzy, const double* __restrict__ gyyy,
+    const double* __restrict__ gyzy, const double* __restrict__ gzzy,
+    const double* __restrict__ gxxz, const double* __restrict__ gxyz,
+    const double* __restrict__ gxzz, const double* __restrict__ gyyz,
+    const double* __restrict__ gyzz, const double* __restrict__ gzzz,
+    double* __restrict__ Gmx_Res, double* __restrict__ Gmy_Res,
+    double* __restrict__ Gmz_Res)
+{
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double uxx=gupxx[i], uxy=gupxy[i], uxz=gupxz[i];
+        double uyy=gupyy[i], uyz=gupyz[i], uzz=gupzz[i];
+
+        Gmx_Res[i] = Gamx[i] - (
+            uxx*(uxx*gxxx[i]+uxy*gxyx[i]+uxz*gxzx[i]) +
+            uxy*(uxx*gxyx[i]+uxy*gyyx[i]+uxz*gyzx[i]) +
+            uxz*(uxx*gxzx[i]+uxy*gyzx[i]+uxz*gzzx[i]) +
+            uxx*(uxy*gxxy[i]+uyy*gxyy[i]+uyz*gxzy[i]) +
+            uxy*(uxy*gxyy[i]+uyy*gyyy[i]+uyz*gyzy[i]) +
+            uxz*(uxy*gxzy[i]+uyy*gyzy[i]+uyz*gzzy[i]) +
+            uxx*(uxz*gxxz[i]+uyz*gxyz[i]+uzz*gxzz[i]) +
+            uxy*(uxz*gxyz[i]+uyz*gyyz[i]+uzz*gyzz[i]) +
+            uxz*(uxz*gxzz[i]+uyz*gyzz[i]+uzz*gzzz[i]));
+
+        Gmy_Res[i] = Gamy[i] - (
+            uxx*(uxy*gxxx[i]+uyy*gxyx[i]+uyz*gxzx[i]) +
+            uxy*(uxy*gxyx[i]+uyy*gyyx[i]+uyz*gyzx[i]) +
+            uxz*(uxy*gxzx[i]+uyy*gyzx[i]+uyz*gzzx[i]) +
+            uxy*(uxy*gxxy[i]+uyy*gxyy[i]+uyz*gxzy[i]) +
+            uyy*(uxy*gxyy[i]+uyy*gyyy[i]+uyz*gyzy[i]) +
+            uyz*(uxy*gxzy[i]+uyy*gyzy[i]+uyz*gzzy[i]) +
+            uxy*(uxz*gxxz[i]+uyz*gxyz[i]+uzz*gxzz[i]) +
+            uyy*(uxz*gxyz[i]+uyz*gyyz[i]+uzz*gyzz[i]) +
+            uyz*(uxz*gxzz[i]+uyz*gyzz[i]+uzz*gzzz[i]));
+
+        Gmz_Res[i] = Gamz[i] - (
+            uxx*(uxz*gxxx[i]+uyz*gxyx[i]+uzz*gxzx[i]) +
+            uxy*(uxz*gxyx[i]+uyz*gyyx[i]+uzz*gyzx[i]) +
+            uxz*(uxz*gxzx[i]+uyz*gyzx[i]+uzz*gzzx[i]) +
+            uxy*(uxz*gxxy[i]+uyz*gxyy[i]+uzz*gxzy[i]) +
+            uyy*(uxz*gxyy[i]+uyz*gyyy[i]+uzz*gyzy[i]) +
+            uyz*(uxz*gxzy[i]+uyz*gyzy[i]+uzz*gzzy[i]) +
+            uxz*(uxz*gxxz[i]+uyz*gxyz[i]+uzz*gxzz[i]) +
+            uyz*(uxz*gxyz[i]+uyz*gyyz[i]+uzz*gyzz[i]) +
+            uzz*(uxz*gxzz[i]+uyz*gyzz[i]+uzz*gzzz[i]));
+    }
+}
+
+/* Phase 4: 18 Christoffel symbols */
+__global__ __launch_bounds__(128, 4)
+void kern_phase4_christoffel(
+    const double* __restrict__ gupxx, const double* __restrict__ gupxy,
+    const double* __restrict__ gupxz, const double* __restrict__ gupyy,
+    const double* __restrict__ gupyz, const double* __restrict__ gupzz,
+    const double* __restrict__ gxxx, const double* __restrict__ gxyx,
+    const double* __restrict__ gxzx, const double* __restrict__ gyyx,
+    const double* __restrict__ gyzx, const double* __restrict__ gzzx,
+    const double* __restrict__ gxxy, const double* __restrict__ gxyy,
+    const double* __restrict__ gxzy, const double* __restrict__ gyyy,
+    const double* __restrict__ gyzy, const double* __restrict__ gzzy,
+    const double* __restrict__ gxxz, const double* __restrict__ gxyz,
+    const double* __restrict__ gxzz, const double* __restrict__ gyyz,
+    const double* __restrict__ gyzz, const double* __restrict__ gzzz,
+    double* __restrict__ Gxxx, double* __restrict__ Gxxy, double* __restrict__ Gxxz,
+    double* __restrict__ Gxyy, double* __restrict__ Gxyz, double* __restrict__ Gxzz,
+    double* __restrict__ Gyxx, double* __restrict__ Gyxy, double* __restrict__ Gyxz,
+    double* __restrict__ Gyyy, double* __restrict__ Gyyz, double* __restrict__ Gyzz,
+    double* __restrict__ Gzxx, double* __restrict__ Gzxy, double* __restrict__ Gzxz,
+    double* __restrict__ Gzyy, double* __restrict__ Gzyz, double* __restrict__ Gzzz_o)
+{
+    const double H = 0.5, TWO = 2.0;
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double uxx=gupxx[i],uxy=gupxy[i],uxz=gupxz[i];
+        double uyy=gupyy[i],uyz=gupyz[i],uzz=gupzz[i];
+        /* Gamma^x_{xx} */
+        Gxxx[i]=H*(uxx*gxxx[i]+uxy*(TWO*gxyx[i]-gxxy[i])+uxz*(TWO*gxzx[i]-gxxz[i]));
+        Gyxx[i]=H*(uxy*gxxx[i]+uyy*(TWO*gxyx[i]-gxxy[i])+uyz*(TWO*gxzx[i]-gxxz[i]));
+        Gzxx[i]=H*(uxz*gxxx[i]+uyz*(TWO*gxyx[i]-gxxy[i])+uzz*(TWO*gxzx[i]-gxxz[i]));
+        /* yy */
+        Gxyy[i]=H*(uxx*(TWO*gxyy[i]-gyyx[i])+uxy*gyyy[i]+uxz*(TWO*gyzy[i]-gyyz[i]));
+        Gyyy[i]=H*(uxy*(TWO*gxyy[i]-gyyx[i])+uyy*gyyy[i]+uyz*(TWO*gyzy[i]-gyyz[i]));
+        Gzyy[i]=H*(uxz*(TWO*gxyy[i]-gyyx[i])+uyz*gyyy[i]+uzz*(TWO*gyzy[i]-gyyz[i]));
+        /* zz */
+        Gxzz[i]=H*(uxx*(TWO*gxzz[i]-gzzx[i])+uxy*(TWO*gyzz[i]-gzzy[i])+uxz*gzzz[i]);
+        Gyzz[i]=H*(uxy*(TWO*gxzz[i]-gzzx[i])+uyy*(TWO*gyzz[i]-gzzy[i])+uyz*gzzz[i]);
+        Gzzz_o[i]=H*(uxz*(TWO*gxzz[i]-gzzx[i])+uyz*(TWO*gyzz[i]-gzzy[i])+uzz*gzzz[i]);
+        /* xy */
+        Gxxy[i]=H*(uxx*gxxy[i]+uxy*gyyx[i]+uxz*(gxzy[i]+gyzx[i]-gxyz[i]));
+        Gyxy[i]=H*(uxy*gxxy[i]+uyy*gyyx[i]+uyz*(gxzy[i]+gyzx[i]-gxyz[i]));
+        Gzxy[i]=H*(uxz*gxxy[i]+uyz*gyyx[i]+uzz*(gxzy[i]+gyzx[i]-gxyz[i]));
+        /* xz */
+        Gxxz[i]=H*(uxx*gxxz[i]+uxy*(gxyz[i]+gyzx[i]-gxzy[i])+uxz*gzzx[i]);
+        Gyxz[i]=H*(uxy*gxxz[i]+uyy*(gxyz[i]+gyzx[i]-gxzy[i])+uyz*gzzx[i]);
+        Gzxz[i]=H*(uxz*gxxz[i]+uyz*(gxyz[i]+gyzx[i]-gxzy[i])+uzz*gzzx[i]);
+        /* yz */
+        Gxyz[i]=H*(uxx*(gxyz[i]+gxzy[i]-gyzx[i])+uxy*gyyz[i]+uxz*gzzy[i]);
+        Gyyz[i]=H*(uxy*(gxyz[i]+gxzy[i]-gyzx[i])+uyy*gyyz[i]+uyz*gzzy[i]);
+        Gzyz[i]=H*(uxz*(gxyz[i]+gxzy[i]-gyzx[i])+uyz*gyyz[i]+uzz*gzzy[i]);
+    }
+}
+
+/* Phase 5: A^ij = gup^ia gup^jb A_ab  (stored temporarily in Rxx..Rzz) */
+__global__ void kern_phase5_raise_A(
+    const double* __restrict__ gupxx, const double* __restrict__ gupxy,
+    const double* __restrict__ gupxz, const double* __restrict__ gupyy,
+    const double* __restrict__ gupyz, const double* __restrict__ gupzz,
+    const double* __restrict__ Axx, const double* __restrict__ Axy,
+    const double* __restrict__ Axz, const double* __restrict__ Ayy,
+    const double* __restrict__ Ayz, const double* __restrict__ Azz,
+    double* __restrict__ Rxx, double* __restrict__ Rxy, double* __restrict__ Rxz,
+    double* __restrict__ Ryy, double* __restrict__ Ryz, double* __restrict__ Rzz)
+{
+    const double TWO = 2.0;
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double uxx=gupxx[i],uxy=gupxy[i],uxz=gupxz[i];
+        double uyy=gupyy[i],uyz=gupyz[i],uzz=gupzz[i];
+        Rxx[i]=uxx*uxx*Axx[i]+uxy*uxy*Ayy[i]+uxz*uxz*Azz[i]
+              +TWO*(uxx*uxy*Axy[i]+uxx*uxz*Axz[i]+uxy*uxz*Ayz[i]);
+        Ryy[i]=uxy*uxy*Axx[i]+uyy*uyy*Ayy[i]+uyz*uyz*Azz[i]
+              +TWO*(uxy*uyy*Axy[i]+uxy*uyz*Axz[i]+uyy*uyz*Ayz[i]);
+        Rzz[i]=uxz*uxz*Axx[i]+uyz*uyz*Ayy[i]+uzz*uzz*Azz[i]
+              +TWO*(uxz*uyz*Axy[i]+uxz*uzz*Axz[i]+uyz*uzz*Ayz[i]);
+        Rxy[i]=uxx*uxy*Axx[i]+uxy*uyy*Ayy[i]+uxz*uyz*Azz[i]
+              +(uxx*uyy+uxy*uxy)*Axy[i]+(uxx*uyz+uxz*uxy)*Axz[i]+(uxy*uyz+uxz*uyy)*Ayz[i];
+        Rxz[i]=uxx*uxz*Axx[i]+uxy*uyz*Ayy[i]+uxz*uzz*Azz[i]
+              +(uxx*uyz+uxy*uxz)*Axy[i]+(uxx*uzz+uxz*uxz)*Axz[i]+(uxy*uzz+uxz*uyz)*Ayz[i];
+        Ryz[i]=uxy*uxz*Axx[i]+uyy*uyz*Ayy[i]+uyz*uzz*Azz[i]
+              +(uxy*uyz+uyy*uxz)*Axy[i]+(uxy*uzz+uyz*uxz)*Axz[i]+(uyy*uzz+uyz*uyz)*Ayz[i];
+    }
+}
+
+/* Phase 6: Gamma_rhs part 1 (before fdderivs(beta) and fderivs(Gamma)) */
+__global__ __launch_bounds__(128, 4)
+void kern_phase6_gamma_rhs_part1(
+    const double* __restrict__ Lapx, const double* __restrict__ Lapy,
+    const double* __restrict__ Lapz,
+    const double* __restrict__ alpn1, const double* __restrict__ chin1,
+    const double* __restrict__ chix, const double* __restrict__ chiy,
+    const double* __restrict__ chiz,
+    const double* __restrict__ gupxx, const double* __restrict__ gupxy,
+    const double* __restrict__ gupxz, const double* __restrict__ gupyy,
+    const double* __restrict__ gupyz, const double* __restrict__ gupzz,
+    const double* __restrict__ Kx, const double* __restrict__ Ky,
+    const double* __restrict__ Kz,
+    const double* __restrict__ Sx, const double* __restrict__ Sy,
+    const double* __restrict__ Sz,
+    const double* __restrict__ Rxx, const double* __restrict__ Rxy,
+    const double* __restrict__ Rxz, const double* __restrict__ Ryy,
+    const double* __restrict__ Ryz, const double* __restrict__ Rzz,
+    const double* __restrict__ Gxxx, const double* __restrict__ Gxxy,
+    const double* __restrict__ Gxxz, const double* __restrict__ Gxyy,
+    const double* __restrict__ Gxyz, const double* __restrict__ Gxzz,
+    const double* __restrict__ Gyxx, const double* __restrict__ Gyxy,
+    const double* __restrict__ Gyxz, const double* __restrict__ Gyyy,
+    const double* __restrict__ Gyyz, const double* __restrict__ Gyzz,
+    const double* __restrict__ Gzxx, const double* __restrict__ Gzxy,
+    const double* __restrict__ Gzxz, const double* __restrict__ Gzyy,
+    const double* __restrict__ Gzyz, const double* __restrict__ Gzzz,
+    double* __restrict__ Gamx_rhs, double* __restrict__ Gamy_rhs,
+    double* __restrict__ Gamz_rhs)
+{
+    const double TWO=2.0, F3o2=1.5, F2o3=2.0/3.0, EIGHT=8.0;
+    const double PI_V = 3.14159265358979323846;
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double uxx=gupxx[i],uxy=gupxy[i],uxz=gupxz[i];
+        double uyy=gupyy[i],uyz=gupyz[i],uzz=gupzz[i];
+        double lx=Lapx[i],ly=Lapy[i],lz=Lapz[i];
+        double a=alpn1[i], c1=chin1[i];
+        double cx=chix[i],cy=chiy[i],cz=chiz[i];
+
+        Gamx_rhs[i] = -TWO*(lx*Rxx[i]+ly*Rxy[i]+lz*Rxz[i])
+            + TWO*a*(
+                -F3o2/c1*(cx*Rxx[i]+cy*Rxy[i]+cz*Rxz[i])
+                -uxx*(F2o3*Kx[i]+EIGHT*PI_V*Sx[i])
+                -uxy*(F2o3*Ky[i]+EIGHT*PI_V*Sy[i])
+                -uxz*(F2o3*Kz[i]+EIGHT*PI_V*Sz[i])
+                +Gxxx[i]*Rxx[i]+Gxyy[i]*Ryy[i]+Gxzz[i]*Rzz[i]
+                +TWO*(Gxxy[i]*Rxy[i]+Gxxz[i]*Rxz[i]+Gxyz[i]*Ryz[i]));
+
+        Gamy_rhs[i] = -TWO*(lx*Rxy[i]+ly*Ryy[i]+lz*Ryz[i])
+            + TWO*a*(
+                -F3o2/c1*(cx*Rxy[i]+cy*Ryy[i]+cz*Ryz[i])
+                -uxy*(F2o3*Kx[i]+EIGHT*PI_V*Sx[i])
+                -uyy*(F2o3*Ky[i]+EIGHT*PI_V*Sy[i])
+                -uyz*(F2o3*Kz[i]+EIGHT*PI_V*Sz[i])
+                +Gyxx[i]*Rxx[i]+Gyyy[i]*Ryy[i]+Gyzz[i]*Rzz[i]
+                +TWO*(Gyxy[i]*Rxy[i]+Gyxz[i]*Rxz[i]+Gyyz[i]*Ryz[i]));
+
+        Gamz_rhs[i] = -TWO*(lx*Rxz[i]+ly*Ryz[i]+lz*Rzz[i])
+            + TWO*a*(
+                -F3o2/c1*(cx*Rxz[i]+cy*Ryz[i]+cz*Rzz[i])
+                -uxz*(F2o3*Kx[i]+EIGHT*PI_V*Sx[i])
+                -uyz*(F2o3*Ky[i]+EIGHT*PI_V*Sy[i])
+                -uzz*(F2o3*Kz[i]+EIGHT*PI_V*Sz[i])
+                +Gzxx[i]*Rxx[i]+Gzyy[i]*Ryy[i]+Gzzz[i]*Rzz[i]
+                +TWO*(Gzxy[i]*Rxy[i]+Gzxz[i]*Rxz[i]+Gzyz[i]*Ryz[i]));
+    }
+}
+
+/* Phase 8: Gamma_rhs part 2 — after fdderivs(beta) and fderivs(Gamma)
+ * Computes: fxx=div(beta_xx), Gamxa, then updates Gamx_rhs etc.
+ * Input arrays gxxx..gzzz here hold fdderivs(beta) results,
+ * Gamxx..Gamzz hold fderivs(Gamma) results.
+ */
+__global__ __launch_bounds__(128, 4)
+void kern_phase8_gamma_rhs_part2(
+    const double* __restrict__ gupxx, const double* __restrict__ gupxy,
+    const double* __restrict__ gupxz, const double* __restrict__ gupyy,
+    const double* __restrict__ gupyz, const double* __restrict__ gupzz,
+    /* fdderivs(betax) -> gxxx,gxyx,gxzx,gyyx,gyzx,gzzx */
+    const double* __restrict__ bxx_xx, const double* __restrict__ bxx_xy,
+    const double* __restrict__ bxx_xz, const double* __restrict__ bxx_yy,
+    const double* __restrict__ bxx_yz, const double* __restrict__ bxx_zz,
+    /* fdderivs(betay) -> gxxy,gxyy,gxzy,gyyy,gyzy,gzzy */
+    const double* __restrict__ bxy_xx, const double* __restrict__ bxy_xy,
+    const double* __restrict__ bxy_xz, const double* __restrict__ bxy_yy,
+    const double* __restrict__ bxy_yz, const double* __restrict__ bxy_zz,
+    /* fdderivs(betaz) -> gxxz,gxyz,gxzz,gyyz,gyzz,gzzz */
+    const double* __restrict__ bxz_xx, const double* __restrict__ bxz_xy,
+    const double* __restrict__ bxz_xz, const double* __restrict__ bxz_yy,
+    const double* __restrict__ bxz_yz, const double* __restrict__ bxz_zz,
+    /* fderivs(Gamx) -> Gamxx,Gamxy,Gamxz */
+    const double* __restrict__ Gamxx, const double* __restrict__ Gamxy,
+    const double* __restrict__ Gamxz,
+    /* fderivs(Gamy) -> Gamyx,Gamyy,Gamyz */
+    const double* __restrict__ Gamyx, const double* __restrict__ Gamyy_d,
+    const double* __restrict__ Gamyz_d,
+    /* fderivs(Gamz) -> Gamzx,Gamzy,Gamzz */
+    const double* __restrict__ Gamzx, const double* __restrict__ Gamzy,
+    const double* __restrict__ Gamzz_d,
+    /* Christoffel symbols */
+    const double* __restrict__ Gxxx, const double* __restrict__ Gxxy,
+    const double* __restrict__ Gxxz, const double* __restrict__ Gxyy,
+    const double* __restrict__ Gxyz, const double* __restrict__ Gxzz,
+    const double* __restrict__ Gyxx, const double* __restrict__ Gyxy,
+    const double* __restrict__ Gyxz, const double* __restrict__ Gyyy,
+    const double* __restrict__ Gyyz, const double* __restrict__ Gyzz,
+    const double* __restrict__ Gzxx, const double* __restrict__ Gzxy,
+    const double* __restrict__ Gzxz, const double* __restrict__ Gzyy,
+    const double* __restrict__ Gzyz, const double* __restrict__ Gzzz,
+    /* betaij first derivs */
+    const double* __restrict__ betaxx, const double* __restrict__ betaxy,
+    const double* __restrict__ betaxz, const double* __restrict__ betayx,
+    const double* __restrict__ betayy, const double* __restrict__ betayz,
+    const double* __restrict__ betazx, const double* __restrict__ betazy,
+    const double* __restrict__ betazz,
+    double* __restrict__ Gamx_rhs, double* __restrict__ Gamy_rhs,
+    double* __restrict__ Gamz_rhs,
+    double* __restrict__ Gamxa_out, double* __restrict__ Gamya_out,
+    double* __restrict__ Gamza_out)
+{
+    const double TWO=2.0, F2o3=2.0/3.0, F1o3=1.0/3.0;
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double uxx=gupxx[i],uxy=gupxy[i],uxz=gupxz[i];
+        double uyy=gupyy[i],uyz=gupyz[i],uzz=gupzz[i];
+        /* div(beta_second_derivs) */
+        double fxx_v = bxx_xx[i]+bxy_xy[i]+bxz_xz[i];
+        double fxy_v = bxx_xy[i]+bxy_yy[i]+bxz_yz[i];
+        double fxz_v = bxx_xz[i]+bxy_yz[i]+bxz_zz[i];
+        /* Gamma^a contracted */
+        double Ga_x = uxx*Gxxx[i]+uyy*Gxyy[i]+uzz*Gxzz[i]
+                     +TWO*(uxy*Gxxy[i]+uxz*Gxxz[i]+uyz*Gxyz[i]);
+        double Ga_y = uxx*Gyxx[i]+uyy*Gyyy[i]+uzz*Gyzz[i]
+                     +TWO*(uxy*Gyxy[i]+uxz*Gyxz[i]+uyz*Gyyz[i]);
+        double Ga_z = uxx*Gzxx[i]+uyy*Gzyy[i]+uzz*Gzzz[i]
+                     +TWO*(uxy*Gzxy[i]+uxz*Gzxz[i]+uyz*Gzyz[i]);
+        Gamxa_out[i]=Ga_x; Gamya_out[i]=Ga_y; Gamza_out[i]=Ga_z;
+        double db = betaxx[i] + betayy[i] + betazz[i];
+        Gamx_rhs[i] += F2o3*Ga_x*db
+            - Ga_x*betaxx[i] - Ga_y*betaxy[i] - Ga_z*betaxz[i]
+            + F1o3*(uxx*fxx_v+uxy*fxy_v+uxz*fxz_v)
+            + uxx*bxx_xx[i]+uyy*bxx_yy[i]+uzz*bxx_zz[i]
+            + TWO*(uxy*bxx_xy[i]+uxz*bxx_xz[i]+uyz*bxx_yz[i]);
+        Gamy_rhs[i] += F2o3*Ga_y*db
+            - Ga_x*betayx[i] - Ga_y*betayy[i] - Ga_z*betayz[i]
+            + F1o3*(uxy*fxx_v+uyy*fxy_v+uyz*fxz_v)
+            + uxx*bxy_xx[i]+uyy*bxy_yy[i]+uzz*bxy_zz[i]
+            + TWO*(uxy*bxy_xy[i]+uxz*bxy_xz[i]+uyz*bxy_yz[i]);
+        Gamz_rhs[i] += F2o3*Ga_z*db
+            - Ga_x*betazx[i] - Ga_y*betazy[i] - Ga_z*betazz[i]
+            + F1o3*(uxz*fxx_v+uyz*fxy_v+uzz*fxz_v)
+            + uxx*bxz_xx[i]+uyy*bxz_yy[i]+uzz*bxz_zz[i]
+            + TWO*(uxy*bxz_xy[i]+uxz*bxz_xz[i]+uyz*bxz_yz[i]);
+    }
+}
+
+/* Phase 9: Christoffel contract — compute g_{ia} Gamma^a_{bc} products
+ * Overwrites gxxx..gzzz with lowered Christoffel products needed for Ricci.
+ */
+__global__ __launch_bounds__(128, 4)
+void kern_phase9_christoffel_contract(
+    const double* __restrict__ gxx, const double* __restrict__ gxy,
+    const double* __restrict__ gxz, const double* __restrict__ gyy,
+    const double* __restrict__ gyz, const double* __restrict__ gzz,
+    const double* __restrict__ Gxxx, const double* __restrict__ Gxxy,
+    const double* __restrict__ Gxxz, const double* __restrict__ Gxyy,
+    const double* __restrict__ Gxyz, const double* __restrict__ Gxzz,
+    const double* __restrict__ Gyxx, const double* __restrict__ Gyxy,
+    const double* __restrict__ Gyxz, const double* __restrict__ Gyyy,
+    const double* __restrict__ Gyyz, const double* __restrict__ Gyzz,
+    const double* __restrict__ Gzxx, const double* __restrict__ Gzxy,
+    const double* __restrict__ Gzxz, const double* __restrict__ Gzyy,
+    const double* __restrict__ Gzyz, const double* __restrict__ Gzzz,
+    /* output: lowered products g_{ia} Gamma^a_{bc} */
+    double* __restrict__ o_gxxx, double* __restrict__ o_gxyx,
+    double* __restrict__ o_gxzx, double* __restrict__ o_gyyx,
+    double* __restrict__ o_gyzx, double* __restrict__ o_gzzx,
+    double* __restrict__ o_gxxy, double* __restrict__ o_gxyy,
+    double* __restrict__ o_gxzy, double* __restrict__ o_gyyy,
+    double* __restrict__ o_gyzy, double* __restrict__ o_gzzy,
+    double* __restrict__ o_gxxz, double* __restrict__ o_gxyz,
+    double* __restrict__ o_gxzz, double* __restrict__ o_gyyz,
+    double* __restrict__ o_gyzz, double* __restrict__ o_gzzz)
+{
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double g11=gxx[i],g12=gxy[i],g13=gxz[i];
+        double g22=gyy[i],g23=gyz[i],g33=gzz[i];
+        /* row x: g_{x,a} Gamma^a_{bc} */
+        o_gxxx[i]=g11*Gxxx[i]+g12*Gyxx[i]+g13*Gzxx[i];
+        o_gxyx[i]=g11*Gxxy[i]+g12*Gyxy[i]+g13*Gzxy[i];
+        o_gxzx[i]=g11*Gxxz[i]+g12*Gyxz[i]+g13*Gzxz[i];
+        o_gyyx[i]=g11*Gxyy[i]+g12*Gyyy[i]+g13*Gzyy[i];
+        o_gyzx[i]=g11*Gxyz[i]+g12*Gyyz[i]+g13*Gzyz[i];
+        o_gzzx[i]=g11*Gxzz[i]+g12*Gyzz[i]+g13*Gzzz[i];
+        /* row y: g_{y,a} Gamma^a_{bc} */
+        o_gxxy[i]=g12*Gxxx[i]+g22*Gyxx[i]+g23*Gzxx[i];
+        o_gxyy[i]=g12*Gxxy[i]+g22*Gyxy[i]+g23*Gzxy[i];
+        o_gxzy[i]=g12*Gxxz[i]+g22*Gyxz[i]+g23*Gzxz[i];
+        o_gyyy[i]=g12*Gxyy[i]+g22*Gyyy[i]+g23*Gzyy[i];
+        o_gyzy[i]=g12*Gxyz[i]+g22*Gyyz[i]+g23*Gzyz[i];
+        o_gzzy[i]=g12*Gxzz[i]+g22*Gyzz[i]+g23*Gzzz[i];
+        /* row z: g_{z,a} Gamma^a_{bc} */
+        o_gxxz[i]=g13*Gxxx[i]+g23*Gyxx[i]+g33*Gzxx[i];
+        o_gxyz[i]=g13*Gxxy[i]+g23*Gyxy[i]+g33*Gzxy[i];
+        o_gxzz[i]=g13*Gxxz[i]+g23*Gyxz[i]+g33*Gzxz[i];
+        o_gyyz[i]=g13*Gxyy[i]+g23*Gyyy[i]+g33*Gzyy[i];
+        o_gyzz[i]=g13*Gxyz[i]+g23*Gyyz[i]+g33*Gzyz[i];
+        o_gzzz[i]=g13*Gxzz[i]+g23*Gyzz[i]+g33*Gzzz[i];
+    }
+}
+
+/* Phase 10: After fdderivs of a metric component, contract with gup^{ij}
+ * R_comp = gup^xx*fxx + gup^yy*fyy + gup^zz*fzz + 2*(gup^xy*fxy + gup^xz*fxz + gup^yz*fyz)
+ */
+__global__ void kern_phase10_ricci_contract(
+    const double* __restrict__ gupxx, const double* __restrict__ gupxy,
+    const double* __restrict__ gupxz, const double* __restrict__ gupyy,
+    const double* __restrict__ gupyz, const double* __restrict__ gupzz,
+    const double* __restrict__ fxx, const double* __restrict__ fxy,
+    const double* __restrict__ fxz, const double* __restrict__ fyy,
+    const double* __restrict__ fyz, const double* __restrict__ fzz,
+    double* __restrict__ R_comp)
+{
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        R_comp[i] = gupxx[i]*fxx[i] + gupyy[i]*fyy[i] + gupzz[i]*fzz[i]
+                  + 2.0*(gupxy[i]*fxy[i] + gupxz[i]*fxz[i] + gupyz[i]*fyz[i]);
+    }
+}
+
+/* Phase 11a: Ricci diagonal assembly (Rxx, Ryy, Rzz) */
+__global__ __launch_bounds__(128, 4)
+void kern_phase11_ricci_diag(
+    const double* __restrict__ gxx, const double* __restrict__ gxy,
+    const double* __restrict__ gxz, const double* __restrict__ gyy,
+    const double* __restrict__ gyz, const double* __restrict__ gzz,
+    const double* __restrict__ gupxx, const double* __restrict__ gupxy,
+    const double* __restrict__ gupxz, const double* __restrict__ gupyy,
+    const double* __restrict__ gupyz, const double* __restrict__ gupzz,
+    const double* __restrict__ Gamxa, const double* __restrict__ Gamya,
+    const double* __restrict__ Gamza,
+    const double* __restrict__ Gamxx, const double* __restrict__ Gamxy,
+    const double* __restrict__ Gamxz,
+    const double* __restrict__ Gamyx, const double* __restrict__ Gamyy_d,
+    const double* __restrict__ Gamyz_d,
+    const double* __restrict__ Gamzx, const double* __restrict__ Gamzy,
+    const double* __restrict__ Gamzz_d,
+    const double* __restrict__ Gxxx, const double* __restrict__ Gxxy,
+    const double* __restrict__ Gxxz, const double* __restrict__ Gxyy,
+    const double* __restrict__ Gxyz, const double* __restrict__ Gxzz,
+    const double* __restrict__ Gyxx, const double* __restrict__ Gyxy,
+    const double* __restrict__ Gyxz, const double* __restrict__ Gyyy,
+    const double* __restrict__ Gyyz, const double* __restrict__ Gyzz,
+    const double* __restrict__ Gzxx, const double* __restrict__ Gzxy,
+    const double* __restrict__ Gzxz, const double* __restrict__ Gzyy,
+    const double* __restrict__ Gzyz, const double* __restrict__ Gzzz,
+    /* lowered Christoffel products */
+    const double* __restrict__ lxxx, const double* __restrict__ lxyx,
+    const double* __restrict__ lxzx, const double* __restrict__ lyyx,
+    const double* __restrict__ lyzx, const double* __restrict__ lzzx,
+    const double* __restrict__ lxxy, const double* __restrict__ lxyy,
+    const double* __restrict__ lxzy, const double* __restrict__ lyyy,
+    const double* __restrict__ lyzy, const double* __restrict__ lzzy,
+    const double* __restrict__ lxxz, const double* __restrict__ lxyz,
+    const double* __restrict__ lxzz, const double* __restrict__ lyyz,
+    const double* __restrict__ lyzz, const double* __restrict__ lzzz,
+    double* __restrict__ Rxx, double* __restrict__ Ryy, double* __restrict__ Rzz)
+{
+    const double H = 0.5, TWO = 2.0;
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double uxx=gupxx[i],uxy=gupxy[i],uxz=gupxz[i];
+        double uyy=gupyy[i],uyz=gupyz[i],uzz=gupzz[i];
+        /* Rxx */
+        Rxx[i] = -H*Rxx[i]
+            + gxx[i]*Gamxx[i]+gxy[i]*Gamyx[i]+gxz[i]*Gamzx[i]
+            + Gamxa[i]*lxxx[i]+Gamya[i]*lxyx[i]+Gamza[i]*lxzx[i]
+            + uxx*(TWO*(Gxxx[i]*lxxx[i]+Gyxx[i]*lxyx[i]+Gzxx[i]*lxzx[i])
+                  +(Gxxx[i]*lxxx[i]+Gyxx[i]*lxxy[i]+Gzxx[i]*lxxz[i]))
+            + uxy*(TWO*(Gxxx[i]*lxyx[i]+Gyxx[i]*lyyx[i]+Gzxx[i]*lyzx[i]
+                       +Gxxy[i]*lxxx[i]+Gyxy[i]*lxyx[i]+Gzxy[i]*lxzx[i])
+                  +(Gxxy[i]*lxxx[i]+Gyxy[i]*lxxy[i]+Gzxy[i]*lxxz[i])
+                  +(Gxxx[i]*lxyx[i]+Gyxx[i]*lxyy[i]+Gzxx[i]*lxyz[i]))
+            + uxz*(TWO*(Gxxx[i]*lxzx[i]+Gyxx[i]*lyzx[i]+Gzxx[i]*lzzx[i]
+                       +Gxxz[i]*lxxx[i]+Gyxz[i]*lxyx[i]+Gzxz[i]*lxzx[i])
+                  +(Gxxz[i]*lxxx[i]+Gyxz[i]*lxxy[i]+Gzxz[i]*lxxz[i])
+                  +(Gxxx[i]*lxzx[i]+Gyxx[i]*lxzy[i]+Gzxx[i]*lxzz[i]))
+            + uyy*(TWO*(Gxxy[i]*lxyx[i]+Gyxy[i]*lyyx[i]+Gzxy[i]*lyzx[i])
+                  +(Gxxy[i]*lxyx[i]+Gyxy[i]*lxyy[i]+Gzxy[i]*lxyz[i]))
+            + uyz*(TWO*(Gxxy[i]*lxzx[i]+Gyxy[i]*lyzx[i]+Gzxy[i]*lzzx[i]
+                       +Gxxz[i]*lxyx[i]+Gyxz[i]*lyyx[i]+Gzxz[i]*lyzx[i])
+                  +(Gxxz[i]*lxyx[i]+Gyxz[i]*lxyy[i]+Gzxz[i]*lxyz[i])
+                  +(Gxxy[i]*lxzx[i]+Gyxy[i]*lxzy[i]+Gzxy[i]*lxzz[i]))
+            + uzz*(TWO*(Gxxz[i]*lxzx[i]+Gyxz[i]*lyzx[i]+Gzxz[i]*lzzx[i])
+                  +(Gxxz[i]*lxzx[i]+Gyxz[i]*lxzy[i]+Gzxz[i]*lxzz[i]));
+
+        /* Ryy */
+        Ryy[i] = -H*Ryy[i]
+            + gxy[i]*Gamxy[i]+gyy[i]*Gamyy_d[i]+gyz[i]*Gamzy[i]
+            + Gamxa[i]*lxyy[i]+Gamya[i]*lyyy[i]+Gamza[i]*lyzy[i]
+            + uxx*(TWO*(Gxxy[i]*lxxy[i]+Gyxy[i]*lxyy[i]+Gzxy[i]*lxzy[i])
+                  +(Gxxy[i]*lxyx[i]+Gyxy[i]*lxyy[i]+Gzxy[i]*lxyz[i]))
+            + uxy*(TWO*(Gxxy[i]*lxyy[i]+Gyxy[i]*lyyy[i]+Gzxy[i]*lyzy[i]
+                       +Gxyy[i]*lxxy[i]+Gyyy[i]*lxyy[i]+Gzyy[i]*lxzy[i])
+                  +(Gxyy[i]*lxyx[i]+Gyyy[i]*lxyy[i]+Gzyy[i]*lxyz[i])
+                  +(Gxxy[i]*lyyx[i]+Gyxy[i]*lyyy[i]+Gzxy[i]*lyyz[i]))
+            + uxz*(TWO*(Gxxy[i]*lxzy[i]+Gyxy[i]*lyzy[i]+Gzxy[i]*lzzy[i]
+                       +Gxyz[i]*lxxy[i]+Gyyz[i]*lxyy[i]+Gzyz[i]*lxzy[i])
+                  +(Gxyz[i]*lxyx[i]+Gyyz[i]*lxyy[i]+Gzyz[i]*lxyz[i])
+                  +(Gxxy[i]*lyzx[i]+Gyxy[i]*lyzy[i]+Gzxy[i]*lyzz[i]))
+            + uyy*(TWO*(Gxyy[i]*lxyy[i]+Gyyy[i]*lyyy[i]+Gzyy[i]*lyzy[i])
+                  +(Gxyy[i]*lyyx[i]+Gyyy[i]*lyyy[i]+Gzyy[i]*lyyz[i]))
+            + uyz*(TWO*(Gxyy[i]*lxzy[i]+Gyyy[i]*lyzy[i]+Gzyy[i]*lzzy[i]
+                       +Gxyz[i]*lxyy[i]+Gyyz[i]*lyyy[i]+Gzyz[i]*lyzy[i])
+                  +(Gxyz[i]*lyyx[i]+Gyyz[i]*lyyy[i]+Gzyz[i]*lyyz[i])
+                  +(Gxyy[i]*lyzx[i]+Gyyy[i]*lyzy[i]+Gzyy[i]*lyzz[i]))
+            + uzz*(TWO*(Gxyz[i]*lxzy[i]+Gyyz[i]*lyzy[i]+Gzyz[i]*lzzy[i])
+                  +(Gxyz[i]*lyzx[i]+Gyyz[i]*lyzy[i]+Gzyz[i]*lyzz[i]));
+
+        /* Rzz */
+        Rzz[i] = -H*Rzz[i]
+            + gxz[i]*Gamxz[i]+gyz[i]*Gamyz_d[i]+gzz[i]*Gamzz_d[i]
+            + Gamxa[i]*lxzz[i]+Gamya[i]*lyzz[i]+Gamza[i]*lzzz[i]
+            + uxx*(TWO*(Gxxz[i]*lxxz[i]+Gyxz[i]*lxyz[i]+Gzxz[i]*lxzz[i])
+                  +(Gxxz[i]*lxzx[i]+Gyxz[i]*lxzy[i]+Gzxz[i]*lxzz[i]))
+            + uxy*(TWO*(Gxxz[i]*lxyz[i]+Gyxz[i]*lyyz[i]+Gzxz[i]*lyzz[i]
+                       +Gxyz[i]*lxxz[i]+Gyyz[i]*lxyz[i]+Gzyz[i]*lxzz[i])
+                  +(Gxyz[i]*lxzx[i]+Gyyz[i]*lxzy[i]+Gzyz[i]*lxzz[i])
+                  +(Gxxz[i]*lyzx[i]+Gyxz[i]*lyzy[i]+Gzxz[i]*lyzz[i]))
+            + uxz*(TWO*(Gxxz[i]*lxzz[i]+Gyxz[i]*lyzz[i]+Gzxz[i]*lzzz[i]
+                       +Gxzz[i]*lxxz[i]+Gyzz[i]*lxyz[i]+Gzzz[i]*lxzz[i])
+                  +(Gxzz[i]*lxzx[i]+Gyzz[i]*lxzy[i]+Gzzz[i]*lxzz[i])
+                  +(Gxxz[i]*lzzx[i]+Gyxz[i]*lzzy[i]+Gzxz[i]*lzzz[i]))
+            + uyy*(TWO*(Gxyz[i]*lxyz[i]+Gyyz[i]*lyyz[i]+Gzyz[i]*lyzz[i])
+                  +(Gxyz[i]*lyzx[i]+Gyyz[i]*lyzy[i]+Gzyz[i]*lyzz[i]))
+            + uyz*(TWO*(Gxyz[i]*lxzz[i]+Gyyz[i]*lyzz[i]+Gzyz[i]*lzzz[i]
+                       +Gxzz[i]*lxyz[i]+Gyzz[i]*lyyz[i]+Gzzz[i]*lyzz[i])
+                  +(Gxzz[i]*lyzx[i]+Gyzz[i]*lyzy[i]+Gzzz[i]*lyzz[i])
+                  +(Gxyz[i]*lzzx[i]+Gyyz[i]*lzzy[i]+Gzyz[i]*lzzz[i]))
+            + uzz*(TWO*(Gxzz[i]*lxzz[i]+Gyzz[i]*lyzz[i]+Gzzz[i]*lzzz[i])
+                  +(Gxzz[i]*lzzx[i]+Gyzz[i]*lzzy[i]+Gzzz[i]*lzzz[i]));
+    }
+}
+
+/* Phase 11b: Ricci off-diagonal assembly (Rxy, Rxz, Ryz) */
+__global__ __launch_bounds__(128, 4)
+void kern_phase11_ricci_offdiag(
+    const double* __restrict__ gxx, const double* __restrict__ gxy,
+    const double* __restrict__ gxz, const double* __restrict__ gyy,
+    const double* __restrict__ gyz, const double* __restrict__ gzz,
+    const double* __restrict__ gupxx, const double* __restrict__ gupxy,
+    const double* __restrict__ gupxz, const double* __restrict__ gupyy,
+    const double* __restrict__ gupyz, const double* __restrict__ gupzz,
+    const double* __restrict__ Gamxa, const double* __restrict__ Gamya,
+    const double* __restrict__ Gamza,
+    const double* __restrict__ Gamxx, const double* __restrict__ Gamxy,
+    const double* __restrict__ Gamxz,
+    const double* __restrict__ Gamyx, const double* __restrict__ Gamyy_d,
+    const double* __restrict__ Gamyz_d,
+    const double* __restrict__ Gamzx, const double* __restrict__ Gamzy,
+    const double* __restrict__ Gamzz_d,
+    const double* __restrict__ Gxxx, const double* __restrict__ Gxxy,
+    const double* __restrict__ Gxxz, const double* __restrict__ Gxyy,
+    const double* __restrict__ Gxyz, const double* __restrict__ Gxzz,
+    const double* __restrict__ Gyxx, const double* __restrict__ Gyxy,
+    const double* __restrict__ Gyxz, const double* __restrict__ Gyyy,
+    const double* __restrict__ Gyyz, const double* __restrict__ Gyzz,
+    const double* __restrict__ Gzxx, const double* __restrict__ Gzxy,
+    const double* __restrict__ Gzxz, const double* __restrict__ Gzyy,
+    const double* __restrict__ Gzyz, const double* __restrict__ Gzzz,
+    const double* __restrict__ lxxx, const double* __restrict__ lxyx,
+    const double* __restrict__ lxzx, const double* __restrict__ lyyx,
+    const double* __restrict__ lyzx, const double* __restrict__ lzzx,
+    const double* __restrict__ lxxy, const double* __restrict__ lxyy,
+    const double* __restrict__ lxzy, const double* __restrict__ lyyy,
+    const double* __restrict__ lyzy, const double* __restrict__ lzzy,
+    const double* __restrict__ lxxz, const double* __restrict__ lxyz,
+    const double* __restrict__ lxzz, const double* __restrict__ lyyz,
+    const double* __restrict__ lyzz, const double* __restrict__ lzzz,
+    double* __restrict__ Rxy, double* __restrict__ Rxz, double* __restrict__ Ryz)
+{
+    const double H = 0.5, TWO = 2.0;
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double uxx=gupxx[i],uxy=gupxy[i],uxz=gupxz[i];
+        double uyy=gupyy[i],uyz=gupyz[i],uzz=gupzz[i];
+
+        /* Rxy */
+        Rxy[i] = H*(
+            -Rxy[i]
+            +gxx[i]*Gamxy[i]+gxy[i]*Gamyy_d[i]+gxz[i]*Gamzy[i]
+            +gxy[i]*Gamxx[i]+gyy[i]*Gamyx[i]+gyz[i]*Gamzx[i]
+            +Gamxa[i]*lxyx[i]+Gamya[i]*lyyx[i]+Gamza[i]*lyzx[i]
+            +Gamxa[i]*lxxy[i]+Gamya[i]*lxyy[i]+Gamza[i]*lxzy[i])
+            +uxx*(Gxxx[i]*lxxy[i]+Gyxx[i]*lxyy[i]+Gzxx[i]*lxzy[i]
+                  +Gxxy[i]*lxxx[i]+Gyxy[i]*lxyx[i]+Gzxy[i]*lxzx[i]
+                  +Gxxx[i]*lxyx[i]+Gyxx[i]*lxyy[i]+Gzxx[i]*lxyz[i])
+            +uxy*(Gxxx[i]*lxyy[i]+Gyxx[i]*lyyy[i]+Gzxx[i]*lyzy[i]
+                  +Gxxy[i]*lxyx[i]+Gyxy[i]*lyyx[i]+Gzxy[i]*lyzx[i]
+                  +Gxxy[i]*lxyx[i]+Gyxy[i]*lxyy[i]+Gzxy[i]*lxyz[i]
+                  +Gxxy[i]*lxxy[i]+Gyxy[i]*lxyy[i]+Gzxy[i]*lxzy[i]
+                  +Gxyy[i]*lxxx[i]+Gyyy[i]*lxyx[i]+Gzyy[i]*lxzx[i]
+                  +Gxxx[i]*lyyx[i]+Gyxx[i]*lyyy[i]+Gzxx[i]*lyyz[i])
+            +uxz*(Gxxx[i]*lxzy[i]+Gyxx[i]*lyzy[i]+Gzxx[i]*lzzy[i]
+                  +Gxxy[i]*lxzx[i]+Gyxy[i]*lyzx[i]+Gzxy[i]*lzzx[i]
+                  +Gxxz[i]*lxyx[i]+Gyxz[i]*lxyy[i]+Gzxz[i]*lxyz[i]
+                  +Gxxz[i]*lxxy[i]+Gyxz[i]*lxyy[i]+Gzxz[i]*lxzy[i]
+                  +Gxyz[i]*lxxx[i]+Gyyz[i]*lxyx[i]+Gzyz[i]*lxzx[i]
+                  +Gxxx[i]*lyzx[i]+Gyxx[i]*lyzy[i]+Gzxx[i]*lyzz[i])
+            +uyy*(Gxxy[i]*lxyy[i]+Gyxy[i]*lyyy[i]+Gzxy[i]*lyzy[i]
+                  +Gxyy[i]*lxyx[i]+Gyyy[i]*lyyx[i]+Gzyy[i]*lyzx[i]
+                  +Gxxy[i]*lyyx[i]+Gyxy[i]*lyyy[i]+Gzxy[i]*lyyz[i])
+            +uyz*(Gxxy[i]*lxzy[i]+Gyxy[i]*lyzy[i]+Gzxy[i]*lzzy[i]
+                  +Gxyy[i]*lxzx[i]+Gyyy[i]*lyzx[i]+Gzyy[i]*lzzx[i]
+                  +Gxxz[i]*lyyx[i]+Gyxz[i]*lyyy[i]+Gzxz[i]*lyyz[i]
+                  +Gxxz[i]*lxyy[i]+Gyxz[i]*lyyy[i]+Gzxz[i]*lyzy[i]
+                  +Gxyz[i]*lxyx[i]+Gyyz[i]*lyyx[i]+Gzyz[i]*lyzx[i]
+                  +Gxxy[i]*lyzx[i]+Gyxy[i]*lyzy[i]+Gzxy[i]*lyzz[i])
+            +uzz*(Gxxz[i]*lxzy[i]+Gyxz[i]*lyzy[i]+Gzxz[i]*lzzy[i]
+                  +Gxyz[i]*lxzx[i]+Gyyz[i]*lyzx[i]+Gzyz[i]*lzzx[i]
+                  +Gxxz[i]*lyzx[i]+Gyxz[i]*lyzy[i]+Gzxz[i]*lyzz[i]);
+
+        /* Rxz */
+        Rxz[i] = H*(
+            -Rxz[i]
+            +gxx[i]*Gamxz[i]+gxy[i]*Gamyz_d[i]+gxz[i]*Gamzz_d[i]
+            +gxz[i]*Gamxx[i]+gyz[i]*Gamyx[i]+gzz[i]*Gamzx[i]
+            +Gamxa[i]*lxzx[i]+Gamya[i]*lyzx[i]+Gamza[i]*lzzx[i]
+            +Gamxa[i]*lxxz[i]+Gamya[i]*lxyz[i]+Gamza[i]*lxzz[i])
+            +uxx*(Gxxx[i]*lxxz[i]+Gyxx[i]*lxyz[i]+Gzxx[i]*lxzz[i]
+                  +Gxxz[i]*lxxx[i]+Gyxz[i]*lxyx[i]+Gzxz[i]*lxzx[i]
+                  +Gxxx[i]*lxzx[i]+Gyxx[i]*lxzy[i]+Gzxx[i]*lxzz[i])
+            +uxy*(Gxxx[i]*lxyz[i]+Gyxx[i]*lyyz[i]+Gzxx[i]*lyzz[i]
+                  +Gxxz[i]*lxyx[i]+Gyxz[i]*lyyx[i]+Gzxz[i]*lyzx[i]
+                  +Gxxy[i]*lxzx[i]+Gyxy[i]*lxzy[i]+Gzxy[i]*lxzz[i]
+                  +Gxxy[i]*lxxz[i]+Gyxy[i]*lxyz[i]+Gzxy[i]*lxzz[i]
+                  +Gxyz[i]*lxxx[i]+Gyyz[i]*lxyx[i]+Gzyz[i]*lxzx[i]
+                  +Gxxx[i]*lyzx[i]+Gyxx[i]*lyzy[i]+Gzxx[i]*lyzz[i])
+            +uxz*(Gxxx[i]*lxzz[i]+Gyxx[i]*lyzz[i]+Gzxx[i]*lzzz[i]
+                  +Gxxz[i]*lxzx[i]+Gyxz[i]*lyzx[i]+Gzxz[i]*lzzx[i]
+                  +Gxxz[i]*lxzx[i]+Gyxz[i]*lxzy[i]+Gzxz[i]*lxzz[i]
+                  +Gxxz[i]*lxxz[i]+Gyxz[i]*lxyz[i]+Gzxz[i]*lxzz[i]
+                  +Gxzz[i]*lxxx[i]+Gyzz[i]*lxyx[i]+Gzzz[i]*lxzx[i]
+                  +Gxxx[i]*lzzx[i]+Gyxx[i]*lzzy[i]+Gzxx[i]*lzzz[i])
+            +uyy*(Gxxy[i]*lxyz[i]+Gyxy[i]*lyyz[i]+Gzxy[i]*lyzz[i]
+                  +Gxyz[i]*lxyx[i]+Gyyz[i]*lyyx[i]+Gzyz[i]*lyzx[i]
+                  +Gxxy[i]*lyzx[i]+Gyxy[i]*lyzy[i]+Gzxy[i]*lyzz[i])
+            +uyz*(Gxxy[i]*lxzz[i]+Gyxy[i]*lyzz[i]+Gzxy[i]*lzzz[i]
+                  +Gxyz[i]*lxzx[i]+Gyyz[i]*lyzx[i]+Gzyz[i]*lzzx[i]
+                  +Gxxz[i]*lyzx[i]+Gyxz[i]*lyzy[i]+Gzxz[i]*lyzz[i]
+                  +Gxxz[i]*lxyz[i]+Gyxz[i]*lyyz[i]+Gzxz[i]*lyzz[i]
+                  +Gxzz[i]*lxyx[i]+Gyzz[i]*lyyx[i]+Gzzz[i]*lyzx[i]
+                  +Gxxy[i]*lzzx[i]+Gyxy[i]*lzzy[i]+Gzxy[i]*lzzz[i])
+            +uzz*(Gxxz[i]*lxzz[i]+Gyxz[i]*lyzz[i]+Gzxz[i]*lzzz[i]
+                  +Gxzz[i]*lxzx[i]+Gyzz[i]*lyzx[i]+Gzzz[i]*lzzx[i]
+                  +Gxxz[i]*lzzx[i]+Gyxz[i]*lzzy[i]+Gzxz[i]*lzzz[i]);
+
+        /* Ryz */
+        Ryz[i] = H*(
+            -Ryz[i]
+            +gxy[i]*Gamxz[i]+gyy[i]*Gamyz_d[i]+gyz[i]*Gamzz_d[i]
+            +gxz[i]*Gamxy[i]+gyz[i]*Gamyy_d[i]+gzz[i]*Gamzy[i]
+            +Gamxa[i]*lxzy[i]+Gamya[i]*lyzy[i]+Gamza[i]*lzzy[i]
+            +Gamxa[i]*lxyz[i]+Gamya[i]*lyyz[i]+Gamza[i]*lyzz[i])
+            +uxx*(Gxxy[i]*lxxz[i]+Gyxy[i]*lxyz[i]+Gzxy[i]*lxzz[i]
+                  +Gxxz[i]*lxxy[i]+Gyxz[i]*lxyy[i]+Gzxz[i]*lxzy[i]
+                  +Gxxy[i]*lxzx[i]+Gyxy[i]*lxzy[i]+Gzxy[i]*lxzz[i])
+            +uxy*(Gxxy[i]*lxyz[i]+Gyxy[i]*lyyz[i]+Gzxy[i]*lyzz[i]
+                  +Gxxz[i]*lxyy[i]+Gyxz[i]*lyyy[i]+Gzxz[i]*lyzy[i]
+                  +Gxyy[i]*lxzx[i]+Gyyy[i]*lxzy[i]+Gzyy[i]*lxzz[i]
+                  +Gxyy[i]*lxxz[i]+Gyyy[i]*lxyz[i]+Gzyy[i]*lxzz[i]
+                  +Gxyz[i]*lxxy[i]+Gyyz[i]*lxyy[i]+Gzyz[i]*lxzy[i]
+                  +Gxxy[i]*lyzx[i]+Gyxy[i]*lyzy[i]+Gzxy[i]*lyzz[i])
+            +uxz*(Gxxy[i]*lxzz[i]+Gyxy[i]*lyzz[i]+Gzxy[i]*lzzz[i]
+                  +Gxxz[i]*lxzy[i]+Gyxz[i]*lyzy[i]+Gzxz[i]*lzzy[i]
+                  +Gxyz[i]*lxzx[i]+Gyyz[i]*lxzy[i]+Gzyz[i]*lxzz[i]
+                  +Gxyz[i]*lxxz[i]+Gyyz[i]*lxyz[i]+Gzyz[i]*lxzz[i]
+                  +Gxzz[i]*lxxy[i]+Gyzz[i]*lxyy[i]+Gzzz[i]*lxzy[i]
+                  +Gxxy[i]*lzzx[i]+Gyxy[i]*lzzy[i]+Gzxy[i]*lzzz[i])
+            +uyy*(Gxyy[i]*lxyz[i]+Gyyy[i]*lyyz[i]+Gzyy[i]*lyzz[i]
+                  +Gxyz[i]*lxyy[i]+Gyyz[i]*lyyy[i]+Gzyz[i]*lyzy[i]
+                  +Gxyy[i]*lyzx[i]+Gyyy[i]*lyzy[i]+Gzyy[i]*lyzz[i])
+            +uyz*(Gxyy[i]*lxzz[i]+Gyyy[i]*lyzz[i]+Gzyy[i]*lzzz[i]
+                  +Gxyz[i]*lxzy[i]+Gyyz[i]*lyzy[i]+Gzyz[i]*lzzy[i]
+                  +Gxyz[i]*lyzx[i]+Gyyz[i]*lyzy[i]+Gzyz[i]*lyzz[i]
+                  +Gxyz[i]*lxyz[i]+Gyyz[i]*lyyz[i]+Gzyz[i]*lyzz[i]
+                  +Gxzz[i]*lxyy[i]+Gyzz[i]*lyyy[i]+Gzzz[i]*lyzy[i]
+                  +Gxyy[i]*lzzx[i]+Gyyy[i]*lzzy[i]+Gzyy[i]*lzzz[i])
+            +uzz*(Gxyz[i]*lxzz[i]+Gyyz[i]*lyzz[i]+Gzyz[i]*lzzz[i]
+                  +Gxzz[i]*lxzy[i]+Gyzz[i]*lyzy[i]+Gzzz[i]*lzzy[i]
+                  +Gxyz[i]*lzzx[i]+Gyyz[i]*lzzy[i]+Gzyz[i]*lzzz[i]);
+    }
+}
+
+/* Phase 13: chi correction to Ricci tensor
+ * After fdderivs(chi), subtract Christoffel*chi_deriv, compute conformal factor f,
+ * then add chi contribution to Rxx..Rzz.
+ */
+__global__ __launch_bounds__(128, 4)
+void kern_phase13_chi_correction(
+    const double* __restrict__ chin1,
+    const double* __restrict__ chix, const double* __restrict__ chiy,
+    const double* __restrict__ chiz,
+    const double* __restrict__ gxx, const double* __restrict__ gxy,
+    const double* __restrict__ gxz, const double* __restrict__ gyy,
+    const double* __restrict__ gyz, const double* __restrict__ gzz,
+    const double* __restrict__ gupxx, const double* __restrict__ gupxy,
+    const double* __restrict__ gupxz, const double* __restrict__ gupyy,
+    const double* __restrict__ gupyz, const double* __restrict__ gupzz,
+    const double* __restrict__ Gxxx, const double* __restrict__ Gxxy,
+    const double* __restrict__ Gxxz, const double* __restrict__ Gxyy,
+    const double* __restrict__ Gxyz, const double* __restrict__ Gxzz,
+    const double* __restrict__ Gyxx, const double* __restrict__ Gyxy,
+    const double* __restrict__ Gyxz, const double* __restrict__ Gyyy,
+    const double* __restrict__ Gyyz, const double* __restrict__ Gyzz,
+    const double* __restrict__ Gzxx, const double* __restrict__ Gzxy,
+    const double* __restrict__ Gzxz, const double* __restrict__ Gzyy,
+    const double* __restrict__ Gzyz, const double* __restrict__ Gzzz,
+    double* __restrict__ fxx, double* __restrict__ fxy,
+    double* __restrict__ fxz, double* __restrict__ fyy,
+    double* __restrict__ fyz, double* __restrict__ fzz,
+    double* __restrict__ Rxx, double* __restrict__ Rxy,
+    double* __restrict__ Rxz, double* __restrict__ Ryy,
+    double* __restrict__ Ryz, double* __restrict__ Rzz)
+{
+    const double H=0.5, TWO=2.0, F3o2=1.5;
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double cx=chix[i],cy=chiy[i],cz=chiz[i],c1=chin1[i];
+        /* subtract Christoffel * chi_deriv */
+        fxx[i] -= Gxxx[i]*cx+Gyxx[i]*cy+Gzxx[i]*cz;
+        fxy[i] -= Gxxy[i]*cx+Gyxy[i]*cy+Gzxy[i]*cz;
+        fxz[i] -= Gxxz[i]*cx+Gyxz[i]*cy+Gzxz[i]*cz;
+        fyy[i] -= Gxyy[i]*cx+Gyyy[i]*cy+Gzyy[i]*cz;
+        fyz[i] -= Gxyz[i]*cx+Gyyz[i]*cy+Gzyz[i]*cz;
+        fzz[i] -= Gxzz[i]*cx+Gyzz[i]*cy+Gzzz[i]*cz;
+
+        double uxx=gupxx[i],uxy=gupxy[i],uxz=gupxz[i];
+        double uyy=gupyy[i],uyz=gupyz[i],uzz=gupzz[i];
+        double f_val = uxx*(fxx[i]-F3o2/c1*cx*cx)
+                     + uyy*(fyy[i]-F3o2/c1*cy*cy)
+                     + uzz*(fzz[i]-F3o2/c1*cz*cz)
+                     + TWO*uxy*(fxy[i]-F3o2/c1*cx*cy)
+                     + TWO*uxz*(fxz[i]-F3o2/c1*cx*cz)
+                     + TWO*uyz*(fyz[i]-F3o2/c1*cy*cz);
+
+        double inv2c = 1.0/(c1*TWO);
+        Rxx[i] += (fxx[i]-cx*cx*inv2c+gxx[i]*f_val)*inv2c;
+        Ryy[i] += (fyy[i]-cy*cy*inv2c+gyy[i]*f_val)*inv2c;
+        Rzz[i] += (fzz[i]-cz*cz*inv2c+gzz[i]*f_val)*inv2c;
+        Rxy[i] += (fxy[i]-cx*cy*inv2c+gxy[i]*f_val)*inv2c;
+        Rxz[i] += (fxz[i]-cx*cz*inv2c+gxz[i]*f_val)*inv2c;
+        Ryz[i] += (fyz[i]-cy*cz*inv2c+gyz[i]*f_val)*inv2c;
+    }
+}
+
+/* Phase 15: trK_rhs, Aij_rhs, gauge (after fdderivs(Lap) and fderivs(chi))
+ * Also updates Christoffel with physical chi correction, computes Lap_rhs, beta_rhs, dtSf_rhs.
+ */
+__global__ __launch_bounds__(128, 4)
+void kern_phase15_trK_Aij_gauge(
+    const double* __restrict__ alpn1, const double* __restrict__ chin1,
+    const double* __restrict__ chix, const double* __restrict__ chiy,
+    const double* __restrict__ chiz,
+    const double* __restrict__ gxx, const double* __restrict__ gxy,
+    const double* __restrict__ gxz, const double* __restrict__ gyy,
+    const double* __restrict__ gyz, const double* __restrict__ gzz,
+    const double* __restrict__ gupxx, const double* __restrict__ gupxy,
+    const double* __restrict__ gupxz, const double* __restrict__ gupyy,
+    const double* __restrict__ gupyz, const double* __restrict__ gupzz,
+    const double* __restrict__ trK,
+    const double* __restrict__ Axx, const double* __restrict__ Axy,
+    const double* __restrict__ Axz, const double* __restrict__ Ayy,
+    const double* __restrict__ Ayz, const double* __restrict__ Azz,
+    const double* __restrict__ Lapx, const double* __restrict__ Lapy,
+    const double* __restrict__ Lapz,
+    const double* __restrict__ betaxx, const double* __restrict__ betaxy,
+    const double* __restrict__ betaxz, const double* __restrict__ betayx,
+    const double* __restrict__ betayy, const double* __restrict__ betayz,
+    const double* __restrict__ betazx, const double* __restrict__ betazy,
+    const double* __restrict__ betazz,
+    const double* __restrict__ rho,
+    const double* __restrict__ Sx_m, const double* __restrict__ Sy_m,
+    const double* __restrict__ Sz_m,
+    const double* __restrict__ Sxx_m, const double* __restrict__ Sxy_m,
+    const double* __restrict__ Sxz_m, const double* __restrict__ Syy_m,
+    const double* __restrict__ Syz_m, const double* __restrict__ Szz_m,
+    const double* __restrict__ dtSfx, const double* __restrict__ dtSfy,
+    const double* __restrict__ dtSfz,
+    const double* __restrict__ Rxx, const double* __restrict__ Rxy,
+    const double* __restrict__ Rxz, const double* __restrict__ Ryy,
+    const double* __restrict__ Ryz, const double* __restrict__ Rzz,
+    double* __restrict__ Gxxx, double* __restrict__ Gxxy,
+    double* __restrict__ Gxxz, double* __restrict__ Gxyy,
+    double* __restrict__ Gxyz_o, double* __restrict__ Gxzz,
+    double* __restrict__ Gyxx, double* __restrict__ Gyxy,
+    double* __restrict__ Gyxz, double* __restrict__ Gyyy,
+    double* __restrict__ Gyyz, double* __restrict__ Gyzz,
+    double* __restrict__ Gzxx, double* __restrict__ Gzxy,
+    double* __restrict__ Gzxz, double* __restrict__ Gzyy,
+    double* __restrict__ Gzyz, double* __restrict__ Gzzz,
+    /* fxx..fzz = fdderivs(Lap) output */
+    double* __restrict__ fxx, double* __restrict__ fxy,
+    double* __restrict__ fxz, double* __restrict__ fyy,
+    double* __restrict__ fyz, double* __restrict__ fzz,
+    /* dtSfx_rhs..dtSfz_rhs = fderivs(chi) output, then overwritten */
+    double* __restrict__ dtSfx_rhs, double* __restrict__ dtSfy_rhs,
+    double* __restrict__ dtSfz_rhs,
+    double* __restrict__ trK_rhs,
+    double* __restrict__ Axx_rhs, double* __restrict__ Axy_rhs,
+    double* __restrict__ Axz_rhs, double* __restrict__ Ayy_rhs,
+    double* __restrict__ Ayz_rhs, double* __restrict__ Azz_rhs,
+    double* __restrict__ Lap_rhs,
+    double* __restrict__ betax_rhs, double* __restrict__ betay_rhs,
+    double* __restrict__ betaz_rhs,
+    double* __restrict__ Gamx_rhs, double* __restrict__ Gamy_rhs,
+    double* __restrict__ Gamz_rhs,
+    double* __restrict__ f_arr, double* __restrict__ S_arr)
+{
+    const double TWO=2.0, FOUR=4.0, EIGHT=8.0, H=0.5;
+    const double F1o3=1.0/3.0, F2o3=2.0/3.0, F3o2=1.5;
+    const double PI_V=3.14159265358979323846;
+    const double F16=16.0, F8=8.0;
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all; i += blockDim.x*gridDim.x) {
+        double uxx=gupxx[i],uxy=gupxy[i],uxz=gupxz[i];
+        double uyy=gupyy[i],uyz=gupyz[i],uzz=gupzz[i];
+        double a=alpn1[i], c1=chin1[i];
+        double cx=chix[i],cy=chiy[i],cz=chiz[i];
+        double lx=Lapx[i],ly=Lapy[i],lz=Lapz[i];
+
+        /* raised chi/chi */
+        double gx=(uxx*cx+uxy*cy+uxz*cz)/c1;
+        double gy=(uxy*cx+uyy*cy+uyz*cz)/c1;
+        double gz=(uxz*cx+uyz*cy+uzz*cz)/c1;
+
+        /* Christoffel physical correction */
+        Gxxx[i]-=((cx+cx)/c1-gxx[i]*gx)*H;
+        Gyxx[i]-=(0.0-gxx[i]*gy)*H;
+        Gzxx[i]-=(0.0-gxx[i]*gz)*H;
+        Gxyy[i]-=(0.0-gyy[i]*gx)*H;
+        Gyyy[i]-=((cy+cy)/c1-gyy[i]*gy)*H;
+        Gzyy[i]-=(0.0-gyy[i]*gz)*H;
+        Gxzz[i]-=(0.0-gzz[i]*gx)*H;
+        Gyzz[i]-=(0.0-gzz[i]*gy)*H;
+        Gzzz[i]-=((cz+cz)/c1-gzz[i]*gz)*H;
+        Gxxy[i]-=(cy/c1-gxy[i]*gx)*H;
+        Gyxy[i]-=(cx/c1-gxy[i]*gy)*H;
+        Gzxy[i]-=(0.0-gxy[i]*gz)*H;
+        Gxxz[i]-=(cz/c1-gxz[i]*gx)*H;
+        Gyxz[i]-=(0.0-gxz[i]*gy)*H;
+        Gzxz[i]-=(cx/c1-gxz[i]*gz)*H;
+        Gxyz_o[i]-=(0.0-gyz[i]*gx)*H;
+        Gyyz[i]-=(cz/c1-gyz[i]*gy)*H;
+        Gzyz[i]-=(cy/c1-gyz[i]*gz)*H;
+
+        /* fxx..fzz correction: subtract Gamma*Lap_deriv */
+        fxx[i]-=Gxxx[i]*lx+Gyxx[i]*ly+Gzxx[i]*lz;
+        fyy[i]-=Gxyy[i]*lx+Gyyy[i]*ly+Gzyy[i]*lz;
+        fzz[i]-=Gxzz[i]*lx+Gyzz[i]*ly+Gzzz[i]*lz;
+        fxy[i]-=Gxxy[i]*lx+Gyxy[i]*ly+Gzxy[i]*lz;
+        fxz[i]-=Gxxz[i]*lx+Gyxz[i]*ly+Gzxz[i]*lz;
+        fyz[i]-=Gxyz_o[i]*lx+Gyyz[i]*ly+Gzyz[i]*lz;
+
+        /* D^i D_i alpha */
+        double DDA = uxx*fxx[i]+uyy*fyy[i]+uzz*fzz[i]
+                   +TWO*(uxy*fxy[i]+uxz*fxz[i]+uyz*fyz[i]);
+
+        /* trace of S_ij (physical) */
+        double S_v = c1*(uxx*Sxx_m[i]+uyy*Syy_m[i]+uzz*Szz_m[i]
+                    +TWO*(uxy*Sxy_m[i]+uxz*Sxz_m[i]+uyz*Syz_m[i]));
+
+        /* A^ij A_ij */
+        double AijAij =
+            uxx*(uxx*Axx[i]*Axx[i]+uyy*Axy[i]*Axy[i]+uzz*Axz[i]*Axz[i]
+                +TWO*(uxy*Axx[i]*Axy[i]+uxz*Axx[i]*Axz[i]+uyz*Axy[i]*Axz[i]))
+           +uyy*(uxx*Axy[i]*Axy[i]+uyy*Ayy[i]*Ayy[i]+uzz*Ayz[i]*Ayz[i]
+                +TWO*(uxy*Axy[i]*Ayy[i]+uxz*Axy[i]*Ayz[i]+uyz*Ayy[i]*Ayz[i]))
+           +uzz*(uxx*Axz[i]*Axz[i]+uyy*Ayz[i]*Ayz[i]+uzz*Azz[i]*Azz[i]
+                +TWO*(uxy*Axz[i]*Ayz[i]+uxz*Axz[i]*Azz[i]+uyz*Ayz[i]*Azz[i]))
+           +TWO*(
+                uxy*(uxx*Axx[i]*Axy[i]+uyy*Axy[i]*Ayy[i]+uzz*Axz[i]*Ayz[i]
+                    +uxy*(Axx[i]*Ayy[i]+Axy[i]*Axy[i])
+                    +uxz*(Axx[i]*Ayz[i]+Axz[i]*Axy[i])
+                    +uyz*(Axy[i]*Ayz[i]+Axz[i]*Ayy[i]))
+               +uxz*(uxx*Axx[i]*Axz[i]+uyy*Axy[i]*Ayz[i]+uzz*Axz[i]*Azz[i]
+                    +uxy*(Axx[i]*Ayz[i]+Axy[i]*Axz[i])
+                    +uxz*(Axx[i]*Azz[i]+Axz[i]*Axz[i])
+                    +uyz*(Axy[i]*Azz[i]+Axz[i]*Ayz[i]))
+               +uyz*(uxx*Axy[i]*Axz[i]+uyy*Ayy[i]*Ayz[i]+uzz*Ayz[i]*Azz[i]
+                    +uxy*(Axy[i]*Ayz[i]+Ayy[i]*Axz[i])
+                    +uxz*(Axy[i]*Azz[i]+Ayz[i]*Axz[i])
+                    +uyz*(Ayy[i]*Azz[i]+Ayz[i]*Ayz[i])));
+
+        double trK_v = trK[i];
+        double db = betaxx[i] + betayy[i] + betazz[i];
+
+        /* trK_rhs step 1: store D^iD_i alpha * chin1 */
+        trK_rhs[i] = c1 * DDA;
+
+        /* f_arr = -(1/3) * (DDA + alpha/chi * (2/3*K^2 - AijAij - 16pi*rho + 8pi*S)) */
+        double f_v = F2o3*trK_v*trK_v - AijAij - F16*PI_V*rho[i] + EIGHT*PI_V*S_v;
+        f_arr[i] = -F1o3*(uxx*fxx[i]+uyy*fyy[i]+uzz*fzz[i]
+                         +TWO*(uxy*fxy[i]+uxz*fxz[i]+uyz*fyz[i])
+                         +(a/c1)*f_v);
+
+        /* fij = alpha*(Rij - 8pi*Sij) - D_iD_j alpha */
+        double fxx_v=a*(Rxx[i]-EIGHT*PI_V*Sxx_m[i])-fxx[i];
+        double fxy_v=a*(Rxy[i]-EIGHT*PI_V*Sxy_m[i])-fxy[i];
+        double fxz_v=a*(Rxz[i]-EIGHT*PI_V*Sxz_m[i])-fxz[i];
+        double fyy_v=a*(Ryy[i]-EIGHT*PI_V*Syy_m[i])-fyy[i];
+        double fyz_v=a*(Ryz[i]-EIGHT*PI_V*Syz_m[i])-fyz[i];
+        double fzz_v=a*(Rzz[i]-EIGHT*PI_V*Szz_m[i])-fzz[i];
+
+        /* Aij_rhs = chi*(fij - gij*f) */
+        Axx_rhs[i]=fxx_v-gxx[i]*f_arr[i];
+        Ayy_rhs[i]=fyy_v-gyy[i]*f_arr[i];
+        Azz_rhs[i]=fzz_v-gzz[i]*f_arr[i];
+        Axy_rhs[i]=fxy_v-gxy[i]*f_arr[i];
+        Axz_rhs[i]=fxz_v-gxz[i]*f_arr[i];
+        Ayz_rhs[i]=fyz_v-gyz[i]*f_arr[i];
+
+        /* A_il A^l_j */
+        double AA_xx=uxx*Axx[i]*Axx[i]+uyy*Axy[i]*Axy[i]+uzz*Axz[i]*Axz[i]
+                    +TWO*(uxy*Axx[i]*Axy[i]+uxz*Axx[i]*Axz[i]+uyz*Axy[i]*Axz[i]);
+        double AA_yy=uxx*Axy[i]*Axy[i]+uyy*Ayy[i]*Ayy[i]+uzz*Ayz[i]*Ayz[i]
+                    +TWO*(uxy*Axy[i]*Ayy[i]+uxz*Axy[i]*Ayz[i]+uyz*Ayy[i]*Ayz[i]);
+        double AA_zz=uxx*Axz[i]*Axz[i]+uyy*Ayz[i]*Ayz[i]+uzz*Azz[i]*Azz[i]
+                    +TWO*(uxy*Axz[i]*Ayz[i]+uxz*Axz[i]*Azz[i]+uyz*Ayz[i]*Azz[i]);
+        double AA_xy=uxx*Axx[i]*Axy[i]+uyy*Axy[i]*Ayy[i]+uzz*Axz[i]*Ayz[i]
+                    +uxy*(Axx[i]*Ayy[i]+Axy[i]*Axy[i])
+                    +uxz*(Axx[i]*Ayz[i]+Axz[i]*Axy[i])
+                    +uyz*(Axy[i]*Ayz[i]+Axz[i]*Ayy[i]);
+        double AA_xz=uxx*Axx[i]*Axz[i]+uyy*Axy[i]*Ayz[i]+uzz*Axz[i]*Azz[i]
+                    +uxy*(Axx[i]*Ayz[i]+Axy[i]*Axz[i])
+                    +uxz*(Axx[i]*Azz[i]+Axz[i]*Axz[i])
+                    +uyz*(Axy[i]*Azz[i]+Axz[i]*Ayz[i]);
+        double AA_yz=uxx*Axy[i]*Axz[i]+uyy*Ayy[i]*Ayz[i]+uzz*Ayz[i]*Azz[i]
+                    +uxy*(Axy[i]*Ayz[i]+Ayy[i]*Axz[i])
+                    +uxz*(Axy[i]*Azz[i]+Ayz[i]*Axz[i])
+                    +uyz*(Ayy[i]*Azz[i]+Ayz[i]*Ayz[i]);
+
+        /* trK_rhs final */
+        trK_rhs[i] = -trK_rhs[i]
+            + a*(F1o3*trK_v*trK_v
+                +uxx*AA_xx+uyy*AA_yy+uzz*AA_zz
+                +TWO*(uxy*AA_xy+uxz*AA_xz+uyz*AA_yz)
+                +FOUR*PI_V*(rho[i]+S_v));
+
+        /* Aij_rhs final */
+        Axx_rhs[i]=c1*Axx_rhs[i]+a*(trK_v*Axx[i]-TWO*AA_xx)
+            +TWO*(Axx[i]*betaxx[i]+Axy[i]*betayx[i]+Axz[i]*betazx[i])-F2o3*Axx[i]*db;
+        Ayy_rhs[i]=c1*Ayy_rhs[i]+a*(trK_v*Ayy[i]-TWO*AA_yy)
+            +TWO*(Axy[i]*betaxy[i]+Ayy[i]*betayy[i]+Ayz[i]*betazy[i])-F2o3*Ayy[i]*db;
+        Azz_rhs[i]=c1*Azz_rhs[i]+a*(trK_v*Azz[i]-TWO*AA_zz)
+            +TWO*(Axz[i]*betaxz[i]+Ayz[i]*betayz[i]+Azz[i]*betazz[i])-F2o3*Azz[i]*db;
+        Axy_rhs[i]=c1*Axy_rhs[i]+a*(trK_v*Axy[i]-TWO*AA_xy)
+            +Axx[i]*betaxy[i]+Axz[i]*betazy[i]+Ayy[i]*betayx[i]
+            +Ayz[i]*betazx[i]+F1o3*Axy[i]*db-Axy[i]*betazz[i];
+        Ayz_rhs[i]=c1*Ayz_rhs[i]+a*(trK_v*Ayz[i]-TWO*AA_yz)
+            +Axy[i]*betaxz[i]+Ayy[i]*betayz[i]+Axz[i]*betaxy[i]
+            +Azz[i]*betazy[i]+F1o3*Ayz[i]*db-Ayz[i]*betaxx[i];
+        Axz_rhs[i]=c1*Axz_rhs[i]+a*(trK_v*Axz[i]-TWO*AA_xz)
+            +Axx[i]*betaxz[i]+Axy[i]*betayz[i]+Ayz[i]*betayx[i]
+            +Azz[i]*betazx[i]+F1o3*Axz[i]*db-Axz[i]*betayy[i];
+
+        /* gauge */
+        Lap_rhs[i] = -TWO*a*trK_v;
+        betax_rhs[i] = 0.75*dtSfx[i];
+        betay_rhs[i] = 0.75*dtSfy[i];
+        betaz_rhs[i] = 0.75*dtSfz[i];
+#if (GAUGE == 0)
+        dtSfx_rhs[i] = Gamx_rhs[i] - 2.0*dtSfx[i];
+        dtSfy_rhs[i] = Gamy_rhs[i] - 2.0*dtSfy[i];
+        dtSfz_rhs[i] = Gamz_rhs[i] - 2.0*dtSfz[i];
+#endif
+    }
+}
+
+/* Phase 18: Hamilton & momentum constraints (co==0 only) */
+__global__ __launch_bounds__(128, 4)
+void kern_phase18_constraints(
+    const double* __restrict__ chin1,
+    const double* __restrict__ chix, const double* __restrict__ chiy,
+    const double* __restrict__ chiz,
+    const double* __restrict__ gupxx, const double* __restrict__ gupxy,
+    const double* __restrict__ gupxz, const double* __restrict__ gupyy,
+    const double* __restrict__ gupyz, const double* __restrict__ gupzz,
+    const double* __restrict__ trK,
+    const double* __restrict__ Axx, const double* __restrict__ Axy,
+    const double* __restrict__ Axz, const double* __restrict__ Ayy,
+    const double* __restrict__ Ayz, const double* __restrict__ Azz,
+    const double* __restrict__ Rxx, const double* __restrict__ Rxy,
+    const double* __restrict__ Rxz, const double* __restrict__ Ryy,
+    const double* __restrict__ Ryz, const double* __restrict__ Rzz,
+    const double* __restrict__ rho,
+    const double* __restrict__ Sx_m, const double* __restrict__ Sy_m,
+    const double* __restrict__ Sz_m,
+    const double* __restrict__ Kx, const double* __restrict__ Ky,
+    const double* __restrict__ Kz,
+    const double* __restrict__ Gxxx, const double* __restrict__ Gxxy,
+    const double* __restrict__ Gxxz, const double* __restrict__ Gxyy,
+    const double* __restrict__ Gxyz, const double* __restrict__ Gxzz,
+    const double* __restrict__ Gyxx, const double* __restrict__ Gyxy,
+    const double* __restrict__ Gyxz, const double* __restrict__ Gyyy,
+    const double* __restrict__ Gyyz, const double* __restrict__ Gyzz,
+    const double* __restrict__ Gzxx, const double* __restrict__ Gzxy,
+    const double* __restrict__ Gzxz, const double* __restrict__ Gzyy,
+    const double* __restrict__ Gzyz, const double* __restrict__ Gzzz,
+    /* dA/dx arrays (fderivs of Aij) */
+    const double* __restrict__ dAxx_x, const double* __restrict__ dAxx_y,
+    const double* __restrict__ dAxx_z,
+    const double* __restrict__ dAxy_x, const double* __restrict__ dAxy_y,
+    const double* __restrict__ dAxy_z,
+    const double* __restrict__ dAxz_x, const double* __restrict__ dAxz_y,
+    const double* __restrict__ dAxz_z,
+    const double* __restrict__ dAyy_x, const double* __restrict__ dAyy_y,
+    const double* __restrict__ dAyy_z,
+    const double* __restrict__ dAyz_x, const double* __restrict__ dAyz_y,
+    const double* __restrict__ dAyz_z,
+    const double* __restrict__ dAzz_x, const double* __restrict__ dAzz_y,
+    const double* __restrict__ dAzz_z,
+    double* __restrict__ ham_Res,
+    double* __restrict__ movx_Res, double* __restrict__ movy_Res,
+    double* __restrict__ movz_Res)
+{
+    const double TWO=2.0, F2o3=2.0/3.0, F8=8.0, F16=16.0;
+    const double PI_V=3.14159265358979323846;
+    for (int i = blockIdx.x*blockDim.x+threadIdx.x; i < d_gp.all;
+         i += blockDim.x*gridDim.x)
+    {
+        double uxx=gupxx[i],uxy=gupxy[i],uxz=gupxz[i];
+        double uyy=gupyy[i],uyz=gupyz[i],uzz=gupzz[i];
+        double c1=chin1[i];
+
+        /* Hamiltonian constraint */
+        double R_sc = uxx*Rxx[i]+uyy*Ryy[i]+uzz*Rzz[i]
+                    +TWO*(uxy*Rxy[i]+uxz*Rxz[i]+uyz*Ryz[i]);
+        /* AijAij (same as in phase15) */
+        double AijAij =
+            uxx*(uxx*Axx[i]*Axx[i]+uyy*Axy[i]*Axy[i]+uzz*Axz[i]*Axz[i]
+                +TWO*(uxy*Axx[i]*Axy[i]+uxz*Axx[i]*Axz[i]+uyz*Axy[i]*Axz[i]))
+           +uyy*(uxx*Axy[i]*Axy[i]+uyy*Ayy[i]*Ayy[i]+uzz*Ayz[i]*Ayz[i]
+                +TWO*(uxy*Axy[i]*Ayy[i]+uxz*Axy[i]*Ayz[i]+uyz*Ayy[i]*Ayz[i]))
+           +uzz*(uxx*Axz[i]*Axz[i]+uyy*Ayz[i]*Ayz[i]+uzz*Azz[i]*Azz[i]
+                +TWO*(uxy*Axz[i]*Ayz[i]+uxz*Axz[i]*Azz[i]+uyz*Ayz[i]*Azz[i]))
+           +TWO*(uxy*(uxx*Axx[i]*Axy[i]+uyy*Axy[i]*Ayy[i]+uzz*Axz[i]*Ayz[i]
+                      +uxy*(Axx[i]*Ayy[i]+Axy[i]*Axy[i])
+                      +uxz*(Axx[i]*Ayz[i]+Axz[i]*Axy[i])
+                      +uyz*(Axy[i]*Ayz[i]+Axz[i]*Ayy[i]))
+                 +uxz*(uxx*Axx[i]*Axz[i]+uyy*Axy[i]*Ayz[i]+uzz*Axz[i]*Azz[i]
+                      +uxy*(Axx[i]*Ayz[i]+Axy[i]*Axz[i])
+                      +uxz*(Axx[i]*Azz[i]+Axz[i]*Axz[i])
+                      +uyz*(Axy[i]*Azz[i]+Axz[i]*Ayz[i]))
+                 +uyz*(uxx*Axy[i]*Axz[i]+uyy*Ayy[i]*Ayz[i]+uzz*Ayz[i]*Azz[i]
+                      +uxy*(Axy[i]*Ayz[i]+Ayy[i]*Axz[i])
+                      +uxz*(Axy[i]*Azz[i]+Ayz[i]*Axz[i])
+                      +uyz*(Ayy[i]*Azz[i]+Ayz[i]*Ayz[i])));
+
+        ham_Res[i] = c1*R_sc + F2o3*trK[i]*trK[i] - AijAij - F16*PI_V*rho[i];
+
+        /* Momentum constraints: need covariant derivative of A */
+        double cx=chix[i],cy=chiy[i],cz=chiz[i];
+        /* D_j A^j_x etc — subtract Christoffel and chi terms */
+        /* gxxx = dAxx_x - 2*Gxxx*Axx - ... - chix*Axx/chin1 etc */
+        double mx_xx = dAxx_x[i]-(Gxxx[i]*Axx[i]+Gyxx[i]*Axy[i]+Gzxx[i]*Axz[i]
+                                  +Gxxx[i]*Axx[i]+Gyxx[i]*Axy[i]+Gzxx[i]*Axz[i])-cx*Axx[i]/c1;
+        double mx_xy = dAxy_x[i]-(Gxxy[i]*Axx[i]+Gyxy[i]*Axy[i]+Gzxy[i]*Axz[i]
+                                  +Gxxx[i]*Axy[i]+Gyxx[i]*Ayy[i]+Gzxx[i]*Ayz[i])-cx*Axy[i]/c1;
+        double mx_xz = dAxz_x[i]-(Gxxz[i]*Axx[i]+Gyxz[i]*Axy[i]+Gzxz[i]*Axz[i]
+                                  +Gxxx[i]*Axz[i]+Gyxx[i]*Ayz[i]+Gzxx[i]*Azz[i])-cx*Axz[i]/c1;
+        double mx_yy = dAyy_x[i]-(Gxxy[i]*Axy[i]+Gyxy[i]*Ayy[i]+Gzxy[i]*Ayz[i]
+                                  +Gxxy[i]*Axy[i]+Gyxy[i]*Ayy[i]+Gzxy[i]*Ayz[i])-cx*Ayy[i]/c1;
+        double mx_yz = dAyz_x[i]-(Gxxz[i]*Axy[i]+Gyxz[i]*Ayy[i]+Gzxz[i]*Ayz[i]
+                                  +Gxxy[i]*Axz[i]+Gyxy[i]*Ayz[i]+Gzxy[i]*Azz[i])-cx*Ayz[i]/c1;
+        double mx_zz = dAzz_x[i]-(Gxxz[i]*Axz[i]+Gyxz[i]*Ayz[i]+Gzxz[i]*Azz[i]
+                                  +Gxxz[i]*Axz[i]+Gyxz[i]*Ayz[i]+Gzxz[i]*Azz[i])-cx*Azz[i]/c1;
+
+        double my_xx = dAxx_y[i]-(Gxxy[i]*Axx[i]+Gyxy[i]*Axy[i]+Gzxy[i]*Axz[i]
+                                  +Gxxy[i]*Axx[i]+Gyxy[i]*Axy[i]+Gzxy[i]*Axz[i])-cy*Axx[i]/c1;
+        double my_xy = dAxy_y[i]-(Gxyy[i]*Axx[i]+Gyyy[i]*Axy[i]+Gzyy[i]*Axz[i]
+                                  +Gxxy[i]*Axy[i]+Gyxy[i]*Ayy[i]+Gzxy[i]*Ayz[i])-cy*Axy[i]/c1;
+        double my_xz = dAxz_y[i]-(Gxyz[i]*Axx[i]+Gyyz[i]*Axy[i]+Gzyz[i]*Axz[i]
+                                  +Gxxy[i]*Axz[i]+Gyxy[i]*Ayz[i]+Gzxy[i]*Azz[i])-cy*Axz[i]/c1;
+        double my_yy = dAyy_y[i]-(Gxyy[i]*Axy[i]+Gyyy[i]*Ayy[i]+Gzyy[i]*Ayz[i]
+                                  +Gxyy[i]*Axy[i]+Gyyy[i]*Ayy[i]+Gzyy[i]*Ayz[i])-cy*Ayy[i]/c1;
+        double my_yz = dAyz_y[i]-(Gxyz[i]*Axy[i]+Gyyz[i]*Ayy[i]+Gzyz[i]*Ayz[i]
+                                  +Gxyy[i]*Axz[i]+Gyyy[i]*Ayz[i]+Gzyy[i]*Azz[i])-cy*Ayz[i]/c1;
+        double my_zz = dAzz_y[i]-(Gxyz[i]*Axz[i]+Gyyz[i]*Ayz[i]+Gzyz[i]*Azz[i]
+                                  +Gxyz[i]*Axz[i]+Gyyz[i]*Ayz[i]+Gzyz[i]*Azz[i])-cy*Azz[i]/c1;
+
+        double mz_xx = dAxx_z[i]-(Gxxz[i]*Axx[i]+Gyxz[i]*Axy[i]+Gzxz[i]*Axz[i]
+                                  +Gxxz[i]*Axx[i]+Gyxz[i]*Axy[i]+Gzxz[i]*Axz[i])-cz*Axx[i]/c1;
+        double mz_xy = dAxy_z[i]-(Gxyz[i]*Axx[i]+Gyyz[i]*Axy[i]+Gzyz[i]*Axz[i]
+                                  +Gxxz[i]*Axy[i]+Gyxz[i]*Ayy[i]+Gzxz[i]*Ayz[i])-cz*Axy[i]/c1;
+        double mz_xz = dAxz_z[i]-(Gxzz[i]*Axx[i]+Gyzz[i]*Axy[i]+Gzzz[i]*Axz[i]
+                                  +Gxxz[i]*Axz[i]+Gyxz[i]*Ayz[i]+Gzxz[i]*Azz[i])-cz*Axz[i]/c1;
+        double mz_yy = dAyy_z[i]-(Gxyz[i]*Axy[i]+Gyyz[i]*Ayy[i]+Gzyz[i]*Ayz[i]
+                                  +Gxyz[i]*Axy[i]+Gyyz[i]*Ayy[i]+Gzyz[i]*Ayz[i])-cz*Ayy[i]/c1;
+        double mz_yz = dAyz_z[i]-(Gxzz[i]*Axy[i]+Gyzz[i]*Ayy[i]+Gzzz[i]*Ayz[i]
+                                  +Gxyz[i]*Axz[i]+Gyyz[i]*Ayz[i]+Gzyz[i]*Azz[i])-cz*Ayz[i]/c1;
+        double mz_zz = dAzz_z[i]-(Gxzz[i]*Axz[i]+Gyzz[i]*Ayz[i]+Gzzz[i]*Azz[i]
+                                  +Gxzz[i]*Axz[i]+Gyzz[i]*Ayz[i]+Gzzz[i]*Azz[i])-cz*Azz[i]/c1;
+
+        movx_Res[i] = uxx*mx_xx+uyy*my_xy+uzz*mz_xz
+                     +uxy*mx_xy+uxz*mx_xz+uyz*my_xz
+                     +uxy*my_xx+uxz*mz_xx+uyz*mz_xy
+                     - F2o3*Kx[i] - F8*PI_V*Sx_m[i];
+        movy_Res[i] = uxx*mx_xy+uyy*my_yy+uzz*mz_yz
+                     +uxy*mx_yy+uxz*mx_yz+uyz*my_yz
+                     +uxy*my_xy+uxz*mz_xy+uyz*mz_yy
+                     - F2o3*Ky[i] - F8*PI_V*Sy_m[i];
+        movz_Res[i] = uxx*mx_xz+uyy*my_yz+uzz*mz_zz
+                     +uxy*mx_yz+uxz*mx_zz+uyz*my_zz
+                     +uxy*my_xz+uxz*mz_xz+uyz*mz_yz
+                     - F2o3*Kz[i] - F8*PI_V*Sz_m[i];
+    }
+}
+
+/* ================================================================== */
+/*  Main host function — drop-in replacement for bssn_rhs_c.C          */
+/* ================================================================== */
+
+extern "C"
+int f_compute_rhs_bssn(int *ex, double &T,
+    double *X, double *Y, double *Z,
+    double *chi, double *trK,
+    double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+    double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+    double *Gamx, double *Gamy, double *Gamz,
+    double *Lap, double *betax, double *betay, double *betaz,
+    double *dtSfx, double *dtSfy, double *dtSfz,
+    double *chi_rhs, double *trK_rhs,
+    double *gxx_rhs, double *gxy_rhs, double *gxz_rhs,
+    double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+    double *Axx_rhs, double *Axy_rhs, double *Axz_rhs,
+    double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+    double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+    double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+    double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+    double *rho, double *Sx, double *Sy, double *Sz,
+    double *Sxx, double *Sxy_m, double *Sxz, double *Syy, double *Syz_m, double *Szz,
+    double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy,
+    double *Gamxyz, double *Gamxzz,
+    double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy,
+    double *Gamyyz, double *Gamyzz,
+    double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy,
+    double *Gamzyz, double *Gamzzz,
+    double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
+    double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
+    double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
+    int &Symmetry, int &Lev, double &eps, int &co)
+{
+    /* --- Multi-GPU: select device --- */
+    init_gpu_dispatch();
+    CUDA_CHECK(cudaSetDevice(g_dispatch.my_device));
+
+    const int nx = ex[0], ny = ex[1], nz = ex[2];
+    const int all = nx * ny * nz;
+    const double dX = X[1]-X[0], dY = Y[1]-Y[0], dZ = Z[1]-Z[0];
+    const int NO_SYMM = 0, EQ_SYMM = 1;
+    const double SYM = 1.0, ANTI = -1.0;
+
+    /* --- Allocate GPU buffers --- */
+    ensure_gpu_buffers(nx, ny, nz);
+
+    /* --- Setup GridParams --- */
+    GridParams gp;
+    gp.ex[0]=nx; gp.ex[1]=ny; gp.ex[2]=nz;
+    gp.all=all; gp.dX=dX; gp.dY=dY; gp.dZ=dZ;
+    gp.d12dx=1.0/(12.0*dX); gp.d12dy=1.0/(12.0*dY); gp.d12dz=1.0/(12.0*dZ);
+    gp.d2dx=1.0/(2.0*dX);   gp.d2dy=1.0/(2.0*dY);   gp.d2dz=1.0/(2.0*dZ);
+    gp.Fdxdx=1.0/(12.0*dX*dX); gp.Fdydy=1.0/(12.0*dY*dY); gp.Fdzdz=1.0/(12.0*dZ*dZ);
+    gp.Sdxdx=1.0/(dX*dX);      gp.Sdydy=1.0/(dY*dY);      gp.Sdzdz=1.0/(dZ*dZ);
+    gp.Fdxdy=1.0/(144.0*dX*dY); gp.Fdxdz=1.0/(144.0*dX*dZ); gp.Fdydz=1.0/(144.0*dY*dZ);
+    gp.Sdxdy=0.25/(dX*dY);      gp.Sdxdz=0.25/(dX*dZ);      gp.Sdydz=0.25/(dY*dZ);
+    gp.imaxF=nx; gp.jmaxF=ny; gp.kmaxF=nz;
+    gp.iminF=1; gp.jminF=1; gp.kminF=1;
+    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) gp.kminF = -1;
+    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) gp.iminF = -1;
+    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) gp.jminF = -1;
+    gp.iminF3=1; gp.jminF3=1; gp.kminF3=1;
+    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) gp.kminF3 = -2;
+    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) gp.iminF3 = -2;
+    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) gp.jminF3 = -2;
+    gp.Symmetry=Symmetry; gp.eps=eps; gp.co=co;
+    gp.fh2_nx=nx+2; gp.fh2_ny=ny+2; gp.fh2_nz=nz+2;
+    gp.fh3_nx=nx+3; gp.fh3_ny=ny+3; gp.fh3_nz=nz+3;
+    CUDA_CHECK(cudaMemcpyToSymbol(d_gp, &gp, sizeof(GridParams)));
+
+    /* --- Shorthand for device slot pointers --- */
+    #define D(s) g_buf.slot[s]
+    const size_t bytes = (size_t)all * sizeof(double);
+
+    /* --- H2D: stage all inputs, then one bulk copy --- */
+    double *h2d_src[] = {
+        chi, trK, dxx, gxy, gxz, dyy, gyz, dzz,
+        Axx, Axy, Axz, Ayy, Ayz, Azz,
+        Gamx, Gamy, Gamz,
+        Lap, betax, betay, betaz,
+        dtSfx, dtSfy, dtSfz,
+        rho, Sx, Sy, Sz,
+        Sxx, Sxy_m, Sxz, Syy, Syz_m, Szz
+    };
+    static_assert((int)(sizeof(h2d_src) / sizeof(h2d_src[0])) == H2D_INPUT_SLOT_COUNT,
+                  "h2d_src list must match H2D_INPUT_SLOT_COUNT");
+    for (int s = 0; s < H2D_INPUT_SLOT_COUNT; ++s) {
+        std::memcpy(g_buf.h_stage + (size_t)s * all, h2d_src[s], bytes);
+    }
+    CUDA_CHECK(cudaMemcpy(D(S_chi), g_buf.h_stage,
+                          (size_t)H2D_INPUT_SLOT_COUNT * bytes,
+                          cudaMemcpyHostToDevice));
+
+    /* ============================================================ */
+    /*  Phase 1: prep — alpn1, chin1, gxx, gyy, gzz                 */
+    /* ============================================================ */
+    kern_phase1_prep<<<grid(all),BLK>>>(
+        D(S_Lap), D(S_chi), D(S_dxx), D(S_dyy), D(S_dzz),
+        D(S_alpn1), D(S_chin1), D(S_gxx), D(S_gyy), D(S_gzz));
+
+    /* 12x fderivs */
+    gpu_fderivs(D(S_betax), D(S_betaxx),D(S_betaxy),D(S_betaxz), ANTI,SYM,SYM, all);
+    gpu_fderivs(D(S_betay), D(S_betayx),D(S_betayy),D(S_betayz), SYM,ANTI,SYM, all);
+    gpu_fderivs(D(S_betaz), D(S_betazx),D(S_betazy),D(S_betazz), SYM,SYM,ANTI, all);
+    gpu_fderivs(D(S_chi),   D(S_chix),D(S_chiy),D(S_chiz),       SYM,SYM,SYM, all);
+    gpu_fderivs(D(S_dxx),   D(S_gxxx),D(S_gxxy),D(S_gxxz),       SYM,SYM,SYM, all);
+    gpu_fderivs(D(S_gxy),   D(S_gxyx),D(S_gxyy),D(S_gxyz),       ANTI,ANTI,SYM, all);
+    gpu_fderivs(D(S_gxz),   D(S_gxzx),D(S_gxzy),D(S_gxzz),       ANTI,SYM,ANTI, all);
+    gpu_fderivs(D(S_dyy),   D(S_gyyx),D(S_gyyy),D(S_gyyz),       SYM,SYM,SYM, all);
+    gpu_fderivs(D(S_gyz),   D(S_gyzx),D(S_gyzy),D(S_gyzz),       SYM,ANTI,ANTI, all);
+    gpu_fderivs(D(S_dzz),   D(S_gzzx),D(S_gzzy),D(S_gzzz),       SYM,SYM,SYM, all);
+    gpu_fderivs(D(S_Lap),   D(S_Lapx),D(S_Lapy),D(S_Lapz),       SYM,SYM,SYM, all);
+    gpu_fderivs(D(S_trK),   D(S_Kx),D(S_Ky),D(S_Kz),             SYM,SYM,SYM, all);
+
+    /* ============================================================ */
+    /*  Phase 2: metric RHS + inverse                                */
+    /* ============================================================ */
+    kern_phase2_metric_rhs<<<grid(all),BLK>>>(
+        D(S_alpn1), D(S_chin1),
+        D(S_gxx), D(S_gxy), D(S_gxz), D(S_gyy), D(S_gyz), D(S_gzz),
+        D(S_trK),
+        D(S_Axx), D(S_Axy), D(S_Axz), D(S_Ayy), D(S_Ayz), D(S_Azz),
+        D(S_betaxx), D(S_betaxy), D(S_betaxz),
+        D(S_betayx), D(S_betayy), D(S_betayz),
+        D(S_betazx), D(S_betazy), D(S_betazz),
+        D(S_chi_rhs), D(S_gxx_rhs), D(S_gyy_rhs), D(S_gzz_rhs),
+        D(S_gxy_rhs), D(S_gyz_rhs), D(S_gxz_rhs));
+
+    kern_phase2_inverse<<<grid(all),BLK>>>(
+        D(S_gxx), D(S_gxy), D(S_gxz), D(S_gyy), D(S_gyz), D(S_gzz),
+        D(S_gupxx), D(S_gupxy), D(S_gupxz),
+        D(S_gupyy), D(S_gupyz), D(S_gupzz));
+
+    /* Phase 3: Gamma constraint (co==0) */
+    if (co == 0) {
+        kern_phase3_gamma_constraint<<<grid(all),BLK>>>(
+            D(S_Gamx), D(S_Gamy), D(S_Gamz),
+            D(S_gupxx), D(S_gupxy), D(S_gupxz),
+            D(S_gupyy), D(S_gupyz), D(S_gupzz),
+            D(S_gxxx), D(S_gxyx), D(S_gxzx), D(S_gyyx), D(S_gyzx), D(S_gzzx),
+            D(S_gxxy), D(S_gxyy), D(S_gxzy), D(S_gyyy), D(S_gyzy), D(S_gzzy),
+            D(S_gxxz), D(S_gxyz), D(S_gxzz), D(S_gyyz), D(S_gyzz), D(S_gzzz),
+            D(S_Gmx_Res), D(S_Gmy_Res), D(S_Gmz_Res));
+    }
+
+    /* Phase 4: Christoffel symbols */
+    kern_phase4_christoffel<<<grid(all),BLK>>>(
+        D(S_gupxx), D(S_gupxy), D(S_gupxz),
+        D(S_gupyy), D(S_gupyz), D(S_gupzz),
+        D(S_gxxx), D(S_gxyx), D(S_gxzx), D(S_gyyx), D(S_gyzx), D(S_gzzx),
+        D(S_gxxy), D(S_gxyy), D(S_gxzy), D(S_gyyy), D(S_gyzy), D(S_gzzy),
+        D(S_gxxz), D(S_gxyz), D(S_gxzz), D(S_gyyz), D(S_gyzz), D(S_gzzz),
+        D(S_Gamxxx), D(S_Gamxxy), D(S_Gamxxz),
+        D(S_Gamxyy), D(S_Gamxyz), D(S_Gamxzz),
+        D(S_Gamyxx), D(S_Gamyxy), D(S_Gamyxz),
+        D(S_Gamyyy), D(S_Gamyyz), D(S_Gamyzz),
+        D(S_Gamzxx), D(S_Gamzxy), D(S_Gamzxz),
+        D(S_Gamzyy), D(S_Gamzyz), D(S_Gamzzz));
+
+    /* Phase 5: Raise A index (stored in Rxx..Rzz temporarily) */
+    kern_phase5_raise_A<<<grid(all),BLK>>>(
+        D(S_gupxx), D(S_gupxy), D(S_gupxz),
+        D(S_gupyy), D(S_gupyz), D(S_gupzz),
+        D(S_Axx), D(S_Axy), D(S_Axz), D(S_Ayy), D(S_Ayz), D(S_Azz),
+        D(S_Rxx), D(S_Rxy), D(S_Rxz), D(S_Ryy), D(S_Ryz), D(S_Rzz));
+
+    /* Phase 6: Gamma_rhs part 1 */
+    kern_phase6_gamma_rhs_part1<<<grid(all),BLK>>>(
+        D(S_Lapx), D(S_Lapy), D(S_Lapz),
+        D(S_alpn1), D(S_chin1),
+        D(S_chix), D(S_chiy), D(S_chiz),
+        D(S_gupxx), D(S_gupxy), D(S_gupxz),
+        D(S_gupyy), D(S_gupyz), D(S_gupzz),
+        D(S_Kx), D(S_Ky), D(S_Kz),
+        D(S_Sx), D(S_Sy), D(S_Sz),
+        D(S_Rxx), D(S_Rxy), D(S_Rxz),
+        D(S_Ryy), D(S_Ryz), D(S_Rzz),
+        D(S_Gamxxx), D(S_Gamxxy), D(S_Gamxxz),
+        D(S_Gamxyy), D(S_Gamxyz), D(S_Gamxzz),
+        D(S_Gamyxx), D(S_Gamyxy), D(S_Gamyxz),
+        D(S_Gamyyy), D(S_Gamyyz), D(S_Gamyzz),
+        D(S_Gamzxx), D(S_Gamzxy), D(S_Gamzxz),
+        D(S_Gamzyy), D(S_Gamzyz), D(S_Gamzzz),
+        D(S_Gamx_rhs), D(S_Gamy_rhs), D(S_Gamz_rhs));
+
+    /* Phase 7: fdderivs(beta) + fderivs(Gamma) */
+    gpu_fdderivs(D(S_betax), D(S_gxxx),D(S_gxyx),D(S_gxzx),
+                 D(S_gyyx),D(S_gyzx),D(S_gzzx), ANTI,SYM,SYM, all);
+    gpu_fdderivs(D(S_betay), D(S_gxxy),D(S_gxyy),D(S_gxzy),
+                 D(S_gyyy),D(S_gyzy),D(S_gzzy), SYM,ANTI,SYM, all);
+    gpu_fdderivs(D(S_betaz), D(S_gxxz),D(S_gxyz),D(S_gxzz),
+                 D(S_gyyz),D(S_gyzz),D(S_gzzz), SYM,SYM,ANTI, all);
+    gpu_fderivs(D(S_Gamx), D(S_Gamxx),D(S_Gamxy),D(S_Gamxz), ANTI,SYM,SYM, all);
+    gpu_fderivs(D(S_Gamy), D(S_Gamyx),D(S_Gamyy_t),D(S_Gamyz_t), SYM,ANTI,SYM, all);
+    gpu_fderivs(D(S_Gamz), D(S_Gamzx),D(S_Gamzy),D(S_Gamzz_t), SYM,SYM,ANTI, all);
+
+    /* Phase 8: Gamma_rhs part 2 */
+    kern_phase8_gamma_rhs_part2<<<grid(all),BLK>>>(
+        D(S_gupxx), D(S_gupxy), D(S_gupxz),
+        D(S_gupyy), D(S_gupyz), D(S_gupzz),
+        D(S_gxxx),D(S_gxyx),D(S_gxzx),D(S_gyyx),D(S_gyzx),D(S_gzzx),
+        D(S_gxxy),D(S_gxyy),D(S_gxzy),D(S_gyyy),D(S_gyzy),D(S_gzzy),
+        D(S_gxxz),D(S_gxyz),D(S_gxzz),D(S_gyyz),D(S_gyzz),D(S_gzzz),
+        D(S_Gamxx),D(S_Gamxy),D(S_Gamxz),
+        D(S_Gamyx),D(S_Gamyy_t),D(S_Gamyz_t),
+        D(S_Gamzx),D(S_Gamzy),D(S_Gamzz_t),
+        D(S_Gamxxx),D(S_Gamxxy),D(S_Gamxxz),
+        D(S_Gamxyy),D(S_Gamxyz),D(S_Gamxzz),
+        D(S_Gamyxx),D(S_Gamyxy),D(S_Gamyxz),
+        D(S_Gamyyy),D(S_Gamyyz),D(S_Gamyzz),
+        D(S_Gamzxx),D(S_Gamzxy),D(S_Gamzxz),
+        D(S_Gamzyy),D(S_Gamzyz),D(S_Gamzzz),
+        D(S_betaxx),D(S_betaxy),D(S_betaxz),
+        D(S_betayx),D(S_betayy),D(S_betayz),
+        D(S_betazx),D(S_betazy),D(S_betazz),
+        D(S_Gamx_rhs),D(S_Gamy_rhs),D(S_Gamz_rhs),
+        D(S_Gamxa),D(S_Gamya),D(S_Gamza));
+
+    /* Phase 9: Christoffel contract (lowered products for Ricci) */
+    kern_phase9_christoffel_contract<<<grid(all),BLK>>>(
+        D(S_gxx),D(S_gxy),D(S_gxz),D(S_gyy),D(S_gyz),D(S_gzz),
+        D(S_Gamxxx),D(S_Gamxxy),D(S_Gamxxz),
+        D(S_Gamxyy),D(S_Gamxyz),D(S_Gamxzz),
+        D(S_Gamyxx),D(S_Gamyxy),D(S_Gamyxz),
+        D(S_Gamyyy),D(S_Gamyyz),D(S_Gamyzz),
+        D(S_Gamzxx),D(S_Gamzxy),D(S_Gamzxz),
+        D(S_Gamzyy),D(S_Gamzyz),D(S_Gamzzz),
+        D(S_gxxx),D(S_gxyx),D(S_gxzx),D(S_gyyx),D(S_gyzx),D(S_gzzx),
+        D(S_gxxy),D(S_gxyy),D(S_gxzy),D(S_gyyy),D(S_gyzy),D(S_gzzy),
+        D(S_gxxz),D(S_gxyz),D(S_gxzz),D(S_gyyz),D(S_gyzz),D(S_gzzz));
+
+    /* Phase 10: 6x fdderivs(metric) + Ricci contract */
+    gpu_fdderivs(D(S_dxx), D(S_fxx),D(S_fxy),D(S_fxz),
+                 D(S_fyy),D(S_fyz),D(S_fzz), SYM,SYM,SYM, all);
+    kern_phase10_ricci_contract<<<grid(all),BLK>>>(
+        D(S_gupxx),D(S_gupxy),D(S_gupxz),D(S_gupyy),D(S_gupyz),D(S_gupzz),
+        D(S_fxx),D(S_fxy),D(S_fxz),D(S_fyy),D(S_fyz),D(S_fzz), D(S_Rxx));
+
+    gpu_fdderivs(D(S_dyy), D(S_fxx),D(S_fxy),D(S_fxz),
+                 D(S_fyy),D(S_fyz),D(S_fzz), SYM,SYM,SYM, all);
+    kern_phase10_ricci_contract<<<grid(all),BLK>>>(
+        D(S_gupxx),D(S_gupxy),D(S_gupxz),D(S_gupyy),D(S_gupyz),D(S_gupzz),
+        D(S_fxx),D(S_fxy),D(S_fxz),D(S_fyy),D(S_fyz),D(S_fzz), D(S_Ryy));
+
+    gpu_fdderivs(D(S_dzz), D(S_fxx),D(S_fxy),D(S_fxz),
+                 D(S_fyy),D(S_fyz),D(S_fzz), SYM,SYM,SYM, all);
+    kern_phase10_ricci_contract<<<grid(all),BLK>>>(
+        D(S_gupxx),D(S_gupxy),D(S_gupxz),D(S_gupyy),D(S_gupyz),D(S_gupzz),
+        D(S_fxx),D(S_fxy),D(S_fxz),D(S_fyy),D(S_fyz),D(S_fzz), D(S_Rzz));
+
+    gpu_fdderivs(D(S_gxy), D(S_fxx),D(S_fxy),D(S_fxz),
+                 D(S_fyy),D(S_fyz),D(S_fzz), ANTI,ANTI,SYM, all);
+    kern_phase10_ricci_contract<<<grid(all),BLK>>>(
+        D(S_gupxx),D(S_gupxy),D(S_gupxz),D(S_gupyy),D(S_gupyz),D(S_gupzz),
+        D(S_fxx),D(S_fxy),D(S_fxz),D(S_fyy),D(S_fyz),D(S_fzz), D(S_Rxy));
+
+    gpu_fdderivs(D(S_gxz), D(S_fxx),D(S_fxy),D(S_fxz),
+                 D(S_fyy),D(S_fyz),D(S_fzz), ANTI,SYM,ANTI, all);
+    kern_phase10_ricci_contract<<<grid(all),BLK>>>(
+        D(S_gupxx),D(S_gupxy),D(S_gupxz),D(S_gupyy),D(S_gupyz),D(S_gupzz),
+        D(S_fxx),D(S_fxy),D(S_fxz),D(S_fyy),D(S_fyz),D(S_fzz), D(S_Rxz));
+
+    gpu_fdderivs(D(S_gyz), D(S_fxx),D(S_fxy),D(S_fxz),
+                 D(S_fyy),D(S_fyz),D(S_fzz), SYM,ANTI,ANTI, all);
+    kern_phase10_ricci_contract<<<grid(all),BLK>>>(
+        D(S_gupxx),D(S_gupxy),D(S_gupxz),D(S_gupyy),D(S_gupyz),D(S_gupzz),
+        D(S_fxx),D(S_fxy),D(S_fxz),D(S_fyy),D(S_fyz),D(S_fzz), D(S_Ryz));
+
+    /* Phase 11: Ricci assembly (diagonal + off-diagonal) */
+    kern_phase11_ricci_diag<<<grid(all),BLK>>>(
+        D(S_gxx),D(S_gxy),D(S_gxz),D(S_gyy),D(S_gyz),D(S_gzz),
+        D(S_gupxx),D(S_gupxy),D(S_gupxz),D(S_gupyy),D(S_gupyz),D(S_gupzz),
+        D(S_Gamxa),D(S_Gamya),D(S_Gamza),
+        D(S_Gamxx),D(S_Gamxy),D(S_Gamxz),
+        D(S_Gamyx),D(S_Gamyy_t),D(S_Gamyz_t),
+        D(S_Gamzx),D(S_Gamzy),D(S_Gamzz_t),
+        D(S_Gamxxx),D(S_Gamxxy),D(S_Gamxxz),
+        D(S_Gamxyy),D(S_Gamxyz),D(S_Gamxzz),
+        D(S_Gamyxx),D(S_Gamyxy),D(S_Gamyxz),
+        D(S_Gamyyy),D(S_Gamyyz),D(S_Gamyzz),
+        D(S_Gamzxx),D(S_Gamzxy),D(S_Gamzxz),
+        D(S_Gamzyy),D(S_Gamzyz),D(S_Gamzzz),
+        D(S_gxxx),D(S_gxyx),D(S_gxzx),D(S_gyyx),D(S_gyzx),D(S_gzzx),
+        D(S_gxxy),D(S_gxyy),D(S_gxzy),D(S_gyyy),D(S_gyzy),D(S_gzzy),
+        D(S_gxxz),D(S_gxyz),D(S_gxzz),D(S_gyyz),D(S_gyzz),D(S_gzzz),
+        D(S_Rxx),D(S_Ryy),D(S_Rzz));
+
+    kern_phase11_ricci_offdiag<<<grid(all),BLK>>>(
+        D(S_gxx),D(S_gxy),D(S_gxz),D(S_gyy),D(S_gyz),D(S_gzz),
+        D(S_gupxx),D(S_gupxy),D(S_gupxz),D(S_gupyy),D(S_gupyz),D(S_gupzz),
+        D(S_Gamxa),D(S_Gamya),D(S_Gamza),
+        D(S_Gamxx),D(S_Gamxy),D(S_Gamxz),
+        D(S_Gamyx),D(S_Gamyy_t),D(S_Gamyz_t),
+        D(S_Gamzx),D(S_Gamzy),D(S_Gamzz_t),
+        D(S_Gamxxx),D(S_Gamxxy),D(S_Gamxxz),
+        D(S_Gamxyy),D(S_Gamxyz),D(S_Gamxzz),
+        D(S_Gamyxx),D(S_Gamyxy),D(S_Gamyxz),
+        D(S_Gamyyy),D(S_Gamyyz),D(S_Gamyzz),
+        D(S_Gamzxx),D(S_Gamzxy),D(S_Gamzxz),
+        D(S_Gamzyy),D(S_Gamzyz),D(S_Gamzzz),
+        D(S_gxxx),D(S_gxyx),D(S_gxzx),D(S_gyyx),D(S_gyzx),D(S_gzzx),
+        D(S_gxxy),D(S_gxyy),D(S_gxzy),D(S_gyyy),D(S_gyzy),D(S_gzzy),
+        D(S_gxxz),D(S_gxyz),D(S_gxzz),D(S_gyyz),D(S_gyzz),D(S_gzzz),
+        D(S_Rxy),D(S_Rxz),D(S_Ryz));
+
+    /* ============================================================ */
+    /*  Phase 12: fdderivs(chi)                                      */
+    /* ============================================================ */
+    gpu_fdderivs(D(S_chi), D(S_fxx),D(S_fxy),D(S_fxz),
+                 D(S_fyy),D(S_fyz),D(S_fzz), SYM,SYM,SYM, all);
+
+    /* ============================================================ */
+    /*  Phase 13: chi correction to Ricci                            */
+    /* ============================================================ */
+    kern_phase13_chi_correction<<<grid(all),BLK>>>(
+        D(S_chin1),
+        D(S_chix), D(S_chiy), D(S_chiz),
+        D(S_gxx), D(S_gxy), D(S_gxz), D(S_gyy), D(S_gyz), D(S_gzz),
+        D(S_gupxx), D(S_gupxy), D(S_gupxz),
+        D(S_gupyy), D(S_gupyz), D(S_gupzz),
+        D(S_Gamxxx), D(S_Gamxxy), D(S_Gamxxz),
+        D(S_Gamxyy), D(S_Gamxyz), D(S_Gamxzz),
+        D(S_Gamyxx), D(S_Gamyxy), D(S_Gamyxz),
+        D(S_Gamyyy), D(S_Gamyyz), D(S_Gamyzz),
+        D(S_Gamzxx), D(S_Gamzxy), D(S_Gamzxz),
+        D(S_Gamzyy), D(S_Gamzyz), D(S_Gamzzz),
+        D(S_fxx), D(S_fxy), D(S_fxz),
+        D(S_fyy), D(S_fyz), D(S_fzz),
+        D(S_Rxx), D(S_Rxy), D(S_Rxz),
+        D(S_Ryy), D(S_Ryz), D(S_Rzz));
+
+    /* ============================================================ */
+    /*  Phase 14: fdderivs(Lap) + fderivs(chi)                       */
+    /* ============================================================ */
+    gpu_fdderivs(D(S_Lap), D(S_fxx),D(S_fxy),D(S_fxz),
+                 D(S_fyy),D(S_fyz),D(S_fzz), SYM,SYM,SYM, all);
+    gpu_fderivs(D(S_chi), D(S_dtSfx_rhs),D(S_dtSfy_rhs),D(S_dtSfz_rhs),
+                SYM,SYM,SYM, all);
+
+    /* ============================================================ */
+    /*  Phase 15: trK_rhs, Aij_rhs, gauge                            */
+    /* ============================================================ */
+    kern_phase15_trK_Aij_gauge<<<grid(all),BLK>>>(
+        D(S_alpn1), D(S_chin1),
+        D(S_chix), D(S_chiy), D(S_chiz),
+        D(S_gxx), D(S_gxy), D(S_gxz), D(S_gyy), D(S_gyz), D(S_gzz),
+        D(S_gupxx), D(S_gupxy), D(S_gupxz),
+        D(S_gupyy), D(S_gupyz), D(S_gupzz),
+        D(S_trK),
+        D(S_Axx), D(S_Axy), D(S_Axz), D(S_Ayy), D(S_Ayz), D(S_Azz),
+        D(S_Lapx), D(S_Lapy), D(S_Lapz),
+        D(S_betaxx), D(S_betaxy), D(S_betaxz),
+        D(S_betayx), D(S_betayy), D(S_betayz),
+        D(S_betazx), D(S_betazy), D(S_betazz),
+        D(S_rho),
+        D(S_Sx), D(S_Sy), D(S_Sz),
+        D(S_Sxx), D(S_Sxy), D(S_Sxz), D(S_Syy), D(S_Syz), D(S_Szz),
+        D(S_dtSfx), D(S_dtSfy), D(S_dtSfz),
+        D(S_Rxx), D(S_Rxy), D(S_Rxz), D(S_Ryy), D(S_Ryz), D(S_Rzz),
+        D(S_Gamxxx), D(S_Gamxxy), D(S_Gamxxz),
+        D(S_Gamxyy), D(S_Gamxyz), D(S_Gamxzz),
+        D(S_Gamyxx), D(S_Gamyxy), D(S_Gamyxz),
+        D(S_Gamyyy), D(S_Gamyyz), D(S_Gamyzz),
+        D(S_Gamzxx), D(S_Gamzxy), D(S_Gamzxz),
+        D(S_Gamzyy), D(S_Gamzyz), D(S_Gamzzz),
+        D(S_fxx), D(S_fxy), D(S_fxz),
+        D(S_fyy), D(S_fyz), D(S_fzz),
+        D(S_dtSfx_rhs), D(S_dtSfy_rhs), D(S_dtSfz_rhs),
+        D(S_trK_rhs),
+        D(S_Axx_rhs), D(S_Axy_rhs), D(S_Axz_rhs),
+        D(S_Ayy_rhs), D(S_Ayz_rhs), D(S_Azz_rhs),
+        D(S_Lap_rhs),
+        D(S_betax_rhs), D(S_betay_rhs), D(S_betaz_rhs),
+        D(S_Gamx_rhs), D(S_Gamy_rhs), D(S_Gamz_rhs),
+        D(S_f_arr), D(S_S_arr));
+
+    /* ============================================================ */
+    /*  Phase 16/17: advection + KO dissipation (shared ord=3 pack)  */
+    /* ============================================================ */
+    gpu_lopsided_kodis(D(S_gxx),   D(S_dxx),   D(S_gxx_rhs),   D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_Gamz),  D(S_Gamz),  D(S_Gamz_rhs),  D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,ANTI,   eps, all);
+    gpu_lopsided_kodis(D(S_gxy),   D(S_gxy),   D(S_gxy_rhs),   D(S_betax),D(S_betay),D(S_betaz), ANTI,ANTI,SYM,   eps, all);
+    gpu_lopsided_kodis(D(S_Lap),   D(S_Lap),   D(S_Lap_rhs),   D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_gxz),   D(S_gxz),   D(S_gxz_rhs),   D(S_betax),D(S_betay),D(S_betaz), ANTI,SYM,ANTI,   eps, all);
+    gpu_lopsided_kodis(D(S_betax), D(S_betax), D(S_betax_rhs), D(S_betax),D(S_betay),D(S_betaz), ANTI,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_gyy),   D(S_dyy),   D(S_gyy_rhs),   D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_betay), D(S_betay), D(S_betay_rhs), D(S_betax),D(S_betay),D(S_betaz), SYM,ANTI,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_gyz),   D(S_gyz),   D(S_gyz_rhs),   D(S_betax),D(S_betay),D(S_betaz), SYM,ANTI,ANTI,   eps, all);
+    gpu_lopsided_kodis(D(S_betaz), D(S_betaz), D(S_betaz_rhs), D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,ANTI,    eps, all);
+    gpu_lopsided_kodis(D(S_gzz),   D(S_dzz),   D(S_gzz_rhs),   D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_dtSfx), D(S_dtSfx), D(S_dtSfx_rhs), D(S_betax),D(S_betay),D(S_betaz), ANTI,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_Axx),   D(S_Axx),   D(S_Axx_rhs),   D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_dtSfy), D(S_dtSfy), D(S_dtSfy_rhs), D(S_betax),D(S_betay),D(S_betaz), SYM,ANTI,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_Axy),   D(S_Axy),   D(S_Axy_rhs),   D(S_betax),D(S_betay),D(S_betaz), ANTI,ANTI,SYM,   eps, all);
+    gpu_lopsided_kodis(D(S_dtSfz), D(S_dtSfz), D(S_dtSfz_rhs), D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,ANTI,    eps, all);
+    gpu_lopsided_kodis(D(S_Axz),   D(S_Axz),   D(S_Axz_rhs),   D(S_betax),D(S_betay),D(S_betaz), ANTI,SYM,ANTI,   eps, all);
+    gpu_lopsided_kodis(D(S_Ayy),   D(S_Ayy),   D(S_Ayy_rhs),   D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_Ayz),   D(S_Ayz),   D(S_Ayz_rhs),   D(S_betax),D(S_betay),D(S_betaz), SYM,ANTI,ANTI,   eps, all);
+    gpu_lopsided_kodis(D(S_Azz),   D(S_Azz),   D(S_Azz_rhs),   D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_chi),   D(S_chi),   D(S_chi_rhs),   D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_trK),   D(S_trK),   D(S_trK_rhs),   D(S_betax),D(S_betay),D(S_betaz), SYM,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_Gamx),  D(S_Gamx),  D(S_Gamx_rhs),  D(S_betax),D(S_betay),D(S_betaz), ANTI,SYM,SYM,    eps, all);
+    gpu_lopsided_kodis(D(S_Gamy),  D(S_Gamy),  D(S_Gamy_rhs),  D(S_betax),D(S_betay),D(S_betaz), SYM,ANTI,SYM,    eps, all);
+
+    /* ============================================================ */
+    /*  Phase 18: Hamilton & momentum constraints (co==0)             */
+    /* ============================================================ */
+    if (co == 0) {
+        /* 6x fderivs on Aij — reuse gxxx..gzzz slots for dA/dx output */
+        gpu_fderivs(D(S_Axx), D(S_gxxx),D(S_gxxy),D(S_gxxz), SYM,SYM,SYM,      all);
+        gpu_fderivs(D(S_Axy), D(S_gxyx),D(S_gxyy),D(S_gxyz), ANTI,ANTI,SYM,     all);
+        gpu_fderivs(D(S_Axz), D(S_gxzx),D(S_gxzy),D(S_gxzz), ANTI,SYM,ANTI,     all);
+        gpu_fderivs(D(S_Ayy), D(S_gyyx),D(S_gyyy),D(S_gyyz), SYM,SYM,SYM,       all);
+        gpu_fderivs(D(S_Ayz), D(S_gyzx),D(S_gyzy),D(S_gyzz), SYM,ANTI,ANTI,     all);
+        gpu_fderivs(D(S_Azz), D(S_gzzx),D(S_gzzy),D(S_gzzz), SYM,SYM,SYM,       all);
+
+        kern_phase18_constraints<<<grid(all),BLK>>>(
+            D(S_chin1),
+            D(S_chix), D(S_chiy), D(S_chiz),
+            D(S_gupxx), D(S_gupxy), D(S_gupxz),
+            D(S_gupyy), D(S_gupyz), D(S_gupzz),
+            D(S_trK),
+            D(S_Axx), D(S_Axy), D(S_Axz), D(S_Ayy), D(S_Ayz), D(S_Azz),
+            D(S_Rxx), D(S_Rxy), D(S_Rxz), D(S_Ryy), D(S_Ryz), D(S_Rzz),
+            D(S_rho), D(S_Sx), D(S_Sy), D(S_Sz),
+            D(S_Kx), D(S_Ky), D(S_Kz),
+            D(S_Gamxxx), D(S_Gamxxy), D(S_Gamxxz),
+            D(S_Gamxyy), D(S_Gamxyz), D(S_Gamxzz),
+            D(S_Gamyxx), D(S_Gamyxy), D(S_Gamyxz),
+            D(S_Gamyyy), D(S_Gamyyz), D(S_Gamyzz),
+            D(S_Gamzxx), D(S_Gamzxy), D(S_Gamzxz),
+            D(S_Gamzyy), D(S_Gamzyz), D(S_Gamzzz),
+            /* dA/dx arrays */
+            D(S_gxxx), D(S_gxxy), D(S_gxxz),
+            D(S_gxyx), D(S_gxyy), D(S_gxyz),
+            D(S_gxzx), D(S_gxzy), D(S_gxzz),
+            D(S_gyyx), D(S_gyyy), D(S_gyyz),
+            D(S_gyzx), D(S_gyzy), D(S_gyzz),
+            D(S_gzzx), D(S_gzzy), D(S_gzzz),
+            D(S_ham_Res), D(S_movx_Res), D(S_movy_Res), D(S_movz_Res));
+    }
+
+    /* ============================================================ */
+    /*  D2H: copy all output arrays back to host                     */
+    /* ============================================================ */
+    const int d2h_slot_count = D2H_BASE_SLOT_COUNT +
+                               ((co == 0) ? D2H_CONSTRAINT_SLOT_COUNT : 0);
+    CUDA_CHECK(cudaMemcpy(g_buf.h_stage, D(S_chi_rhs),
+                          (size_t)d2h_slot_count * bytes,
+                          cudaMemcpyDeviceToHost));
+
+    double *d2h_dst[] = {
+        chi_rhs, trK_rhs,
+        gxx_rhs, gxy_rhs, gxz_rhs, gyy_rhs, gyz_rhs, gzz_rhs,
+        Axx_rhs, Axy_rhs, Axz_rhs, Ayy_rhs, Ayz_rhs, Azz_rhs,
+        Gamx_rhs, Gamy_rhs, Gamz_rhs,
+        Lap_rhs, betax_rhs, betay_rhs, betaz_rhs,
+        dtSfx_rhs, dtSfy_rhs, dtSfz_rhs,
+        Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
+        Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
+        Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
+        Rxx, Rxy, Rxz, Ryy, Ryz, Rzz
+    };
+    static_assert((int)(sizeof(d2h_dst) / sizeof(d2h_dst[0])) == D2H_BASE_SLOT_COUNT,
+                  "d2h_dst list must match D2H_BASE_SLOT_COUNT");
+    for (int s = 0; s < D2H_BASE_SLOT_COUNT; ++s) {
+        std::memcpy(d2h_dst[s], g_buf.h_stage + (size_t)s * all, bytes);
+    }
+    if (co == 0) {
+        double *d2h_dst_co[] = {
+            ham_Res, movx_Res, movy_Res, movz_Res, Gmx_Res, Gmy_Res, Gmz_Res
+        };
+        static_assert((int)(sizeof(d2h_dst_co) / sizeof(d2h_dst_co[0])) ==
+                          D2H_CONSTRAINT_SLOT_COUNT,
+                      "d2h_dst_co list must match D2H_CONSTRAINT_SLOT_COUNT");
+        for (int s = 0; s < D2H_CONSTRAINT_SLOT_COUNT; ++s) {
+            std::memcpy(d2h_dst_co[s],
+                        g_buf.h_stage + (size_t)(D2H_BASE_SLOT_COUNT + s) * all,
+                        bytes);
+        }
+    }
+
+    #undef D
+    return 0;
+}
diff --git a/AMSS_NCKU_source/bssn_rhs_cuda.h b/AMSS_NCKU_source/bssn_rhs_cuda.h
new file mode 100644
index 0000000..cec0111
--- /dev/null
+++ b/AMSS_NCKU_source/bssn_rhs_cuda.h
@@ -0,0 +1,36 @@
+#ifndef BSSN_RHS_CUDA_H
+#define BSSN_RHS_CUDA_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+int f_compute_rhs_bssn(int *ex, double &T,
+                       double *X, double *Y, double *Z,
+                       double *chi, double *trK,
+                       double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+                       double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+                       double *Gamx, double *Gamy, double *Gamz,
+                       double *Lap, double *betax, double *betay, double *betaz,
+                       double *dtSfx, double *dtSfy, double *dtSfz,
+                       double *chi_rhs, double *trK_rhs,
+                       double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+                       double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+                       double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+                       double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+                       double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+                       double *rho, double *Sx, double *Sy, double *Sz,
+                       double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
+                       double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
+                       double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
+                       double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
+                       double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
+                       double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
+                       double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
+                       int &Symmetry, int &Lev, double &eps, int &co);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/AMSS_NCKU_source/bssn_step_gpu.C b/AMSS_NCKU_source/bssn_step_gpu.C
deleted file mode 100644
index 45ee555..0000000
--- a/AMSS_NCKU_source/bssn_step_gpu.C
+++ /dev/null
@@ -1,1942 +0,0 @@
-// includes, system
-#include <stdlib.h>
-#include <stdio.h>
-#include <string.h>
-#include <math.h>
-#include <iostream>
-#include <sys/time.h>
-
-#ifdef RESULT_CHECK
-#include <fstream>
-#endif
-
-// include BSSN class files
-#include "macrodef.h"
-#include "fmisc.h"
-#include "bssn_gpu_class.h"
-#include "bssn_rhs.h"
-#include "enforce_algebra.h"
-#include "rungekutta4_rout.h"
-#include "sommerfeld_rout.h"
-
-// include gpu files
-#include "bssn_gpu.h"
-
-#if (PSTR == 0)
-#if 1
-void bssn_class::Step_GPU(int lev, int YN)
-{
-  setpbh(BH_num, Porg0, Mass, BH_num_input);
-
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-
-// new code 2013-2-15, zjcao
-#if (MAPBH == 1)
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      for (int ith = 0; ith < 3; ith++)
-        Porg1[ithBH][ith] = Porg0[ithBH][ith] + Porg_rhs[ithBH][ith] * dT_lev;
-      if (Symmetry > 0)
-        Porg1[ithBH][2] = fabs(Porg1[ithBH][2]);
-      if (Symmetry == 2)
-      {
-        Porg1[ithBH][0] = fabs(Porg1[ithBH][0]);
-        Porg1[ithBH][1] = fabs(Porg1[ithBH][1]);
-      }
-      if (!finite(Porg1[ithBH][0]) || !finite(Porg1[ithBH][1]) || !finite(Porg1[ithBH][2]))
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "predictor step finds NaN for BH's position from ("
-                                << Porg0[ithBH][0] << "," << Porg0[ithBH][1] << "," << Porg0[ithBH][2] << ")" << endl;
-
-        MyList<var> *DG_List = new MyList<var>(Sfx0);
-        DG_List->insert(Sfx0);
-        DG_List->insert(Sfy0);
-        DG_List->insert(Sfz0);
-        Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-        DG_List->clearList();
-      }
-    }
-  }
-
-  // data analysis part
-  // Warning NOTE: the variables1 are used as temp storege room
-  if (lev == a_lev)
-  {
-    AnalysisStuff(lev, dT_lev);
-  }
-#endif
-
-#ifdef With_AHF
-  AH_Step_Find(lev, dT_lev);
-#endif
-  bool BB = fgt(PhysTime, StartTime, dT_lev / 2);
-  double ndeps = numepss;
-  if (lev < GH->movls)
-    ndeps = numepsb;
-  double TRK4 = PhysTime;
-  int iter_count = 0; // count RK4 substeps
-  int pre = 0, cor = 1;
-  int ERROR = 0;
-
-  MyList<ss_patch> *sPp;
-  // Predictor
-  MyList<Patch> *Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-#if (AGM == 0)
-        f_enforce_ga(cg->shape,
-                     cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                     cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-        if (gpu_rhs(CALLED_BY_STEP, myrank, RHS_PARA_CALLED_FIRST_TIME))
-        {
-          cout << "find NaN in domain: (" << cg->bbox[0] << ":" << cg->bbox[3] << "," << cg->bbox[1] << ":" << cg->bbox[4] << ","
-               << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-          ERROR = 1;
-        }
-
-        // rk4 substep and boundary
-        {
-          MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; // we do not check the correspondence here
-          while (varl0)
-          {
-#if (SommerType == 0)
-#ifndef WithShell
-            if (lev == 0) // sommerfeld indeed
-              f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                   Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                   cg->fgfs[varlrhs->data->sgfn],
-                                   cg->fgfs[varl0->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                   Symmetry);
-
-#endif
-#endif
-            f_rungekutta4_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                               iter_count);
-#ifndef WithShell
-            if (lev > 0) // fix BD point
-#endif
-              f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                dT_lev, cg->fgfs[phi0->sgfn],
-                                cg->fgfs[Lap0->sgfn], cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], varl0->data->SoA,
-                                Symmetry, cor);
-
-#if (SommerType == 1)
-#warning "shell part still bam type"
-            if (lev == 0) // Shibata type sommerfeld
-              f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                dT_lev, cg->fgfs[phi0->sgfn],
-                                cg->fgfs[Lap0->sgfn], cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], varl0->data->SoA,
-                                Symmetry, pre);
-#endif
-
-            varl0 = varl0->next;
-            varl = varl->next;
-            varlrhs = varlrhs->next;
-          }
-        }
-        f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
-#ifdef WithShell
-  // evolve Shell Patches
-  if (lev == 0)
-  {
-    sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      int fngfs = sPp->data->fngfs;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-#if (AGM == 0)
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                       cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-          if (gpu_rhs_ss(CALLED_BY_STEP, myrank, RHS_SS_PARA_CALLED_FIRST_TIME))
-          {
-            cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                 << cg->bbox[1] << ":" << cg->bbox[4] << "," << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-            ERROR = 1;
-          }
-
-          // rk4 substep and boundary
-          {
-            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; // we do not check the correspondence here
-            while (varl0)
-            {
-              // sommerfeld indeed for outter boudary while fix BD for inner boundary
-              f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                      sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                      cg->fgfs[varlrhs->data->sgfn],
-                                      cg->fgfs[varl0->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                      Symmetry);
-
-              f_rungekutta4_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                                 iter_count);
-
-              varl0 = varl0->next;
-              varl = varl->next;
-              varlrhs = varlrhs->next;
-            }
-          }
-          f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-        }
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-#if 0 
-// check rhs    
-  {
-         SH->Dump_Data(RHSList,0,PhysTime,dT_lev);
-         if(myrank == 0)
-	 {
-            cout<<"check rhs"<<endl;
-	    MPI_Abort(MPI_COMM_WORLD,1);
-	 }
-  }
-#endif
-  }
-
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-
-  if (ERROR)
-  {
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-#endif
-
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "Shell stuff synchronization used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-    }
-  }
-#endif
-
-#if (MAPBH == 0)
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][0], Porg[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][1], Porg[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][2], Porg[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-      if (Symmetry > 0)
-        Porg[ithBH][2] = fabs(Porg[ithBH][2]);
-      if (Symmetry == 2)
-      {
-        Porg[ithBH][0] = fabs(Porg[ithBH][0]);
-        Porg[ithBH][1] = fabs(Porg[ithBH][1]);
-      }
-      if (!finite(Porg[ithBH][0]) || !finite(Porg[ithBH][1]) || !finite(Porg[ithBH][2]))
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "predictor step finds NaN for BH's position from ("
-                                << Porg0[ithBH][0] << "," << Porg0[ithBH][1] << "," << Porg0[ithBH][2] << ")" << endl;
-
-        MyList<var> *DG_List = new MyList<var>(Sfx0);
-        DG_List->insert(Sfx0);
-        DG_List->insert(Sfy0);
-        DG_List->insert(Sfz0);
-        Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-        DG_List->clearList();
-      }
-    }
-  }
-  // data analysis part
-  // Warning NOTE: the variables1 are used as temp storege room
-  if (lev == a_lev)
-  {
-    AnalysisStuff(lev, dT_lev);
-  }
-#endif
-
-  // corrector
-  for (iter_count = 1; iter_count < 4; iter_count++)
-  {
-    // for RK4: t0, t0+dt/2, t0+dt/2, t0+dt;
-    if (iter_count == 1 || iter_count == 3)
-      TRK4 += dT_lev / 2;
-    Pp = GH->PatL[lev];
-    while (Pp)
-    {
-      MyList<Block> *BP = Pp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-#if (AGM == 0)
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                       cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-          if (iter_count == 3)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-          if (gpu_rhs(CALLED_BY_STEP, myrank, RHS_PARA_CALLED_THEN))
-          {
-            cout << "find NaN in domain: (" << cg->bbox[0] << ":" << cg->bbox[3] << "," << cg->bbox[1] << ":" << cg->bbox[4] << ","
-                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-            ERROR = 1;
-          }
-          // rk4 substep and boundary
-          {
-            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; // we do not check the correspondence here
-            while (varl0)
-            {
-#if (SommerType == 0)
-#ifndef WithShell
-              if (lev == 0) // sommerfeld indeed
-                f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                     Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                     cg->fgfs[varl1->data->sgfn],
-                                     cg->fgfs[varl->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                     Symmetry);
-#endif
-#endif
-              f_rungekutta4_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                                 iter_count);
-
-#ifndef WithShell
-              if (lev > 0) // fix BD point
-#endif
-                f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                  Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                  dT_lev, cg->fgfs[phi0->sgfn],
-                                  cg->fgfs[Lap0->sgfn], cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], varl0->data->SoA,
-                                  Symmetry, cor);
-
-#if (SommerType == 1)
-              if (lev == 1) // shibata type sommerfeld
-                f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                  Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                  dT_lev, cg->fgfs[phi0->sgfn],
-                                  cg->fgfs[Lap0->sgfn], cg->fgfs[varl->data->sgfn], cg->fgfs[varl1->data->sgfn], varl0->data->SoA,
-                                  Symmetry, cor);
-#endif
-
-              varl0 = varl0->next;
-              varl = varl->next;
-              varl1 = varl1->next;
-              varlrhs = varlrhs->next;
-            }
-          }
-          f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-        }
-        if (BP == Pp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      Pp = Pp->next;
-    }
-
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count << " variables at t = " << PhysTime << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
-#ifdef WithShell
-    // evolve Shell Patches
-    if (lev == 0)
-    {
-      sPp = SH->PatL;
-      while (sPp)
-      {
-        MyList<Block> *BP = sPp->data->blb;
-        int fngfs = sPp->data->fngfs;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          if (myrank == cg->rank)
-          {
-#if (AGM == 0)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-            if (iter_count == 3)
-              f_enforce_ga(cg->shape,
-                           cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                           cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-            if (gpu_rhs_ss(CALLED_BY_STEP, myrank, RHS_SS_PARA_CALLED_THEN))
-            {
-              cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                   << cg->bbox[1] << ":" << cg->bbox[4] << "," << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-              ERROR = 1;
-            }
-            // rk4 substep and boundary
-            {
-              MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; // we do not check the correspondence here
-              while (varl0)
-              {
-                // sommerfeld indeed for outter boudary while fix BD for inner boundary
-                f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                        sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                        cg->fgfs[varl1->data->sgfn],
-                                        cg->fgfs[varl->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                        Symmetry);
-
-                f_rungekutta4_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                                   iter_count);
-
-                varl0 = varl0->next;
-                varl = varl->next;
-                varl1 = varl1->next;
-                varlrhs = varlrhs->next;
-              }
-            }
-            f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-          }
-          if (BP == sPp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        sPp = sPp->next;
-      }
-    }
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count << " variables at t = " << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-#endif
-
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-
-#ifdef WithShell
-    if (lev == 0)
-    {
-      clock_t prev_clock, curr_clock;
-      if (myrank == 0)
-        curr_clock = clock();
-      SH->Synch(SynchList_cor, Symmetry);
-      if (myrank == 0)
-      {
-        prev_clock = curr_clock;
-        curr_clock = clock();
-        cout << "Shell stuff synchronization used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-      }
-    }
-#endif
-
-#if (MAPBH == 0)
-    // for black hole position
-    if (BH_num > 0 && lev == GH->levels - 1)
-    {
-      compute_Porg_rhs(Porg, Porg1, Sfx, Sfy, Sfz, lev);
-      for (int ithBH = 0; ithBH < BH_num; ithBH++)
-      {
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][0], Porg1[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][1], Porg1[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][2], Porg1[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-        if (Symmetry > 0)
-          Porg1[ithBH][2] = fabs(Porg1[ithBH][2]);
-        if (Symmetry == 2)
-        {
-          Porg1[ithBH][0] = fabs(Porg1[ithBH][0]);
-          Porg1[ithBH][1] = fabs(Porg1[ithBH][1]);
-        }
-        if (!finite(Porg1[ithBH][0]) || !finite(Porg1[ithBH][1]) || !finite(Porg1[ithBH][2]))
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << iter_count << " corrector step finds NaN for BH's position from ("
-                                  << Porg[ithBH][0] << "," << Porg[ithBH][1] << "," << Porg[ithBH][2] << ")" << endl;
-
-          MyList<var> *DG_List = new MyList<var>(Sfx0);
-          DG_List->insert(Sfx0);
-          DG_List->insert(Sfy0);
-          DG_List->insert(Sfz0);
-          Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-          DG_List->clearList();
-        }
-      }
-    }
-#endif
-
-    // swap time level
-    if (iter_count < 3)
-    {
-      Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BP = Pp->data->blb;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          cg->swapList(SynchList_pre, SynchList_cor, myrank);
-          if (BP == Pp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        Pp = Pp->next;
-      }
-#ifdef WithShell
-      if (lev == 0)
-      {
-        sPp = SH->PatL;
-        while (sPp)
-        {
-          MyList<Block> *BP = sPp->data->blb;
-          while (BP)
-          {
-            Block *cg = BP->data;
-            cg->swapList(SynchList_pre, SynchList_cor, myrank);
-            if (BP == sPp->data->ble)
-              break;
-            BP = BP->next;
-          }
-          sPp = sPp->next;
-        }
-      }
-#endif
-
-#if (MAPBH == 0)
-      // for black hole position
-      if (BH_num > 0 && lev == GH->levels - 1)
-      {
-        for (int ithBH = 0; ithBH < BH_num; ithBH++)
-        {
-          Porg[ithBH][0] = Porg1[ithBH][0];
-          Porg[ithBH][1] = Porg1[ithBH][1];
-          Porg[ithBH][2] = Porg1[ithBH][2];
-        }
-      }
-#endif
-    }
-  }
-#if (RPS == 0)
-  // mesh refinement boundary part
-  RestrictProlong(lev, YN, BB);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->CS_Inter(SynchList_cor, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "CS_Inter used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-    }
-  }
-#endif
-
-#endif
-  // note the data structure before update
-  // SynchList_cor 1   -----------
-  //
-  // StateList     0   -----------
-  //
-  // OldStateList  old -----------
-  // update
-  Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      cg->swapList(StateList, SynchList_cor, myrank);
-      cg->swapList(OldStateList, SynchList_cor, myrank);
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-#ifdef WithShell
-  if (lev == 0)
-  {
-    sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        cg->swapList(StateList, SynchList_cor, myrank);
-        cg->swapList(OldStateList, SynchList_cor, myrank);
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-#if 0
-// check StateList   
-  {
-         SH->Dump_Data(StateList,0,PhysTime,dT_lev);
-         if(myrank == 0)
-	 {
-            cout<<"check StateList"<<endl;
-	    MPI_Abort(MPI_COMM_WORLD,1);
-	 }
-  }
-#endif
-  }
-#endif
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      Porg0[ithBH][0] = Porg1[ithBH][0];
-      Porg0[ithBH][1] = Porg1[ithBH][1];
-      Porg0[ithBH][2] = Porg1[ithBH][2];
-    }
-  }
-}
-#else // #if 1
-// ICN for bam comparison
-void bssn_class::Step_GPU(int lev, int YN)
-{
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-#ifdef With_AHF
-  AH_Step_Find(lev, dT_lev);
-#endif
-  bool BB = fgt(PhysTime, StartTime, dT_lev / 2);
-  double ndeps = numepss;
-  if (lev < GH->movls)
-    ndeps = numepsb;
-  double TRK4 = PhysTime;
-  int iter_count = 0; // count RK4 substeps
-  int pre = 0, cor = 1;
-  int ERROR = 0;
-
-  MyList<ss_patch> *sPp;
-  // Predictor
-  MyList<Patch> *Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-#if (AGM == 0)
-        f_enforce_ga(cg->shape,
-                     cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                     cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-        if (gpu_rhs(CALLED_BY_STEP, myrank, RHS_PARA_CALLED_FIRST_TIME))
-        {
-          cout << "find NaN in domain: (" << cg->bbox[0] << ":" << cg->bbox[3] << "," << cg->bbox[1] << ":" << cg->bbox[4] << ","
-               << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-          ERROR = 1;
-        }
-
-        // rk4 substep and boundary
-        {
-          MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; // we do not check the correspondence here
-          while (varl0)
-          {
-#ifndef WithShell
-            if (lev == 0) // sommerfeld indeed
-              f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                   Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                   cg->fgfs[varlrhs->data->sgfn],
-                                   cg->fgfs[varl0->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                   Symmetry);
-
-#endif
-            f_icn_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                       iter_count);
-#ifndef WithShell
-            if (lev > 0) // fix BD point
-#endif
-              f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                dT_lev, cg->fgfs[phi0->sgfn],
-                                cg->fgfs[Lap0->sgfn], cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], varl0->data->SoA,
-                                Symmetry, cor);
-
-            varl0 = varl0->next;
-            varl = varl->next;
-            varlrhs = varlrhs->next;
-          }
-        }
-        f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
-#ifdef WithShell
-  // evolve Shell Patches
-  if (lev == 0)
-  {
-    sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      int fngfs = sPp->data->fngfs;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-#if (AGM == 0)
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                       cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-          if (gpu_rhs_ss(CALLED_BY_STEP, myrank, RHS_SS_PARA_CALLED_FIRST_TIME))
-          {
-            cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                 << cg->bbox[1] << ":" << cg->bbox[4] << "," << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-            ERROR = 1;
-          }
-
-          // rk4 substep and boundary
-          {
-            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; // we do not check the correspondence here
-            while (varl0)
-            {
-              // sommerfeld indeed for outter boudary while fix BD for inner boundary
-              f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                      sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                      cg->fgfs[varlrhs->data->sgfn],
-                                      cg->fgfs[varl0->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                      Symmetry);
-
-              f_icn_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                         iter_count);
-
-              varl0 = varl0->next;
-              varl = varl->next;
-              varlrhs = varlrhs->next;
-            }
-          }
-          f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-        }
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-#if 0 
-// check rhs    
-  {
-         SH->Dump_Data(RHSList,0,PhysTime,dT_lev);
-         if(myrank == 0)
-	 {
-            cout<<"check rhs"<<endl;
-	    MPI_Abort(MPI_COMM_WORLD,1);
-	 }
-  }
-#endif
-  }
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-  if (ERROR)
-  {
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-#endif
-
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "Shell stuff synchronization used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-    }
-  }
-#endif
-
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      f_icn_scalar(dT_lev, Porg0[ithBH][0], Porg[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-      f_icn_scalar(dT_lev, Porg0[ithBH][1], Porg[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-      f_icn_scalar(dT_lev, Porg0[ithBH][2], Porg[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-      if (Symmetry > 0)
-        Porg[ithBH][2] = fabs(Porg[ithBH][2]);
-      if (Symmetry == 2)
-      {
-        Porg[ithBH][0] = fabs(Porg[ithBH][0]);
-        Porg[ithBH][1] = fabs(Porg[ithBH][1]);
-      }
-      if (!finite(Porg[ithBH][0]) || !finite(Porg[ithBH][1]) || !finite(Porg[ithBH][2]))
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "predictor step finds NaN for BH's position from ("
-                                << Porg0[ithBH][0] << "," << Porg0[ithBH][1] << "," << Porg0[ithBH][2] << ")" << endl;
-
-        MyList<var> *DG_List = new MyList<var>(Sfx0);
-        DG_List->insert(Sfx0);
-        DG_List->insert(Sfy0);
-        DG_List->insert(Sfz0);
-        Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-        DG_List->clearList();
-      }
-    }
-  }
-  // data analysis part
-  // Warning NOTE: the variables1 are used as temp storege room
-  if (lev == a_lev)
-  {
-    AnalysisStuff(lev, dT_lev);
-  }
-  // corrector
-  for (iter_count = 1; iter_count < 3; iter_count++)
-  {
-    Pp = GH->PatL[lev];
-    while (Pp)
-    {
-      MyList<Block> *BP = Pp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-#if (AGM == 0)
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                       cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-          if (iter_count == 3)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-          if (gpu_rhs(CALLED_BY_STEP, myrank, RHS_PARA_CALLED_THEN))
-          {
-            cout << "find NaN in domain: (" << cg->bbox[0] << ":" << cg->bbox[3] << "," << cg->bbox[1] << ":" << cg->bbox[4] << ","
-                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-            ERROR = 1;
-          }
-          // rk4 substep and boundary
-          {
-            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; // we do not check the correspondence here
-            while (varl0)
-            {
-#ifndef WithShell
-              if (lev == 0) // sommerfeld indeed
-                f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                     Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                     cg->fgfs[varl1->data->sgfn],
-                                     cg->fgfs[varl->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                     Symmetry);
-#endif
-              f_icn_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                         iter_count);
-
-#ifndef WithShell
-              if (lev > 0) // fix BD point
-#endif
-                f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                  Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                  dT_lev, cg->fgfs[phi0->sgfn],
-                                  cg->fgfs[Lap0->sgfn], cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], varl0->data->SoA,
-                                  Symmetry, cor);
-
-              varl0 = varl0->next;
-              varl = varl->next;
-              varl1 = varl1->next;
-              varlrhs = varlrhs->next;
-            }
-          }
-          f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-        }
-        if (BP == Pp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      Pp = Pp->next;
-    }
-
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count << " variables at t = " << PhysTime << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
-#ifdef WithShell
-    // evolve Shell Patches
-    if (lev == 0)
-    {
-      sPp = SH->PatL;
-      while (sPp)
-      {
-        MyList<Block> *BP = sPp->data->blb;
-        int fngfs = sPp->data->fngfs;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          if (myrank == cg->rank)
-          {
-#if (AGM == 0)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-            if (iter_count == 3)
-              f_enforce_ga(cg->shape,
-                           cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                           cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-            if (gpu_rhs_ss(CALLED_BY_STEP, myrank, RHS_SS_PARA_CALLED_THEN))
-            {
-              cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                   << cg->bbox[1] << ":" << cg->bbox[4] << "," << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-              ERROR = 1;
-            }
-            // rk4 substep and boundary
-            {
-              MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; // we do not check the correspondence here
-              while (varl0)
-              {
-                // sommerfeld indeed for outter boudary while fix BD for inner boundary
-                f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                        sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                        cg->fgfs[varl1->data->sgfn],
-                                        cg->fgfs[varl->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                        Symmetry);
-
-                f_rungekutta4_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                                   iter_count);
-
-                varl0 = varl0->next;
-                varl = varl->next;
-                varl1 = varl1->next;
-                varlrhs = varlrhs->next;
-              }
-            }
-            f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-          }
-          if (BP == sPp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        sPp = sPp->next;
-      }
-    }
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count << " variables at t = " << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-#endif
-
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-
-#ifdef WithShell
-    if (lev == 0)
-    {
-      clock_t prev_clock, curr_clock;
-      if (myrank == 0)
-        curr_clock = clock();
-      SH->Synch(SynchList_cor, Symmetry);
-      if (myrank == 0)
-      {
-        prev_clock = curr_clock;
-        curr_clock = clock();
-        cout << "Shell stuff synchronization used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-      }
-    }
-#endif
-    // for black hole position
-    if (BH_num > 0 && lev == GH->levels - 1)
-    {
-      compute_Porg_rhs(Porg, Porg1, Sfx, Sfy, Sfz, lev);
-      for (int ithBH = 0; ithBH < BH_num; ithBH++)
-      {
-        f_icn_scalar(dT_lev, Porg0[ithBH][0], Porg1[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-        f_icn_scalar(dT_lev, Porg0[ithBH][1], Porg1[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-        f_icn_scalar(dT_lev, Porg0[ithBH][2], Porg1[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-        if (Symmetry > 0)
-          Porg1[ithBH][2] = fabs(Porg1[ithBH][2]);
-        if (Symmetry == 2)
-        {
-          Porg1[ithBH][0] = fabs(Porg1[ithBH][0]);
-          Porg1[ithBH][1] = fabs(Porg1[ithBH][1]);
-        }
-        if (!finite(Porg1[ithBH][0]) || !finite(Porg1[ithBH][1]) || !finite(Porg1[ithBH][2]))
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << iter_count << " corrector step finds NaN for BH's position from ("
-                                  << Porg[ithBH][0] << "," << Porg[ithBH][1] << "," << Porg[ithBH][2] << ")" << endl;
-
-          MyList<var> *DG_List = new MyList<var>(Sfx0);
-          DG_List->insert(Sfx0);
-          DG_List->insert(Sfy0);
-          DG_List->insert(Sfz0);
-          Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-          DG_List->clearList();
-        }
-      }
-    }
-    // swap time level
-    if (iter_count < 3)
-    {
-      Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BP = Pp->data->blb;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          cg->swapList(SynchList_pre, SynchList_cor, myrank);
-          if (BP == Pp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        Pp = Pp->next;
-      }
-#ifdef WithShell
-      if (lev == 0)
-      {
-        sPp = SH->PatL;
-        while (sPp)
-        {
-          MyList<Block> *BP = sPp->data->blb;
-          while (BP)
-          {
-            Block *cg = BP->data;
-            cg->swapList(SynchList_pre, SynchList_cor, myrank);
-            if (BP == sPp->data->ble)
-              break;
-            BP = BP->next;
-          }
-          sPp = sPp->next;
-        }
-      }
-#endif
-      // for black hole position
-      if (BH_num > 0 && lev == GH->levels - 1)
-      {
-        for (int ithBH = 0; ithBH < BH_num; ithBH++)
-        {
-          Porg[ithBH][0] = Porg1[ithBH][0];
-          Porg[ithBH][1] = Porg1[ithBH][1];
-          Porg[ithBH][2] = Porg1[ithBH][2];
-        }
-      }
-    }
-  }
-#if (RPS == 0)
-  // mesh refinement boundary part
-  RestrictProlong(lev, YN, BB);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->CS_Inter(SynchList_cor, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "CS_Inter used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-    }
-  }
-#endif
-
-#endif
-  // note the data structure before update
-  // SynchList_cor 1   -----------
-  //
-  // StateList     0   -----------
-  //
-  // OldStateList  old -----------
-  // update
-  Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      cg->swapList(StateList, SynchList_cor, myrank);
-      cg->swapList(OldStateList, SynchList_cor, myrank);
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-#ifdef WithShell
-  if (lev == 0)
-  {
-    sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        cg->swapList(StateList, SynchList_cor, myrank);
-        cg->swapList(OldStateList, SynchList_cor, myrank);
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-#if 0
-// check StateList   
-  {
-         SH->Dump_Data(StateList,0,PhysTime,dT_lev);
-         if(myrank == 0)
-	 {
-            cout<<"check StateList"<<endl;
-	    MPI_Abort(MPI_COMM_WORLD,1);
-	 }
-  }
-#endif
-  }
-#endif
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      Porg0[ithBH][0] = Porg1[ithBH][0];
-      Porg0[ithBH][1] = Porg1[ithBH][1];
-      Porg0[ithBH][2] = Porg1[ithBH][2];
-    }
-  }
-}
-#endif
-
-#elif (PSTR == 1)
-void bssn_class::Step_GPU(int lev, int YN)
-{
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"start Step");
-
-  setpbh(BH_num, Porg0, Mass, BH_num_input);
-
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-
-// new code 2013-2-15, zjcao
-#if (MAPBH == 1)
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      for (int ith = 0; ith < 3; ith++)
-        Porg1[ithBH][ith] = Porg0[ithBH][ith] + Porg_rhs[ithBH][ith] * dT_lev;
-      if (Symmetry > 0)
-        Porg1[ithBH][2] = fabs(Porg1[ithBH][2]);
-      if (Symmetry == 2)
-      {
-        Porg1[ithBH][0] = fabs(Porg1[ithBH][0]);
-        Porg1[ithBH][1] = fabs(Porg1[ithBH][1]);
-      }
-      if (!finite(Porg1[ithBH][0]) || !finite(Porg1[ithBH][1]) || !finite(Porg1[ithBH][2]))
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "predictor step finds NaN for BH's position from ("
-                                << Porg0[ithBH][0] << "," << Porg0[ithBH][1] << "," << Porg0[ithBH][2] << ")" << endl;
-
-        MyList<var> *DG_List = new MyList<var>(Sfx0);
-        DG_List->insert(Sfx0);
-        DG_List->insert(Sfy0);
-        DG_List->insert(Sfz0);
-        Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-        DG_List->clearList();
-      }
-    }
-  }
-#endif //(MAPBH == 1)
-
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor");
-
-#ifdef With_AHF
-  AH_Step_Find(lev, dT_lev);
-#endif
-  bool BB = fgt(PhysTime, StartTime, dT_lev / 2);
-  double ndeps = numepss;
-  if (lev < GH->movls)
-    ndeps = numepsb;
-  double TRK4 = PhysTime;
-  int iter_count = 0; // count RK4 substeps
-  int pre = 0, cor = 1;
-  int ERROR = 0;
-
-  MyList<ss_patch> *sPp;
-  // Predictor
-  MyList<Patch> *Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-#if (AGM == 0)
-        f_enforce_ga(cg->shape,
-                     cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                     cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-        if (gpu_rhs(CALLED_BY_STEP, myrank, RHS_PARA_CALLED_FIRST_TIME))
-        {
-          cout << "find NaN in domain: (" << cg->bbox[0] << ":" << cg->bbox[3] << "," << cg->bbox[1] << ":" << cg->bbox[4] << ","
-               << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-          ERROR = 1;
-        }
-
-        // rk4 substep and boundary
-        {
-          MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; // we do not check the correspondence here
-          while (varl0)
-          {
-#if (SommerType == 0)
-#ifndef WithShell
-            if (lev == 0) // sommerfeld indeed
-              f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                   Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                   cg->fgfs[varlrhs->data->sgfn],
-                                   cg->fgfs[varl0->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                   Symmetry);
-
-#endif
-#endif
-            f_rungekutta4_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                               iter_count);
-#ifndef WithShell
-            if (lev > 0) // fix BD point
-#endif
-              f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                dT_lev, cg->fgfs[phi0->sgfn],
-                                cg->fgfs[Lap0->sgfn], cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], varl0->data->SoA,
-                                Symmetry, cor);
-
-#if (SommerType == 1)
-#warning "shell part still bam type"
-            if (lev == 0) // Shibata type sommerfeld
-              f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                dT_lev, cg->fgfs[phi0->sgfn],
-                                cg->fgfs[Lap0->sgfn], cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], varl0->data->SoA,
-                                Symmetry, pre);
-#endif
-
-            varl0 = varl0->next;
-            varl = varl->next;
-            varlrhs = varlrhs->next;
-          }
-        }
-        f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Predictor rhs calculation");
-
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
-  }
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor sync");
-
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-
-#if (MAPBH == 0)
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][0], Porg[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][1], Porg[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][2], Porg[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-      if (Symmetry > 0)
-        Porg[ithBH][2] = fabs(Porg[ithBH][2]);
-      if (Symmetry == 2)
-      {
-        Porg[ithBH][0] = fabs(Porg[ithBH][0]);
-        Porg[ithBH][1] = fabs(Porg[ithBH][1]);
-      }
-      if (!finite(Porg[ithBH][0]) || !finite(Porg[ithBH][1]) || !finite(Porg[ithBH][2]))
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "predictor step finds NaN for BH's position from ("
-                                << Porg0[ithBH][0] << "," << Porg0[ithBH][1] << "," << Porg0[ithBH][2] << ")" << endl;
-
-        MyList<var> *DG_List = new MyList<var>(Sfx0);
-        DG_List->insert(Sfx0);
-        DG_List->insert(Sfy0);
-        DG_List->insert(Sfz0);
-        Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-        DG_List->clearList();
-      }
-    }
-  }
-#endif
-
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector");
-
-  // corrector
-  for (iter_count = 1; iter_count < 4; iter_count++)
-  {
-    //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"head of Corrector");
-
-    // for RK4: t0, t0+dt/2, t0+dt/2, t0+dt;
-    if (iter_count == 1 || iter_count == 3)
-      TRK4 += dT_lev / 2;
-    Pp = GH->PatL[lev];
-    while (Pp)
-    {
-      MyList<Block> *BP = Pp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-#if (AGM == 0)
-          f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                       cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-          if (iter_count == 3)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-          if (gpu_rhs(CALLED_BY_STEP, myrank, RHS_PARA_CALLED_THEN))
-          {
-            cout << "find NaN in domain: (" << cg->bbox[0] << ":" << cg->bbox[3] << "," << cg->bbox[1] << ":" << cg->bbox[4] << ","
-                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-            ERROR = 1;
-          }
-          // rk4 substep and boundary
-          {
-            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; // we do not check the correspondence here
-            while (varl0)
-            {
-#if (SommerType == 0)
-#ifndef WithShell
-              if (lev == 0) // sommerfeld indeed
-                f_sommerfeld_routbam(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                     Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                     cg->fgfs[varl1->data->sgfn],
-                                     cg->fgfs[varl->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                     Symmetry);
-#endif
-#endif
-              f_rungekutta4_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                                 iter_count);
-
-#ifndef WithShell
-              if (lev > 0) // fix BD point
-#endif
-                f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                  Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                  dT_lev, cg->fgfs[phi0->sgfn],
-                                  cg->fgfs[Lap0->sgfn], cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], varl0->data->SoA,
-                                  Symmetry, cor);
-
-#if (SommerType == 1)
-              if (lev == 1) // shibata type sommerfeld
-                f_sommerfeld_rout(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                  Pp->data->bbox[0], Pp->data->bbox[1], Pp->data->bbox[2], Pp->data->bbox[3], Pp->data->bbox[4], Pp->data->bbox[5],
-                                  dT_lev, cg->fgfs[phi0->sgfn],
-                                  cg->fgfs[Lap0->sgfn], cg->fgfs[varl->data->sgfn], cg->fgfs[varl1->data->sgfn], varl0->data->SoA,
-                                  Symmetry, cor);
-#endif
-
-              varl0 = varl0->next;
-              varl = varl->next;
-              varl1 = varl1->next;
-              varlrhs = varlrhs->next;
-            }
-          }
-          f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-        }
-        if (BP == Pp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      Pp = Pp->next;
-    }
-
-    //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector error check");
-
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
-    }
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count << " variables at t = " << PhysTime << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector sync");
-
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector sync");
-
-#if (MAPBH == 0)
-    // for black hole position
-    if (BH_num > 0 && lev == GH->levels - 1)
-    {
-      compute_Porg_rhs(Porg, Porg1, Sfx, Sfy, Sfz, lev);
-      for (int ithBH = 0; ithBH < BH_num; ithBH++)
-      {
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][0], Porg1[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][1], Porg1[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][2], Porg1[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-        if (Symmetry > 0)
-          Porg1[ithBH][2] = fabs(Porg1[ithBH][2]);
-        if (Symmetry == 2)
-        {
-          Porg1[ithBH][0] = fabs(Porg1[ithBH][0]);
-          Porg1[ithBH][1] = fabs(Porg1[ithBH][1]);
-        }
-        if (!finite(Porg1[ithBH][0]) || !finite(Porg1[ithBH][1]) || !finite(Porg1[ithBH][2]))
-        {
-          if (ErrorMonitor->outfile)
-            ErrorMonitor->outfile << iter_count << " corrector step finds NaN for BH's position from ("
-                                  << Porg[ithBH][0] << "," << Porg[ithBH][1] << "," << Porg[ithBH][2] << ")" << endl;
-
-          MyList<var> *DG_List = new MyList<var>(Sfx0);
-          DG_List->insert(Sfx0);
-          DG_List->insert(Sfy0);
-          DG_List->insert(Sfz0);
-          Parallel::Dump_Data(GH->PatL[lev], DG_List, 0, PhysTime, dT_lev);
-          DG_List->clearList();
-        }
-      }
-    }
-    misc::tillherecheck(GH->Commlev[lev], GH->start_rank[lev], "after Corrector of black hole position");
-#endif
-
-    // swap time level
-    if (iter_count < 3)
-    {
-      Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BP = Pp->data->blb;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          cg->swapList(SynchList_pre, SynchList_cor, myrank);
-          if (BP == Pp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        Pp = Pp->next;
-      }
-      //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after pre cor swap");
-
-#if (MAPBH == 0)
-      // for black hole position
-      if (BH_num > 0 && lev == GH->levels - 1)
-      {
-        for (int ithBH = 0; ithBH < BH_num; ithBH++)
-        {
-          Porg[ithBH][0] = Porg1[ithBH][0];
-          Porg[ithBH][1] = Porg1[ithBH][1];
-          Porg[ithBH][2] = Porg1[ithBH][2];
-        }
-      }
-#endif
-    }
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"tail of corrector");
-  }
-#if (RPS == 0)
-  // mesh refinement boundary part
-  misc::tillherecheck(GH->Commlev[lev], GH->start_rank[lev], "before RestrictProlong");
-  RestrictProlong(lev, YN, BB);
-#endif
-  // note the data structure before update
-  // SynchList_cor 1   -----------
-  //
-  // StateList     0   -----------
-  //
-  // OldStateList  old -----------
-  // update
-  Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      cg->swapList(StateList, SynchList_cor, myrank);
-      cg->swapList(OldStateList, SynchList_cor, myrank);
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-  // for black hole position
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      Porg0[ithBH][0] = Porg1[ithBH][0];
-      Porg0[ithBH][1] = Porg1[ithBH][1];
-      Porg0[ithBH][2] = Porg1[ithBH][2];
-      //	 if(myrank==GH->start_rank[lev]) cout<<Porg0[ithBH][0]<<","<<Porg0[ithBH][1]<<","<<Porg0[ithBH][2]<<endl;
-    }
-  }
-
-  //     if(myrank==GH->start_rank[lev]) cout<<GH->mylev<<endl;
-  //     misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"complet GH Step");
-}
-#endif // PSTR == ?
-
-//--------------------------With Shell--------------------------
-
-#ifdef WithShell
-void bssn_class::SHStep()
-{
-  int lev = 0;
-  // #if (PSTR == 1)
-  //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"start Step");
-  // #endif
-
-  setpbh(BH_num, Porg0, Mass, BH_num_input);
-
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-
-  // #if (PSTR == 1)
-  //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor");
-  // #endif
-
-#ifdef With_AHF
-  AH_Step_Find(lev, dT_lev);
-#endif
-  bool BB = fgt(PhysTime, StartTime, dT_lev / 2);
-  double ndeps = numepss;
-  if (lev < GH->movls)
-    ndeps = numepsb;
-  double TRK4 = PhysTime;
-  int iter_count = 0; // count RK4 substeps
-  int pre = 0, cor = 1;
-  int ERROR = 0;
-
-  MyList<ss_patch> *sPp;
-  // Predictor
-  sPp = SH->PatL;
-  while (sPp)
-  {
-    MyList<Block> *BP = sPp->data->blb;
-    int fngfs = sPp->data->fngfs;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-#if (AGM == 0)
-        f_enforce_ga(cg->shape,
-                     cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                     cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-        if (gpu_rhs_ss(RHS_SS_PARA_CALLED_FIRST_TIME))
-        {
-          cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" << cg->bbox[0] << ":" << cg->bbox[3] << ","
-               << cg->bbox[1] << ":" << cg->bbox[4] << "," << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-          ERROR = 1;
-        }
-
-        // rk4 substep and boundary
-        {
-          MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; // we do not check the correspondence here
-          while (varl0)
-          {
-            // sommerfeld indeed for outter boudary while fix BD for inner boundary
-            f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                    sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                    cg->fgfs[varlrhs->data->sgfn],
-                                    cg->fgfs[varl0->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                    Symmetry);
-
-            f_rungekutta4_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                               iter_count);
-
-            varl0 = varl0->next;
-            varl = varl->next;
-            varlrhs = varlrhs->next;
-          }
-        }
-        f_lowerboundset(cg->shape, cg->fgfs[phi->sgfn], chitiny);
-      }
-      if (BP == sPp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    sPp = sPp->next;
-  }
-
-#if (PSTR == 1)
-//   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor's error check");
-#endif
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-
-  if (ERROR)
-  {
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "Shell stuff synchronization used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-    }
-  }
-
-  // corrector
-  for (iter_count = 1; iter_count < 4; iter_count++)
-  {
-    // for RK4: t0, t0+dt/2, t0+dt/2, t0+dt;
-    if (iter_count == 1 || iter_count == 3)
-      TRK4 += dT_lev / 2;
-
-    {
-      sPp = SH->PatL;
-      while (sPp)
-      {
-        MyList<Block> *BP = sPp->data->blb;
-        int fngfs = sPp->data->fngfs;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          if (myrank == cg->rank)
-          {
-#if (AGM == 0)
-            f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#elif (AGM == 1)
-            if (iter_count == 3)
-              f_enforce_ga(cg->shape,
-                           cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                           cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-            if (gpu_rhs_ss(RHS_SS_PARA_CALLED_THEN))
-            {
-              cout << "find NaN in Shell domain: sst = " << sPp->data->sst << ", (" << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                   << cg->bbox[1] << ":" << cg->bbox[4] << "," << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-              ERROR = 1;
-            }
-            // rk4 substep and boundary
-            {
-              MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; // we do not check the correspondence here
-              while (varl0)
-              {
-                // sommerfeld indeed for outter boudary while fix BD for inner boundary
-                f_sommerfeld_routbam_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                        sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2], sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                                        cg->fgfs[varl1->data->sgfn],
-                                        cg->fgfs[varl->data->sgfn], varl0->data->propspeed, varl0->data->SoA,
-                                        Symmetry);
-
-                f_rungekutta4_rout(cg->shape, dT_lev, cg->fgfs[varl0->data->sgfn], cg->fgfs[varl1->data->sgfn], cg->fgfs[varlrhs->data->sgfn],
-                                   iter_count);
-
-                varl0 = varl0->next;
-                varl = varl->next;
-                varl1 = varl1->next;
-                varlrhs = varlrhs->next;
-              }
-            }
-            f_lowerboundset(cg->shape, cg->fgfs[phi1->sgfn], chitiny);
-          }
-          if (BP == sPp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        sPp = sPp->next;
-      }
-    }
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count << " variables at t = " << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
-    {
-      clock_t prev_clock, curr_clock;
-      if (myrank == 0)
-        curr_clock = clock();
-      SH->Synch(SynchList_cor, Symmetry);
-      if (myrank == 0)
-      {
-        prev_clock = curr_clock;
-        curr_clock = clock();
-        cout << "Shell stuff synchronization used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-      }
-    }
-
-    sPp = SH->PatL;
-    while (sPp)
-    {
-      MyList<Block> *BP = sPp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        cg->swapList(SynchList_pre, SynchList_cor, myrank);
-        if (BP == sPp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      sPp = sPp->next;
-    }
-  }
-#if (RPS == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->CS_Inter(SynchList_cor, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << "CS_Inter used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
-    }
-  }
-#endif
-  // note the data structure before update
-  // SynchList_cor 1   -----------
-  //
-  // StateList     0   -----------
-  //
-  // OldStateList  old -----------
-  // update
-  sPp = SH->PatL;
-  while (sPp)
-  {
-    MyList<Block> *BP = sPp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      cg->swapList(StateList, SynchList_cor, myrank);
-      cg->swapList(OldStateList, SynchList_cor, myrank);
-      if (BP == sPp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    sPp = sPp->next;
-  }
-}
-d
-#endif // withshell
diff --git a/AMSS_NCKU_source/makefile b/AMSS_NCKU_source/makefile
index 72b9cbd..7a8878b 100644
--- a/AMSS_NCKU_source/makefile
+++ b/AMSS_NCKU_source/makefile
@@ -1,35 +1,35 @@
 
 
-include makefile.inc
-
-## polint(ordn=6) kernel selector:
-##   1 (default): barycentric fast path
-##   0          : fallback to Neville path
-POLINT6_USE_BARY ?= 1
-POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
-
-## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
-##   make                        -> opt  (PGO-guided, maximum performance)
-##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
-PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
+include makefile.inc
+
+## polint(ordn=6) kernel selector:
+##   1 (default): barycentric fast path
+##   0          : fallback to Neville path
+POLINT6_USE_BARY ?= 1
+POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
+
+## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
+##   make                        -> opt  (PGO-guided, maximum performance)
+##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
+PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
 
 ifeq ($(PGO_MODE),instrument)
 ## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
-CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
-else
-## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
-## PGO has been turned off, now tested and found to be negative optimization
-## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
-
-
-CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
-endif
+CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
+f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+else
+## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
+## PGO has been turned off, now tested and found to be negative optimization
+## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
+
+
+CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
+f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+endif
 
 .SUFFIXES: .o .f90 .C .for .cu
 
@@ -42,12 +42,16 @@ endif
 .for.o:
 	$(f77) -c $< -o $@
 
-.cu.o:
-	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
-
-# C rewrite of BSSN RHS kernel and helpers
-bssn_rhs_c.o: bssn_rhs_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+.cu.o:
+	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
+
+# CUDA rewrite of BSSN RHS (drop-in replacement for bssn_rhs_c + stencil helpers)
+bssn_rhs_cuda.o: bssn_rhs_cuda.cu bssn_rhs.h macrodef.h
+	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
+
+# C rewrite of BSSN RHS kernel and helpers
+bssn_rhs_c.o: bssn_rhs_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
 fderivs_c.o: fderivs_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
@@ -58,14 +62,14 @@ fdderivs_c.o: fdderivs_c.C
 kodiss_c.o: kodiss_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-lopsided_c.o: lopsided_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-lopsided_kodis_c.o: lopsided_kodis_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
-#	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+lopsided_c.o: lopsided_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+lopsided_kodis_c.o: lopsided_kodis_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
+#	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
 ## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
 TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
@@ -79,24 +83,46 @@ TwoPunctures.o: TwoPunctures.C
 TwoPunctureABE.o: TwoPunctureABE.C
 	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
 
-# Input files
-
-## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
+# Input files
+
+## CUDA BSSN RHS switch
+##   1 : use the rewritten CUDA bssn_rhs backend
+##   0 : keep the normal CPU/Fortran selection below
+USE_CUDA_BSSN ?= 0
+
+## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
 ifeq ($(USE_CXX_KERNELS),0)
 # Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
-CFILES =
+CFILES_CPU =
 else
 # C++ mode (default): C rewrite of bssn_rhs and helper kernels
-CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
+CFILES_CPU = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
+endif
+
+CFILES_CUDA_BSSN = bssn_rhs_cuda.o
+
+ifeq ($(USE_CUDA_BSSN),1)
+CFILES = $(CFILES_CUDA_BSSN)
+else
+CFILES = $(CFILES_CPU)
 endif
 
 ## RK4 kernel switch (independent from USE_CXX_KERNELS)
 ifeq ($(USE_CXX_RK4),1)
-CFILES += rungekutta4_rout_c.o
+RK4_C_OBJ = rungekutta4_rout_c.o
 RK4_F90_OBJ =
 else
+RK4_C_OBJ =
 RK4_F90_OBJ = rungekutta4_rout.o
 endif
+
+CFILES += $(RK4_C_OBJ)
+ABE_CUDA_CFILES = $(CFILES_CUDA_BSSN) $(RK4_C_OBJ)
+
+ABE_LDLIBS = $(LDLIBS)
+ifeq ($(USE_CUDA_BSSN),1)
+ABE_LDLIBS += -lcudart $(CUDA_LIB_PATH)
+endif
 
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            cgh.o bssn_class.o surface_integral.o ShellPatch.o\
@@ -105,7 +131,7 @@ C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
 	   NullShellPatch2_Evo.o writefile_f.o interp_lb_profile.o
 	   
-C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
+#C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            cgh.o surface_integral.o ShellPatch.o\
 	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
 	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
@@ -113,12 +139,12 @@ C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o
 	   NullShellPatch2_Evo.o \
 	   bssn_gpu_class.o bssn_step_gpu.o bssn_macro.o writefile_f.o
 
-F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
-	   prolongrestrict_cell.o prolongrestrict_vertex.o\
-	   $(RK4_F90_OBJ) diff_new.o kodiss.o kodiss_sh.o\
-	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
-	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
-           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
+F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
+	   prolongrestrict_cell.o prolongrestrict_vertex.o\
+	   $(RK4_F90_OBJ) diff_new.o kodiss.o kodiss_sh.o\
+	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
+	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
+           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
            fadmquantites_bssn.o Z4c_rhs.o Z4c_rhs_ss.o point_diff_new_sh.o\
 	   cpbc.o getnp4old.o NullEvol.o initial_null.o initial_maxwell.o\
 	   getnpem2.o empart.o NullNews.o fourdcurvature.o\
@@ -143,10 +169,10 @@ initial_guess.o Newton.o Jacobian.o ilucg.o IntPnts0.o IntPnts.o
 
 TwoPunctureFILES = TwoPunctureABE.o TwoPunctures.o 
 
-CUDAFILES = bssn_gpu.o bssn_gpu_rhs_ss.o
+#CUDAFILES = bssn_gpu.o bssn_gpu_rhs_ss.o
 
-# file dependences
-$(C++FILES) $(C++FILES_GPU) $(F90FILES) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
+# file dependences
+$(C++FILES) $(C++FILES_GPU) $(F90FILES) $(CFILES) $(ABE_CUDA_CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
 
 $(C++FILES): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
 	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
@@ -157,7 +183,7 @@ $(C++FILES): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
 	     empart.h NullNews.h kodiss.h Parallel_bam.h ricci_gamma.h\
              initial_null2.h NullShellPatch2.h 
              
-$(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
+#$(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
 	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
 	     rungekutta4_rout.h var.h bssn_rhs.h sommerfeld_rout.h\
 	     cgh.h surface_integral.h ShellPatch.h shellfunctions.h perf.h\
@@ -169,7 +195,7 @@ $(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h
              
 $(AHFDOBJS): cctk.h cctk_Config.h cctk_Types.h cctk_Constants.h myglobal.h
 
-$(C++FILES) $(C++FILES_GPU) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.h
+$(C++FILES) $(C++FILES_GPU) $(CFILES) $(ABE_CUDA_CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.h
 
 TwoPunctureFILES: TwoPunctures.h
 
@@ -177,15 +203,18 @@ $(CUDAFILES): bssn_gpu.h gpu_mem.h gpu_rhsSS_mem.h
 
 misc.o : zbesh.o
 
-# projects
-ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
-	
-ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
+# projects
+ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(ABE_LDLIBS)
+
+ABE_CUDA: $(C++FILES) $(ABE_CUDA_CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(ABE_CUDA_CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS) -lcudart $(CUDA_LIB_PATH)
+	
+#ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
+#	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
 
 TwoPunctureABE: $(TwoPunctureFILES)
 	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
-clean:
-	rm *.o ABE ABEGPU TwoPunctureABE make.log -f
+clean:
+	rm *.o ABE ABE_CUDA ABEGPU TwoPunctureABE make.log -f
diff --git a/AMSS_NCKU_source/makefile.inc b/AMSS_NCKU_source/makefile.inc
index 331cff1..69fe86b 100755
--- a/AMSS_NCKU_source/makefile.inc
+++ b/AMSS_NCKU_source/makefile.inc
@@ -63,3 +63,7 @@ Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
 #CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -arch compute_13 -code compute_13,sm_13 -Dfortran3 -Dnewc
 CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc
+CUDA_ARCH ?= sm_80
+ifneq ($(strip $(CUDA_ARCH)),)
+CUDA_APP_FLAGS += -arch=$(CUDA_ARCH)
+endif
diff --git a/generate_macrodef.py b/generate_macrodef.py
index 40c76e9..efa9d72 100755
--- a/generate_macrodef.py
+++ b/generate_macrodef.py
@@ -148,7 +148,7 @@ def generate_macrodef_h():
     # use GPU or not
     
     if ( input_data.GPU_Calculation == "yes"):
-        print( "#define USE_GPU",   file=file1 )
+        print( "//#define USE_GPU",   file=file1 )
         print(                      file=file1 )
     elif ( input_data.GPU_Calculation == "no"):
         print( "//#define USE_GPU", file=file1 )
diff --git a/makefile_and_run.py b/makefile_and_run.py
index 5682476..5d403a6 100755
--- a/makefile_and_run.py
+++ b/makefile_and_run.py
@@ -72,7 +72,7 @@ def makefile_ABE():
     if (input_data.GPU_Calculation == "no"):
         makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off ABE"
     elif (input_data.GPU_Calculation == "yes"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off ABE_CUDA"
     else:
         print( " CPU/GPU numerical calculation setting is wrong " )
         print(                                                    )
@@ -151,7 +151,7 @@ def run_ABE():
         #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE_CUDA"
         mpi_command_outfile = "ABEGPU_out.log"
  
     ## Execute the MPI command and stream output