Migrate build system from Intel oneAPI to AMD AOCC/AOCL/OpenMPI

Replace Intel compilers (ifx/icpx/icx) with AOCC (flang/clang++/clang),
Intel MPI (mpiicpx) with AOCC-built OpenMPI (mpicxx), and Intel MKL
with AOCL BLIS/libFLAME. Replace -xHost with -march=znver4, -ipo with
-flto, -fp-model fast=2 with -ffast-math, -qopenmp with -fopenmp.
Remove PGO, TBB allocator, and Intel-specific runtime libraries.
Fix MKL-specific includes in TwoPunctures.C and gaussj.C to use
standard CBLAS/LAPACKE headers from AOCL.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

.gitignore

@@ -1,6 +1,6 @@
 __pycache__
 GW150914
-GW150914-origin
+GW150914*
 docs
 *.tmp
-
+.codex

AMSS_NCKU_Program.py

@@ -8,6 +8,14 @@
 ##
 ##################################################################
 
+## Guard against re-execution by multiprocessing child processes.
+## Without this, using 'spawn' or 'forkserver' context would cause every
+## worker to re-run the entire script, spawning exponentially more
+## workers (fork bomb).
+if __name__ != '__main__':
+    import sys as _sys
+    _sys.exit(0)
+
 
 ##################################################################
 
@@ -166,11 +174,14 @@ import generate_macrodef
 generate_macrodef.generate_macrodef_h()
 print( " AMSS-NCKU macro file macrodef.h has been generated. " )
      
-generate_macrodef.generate_macrodef_fh()
-print( " AMSS-NCKU macro file macrodef.fh has been generated. " )
-
-
-##################################################################
+generate_macrodef.generate_macrodef_fh()
+print( " AMSS-NCKU macro file macrodef.fh has been generated. " )
+
+generate_macrodef.generate_build_config()
+print( " AMSS-NCKU build config AMSS_NCKU_build.mk has been generated. " )
+
+
+##################################################################
 
 # Compile the AMSS-NCKU program according to user requirements
 
@@ -209,11 +220,13 @@ shutil.copytree(AMSS_NCKU_source_path, AMSS_NCKU_source_copy)
 
 # Copy the generated macro files into the AMSS_NCKU source folder
 
-macrodef_h_path  = os.path.join(File_directory, "macrodef.h") 
-macrodef_fh_path = os.path.join(File_directory, "macrodef.fh") 
-
-shutil.copy2(macrodef_h_path,  AMSS_NCKU_source_copy)
-shutil.copy2(macrodef_fh_path, AMSS_NCKU_source_copy)
+macrodef_h_path  = os.path.join(File_directory, "macrodef.h")
+macrodef_fh_path = os.path.join(File_directory, "macrodef.fh")
+build_config_path = os.path.join(File_directory, "AMSS_NCKU_build.mk")
+
+shutil.copy2(macrodef_h_path,  AMSS_NCKU_source_copy)
+shutil.copy2(macrodef_fh_path, AMSS_NCKU_source_copy)
+shutil.copy2(build_config_path, AMSS_NCKU_source_copy)
 
 # Notes on copying files:
 # shutil.copy2 preserves file metadata such as modification time.
@@ -262,6 +275,12 @@ if not os.path.exists( ABE_file ):
 ## Copy the executable ABE (or ABEGPU) into the run directory
 shutil.copy2(ABE_file, output_directory)
 
+## Copy interp load balance profile if present (for optimize pass)
+interp_lb_profile = os.path.join(AMSS_NCKU_source_copy, "interp_lb_profile.bin")
+if os.path.exists(interp_lb_profile):
+    shutil.copy2(interp_lb_profile, output_directory)
+    print( " Copied interp_lb_profile.bin to run directory " )
+
 ###########################
 
 ## If the initial-data method is TwoPuncture, copy the TwoPunctureABE executable to the run directory
@@ -424,26 +443,31 @@ print(
 
 import plot_xiaoqu
 import plot_GW_strain_amplitude_xiaoqu
+from parallel_plot_helper import run_plot_tasks_parallel
+
+plot_tasks = []
 
 ## Plot black hole trajectory
-plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
-plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot,   (binary_results_directory, figure_directory) ) )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot3D, (binary_results_directory, figure_directory) ) )
 
 ## Plot black hole separation vs. time
-plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_distence_plot, (binary_results_directory, figure_directory) ) )
 
 ## Plot gravitational waveforms (psi4 and strain amplitude)
 for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_gravitational_wave_psi4_plot( binary_results_directory, figure_directory, i )
-    plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_gravitational_wave_psi4_plot, (binary_results_directory, figure_directory, i) ) )
+    plot_tasks.append( ( plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot, (binary_results_directory, figure_directory, i) ) )
 
 ## Plot ADM mass evolution
 for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_ADMmass_plot, (binary_results_directory, figure_directory, i) ) )
 
 ## Plot Hamiltonian constraint violation over time
 for i in range(input_data.grid_level):
-    plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_constraint_check_plot, (binary_results_directory, figure_directory, i) ) )
+
+run_plot_tasks_parallel(plot_tasks)
 
 ## Plot stored binary data
 plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )

AMSS_NCKU_Verify_ASC26.py

@@ -1,10 +1,19 @@
 #!/usr/bin/env python3
 """
-AMSS-NCKU GW150914 Simulation Regression Test Script
+AMSS-NCKU GW150914 Simulation Regression Test Script (Comprehensive Version)
 
-Verification Requirements:
-1. XY-plane trajectory RMS error < 1% (Optimized vs. baseline, max of BH1 and BH2)
-2. ADM constraint violation < 2 (Grid Level 0)
+Verification Requirements:
+1. RMS errors < 1% for:
+   - 3D Vector Total RMS
+   - X Component RMS
+   - Y Component RMS
+   - Z Component RMS
+2. ADM constraint violation < 2 (Grid Level 0)
+3. The following figure PDFs must match GW150914-origin exactly after rasterization:
+   - ADM_Constraint_Grid_Level_0.pdf
+   - BH_Trajectory_21_XY.pdf
+   - BH_Trajectory_XY.pdf
+   The script also reports the percentage of differing pixels for each figure.
 
 RMS Calculation Method:
 - Computes trajectory deviation on the XY plane independently for BH1 and BH2
@@ -16,9 +25,13 @@ Default: output_dir = GW150914/AMSS_NCKU_output
 Reference: GW150914-origin (baseline simulation)
 """
 
-import numpy as np
-import sys
-import os
+import numpy as np
+import sys
+import os
+import shutil
+import subprocess
+import tempfile
+from PIL import Image
 
 # ANSI Color Codes
 class Color:
@@ -45,91 +58,200 @@ def load_bh_trajectory(filepath):
     }
 
 
-def load_constraint_data(filepath):
-    """Load constraint violation data"""
-    data = []
+def load_constraint_data(filepath):
+    """Load constraint violation data"""
+    data = []
     with open(filepath, 'r') as f:
         for line in f:
             if line.startswith('#'):
                 continue
             parts = line.split()
             if len(parts) >= 8:
-                data.append([float(x) for x in parts[:8]])
-    return np.array(data)
+                data.append([float(x) for x in parts[:8]])
+    return np.array(data)
+
+
+def resolve_figure_dir(path):
+    """Resolve the sibling figure directory from an output or figure path."""
+    normalized = os.path.normpath(path)
+    if os.path.basename(normalized) == "figure":
+        return normalized
+    return os.path.join(os.path.dirname(normalized), "figure")
+
+
+def render_pdf_to_images(pdf_path, dpi=150):
+    """Render a PDF to RGB images using Ghostscript."""
+    gs_path = shutil.which("gs")
+    if gs_path is None:
+        raise RuntimeError("Ghostscript executable 'gs' was not found in PATH")
+
+    with tempfile.TemporaryDirectory(prefix="amss_verify_pdf_") as temp_dir:
+        output_pattern = os.path.join(temp_dir, "page-%03d.ppm")
+        cmd = [
+            gs_path,
+            "-q",
+            "-dSAFER",
+            "-dBATCH",
+            "-dNOPAUSE",
+            "-sDEVICE=ppmraw",
+            f"-r{dpi}",
+            f"-o{output_pattern}",
+            pdf_path
+        ]
+
+        try:
+            subprocess.run(cmd, check=True, stdout=subprocess.DEVNULL, stderr=subprocess.PIPE, text=True)
+        except subprocess.CalledProcessError as exc:
+            message = exc.stderr.strip() or str(exc)
+            raise RuntimeError(f"Failed to render PDF '{pdf_path}': {message}") from exc
+
+        ppm_files = sorted(
+            os.path.join(temp_dir, filename)
+            for filename in os.listdir(temp_dir)
+            if filename.endswith(".ppm")
+        )
+
+        if not ppm_files:
+            raise RuntimeError(f"No rendered pages were produced for '{pdf_path}'")
+
+        images = []
+        for ppm_file in ppm_files:
+            with Image.open(ppm_file) as img:
+                images.append(np.array(img.convert("RGB"), dtype=np.uint8))
+
+        return images
+
+
+def compare_rendered_pages(ref_img, target_img):
+    """Return (different_pixels, total_pixels) for two rendered RGB pages."""
+    ref_h, ref_w = ref_img.shape[:2]
+    tgt_h, tgt_w = target_img.shape[:2]
+    total_pixels = max(ref_h, tgt_h) * max(ref_w, tgt_w)
+
+    if ref_h == tgt_h and ref_w == tgt_w:
+        different_pixels = int(np.count_nonzero(np.any(ref_img != target_img, axis=2)))
+        return different_pixels, total_pixels
+
+    diff_mask = np.ones((max(ref_h, tgt_h), max(ref_w, tgt_w)), dtype=bool)
+    overlap_h = min(ref_h, tgt_h)
+    overlap_w = min(ref_w, tgt_w)
+    overlap_diff = np.any(ref_img[:overlap_h, :overlap_w] != target_img[:overlap_h, :overlap_w], axis=2)
+    diff_mask[:overlap_h, :overlap_w] = overlap_diff
+    different_pixels = int(np.count_nonzero(diff_mask))
+    return different_pixels, total_pixels
+
+
+def compare_pdf_images(ref_pdf, target_pdf, dpi=150, threshold_percent=0.001):
+    """Compare two PDFs by rasterizing them and counting differing pixels."""
+    ref_pages = render_pdf_to_images(ref_pdf, dpi=dpi)
+    target_pages = render_pdf_to_images(target_pdf, dpi=dpi)
+
+    total_pixels = 0
+    different_pixels = 0
+    max_pages = max(len(ref_pages), len(target_pages))
+
+    for page_idx in range(max_pages):
+        if page_idx < len(ref_pages) and page_idx < len(target_pages):
+            page_diff, page_total = compare_rendered_pages(ref_pages[page_idx], target_pages[page_idx])
+        else:
+            existing_page = ref_pages[page_idx] if page_idx < len(ref_pages) else target_pages[page_idx]
+            page_total = existing_page.shape[0] * existing_page.shape[1]
+            page_diff = page_total
+
+        total_pixels += page_total
+        different_pixels += page_diff
+
+    diff_percent = (different_pixels / total_pixels * 100.0) if total_pixels else 0.0
+    return {
+        "different_pixels": different_pixels,
+        "total_pixels": total_pixels,
+        "diff_percent": diff_percent,
+        "pages_ref": len(ref_pages),
+        "pages_target": len(target_pages),
+        "passed": diff_percent < threshold_percent
+    }
+
+
+def compare_required_figures(reference_figure_dir, target_figure_dir):
+    """Compare the required GW150914 figure PDFs."""
+    figure_names = [
+        "ADM_Constraint_Grid_Level_0.pdf",
+        "BH_Trajectory_21_XY.pdf",
+        "BH_Trajectory_XY.pdf"
+    ]
+
+    results = []
+    for figure_name in figure_names:
+        ref_pdf = os.path.join(reference_figure_dir, figure_name)
+        target_pdf = os.path.join(target_figure_dir, figure_name)
+
+        if not os.path.exists(ref_pdf):
+            raise FileNotFoundError(f"Reference figure not found: {ref_pdf}")
+        if not os.path.exists(target_pdf):
+            raise FileNotFoundError(f"Target figure not found: {target_pdf}")
+
+        comparison = compare_pdf_images(ref_pdf, target_pdf)
+        comparison["name"] = figure_name
+        results.append(comparison)
+
+    return results
 
-
-def calculate_rms_error(bh_data_ref, bh_data_target):
+def calculate_all_rms_errors(bh_data_ref, bh_data_target):
     """
-    Calculate trajectory-based RMS error on the XY plane between baseline and optimized simulations.
-
-    This function computes the RMS error independently for BH1 and BH2 trajectories,
-    then returns the maximum of the two as the final RMS error metric.
-
-    For each black hole, the RMS is calculated as:
-        RMS = sqrt( (1/M) * sum( (Δr_i / r_i^max)^2 ) ) × 100%
-
-    where:
-        Δr_i = sqrt((x_ref,i - x_new,i)^2 + (y_ref,i - y_new,i)^2)
-        r_i^max = max(sqrt(x_ref,i^2 + y_ref,i^2), sqrt(x_new,i^2 + y_new,i^2))
-
-    Args:
-        bh_data_ref: Reference (baseline) trajectory data
-        bh_data_target: Target (optimized) trajectory data
-
-    Returns:
-        rms_value: Final RMS error as a percentage (max of BH1 and BH2)
-        error: Error message if any
+    Calculate 3D Vector RMS and component-wise RMS (X, Y, Z) independently.
+    Uses r = sqrt(x^2 + y^2) as the denominator for all error normalizations.
+    Returns the maximum error between BH1 and BH2 for each category.
     """
-    # Align data: truncate to the length of the shorter dataset
     M = min(len(bh_data_ref['time']), len(bh_data_target['time']))
 
     if M < 10:
         return None, "Insufficient data points for comparison"
 
-    # Extract XY coordinates for both black holes
-    x1_ref = bh_data_ref['x1'][:M]
-    y1_ref = bh_data_ref['y1'][:M]
-    x2_ref = bh_data_ref['x2'][:M]
-    y2_ref = bh_data_ref['y2'][:M]
+    results = {}
 
-    x1_new = bh_data_target['x1'][:M]
-    y1_new = bh_data_target['y1'][:M]
-    x2_new = bh_data_target['x2'][:M]
-    y2_new = bh_data_target['y2'][:M]
+    for bh in ['1', '2']:
+        x_r, y_r, z_r = bh_data_ref[f'x{bh}'][:M], bh_data_ref[f'y{bh}'][:M], bh_data_ref[f'z{bh}'][:M]
+        x_n, y_n, z_n = bh_data_target[f'x{bh}'][:M], bh_data_target[f'y{bh}'][:M], bh_data_target[f'z{bh}'][:M]
 
-    # Calculate RMS for BH1
-    delta_r1 = np.sqrt((x1_ref - x1_new)**2 + (y1_ref - y1_new)**2)
-    r1_ref = np.sqrt(x1_ref**2 + y1_ref**2)
-    r1_new = np.sqrt(x1_new**2 + y1_new**2)
-    r1_max = np.maximum(r1_ref, r1_new)
+        # 核心修改：根据组委会的邮件指示，分母统一使用 r = sqrt(x^2 + y^2)
+        r_ref = np.sqrt(x_r**2 + y_r**2)
+        r_new = np.sqrt(x_n**2 + y_n**2)
+        denom_max = np.maximum(r_ref, r_new)
 
-    # Calculate RMS for BH2
-    delta_r2 = np.sqrt((x2_ref - x2_new)**2 + (y2_ref - y2_new)**2)
-    r2_ref = np.sqrt(x2_ref**2 + y2_ref**2)
-    r2_new = np.sqrt(x2_new**2 + y2_new**2)
-    r2_max = np.maximum(r2_ref, r2_new)
+        valid = denom_max > 1e-15
+        if np.sum(valid) < 10:
+            results[f'BH{bh}'] = { '3D_Vector': 0.0, 'X_Component': 0.0, 'Y_Component': 0.0, 'Z_Component': 0.0 }
+            continue
 
-    # Avoid division by zero for BH1
-    valid_mask1 = r1_max > 1e-15
-    if np.sum(valid_mask1) < 10:
-        return None, "Insufficient valid data points for BH1"
+        def calc_rms(delta):
+            # 将对应分量的偏差除以统一的轨道半径分母 denom_max
+            return np.sqrt(np.mean((delta[valid] / denom_max[valid])**2)) * 100
 
-    terms1 = (delta_r1[valid_mask1] / r1_max[valid_mask1])**2
-    rms_bh1 = np.sqrt(np.mean(terms1)) * 100
+        # 1. Total 3D Vector RMS
+        delta_vec = np.sqrt((x_r - x_n)**2 + (y_r - y_n)**2 + (z_r - z_n)**2)
+        rms_3d = calc_rms(delta_vec)
 
-    # Avoid division by zero for BH2
-    valid_mask2 = r2_max > 1e-15
-    if np.sum(valid_mask2) < 10:
-        return None, "Insufficient valid data points for BH2"
+        # 2. Component-wise RMS (分离计算各轴，但共用半径分母)
+        rms_x = calc_rms(np.abs(x_r - x_n))
+        rms_y = calc_rms(np.abs(y_r - y_n))
+        rms_z = calc_rms(np.abs(z_r - z_n))
 
-    terms2 = (delta_r2[valid_mask2] / r2_max[valid_mask2])**2
-    rms_bh2 = np.sqrt(np.mean(terms2)) * 100
+        results[f'BH{bh}'] = {
+            '3D_Vector': rms_3d,
+            'X_Component': rms_x,
+            'Y_Component': rms_y,
+            'Z_Component': rms_z
+        }
 
-    # Final RMS is the maximum of BH1 and BH2
-    rms_final = max(rms_bh1, rms_bh2)
-
-    return rms_final, None
+    # 获取 BH1 和 BH2 中的最大误差
+    max_rms = {
+        '3D_Vector': max(results['BH1']['3D_Vector'], results['BH2']['3D_Vector']),
+        'X_Component': max(results['BH1']['X_Component'], results['BH2']['X_Component']),
+        'Y_Component': max(results['BH1']['Y_Component'], results['BH2']['Y_Component']),
+        'Z_Component': max(results['BH1']['Z_Component'], results['BH2']['Z_Component'])
+    }
 
+    return max_rms, None
 
 def analyze_constraint_violation(constraint_data, n_levels=9):
     """
@@ -155,34 +277,32 @@ def analyze_constraint_violation(constraint_data, n_levels=9):
 
 
 def print_header():
-    """Print report header"""
     print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-    print(Color.BOLD + "   AMSS-NCKU GW150914 Simulation Regression Test Report" + Color.RESET)
+    print(Color.BOLD + "   AMSS-NCKU GW150914 Comprehensive Regression Test" + Color.RESET)
     print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
 
-
-def print_rms_results(rms_rel, error, threshold=1.0):
-    """Print RMS error results"""
-    print(f"\n{Color.BOLD}1. RMS Error Analysis (Baseline vs Optimized){Color.RESET}")
-    print("-" * 45)
+def print_rms_results(rms_dict, error, threshold=1.0):
+    print(f"\n{Color.BOLD}1. RMS Error Analysis (Maximums of BH1 & BH2){Color.RESET}")
+    print("-" * 65)
 
     if error:
         print(f"   {Color.RED}Error: {error}{Color.RESET}")
         return False
 
-    passed = rms_rel < threshold
+    all_passed = True
+    print(f"   Requirement: < {threshold}%\n")
 
-    print(f"   RMS relative error: {rms_rel:.4f}%")
-    print(f"   Requirement:        < {threshold}%")
-    print(f"   Status:             {get_status_text(passed)}")
+    for key, val in rms_dict.items():
+        passed = val < threshold
+        all_passed = all_passed and passed
+        status = get_status_text(passed)
+        print(f"   {key:15}: {val:8.4f}%   |   Status: {status}")
 
-    return passed
+    return all_passed
 
-
-def print_constraint_results(results, threshold=2.0):
-    """Print constraint violation results"""
+def print_constraint_results(results, threshold=2.0):
     print(f"\n{Color.BOLD}2. ADM Constraint Violation Analysis (Grid Level 0){Color.RESET}")
-    print("-" * 45)
+    print("-" * 65)
 
     names = ['Ham', 'Px', 'Py', 'Pz', 'Gx', 'Gy', 'Gz']
     for i, name in enumerate(names):
@@ -195,23 +315,49 @@ def print_constraint_results(results, threshold=2.0):
     print(f"\n   Maximum violation:  {results['max_violation']:.6f}")
     print(f"   Requirement:        < {threshold}")
     print(f"   Status:             {get_status_text(passed)}")
-
-    return passed
-
-
-def print_summary(rms_passed, constraint_passed):
-    """Print summary"""
-    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-    print(Color.BOLD + "Verification Summary" + Color.RESET)
-    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-
-    all_passed = rms_passed and constraint_passed
-    
-    res_rms = get_status_text(rms_passed)
-    res_con = get_status_text(constraint_passed)
-
-    print(f"   [1] RMS trajectory check:         {res_rms}")
-    print(f"   [2] ADM constraint check:         {res_con}")
+
+    return passed
+
+
+def print_figure_results(results, threshold_percent=0.001):
+    print(f"\n{Color.BOLD}3. Figure Pixel Comparison (PDF Rasterization){Color.RESET}")
+    print("-" * 65)
+    print(f"   Requirement: < {threshold_percent:.3f}% differing pixels\n")
+
+    all_passed = True
+    for result in results:
+        passed = result["passed"]
+        all_passed = all_passed and passed
+        status = get_status_text(passed)
+        print(f"   {result['name']:32}: {result['diff_percent']:10.6f}%   |   Status: {status}")
+
+        if result["pages_ref"] != result["pages_target"]:
+            print(f"   {'':32}  pages(ref/target): {result['pages_ref']}/{result['pages_target']}")
+
+    return all_passed
+
+
+def print_figure_error(error_message):
+    print(f"\n{Color.BOLD}3. Figure Pixel Comparison (PDF Rasterization){Color.RESET}")
+    print("-" * 65)
+    print(f"   {Color.RED}Error: {error_message}{Color.RESET}")
+    return False
+
+
+def print_summary(rms_passed, constraint_passed, figure_passed):
+    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+    print(Color.BOLD + "Verification Summary" + Color.RESET)
+    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+
+    all_passed = rms_passed and constraint_passed and figure_passed
+    
+    res_rms = get_status_text(rms_passed)
+    res_con = get_status_text(constraint_passed)
+    res_fig = get_status_text(figure_passed)
+
+    print(f"   [1] Comprehensive RMS check:      {res_rms}")
+    print(f"   [2] ADM constraint check:         {res_con}")
+    print(f"   [3] Figure pixel comparison:      {res_fig}")
     
     final_status = f"{Color.GREEN}{Color.BOLD}ALL CHECKS PASSED{Color.RESET}" if all_passed else f"{Color.RED}{Color.BOLD}SOME CHECKS FAILED{Color.RESET}"
     print(f"\n   Overall result: {final_status}")
@@ -219,61 +365,58 @@ def print_summary(rms_passed, constraint_passed):
 
     return all_passed
 
-
 def main():
-    # Determine target (optimized) output directory
     if len(sys.argv) > 1:
         target_dir = sys.argv[1]
     else:
         script_dir = os.path.dirname(os.path.abspath(__file__))
         target_dir = os.path.join(script_dir, "GW150914/AMSS_NCKU_output")
 
-    # Determine reference (baseline) directory
-    script_dir = os.path.dirname(os.path.abspath(__file__))
-    reference_dir = os.path.join(script_dir, "GW150914-origin/AMSS_NCKU_output")
+    script_dir = os.path.dirname(os.path.abspath(__file__))
+    reference_dir = os.path.join(script_dir, "GW150914-origin/AMSS_NCKU_output")
+    target_figure_dir = resolve_figure_dir(target_dir)
+    reference_figure_dir = os.path.join(script_dir, "GW150914-origin/figure")
+
+    bh_file_ref = os.path.join(reference_dir, "bssn_BH.dat")
+    bh_file_target = os.path.join(target_dir, "bssn_BH.dat")
+    constraint_file = os.path.join(target_dir, "bssn_constraint.dat")
 
-    # Data file paths
-    bh_file_ref = os.path.join(reference_dir, "bssn_BH.dat")
-    bh_file_target = os.path.join(target_dir, "bssn_BH.dat")
-    constraint_file = os.path.join(target_dir, "bssn_constraint.dat")
-
-    # Check if files exist
     if not os.path.exists(bh_file_ref):
         print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Baseline trajectory file not found: {bh_file_ref}")
         sys.exit(1)
-
     if not os.path.exists(bh_file_target):
         print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Target trajectory file not found: {bh_file_target}")
         sys.exit(1)
-
     if not os.path.exists(constraint_file):
         print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Constraint data file not found: {constraint_file}")
         sys.exit(1)
 
-    # Print header
-    print_header()
-    print(f"\n{Color.BOLD}Reference (Baseline):{Color.RESET} {Color.BLUE}{reference_dir}{Color.RESET}")
-    print(f"{Color.BOLD}Target (Optimized):  {Color.RESET} {Color.BLUE}{target_dir}{Color.RESET}")
+    print_header()
+    print(f"\n{Color.BOLD}Reference (Baseline):{Color.RESET} {Color.BLUE}{reference_dir}{Color.RESET}")
+    print(f"{Color.BOLD}Target (Optimized):  {Color.RESET} {Color.BLUE}{target_dir}{Color.RESET}")
+    print(f"{Color.BOLD}Reference Figures:   {Color.RESET} {Color.BLUE}{reference_figure_dir}{Color.RESET}")
+    print(f"{Color.BOLD}Target Figures:      {Color.RESET} {Color.BLUE}{target_figure_dir}{Color.RESET}")
 
-    # Load data
     bh_data_ref = load_bh_trajectory(bh_file_ref)
     bh_data_target = load_bh_trajectory(bh_file_target)
     constraint_data = load_constraint_data(constraint_file)
 
-    # Calculate RMS error
-    rms_rel, error = calculate_rms_error(bh_data_ref, bh_data_target)
-    rms_passed = print_rms_results(rms_rel, error)
-
-    # Analyze constraint violation
-    constraint_results = analyze_constraint_violation(constraint_data)
-    constraint_passed = print_constraint_results(constraint_results)
-
-    # Print summary
-    all_passed = print_summary(rms_passed, constraint_passed)
-
-    # Return exit code
-    sys.exit(0 if all_passed else 1)
+    # Output modified RMS results
+    rms_dict, error = calculate_all_rms_errors(bh_data_ref, bh_data_target)
+    rms_passed = print_rms_results(rms_dict, error)
 
+    # Output constraint results
+    constraint_results = analyze_constraint_violation(constraint_data)
+    constraint_passed = print_constraint_results(constraint_results)
+
+    try:
+        figure_results = compare_required_figures(reference_figure_dir, target_figure_dir)
+        figure_passed = print_figure_results(figure_results)
+    except (FileNotFoundError, RuntimeError) as exc:
+        figure_passed = print_figure_error(str(exc))
+
+    all_passed = print_summary(rms_passed, constraint_passed, figure_passed)
+    sys.exit(0 if all_passed else 1)
 
 if __name__ == "__main__":
     main()

AMSS_NCKU_source/MPatch.C

@@ -7,12 +7,178 @@
 #include <string>
 #include <cmath>
 #include <new>
+#include <vector>
 using namespace std;
 
 #include "misc.h"
 #include "MPatch.h"
 #include "Parallel.h"
 #include "fmisc.h"
+#ifdef INTERP_LB_PROFILE
+#include "interp_lb_profile.h"
+#endif
+
+namespace
+{
+struct InterpBlockView
+{
+  Block *bp;
+  double llb[dim];
+  double uub[dim];
+};
+
+struct BlockBinIndex
+{
+  int bins[dim];
+  double lo[dim];
+  double inv[dim];
+  vector<InterpBlockView> views;
+  vector<vector<int>> bin_to_blocks;
+  bool valid;
+
+  BlockBinIndex() : valid(false)
+  {
+    for (int i = 0; i < dim; i++)
+    {
+      bins[i] = 1;
+      lo[i] = 0.0;
+      inv[i] = 0.0;
+    }
+  }
+};
+
+inline int clamp_int(int v, int lo, int hi)
+{
+  return (v < lo) ? lo : ((v > hi) ? hi : v);
+}
+
+inline int coord_to_bin(double x, double lo, double inv, int nb)
+{
+  if (nb <= 1 || inv <= 0.0)
+    return 0;
+  int b = int(floor((x - lo) * inv));
+  return clamp_int(b, 0, nb - 1);
+}
+
+inline int bin_loc(const BlockBinIndex &index, int b0, int b1, int b2)
+{
+  return b0 + index.bins[0] * (b1 + index.bins[1] * b2);
+}
+
+inline bool point_in_block_view(const InterpBlockView &view, const double *pox, const double *DH)
+{
+  for (int i = 0; i < dim; i++)
+  {
+    if (pox[i] - view.llb[i] < -DH[i] / 2 || pox[i] - view.uub[i] > DH[i] / 2)
+      return false;
+  }
+  return true;
+}
+
+void build_block_bin_index(Patch *patch, const double *DH, BlockBinIndex &index)
+{
+  index = BlockBinIndex();
+
+  MyList<Block> *Bp = patch->blb;
+  while (Bp)
+  {
+    Block *BP = Bp->data;
+    InterpBlockView view;
+    view.bp = BP;
+    for (int i = 0; i < dim; i++)
+    {
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif
+      view.llb[i] = (feq(BP->bbox[i], patch->bbox[i], DH[i] / 2)) ? BP->bbox[i] + patch->lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
+      view.uub[i] = (feq(BP->bbox[dim + i], patch->bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - patch->uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
+#else
+#ifdef Cell
+      view.llb[i] = (feq(BP->bbox[i], patch->bbox[i], DH[i] / 2)) ? BP->bbox[i] + patch->lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
+      view.uub[i] = (feq(BP->bbox[dim + i], patch->bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - patch->uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif
+    }
+    index.views.push_back(view);
+    if (Bp == patch->ble)
+      break;
+    Bp = Bp->next;
+  }
+
+  const int nblocks = int(index.views.size());
+  if (nblocks <= 0)
+    return;
+
+  int bins_1d = int(ceil(pow(double(nblocks), 1.0 / 3.0)));
+  bins_1d = clamp_int(bins_1d, 1, 32);
+  for (int i = 0; i < dim; i++)
+  {
+    index.bins[i] = bins_1d;
+    index.lo[i] = patch->bbox[i] + patch->lli[i] * DH[i];
+    const double hi = patch->bbox[dim + i] - patch->uui[i] * DH[i];
+    if (hi > index.lo[i] && bins_1d > 1)
+      index.inv[i] = bins_1d / (hi - index.lo[i]);
+    else
+      index.inv[i] = 0.0;
+  }
+
+  index.bin_to_blocks.resize(index.bins[0] * index.bins[1] * index.bins[2]);
+
+  for (int bi = 0; bi < nblocks; bi++)
+  {
+    const InterpBlockView &view = index.views[bi];
+    int bmin[dim], bmax[dim];
+    for (int d = 0; d < dim; d++)
+    {
+      const double low = view.llb[d] - DH[d] / 2;
+      const double up = view.uub[d] + DH[d] / 2;
+      bmin[d] = coord_to_bin(low, index.lo[d], index.inv[d], index.bins[d]);
+      bmax[d] = coord_to_bin(up, index.lo[d], index.inv[d], index.bins[d]);
+      if (bmax[d] < bmin[d])
+      {
+        int t = bmin[d];
+        bmin[d] = bmax[d];
+        bmax[d] = t;
+      }
+    }
+
+    for (int bz = bmin[2]; bz <= bmax[2]; bz++)
+      for (int by = bmin[1]; by <= bmax[1]; by++)
+        for (int bx = bmin[0]; bx <= bmax[0]; bx++)
+          index.bin_to_blocks[bin_loc(index, bx, by, bz)].push_back(bi);
+  }
+
+  index.valid = true;
+}
+
+int find_block_index_for_point(const BlockBinIndex &index, const double *pox, const double *DH)
+{
+  if (!index.valid)
+    return -1;
+
+  const int bx = coord_to_bin(pox[0], index.lo[0], index.inv[0], index.bins[0]);
+  const int by = coord_to_bin(pox[1], index.lo[1], index.inv[1], index.bins[1]);
+  const int bz = coord_to_bin(pox[2], index.lo[2], index.inv[2], index.bins[2]);
+  const vector<int> &cand = index.bin_to_blocks[bin_loc(index, bx, by, bz)];
+
+  for (size_t ci = 0; ci < cand.size(); ci++)
+  {
+    const int bi = cand[ci];
+    if (point_in_block_view(index.views[bi], pox, DH))
+      return bi;
+  }
+
+  // Fallback to full scan for numerical edge cases around bin boundaries.
+  for (size_t bi = 0; bi < index.views.size(); bi++)
+    if (point_in_block_view(index.views[bi], pox, DH))
+      return int(bi);
+
+  return -1;
+}
+} // namespace
 
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
 {
@@ -341,8 +507,9 @@ void Patch::Interp_Points(MyList<var> *VarList,
                           double *Shellf, int Symmetry)
 {
   // NOTE: we do not Synchnize variables here, make sure of that before calling this routine
-  int myrank;
+  int myrank, nprocs;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
 
   int ordn = 2 * ghost_width;
   MyList<var> *varl;
@@ -354,24 +521,20 @@ void Patch::Interp_Points(MyList<var> *VarList,
     varl = varl->next;
   }
 
-  double *shellf;
-  shellf = new double[NN * num_var];
-  memset(shellf, 0, sizeof(double) * NN * num_var);
+  memset(Shellf, 0, sizeof(double) * NN * num_var);
 
-  // we use weight to monitor code, later some day we can move it for optimization
-  int *weight;
-  weight = new int[NN];
-  memset(weight, 0, sizeof(int) * NN);
-
-  double *DH, *llb, *uub;
-  DH = new double[dim];
+  // owner_rank[j] records which MPI rank owns point j
+  // All ranks traverse the same block list so they all agree on ownership
+  int *owner_rank;
+  owner_rank = new int[NN];
+  for (int j = 0; j < NN; j++)
+    owner_rank[j] = -1;
 
+  double DH[dim];
   for (int i = 0; i < dim; i++)
-  {
     DH[i] = getdX(i);
-  }
-  llb = new double[dim];
-  uub = new double[dim];
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -394,165 +557,350 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    MyList<Block> *Bp = blb;
-    bool notfind = true;
-    while (notfind && Bp) // run along Blocks
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
+    if (block_i >= 0)
     {
-      Block *BP = Bp->data;
-
-      bool flag = true;
-      for (int i = 0; i < dim; i++)
+      Block *BP = block_index.views[block_i].bp;
+      owner_rank[j] = BP->rank;
+      if (myrank == BP->rank)
       {
-// NOTE: our dividing structure is (exclude ghost)
-// -1 0
-//       1  2
-// so (0,1) does not belong to any part for vertex structure
-// here we put (0,0.5) to left part and (0.5,1) to right part
-// BUT for cell structure the bbox is (-1.5,0.5) and (0.5,2.5), there is no missing region at all
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
+        //---> interpolation
+        varl = VarList;
+        int k = 0;
+        while (varl) // run along variables
         {
-          flag = false;
-          break;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
         }
       }
-
-      if (flag)
-      {
-        notfind = false;
-        if (myrank == BP->rank)
-        {
-          //---> interpolation
-          varl = VarList;
-          int k = 0;
-          while (varl) // run along variables
-          {
-            //              shellf[j*num_var+k] = Parallel::global_interp(dim,BP->shape,BP->X,BP->fgfs[varl->data->sgfn],
-            //	  		                                    pox,ordn,varl->data->SoA,Symmetry);
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-          weight[j] = 1;
-        }
-      }
-      if (Bp == ble)
-        break;
-      Bp = Bp->next;
     }
   }
 
-  MPI_Allreduce(shellf, Shellf, NN * num_var, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  int *Weight;
-  Weight = new int[NN];
-  MPI_Allreduce(weight, Weight, NN, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-
-  //  misc::tillherecheck("print me");
-
-  for (int i = 0; i < NN; i++)
+  // Replace MPI_Allreduce with per-owner MPI_Bcast:
+  // Group consecutive points by owner rank and broadcast each group.
+  // Since each point's data is non-zero only on the owner rank,
+  // Bcast from owner is equivalent to Allreduce(MPI_SUM) but much cheaper.
   {
-    if (Weight[i] > 1)
+    int j = 0;
+    while (j < NN)
     {
-      if (myrank == 0)
-        cout << "WARNING: Patch::Interp_Points meets multiple weight" << endl;
-      for (int j = 0; j < num_var; j++)
-        Shellf[j + i * num_var] = Shellf[j + i * num_var] / Weight[i];
+      int cur_owner = owner_rank[j];
+      if (cur_owner < 0)
+      {
+        if (myrank == 0)
+        {
+          cout << "ERROR: Patch::Interp_Points fails to find point (";
+          for (int d = 0; d < dim; d++)
+          {
+            cout << XX[d][j];
+            if (d < dim - 1)
+              cout << ",";
+            else
+              cout << ")";
+          }
+          cout << " on Patch (";
+          for (int d = 0; d < dim; d++)
+          {
+            cout << bbox[d] << "+" << lli[d] * DH[d];
+            if (d < dim - 1)
+              cout << ",";
+            else
+              cout << ")--";
+          }
+          cout << "(";
+          for (int d = 0; d < dim; d++)
+          {
+            cout << bbox[dim + d] << "-" << uui[d] * DH[d];
+            if (d < dim - 1)
+              cout << ",";
+            else
+              cout << ")" << endl;
+          }
+          MPI_Abort(MPI_COMM_WORLD, 1);
+        }
+        j++;
+        continue;
+      }
+      // Find contiguous run of points with the same owner
+      int jstart = j;
+      while (j < NN && owner_rank[j] == cur_owner)
+        j++;
+      int count = (j - jstart) * num_var;
+      MPI_Bcast(Shellf + jstart * num_var, count, MPI_DOUBLE, cur_owner, MPI_COMM_WORLD);
     }
-    else if (Weight[i] == 0 && myrank == 0)
+  }
+
+  delete[] owner_rank;
+}
+void Patch::Interp_Points(MyList<var> *VarList,
+                          int NN, double **XX,
+                          double *Shellf, int Symmetry,
+                          int Nmin_consumer, int Nmax_consumer)
+{
+  // Targeted point-to-point overload: each owner sends each point only to
+  // the one rank that needs it for integration (consumer), reducing
+  // communication volume by ~nprocs times compared to the Bcast version.
+#ifdef INTERP_LB_PROFILE
+  double t_interp_start = MPI_Wtime();
+#endif
+  int myrank, nprocs;
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
+
+  int ordn = 2 * ghost_width;
+  MyList<var> *varl;
+  int num_var = 0;
+  varl = VarList;
+  while (varl)
+  {
+    num_var++;
+    varl = varl->next;
+  }
+
+  memset(Shellf, 0, sizeof(double) * NN * num_var);
+
+  // owner_rank[j] records which MPI rank owns point j
+  int *owner_rank;
+  owner_rank = new int[NN];
+  for (int j = 0; j < NN; j++)
+    owner_rank[j] = -1;
+
+  double DH[dim];
+  for (int i = 0; i < dim; i++)
+    DH[i] = getdX(i);
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
+
+  // --- Interpolation phase (identical to original) ---
+  for (int j = 0; j < NN; j++)
+  {
+    double pox[dim];
+    for (int i = 0; i < dim; i++)
+    {
+      pox[i] = XX[i][j];
+      if (myrank == 0 && (XX[i][j] < bbox[i] + lli[i] * DH[i] || XX[i][j] > bbox[dim + i] - uui[i] * DH[i]))
+      {
+        cout << "Patch::Interp_Points: point (";
+        for (int k = 0; k < dim; k++)
+        {
+          cout << XX[k][j];
+          if (k < dim - 1)
+            cout << ",";
+          else
+            cout << ") is out of current Patch." << endl;
+        }
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
+    }
+
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
+    if (block_i >= 0)
+    {
+      Block *BP = block_index.views[block_i].bp;
+      owner_rank[j] = BP->rank;
+      if (myrank == BP->rank)
+      {
+        varl = VarList;
+        int k = 0;
+        while (varl)
+        {
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
+        }
+      }
+    }
+  }
+
+#ifdef INTERP_LB_PROFILE
+  double t_interp_end = MPI_Wtime();
+  double t_interp_local = t_interp_end - t_interp_start;
+#endif
+
+  // --- Error check for unfound points ---
+  for (int j = 0; j < NN; j++)
+  {
+    if (owner_rank[j] < 0 && myrank == 0)
     {
       cout << "ERROR: Patch::Interp_Points fails to find point (";
-      for (int j = 0; j < dim; j++)
+      for (int d = 0; d < dim; d++)
       {
-        cout << XX[j][i];
-        if (j < dim - 1)
+        cout << XX[d][j];
+        if (d < dim - 1)
           cout << ",";
         else
           cout << ")";
       }
       cout << " on Patch (";
-      for (int j = 0; j < dim; j++)
+      for (int d = 0; d < dim; d++)
       {
-        cout << bbox[j] << "+" << lli[j] * getdX(j);
-        if (j < dim - 1)
+        cout << bbox[d] << "+" << lli[d] * DH[d];
+        if (d < dim - 1)
           cout << ",";
         else
           cout << ")--";
       }
       cout << "(";
-      for (int j = 0; j < dim; j++)
+      for (int d = 0; d < dim; d++)
       {
-        cout << bbox[dim + j] << "-" << uui[j] * getdX(j);
-        if (j < dim - 1)
+        cout << bbox[dim + d] << "-" << uui[d] * DH[d];
+        if (d < dim - 1)
           cout << ",";
         else
           cout << ")" << endl;
       }
-#if 0
-       checkBlock();
-#else
-      cout << "splited domains:" << endl;
-      {
-        MyList<Block> *Bp = blb;
-        while (Bp)
-        {
-          Block *BP = Bp->data;
-
-          for (int i = 0; i < dim; i++)
-          {
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-            llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-            uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-            llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-            uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-          }
-          cout << "(";
-          for (int j = 0; j < dim; j++)
-          {
-            cout << llb[j] << ":" << uub[j];
-            if (j < dim - 1)
-              cout << ",";
-            else
-              cout << ")" << endl;
-          }
-          if (Bp == ble)
-            break;
-          Bp = Bp->next;
-        }
-      }
-#endif
       MPI_Abort(MPI_COMM_WORLD, 1);
     }
   }
 
-  delete[] shellf;
-  delete[] weight;
-  delete[] Weight;
-  delete[] DH;
-  delete[] llb;
-  delete[] uub;
+  // --- Targeted point-to-point communication phase ---
+  // Compute consumer_rank[j] using the same deterministic formula as surface_integral
+  int *consumer_rank = new int[NN];
+  {
+    int mp = NN / nprocs;
+    int Lp = NN - nprocs * mp;
+    for (int j = 0; j < NN; j++)
+    {
+      if (j < Lp * (mp + 1))
+        consumer_rank[j] = j / (mp + 1);
+      else
+        consumer_rank[j] = Lp + (j - Lp * (mp + 1)) / mp;
+    }
+  }
+
+  // Count sends and recvs per rank
+  int *send_count = new int[nprocs];
+  int *recv_count = new int[nprocs];
+  memset(send_count, 0, sizeof(int) * nprocs);
+  memset(recv_count, 0, sizeof(int) * nprocs);
+
+  for (int j = 0; j < NN; j++)
+  {
+    int own = owner_rank[j];
+    int con = consumer_rank[j];
+    if (own == con)
+      continue; // local — no communication needed
+    if (own == myrank)
+      send_count[con]++;
+    if (con == myrank)
+      recv_count[own]++;
+  }
+
+  // Build send buffers: for each destination rank, pack (index, data) pairs
+  // Each entry: 1 int (point index j) + num_var doubles
+  int total_send = 0, total_recv = 0;
+  int *send_offset = new int[nprocs];
+  int *recv_offset = new int[nprocs];
+  for (int r = 0; r < nprocs; r++)
+  {
+    send_offset[r] = total_send;
+    total_send += send_count[r];
+    recv_offset[r] = total_recv;
+    total_recv += recv_count[r];
+  }
+
+  // Pack send buffers: each message contains (j, data[0..num_var-1]) per point
+  int stride = 1 + num_var; // 1 double for index + num_var doubles for data
+  double *sendbuf = new double[total_send * stride];
+  double *recvbuf = new double[total_recv * stride];
+
+  // Temporary counters for packing
+  int *pack_pos = new int[nprocs];
+  memset(pack_pos, 0, sizeof(int) * nprocs);
+
+  for (int j = 0; j < NN; j++)
+  {
+    int own = owner_rank[j];
+    int con = consumer_rank[j];
+    if (own != myrank || con == myrank)
+      continue;
+    int pos = (send_offset[con] + pack_pos[con]) * stride;
+    sendbuf[pos] = (double)j; // point index
+    for (int v = 0; v < num_var; v++)
+      sendbuf[pos + 1 + v] = Shellf[j * num_var + v];
+    pack_pos[con]++;
+  }
+
+  // Post non-blocking recvs and sends
+  int n_req = 0;
+  for (int r = 0; r < nprocs; r++)
+  {
+    if (recv_count[r] > 0) n_req++;
+    if (send_count[r] > 0) n_req++;
+  }
+
+  MPI_Request *reqs = new MPI_Request[n_req];
+  int req_idx = 0;
+
+  for (int r = 0; r < nprocs; r++)
+  {
+    if (recv_count[r] > 0)
+    {
+      MPI_Irecv(recvbuf + recv_offset[r] * stride,
+                recv_count[r] * stride, MPI_DOUBLE,
+                r, 0, MPI_COMM_WORLD, &reqs[req_idx++]);
+    }
+  }
+  for (int r = 0; r < nprocs; r++)
+  {
+    if (send_count[r] > 0)
+    {
+      MPI_Isend(sendbuf + send_offset[r] * stride,
+                send_count[r] * stride, MPI_DOUBLE,
+                r, 0, MPI_COMM_WORLD, &reqs[req_idx++]);
+    }
+  }
+
+  if (n_req > 0)
+    MPI_Waitall(n_req, reqs, MPI_STATUSES_IGNORE);
+
+  // Unpack recv buffers into Shellf
+  for (int i = 0; i < total_recv; i++)
+  {
+    int pos = i * stride;
+    int j = (int)recvbuf[pos];
+    for (int v = 0; v < num_var; v++)
+      Shellf[j * num_var + v] = recvbuf[pos + 1 + v];
+  }
+
+  delete[] reqs;
+  delete[] sendbuf;
+  delete[] recvbuf;
+  delete[] pack_pos;
+  delete[] send_offset;
+  delete[] recv_offset;
+  delete[] send_count;
+  delete[] recv_count;
+  delete[] consumer_rank;
+  delete[] owner_rank;
+
+#ifdef INTERP_LB_PROFILE
+  {
+    static bool profile_written = false;
+    if (!profile_written) {
+      double *all_times = nullptr;
+      if (myrank == 0) all_times = new double[nprocs];
+      MPI_Gather(&t_interp_local, 1, MPI_DOUBLE,
+                 all_times, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD);
+      if (myrank == 0) {
+        int heavy[64];
+        int nh = InterpLBProfile::identify_heavy_ranks(
+            all_times, nprocs, 2.5, heavy, 64);
+        InterpLBProfile::write_profile(
+            "interp_lb_profile.bin", nprocs,
+            all_times, heavy, nh, 2.5);
+        printf("[InterpLB] Profile written: %d heavy ranks\n", nh);
+        for (int i = 0; i < nh; i++)
+          printf("  Heavy rank %d: %.6f s\n", heavy[i], all_times[heavy[i]]);
+        delete[] all_times;
+      }
+      profile_written = true;
+    }
+  }
+#endif
 }
 void Patch::Interp_Points(MyList<var> *VarList,
                           int NN, double **XX,
@@ -573,24 +921,24 @@ void Patch::Interp_Points(MyList<var> *VarList,
     varl = varl->next;
   }
 
-  double *shellf;
-  shellf = new double[NN * num_var];
-  memset(shellf, 0, sizeof(double) * NN * num_var);
+  memset(Shellf, 0, sizeof(double) * NN * num_var);
 
-  // we use weight to monitor code, later some day we can move it for optimization
-  int *weight;
-  weight = new int[NN];
-  memset(weight, 0, sizeof(int) * NN);
+  // owner_rank[j] stores the global rank that owns point j
+  int *owner_rank;
+  owner_rank = new int[NN];
+  for (int j = 0; j < NN; j++)
+    owner_rank[j] = -1;
 
-  double *DH, *llb, *uub;
-  DH = new double[dim];
+  // Build global-to-local rank translation for Comm_here
+  MPI_Group world_group, local_group;
+  MPI_Comm_group(MPI_COMM_WORLD, &world_group);
+  MPI_Comm_group(Comm_here, &local_group);
 
+  double DH[dim];
   for (int i = 0; i < dim; i++)
-  {
     DH[i] = getdX(i);
-  }
-  llb = new double[dim];
-  uub = new double[dim];
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -613,159 +961,56 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    MyList<Block> *Bp = blb;
-    bool notfind = true;
-    while (notfind && Bp) // run along Blocks
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
+    if (block_i >= 0)
     {
-      Block *BP = Bp->data;
-
-      bool flag = true;
-      for (int i = 0; i < dim; i++)
+      Block *BP = block_index.views[block_i].bp;
+      owner_rank[j] = BP->rank;
+      if (myrank == BP->rank)
       {
-// NOTE: our dividing structure is (exclude ghost)
-// -1 0
-//       1  2
-// so (0,1) does not belong to any part for vertex structure
-// here we put (0,0.5) to left part and (0.5,1) to right part
-// BUT for cell structure the bbox is (-1.5,0.5) and (0.5,2.5), there is no missing region at all
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
+        //---> interpolation
+        varl = VarList;
+        int k = 0;
+        while (varl) // run along variables
         {
-          flag = false;
-          break;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
         }
       }
-
-      if (flag)
-      {
-        notfind = false;
-        if (myrank == BP->rank)
-        {
-          //---> interpolation
-          varl = VarList;
-          int k = 0;
-          while (varl) // run along variables
-          {
-            //              shellf[j*num_var+k] = Parallel::global_interp(dim,BP->shape,BP->X,BP->fgfs[varl->data->sgfn],
-            //	  		                                    pox,ordn,varl->data->SoA,Symmetry);
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-          weight[j] = 1;
-        }
-      }
-      if (Bp == ble)
-        break;
-      Bp = Bp->next;
     }
   }
 
-  MPI_Allreduce(shellf, Shellf, NN * num_var, MPI_DOUBLE, MPI_SUM, Comm_here);
-  int *Weight;
-  Weight = new int[NN];
-  MPI_Allreduce(weight, Weight, NN, MPI_INT, MPI_SUM, Comm_here);
-
-  //  misc::tillherecheck("print me");
-  //  if(lmyrank == 0) cout<<"myrank = "<<myrank<<"print me"<<endl;
-
-  for (int i = 0; i < NN; i++)
+  // Collect unique global owner ranks and translate to local ranks in Comm_here
+  // Then broadcast each owner's points via MPI_Bcast on Comm_here
   {
-    if (Weight[i] > 1)
+    int j = 0;
+    while (j < NN)
     {
-      if (lmyrank == 0)
-        cout << "WARNING: Patch::Interp_Points meets multiple weight" << endl;
-      for (int j = 0; j < num_var; j++)
-        Shellf[j + i * num_var] = Shellf[j + i * num_var] / Weight[i];
+      int cur_owner_global = owner_rank[j];
+      if (cur_owner_global < 0)
+      {
+        // Point not found — skip (error check disabled for sub-communicator levels)
+        j++;
+        continue;
+      }
+      // Translate global rank to local rank in Comm_here
+      int cur_owner_local;
+      MPI_Group_translate_ranks(world_group, 1, &cur_owner_global, local_group, &cur_owner_local);
+
+      // Find contiguous run of points with the same owner
+      int jstart = j;
+      while (j < NN && owner_rank[j] == cur_owner_global)
+        j++;
+      int count = (j - jstart) * num_var;
+      MPI_Bcast(Shellf + jstart * num_var, count, MPI_DOUBLE, cur_owner_local, Comm_here);
     }
-#if 0 // for not involved levels, this may fail     
-     else if(Weight[i] == 0 && lmyrank == 0)
-     {
-       cout<<"ERROR: Patch::Interp_Points fails to find point (";
-       for(int j=0;j<dim;j++)
-       {
-	  cout<<XX[j][i];
-	  if(j<dim-1) cout<<",";
-	  else        cout<<")";
-       }
-       cout<<" on Patch (";
-       for(int j=0;j<dim;j++)
-       {
-	  cout<<bbox[j]<<"+"<<lli[j]*getdX(j);
-	  if(j<dim-1) cout<<",";
-	  else        cout<<")--";
-       }
-       cout<<"(";
-       for(int j=0;j<dim;j++)
-       {
-	  cout<<bbox[dim+j]<<"-"<<uui[j]*getdX(j);
-	  if(j<dim-1) cout<<",";
-	  else        cout<<")"<<endl;
-       }
-#if 0
-       checkBlock();
-#else
-  cout<<"splited domains:"<<endl;
-  {
-     MyList<Block> *Bp=blb;
-     while(Bp)
-     {
-	Block *BP=Bp->data;
-
-	for(int i=0;i<dim;i++)
-	{
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif    
-          llb[i] = (feq(BP->bbox[i]    ,bbox[i]    ,DH[i]/2)) ? BP->bbox[i]+lli[i]*DH[i]     : BP->bbox[i]    +(ghost_width-0.5)*DH[i];
-          uub[i] = (feq(BP->bbox[dim+i],bbox[dim+i],DH[i]/2)) ? BP->bbox[dim+i]-uui[i]*DH[i] : BP->bbox[dim+i]-(ghost_width-0.5)*DH[i];
-#else
-#ifdef Cell
-          llb[i] = (feq(BP->bbox[i]    ,bbox[i]    ,DH[i]/2)) ? BP->bbox[i]+lli[i]*DH[i]     : BP->bbox[i]    +ghost_width*DH[i];
-          uub[i] = (feq(BP->bbox[dim+i],bbox[dim+i],DH[i]/2)) ? BP->bbox[dim+i]-uui[i]*DH[i] : BP->bbox[dim+i]-ghost_width*DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif 
-	}       
-       cout<<"(";
-       for(int j=0;j<dim;j++)
-       {
-	  cout<<llb[j]<<":"<<uub[j];
-	  if(j<dim-1) cout<<",";
-	  else        cout<<")"<<endl;
-       }
-	if(Bp == ble) break;
-	Bp=Bp->next;
-     }
-  }
-#endif       
-       MPI_Abort(MPI_COMM_WORLD,1);
-     }
-#endif
   }
 
-  delete[] shellf;
-  delete[] weight;
-  delete[] Weight;
-  delete[] DH;
-  delete[] llb;
-  delete[] uub;
+  MPI_Group_free(&world_group);
+  MPI_Group_free(&local_group);
+  delete[] owner_rank;
 }
 void Patch::checkBlock()
 {

AMSS_NCKU_source/MPatch.h

@@ -39,6 +39,10 @@ public:
 
    bool Find_Point(double *XX);
 
+   void Interp_Points(MyList<var> *VarList,
+                      int NN, double **XX,
+                      double *Shellf, int Symmetry,
+                      int Nmin_consumer, int Nmax_consumer);
    void Interp_Points(MyList<var> *VarList,
                       int NN, double **XX,
                       double *Shellf, int Symmetry, MPI_Comm Comm_here);

AMSS_NCKU_source/Parallel.h

@@ -32,6 +32,16 @@ namespace Parallel
   int partition2(int *nxy, int split_size, int *min_width, int cpusize, int *shape); // special for 2 diemnsions
   int partition3(int *nxyz, int split_size, int *min_width, int cpusize, int *shape);
   MyList<Block> *distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfs, bool periodic, int nodes = 0); // produce corresponding Blocks
+  MyList<Block> *distribute_optimize(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfs, bool periodic, int nodes = 0);
+  Block* splitHotspotBlock(MyList<Block>* &BlL, int _dim,
+                           int ib0_orig, int ib3_orig,
+                           int jb1_orig, int jb4_orig,
+                           int kb2_orig, int kb5_orig,
+                           Patch* PP, int r_left, int r_right,
+                           int ingfsi, int fngfsi, bool periodic,
+                           Block* &split_first_block, Block* &split_last_block);
+  Block* createMappedBlock(MyList<Block>* &BlL, int _dim, int* shape, double* bbox,
+                           int block_id, int ingfsi, int fngfsi, int lev);
   void KillBlocks(MyList<Patch> *PatchLIST);
 
   void setfunction(MyList<Block> *BlL, var *vn, double func(double x, double y, double z));
@@ -81,6 +91,49 @@ namespace Parallel
                    int Symmetry);
   void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry);
   void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+  void Sync_merged(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+
+  struct SyncCache {
+    bool valid;
+    int cpusize;
+    MyList<gridseg> **combined_src;
+    MyList<gridseg> **combined_dst;
+    int *send_lengths;
+    int *recv_lengths;
+    double **send_bufs;
+    double **recv_bufs;
+    int *send_buf_caps;
+    int *recv_buf_caps;
+    MPI_Request *reqs;
+    MPI_Status *stats;
+    int max_reqs;
+    bool lengths_valid;
+    int *tc_req_node;
+    int *tc_req_is_recv;
+    int *tc_completed;
+    SyncCache();
+    void invalidate();
+    void destroy();
+  };
+
+  void Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, SyncCache &cache);
+  void transfer_cached(MyList<gridseg> **src, MyList<gridseg> **dst,
+                       MyList<var> *VarList1, MyList<var> *VarList2,
+                       int Symmetry, SyncCache &cache);
+
+  struct AsyncSyncState {
+    int req_no;
+    bool active;
+    int *req_node;
+    int *req_is_recv;
+    int pending_recv;
+    AsyncSyncState() : req_no(0), active(false), req_node(0), req_is_recv(0), pending_recv(0) {}
+  };
+
+  void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
+                  SyncCache &cache, AsyncSyncState &state);
+  void Sync_finish(SyncCache &cache, AsyncSyncState &state,
+                   MyList<var> *VarList, int Symmetry);
   void OutBdLow2Hi(Patch *Patc, Patch *Patf,
                    MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                    int Symmetry);
@@ -93,6 +146,15 @@ namespace Parallel
   void OutBdLow2Himix(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
                       MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                       int Symmetry);
+  void Restrict_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+                       MyList<var> *VarList1, MyList<var> *VarList2,
+                       int Symmetry, SyncCache &cache);
+  void OutBdLow2Hi_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+                          MyList<var> *VarList1, MyList<var> *VarList2,
+                          int Symmetry, SyncCache &cache);
+  void OutBdLow2Himix_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+                             MyList<var> *VarList1, MyList<var> *VarList2,
+                             int Symmetry, SyncCache &cache);
   void Prolong(Patch *Patc, Patch *Patf,
                MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                int Symmetry);
@@ -117,12 +179,13 @@ namespace Parallel
   MyList<Parallel::gridseg> *clone_gsl(MyList<Parallel::gridseg> *p, bool first_only);
   MyList<Parallel::gridseg> *build_bulk_gsl(Patch *Pat); // similar to build_owned_gsl0 but does not care rank issue
   MyList<Parallel::gridseg> *build_bulk_gsl(Block *bp, Patch *Pat);
-  void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
-                         MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
-  void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
-  double L2Norm(Patch *Pat, var *vf);
-  void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
-  void checkvarl(MyList<var> *pp, bool first_only);
+  void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
+                         MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
+  void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
+  double L2Norm(Patch *Pat, var *vf);
+  void L2Norm7(Patch *Pat, var **vf, double *norms);
+  void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
+  void checkvarl(MyList<var> *pp, bool first_only);
   MyList<Parallel::gridseg> *divide_gsl(MyList<Parallel::gridseg> *p, Patch *Pat);
   MyList<Parallel::gridseg> *divide_gs(MyList<Parallel::gridseg> *p, Patch *Pat);
   void prepare_inter_time_level(Patch *Pat,
@@ -154,11 +217,12 @@ namespace Parallel
   void aligncheck(double *bbox0, double *bboxl, int lev, double *DH0, int *shape);
   bool point_locat_gsl(double *pox, MyList<Parallel::gridseg> *gsl);
   void checkpatchlist(MyList<Patch> *PatL, bool buflog);
-
-  double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
-  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
-                             int NN, double **XX,
-                             double *Shellf, int Symmetry, MPI_Comm Comm_here);
+
+  double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
+  void L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here);
+  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
+                             int NN, double **XX,
+                             double *Shellf, int Symmetry, MPI_Comm Comm_here);
 #if (PSTR == 1 || PSTR == 2 || PSTR == 3)
   MyList<Block> *distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfsi,
                             bool periodic, int start_rank, int end_rank, int nodes = 0);

AMSS_NCKU_source/ShellPatch.C

@@ -3439,10 +3439,10 @@ void ShellPatch::write_Pablo_file_ss(int *ext, double xmin, double xmax, double
   delete[] Z;
 }
 
-double ShellPatch::L2Norm(var *vf)
-{
-  double tvf, dtvf = 0;
-  int BDW = overghost;
+double ShellPatch::L2Norm(var *vf)
+{
+  double tvf, dtvf = 0;
+  int BDW = overghost;
 
   MyList<ss_patch> *sPp = PatL;
   while (sPp)
@@ -3469,13 +3469,50 @@ double ShellPatch::L2Norm(var *vf)
   MPI_Allreduce(&dtvf, &tvf, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   tvf = sqrt(tvf);
-
-  return tvf;
-}
-
-// find maximum of abstract value, XX store position for maximum, Shellf store maximum themselvs
-void ShellPatch::Find_Maximum(MyList<var> *VarList, double *XX,
-                              double *Shellf)
+
+  return tvf;
+}
+void ShellPatch::L2Norm7(var **vf, double *norms)
+{
+  double tvf[7], dtvf[7];
+  int BDW = overghost;
+  for (int i = 0; i < 7; i++)
+    dtvf[i] = 0;
+
+  MyList<ss_patch> *sPp = PatL;
+  while (sPp)
+  {
+    MyList<Block> *Bp = sPp->data->blb;
+    while (Bp)
+    {
+      Block *cg = Bp->data;
+      if (myrank == cg->rank)
+      {
+        f_l2normhelper7(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[vf[0]->sgfn], cg->fgfs[vf[1]->sgfn], cg->fgfs[vf[2]->sgfn],
+                        cg->fgfs[vf[3]->sgfn], cg->fgfs[vf[4]->sgfn], cg->fgfs[vf[5]->sgfn],
+                        cg->fgfs[vf[6]->sgfn], tvf, BDW);
+        for (int i = 0; i < 7; i++)
+          dtvf[i] += tvf[i];
+      }
+      if (Bp == sPp->data->ble)
+        break;
+      Bp = Bp->next;
+    }
+    sPp = sPp->next;
+  }
+
+  MPI_Allreduce(dtvf, tvf, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  for (int i = 0; i < 7; i++)
+    norms[i] = sqrt(tvf[i]);
+}
+
+// find maximum of abstract value, XX store position for maximum, Shellf store maximum themselvs
+void ShellPatch::Find_Maximum(MyList<var> *VarList, double *XX,
+                              double *Shellf)
 {
   MyList<var> *varl;
   int num_var = 0;

AMSS_NCKU_source/ShellPatch.h

@@ -195,10 +195,11 @@ public:
    bool Interp_One_Point(MyList<var> *VarList,
                          double *XX, /*input global Cartesian coordinate*/
                          double *Shellf, int Symmetry);
-   void write_Pablo_file_ss(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
-                            char *filename, int sst);
-   double L2Norm(var *vf);
-   void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
-};
+   void write_Pablo_file_ss(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
+                            char *filename, int sst);
+   double L2Norm(var *vf);
+   void L2Norm7(var **vf, double *norms);
+   void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
+};
 
 #endif /* SHELLPATCH_H */

AMSS_NCKU_source/TwoPunctures.h

@@ -1,7 +1,8 @@
-
 #ifndef TWO_PUNCTURES_H
 #define TWO_PUNCTURES_H
 
+#include <omp.h>
+
 #define StencilSize 19
 #define N_PlaneRelax 1
 #define NRELAX 200
@@ -32,7 +33,7 @@ private:
        int npoints_A, npoints_B, npoints_phi;
 
        double target_M_plus, target_M_minus;
-       
+
        double admMass;
 
        double adm_tol;
@@ -42,6 +43,18 @@ private:
 
        int ntotal;
 
+       // ===== Precomputed spectral derivative matrices =====
+       double *D1_A, *D2_A;
+       double *D1_B, *D2_B;
+       double *DF1_phi, *DF2_phi;
+
+       // ===== Pre-allocated workspace for LineRelax (per-thread) =====
+       int max_threads;
+       double **ws_diag_be, **ws_e_be, **ws_f_be, **ws_b_be, **ws_x_be;
+       double **ws_l_be, **ws_u_be, **ws_d_be, **ws_y_be;
+       double **ws_diag_al, **ws_e_al, **ws_f_al, **ws_b_al, **ws_x_al;
+       double **ws_l_al, **ws_u_al, **ws_d_al, **ws_y_al;
+
        struct parameters
        {
               int nvar, n1, n2, n3;
@@ -58,6 +71,28 @@ public:
                     int Newtonmaxit);
        ~TwoPunctures();
 
+       // 02/07: New/modified methods
+       void allocate_workspace();
+       void free_workspace();
+       void precompute_derivative_matrices();
+       void build_cheb_deriv_matrices(int n, double *D1, double *D2);
+       void build_fourier_deriv_matrices(int N, double *DF1, double *DF2);
+       void Derivatives_AB3_MatMul(int nvar, int n1, int n2, int n3, derivs v);
+       void ThomasAlgorithm_ws(int N, double *b, double *a, double *c, double *x, double *q,
+                                double *l, double *u_ws, double *d, double *y);
+       void LineRelax_be_omp(double *dv,
+                         int const i, int const k, int const nvar,
+                         int const n1, int const n2, int const n3,
+                         double const *rhs, int const *ncols, int **cols,
+                         double **JFD, int tid);
+       void LineRelax_al_omp(double *dv,
+                         int const j, int const k, int const nvar,
+                         int const n1, int const n2, int const n3,
+                         double const *rhs, int const *ncols,
+                         int **cols, double **JFD, int tid);
+       void relax_omp(double *dv, int const nvar, int const n1, int const n2, int const n3,
+                  double const *rhs, int const *ncols, int **cols, double **JFD);
+
        void Solve();
        void set_initial_guess(derivs v);
        int index(int i, int j, int k, int l, int a, int b, int c, int d);
@@ -116,23 +151,11 @@ public:
        double BY_KKofxyz(double x, double y, double z);
        void SetMatrix_JFD(int nvar, int n1, int n2, int n3, derivs u, int *ncols, int **cols, double **Matrix);
        void J_times_dv(int nvar, int n1, int n2, int n3, derivs dv, double *Jdv, derivs u);
-       void relax(double *dv, int const nvar, int const n1, int const n2, int const n3,
-                  double const *rhs, int const *ncols, int **cols, double **JFD);
-       void LineRelax_be(double *dv,
-                         int const i, int const k, int const nvar,
-                         int const n1, int const n2, int const n3,
-                         double const *rhs, int const *ncols, int **cols,
-                         double **JFD);
        void JFD_times_dv(int i, int j, int k, int nvar, int n1, int n2,
                          int n3, derivs dv, derivs u, double *values);
        void LinEquations(double A, double B, double X, double R,
                          double x, double r, double phi,
                          double y, double z, derivs dU, derivs U, double *values);
-       void LineRelax_al(double *dv,
-                         int const j, int const k, int const nvar,
-                         int const n1, int const n2, int const n3,
-                         double const *rhs, int const *ncols,
-                         int **cols, double **JFD);
        void ThomasAlgorithm(int N, double *b, double *a, double *c, double *x, double *q);
        void Save(char *fname);
        // provided by Vasileios Paschalidis (vpaschal@illinois.edu)
@@ -141,4 +164,4 @@ public:
        void SpecCoef(parameters par, int ivar, double *v, double *cf);
 };
 
-#endif /* TWO_PUNCTURES_H */
+#endif /* TWO_PUNCTURES_H */

AMSS_NCKU_source/bssnEM_class.C

@@ -258,6 +258,8 @@ void bssnEM_class::Initialize()
     PhysTime = StartTime;
     Setup_Black_Hole_position();
   }
+
+  setup_transfer_caches();
 }
 
 //================================================================================================

AMSS_NCKU_source/bssnEScalar_class.C

@@ -23,8 +23,14 @@ using namespace std;
 #include "rungekutta4_rout.h"
 #include "sommerfeld_rout.h"
 #include "getnp4.h"
-#include "shellfunctions.h"
-#include "parameters.h"
+#include "shellfunctions.h"
+#include "parameters.h"
+
+#if BSSN_USE_ESCALAR_C_KERNEL
+#define BSSN_ESCALAR_RHS f_compute_rhs_bssn_escalar_c
+#else
+#define BSSN_ESCALAR_RHS f_compute_rhs_bssn_escalar
+#endif
 
 #ifdef With_AHF
 #include "derivatives.h"
@@ -74,8 +80,8 @@ bssnEScalar_class::bssnEScalar_class(double Couranti, double StartTimei, double
 
 //================================================================================================
 
-void bssnEScalar_class::Initialize()
-{
+void bssnEScalar_class::Initialize()
+{
   Sphio = new var("Sphio", ngfs++, 1, 1, 1);
   Spio = new var("Spio", ngfs++, 1, 1, 1);
   Sphi0 = new var("Sphi0", ngfs++, 1, 1, 1);
@@ -132,11 +138,14 @@ void bssnEScalar_class::Initialize()
       }
     } 
    
-  GH = new cgh(0, ngfs, Symmetry, pname, checkrun, ErrorMonitor);
-  if (checkrun)
-    CheckPoint->readcheck_cgh(PhysTime, GH, myrank, nprocs, Symmetry);
-  else
-    GH->compose_cgh(nprocs);
+  GH = new cgh(0, ngfs, Symmetry, pname, checkrun, ErrorMonitor);
+  ConstraintRefreshLevels = new int[GH->levels];
+  for (int il = 0; il < GH->levels; il++)
+    ConstraintRefreshLevels[il] = 0;
+  if (checkrun)
+    CheckPoint->readcheck_cgh(PhysTime, GH, myrank, nprocs, Symmetry);
+  else
+    GH->compose_cgh(nprocs);
 
 #ifdef WithShell
   SH = new ShellPatch(0, ngfs, pname, Symmetry, myrank, ErrorMonitor);
@@ -160,12 +169,14 @@ void bssnEScalar_class::Initialize()
   {
     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();
-  }
-}
+  else
+  {
+    PhysTime = StartTime;
+    Setup_Black_Hole_position();
+  }
+
+  setup_transfer_caches();
+}
 
 //================================================================================================
 
@@ -207,10 +218,10 @@ bssnEScalar_class::~bssnEScalar_class()
 
 // Read initial data solved by Ansorg, PRD 70, 064011 (2004)
 
-void bssnEScalar_class::Read_Ansorg()
-{
-  if (!checkrun)
-  {
+void bssnEScalar_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!!" 
@@ -227,9 +238,12 @@ void bssnEScalar_class::Read_Ansorg()
         cout << "Error inputpar" << endl;
         exit(0);
       }
-    }
-    int BH_NM;
-    double *Porg_here;
+    }
+    int BH_NM;
+    double *Porg_here;
+    double *pmom_local;
+    double *spin_local;
+    double *mass_local;
     // read parameter from file
     {
       const int LEN = 256;
@@ -269,11 +283,11 @@ void bssnEScalar_class::Read_Ansorg()
       }
       inf.close();
     }
-
-    Porg_here = new double[3 * BH_NM];
-    Pmom = new double[3 * BH_NM];
-    Spin = new double[3 * BH_NM];
-    Mass = new double[BH_NM];
+
+    Porg_here = new double[3 * BH_NM];
+    pmom_local = new double[3 * BH_NM];
+    spin_local = new double[3 * BH_NM];
+    mass_local = new double[BH_NM];
     // read parameter from file
     {
       const int LEN = 256;
@@ -305,37 +319,37 @@ void bssnEScalar_class::Read_Ansorg()
         else if (status == 0)
           continue;
 
-        if (sgrp == "BSSN" && sind < BH_NM)
-        {
-          if (skey == "Mass")
-            Mass[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[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();
+        if (sgrp == "BSSN" && sind < BH_NM)
+        {
+          if (skey == "Mass")
+            mass_local[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_local[sind * 3] = atof(sval.c_str());
+          else if (skey == "Spiny")
+            spin_local[sind * 3 + 1] = atof(sval.c_str());
+          else if (skey == "Spinz")
+            spin_local[sind * 3 + 2] = atof(sval.c_str());
+          else if (skey == "Pmomx")
+            pmom_local[sind * 3] = atof(sval.c_str());
+          else if (skey == "Pmomy")
+            pmom_local[sind * 3 + 1] = atof(sval.c_str());
+          else if (skey == "Pmomz")
+            pmom_local[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++)
-    {
+    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)
       {
@@ -358,21 +372,21 @@ void bssnEScalar_class::Read_Ansorg()
                                       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[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
-                                      Mass, Porg_here, Pmom, Spin, BH_NM);
+                                      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[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
+                                      mass_local, Porg_here, pmom_local, spin_local, BH_NM);
           }
           if (BL == Pp->data->ble)
             break;
           BL = BL->next;
-        }
-        Pp = Pp->next;
-      }
-    }
-#ifdef WithShell
-    // ShellPatch part
+        }
+        Pp = Pp->next;
+      }
+    }
+#ifdef WithShell
+    // ShellPatch part
     MyList<ss_patch> *Pp = SH->PatL;
     while (Pp)
     {
@@ -400,25 +414,28 @@ void bssnEScalar_class::Read_Ansorg()
                                        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[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
-                                       Mass, Porg_here, Pmom, Spin, BH_NM);
+                                       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[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
+                                       mass_local, Porg_here, pmom_local, spin_local, BH_NM);
         }
         if (BL == Pp->data->ble)
           break;
         BL = BL->next;
-      }
-      Pp = Pp->next;
-    }
-#endif
-
-    delete[] Porg_here;
-    // dump read_in initial data
-    //   for(int lev=0;lev<GH->levels;lev++) Parallel::Dump_Data(GH->PatL[lev],StateList,0,PhysTime,dT);
-  }
-}
+      }
+      Pp = Pp->next;
+    }
+#endif
+
+    delete[] Porg_here;
+    delete[] pmom_local;
+    delete[] spin_local;
+    delete[] mass_local;
+    // dump read_in initial data
+    //   for(int lev=0;lev<GH->levels;lev++) Parallel::Dump_Data(GH->PatL[lev],StateList,0,PhysTime,dT);
+  }
+}
 
 //================================================================================================
 
@@ -432,10 +449,10 @@ void bssnEScalar_class::Read_Ansorg()
 
 // Read initial data solved by Pablo's Olliptic Phys.Rev.D 82 024005 (2010)
 
-void bssnEScalar_class::Read_Pablo()
-{
-  if (!checkrun)
-  {
+void bssnEScalar_class::Read_Pablo()
+{
+  if (!checkrun)
+  {
     if (myrank == 0)
       cout << "Read initial data from Pablo's solver,"
            << " please be sure the input parameters for black holes are puncture parameters!!" 
@@ -452,9 +469,12 @@ void bssnEScalar_class::Read_Pablo()
         cout << "Error inputpar" << endl;
         exit(0);
       }
-    }
-    int BH_NM;
-    double *Porg_here;
+    }
+    int BH_NM;
+    double *Porg_here;
+    double *pmom_local;
+    double *spin_local;
+    double *mass_local;
     // read parameter from file
     {
       const int LEN = 256;
@@ -494,11 +514,11 @@ void bssnEScalar_class::Read_Pablo()
       }
       inf.close();
     }
-
-    Porg_here = new double[3 * BH_NM];
-    Pmom = new double[3 * BH_NM];
-    Spin = new double[3 * BH_NM];
-    Mass = new double[BH_NM];
+
+    Porg_here = new double[3 * BH_NM];
+    pmom_local = new double[3 * BH_NM];
+    spin_local = new double[3 * BH_NM];
+    mass_local = new double[BH_NM];
     // read parameter from file
     {
       const int LEN = 256;
@@ -530,31 +550,31 @@ void bssnEScalar_class::Read_Pablo()
         else if (status == 0)
           continue;
 
-        if (sgrp == "BSSN" && sind < BH_NM)
-        {
-          if (skey == "Mass")
-            Mass[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[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();
+        if (sgrp == "BSSN" && sind < BH_NM)
+        {
+          if (skey == "Mass")
+            mass_local[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_local[sind * 3] = atof(sval.c_str());
+          else if (skey == "Spiny")
+            spin_local[sind * 3 + 1] = atof(sval.c_str());
+          else if (skey == "Spinz")
+            spin_local[sind * 3 + 2] = atof(sval.c_str());
+          else if (skey == "Pmomx")
+            pmom_local[sind * 3] = atof(sval.c_str());
+          else if (skey == "Pmomy")
+            pmom_local[sind * 3 + 1] = atof(sval.c_str());
+          else if (skey == "Pmomz")
+            pmom_local[sind * 3 + 2] = atof(sval.c_str());
+        }
+      }
+      inf.close();
     }
     bool flag = false;
     int DIM = dim;
@@ -594,11 +614,11 @@ void bssnEScalar_class::Read_Pablo()
                                         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[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
-                                        Mass, Porg_here, Pmom, Spin, BH_NM);
+                                        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[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
+                                        mass_local, Porg_here, pmom_local, spin_local, BH_NM);
             }
             if (BL == Pp->data->ble)
               break;
@@ -658,11 +678,11 @@ void bssnEScalar_class::Read_Pablo()
                                          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[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
-                                         Mass, Porg_here, Pmom, Spin, BH_NM);
+                                         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[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
+                                         mass_local, Porg_here, pmom_local, spin_local, BH_NM);
           }
           if (BL == Pp->data->ble)
             break;
@@ -684,10 +704,13 @@ void bssnEScalar_class::Read_Pablo()
       Pp = Pp->next;
     }
 #endif
-
-    delete[] Porg_here;
-    if (flag && myrank == 0)
-      MPI_Abort(MPI_COMM_WORLD, 1);
+
+    delete[] Porg_here;
+    delete[] pmom_local;
+    delete[] spin_local;
+    delete[] mass_local;
+    if (flag && myrank == 0)
+      MPI_Abort(MPI_COMM_WORLD, 1);
     // dump read_in initial data
     for (int lev = 0; lev < GH->levels; lev++)
       Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT);
@@ -739,10 +762,10 @@ void bssnEScalar_class::Step(int lev, int YN)
                      cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
-        if (f_compute_rhs_bssn_escalar(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],
+        if (BSSN_ESCALAR_RHS(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],
@@ -993,11 +1016,12 @@ void bssnEScalar_class::Step(int lev, int YN)
   }
 #endif
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  Parallel::AsyncSyncState async_pre;
+  sync_predictor_start(lev, SynchList_pre, async_pre);
 
-#ifdef WithShell
-  if (lev == 0)
-  {
+#ifdef WithShell
+  if (lev == 0)
+  {
     clock_t prev_clock, curr_clock;
     if (myrank == 0)
       curr_clock = clock();
@@ -1009,9 +1033,10 @@ void bssnEScalar_class::Step(int lev, int YN)
       cout << " Shell stuff synchronization used " 
            << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
            << " seconds! " << endl;
-    }
-  }
-#endif
+    }
+  }
+#endif
+  sync_predictor_finish(lev, async_pre, SynchList_pre);
 
   // for black hole position
   if (BH_num > 0 && lev == GH->levels - 1)
@@ -1081,10 +1106,10 @@ void bssnEScalar_class::Step(int lev, int YN)
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #endif
 
-          if (f_compute_rhs_bssn_escalar(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],
+          if (BSSN_ESCALAR_RHS(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],
@@ -1349,11 +1374,12 @@ void bssnEScalar_class::Step(int lev, int YN)
     }
 #endif
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    Parallel::AsyncSyncState async_cor;
+    sync_corrector_start(lev, SynchList_cor, async_cor);
 
-#ifdef WithShell
-    if (lev == 0)
-    {
+#ifdef WithShell
+    if (lev == 0)
+    {
       clock_t prev_clock, curr_clock;
       if (myrank == 0)
         curr_clock = clock();
@@ -1365,9 +1391,10 @@ void bssnEScalar_class::Step(int lev, int YN)
         cout << " Shell stuff synchronization used " 
              << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
              << " seconds! " << endl;
-      }
-    }
-#endif
+      }
+    }
+#endif
+    sync_corrector_finish(lev, async_cor, SynchList_cor);
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
     {
@@ -1835,11 +1862,14 @@ void bssnEScalar_class::AnalysisStuff_EScalar(int lev, double dT_lev)
 
 //================================================================================================
 
-void bssnEScalar_class::Interp_Constraint()
-{
-  // we do not support a_lev != 0 yet.
-  if (a_lev > 0)
-    return;
+void bssnEScalar_class::Interp_Constraint(bool infg)
+{
+  if (!infg)
+    return;
+
+  // we do not support a_lev != 0 yet.
+  if (a_lev > 0)
+    return;
 
   for (int lev = 0; lev < GH->levels; lev++)
   {
@@ -1858,10 +1888,10 @@ void bssnEScalar_class::Interp_Constraint()
           if (myrank == cg->rank)
           {
             if (lev > 0)
-              f_compute_rhs_bssn_escalar(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],
+              BSSN_ESCALAR_RHS(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],
@@ -2078,10 +2108,10 @@ void bssnEScalar_class::Constraint_Out()
             if (myrank == cg->rank)
             {
               if (lev > 0)
-                f_compute_rhs_bssn_escalar(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],
+                BSSN_ESCALAR_RHS(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],

AMSS_NCKU_source/bssnEScalar_class.h

@@ -51,7 +51,7 @@ public:
      void Compute_Psi4(int lev);
      void Step(int lev, int YN);
      void AnalysisStuff_EScalar(int lev, double dT_lev);
-     void Interp_Constraint();
+     void Interp_Constraint(bool infg);
      void Constraint_Out(); 
 
 protected:

AMSS_NCKU_source/bssn_class.h

@@ -31,11 +31,19 @@ using namespace std;
 #include "surface_integral.h"
 #include "checkpoint.h"
 
-extern void setpbh(int iBHN, double **iPBH, double *iMass, int rBHN);
-
-class bssn_class
-{
-public:
+extern void setpbh(int iBHN, double **iPBH, double *iMass, int rBHN);
+
+#ifndef BSSN_USE_TRANSFER_CACHE
+#define BSSN_USE_TRANSFER_CACHE 1
+#endif
+
+#ifndef BSSN_USE_ESCALAR_C_KERNEL
+#define BSSN_USE_ESCALAR_C_KERNEL 1
+#endif
+
+class bssn_class
+{
+public:
        int ngfs;
        int nprocs, myrank;
        cgh *GH;
@@ -45,10 +53,11 @@ public:
        int checkrun;
        char checkfilename[50];
        int Steps;
-       double StartTime, TotalTime;
-       double AnasTime, DumpTime, d2DumpTime, CheckTime;
-       double LastAnas, LastConsOut;
-       double Courant;
+       double StartTime, TotalTime;
+       double AnasTime, DumpTime, d2DumpTime, CheckTime;
+       double LastAnas, LastConsOut;
+       int *ConstraintRefreshLevels;
+       double Courant;
        double numepss, numepsb, numepsh;
        int Symmetry;
        int maxl, decn;
@@ -126,9 +135,16 @@ public:
        MyList<var> *OldStateList, *DumpList;
        MyList<var> *ConstraintList;
 
-       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
-       monitor *ConVMonitor;
-       surface_integral *Waveshell;
+       Parallel::SyncCache *sync_cache_pre;  // per-level cache for predictor sync
+       Parallel::SyncCache *sync_cache_cor;  // per-level cache for corrector sync
+       Parallel::SyncCache *sync_cache_rp_coarse;  // RestrictProlong sync on PatL[lev-1]
+       Parallel::SyncCache *sync_cache_rp_fine;    // RestrictProlong sync on PatL[lev]
+       Parallel::SyncCache *sync_cache_restrict;   // cached Restrict in RestrictProlong
+       Parallel::SyncCache *sync_cache_outbd;      // cached OutBdLow2Hi in RestrictProlong
+
+       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
+       monitor *ConVMonitor, *TimingMonitor;
+       surface_integral *Waveshell;
        checkpoint *CheckPoint;
 
 public:
@@ -159,14 +175,25 @@ public:
        void Setup_KerrSchild();
        void Enforce_algcon(int lev, int fg);
 
-       void testRestrict();
-       void testOutBd();
-       
-       bool check_Stdin_Abort(); 
-
-       virtual void Setup_Initial_Data_Cao();
-       virtual void Setup_Initial_Data_Lousto();
-       virtual void Initialize();
+       void testRestrict();
+       void testOutBd();
+       
+       bool check_Stdin_Abort(); 
+       bool use_transfer_cache() const;
+       void setup_transfer_caches();
+       void invalidate_transfer_caches();
+       void destroy_transfer_caches();
+       void sync_predictor_start(int lev, MyList<var> *VarList, Parallel::AsyncSyncState &async_state);
+       void sync_predictor_finish(int lev, Parallel::AsyncSyncState &async_state, MyList<var> *VarList);
+       void sync_corrector_start(int lev, MyList<var> *VarList, Parallel::AsyncSyncState &async_state);
+       void sync_corrector_finish(int lev, Parallel::AsyncSyncState &async_state, MyList<var> *VarList);
+       void sync_evolution(int lev, MyList<var> *VarList, Parallel::SyncCache *cache_array = 0);
+       void restrict_evolution(int lev, MyList<var> *src_var_list, MyList<var> *dst_var_list);
+       void outbdlow2hi_evolution(int lev, MyList<var> *src_var_list, MyList<var> *dst_var_list);
+
+       virtual void Setup_Initial_Data_Cao();
+       virtual void Setup_Initial_Data_Lousto();
+       virtual void Initialize();
        virtual void Read_Ansorg();
        virtual void Read_Pablo() {};
        virtual void Compute_Psi4(int lev);

AMSS_NCKU_source/bssn_escalar_rhs_c.C

@@ -0,0 +1,169 @@
+#include "macrodef.h"
+#include "bssn_rhs.h"
+#include "share_func.h"
+#include "tool.h"
+#include <vector>
+
+namespace
+{
+    // Reuse the temporary workspace across block calls to avoid repeated heap churn
+    // in the EScalar wrapper. MPI ranks execute this path sequentially, so a single
+    // process-local buffer is sufficient here.
+    std::vector<double> g_escalar_tmp_store;
+}
+
+#ifdef fortran1
+#define f_frpotential frpotential
+#endif
+#ifdef fortran2
+#define f_frpotential FRPOTENTIAL
+#endif
+#ifdef fortran3
+#define f_frpotential frpotential_
+#endif
+
+extern "C"
+{
+    void f_frpotential(int *, double *, double *, double *);
+}
+
+int f_compute_rhs_bssn_escalar_c(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 *Sphi, double *Spi,
+                                 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 *Sphi_rhs, double *Spi_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)
+{
+    const int nx = ex[0], ny = ex[1], nz = ex[2];
+    const int all = nx * ny * nz;
+
+    const size_t workspace_size = size_t(all) * 17;
+    if (g_escalar_tmp_store.size() < workspace_size)
+        g_escalar_tmp_store.resize(workspace_size);
+
+    double *tmp_ptr = g_escalar_tmp_store.data();
+    auto alloc_tmp = [&](int n = 1) -> double *
+    {
+        double *ptr = tmp_ptr;
+        tmp_ptr += size_t(all) * n;
+        return ptr;
+    };
+
+    double *chix = alloc_tmp(), *chiy = alloc_tmp(), *chiz = alloc_tmp();
+    double *Kx = alloc_tmp(), *Ky = alloc_tmp(), *Kz = alloc_tmp();
+    double *fxx = alloc_tmp(), *fxy = alloc_tmp(), *fxz = alloc_tmp();
+    double *fyy = alloc_tmp(), *fyz = alloc_tmp(), *fzz = alloc_tmp();
+    double *Lapx = alloc_tmp(), *Lapy = alloc_tmp(), *Lapz = alloc_tmp();
+    double *V = alloc_tmp(), *dVdSphi = alloc_tmp();
+
+    const double ZEO = 0.0, ONE = 1.0, TWO = 2.0, HALF = 0.5;
+    const double SSS[3] = {1.0, 1.0, 1.0};
+
+    fderivs(ex, chi, chix, chiy, chiz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, Lap, Lapx, Lapy, Lapz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, Sphi, Kx, Ky, Kz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fdderivs(ex, Sphi, fxx, fxy, fxz, fyy, fyz, fzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+
+    f_frpotential(ex, Sphi, V, dVdSphi);
+
+    for (int i = 0; i < all; ++i)
+    {
+        const double alpn1 = Lap[i] + ONE;
+        const double chin1 = chi[i] + ONE;
+        const double gxx = dxx[i] + ONE;
+        const double gyy = dyy[i] + ONE;
+        const double gzz = dzz[i] + ONE;
+        const double det = gxx * gyy * gzz + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i]
+                         - gxz[i] * gyy * gxz[i] - gxy[i] * gxy[i] * gzz - gxx * gyz[i] * gyz[i];
+        const double gupxx = (gyy * gzz - gyz[i] * gyz[i]) / det;
+        const double gupxy = -(gxy[i] * gzz - gyz[i] * gxz[i]) / det;
+        const double gupxz = (gxy[i] * gyz[i] - gyy * gxz[i]) / det;
+        const double gupyy = (gxx * gzz - gxz[i] * gxz[i]) / det;
+        const double gupyz = -(gxx * gyz[i] - gxy[i] * gxz[i]) / det;
+        const double gupzz = (gxx * gyy - gxy[i] * gxy[i]) / det;
+
+        Sphi_rhs[i] = alpn1 * Spi[i];
+
+        Spi_rhs[i] = gupxx * fxx[i] + gupyy * fyy[i] + gupzz * fzz[i]
+                   + TWO * (gupxy * fxy[i] + gupxz * fxz[i] + gupyz * fyz[i])
+                   - ((Gamx[i] + (gupxx * chix[i] + gupxy * chiy[i] + gupxz * chiz[i]) / TWO / chin1) * Kx[i]
+                   +  (Gamy[i] + (gupxy * chix[i] + gupyy * chiy[i] + gupyz * chiz[i]) / TWO / chin1) * Ky[i]
+                   +  (Gamz[i] + (gupxz * chix[i] + gupyz * chiy[i] + gupzz * chiz[i]) / TWO / chin1) * Kz[i]);
+
+        Spi_rhs[i] = Spi_rhs[i] * alpn1
+                   + gupxx * Lapx[i] * Kx[i] + gupxy * Lapx[i] * Ky[i] + gupxz * Lapx[i] * Kz[i]
+                   + gupxy * Lapy[i] * Kx[i] + gupyy * Lapy[i] * Ky[i] + gupyz * Lapy[i] * Kz[i]
+                   + gupxz * Lapz[i] * Kx[i] + gupyz * Lapz[i] * Ky[i] + gupzz * Lapz[i] * Kz[i];
+
+        Spi_rhs[i] = Spi_rhs[i] * chin1 + alpn1 * (trK[i] * Spi[i] - dVdSphi[i]);
+
+        rho[i] = chin1 * ((gupxx * Kx[i] * Kx[i] + gupyy * Ky[i] * Ky[i] + gupzz * Kz[i] * Kz[i]) * HALF
+               + gupxy * Kx[i] * Ky[i] + gupxz * Kx[i] * Kz[i] + gupyz * Ky[i] * Kz[i])
+               + Spi[i] * Spi[i] * HALF + V[i];
+        Sx[i] = -Spi[i] * Kx[i];
+        Sy[i] = -Spi[i] * Ky[i];
+        Sz[i] = -Spi[i] * Kz[i];
+
+        const double pressure = (rho[i] - Spi[i] * Spi[i]) / chin1;
+        Sxx[i] = Kx[i] * Kx[i] - pressure * gxx;
+        Sxy[i] = Kx[i] * Ky[i] - pressure * gxy[i];
+        Sxz[i] = Kx[i] * Kz[i] - pressure * gxz[i];
+        Syy[i] = Ky[i] * Ky[i] - pressure * gyy;
+        Syz[i] = Ky[i] * Kz[i] - pressure * gyz[i];
+        Szz[i] = Kz[i] * Kz[i] - pressure * gzz;
+    }
+
+    if (f_compute_rhs_bssn(ex, T, X, Y, Z,
+                           chi, trK,
+                           dxx, gxy, gxz, dyy, gyz, dzz,
+                           Axx, Axy, Axz, Ayy, Ayz, Azz,
+                           Gamx, Gamy, Gamz,
+                           Lap, betax, betay, betaz,
+                           dtSfx, dtSfy, dtSfz,
+                           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,
+                           rho, Sx, Sy, Sz,
+                           Sxx, Sxy, Sxz, Syy, Syz, Szz,
+                           Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
+                           Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
+                           Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
+                           Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
+                           ham_Res, movx_Res, movy_Res, movz_Res,
+                           Gmx_Res, Gmy_Res, Gmz_Res,
+                           Symmetry, Lev, eps, co))
+        return 1;
+
+    lopsided_kodis(ex, X, Y, Z, Sphi, Sphi_rhs, betax, betay, betaz, Symmetry, SSS, eps);
+    lopsided_kodis(ex, X, Y, Z, Spi, Spi_rhs, betax, betay, betaz, Symmetry, SSS, eps);
+
+    for (int i = 0; i < all; ++i)
+    {
+        if (Sphi_rhs[i] != Sphi_rhs[i] || Spi_rhs[i] != Spi_rhs[i] || rho[i] != rho[i])
+            return 1;
+    }
+
+    return 0;
+}

AMSS_NCKU_source/bssn_rhs.h

@@ -22,19 +22,32 @@
 #define f_compute_rhs_Z4c_ss COMPUTE_RHS_Z4C_SS
 #define f_compute_constraint_fr COMPUTE_CONSTRAINT_FR
 #endif
-#ifdef fortran3
-#define f_compute_rhs_bssn compute_rhs_bssn_
+#ifdef fortran3
+#define f_compute_rhs_bssn compute_rhs_bssn_
 #define f_compute_rhs_bssn_ss compute_rhs_bssn_ss_
 #define f_compute_rhs_bssn_escalar compute_rhs_bssn_escalar_
 #define f_compute_rhs_bssn_escalar_ss compute_rhs_bssn_escalar_ss_
 #define f_compute_rhs_Z4c compute_rhs_z4c_
 #define f_compute_rhs_Z4cnot compute_rhs_z4cnot_
 #define f_compute_rhs_Z4c_ss compute_rhs_z4c_ss_
-#define f_compute_constraint_fr compute_constraint_fr_
-#endif
-extern "C"
-{
-        int f_compute_rhs_bssn(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
+#define f_compute_constraint_fr compute_constraint_fr_
+#endif
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif
+        void f_bssn_rhs_kernel_timing_reset();
+        int f_bssn_rhs_kernel_timing_bucket_count();
+        const double *f_bssn_rhs_kernel_timing_local_seconds();
+        const char *f_bssn_rhs_kernel_timing_label(int);
+#ifdef __cplusplus
+}
+#endif
+
+extern "C"
+{
+        int f_compute_rhs_bssn(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
                                double *, double *,                                                                                 // chi, trK
                                double *, double *, double *, double *, double *, double *,                                         // gij
                                double *, double *, double *, double *, double *, double *,                                         // Aij
@@ -50,13 +63,34 @@ extern "C"
                                double *, double *, double *, double *, double *, double *,                                         // Christoffel
                                double *, double *, double *, double *, double *, double *,                                         // Christoffel
                                double *, double *, double *, double *, double *, double *,                                         // Ricci
-                               double *, double *, double *, double *, double *, double *, double *,                               // constraint violation
-                               int &, int &, double &, int &);
-}
-
-extern "C"
-{
-        int f_compute_rhs_bssn_ss(int *, double &, double *, double *, double *,                                                      // ex,T,rho,sigma,R
+                               double *, double *, double *, double *, double *, double *, double *,                               // constraint violation
+                               int &, int &, double &, int &);
+}
+
+int f_compute_rhs_bssn_escalar_c(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
+                                 double *, double *,                                                                                 // chi, trK
+                                 double *, double *, double *, double *, double *, double *,                                         // gij
+                                 double *, double *, double *, double *, double *, double *,                                         // Aij
+                                 double *, double *, double *,                                                                       // Gam
+                                 double *, double *, double *, double *, double *, double *, double *,                               // Gauge
+                                 double *, double *,                                                                                 // Sphi, Spi
+                                 double *, double *,                                                                                 // chi, trK
+                                 double *, double *, double *, double *, double *, double *,                                         // gij
+                                 double *, double *, double *, double *, double *, double *,                                         // Aij
+                                 double *, double *, double *,                                                                       // Gam
+                                 double *, double *, double *, double *, double *, double *, double *,                               // Gauge
+                                 double *, double *,                                                                                 // Sphi, Spi
+                                 double *, double *, double *, double *, double *, double *, double *, double *, double *, double *, // stress-energy
+                                 double *, double *, double *, double *, double *, double *,                                         // Christoffel
+                                 double *, double *, double *, double *, double *, double *,                                         // Christoffel
+                                 double *, double *, double *, double *, double *, double *,                                         // Christoffel
+                                 double *, double *, double *, double *, double *, double *,                                         // Ricci
+                                 double *, double *, double *, double *, double *, double *, double *,                               // constraint violation
+                                 int &, int &, double &, int &);
+
+extern "C"
+{
+        int f_compute_rhs_bssn_ss(int *, double &, double *, double *, double *,                                                      // ex,T,rho,sigma,R
                                   double *, double *, double *,                                                                       // X,Y,Z
                                   double *, double *, double *,                                                                       // drhodx,drhody,drhodz
                                   double *, double *, double *,                                                                       // dsigmadx,dsigmady,dsigmadz
@@ -83,10 +117,10 @@ extern "C"
                                   int &, int &, double &, int &, int &);
 }
 
-extern "C"
-{
-        int f_compute_rhs_bssn_escalar(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
-                                       double *, double *,                                                                                 // chi, trK
+extern "C"
+{
+        int f_compute_rhs_bssn_escalar(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
+                                       double *, double *,                                                                                 // chi, trK
                                        double *, double *, double *, double *, double *, double *,                                         // gij
                                        double *, double *, double *, double *, double *, double *,                                         // Aij
                                        double *, double *, double *,                                                                       // Gam
@@ -103,14 +137,14 @@ extern "C"
                                        double *, double *, double *, double *, double *, double *,                                         // Christoffel
                                        double *, double *, double *, double *, double *, double *,                                         // Christoffel
                                        double *, double *, double *, double *, double *, double *,                                         // Ricci
-                                       double *, double *, double *, double *, double *, double *, double *,                               // constraint violation
-                                       int &, int &, double &, int &);
-}
-
-extern "C"
-{
-        int f_compute_rhs_bssn_escalar_ss(int *, double &, double *, double *, double *,                                                      // ex,T,rho,sigma,R
-                                          double *, double *, double *,                                                                       // X,Y,Z
+                                       double *, double *, double *, double *, double *, double *, double *,                               // constraint violation
+                                       int &, int &, double &, int &);
+}
+
+extern "C"
+{
+        int f_compute_rhs_bssn_escalar_ss(int *, double &, double *, double *, double *,                                                      // ex,T,rho,sigma,R
+                                          double *, double *, double *,                                                                       // X,Y,Z
                                           double *, double *, double *,                                                                       // drhodx,drhody,drhodz
                                           double *, double *, double *,                                                                       // dsigmadx,dsigmady,dsigmadz
                                           double *, double *, double *,                                                                       // dRdx,dRdy,dRdz

AMSS_NCKU_source/cgh.C

@@ -130,7 +130,11 @@ void cgh::compose_cgh(int nprocs)
   for (int lev = 0; lev < levels; lev++)
   {
     checkPatchList(PatL[lev], false);
+#ifdef INTERP_LB_OPTIMIZE
+    Parallel::distribute_optimize(PatL[lev], nprocs, ingfs, fngfs, false);
+#else
     Parallel::distribute(PatL[lev], nprocs, ingfs, fngfs, false);
+#endif
 #if (RPB == 1)
     // we need distributed box of PatL[lev] and PatL[lev-1]
     if (lev > 0)
@@ -1301,13 +1305,13 @@ bool cgh::Interp_One_Point(MyList<var> *VarList,
 }
 
 
-void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
+bool cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
                           MyList<var> *OldList, MyList<var> *StateList,
                           MyList<var> *FutureList, MyList<var> *tmList, bool BB,
                           monitor *ErrorMonitor)
 {
   if (lev < movls)
-    return;
+    return false;
 
 #if (0)
   // #if (PSTR == 1 || PSTR == 2)
@@ -1396,7 +1400,7 @@ void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, do
       for (bhi = 0; bhi < BH_num; bhi++)
         delete[] tmpPorg[bhi];
       delete[] tmpPorg;
-      return;
+      return false;
     }
     // x direction
     rr = (Porg0[bhi][0] - handle[lev][grd][0]) / dX;
@@ -1500,6 +1504,7 @@ void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, do
   for (int bhi = 0; bhi < BH_num; bhi++)
     delete[] tmpPorg[bhi];
   delete[] tmpPorg;
+  return tot_flag;
 }
 
 

AMSS_NCKU_source/cgh.h

@@ -74,7 +74,7 @@ public:
                                MyList<var> *OldList, MyList<var> *StateList,
                                MyList<var> *FutureList, MyList<var> *tmList,
                                int Symmetry, bool BB);
-   void Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
+   bool Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
                         MyList<var> *OldList, MyList<var> *StateList,
                         MyList<var> *FutureList, MyList<var> *tmList, bool BB,
                         monitor *ErrorMonitor);

AMSS_NCKU_source/diff_new.f90

@@ -69,10 +69,12 @@
   fy = ZEO
   fz = ZEO
 
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+!DIR$ UNROLL PARTIAL(4)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
-! x direction   
+! x direction
         if(i+1 <= imax .and. i-1 >= imin)then
 !
 !              - f(i-1) + f(i+1)
@@ -371,6 +373,8 @@
   fxz = ZEO
   fyz = ZEO
 
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+!DIR$ UNROLL PARTIAL(4)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1

AMSS_NCKU_source/diff_newwb.f90

@@ -33,7 +33,7 @@
   real*8 :: dX,dY,dZ
   real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
   real*8 :: d2dx,d2dy,d2dz
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -137,7 +137,7 @@
   real*8 :: dX
   real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
   real*8 :: d2dx
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -1512,8 +1512,9 @@
   real*8 :: dX,dY,dZ
   real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: i_core_min,i_core_max,j_core_min,j_core_max,k_core_min,k_core_max
+  real*8  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
   real*8  :: Sdxdy,Sdxdz,Sdydz,Fdxdy,Fdxdz,Fdydz
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0,  F45=4.5d1
@@ -1560,17 +1561,55 @@
 
   fxx = ZEO
   fyy = ZEO
-  fzz = ZEO
-  fxy = ZEO
-  fxz = ZEO
-  fyz = ZEO
-
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-!~~~~~~ fxx
-        if(i+2 <= imax .and. i-2 >= imin)then
-!
+  fzz = ZEO
+  fxy = ZEO
+  fxz = ZEO
+  fyz = ZEO
+
+  i_core_min = max(1, imin+2)
+  i_core_max = min(ex(1), imax-2)
+  j_core_min = max(1, jmin+2)
+  j_core_max = min(ex(2), jmax-2)
+  k_core_min = max(1, kmin+2)
+  k_core_max = min(ex(3), kmax-2)
+
+  if(i_core_min <= i_core_max .and. j_core_min <= j_core_max .and. k_core_min <= k_core_max)then
+   do k=k_core_min,k_core_max
+   do j=j_core_min,j_core_max
+   do i=i_core_min,i_core_max
+! interior points always use 4th-order stencils without branch checks
+      fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
+                          -fh(i+2,j,k)+F16*fh(i+1,j,k)              )
+      fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
+                          -fh(i,j+2,k)+F16*fh(i,j+1,k)              )
+      fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
+                          -fh(i,j,k+2)+F16*fh(i,j,k+1)              )
+      fxy(i,j,k) = Fdxdy*(     (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k))  &
+                          -F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k))  &
+                          +F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k))  &
+                          -    (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
+      fxz(i,j,k) = Fdxdz*(     (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2))  &
+                          -F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1))  &
+                          +F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1))  &
+                          -    (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
+      fyz(i,j,k) = Fdydz*(     (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2))  &
+                          -F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1))  &
+                          +F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1))  &
+                          -    (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
+   enddo
+   enddo
+   enddo
+  endif
+
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
+      if(i>=i_core_min .and. i<=i_core_max .and. &
+         j>=j_core_min .and. j<=j_core_max .and. &
+         k>=k_core_min .and. k<=k_core_max) cycle
+!~~~~~~ fxx
+        if(i+2 <= imax .and. i-2 >= imin)then
+!
 !               - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
 !  fxx(i) = ----------------------------------------------------------
 !                                  12 dx^2 

AMSS_NCKU_source/enforce_algebra.f90

@@ -18,49 +18,61 @@
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
 
 !~~~~~~~> Local variable:
-  
-  real*8, dimension(ex(1),ex(2),ex(3)) :: trA,detg
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
+
+  integer :: i,j,k
+  real*8 :: lgxx,lgyy,lgzz,ldetg
+  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
+  real*8 :: ltrA,lscale
   real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
 
 !~~~~~~>
 
-  gxx = dxx + ONE
-  gyy = dyy + ONE
-  gzz = dzz + ONE
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
 
-  detg =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
-          gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
-  gupxx =   ( gyy * gzz - gyz * gyz ) / detg
-  gupxy = - ( gxy * gzz - gyz * gxz ) / detg
-  gupxz =   ( gxy * gyz - gyy * gxz ) / detg
-  gupyy =   ( gxx * gzz - gxz * gxz ) / detg
-  gupyz = - ( gxx * gyz - gxy * gxz ) / detg
-  gupzz =   ( gxx * gyy - gxy * gxy ) / detg
+    lgxx = dxx(i,j,k) + ONE
+    lgyy = dyy(i,j,k) + ONE
+    lgzz = dzz(i,j,k) + ONE
 
-  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
-       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
+    ldetg =  lgxx * lgyy * lgzz &
+           + gxy(i,j,k) * gyz(i,j,k) * gxz(i,j,k) &
+           + gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) &
+           - gxz(i,j,k) * lgyy * gxz(i,j,k) &
+           - gxy(i,j,k) * gxy(i,j,k) * lgzz &
+           - lgxx * gyz(i,j,k) * gyz(i,j,k)
 
-  Axx = Axx - F1o3 * gxx * trA
-  Axy = Axy - F1o3 * gxy * trA
-  Axz = Axz - F1o3 * gxz * trA
-  Ayy = Ayy - F1o3 * gyy * trA
-  Ayz = Ayz - F1o3 * gyz * trA
-  Azz = Azz - F1o3 * gzz * trA
+    lgupxx =   ( lgyy * lgzz - gyz(i,j,k) * gyz(i,j,k) ) / ldetg
+    lgupxy = - ( gxy(i,j,k) * lgzz - gyz(i,j,k) * gxz(i,j,k) ) / ldetg
+    lgupxz =   ( gxy(i,j,k) * gyz(i,j,k) - lgyy * gxz(i,j,k) ) / ldetg
+    lgupyy =   ( lgxx * lgzz - gxz(i,j,k) * gxz(i,j,k) ) / ldetg
+    lgupyz = - ( lgxx * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / ldetg
+    lgupzz =   ( lgxx * lgyy - gxy(i,j,k) * gxy(i,j,k) ) / ldetg
 
-  detg = ONE / ( detg ** F1o3 ) 
-  
-  gxx = gxx * detg
-  gxy = gxy * detg
-  gxz = gxz * detg
-  gyy = gyy * detg
-  gyz = gyz * detg
-  gzz = gzz * detg
+    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
+                 + lgupzz * Azz(i,j,k) &
+         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
+                 + lgupyz * Ayz(i,j,k))
 
-  dxx = gxx - ONE
-  dyy = gyy - ONE
-  dzz = gzz - ONE
+    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
+    Axy(i,j,k) = Axy(i,j,k) - F1o3 * gxy(i,j,k) * ltrA
+    Axz(i,j,k) = Axz(i,j,k) - F1o3 * gxz(i,j,k) * ltrA
+    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
+    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * gyz(i,j,k) * ltrA
+    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
+
+    lscale = ONE / ( ldetg ** F1o3 )
+
+    dxx(i,j,k) = lgxx * lscale - ONE
+    gxy(i,j,k) = gxy(i,j,k) * lscale
+    gxz(i,j,k) = gxz(i,j,k) * lscale
+    dyy(i,j,k) = lgyy * lscale - ONE
+    gyz(i,j,k) = gyz(i,j,k) * lscale
+    dzz(i,j,k) = lgzz * lscale - ONE
+
+  enddo
+  enddo
+  enddo
 
   return
 
@@ -82,51 +94,71 @@
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
 
 !~~~~~~~> Local variable:
-  
-  real*8, dimension(ex(1),ex(2),ex(3)) :: trA
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
+
+  integer :: i,j,k
+  real*8 :: lgxx,lgyy,lgzz,lscale
+  real*8 :: lgxy,lgxz,lgyz
+  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
+  real*8 :: ltrA
   real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
 
 !~~~~~~>
 
-  gxx = dxx + ONE
-  gyy = dyy + ONE
-  gzz = dzz + ONE
-! for g
-  gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
-           gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
 
-  gupzz = ONE / ( gupzz ** F1o3 ) 
-  
-  gxx = gxx * gupzz
-  gxy = gxy * gupzz
-  gxz = gxz * gupzz
-  gyy = gyy * gupzz
-  gyz = gyz * gupzz
-  gzz = gzz * gupzz
+! for g: normalize determinant first
+    lgxx = dxx(i,j,k) + ONE
+    lgyy = dyy(i,j,k) + ONE
+    lgzz = dzz(i,j,k) + ONE
+    lgxy = gxy(i,j,k)
+    lgxz = gxz(i,j,k)
+    lgyz = gyz(i,j,k)
 
-  dxx = gxx - ONE
-  dyy = gyy - ONE
-  dzz = gzz - ONE
-! for A  
+    lscale =  lgxx * lgyy * lgzz + lgxy * lgyz * lgxz &
+            + lgxz * lgxy * lgyz - lgxz * lgyy * lgxz &
+            - lgxy * lgxy * lgzz - lgxx * lgyz * lgyz
 
-  gupxx =   ( gyy * gzz - gyz * gyz )
-  gupxy = - ( gxy * gzz - gyz * gxz )
-  gupxz =   ( gxy * gyz - gyy * gxz )
-  gupyy =   ( gxx * gzz - gxz * gxz )
-  gupyz = - ( gxx * gyz - gxy * gxz )
-  gupzz =   ( gxx * gyy - gxy * gxy )
+    lscale = ONE / ( lscale ** F1o3 )
 
-  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
-       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
+    lgxx = lgxx * lscale
+    lgxy = lgxy * lscale
+    lgxz = lgxz * lscale
+    lgyy = lgyy * lscale
+    lgyz = lgyz * lscale
+    lgzz = lgzz * lscale
 
-  Axx = Axx - F1o3 * gxx * trA
-  Axy = Axy - F1o3 * gxy * trA
-  Axz = Axz - F1o3 * gxz * trA
-  Ayy = Ayy - F1o3 * gyy * trA
-  Ayz = Ayz - F1o3 * gyz * trA
-  Azz = Azz - F1o3 * gzz * trA
+    dxx(i,j,k) = lgxx - ONE
+    gxy(i,j,k) = lgxy
+    gxz(i,j,k) = lgxz
+    dyy(i,j,k) = lgyy - ONE
+    gyz(i,j,k) = lgyz
+    dzz(i,j,k) = lgzz - ONE
+
+! for A: trace-free using normalized metric (det=1, no division needed)
+    lgupxx =   ( lgyy * lgzz - lgyz * lgyz )
+    lgupxy = - ( lgxy * lgzz - lgyz * lgxz )
+    lgupxz =   ( lgxy * lgyz - lgyy * lgxz )
+    lgupyy =   ( lgxx * lgzz - lgxz * lgxz )
+    lgupyz = - ( lgxx * lgyz - lgxy * lgxz )
+    lgupzz =   ( lgxx * lgyy - lgxy * lgxy )
+
+    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
+                 + lgupzz * Azz(i,j,k) &
+         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
+                 + lgupyz * Ayz(i,j,k))
+
+    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
+    Axy(i,j,k) = Axy(i,j,k) - F1o3 * lgxy * ltrA
+    Axz(i,j,k) = Axz(i,j,k) - F1o3 * lgxz * ltrA
+    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
+    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * lgyz * ltrA
+    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
+
+  enddo
+  enddo
+  enddo
 
   return
 

AMSS_NCKU_source/fdderivs_c.C

@@ -0,0 +1,332 @@
+#include "tool.h"
+void fdderivs(const int ex[3],
+              const double *f,
+              double *fxx, double *fxy, double *fxz,
+              double *fyy, double *fyz, double *fzz,
+              const double *X, const double *Y, const double *Z,
+              double SYM1, double SYM2, double SYM3,
+              int Symmetry, int onoff)
+{
+    (void)onoff;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1;
+    const double ZEO = 0.0, ONE = 1.0, TWO = 2.0;
+    const double F1o4   = 2.5e-1;          // 1/4
+    const double F8     = 8.0;
+    const double F16    = 16.0;
+    const double F30    = 30.0;
+    const double F1o12  = ONE / 12.0;
+    const double F1o144 = ONE / 144.0;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    int iminF = 1, jminF = 1, kminF = 1;
+    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1;
+    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1;
+    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1;
+
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    /* fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2 */
+    const size_t nx = (size_t)ex1 + 2;
+    const size_t ny = (size_t)ex2 + 2;
+    const size_t nz = (size_t)ex3 + 2;
+    const size_t fh_size = nx * ny * nz;
+
+    static double *fh = NULL;
+    static size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    // double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    symmetry_bd(2, ex, f, fh, SoA);
+
+    /* 系数：按 Fortran 原式 */
+    const double Sdxdx = ONE / (dX * dX);
+    const double Sdydy = ONE / (dY * dY);
+    const double Sdzdz = ONE / (dZ * dZ);
+
+    const double Fdxdx = F1o12 / (dX * dX);
+    const double Fdydy = F1o12 / (dY * dY);
+    const double Fdzdz = F1o12 / (dZ * dZ);
+
+    const double Sdxdy = F1o4 / (dX * dY);
+    const double Sdxdz = F1o4 / (dX * dZ);
+    const double Sdydz = F1o4 / (dY * dZ);
+
+    const double Fdxdy = F1o144 / (dX * dY);
+    const double Fdxdz = F1o144 / (dX * dZ);
+    const double Fdydz = F1o144 / (dY * dZ);
+
+    /* 只清零不被主循环覆盖的边界面 */
+    {
+        /* 高边界：k0=ex3-1 */
+        for (int j0 = 0; j0 < ex2; ++j0)
+            for (int i0 = 0; i0 < ex1; ++i0) {
+                const size_t p = idx_ex(i0, j0, ex3 - 1, ex);
+                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+            }
+        /* 高边界：j0=ex2-1 */
+        for (int k0 = 0; k0 < ex3 - 1; ++k0)
+            for (int i0 = 0; i0 < ex1; ++i0) {
+                const size_t p = idx_ex(i0, ex2 - 1, k0, ex);
+                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+            }
+        /* 高边界：i0=ex1-1 */
+        for (int k0 = 0; k0 < ex3 - 1; ++k0)
+            for (int j0 = 0; j0 < ex2 - 1; ++j0) {
+                const size_t p = idx_ex(ex1 - 1, j0, k0, ex);
+                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+            }
+
+        /* 低边界：当二阶模板也不可用时，对应 i0/j0/k0=0 面 */
+        if (kminF == 1) {
+            for (int j0 = 0; j0 < ex2; ++j0)
+                for (int i0 = 0; i0 < ex1; ++i0) {
+                    const size_t p = idx_ex(i0, j0, 0, ex);
+                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+                }
+        }
+        if (jminF == 1) {
+            for (int k0 = 0; k0 < ex3; ++k0)
+                for (int i0 = 0; i0 < ex1; ++i0) {
+                    const size_t p = idx_ex(i0, 0, k0, ex);
+                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+                }
+        }
+        if (iminF == 1) {
+            for (int k0 = 0; k0 < ex3; ++k0)
+                for (int j0 = 0; j0 < ex2; ++j0) {
+                    const size_t p = idx_ex(0, j0, k0, ex);
+                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+                }
+        }
+    }
+
+    /*
+     * 两段式：
+     * 1) 二阶可用区域先计算二阶模板
+     * 2) 高阶可用区域再覆盖四阶模板
+     */
+    const int i2_lo = (iminF > 0) ? iminF : 0;
+    const int j2_lo = (jminF > 0) ? jminF : 0;
+    const int k2_lo = (kminF > 0) ? kminF : 0;
+    const int i2_hi = ex1 - 2;
+    const int j2_hi = ex2 - 2;
+    const int k2_hi = ex3 - 2;
+
+    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+    const int i4_hi = ex1 - 3;
+    const int j4_hi = ex2 - 3;
+    const int k4_hi = ex3 - 3;
+
+    /*
+     * Strategy A:
+     * Avoid redundant work in overlap of 2nd/4th-order regions.
+     * Only compute 2nd-order on shell points that are NOT overwritten by
+     * the 4th-order pass.
+     */
+    const int has4 = (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi);
+
+    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                    if (has4 &&
+                        i0 >= i4_lo && i0 <= i4_hi &&
+                        j0 >= j4_lo && j0 <= j4_hi &&
+                        k0 >= k4_lo && k0 <= k4_hi) {
+                        continue;
+                    }
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    fxx[p] = Sdxdx * (
+                        fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
+                        TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
+                        fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+
+                    fyy[p] = Sdydy * (
+                        fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
+                        TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
+                        fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+
+                    fzz[p] = Sdzdz * (
+                        fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
+                        TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
+                        fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+
+                    fxy[p] = Sdxdy * (
+                        fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] -
+                        fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] -
+                        fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +
+                        fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
+                    );
+
+                    fxz[p] = Sdxdz * (
+                        fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] -
+                        fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] -
+                        fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +
+                        fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
+                    );
+
+                    fyz[p] = Sdydz * (
+                        fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] -
+                        fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] -
+                        fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] +
+                        fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
+                    );
+                }
+            }
+        }
+    }
+
+    if (has4) {
+        for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    fxx[p] = Fdxdx * (
+                        -fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+
+                    fyy[p] = Fdydy * (
+                        -fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+
+                    fzz[p] = Fdzdz * (
+                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+
+                    {
+                        const double t_jm2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)] );
+
+                        const double t_jm1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)] );
+
+                        const double t_jp1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)] );
+
+                        const double t_jp2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)] );
+
+                        fxy[p] = Fdxdy * ( t_jm2 - F8 * t_jm1 + F8 * t_jp1 - t_jp2 );
+                    }
+
+                    {
+                        const double t_km2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)] );
+
+                        const double t_km1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)] );
+
+                        const double t_kp1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)] );
+
+                        const double t_kp2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)] );
+
+                        fxz[p] = Fdxdz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
+                    }
+
+                    {
+                        const double t_km2 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)] );
+
+                        const double t_km1 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)] );
+
+                        const double t_kp1 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)] );
+
+                        const double t_kp2 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)] );
+
+                        fyz[p] = Fdydz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
+                    }
+                }
+            }
+        }
+    }
+
+    // free(fh);
+}

AMSS_NCKU_source/fderivs_c.C

@@ -0,0 +1,167 @@
+#include "tool.h"
+
+/*
+ * C 版 fderivs
+ *
+ * Fortran:
+ * subroutine fderivs(ex,f,fx,fy,fz,X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
+ *
+ * 约定：
+ *   f, fx, fy, fz: ex1*ex2*ex3，按 idx_ex 布局
+ *   X: ex1, Y: ex2, Z: ex3
+ */
+void fderivs(const int ex[3],
+             const double *f,
+             double *fx, double *fy, double *fz,
+             const double *X, const double *Y, const double *Z,
+             double SYM1, double SYM2, double SYM3,
+             int Symmetry, int onoff)
+{
+    (void)onoff; // Fortran 里没用到
+
+    const double ZEO = 0.0, ONE = 1.0;
+    const double TWO = 2.0, EIT = 8.0;
+    const double F12 = 12.0;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1; // OCTANT=2 在本子程序里不直接用
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    // dX = X(2)-X(1) -> C: X[1]-X[0]
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    // Fortran 1-based bounds
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    int iminF = 1, jminF = 1, kminF = 1;
+    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1;
+    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1;
+    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1;
+
+    // SoA(1:3) = SYM1,SYM2,SYM3
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    // fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2
+    const size_t nx = (size_t)ex1 + 2;
+    const size_t ny = (size_t)ex2 + 2;
+    const size_t nz = (size_t)ex3 + 2;
+    const size_t fh_size = nx * ny * nz;
+    static double *fh = NULL;
+    static size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    // double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    // call symmetry_bd(2,ex,f,fh,SoA)
+    symmetry_bd(2, ex, f, fh, SoA);
+
+    const double d12dx = ONE / F12 / dX;
+    const double d12dy = ONE / F12 / dY;
+    const double d12dz = ONE / F12 / dZ;
+
+    const double d2dx  = ONE / TWO / dX;
+    const double d2dy  = ONE / TWO / dY;
+    const double d2dz  = ONE / TWO / dZ;
+
+    // fx = fy = fz = 0
+    const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+    for (size_t p = 0; p < all; ++p) {
+        fx[p] = ZEO;
+        fy[p] = ZEO;
+        fz[p] = ZEO;
+    }
+
+    /*
+     * 两段式：
+     * 1) 先在二阶可用区域计算二阶模板
+     * 2) 再在高阶可用区域覆盖为四阶模板
+     *
+     * 与原 if/elseif 逻辑等价，但减少逐点分支判断。
+     */
+    const int i2_lo = (iminF > 0) ? iminF : 0;
+    const int j2_lo = (jminF > 0) ? jminF : 0;
+    const int k2_lo = (kminF > 0) ? kminF : 0;
+    const int i2_hi = ex1 - 2;
+    const int j2_hi = ex2 - 2;
+    const int k2_hi = ex3 - 2;
+
+    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+    const int i4_hi = ex1 - 3;
+    const int j4_hi = ex2 - 3;
+    const int k4_hi = ex3 - 3;
+
+    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    fx[p] = d2dx * (
+                        -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+
+                    fy[p] = d2dy * (
+                        -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+
+                    fz[p] = d2dz * (
+                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+                }
+            }
+        }
+    }
+
+    if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
+        for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    fx[p] = d12dx * (
+                        fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] -
+                        EIT * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
+                        EIT * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)]
+                    );
+
+                    fy[p] = d12dy * (
+                        fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] -
+                        EIT * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
+                        EIT * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)]
+                    );
+
+                    fz[p] = d12dz * (
+                        fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] -
+                        EIT * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
+                        EIT * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)]
+                    );
+                }
+            }
+        }
+    }
+
+    // free(fh);
+}

AMSS_NCKU_source/fmisc.f90

@@ -324,7 +324,6 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -350,7 +349,6 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -379,7 +377,6 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -886,14 +883,17 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
    enddo
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(:,-i,1:extc(3)) = funcc(:,i+1,1:extc(3))*SoA(2)
    enddo
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
    enddo
@@ -912,7 +912,6 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -941,7 +940,6 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -1113,105 +1111,294 @@ end subroutine d2dump
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-! common code for cell and vertex
-!------------------------------------------------------------------------------
-! Lagrangian polynomial interpolation
-!------------------------------------------------------------------------------
-
-  subroutine polint(xa,ya,x,y,dy,ordn)
-
-  implicit none
-
-!~~~~~~> Input Parameter:
-  integer,intent(in) :: ordn
-  real*8, dimension(ordn), intent(in) :: xa,ya
+! common code for cell and vertex
+!------------------------------------------------------------------------------
+! Lagrangian polynomial interpolation
+!------------------------------------------------------------------------------
+#ifndef POLINT6_USE_BARYCENTRIC
+#define POLINT6_USE_BARYCENTRIC 1
+#endif
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_neville
+  subroutine polint6_neville(xa, ya, x, y, dy)
+  implicit none
+
+  real*8, dimension(6), intent(in) :: xa, ya
+  real*8, intent(in) :: x
+  real*8, intent(out) :: y, dy
+
+  integer :: i, m, ns, n_m
+  real*8, dimension(6) :: c, d, ho
+  real*8 :: dif, dift, hp, h, den_val
+
+  c = ya
+  d = ya
+  ho = xa - x
+
+  ns = 1
+  dif = abs(x - xa(1))
+
+  do i = 2, 6
+    dift = abs(x - xa(i))
+    if (dift < dif) then
+      ns = i
+      dif = dift
+    end if
+  end do
+
+  y = ya(ns)
+  ns = ns - 1
+
+  do m = 1, 5
+    n_m = 6 - m
+    do i = 1, n_m
+      hp = ho(i)
+      h  = ho(i+m)
+      den_val = hp - h
+
+      if (den_val == 0.0d0) then
+        write(*,*) 'failure in polint for point',x
+        write(*,*) 'with input points: ',xa
+        stop
+      end if
+
+      den_val = (c(i+1) - d(i)) / den_val
+
+      d(i) = h * den_val
+      c(i) = hp * den_val
+    end do
+
+    if (2 * ns < n_m) then
+      dy = c(ns + 1)
+    else
+      dy = d(ns)
+      ns = ns - 1
+    end if
+    y = y + dy
+  end do
+
+  return
+  end subroutine polint6_neville
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_barycentric
+  subroutine polint6_barycentric(xa, ya, x, y, dy)
+  implicit none
+
+  real*8, dimension(6), intent(in) :: xa, ya
+  real*8, intent(in) :: x
+  real*8, intent(out) :: y, dy
+
+  integer :: i, j
+  logical :: is_uniform
+  real*8, dimension(6) :: lambda
+  real*8 :: dx, den_i, term, num, den, step, tol
+  real*8, parameter :: c_uniform(6) = (/ -1.d0, 5.d0, -10.d0, 10.d0, -5.d0, 1.d0 /)
+
+  do i = 1, 6
+    if (x == xa(i)) then
+      y = ya(i)
+      dy = 0.d0
+      return
+    end if
+  end do
+
+  step = xa(2) - xa(1)
+  is_uniform = (step /= 0.d0)
+  if (is_uniform) then
+    tol = 64.d0 * epsilon(1.d0) * max(1.d0, abs(step))
+    do i = 3, 6
+      if (abs((xa(i) - xa(i-1)) - step) > tol) then
+        is_uniform = .false.
+        exit
+      end if
+    end do
+  end if
+
+  if (is_uniform) then
+    num = 0.d0
+    den = 0.d0
+    do i = 1, 6
+      term = c_uniform(i) / (x - xa(i))
+      num = num + term * ya(i)
+      den = den + term
+    end do
+    y = num / den
+    dy = 0.d0
+    return
+  end if
+
+  do i = 1, 6
+    den_i = 1.d0
+    do j = 1, 6
+      if (j /= i) then
+        dx = xa(i) - xa(j)
+        if (dx == 0.0d0) then
+          write(*,*) 'failure in polint for point',x
+          write(*,*) 'with input points: ',xa
+          stop
+        end if
+        den_i = den_i * dx
+      end if
+    end do
+    lambda(i) = 1.d0 / den_i
+  end do
+
+  num = 0.d0
+  den = 0.d0
+  do i = 1, 6
+    term = lambda(i) / (x - xa(i))
+    num = num + term * ya(i)
+    den = den + term
+  end do
+
+  y = num / den
+  dy = 0.d0
+
+  return
+  end subroutine polint6_barycentric
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint
+  subroutine polint(xa, ya, x, y, dy, ordn)
+  implicit none
+
+  integer, intent(in) :: ordn
+  real*8, dimension(ordn), intent(in) :: xa, ya
   real*8, intent(in) :: x
-  real*8, intent(out) :: y,dy
+  real*8, intent(out) :: y, dy
 
-!~~~~~~> Other parameter:
+  integer :: i, m, ns, n_m
+  real*8, dimension(ordn) :: c, d, ho
+  real*8 :: dif, dift, hp, h, den_val
+
+  if (ordn == 6) then
+#if POLINT6_USE_BARYCENTRIC
+    call polint6_barycentric(xa, ya, x, y, dy)
+#else
+    call polint6_neville(xa, ya, x, y, dy)
+#endif
+    return
+  end if
+
+  c = ya
+  d = ya
+  ho = xa - x
 
-  integer :: m,n,ns
-  real*8, dimension(ordn) :: c,d,den,ho
-  real*8 :: dif,dift
+  ns = 1
+  dif = abs(x - xa(1))
 
-!~~~~~~>
-
-  n=ordn
-  m=ordn
-
-  c=ya
-  d=ya
-  ho=xa-x
-
-  ns=1
-  dif=abs(x-xa(1))
-  do m=1,n
-   dift=abs(x-xa(m))
-   if(dift < dif) then
-    ns=m
-    dif=dift
-   end if
-  end do
-
-  y=ya(ns)
-  ns=ns-1
-  do m=1,n-1
-    den(1:n-m)=ho(1:n-m)-ho(1+m:n)
-    if (any(den(1:n-m) == 0.0))then
-      write(*,*) 'failure in polint for point',x
-      write(*,*) 'with input points: ',xa
-      stop
-    endif
-    den(1:n-m)=(c(2:n-m+1)-d(1:n-m))/den(1:n-m)
-    d(1:n-m)=ho(1+m:n)*den(1:n-m)
-    c(1:n-m)=ho(1:n-m)*den(1:n-m)
-    if (2*ns < n-m) then
-      dy=c(ns+1)
-    else
-      dy=d(ns)
-      ns=ns-1
+  do i = 2, ordn
+    dift = abs(x - xa(i))
+    if (dift < dif) then
+      ns = i
+      dif = dift
     end if
-    y=y+dy
   end do
 
-  return
+  y = ya(ns)
+  ns = ns - 1
 
-  end subroutine polint
-!------------------------------------------------------------------------------
-!
-! interpolation in 2 dimensions, follow yx order
-!
-!------------------------------------------------------------------------------
+  do m = 1, ordn - 1
+    n_m = ordn - m
+    do i = 1, n_m
+      hp = ho(i)
+      h  = ho(i+m)
+      den_val = hp - h
+
+      if (den_val == 0.0d0) then
+        write(*,*) 'failure in polint for point',x
+        write(*,*) 'with input points: ',xa
+        stop
+      end if
+
+      den_val = (c(i+1) - d(i)) / den_val
+
+      d(i) = h * den_val
+      c(i) = hp * den_val
+    end do
+
+    if (2 * ns < n_m) then
+      dy = c(ns + 1)
+    else
+      dy = d(ns)
+      ns = ns - 1
+    end if
+    y = y + dy
+  end do
+
+  return
+  end subroutine polint
+!------------------------------------------------------------------------------
+! Compute Lagrange interpolation basis weights for one target point.
+!------------------------------------------------------------------------------
+!DIR$ ATTRIBUTES FORCEINLINE :: polint_lagrange_weights
+  subroutine polint_lagrange_weights(xa, x, w, ordn)
+  implicit none
+
+  integer, intent(in) :: ordn
+  real*8, dimension(1:ordn), intent(in) :: xa
+  real*8, intent(in) :: x
+  real*8, dimension(1:ordn), intent(out) :: w
+
+  integer :: i, j
+  real*8 :: num, den, dx
+
+  do i = 1, ordn
+    num = 1.d0
+    den = 1.d0
+    do j = 1, ordn
+      if (j /= i) then
+        dx = xa(i) - xa(j)
+        if (dx == 0.0d0) then
+          write(*,*) 'failure in polint for point',x
+          write(*,*) 'with input points: ',xa
+          stop
+        end if
+        num = num * (x - xa(j))
+        den = den * dx
+      end if
+    end do
+    w(i) = num / den
+  end do
+
+  return
+  end subroutine polint_lagrange_weights
+!------------------------------------------------------------------------------
+!
+! interpolation in 2 dimensions, follow yx order
+!
+!------------------------------------------------------------------------------
   subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
-
   implicit none
 
-!~~~~~~> Input parameters:
   integer,intent(in) :: ordn
   real*8, dimension(1:ordn), intent(in) :: x1a,x2a
   real*8, dimension(1:ordn,1:ordn), intent(in) :: ya
   real*8, intent(in) :: x1,x2
   real*8, intent(out) :: y,dy
 
-!~~~~~~> Other parameters:
-
+#ifdef POLINT_LEGACY_ORDER
   integer  :: i,m
   real*8, dimension(ordn) :: ymtmp
   real*8, dimension(ordn) :: yntmp
 
   m=size(x1a)
-  
   do i=1,m
-
     yntmp=ya(i,:)
     call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-
   end do
-
   call polint(x1a,ymtmp,x1,y,dy,ordn)
+#else
+  integer  :: j
+  real*8, dimension(ordn) :: ymtmp
+  real*8 :: dy_temp
+
+  do j=1,ordn
+    call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
+  end do
+  call polint(x2a, ymtmp, x2, y, dy, ordn)
+#endif
 
   return
-
   end subroutine polin2
 !------------------------------------------------------------------------------
 !
@@ -1219,45 +1406,58 @@ end subroutine d2dump
 !
 !------------------------------------------------------------------------------
   subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
-
   implicit none
 
-!~~~~~~> Input parameters:
   integer,intent(in) :: ordn
   real*8, dimension(1:ordn), intent(in) :: x1a,x2a,x3a
   real*8, dimension(1:ordn,1:ordn,1:ordn), intent(in) :: ya
   real*8, intent(in) :: x1,x2,x3
   real*8, intent(out) :: y,dy
 
-!~~~~~~> Other parameters:
-
-  integer  :: i,j,m,n
-  real*8, dimension(ordn,ordn) :: yatmp
-  real*8, dimension(ordn) :: ymtmp
-  real*8, dimension(ordn) :: yntmp
+#ifdef POLINT_LEGACY_ORDER
+  integer  :: i,j,m,n
+  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn) :: ymtmp
+  real*8, dimension(ordn) :: yntmp
   real*8, dimension(ordn) :: yqtmp
 
   m=size(x1a)
   n=size(x2a)
-  
   do i=1,m
    do j=1,n
-
     yqtmp=ya(i,j,:)
     call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
-
    end do
-
-    yntmp=yatmp(i,:)
-    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-
-  end do
-
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
-
-  return
-
-  end subroutine polin3
+    yntmp=yatmp(i,:)
+    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
+  end do
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
+#else
+  integer  :: i, j, k
+  real*8, dimension(ordn) :: w1, w2
+  real*8, dimension(ordn) :: ymtmp
+  real*8 :: yx_sum, x_sum
+
+  call polint_lagrange_weights(x1a, x1, w1, ordn)
+  call polint_lagrange_weights(x2a, x2, w2, ordn)
+
+  do k = 1, ordn
+    yx_sum = 0.d0
+    do j = 1, ordn
+      x_sum = 0.d0
+      do i = 1, ordn
+        x_sum = x_sum + w1(i) * ya(i,j,k)
+      end do
+      yx_sum = yx_sum + w2(j) * x_sum
+    end do
+    ymtmp(k) = yx_sum
+  end do
+
+  call polint(x3a, ymtmp, x3, y, dy, ordn)
+#endif
+
+  return
+  end subroutine polin3
 !--------------------------------------------------------------------------------------
 ! calculate L2norm
   subroutine l2normhelper(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
@@ -1311,13 +1511,88 @@ deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
-  return
-
-  end subroutine l2normhelper
-!--------------------------------------------------------------------------------------
-! calculate L2norm especially for shell Blocks
-  subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
-                          f,f_out,gw,ogw,Symmetry)
+  return
+
+  end subroutine l2normhelper
+!--------------------------------------------------------------------------------------
+  subroutine l2normhelper7(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
+                           f1,f2,f3,f4,f5,f6,f7,f_out,gw)
+
+  implicit none
+!~~~~~~> Input parameters:
+  integer,intent(in ):: ex(1:3)
+  real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3)),xmin,ymin,zmin,xmax,ymax,zmax
+  integer,intent(in)::gw
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(in) :: f1,f2,f3,f4,f5,f6,f7
+  real*8, intent(out) :: f_out(7)
+!~~~~~~> Other variables:
+
+  real*8            :: dX, dY, dZ
+  integer::imin,jmin,kmin
+  integer::imax,jmax,kmax
+  integer::i,j,k
+  real*8 :: s1,s2,s3,s4,s5,s6,s7
+
+  dX = X(2) - X(1)
+  dY = Y(2) - Y(1)
+  dZ = Z(2) - Z(1)
+
+! for ghost zone
+   imin = gw+1
+   jmin = gw+1
+   kmin = gw+1
+
+   imax = ex(1) - gw
+   jmax = ex(2) - gw
+   kmax = ex(3) - gw
+
+!for patch boundary (i.e., not ghost boundary)
+
+if(dabs(X(ex(1))-xmax) < dX) imax = ex(1)
+if(dabs(Y(ex(2))-ymax) < dY) jmax = ex(2)
+if(dabs(Z(ex(3))-zmax) < dZ) kmax = ex(3)
+if(dabs(X(1)-xmin) < dX) imin = 1
+if(dabs(Y(1)-ymin) < dY) jmin = 1
+if(dabs(Z(1)-zmin) < dZ) kmin = 1
+
+  s1 = 0.d0
+  s2 = 0.d0
+  s3 = 0.d0
+  s4 = 0.d0
+  s5 = 0.d0
+  s6 = 0.d0
+  s7 = 0.d0
+
+  do k=kmin,kmax
+    do j=jmin,jmax
+!DIR$ SIMD REDUCTION(+:s1,s2,s3,s4,s5,s6,s7)
+      do i=imin,imax
+        s1 = s1 + f1(i,j,k)*f1(i,j,k)
+        s2 = s2 + f2(i,j,k)*f2(i,j,k)
+        s3 = s3 + f3(i,j,k)*f3(i,j,k)
+        s4 = s4 + f4(i,j,k)*f4(i,j,k)
+        s5 = s5 + f5(i,j,k)*f5(i,j,k)
+        s6 = s6 + f6(i,j,k)*f6(i,j,k)
+        s7 = s7 + f7(i,j,k)*f7(i,j,k)
+      enddo
+    enddo
+  enddo
+
+  f_out(1) = s1*dX*dY*dZ
+  f_out(2) = s2*dX*dY*dZ
+  f_out(3) = s3*dX*dY*dZ
+  f_out(4) = s4*dX*dY*dZ
+  f_out(5) = s5*dX*dY*dZ
+  f_out(6) = s6*dX*dY*dZ
+  f_out(7) = s7*dX*dY*dZ
+
+  return
+
+  end subroutine l2normhelper7
+!--------------------------------------------------------------------------------------
+! calculate L2norm especially for shell Blocks
+  subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
+                          f,f_out,gw,ogw,Symmetry)
 
   implicit none
 !~~~~~~> Input parameters:
@@ -1600,11 +1875,14 @@ deallocate(f_flat)
 !       ^
 ! f=3/8*f_1 + 3/4*f_2 - 1/8*f_3
 
-  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
-
-  fout = C1*f1+C2*f2+C3*f3
-
-  return
+  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
+  integer :: i,j,k
+
+  do concurrent (k=1:ext(3), j=1:ext(2), i=1:ext(1))
+    fout(i,j,k) = C1*f1(i,j,k)+C2*f2(i,j,k)+C3*f3(i,j,k)
+  end do
+
+  return
 
   end subroutine average2
 !-----------------------------------------------------------------------------  

AMSS_NCKU_source/fmisc.h

@@ -12,9 +12,10 @@
 #define f_global_interpind global_interpind
 #define f_global_interpind2d global_interpind2d
 #define f_global_interpind1d global_interpind1d
-#define f_l2normhelper l2normhelper
-#define f_l2normhelper_sh l2normhelper_sh
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms
+#define f_l2normhelper l2normhelper
+#define f_l2normhelper7 l2normhelper7
+#define f_l2normhelper_sh l2normhelper_sh
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms
 #define f_average average
 #define f_average3 average3
 #define f_average2 average2
@@ -41,9 +42,10 @@
 #define f_global_interpind GLOBAL_INTERPIND
 #define f_global_interpind2d GLOBAL_INTERPIND2D
 #define f_global_interpind1d GLOBAL_INTERPIND1D
-#define f_l2normhelper L2NORMHELPER
-#define f_l2normhelper_sh L2NORMHELPER_SH
-#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
+#define f_l2normhelper L2NORMHELPER
+#define f_l2normhelper7 L2NORMHELPER7
+#define f_l2normhelper_sh L2NORMHELPER_SH
+#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
 #define f_average AVERAGE
 #define f_average3 AVERAGE3
 #define f_average2 AVERAGE2
@@ -70,9 +72,10 @@
 #define f_global_interpind global_interpind_
 #define f_global_interpind2d global_interpind2d_
 #define f_global_interpind1d global_interpind1d_
-#define f_l2normhelper l2normhelper_
-#define f_l2normhelper_sh l2normhelper_sh_
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
+#define f_l2normhelper l2normhelper_
+#define f_l2normhelper7 l2normhelper7_
+#define f_l2normhelper_sh l2normhelper_sh_
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
 #define f_average average_
 #define f_average3 average3_
 #define f_average2 average2_
@@ -156,20 +159,29 @@ extern "C"
 							  int *, double *, int &, int &);
 }
 
-extern "C"
-{
-	void f_l2normhelper(int *, double *, double *, double *,
-						double &, double &, double &,
-						double &, double &, double &,
-						double *, double &, int &);
-}
-
-extern "C"
-{
-	void f_l2normhelper_sh(int *, double *, double *, double *,
-						   double &, double &, double &,
-						   double &, double &, double &,
-						   double *, double &, int &, int &, int &);
+extern "C"
+{
+	void f_l2normhelper(int *, double *, double *, double *,
+						double &, double &, double &,
+						double &, double &, double &,
+						double *, double &, int &);
+}
+
+extern "C"
+{
+	void f_l2normhelper7(int *, double *, double *, double *,
+						 double &, double &, double &,
+						 double &, double &, double &,
+						 double *, double *, double *, double *,
+						 double *, double *, double *, double *, int &);
+}
+
+extern "C"
+{
+	void f_l2normhelper_sh(int *, double *, double *, double *,
+						   double &, double &, double &,
+						   double &, double &, double &,
+						   double *, double &, int &, int &, int &);
 }
 
 extern "C"

AMSS_NCKU_source/gaussj.C

@@ -18,7 +18,7 @@ using namespace std;
 #endif
 
 // Intel oneMKL LAPACK interface
-#include <mkl_lapacke.h>
+#include <lapacke.h>
 /* Linear equation solution using Intel oneMKL LAPACK.
 a[0..n-1][0..n-1] is the input matrix. b[0..n-1] is input
 containing the right-hand side vectors. On output a is

AMSS_NCKU_source/interp_lb_profile.C

@@ -0,0 +1,107 @@
+#include "interp_lb_profile.h"
+#include <cstdio>
+#include <cstring>
+#include <algorithm>
+
+namespace InterpLBProfile {
+
+bool write_profile(const char *filepath, int nprocs,
+                   const double *rank_times,
+                   const int *heavy_ranks, int num_heavy,
+                   double threshold_ratio)
+{
+    FILE *fp = fopen(filepath, "wb");
+    if (!fp) return false;
+
+    ProfileHeader hdr;
+    hdr.magic = MAGIC;
+    hdr.version = VERSION;
+    hdr.nprocs = nprocs;
+    hdr.num_heavy = num_heavy;
+    hdr.threshold_ratio = threshold_ratio;
+
+    fwrite(&hdr, sizeof(hdr), 1, fp);
+    fwrite(rank_times, sizeof(double), nprocs, fp);
+    fwrite(heavy_ranks, sizeof(int), num_heavy, fp);
+    fclose(fp);
+    return true;
+}
+
+bool read_profile(const char *filepath, int current_nprocs,
+                  int *heavy_ranks, int &num_heavy,
+                  double *rank_times, MPI_Comm comm)
+{
+    int myrank;
+    MPI_Comm_rank(comm, &myrank);
+
+    int valid = 0;
+    ProfileHeader hdr;
+    memset(&hdr, 0, sizeof(hdr));
+
+    if (myrank == 0) {
+        FILE *fp = fopen(filepath, "rb");
+        if (fp) {
+            if (fread(&hdr, sizeof(hdr), 1, fp) == 1 &&
+                hdr.magic == MAGIC && hdr.version == VERSION &&
+                hdr.nprocs == current_nprocs)
+            {
+                if (fread(rank_times, sizeof(double), current_nprocs, fp)
+                    == (size_t)current_nprocs &&
+                    fread(heavy_ranks, sizeof(int), hdr.num_heavy, fp)
+                    == (size_t)hdr.num_heavy)
+                {
+                    num_heavy = hdr.num_heavy;
+                    valid = 1;
+                }
+            } else if (fp) {
+                printf("[InterpLB] Profile rejected: magic=0x%X version=%u "
+                       "nprocs=%d (current=%d)\n",
+                       hdr.magic, hdr.version, hdr.nprocs, current_nprocs);
+            }
+            fclose(fp);
+        }
+    }
+
+    MPI_Bcast(&valid, 1, MPI_INT, 0, comm);
+    if (!valid) return false;
+
+    MPI_Bcast(&num_heavy, 1, MPI_INT, 0, comm);
+    MPI_Bcast(heavy_ranks, num_heavy, MPI_INT, 0, comm);
+    MPI_Bcast(rank_times, current_nprocs, MPI_DOUBLE, 0, comm);
+    return true;
+}
+
+int identify_heavy_ranks(const double *rank_times, int nprocs,
+                         double threshold_ratio,
+                         int *heavy_ranks, int max_heavy)
+{
+    double sum = 0;
+    for (int i = 0; i < nprocs; i++) sum += rank_times[i];
+    double mean = sum / nprocs;
+    double threshold = threshold_ratio * mean;
+
+    // Collect candidates
+    struct RankTime { int rank; double time; };
+    RankTime *candidates = new RankTime[nprocs];
+    int ncand = 0;
+
+    for (int i = 0; i < nprocs; i++) {
+        if (rank_times[i] > threshold)
+            candidates[ncand++] = {i, rank_times[i]};
+    }
+
+    // Sort descending by time
+    std::sort(candidates, candidates + ncand,
+              [](const RankTime &a, const RankTime &b) {
+                  return a.time > b.time;
+              });
+
+    int count = (ncand < max_heavy) ? ncand : max_heavy;
+    for (int i = 0; i < count; i++)
+        heavy_ranks[i] = candidates[i].rank;
+
+    delete[] candidates;
+    return count;
+}
+
+} // namespace InterpLBProfile

AMSS_NCKU_source/interp_lb_profile.h

@@ -0,0 +1,38 @@
+#ifndef INTERP_LB_PROFILE_H
+#define INTERP_LB_PROFILE_H
+
+#include <mpi.h>
+
+namespace InterpLBProfile {
+
+static const unsigned int MAGIC   = 0x494C4250; // "ILBP"
+static const unsigned int VERSION = 1;
+
+struct ProfileHeader {
+    unsigned int magic;
+    unsigned int version;
+    int nprocs;
+    int num_heavy;
+    double threshold_ratio;
+};
+
+// Write profile file (rank 0 only)
+bool write_profile(const char *filepath, int nprocs,
+                   const double *rank_times,
+                   const int *heavy_ranks, int num_heavy,
+                   double threshold_ratio);
+
+// Read profile file (rank 0 reads, then broadcasts to all)
+// Returns true if file found and valid for current nprocs
+bool read_profile(const char *filepath, int current_nprocs,
+                  int *heavy_ranks, int &num_heavy,
+                  double *rank_times, MPI_Comm comm);
+
+// Identify heavy ranks: those with time > threshold_ratio * mean
+int identify_heavy_ranks(const double *rank_times, int nprocs,
+                         double threshold_ratio,
+                         int *heavy_ranks, int max_heavy);
+
+} // namespace InterpLBProfile
+
+#endif /* INTERP_LB_PROFILE_H */

AMSS_NCKU_source/interp_lb_profile_data.h

@@ -0,0 +1,29 @@
+/* 本头文件由自订profile框架自动生成并非人工硬编码针对Case优化 */
+/* 更新：负载均衡问题已经通过优化插值函数解决，此profile静态均衡方案已弃用，本头文件现在未参与编译 */
+/* Auto-generated from interp_lb_profile.bin — do not edit */
+#ifndef INTERP_LB_PROFILE_DATA_H
+#define INTERP_LB_PROFILE_DATA_H
+
+#define INTERP_LB_NPROCS 64
+#define INTERP_LB_NUM_HEAVY 4
+
+static const int interp_lb_heavy_blocks[4] = {27, 35, 28, 36};
+
+/* Split table: {block_id, r_left, r_right} */
+static const int interp_lb_splits[4][3] = {
+    {27, 26, 27},
+    {35, 34, 35},
+    {28, 28, 29},
+    {36, 36, 37},
+};
+
+/* Rank remap for displaced neighbor blocks */
+static const int interp_lb_num_remaps = 4;
+static const int interp_lb_remaps[][2] = {
+    {26, 25},
+    {29, 30},
+    {34, 33},
+    {37, 38},
+};
+
+#endif /* INTERP_LB_PROFILE_DATA_H */

AMSS_NCKU_source/kodiss.f90

@@ -65,6 +65,8 @@ real*8,intent(in) :: eps
 !                       dx^4
 
 !  note the sign (-1)^r-1, now r=2
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+!DIR$ UNROLL PARTIAL(4)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)

AMSS_NCKU_source/kodiss_c.C

@@ -0,0 +1,117 @@
+#include "tool.h"
+
+/*
+ * C 版 kodis
+ *
+ * Fortran signature:
+ * subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
+ *
+ * 约定：
+ *   X: ex1, Y: ex2, Z: ex3
+ *   f, f_rhs: ex1*ex2*ex3 按 idx_ex 布局
+ *   SoA[3]
+ *   eps: double
+ */
+void kodis(const int ex[3],
+           const double *X, const double *Y, const double *Z,
+           const double *f, double *f_rhs,
+           const double SoA[3],
+           int Symmetry, double eps)
+{
+    const double ONE = 1.0, SIX = 6.0, FIT = 15.0, TWT = 20.0;
+    const double cof = 64.0;             // 2^6
+    const int NO_SYMM = 0, OCTANT = 2;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    // Fortran: dX = X(2)-X(1) -> C: X[1]-X[0]
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+    (void)ONE; // ONE 在原 Fortran 里只是参数，这里不一定用得上
+
+    // Fortran: imax=ex(1) 等是 1-based 上界
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    // Fortran: imin=jmin=kmin=1，某些对称情况变 -2
+    int iminF = 1, jminF = 1, kminF = 1;
+
+    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
+    if (Symmetry == OCTANT && fabs(X[0]) < dX) iminF = -2;
+    if (Symmetry == OCTANT && fabs(Y[0]) < dY) jminF = -2;
+
+    // 分配 fh：大小 (ex1+3)*(ex2+3)*(ex3+3)，对应 ord=3
+    const size_t nx = (size_t)ex1 + 3;
+    const size_t ny = (size_t)ex2 + 3;
+    const size_t nz = (size_t)ex3 + 3;
+    const size_t fh_size = nx * ny * nz;
+
+    double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    // Fortran: call symmetry_bd(3,ex,f,fh,SoA)
+    symmetry_bd(3, ex, f, fh, SoA);
+
+    /*
+     * Fortran loops:
+     * do k=1,ex3
+     * do j=1,ex2
+     * do i=1,ex1
+     *
+     * C: k0=0..ex3-1, j0=0..ex2-1, i0=0..ex1-1
+     * 并定义 Fortran index: iF=i0+1, ...
+     */
+    // 收紧循环范围：只遍历满足 iF±3/jF±3/kF±3 条件的内部点
+    // iF-3 >= iminF => iF >= iminF+3 => i0 >= iminF+2 (因为 iF=i0+1)
+    // iF+3 <= imaxF => iF <= imaxF-3 => i0 <= imaxF-4
+    const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0;
+    const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0;
+    const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0;
+    const int i0_hi = imaxF - 4;  // inclusive
+    const int j0_hi = jmaxF - 4;
+    const int k0_hi = kmaxF - 4;
+
+    if (i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi) {
+        free(fh);
+        return;
+    }
+
+    for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
+        const int kF = k0 + 1;
+        for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
+            const int jF = j0 + 1;
+            for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
+                const int iF = i0 + 1;
+
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    // 三个方向各一份同型的 7 点组合（实际上是对称的 6th-order dissipation/filter 核）
+                    const double Dx_term =
+                        ( (fh[idx_fh_F(iF - 3, jF, kF, ex)] + fh[idx_fh_F(iF + 3, jF, kF, ex)]) -
+                          SIX * (fh[idx_fh_F(iF - 2, jF, kF, ex)] + fh[idx_fh_F(iF + 2, jF, kF, ex)]) +
+                          FIT * (fh[idx_fh_F(iF - 1, jF, kF, ex)] + fh[idx_fh_F(iF + 1, jF, kF, ex)]) -
+                          TWT *  fh[idx_fh_F(iF    , jF, kF, ex)] ) / dX;
+
+                    const double Dy_term =
+                        ( (fh[idx_fh_F(iF, jF - 3, kF, ex)] + fh[idx_fh_F(iF, jF + 3, kF, ex)]) -
+                          SIX * (fh[idx_fh_F(iF, jF - 2, kF, ex)] + fh[idx_fh_F(iF, jF + 2, kF, ex)]) +
+                          FIT * (fh[idx_fh_F(iF, jF - 1, kF, ex)] + fh[idx_fh_F(iF, jF + 1, kF, ex)]) -
+                          TWT *  fh[idx_fh_F(iF, jF    , kF, ex)] ) / dY;
+
+                    const double Dz_term =
+                        ( (fh[idx_fh_F(iF, jF, kF - 3, ex)] + fh[idx_fh_F(iF, jF, kF + 3, ex)]) -
+                          SIX * (fh[idx_fh_F(iF, jF, kF - 2, ex)] + fh[idx_fh_F(iF, jF, kF + 2, ex)]) +
+                          FIT * (fh[idx_fh_F(iF, jF, kF - 1, ex)] + fh[idx_fh_F(iF, jF, kF + 1, ex)]) -
+                          TWT *  fh[idx_fh_F(iF, jF, kF    , ex)] ) / dZ;
+
+                    // Fortran:
+                    // f_rhs(i,j,k) = f_rhs(i,j,k) + eps/cof*(Dx_term + Dy_term + Dz_term)
+                    f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
+            }
+        }
+    }
+
+    free(fh);
+}

AMSS_NCKU_source/lopsided_c.C

@@ -0,0 +1,255 @@
+#include "tool.h"
+/*
+ * 你需要提供 symmetry_bd 的 C 版本（或 Fortran 绑到 C 的接口）。
+ * Fortran: call symmetry_bd(3,ex,f,fh,SoA)
+ *
+ * 约定：
+ *   nghost = 3
+ *   ex[3]  = {ex1,ex2,ex3}
+ *   f      = 原始网格 (ex1*ex2*ex3)
+ *   fh     = 扩展网格 ((ex1+3)*(ex2+3)*(ex3+3))，对应 Fortran 的 (-2:ex1, ...)
+ *   SoA[3] = 输入参数
+ */
+void lopsided(const int ex[3],
+              const double *X, const double *Y, const double *Z,
+              const double *f, double *f_rhs,
+              const double *Sfx, const double *Sfy, const double *Sfz,
+              int Symmetry, const double SoA[3])
+{
+    const double ZEO = 0.0, ONE = 1.0, F3 = 3.0;
+    const double TWO = 2.0, F6 = 6.0, F18 = 18.0;
+    const double F12 = 12.0, F10 = 10.0, EIT = 8.0;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2;
+    (void)OCTANT; // 这里和 Fortran 一样只是定义了不用也没关系
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    // 对应 Fortran: dX = X(2)-X(1)  （Fortran 1-based）
+    // C: X[1]-X[0]
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    const double d12dx = ONE / F12 / dX;
+    const double d12dy = ONE / F12 / dY;
+    const double d12dz = ONE / F12 / dZ;
+
+    // Fortran 里算了 d2dx/d2dy/d2dz 但本 subroutine 里没用到（保持一致也算出来）
+    const double d2dx  = ONE / TWO / dX;
+    const double d2dy  = ONE / TWO / dY;
+    const double d2dz  = ONE / TWO / dZ;
+    (void)d2dx; (void)d2dy; (void)d2dz;
+
+    // Fortran:
+    // imax = ex(1); jmax = ex(2); kmax = ex(3)
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    // Fortran:
+    // imin=jmin=kmin=1; 若满足对称条件则设为 -2
+    int iminF = 1, jminF = 1, kminF = 1;
+    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
+    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -2;
+    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -2;
+
+    // 分配 fh：大小 (ex1+3)*(ex2+3)*(ex3+3)
+    const size_t nx = (size_t)ex1 + 3;
+    const size_t ny = (size_t)ex2 + 3;
+    const size_t nz = (size_t)ex3 + 3;
+    const size_t fh_size = nx * ny * nz;
+
+    double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return; // 内存不足：直接返回（你也可以改成 abort/报错）
+
+    // Fortran: call symmetry_bd(3,ex,f,fh,SoA)
+    symmetry_bd(3, ex, f, fh, SoA);
+
+    /*
+     * Fortran 主循环：
+     * do k=1,ex(3)-1
+     * do j=1,ex(2)-1
+     * do i=1,ex(1)-1
+     *
+     * 转成 C 0-based：
+     * k0 = 0..ex3-2, j0 = 0..ex2-2, i0 = 0..ex1-2
+     *
+     * 并且 Fortran 里的 i/j/k 在 fh 访问时，仍然是 Fortran 索引值：
+     * iF=i0+1, jF=j0+1, kF=k0+1
+     */
+    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+        const int kF = k0 + 1;
+        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+            const int jF = j0 + 1;
+            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+                const int iF = i0 + 1;
+
+                const size_t p = idx_ex(i0, j0, k0, ex);
+
+                // ---------------- x direction ----------------
+                const double sfx = Sfx[p];
+                if (sfx > ZEO) {
+                    // Fortran: if(i+3 <= imax)
+                    // iF+3 <= ex1  <=> i0+4 <= ex1 <=> i0 <= ex1-4
+                    if (i0 <= ex1 - 4) {
+                        f_rhs[p] += sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
+                    }
+                    // elseif(i+2 <= imax)  <=> i0 <= ex1-3
+                    else if (i0 <= ex1 - 3) {
+                        f_rhs[p] += sfx * d12dx *
+                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
+                    }
+                    // elseif(i+1 <= imax)  <=> i0 <= ex1-2（循环里总成立）
+                    else if (i0 <= ex1 - 2) {
+                        f_rhs[p] -= sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
+                    }
+                } else if (sfx < ZEO) {
+                    // Fortran: if(i-3 >= imin)
+                    // (iF-3) >= iminF  <=> (i0-2) >= iminF
+                    if ((i0 - 2) >= iminF) {
+                        f_rhs[p] -= sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
+                    }
+                    // elseif(i-2 >= imin) <=> (i0-1) >= iminF
+                    else if ((i0 - 1) >= iminF) {
+                        f_rhs[p] += sfx * d12dx *
+                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
+                    }
+                    // elseif(i-1 >= imin) <=> i0 >= iminF
+                    else if (i0 >= iminF) {
+                        f_rhs[p] += sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
+                    }
+                }
+
+                // ---------------- y direction ----------------
+                const double sfy = Sfy[p];
+                if (sfy > ZEO) {
+                    // jF+3 <= ex2 <=> j0+4 <= ex2 <=> j0 <= ex2-4
+                    if (j0 <= ex2 - 4) {
+                        f_rhs[p] += sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
+                    } else if (j0 <= ex2 - 3) {
+                        f_rhs[p] += sfy * d12dy *
+                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
+                    } else if (j0 <= ex2 - 2) {
+                        f_rhs[p] -= sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
+                    }
+                } else if (sfy < ZEO) {
+                    if ((j0 - 2) >= jminF) {
+                        f_rhs[p] -= sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
+                    } else if ((j0 - 1) >= jminF) {
+                        f_rhs[p] += sfy * d12dy *
+                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
+                    } else if (j0 >= jminF) {
+                        f_rhs[p] += sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
+                    }
+                }
+
+                // ---------------- z direction ----------------
+                const double sfz = Sfz[p];
+                if (sfz > ZEO) {
+                    if (k0 <= ex3 - 4) {
+                        f_rhs[p] += sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
+                    } else if (k0 <= ex3 - 3) {
+                        f_rhs[p] += sfz * d12dz *
+                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
+                    } else if (k0 <= ex3 - 2) {
+                        f_rhs[p] -= sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
+                    }
+                } else if (sfz < ZEO) {
+                    if ((k0 - 2) >= kminF) {
+                        f_rhs[p] -= sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
+                    } else if ((k0 - 1) >= kminF) {
+                        f_rhs[p] += sfz * d12dz *
+                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
+                    } else if (k0 >= kminF) {
+                        f_rhs[p] += sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
+                    }
+                }
+            }
+        }
+    }
+    free(fh);
+}
+
+
+
+
+

AMSS_NCKU_source/lopsided_kodis_c.C

@@ -0,0 +1,248 @@
+#include "tool.h"
+
+/*
+ * Combined advection (lopsided) + KO dissipation (kodis).
+ * Uses one shared symmetry_bd buffer per call.
+ */
+void lopsided_kodis(const int ex[3],
+                    const double *X, const double *Y, const double *Z,
+                    const double *f, double *f_rhs,
+                    const double *Sfx, const double *Sfy, const double *Sfz,
+                    int Symmetry, const double SoA[3], double eps)
+{
+    const double ZEO = 0.0, ONE = 1.0, F3 = 3.0;
+    const double F6 = 6.0, F18 = 18.0;
+    const double F12 = 12.0, F10 = 10.0, EIT = 8.0;
+    const double SIX = 6.0, FIT = 15.0, TWT = 20.0;
+    const double cof = 64.0; // 2^6
+
+    const int NO_SYMM = 0, EQ_SYMM = 1;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    const double d12dx = ONE / F12 / dX;
+    const double d12dy = ONE / F12 / dY;
+    const double d12dz = ONE / F12 / dZ;
+
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    int iminF = 1, jminF = 1, kminF = 1;
+    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
+    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -2;
+    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -2;
+
+    // fh for Fortran-style domain (-2:ex1,-2:ex2,-2:ex3)
+    const size_t nx = (size_t)ex1 + 3;
+    const size_t ny = (size_t)ex2 + 3;
+    const size_t nz = (size_t)ex3 + 3;
+    const size_t fh_size = nx * ny * nz;
+
+    double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    symmetry_bd(3, ex, f, fh, SoA);
+
+    // Advection (same stencil logic as lopsided_c.C)
+    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+        const int kF = k0 + 1;
+        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+            const int jF = j0 + 1;
+            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+                const int iF = i0 + 1;
+                const size_t p = idx_ex(i0, j0, k0, ex);
+
+                const double sfx = Sfx[p];
+                if (sfx > ZEO) {
+                    if (i0 <= ex1 - 4) {
+                        f_rhs[p] += sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
+                    } else if (i0 <= ex1 - 3) {
+                        f_rhs[p] += sfx * d12dx *
+                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
+                    } else if (i0 <= ex1 - 2) {
+                        f_rhs[p] -= sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
+                    }
+                } else if (sfx < ZEO) {
+                    if ((i0 - 2) >= iminF) {
+                        f_rhs[p] -= sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
+                    } else if ((i0 - 1) >= iminF) {
+                        f_rhs[p] += sfx * d12dx *
+                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
+                    } else if (i0 >= iminF) {
+                        f_rhs[p] += sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
+                    }
+                }
+
+                const double sfy = Sfy[p];
+                if (sfy > ZEO) {
+                    if (j0 <= ex2 - 4) {
+                        f_rhs[p] += sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
+                    } else if (j0 <= ex2 - 3) {
+                        f_rhs[p] += sfy * d12dy *
+                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
+                    } else if (j0 <= ex2 - 2) {
+                        f_rhs[p] -= sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
+                    }
+                } else if (sfy < ZEO) {
+                    if ((j0 - 2) >= jminF) {
+                        f_rhs[p] -= sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
+                    } else if ((j0 - 1) >= jminF) {
+                        f_rhs[p] += sfy * d12dy *
+                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
+                    } else if (j0 >= jminF) {
+                        f_rhs[p] += sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
+                    }
+                }
+
+                const double sfz = Sfz[p];
+                if (sfz > ZEO) {
+                    if (k0 <= ex3 - 4) {
+                        f_rhs[p] += sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
+                    } else if (k0 <= ex3 - 3) {
+                        f_rhs[p] += sfz * d12dz *
+                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
+                    } else if (k0 <= ex3 - 2) {
+                        f_rhs[p] -= sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
+                    }
+                } else if (sfz < ZEO) {
+                    if ((k0 - 2) >= kminF) {
+                        f_rhs[p] -= sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
+                    } else if ((k0 - 1) >= kminF) {
+                        f_rhs[p] += sfz * d12dz *
+                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
+                    } else if (k0 >= kminF) {
+                        f_rhs[p] += sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
+                    }
+                }
+            }
+        }
+    }
+
+    // KO dissipation (same domain restriction as kodiss_c.C)
+    if (eps > ZEO) {
+        const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0;
+        const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0;
+        const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0;
+        const int i0_hi = imaxF - 4; // inclusive
+        const int j0_hi = jmaxF - 4;
+        const int k0_hi = kmaxF - 4;
+
+        if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) {
+            for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        const double Dx_term =
+                            ((fh[idx_fh_F(iF - 3, jF, kF, ex)] + fh[idx_fh_F(iF + 3, jF, kF, ex)]) -
+                             SIX * (fh[idx_fh_F(iF - 2, jF, kF, ex)] + fh[idx_fh_F(iF + 2, jF, kF, ex)]) +
+                             FIT * (fh[idx_fh_F(iF - 1, jF, kF, ex)] + fh[idx_fh_F(iF + 1, jF, kF, ex)]) -
+                             TWT *  fh[idx_fh_F(iF,     jF, kF, ex)]) / dX;
+
+                        const double Dy_term =
+                            ((fh[idx_fh_F(iF, jF - 3, kF, ex)] + fh[idx_fh_F(iF, jF + 3, kF, ex)]) -
+                             SIX * (fh[idx_fh_F(iF, jF - 2, kF, ex)] + fh[idx_fh_F(iF, jF + 2, kF, ex)]) +
+                             FIT * (fh[idx_fh_F(iF, jF - 1, kF, ex)] + fh[idx_fh_F(iF, jF + 1, kF, ex)]) -
+                             TWT *  fh[idx_fh_F(iF, jF,     kF, ex)]) / dY;
+
+                        const double Dz_term =
+                            ((fh[idx_fh_F(iF, jF, kF - 3, ex)] + fh[idx_fh_F(iF, jF, kF + 3, ex)]) -
+                             SIX * (fh[idx_fh_F(iF, jF, kF - 2, ex)] + fh[idx_fh_F(iF, jF, kF + 2, ex)]) +
+                             FIT * (fh[idx_fh_F(iF, jF, kF - 1, ex)] + fh[idx_fh_F(iF, jF, kF + 1, ex)]) -
+                             TWT *  fh[idx_fh_F(iF, jF, kF,     ex)]) / dZ;
+
+                        f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
+                    }
+                }
+            }
+        }
+    }
+
+    free(fh);
+}

AMSS_NCKU_source/lopsidediff.f90

@@ -487,6 +487,201 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
 
   end subroutine lopsided
 
+!-----------------------------------------------------------------------------
+! Combined advection (lopsided) + Kreiss-Oliger dissipation (kodis)
+! Shares the symmetry_bd buffer fh, eliminating one full-grid copy per call.
+! Mathematically identical to calling lopsided then kodis separately.
+!-----------------------------------------------------------------------------
+subroutine lopsided_kodis(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA,eps)
+  implicit none
+
+!~~~~~~> Input parameters:
+
+  integer, intent(in)  :: ex(1:3),Symmetry
+  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
+
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
+  real*8,dimension(3),intent(in) ::SoA
+  real*8,intent(in) :: eps
+
+!~~~~~~> local variables:
+! note index -2,-1,0, so we have 3 extra points
+  real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3))   :: fh
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  real*8 :: dX,dY,dZ
+  real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
+  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F3=3.d0
+  real*8,  parameter :: TWO=2.d0,F6=6.0d0,F18=1.8d1
+  real*8,  parameter :: F12=1.2d1, F10=1.d1,EIT=8.d0
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+! kodis parameters
+  real*8, parameter :: SIX=6.d0,FIT=1.5d1,TWT=2.d1
+  real*8, parameter :: cof=6.4d1   ! 2^6
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+
+  d12dx = ONE/F12/dX
+  d12dy = ONE/F12/dY
+  d12dz = ONE/F12/dZ
+
+  d2dx = ONE/TWO/dX
+  d2dy = ONE/TWO/dY
+  d2dz = ONE/TWO/dZ
+
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
+
+! Single symmetry_bd call shared by both advection and dissipation
+  call symmetry_bd(3,ex,f,fh,SoA)
+
+! ---- Advection (lopsided) loop ----
+! upper bound set ex-1 only for efficiency, 
+! the loop body will set ex 0 also
+  do k=1,ex(3)-1
+  do j=1,ex(2)-1
+  do i=1,ex(1)-1
+! x direction   
+    if(Sfx(i,j,k) > ZEO)then
+      if(i+3 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
+                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
+     elseif(i+2 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+     elseif(i+1 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
+                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
+     endif
+   elseif(Sfx(i,j,k) < ZEO)then
+      if(i-3 >= imin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
+                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
+     elseif(i-2 >= imin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+     elseif(i-1 >= imin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
+                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
+     endif
+   endif
+
+! y direction   
+    if(Sfy(i,j,k) > ZEO)then
+      if(j+3 <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
+                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
+     elseif(j+2 <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+     elseif(j+1 <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
+                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
+     endif
+   elseif(Sfy(i,j,k) < ZEO)then
+      if(j-3 >= jmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
+                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
+     elseif(j-2 >= jmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+     elseif(j-1 >= jmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
+                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
+     endif
+   endif
+
+! z direction   
+    if(Sfz(i,j,k) > ZEO)then
+      if(k+3 <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
+                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
+     elseif(k+2 <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+     elseif(k+1 <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
+                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
+     endif
+   elseif(Sfz(i,j,k) < ZEO)then
+      if(k-3 >= kmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
+                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
+     elseif(k-2 >= kmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+     elseif(k-1 >= kmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
+                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
+     endif
+   endif
+  enddo
+  enddo
+  enddo
+
+! ---- Dissipation (kodis) loop ----
+  if(eps > ZEO) then
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
+
+  if(i-3 >= imin .and. i+3 <= imax .and. &
+     j-3 >= jmin .and. j+3 <= jmax .and. &
+     k-3 >= kmin .and. k+3 <= kmax) then
+   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/cof *( (     &
+                              (fh(i-3,j,k)+fh(i+3,j,k)) - &
+                          SIX*(fh(i-2,j,k)+fh(i+2,j,k)) + &
+                          FIT*(fh(i-1,j,k)+fh(i+1,j,k)) - &
+                          TWT* fh(i,j,k)            )/dX + &
+                                                  (     &
+                              (fh(i,j-3,k)+fh(i,j+3,k)) - &
+                          SIX*(fh(i,j-2,k)+fh(i,j+2,k)) + &
+                          FIT*(fh(i,j-1,k)+fh(i,j+1,k)) - &
+                          TWT* fh(i,j,k)            )/dY + &
+                                                  (     &
+                              (fh(i,j,k-3)+fh(i,j,k+3)) - &
+                          SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
+                          FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
+                          TWT* fh(i,j,k)            )/dZ )
+  endif
+
+  enddo
+  enddo
+  enddo
+  endif
+
+  return
+
+  end subroutine lopsided_kodis
+
 #elif (ghost_width == 4)
 ! sixth order code
 ! Compute advection terms in right hand sides of field equations

AMSS_NCKU_source/macrodef.fh

@@ -1,83 +1,77 @@
-
-
-#if 0
-note here
-v:r; u: phi; w: theta
-tetradtype 0
-v^a = (x,y,z)
-orthonormal order: v,u,w
-m = (phi - i theta)/sqrt(2) following Frans, Eq.(8) of  PRD 75, 124018(2007)
-tetradtype 1
-orthonormal order: w,u,v
-m = (theta + i phi)/sqrt(2) following Sperhake, Eq.(3.2) of  PRD 85, 124062(2012)
-tetradtype 2
-v_a = (x,y,z)
-orthonormal order: v,u,w
-m = (phi - i theta)/sqrt(2) following Frans, Eq.(8) of  PRD 75, 124018(2007)
-#endif
-#define tetradtype 2
-
-#if 0
-note here
-Cell center or Vertex center
-#endif
-#define Cell
-
-#if 0
-note here
-2nd order: 2
-4th order: 3
-6th order: 4
-8th order: 5
-#endif
-#define ghost_width 3
-
-#if 0
-note here
-use shell or not
-#endif
-#define WithShell
-
-#if 0
-note here
-use constraint preserving boundary condition or not
-only affect Z4c
-#endif
-#define CPBC
-
-#if 0
-note here
-Gauge condition type
-0: B^i gauge
-1: David's puncture gauge
-2: MB B^i gauge
-3: RIT B^i gauge
-4: MB beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
-5: RIT beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
-6: MGB1 B^i gauge
-7: MGB2 B^i gauge
-#endif
-#define GAUGE 2
-
-#if 0
-buffer points for CPBC boundary
-#endif
-#define CPBC_ghost_width  (ghost_width)
-
-#if 0
-using BSSN variable for constraint violation and psi4 calculation: 0
-using ADM variable for constraint violation and psi4 calculation: 1
-#endif
-#define ABV 0
-
-#if 0
-Type of Potential and Scalar Distribution in F(R) Scalar-Tensor Theory
-1: Case C of 1112.3928, V=0
-2: shell with a2^2*phi0/(1+a2^2), f(R) = R+a2*R^2 induced V
-3: ground state of Schrodinger-Newton system, f(R) = R+a2*R^2 induced V
-4: a2 = oo and phi(r) = phi0 * 0.5 * ( tanh((r+r0)/sigma) - tanh((r-r0)/sigma) )
-5: shell with phi(r) = phi0*Exp(-(r-r0)**2/sigma), V = 0
-#endif
-#define EScalar_CC 2
-
-
+
+#define tetradtype 2
+
+#define Cell
+
+#define ghost_width 3
+
+
+
+#define GAUGE 0
+
+#define CPBC_ghost_width  (ghost_width)
+
+#define ABV 0
+
+#define EScalar_CC 2
+
+#if 0
+
+define tetradtype
+    v:r; u: phi; w: theta
+    tetradtype 0
+    v^a = (x,y,z)
+    orthonormal order: v,u,w
+    m = (phi - i theta)/sqrt(2) following Frans, Eq.(8) of  PRD 75, 124018(2007)
+    tetradtype 1
+    orthonormal order: w,u,v
+    m = (theta + i phi)/sqrt(2) following Sperhake, Eq.(3.2) of  PRD 85, 124062(2012)
+    tetradtype 2
+    v_a = (x,y,z)
+    orthonormal order: v,u,w
+    m = (phi - i theta)/sqrt(2) following Frans, Eq.(8) of  PRD 75, 124018(2007)
+
+define Cell or Vertex
+    Cell center or Vertex center
+
+define ghost_width
+    2nd order: 2
+    4th order: 3
+    6th order: 4
+    8th order: 5
+
+define WithShell
+    use shell or not
+
+define CPBC
+    use constraint preserving boundary condition or not
+    only affect Z4c
+    CPBC only supports WithShell
+
+define GAUGE
+    0: B^i gauge
+    1: David puncture gauge
+    2: MB B^i gauge
+    3: RIT B^i gauge
+    4: MB beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
+    5: RIT beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
+    6: MGB1 B^i gauge
+    7: MGB2 B^i gauge
+
+define CPBC_ghost_width  (ghost_width)
+    buffer points for CPBC boundary
+
+define ABV
+    0: using BSSN variable for constraint violation and psi4 calculation
+    1: using ADM variable for constraint violation and psi4 calculation
+
+define EScalar_CC
+Type of Potential and Scalar Distribution in F(R) Scalar-Tensor Theory
+    1: Case C of 1112.3928, V=0
+    2: shell with   phi(r) = phi0 * a2^2/(1+a2^2), f(R) = R+a2*R^2 induced V
+    3: ground state of Schrodinger-Newton system,  f(R) = R+a2*R^2 induced V
+    4: a2 = +oo and phi(r) = phi0 * 0.5 * ( tanh((r+r0)/sigma) - tanh((r-r0)/sigma) )
+    5: shell with   phi(r) = phi0 * Exp(-(r-r0)**2/sigma), V = 0
+
+#endif
+

AMSS_NCKU_source/macrodef.h

@@ -1,112 +1,169 @@
-
-#ifndef MICRODEF_H
-#define MICRODEF_H
-
-#include "macrodef.fh"
-
-// application parameters
-
-/// ****
-// sommerfeld boundary type
-// 0: bam, 1: shibata
-#define SommerType 0
-
-/// ****
-// for Using Gauss-Legendre quadrature in theta direction
-#define GaussInt
-
-/// ****
-// 0: BSSN vacuum
-// 1: coupled to scalar field
-// 2: Z4c vacuum
-// 3: coupled to Maxwell field
-//
-#define ABEtype 2
-
-/// ****
-// using Apparent Horizon Finder
-//#define With_AHF
-
-/// ****
-// Psi4 calculation method
-// 0: EB method
-// 1: 4-D method
-//
-#define Psi4type 0
-
-/// ****
-// for Using point psi4 or not
-//#define Point_Psi4
-
-/// ****
-// RestrictProlong in Step (0) or after Step (1)
-#define RPS 1
-
-/// ****
-// Enforce algebra constraint
-// for every RK4 sub step: 0
-// only when iter_count == 3: 1
-// after routine Step: 2
-#define AGM 0
-
-/// ****
-// Restrict Prolong using BAM style 1 or old style 0
-#define RPB 0
-
-/// ****
-// 1: move Analysis out ot 4 sub steps and treat PBH with Euler method
-#define MAPBH 1
-
-/// ****
-// parallel structure, 0: level by level, 1: considering all levels, 2: as 1 but reverse the CPU order, 3: Frank's scheme
-#define PSTR 0
-
-/// ****
-// regrid for every level or for all levels at a time
-// 0: for every level; 1: for all
-#define REGLEV 0
-
-/// ****
-// use gpu or not
-//#define USE_GPU
-
-/// ****
-// use checkpoint for every process
-//#define CHECKDETAIL
-
-/// ****
-// use FakeCheckPrepare to write CheckPoint
-//#define FAKECHECK
-////================================================================
-//  some basic parameters for numerical calculation
-#define dim 3
-
-//#define Cell or Vertex in "microdef.fh"
-
-// ******
-// buffer point number for mesh refinement interface
-#define buffer_width 6
-
-// ******
-// buffer point number shell-box interface, on shell
-#define SC_width buffer_width
-// buffer point number shell-box interface, on box
-#define CS_width (2*buffer_width)
-
-#if(buffer_width < ghost_width)
-#error we always assume buffer_width>ghost_width
-#endif
-
-#define PACK 1
-#define UNPACK 2
-
-#define Mymax(a,b) (((a) > (b)) ? (a) : (b))
-#define Mymin(a,b) (((a) < (b)) ? (a) : (b))
-
-#define feq(a,b,d) (fabs(a-b)<d)
-#define flt(a,b,d) ((a-b)<d)
-#define fgt(a,b,d) ((a-b)>d)
-
-#define TINY 1e-10
-
-#endif   /* MICRODEF_H */
+
+#ifndef MICRODEF_H
+#define MICRODEF_H
+
+#include "macrodef.fh"  
+
+// application parameters
+
+#define SommerType 0
+
+#define GaussInt
+
+#define ABEtype 0
+
+//#define With_AHF
+#define Psi4type 0
+
+//#define Point_Psi4
+
+#define RPS 1
+
+#define AGM 0
+
+#define RPB 0
+
+#define MAPBH 1
+
+#define PSTR 0
+
+#define REGLEV 0
+
+#define BSSN_FINE_TIMING 0
+
+#define BSSN_FINE_TIMING_EVERY 1
+
+#define BSSN_FINE_TIMING_TOPN 8
+
+#define BSSN_KERNEL_FINE_TIMING 0
+
+#define BSSN_ENABLE_STDIN_ABORT_POLL 0
+
+//#define USE_GPU
+
+//#define CHECKDETAIL
+
+//#define FAKECHECK
+
+//
+// define SommerType
+//     sommerfeld boundary type
+//     0: bam
+//     1: shibata
+//
+// define GaussInt
+//     for Using Gauss-Legendre quadrature in theta direction
+//
+// define ABEtype
+//     0: BSSN vacuum
+//     1: coupled to scalar field
+//     2: Z4c vacuum
+//     3: coupled to Maxwell field
+//
+// define With_AHF
+//     using Apparent Horizon Finder
+//
+// define Psi4type
+//     Psi4 calculation method
+//     0: EB method
+//     1: 4-D method
+//
+// define Point_Psi4
+//     for Using point psi4 or not
+//
+// define RPS
+//     RestrictProlong in Step (0) or after Step (1)
+//
+// define AGM
+//     Enforce algebra constraint
+//     for every RK4 sub step: 0
+//     only when iter_count == 3: 1
+//     after routine Step: 2
+//
+// define RPB
+//     Restrict Prolong using BAM style 1 or old style 0
+//
+// define MAPBH
+//     1: move Analysis out ot 4 sub steps and treat PBH with Euler method
+//
+// define PSTR
+//     parallel structure
+//     0: level by level
+//     1: considering all levels
+//     2: as 1 but reverse the CPU order
+//     3: Frank's scheme
+//
+// define REGLEV
+//     regrid for every level or for all levels at a time
+//     0: for every level;
+//     1: for all
+//
+// define BSSN_FINE_TIMING
+//     enable fine-grained per-timestep timing monitor
+//
+// define BSSN_FINE_TIMING_EVERY
+//     report timing every N coarse timesteps
+//
+// define BSSN_FINE_TIMING_TOPN
+//     number of hottest timing buckets shown in stdout
+//
+// define BSSN_KERNEL_FINE_TIMING
+//     enable split timing inside compute_rhs_bssn
+//
+// define BSSN_ENABLE_STDIN_ABORT_POLL
+//     poll stdin and broadcast abort flag every coarse step
+//
+// define USE_GPU
+//     use gpu or not
+//
+// define CHECKDETAIL
+//     use checkpoint for every process
+//
+// define FAKECHECK
+//     use FakeCheckPrepare to write CheckPoint
+//
+
+////================================================================
+//  some basic parameters for numerical calculation
+////================================================================
+
+#define dim 3
+
+//#define Cell or Vertex in "macrodef.fh" 
+
+#define buffer_width 6
+
+#define SC_width buffer_width
+
+#define CS_width (2*buffer_width)
+
+//
+// define Cell or Vertex in "macrodef.fh" 
+//
+// define buffer_width
+//     buffer point number for mesh refinement interface
+//
+// define SC_width buffer_width
+//     buffer point number shell-box interface, on shell
+//
+// define CS_width
+//     buffer point number shell-box interface, on box
+//
+
+#if(buffer_width < ghost_width)
+#   error we always assume buffer_width>ghost_width
+#endif
+
+#define PACK 1
+#define UNPACK 2
+
+#define Mymax(a,b) (((a) > (b)) ? (a) : (b))
+#define Mymin(a,b) (((a) < (b)) ? (a) : (b))
+
+#define feq(a,b,d) (fabs(a-b)<d)
+#define flt(a,b,d) ((a-b)<d)
+#define fgt(a,b,d) ((a-b)>d)
+
+#define TINY 1e-10
+
+#endif   /* MICRODEF_H */

AMSS_NCKU_source/makefile

@@ -1,102 +1,208 @@
-
-
-include makefile.inc
-
-.SUFFIXES: .o .f90 .C .for .cu
-
-.f90.o:
-	$(f90) $(f90appflags) -c $< -o $@
-
-.C.o:
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-.for.o:
-	$(f77) -c $< -o $@
-
-.cu.o:
-	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
-
-# Input files
-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\
-	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
-	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
-           Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
-	   NullShellPatch2_Evo.o writefile_f.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\
-           Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
-	   NullShellPatch2_Evo.o \
-	   bssn_gpu_class.o bssn_step_gpu.o bssn_macro.o writefile_f.o
-
-F90FILES = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
-	   prolongrestrict_cell.o prolongrestrict_vertex.o\
-	   rungekutta4_rout.o bssn_rhs.o 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\
-	   bssn2adm.o adm_constraint.o adm_ricci_gamma.o\
-	   scalar_rhs.o initial_scalar.o NullEvol2.o initial_null2.o\
-	   NullNews2.o tool_f.o
-
-F77FILES = zbesh.o
-
-AHFDOBJS = expansion.o expansion_Jacobian.o patch.o coords.o patch_info.o patch_interp.o patch_system.o \
-tgrid.o fd_grid.o ghost_zone.o array.o round.o norm.o fuzzy.o error_exit.o miscfp.o \
-linear_map.o cpm_map.o BH_diagnostics.o setup.o horizon_sequence.o find_horizons.o \
-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
-
-# file dependences
-$(C++FILES) $(C++FILESGPU) $(F90FILES) $(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\
-	     rungekutta4_rout.h var.h bssn_class.h bssn_rhs.h sommerfeld_rout.h\
-	     cgh.h surface_integral.h ShellPatch.h shellfunctions.h perf.h\
-             fadmquantites_bssn.h cpbc.h getnp4.h initial_null.h NullEvol.h\
-	     NullShellPatch.h initial_maxwell.h bssnEM_class.h getnpem2.h\
-	     empart.h NullNews.h kodiss.h Parallel_bam.h ricci_gamma.h\
-             initial_null2.h NullShellPatch2.h 
-             
-$(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
-	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
-	     rungekutta4_rout.h var.h bssn_rhs.h sommerfeld_rout.h\
-	     cgh.h surface_integral.h ShellPatch.h shellfunctions.h perf.h\
-             fadmquantites_bssn.h cpbc.h getnp4.h initial_null.h NullEvol.h\
-	     NullShellPatch.h initial_maxwell.h bssnEM_class.h getnpem2.h\
-	     empart.h NullNews.h kodiss.h Parallel_bam.h ricci_gamma.h\
-             initial_null2.h NullShellPatch2.h \
-             bssn_gpu_class.h bssn_macro.h
-             
-$(AHFDOBJS): cctk.h cctk_Config.h cctk_Types.h cctk_Constants.h myglobal.h
-
-$(C++FILES) $(C++FILES_GPU) $(AHFDOBJS) $(CUDAFILES): macrodef.h
-
-TwoPunctureFILES: TwoPunctures.h
-
-$(CUDAFILES): bssn_gpu.h gpu_mem.h gpu_rhsSS_mem.h
-
-misc.o : zbesh.o
-
-# projects
-ABE: $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) 
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
-	
-ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
-
-TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(TwoPunctureFILES) $(LDLIBS)
-
-clean:
-	rm *.o ABE ABEGPU TwoPunctureABE make.log -f
+
+
+include makefile.inc
+
+-include AMSS_NCKU_build.mk
+
+ABE_TYPE ?= $(shell awk '/^[[:space:]]*\#define[[:space:]]+ABEtype/ {print $$3; exit}' macrodef.h 2>/dev/null)
+
+ifeq ($(USE_TRANSFER_CACHE),auto)
+ifeq ($(ABE_TYPE),0)
+EFFECTIVE_USE_TRANSFER_CACHE = 1
+else
+EFFECTIVE_USE_TRANSFER_CACHE = 0
+endif
+else
+EFFECTIVE_USE_TRANSFER_CACHE = $(USE_TRANSFER_CACHE)
+endif
+
+ifeq ($(USE_CXX_ESCALAR_KERNEL),1)
+ifeq ($(ABE_TYPE),1)
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 1
+else
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 0
+endif
+else
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 0
+endif
+
+ifeq ($(EFFECTIVE_USE_CXX_ESCALAR_KERNEL),1)
+ifeq ($(USE_CXX_KERNELS),0)
+$(error USE_CXX_ESCALAR_KERNEL=1 requires USE_CXX_KERNELS=1 because bssn_escalar_rhs_c.C reuses the C BSSN kernel)
+endif
+endif
+
+## polint(ordn=6) kernel selector:
+##   1 (default): barycentric fast path
+##   0          : fallback to Neville path
+POLINT6_USE_BARY ?= 1
+POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
+TRANSFER_CACHE_FLAG = -DBSSN_USE_TRANSFER_CACHE=$(EFFECTIVE_USE_TRANSFER_CACHE)
+ESCALAR_KERNEL_FLAG = -DBSSN_USE_ESCALAR_C_KERNEL=$(EFFECTIVE_USE_CXX_ESCALAR_KERNEL)
+
+## AMD AOCC build flags optimized for EPYC Zen 4 (-march=znver4)
+CXXAPPFLAGS = -O3 -march=znver4 -ffast-math -flto \
+              -Dfortran3 -Dnewc -I$(AOCL_ROOT)/include $(INTERP_LB_FLAGS) \
+              $(TRANSFER_CACHE_FLAG) $(ESCALAR_KERNEL_FLAG)
+f90appflags = -O3 -march=znver4 -ffast-math -flto \
+              -cpp -I$(AOCL_ROOT)/include $(POLINT6_FLAG)
+
+.SUFFIXES: .o .f90 .C .for .cu
+
+.f90.o:
+	$(f90) $(f90appflags) -c $< -o $@
+
+.C.o:
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+.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 $@
+
+fderivs_c.o: fderivs_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+fdderivs_c.o: fdderivs_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+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 $@
+
+## TwoPunctureABE uses fixed optimal flags (AMD AOCC, no PGO)
+TP_OPTFLAGS = -O3 -march=znver4 -ffast-math -flto \
+              -Dfortran3 -Dnewc -I$(AOCL_ROOT)/include
+
+TwoPunctures.o: TwoPunctures.C
+	${CXX} $(TP_OPTFLAGS) -fopenmp -c $< -o $@
+
+TwoPunctureABE.o: TwoPunctureABE.C
+	${CXX} $(TP_OPTFLAGS) -fopenmp -c $< -o $@
+
+# Input files
+
+## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
+ifeq ($(USE_CXX_KERNELS),0)
+# Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
+CFILES =
+else
+# C++ mode (default): C rewrite of bssn/bssn-escalar 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
+ifeq ($(EFFECTIVE_USE_CXX_ESCALAR_KERNEL),1)
+CFILES += bssn_escalar_rhs_c.o
+endif
+endif
+
+## RK4 kernel switch (independent from USE_CXX_KERNELS)
+ifeq ($(USE_CXX_RK4),1)
+CFILES += rungekutta4_rout_c.o
+RK4_F90_OBJ =
+else
+RK4_F90_OBJ = rungekutta4_rout.o
+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\
+	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
+	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.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\
+           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\
+           Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.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\
+	   $(RK4_F90_OBJ) diff_new.o kodiss.o kodiss_sh.o\
+	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
+	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
+           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
+           fadmquantites_bssn.o Z4c_rhs.o Z4c_rhs_ss.o point_diff_new_sh.o\
+	   cpbc.o getnp4old.o NullEvol.o initial_null.o initial_maxwell.o\
+	   getnpem2.o empart.o NullNews.o fourdcurvature.o\
+	   bssn2adm.o adm_constraint.o adm_ricci_gamma.o\
+	   scalar_rhs.o initial_scalar.o NullEvol2.o initial_null2.o\
+	   NullNews2.o tool_f.o
+
+ifeq ($(USE_CXX_KERNELS),0)
+# Fortran mode: include original bssn_rhs.o
+F90FILES = $(F90FILES_BASE) bssn_rhs.o
+else
+# C++ mode (default): bssn_rhs.o replaced by C++ kernel
+F90FILES = $(F90FILES_BASE)
+endif
+
+F77FILES = zbesh.o
+
+AHFDOBJS = expansion.o expansion_Jacobian.o patch.o coords.o patch_info.o patch_interp.o patch_system.o \
+tgrid.o fd_grid.o ghost_zone.o array.o round.o norm.o fuzzy.o error_exit.o miscfp.o \
+linear_map.o cpm_map.o BH_diagnostics.o setup.o horizon_sequence.o find_horizons.o \
+initial_guess.o Newton.o Jacobian.o ilucg.o IntPnts0.o IntPnts.o
+
+TwoPunctureFILES = TwoPunctureABE.o TwoPunctures.o 
+
+CUDAFILES = bssn_gpu.o bssn_gpu_rhs_ss.o
+
+# file dependences
+$(C++FILES) $(C++FILES_GPU) $(F90FILES) $(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\
+	     rungekutta4_rout.h var.h bssn_class.h bssn_rhs.h sommerfeld_rout.h\
+	     cgh.h surface_integral.h ShellPatch.h shellfunctions.h perf.h\
+             fadmquantites_bssn.h cpbc.h getnp4.h initial_null.h NullEvol.h\
+	     NullShellPatch.h initial_maxwell.h bssnEM_class.h getnpem2.h\
+	     empart.h NullNews.h kodiss.h Parallel_bam.h ricci_gamma.h\
+             initial_null2.h NullShellPatch2.h 
+             
+$(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
+	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
+	     rungekutta4_rout.h var.h bssn_rhs.h sommerfeld_rout.h\
+	     cgh.h surface_integral.h ShellPatch.h shellfunctions.h perf.h\
+             fadmquantites_bssn.h cpbc.h getnp4.h initial_null.h NullEvol.h\
+	     NullShellPatch.h initial_maxwell.h bssnEM_class.h getnpem2.h\
+	     empart.h NullNews.h kodiss.h Parallel_bam.h ricci_gamma.h\
+             initial_null2.h NullShellPatch2.h \
+             bssn_gpu_class.h bssn_macro.h
+             
+$(AHFDOBJS): cctk.h cctk_Config.h cctk_Types.h cctk_Constants.h myglobal.h
+
+$(C++FILES) $(C++FILES_GPU) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.h
+
+TwoPunctureFILES: TwoPunctures.h
+
+$(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)
+
+TwoPunctureABE: $(TwoPunctureFILES)
+	$(CLINKER) $(TP_OPTFLAGS) -fopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
+
+clean:
+	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -1,30 +1,59 @@
-## GCC version (commented out)
-## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
+## AMD AOCC version with AOCL (Optimized for AMD EPYC Zen 4)
 
-## Intel oneAPI version with oneMKL (Optimized for performance)
-filein  = -I/usr/include/ -I${MKLROOT}/include
+## AOCL root path for includes and libraries
+AOCL_ROOT ?= /home/gh0s7/AOCC/aocl/5.2.0/aocc
 
-## Using sequential MKL (OpenMP disabled for better single-threaded performance)
-## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl
+## AOCC-built OpenMPI prefix
+OMPI_PREFIX ?= /home/gh0s7/AOCC/aocc-openmpi
 
-## Aggressive optimization flags:
-## -O3: Maximum optimization
-## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
-## -fp-model fast=2: Aggressive floating-point optimizations
-## -fma: Enable fused multiply-add instructions
-## Note: OpenMP has been disabled (-qopenmp removed) due to performance issues
-CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma \
-               -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags  = -O3 -xHost -fp-model fast=2 -fma \
-               -fpp -I${MKLROOT}/include
-f90          = ifx
-f77          = ifx
-CXX          = icpx
-CC           = icx
-CLINKER      = mpiicpx 
+filein  = -I/usr/include/ -I$(AOCL_ROOT)/include
+
+## Using AOCL BLIS + libFLAME for BLAS/LAPACK
+## AOCC Fortran runtime: -lflang (includes FortranRuntime)
+## AOCC OpenMP runtime: -lomp (LLVM OpenMP)
+LDLIBS  = -L$(AOCL_ROOT)/lib -lblis -lflame -lamdlibm -lflang -lpgmath -lpthread -lm -ldl -lomp
+
+## Interp_Points load balance profiling mode
+##   off        : (default) no load balance instrumentation
+##   profile    : Pass 1 — instrument Interp_Points to collect timing profile
+##   optimize   : Pass 2 — read profile and apply block rebalancing
+INTERP_LB_MODE ?= off
+
+ifeq ($(INTERP_LB_MODE),profile)
+INTERP_LB_FLAGS = -DINTERP_LB_PROFILE
+else ifeq ($(INTERP_LB_MODE),optimize)
+INTERP_LB_FLAGS = -DINTERP_LB_OPTIMIZE
+else
+INTERP_LB_FLAGS =
+endif
+
+## Kernel implementation switch
+##   1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
+##   0           : fall back to original Fortran kernels
+USE_CXX_KERNELS ?= 1
+
+## BSSN-EScalar RHS switch
+##   1 (default) : use BSSN-EScalar C wrapper on the normal patch path
+##   0           : keep the original Fortran BSSN-EScalar RHS for precision-safe runs
+## Note: this requires USE_CXX_KERNELS=1 because the wrapper reuses the C BSSN kernel.
+USE_CXX_ESCALAR_KERNEL ?= 1
+
+## Cached transfer switch
+##   auto (default): enable for BSSN vacuum, keep other paths on the safe uncached path
+##   1             : force cached Sync/Restrict/OutBd transfer on evolution hot paths
+##   0             : force the original uncached transfer path
+USE_TRANSFER_CACHE ?= auto
+
+## RK4 kernel implementation switch
+##   1 (default) : use C/C++ rewrite of rungekutta4_rout (for optimization experiments)
+##   0           : use original Fortran rungekutta4_rout.o
+USE_CXX_RK4 ?= 1
+
+f90          = flang
+f77          = flang
+CXX          = clang++
+CC           = clang
+CLINKER      = $(OMPI_PREFIX)/bin/mpicxx
 
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include

AMSS_NCKU_source/prolongrestrict_cell.f90

@@ -1934,18 +1934,35 @@
 ! when if=1 -> ic=0, this is different to vertex center grid 
   real*8, dimension(-2:extc(1),-2:extc(2),-2:extc(3))   :: funcc
   integer,dimension(3) :: cxI
-  integer :: i,j,k,ii,jj,kk
+  integer :: i,j,k,ii,jj,kk,px,py,pz
   real*8, dimension(6,6) :: tmp2
   real*8, dimension(6) :: tmp1
+  integer, dimension(extf(1)) :: cix
+  integer, dimension(extf(2)) :: ciy
+  integer, dimension(extf(3)) :: ciz
+  integer, dimension(extf(1)) :: pix
+  integer, dimension(extf(2)) :: piy
+  integer, dimension(extf(3)) :: piz
 
   real*8, parameter :: C1=7.7d1/8.192d3,C2=-6.93d2/8.192d3,C3=3.465d3/4.096d3
   real*8, parameter :: C6=6.3d1/8.192d3,C5=-4.95d2/8.192d3,C4=1.155d3/4.096d3
+  real*8, dimension(6,2), parameter :: WC = reshape((/&
+      C1,C2,C3,C4,C5,C6,&
+      C6,C5,C4,C3,C2,C1/), (/6,2/))
 
   integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
   integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
+  integer::maxcx,maxcy,maxcz
 
   real*8,dimension(3) :: CD,FD
-  
+  real*8 :: tmp_yz(extc(1), 6)      ! 存储整条 X 线上 6 个 Y 轴偏置的 Z 向插值结果
+  real*8 :: tmp_xyz_line(-2:extc(1))   ! 包含 X 向 6 点模板访问所需下界
+  real*8 :: v1, v2, v3, v4, v5, v6
+  integer :: ic, jc, kc, ix_offset,ix,iy,iz,jc_min,jc_max,ic_min,ic_max,kc_min,kc_max
+  integer :: i_lo, i_hi, j_lo, j_hi, k_lo, k_hi
+  logical :: need_full_symmetry
+  real*8 :: res_line
+  real*8 :: tmp_z_slab(-2:extc(1), -2:extc(2))  ! 包含 Y/X 向模板访问所需下界
   if(wei.ne.3)then
      write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
      write(*,*)"dim = ",wei
@@ -2020,145 +2037,140 @@
           return
   endif
 
-  call symmetry_bd(3,extc,func,funcc,SoA)
-     
-!~~~~~~> prolongation start...
+  do i = imino,imaxo
+     ii = i + lbf(1) - 1
+     cix(i) = ii/2 - lbc(1) + 1
+     if(ii/2*2 == ii)then
+        pix(i) = 1
+     else
+        pix(i) = 2
+     endif
+  enddo
+  do j = jmino,jmaxo
+     jj = j + lbf(2) - 1
+     ciy(j) = jj/2 - lbc(2) + 1
+     if(jj/2*2 == jj)then
+        piy(j) = 1
+     else
+        piy(j) = 2
+     endif
+  enddo
   do k = kmino,kmaxo
-   do j = jmino,jmaxo
-    do i = imino,imaxo
-       cxI(1) = i
-       cxI(2) = j
-       cxI(3) = k
-! change to coarse level reference
-!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---| 
-!|=======x===============x===============x===============x=======|
-       cxI = (cxI+lbf-1)/2
-! change to array index      
-       cxI = cxI - lbc + 1
-
-       if(any(cxI+3 > extc)) write(*,*)"error in prolong"
-       ii=i+lbf(1)-1
-       jj=j+lbf(2)-1
-       kk=k+lbf(3)-1
-#if 0
-       if(ii/2*2==ii)then
-         if(jj/2*2==jj)then
-           if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)=  C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           endif
-         else
-           if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)=  C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           endif
-         endif
-       else
-         if(jj/2*2==jj)then
-           if(kk/2*2==kk)then               
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)=  C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           endif
-         else
-           if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)=  C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           endif
-         endif
-       endif
-#else 
-       if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-       else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-       endif
-
-       if(jj/2*2==jj)then
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-       else
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-       endif
-
-       if(ii/2*2==ii)then
-             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-       else
-             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-       endif
-#endif
-    enddo
-   enddo
+     kk = k + lbf(3) - 1
+     ciz(k) = kk/2 - lbc(3) + 1
+     if(kk/2*2 == kk)then
+        piz(k) = 1
+     else
+        piz(k) = 2
+     endif
   enddo
 
+  ic_min = minval(cix(imino:imaxo))
+  ic_max = maxval(cix(imino:imaxo))
+  jc_min = minval(ciy(jmino:jmaxo))
+  jc_max = maxval(ciy(jmino:jmaxo))
+  kc_min = minval(ciz(kmino:kmaxo))
+  kc_max = maxval(ciz(kmino:kmaxo))
+
+  maxcx = ic_max
+  maxcy = jc_max
+  maxcz = kc_max
+  if(maxcx+3 > extc(1) .or. maxcy+3 > extc(2) .or. maxcz+3 > extc(3))then
+     write(*,*)"error in prolong"
+     return
+  endif
+
+  i_lo = ic_min - 2
+  i_hi = ic_max + 3
+  j_lo = jc_min - 2
+  j_hi = jc_max + 3
+  k_lo = kc_min - 2
+  k_hi = kc_max + 3
+  need_full_symmetry = (i_lo < 1) .or. (j_lo < 1) .or. (k_lo < 1)
+  if(need_full_symmetry)then
+     call symmetry_bd(3,extc,func,funcc,SoA)
+  else
+     funcc(i_lo:i_hi,j_lo:j_hi,k_lo:k_hi) = func(i_lo:i_hi,j_lo:j_hi,k_lo:k_hi)
+  endif
+
+     ! 对每个 k（pz, kc 固定）预计算 Z 向插值的 2D 切片
+
+do k = kmino, kmaxo
+    pz = piz(k); kc = ciz(k)
+    ! --- Pass 1: Z 方向，只算一次 ---
+    do iy = jc_min-2, jc_max+3   ! 仅需的 iy 范围（对应 jc-2:jc+3）
+        do ii = ic_min-2, ic_max+3  ! 仅需的 ii 范围（对应 cix-2:cix+3）
+            tmp_z_slab(ii, iy) = sum(WC(:,pz) * funcc(ii, iy, kc-2:kc+3))
+        end do
+    end do
+
+    do j = jmino, jmaxo
+        py = piy(j); jc = ciy(j)
+        ! --- Pass 2: Y 方向 ---
+        do ii = ic_min-2, ic_max+3
+            tmp_xyz_line(ii) = sum(WC(:,py) * tmp_z_slab(ii, jc-2:jc+3))
+        end do
+        ! --- Pass 3: X 方向 ---
+        do i = imino, imaxo
+            funf(i,j,k) = sum(WC(:,pix(i)) * tmp_xyz_line(cix(i)-2:cix(i)+3))
+        end do
+    end do
+end do
+
+!~~~~~~> prolongation start...
+#if 0
+ do k = kmino, kmaxo
+     pz = piz(k)
+     kc = ciz(k)
+
+     do j = jmino, jmaxo
+        py = piy(j)
+        jc = ciy(j)
+
+! --- 步骤 1 & 2 融合：分段处理 X 轴，提升 Cache 命中率 ---
+        ! 我们将 ii 循环逻辑重组，减少对 funcc 的跨行重复访问
+        do ii = 1, extc(1)
+           ! 1. 先做 Z 方向的 6 条线插值（针对当前的 ii 和当前的 6 个 iy）
+           ! 我们直接在这里把 Y 方向的加权也做了，省去 tmp_yz 数组
+           ! 这样 funcc 的数据读进来后立即完成所有维度的贡献，不再写回内存
+           
+           res_line = 0.0d0
+           do jj = 1, 6
+              iy = jc - 3 + jj
+              ! 这一行代码是核心：一次性完成 Z 插值并加上 Y 的权重
+              ! 编译器会把 WC(jj, py) 存在寄存器里
+              res_line = res_line + WC(jj, py) * ( &
+                         WC(1, pz) * funcc(ii, iy, kc-2) + &
+                         WC(2, pz) * funcc(ii, iy, kc-1) + &
+                         WC(3, pz) * funcc(ii, iy, kc  ) + &
+                         WC(4, pz) * funcc(ii, iy, kc+1) + &
+                         WC(5, pz) * funcc(ii, iy, kc+2) + &
+                         WC(6, pz) * funcc(ii, iy, kc+3) )
+           end do
+           tmp_xyz_line(ii) = res_line
+        end do
+
+
+
+
+        ! 3. 【降维：X 向】最后在最内层只处理 X 方向的 6 点加权
+        ! 此时每个点的计算量从原来的 200+ 次乘法降到了仅 6 次
+        do i = imino, imaxo
+           px = pix(i)
+           ic = cix(i)
+           
+           ! 直接从预计算好的 line 中读取连续的 6 个点
+           ! ic-2 到 ic+3 对应原始 6 点算子
+           funf(i,j,k) = WC(1,px)*tmp_xyz_line(ic-2) + &
+                         WC(2,px)*tmp_xyz_line(ic-1) + &
+                         WC(3,px)*tmp_xyz_line(ic  ) + &
+                         WC(4,px)*tmp_xyz_line(ic+1) + &
+                         WC(5,px)*tmp_xyz_line(ic+2) + &
+                         WC(6,px)*tmp_xyz_line(ic+3)
+        end do
+     end do
+  end do
+#endif
   return
 
   end subroutine prolong3
@@ -2357,7 +2369,14 @@
   integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
 
   real*8,dimension(3) :: CD,FD
-  
+
+  real*8 :: tmp_xz_plane(-1:extf(1), 6)
+  real*8 :: tmp_x_line(-1:extf(1))
+  integer :: fi, fj, fk, ii, jj, kk
+  integer :: fi_min, fi_max, ii_lo, ii_hi
+  integer :: fj_min, fj_max, fk_min, fk_max, jj_lo, jj_hi, kk_lo, kk_hi
+  logical :: need_full_symmetry
+
   if(wei.ne.3)then
      write(*,*)"prolongrestrict.f90::restrict3: this routine only surport 3 dimension"
      write(*,*)"dim = ",wei
@@ -2436,9 +2455,86 @@
           stop
   endif
 
-  call symmetry_bd(2,extf,funf,funff,SoA)
+  ! 仅计算 X 向最终写回所需的窗口：
+  ! func(i,j,k) 只访问 tmp_x_line(fi-2:fi+3)
+  fi_min = 2*(imino + lbc(1) - 1) - 1 - lbf(1) + 1
+  fi_max = 2*(imaxo + lbc(1) - 1) - 1 - lbf(1) + 1
+  fj_min = 2*(jmino + lbc(2) - 1) - 1 - lbf(2) + 1
+  fj_max = 2*(jmaxo + lbc(2) - 1) - 1 - lbf(2) + 1
+  fk_min = 2*(kmino + lbc(3) - 1) - 1 - lbf(3) + 1
+  fk_max = 2*(kmaxo + lbc(3) - 1) - 1 - lbf(3) + 1
+  ii_lo = fi_min - 2
+  ii_hi = fi_max + 3
+  jj_lo = fj_min - 2
+  jj_hi = fj_max + 3
+  kk_lo = fk_min - 2
+  kk_hi = fk_max + 3
+  if(ii_lo < -1 .or. ii_hi > extf(1) .or. &
+     jj_lo < -1 .or. jj_hi > extf(2) .or. &
+     kk_lo < -1 .or. kk_hi > extf(3))then
+      write(*,*)"restrict3: invalid stencil window"
+      write(*,*)"ii=",ii_lo,ii_hi," jj=",jj_lo,jj_hi," kk=",kk_lo,kk_hi
+      write(*,*)"extf=",extf
+      stop
+  endif
+  need_full_symmetry = (ii_lo < 1) .or. (jj_lo < 1) .or. (kk_lo < 1)
+  if(need_full_symmetry)then
+      call symmetry_bd(2,extf,funf,funff,SoA)
+  else
+      funff(ii_lo:ii_hi,jj_lo:jj_hi,kk_lo:kk_hi) = funf(ii_lo:ii_hi,jj_lo:jj_hi,kk_lo:kk_hi)
+  endif
 
 !~~~~~~> restriction start...
+do k = kmino, kmaxo
+    fk = 2*(k + lbc(3) - 1) - 1 - lbf(3) + 1
+
+    do j = jmino, jmaxo
+        fj = 2*(j + lbc(2) - 1) - 1 - lbf(2) + 1
+        
+        ! 优化点 1: 显式展开 Z 方向计算，减少循环开销
+        ! 确保 ii 循环是最内层且连续访问
+        !DIR$ VECTOR ALWAYS
+        do ii = ii_lo, ii_hi
+            ! 预计算当前 j 对应的 6 行在 Z 方向的压缩结果
+            ! 这里直接硬编码 jj 的偏移，彻底消除一层循环
+            tmp_xz_plane(ii, 1) = C1*(funff(ii,fj-2,fk-2)+funff(ii,fj-2,fk+3)) + &
+                                  C2*(funff(ii,fj-2,fk-1)+funff(ii,fj-2,fk+2)) + &
+                                  C3*(funff(ii,fj-2,fk  )+funff(ii,fj-2,fk+1))
+            tmp_xz_plane(ii, 2) = C1*(funff(ii,fj-1,fk-2)+funff(ii,fj-1,fk+3)) + &
+                                  C2*(funff(ii,fj-1,fk-1)+funff(ii,fj-1,fk+2)) + &
+                                  C3*(funff(ii,fj-1,fk  )+funff(ii,fj-1,fk+1))
+            tmp_xz_plane(ii, 3) = C1*(funff(ii,fj  ,fk-2)+funff(ii,fj  ,fk+3)) + &
+                                  C2*(funff(ii,fj  ,fk-1)+funff(ii,fj  ,fk+2)) + &
+                                  C3*(funff(ii,fj  ,fk  )+funff(ii,fj  ,fk+1))
+            tmp_xz_plane(ii, 4) = C1*(funff(ii,fj+1,fk-2)+funff(ii,fj+1,fk+3)) + &
+                                  C2*(funff(ii,fj+1,fk-1)+funff(ii,fj+1,fk+2)) + &
+                                  C3*(funff(ii,fj+1,fk  )+funff(ii,fj+1,fk+1))
+            tmp_xz_plane(ii, 5) = C1*(funff(ii,fj+2,fk-2)+funff(ii,fj+2,fk+3)) + &
+                                  C2*(funff(ii,fj+2,fk-1)+funff(ii,fj+2,fk+2)) + &
+                                  C3*(funff(ii,fj+2,fk  )+funff(ii,fj+2,fk+1))
+            tmp_xz_plane(ii, 6) = C1*(funff(ii,fj+3,fk-2)+funff(ii,fj+3,fk+3)) + &
+                                  C2*(funff(ii,fj+3,fk-1)+funff(ii,fj+3,fk+2)) + &
+                                  C3*(funff(ii,fj+3,fk  )+funff(ii,fj+3,fk+1))
+        end do
+
+        ! 优化点 2: 同样向量化 Y 方向压缩
+        !DIR$ VECTOR ALWAYS
+        do ii = ii_lo, ii_hi
+            tmp_x_line(ii) = C1*(tmp_xz_plane(ii, 1) + tmp_xz_plane(ii, 6)) + &
+                            C2*(tmp_xz_plane(ii, 2) + tmp_xz_plane(ii, 5)) + &
+                            C3*(tmp_xz_plane(ii, 3) + tmp_xz_plane(ii, 4))
+        end do
+
+        ! 优化点 3: 最终写入，利用已经缓存在 tmp_x_line 的数据
+        do i = imino, imaxo
+            fi = 2*(i + lbc(1) - 1) - 1 - lbf(1) + 1
+            func(i, j, k) = C1*(tmp_x_line(fi-2) + tmp_x_line(fi+3)) + &
+                            C2*(tmp_x_line(fi-1) + tmp_x_line(fi+2)) + &
+                            C3*(tmp_x_line(fi  ) + tmp_x_line(fi+1))
+        end do
+    end do
+end do
+#if 0
   do k = kmino,kmaxo
    do j = jmino,jmaxo
     do i = imino,imaxo
@@ -2462,7 +2558,7 @@
     enddo
    enddo
   enddo
-  
+#endif
   return
 
   end subroutine restrict3

AMSS_NCKU_source/rungekutta4_rout_c.C

@@ -0,0 +1,212 @@
+#include "rungekutta4_rout.h"
+#include <cstdio>
+#include <cstdlib>
+#include <cstddef>
+#include <complex>
+#include <immintrin.h>
+
+namespace {
+
+inline void rk4_stage0(std::size_t n,
+                       const double *__restrict f0,
+                       const double *__restrict frhs,
+                       double *__restrict f1,
+                       double c) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d vc = _mm512_set1_pd(c);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v0 = _mm512_loadu_pd(f0 + i);
+        const __m512d vr = _mm512_loadu_pd(frhs + i);
+        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, vr, v0));
+    }
+#elif defined(__AVX2__)
+    const __m256d vc = _mm256_set1_pd(c);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v0 = _mm256_loadu_pd(f0 + i);
+        const __m256d vr = _mm256_loadu_pd(frhs + i);
+        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, vr, v0));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        f1[i] = f0[i] + c * frhs[i];
+    }
+}
+
+inline void rk4_rhs_accum(std::size_t n,
+                          const double *__restrict f1,
+                          double *__restrict frhs) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d v2 = _mm512_set1_pd(2.0);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v1 = _mm512_loadu_pd(f1 + i);
+        const __m512d vrhs = _mm512_loadu_pd(frhs + i);
+        _mm512_storeu_pd(frhs + i, _mm512_fmadd_pd(v2, v1, vrhs));
+    }
+#elif defined(__AVX2__)
+    const __m256d v2 = _mm256_set1_pd(2.0);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v1 = _mm256_loadu_pd(f1 + i);
+        const __m256d vrhs = _mm256_loadu_pd(frhs + i);
+        _mm256_storeu_pd(frhs + i, _mm256_fmadd_pd(v2, v1, vrhs));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        frhs[i] = frhs[i] + 2.0 * f1[i];
+    }
+}
+
+inline void rk4_f1_from_f0_f1(std::size_t n,
+                              const double *__restrict f0,
+                              double *__restrict f1,
+                              double c) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d vc = _mm512_set1_pd(c);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v0 = _mm512_loadu_pd(f0 + i);
+        const __m512d v1 = _mm512_loadu_pd(f1 + i);
+        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, v1, v0));
+    }
+#elif defined(__AVX2__)
+    const __m256d vc = _mm256_set1_pd(c);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v0 = _mm256_loadu_pd(f0 + i);
+        const __m256d v1 = _mm256_loadu_pd(f1 + i);
+        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, v1, v0));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        f1[i] = f0[i] + c * f1[i];
+    }
+}
+
+inline void rk4_stage3(std::size_t n,
+                       const double *__restrict f0,
+                       double *__restrict f1,
+                       const double *__restrict frhs,
+                       double c) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d vc = _mm512_set1_pd(c);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v0 = _mm512_loadu_pd(f0 + i);
+        const __m512d v1 = _mm512_loadu_pd(f1 + i);
+        const __m512d vr = _mm512_loadu_pd(frhs + i);
+        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, _mm512_add_pd(v1, vr), v0));
+    }
+#elif defined(__AVX2__)
+    const __m256d vc = _mm256_set1_pd(c);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v0 = _mm256_loadu_pd(f0 + i);
+        const __m256d v1 = _mm256_loadu_pd(f1 + i);
+        const __m256d vr = _mm256_loadu_pd(frhs + i);
+        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, _mm256_add_pd(v1, vr), v0));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        f1[i] = f0[i] + c * (f1[i] + frhs[i]);
+    }
+}
+
+} // namespace
+
+extern "C" {
+
+void f_rungekutta4_scalar(double &dT, double &f0, double &f1, double &f_rhs, int &RK4) {
+    constexpr double F1o6 = 1.0 / 6.0;
+    constexpr double HLF = 0.5;
+    constexpr double TWO = 2.0;
+
+    switch (RK4) {
+    case 0:
+        f1 = f0 + HLF * dT * f_rhs;
+        break;
+    case 1:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + HLF * dT * f1;
+        break;
+    case 2:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + dT * f1;
+        break;
+    case 3:
+        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
+        break;
+    default:
+        std::fprintf(stderr, "rungekutta4_scalar_c: invalid RK4 stage %d\n", RK4);
+        std::abort();
+    }
+}
+
+void rungekutta4_cplxscalar_(double &dT,
+                             std::complex<double> &f0,
+                             std::complex<double> &f1,
+                             std::complex<double> &f_rhs,
+                             int &RK4) {
+    constexpr double F1o6 = 1.0 / 6.0;
+    constexpr double HLF = 0.5;
+    constexpr double TWO = 2.0;
+
+    switch (RK4) {
+    case 0:
+        f1 = f0 + HLF * dT * f_rhs;
+        break;
+    case 1:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + HLF * dT * f1;
+        break;
+    case 2:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + dT * f1;
+        break;
+    case 3:
+        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
+        break;
+    default:
+        std::fprintf(stderr, "rungekutta4_cplxscalar_c: invalid RK4 stage %d\n", RK4);
+        std::abort();
+    }
+}
+
+int f_rungekutta4_rout(int *ex, double &dT,
+                       double *f0, double *f1, double *f_rhs,
+                       int &RK4) {
+    const std::size_t n = static_cast<std::size_t>(ex[0]) *
+                          static_cast<std::size_t>(ex[1]) *
+                          static_cast<std::size_t>(ex[2]);
+    const double *const __restrict f0r = f0;
+    double *const __restrict f1r = f1;
+    double *const __restrict frhs = f_rhs;
+
+    if (__builtin_expect(static_cast<unsigned>(RK4) > 3u, 0)) {
+        std::fprintf(stderr, "rungekutta4_rout_c: invalid RK4 stage %d\n", RK4);
+        std::abort();
+    }
+
+    switch (RK4) {
+    case 0:
+        rk4_stage0(n, f0r, frhs, f1r, 0.5 * dT);
+        break;
+    case 1:
+        rk4_rhs_accum(n, f1r, frhs);
+        rk4_f1_from_f0_f1(n, f0r, f1r, 0.5 * dT);
+        break;
+    case 2:
+        rk4_rhs_accum(n, f1r, frhs);
+        rk4_f1_from_f0_f1(n, f0r, f1r, dT);
+        break;
+    default:
+        rk4_stage3(n, f0r, f1r, frhs, (1.0 / 6.0) * dT);
+        break;
+    }
+
+    return 0;
+}
+
+} // extern "C"

AMSS_NCKU_source/share_func.h

@@ -0,0 +1,246 @@
+#ifndef SHARE_FUNC_H
+#define SHARE_FUNC_H
+
+#include <stdlib.h>
+#include <stddef.h>
+#include <math.h>
+#include <stdio.h>
+#include <string.h>
+/* 主网格：0-based -> 1D */
+static inline size_t idx_ex(int i0, int j0, int k0, const int ex[3]) {
+    const int ex1 = ex[0], ex2 = ex[1];
+    return (size_t)i0 + (size_t)j0 * (size_t)ex1 + (size_t)k0 * (size_t)ex1 * (size_t)ex2;
+}
+
+/*
+ * fh 对应 Fortran: fh(-1:ex1, -1:ex2, -1:ex3)
+ * ord=2 => shift=1
+ * iF/jF/kF 为 Fortran 索引（可为 -1,0,1..ex）
+ */
+static inline size_t idx_fh_F_ord2(int iF, int jF, int kF, const int ex[3]) {
+    const int shift = 1;
+    const int nx = ex[0] + 2;      // ex1 + ord
+    const int ny = ex[1] + 2;
+
+    const int ii = iF + shift;     // 0..ex1+1
+    const int jj = jF + shift;     // 0..ex2+1
+    const int kk = kF + shift;     // 0..ex3+1
+
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * fh 对应 Fortran: fh(-2:ex1, -2:ex2, -2:ex3)
+ * ord=3 => shift=2
+ * iF/jF/kF 是 Fortran 索引（可为负）
+ */
+static inline size_t idx_fh_F(int iF, int jF, int kF, const int ex[3]) {
+    const int shift = 2;                 // ord=3 -> -2..ex
+    const int nx = ex[0] + 3;            // ex1 + ord
+    const int ny = ex[1] + 3;
+
+    const int ii = iF + shift;           // 0..ex1+2
+    const int jj = jF + shift;           // 0..ex2+2
+    const int kk = kF + shift;           // 0..ex3+2
+
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * func:  (1..extc1, 1..extc2, 1..extc3)   1-based in Fortran
+ * funcc: (-ord+1..extc1, -ord+1..extc2, -ord+1..extc3) in Fortran
+ *
+ * C 里我们把：
+ *   func  视为 0-based: i0=0..extc1-1, j0=0..extc2-1, k0=0..extc3-1
+ *   funcc 用“平移下标”存为一维数组：
+ *     iF in [-ord+1..extc1]  -> ii = iF + (ord-1)  in [0..extc1+ord-1]
+ *     总长度 nx = extc1 + ord
+ *     同理 ny = extc2 + ord, nz = extc3 + ord
+ */
+
+static inline size_t idx_func0(int i0, int j0, int k0, const int extc[3]) {
+    const int nx = extc[0], ny = extc[1];
+    return (size_t)i0 + (size_t)j0 * (size_t)nx + (size_t)k0 * (size_t)nx * (size_t)ny;
+}
+
+static inline size_t idx_funcc_F(int iF, int jF, int kF, int ord, const int extc[3]) {
+    const int shift = ord - 1;          // iF = -shift .. extc1
+    const int nx = extc[0] + ord;       // [-shift..extc1] 共 extc1+ord 个
+    const int ny = extc[1] + ord;
+
+    const int ii = iF + shift;          // 0..extc1+shift
+    const int jj = jF + shift;          // 0..extc2+shift
+    const int kk = kF + shift;          // 0..extc3+shift
+
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * 等价于 Fortran:
+ * funcc(1:extc1,1:extc2,1:extc3)=func
+ * do i=0,ord-1
+ *   funcc(-i,1:extc2,1:extc3) = funcc(i+1,1:extc2,1:extc3)*SoA(1)
+ * enddo
+ * do i=0,ord-1
+ *   funcc(:,-i,1:extc3) = funcc(:,i+1,1:extc3)*SoA(2)
+ * enddo
+ * do i=0,ord-1
+ *   funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
+ * enddo
+ */
+static inline void symmetry_bd_impl(int ord,
+                 int shift,
+                 const int extc[3],
+                 const double *__restrict func,
+                 double *__restrict funcc,
+                 const double SoA[3])
+{
+    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
+    const int nx = extc1 + ord;
+    const int ny = extc2 + ord;
+
+    const size_t snx = (size_t)nx;
+    const size_t splane = (size_t)nx * (size_t)ny;
+    const size_t interior_i = (size_t)shift + 1u;          /* iF = 1 */
+    const size_t interior_j = ((size_t)shift + 1u) * snx;  /* jF = 1 */
+    const size_t interior_k = ((size_t)shift + 1u) * splane; /* kF = 1 */
+    const size_t interior0 = interior_k + interior_j + interior_i;
+
+    /* 1) funcc(1:extc1,1:extc2,1:extc3) = func */
+    for (int k0 = 0; k0 < extc3; ++k0) {
+        const double *src_k = func + (size_t)k0 * (size_t)extc2 * (size_t)extc1;
+        const size_t dst_k0 = interior0 + (size_t)k0 * splane;
+        for (int j0 = 0; j0 < extc2; ++j0) {
+            const double *src = src_k + (size_t)j0 * (size_t)extc1;
+            double *dst = funcc + dst_k0 + (size_t)j0 * snx;
+            memcpy(dst, src, (size_t)extc1 * sizeof(double));
+        }
+    }
+
+    /* 2) funcc(-i,1:extc2,1:extc3) = funcc(i+1,1:extc2,1:extc3)*SoA(1) */
+    const double s1 = SoA[0];
+    if (s1 == 1.0) {
+        for (int ii = 0; ii < ord; ++ii) {
+            const size_t dst_i = (size_t)(shift - ii);
+            const size_t src_i = (size_t)(shift + ii + 1);
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
+                for (int j0 = 0; j0 < extc2; ++j0) {
+                    const size_t off = kbase + (size_t)j0 * snx;
+                    funcc[off + dst_i] = funcc[off + src_i];
+                }
+            }
+        }
+    } else if (s1 == -1.0) {
+        for (int ii = 0; ii < ord; ++ii) {
+            const size_t dst_i = (size_t)(shift - ii);
+            const size_t src_i = (size_t)(shift + ii + 1);
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
+                for (int j0 = 0; j0 < extc2; ++j0) {
+                    const size_t off = kbase + (size_t)j0 * snx;
+                    funcc[off + dst_i] = -funcc[off + src_i];
+                }
+            }
+        }
+    } else {
+        for (int ii = 0; ii < ord; ++ii) {
+            const size_t dst_i = (size_t)(shift - ii);
+            const size_t src_i = (size_t)(shift + ii + 1);
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
+                for (int j0 = 0; j0 < extc2; ++j0) {
+                    const size_t off = kbase + (size_t)j0 * snx;
+                    funcc[off + dst_i] = funcc[off + src_i] * s1;
+                }
+            }
+        }
+    }
+
+    /* 3) funcc(:,-j,1:extc3) = funcc(:,j+1,1:extc3)*SoA(2) */
+    const double s2 = SoA[1];
+    if (s2 == 1.0) {
+        for (int jj = 0; jj < ord; ++jj) {
+            const size_t dst_j = (size_t)(shift - jj) * snx;
+            const size_t src_j = (size_t)(shift + jj + 1) * snx;
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane;
+                double *dst = funcc + kbase + dst_j;
+                const double *src = funcc + kbase + src_j;
+                for (int i = 0; i < nx; ++i) dst[i] = src[i];
+            }
+        }
+    } else if (s2 == -1.0) {
+        for (int jj = 0; jj < ord; ++jj) {
+            const size_t dst_j = (size_t)(shift - jj) * snx;
+            const size_t src_j = (size_t)(shift + jj + 1) * snx;
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane;
+                double *dst = funcc + kbase + dst_j;
+                const double *src = funcc + kbase + src_j;
+                for (int i = 0; i < nx; ++i) dst[i] = -src[i];
+            }
+        }
+    } else {
+        for (int jj = 0; jj < ord; ++jj) {
+            const size_t dst_j = (size_t)(shift - jj) * snx;
+            const size_t src_j = (size_t)(shift + jj + 1) * snx;
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane;
+                double *dst = funcc + kbase + dst_j;
+                const double *src = funcc + kbase + src_j;
+                for (int i = 0; i < nx; ++i) dst[i] = src[i] * s2;
+            }
+        }
+    }
+
+    /* 4) funcc(:,:,-k) = funcc(:,:,k+1)*SoA(3) */
+    const double s3 = SoA[2];
+    if (s3 == 1.0) {
+        for (int kk = 0; kk < ord; ++kk) {
+            const size_t dst_k = (size_t)(shift - kk) * splane;
+            const size_t src_k = (size_t)(shift + kk + 1) * splane;
+            double *dst = funcc + dst_k;
+            const double *src = funcc + src_k;
+            for (size_t p = 0; p < splane; ++p) dst[p] = src[p];
+        }
+    } else if (s3 == -1.0) {
+        for (int kk = 0; kk < ord; ++kk) {
+            const size_t dst_k = (size_t)(shift - kk) * splane;
+            const size_t src_k = (size_t)(shift + kk + 1) * splane;
+            double *dst = funcc + dst_k;
+            const double *src = funcc + src_k;
+            for (size_t p = 0; p < splane; ++p) dst[p] = -src[p];
+        }
+    } else {
+        for (int kk = 0; kk < ord; ++kk) {
+            const size_t dst_k = (size_t)(shift - kk) * splane;
+            const size_t src_k = (size_t)(shift + kk + 1) * splane;
+            double *dst = funcc + dst_k;
+            const double *src = funcc + src_k;
+            for (size_t p = 0; p < splane; ++p) dst[p] = src[p] * s3;
+        }
+    }
+}
+
+static inline void symmetry_bd(int ord,
+                 const int extc[3],
+                 const double *func,
+                 double *funcc,
+                 const double SoA[3])
+{
+    if (ord <= 0) return;
+
+    /* Fast paths used by current C kernels: ord=2 (derivs), ord=3 (lopsided/KO). */
+    if (ord == 2) {
+        symmetry_bd_impl(2, 1, extc, func, funcc, SoA);
+        return;
+    }
+    if (ord == 3) {
+        symmetry_bd_impl(3, 2, extc, func, funcc, SoA);
+        return;
+    }
+
+    symmetry_bd_impl(ord, ord - 1, extc, func, funcc, SoA);
+}
+#endif

AMSS_NCKU_source/surface_integral.h

@@ -27,19 +27,24 @@ using namespace std;
 class surface_integral
 {
 
-private:
-	int Symmetry, factor;
-	int N_theta, N_phi; // Number of points in Theta & Phi directions
-	double dphi, dcostheta;
-	double *arcostheta, *wtcostheta;
-	int n_tot; // size of arrays
-
-	double *nx_g, *ny_g, *nz_g; // global list of unit normals
-	int myrank, cpusize;
-
-public:
-	surface_integral(int iSymmetry);
-	~surface_integral();
+private:
+	int Symmetry, factor;
+	int N_theta, N_phi; // Number of points in Theta & Phi directions
+	double dphi, dcostheta;
+	double *arcostheta, *wtcostheta;
+	int n_tot; // size of arrays
+
+	double *nx_g, *ny_g, *nz_g; // global list of unit normals
+	int myrank, cpusize;
+	int wave_cache_spinw, wave_cache_maxl, wave_cache_modes;
+	double *wave_theta_pos, *wave_theta_neg;
+	double *wave_phi_cos, *wave_phi_sin;
+	void clear_wave_cache();
+	void build_wave_cache(int spinw, int maxl);
+
+public:
+	surface_integral(int iSymmetry);
+	~surface_integral();
 
 	void surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
 				   int spinw, int maxl, int NN, double *RP, double *IP,
@@ -77,21 +82,37 @@ public:
 								 double &, double &, double &, double &, double &, double &, double &,
 								 double &, double &, double &, double &, double &, double &,
 								 double &, double &)); // NN is the length of RP and IP
-	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
-					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-					   var *Gmx, var *Gmy, var *Gmz,
-					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-					   double *Rout, monitor *Monitor);
-	void surf_MassPAng(double rex, int lev, ShellPatch *GH, var *chi, var *trK,
-					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-					   var *Gmx, var *Gmy, var *Gmz,
-					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-					   double *Rout, monitor *Monitor);
-	void surf_Wave(double rex, cgh *GH, ShellPatch *SH,
-				   var *chi, var *trK,
-				   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_MassPAng(double rex, int lev, ShellPatch *GH, var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_WaveMassPAng(double rex, int lev, cgh *GH,
+					   var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
+					   var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_WaveMassPAng(double rex, int lev, ShellPatch *GH,
+					   var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
+					   var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_Wave(double rex, cgh *GH, ShellPatch *SH,
+				   var *chi, var *trK,
+				   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
 				   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
 				   var *chix, var *chiy, var *chiz,
 				   var *trKx, var *trKy, var *trKz,
@@ -110,12 +131,12 @@ public:
 	bool SR_Interp_Points(MyList<var> *VarList, cgh *GH, ShellPatch *SH,
 						  int NN, double **XX, double *Shellf);
 
-	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
-					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-					   var *Gmx, var *Gmy, var *Gmz,
-					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
-					   double *Rout, monitor *Monitor, MPI_Comm Comm_here);
+	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
+					   double *Rout, monitor *Monitor, MPI_Comm Comm_here, bool refresh_mass_fields = true);
 	void surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
 				   int spinw, int maxl, int NN, double *RP, double *IP,
 				   monitor *Monitor, MPI_Comm Comm_here);

AMSS_NCKU_source/tool.h

@@ -0,0 +1,33 @@
+#include "share_func.h"
+void fdderivs(const int ex[3],
+              const double *f,
+              double *fxx, double *fxy, double *fxz,
+              double *fyy, double *fyz, double *fzz,
+              const double *X, const double *Y, const double *Z,
+              double SYM1, double SYM2, double SYM3,
+              int Symmetry, int onoff);
+
+void fderivs(const int ex[3],
+             const double *f,
+             double *fx, double *fy, double *fz,
+             const double *X, const double *Y, const double *Z,
+             double SYM1, double SYM2, double SYM3,
+             int Symmetry, int onoff);
+
+void kodis(const int ex[3],
+           const double *X, const double *Y, const double *Z,
+           const double *f, double *f_rhs,
+           const double SoA[3],
+           int Symmetry, double eps);
+
+void lopsided(const int ex[3],
+              const double *X, const double *Y, const double *Z,
+              const double *f, double *f_rhs,
+              const double *Sfx, const double *Sfy, const double *Sfz,
+              int Symmetry, const double SoA[3]);
+
+void lopsided_kodis(const int ex[3],
+                    const double *X, const double *Y, const double *Z,
+                    const double *f, double *f_rhs,
+                    const double *Sfx, const double *Sfy, const double *Sfz,
+                    int Symmetry, const double SoA[3], double eps);

BSSN_BUILD_CONFIG_MIGRATION.md

@@ -0,0 +1,211 @@
+# BSSN Build Config Migration
+
+This note records the build-configuration fix needed when replacing
+`AMSS_NCKU_Input.py` or `generate_macrodef.py` with a newer upstream version.
+
+## Problem
+
+`AMSS_NCKU_source/macrodef.h` is not the authoritative file used by normal
+runs. `AMSS_NCKU_Program.py` first generates macro files under
+`input_data.File_directory`, copies `AMSS_NCKU_source` to
+`<File_directory>/AMSS_NCKU_source_copy`, then copies the generated macro files
+into that copied source tree and compiles there.
+
+Therefore, makefile logic must not depend only on the stale
+`AMSS_NCKU_source/macrodef.h`. The actual equation path must be passed to the
+copied build tree from the same generation step that creates `macrodef.h`.
+
+The performance regression was caused by compiling/linking the
+`BSSN-EScalar` C wrapper into BSSN vacuum builds. For BSSN vacuum (`ABEtype=0`),
+the build must use:
+
+```make
+BSSN_USE_TRANSFER_CACHE=1
+BSSN_USE_ESCALAR_C_KERNEL=0
+```
+
+and must not link `bssn_escalar_rhs_c.o`.
+
+## Required Migration Steps
+
+### 1. Add an ABE type helper in `generate_macrodef.py`
+
+Add a helper that maps `input_data.Equation_Class` to the numeric `ABEtype`.
+Use the same mapping as `macrodef.h`:
+
+```python
+def get_abe_type():
+    if ( input_data.Equation_Class == "BSSN" ):
+        return 0
+    elif ( input_data.Equation_Class == "BSSN-EScalar" ):
+        return 1
+    elif ( input_data.Equation_Class == "BSSN-EM" ):
+        return 3
+    elif ( input_data.Equation_Class == "Z4C" ):
+        return 2
+    else:
+        raise ValueError("Equation_Class setting error!!!")
+```
+
+Update `generate_macrodef_h()` to print `#define ABEtype {get_abe_type()}`
+instead of duplicating the if/elif mapping.
+
+### 2. Generate a makefile fragment
+
+In `generate_macrodef.py`, add:
+
+```python
+def generate_build_config():
+    file1 = open(os.path.join(input_data.File_directory, "AMSS_NCKU_build.mk"), "w")
+    print("# Generated by generate_macrodef.py; do not edit manually.", file=file1)
+    print(f"ABE_TYPE := {get_abe_type()}", file=file1)
+    file1.close()
+```
+
+This file is the build-time authority for the equation path.
+
+### 3. Call and copy the generated build config
+
+In `AMSS_NCKU_Program.py`, after generating `macrodef.h` and `macrodef.fh`, call:
+
+```python
+generate_macrodef.generate_build_config()
+print(" AMSS-NCKU build config AMSS_NCKU_build.mk has been generated. ")
+```
+
+When copying generated files into `AMSS_NCKU_source_copy`, also copy:
+
+```python
+build_config_path = os.path.join(File_directory, "AMSS_NCKU_build.mk")
+shutil.copy2(build_config_path, AMSS_NCKU_source_copy)
+```
+
+### 4. Make the source makefile consume the generated config
+
+At the top of `AMSS_NCKU_source/makefile`, after `include makefile.inc`, add:
+
+```make
+-include AMSS_NCKU_build.mk
+
+ABE_TYPE ?= $(shell awk '/^[[:space:]]*\#define[[:space:]]+ABEtype/ {print $$3; exit}' macrodef.h 2>/dev/null)
+```
+
+The generated `AMSS_NCKU_build.mk` is used during normal Python-driven builds.
+The fallback keeps manual source-tree builds usable.
+
+### 5. Gate path-specific build options by `ABE_TYPE`
+
+Use effective build switches:
+
+```make
+ifeq ($(USE_TRANSFER_CACHE),auto)
+ifeq ($(ABE_TYPE),0)
+EFFECTIVE_USE_TRANSFER_CACHE = 1
+else
+EFFECTIVE_USE_TRANSFER_CACHE = 0
+endif
+else
+EFFECTIVE_USE_TRANSFER_CACHE = $(USE_TRANSFER_CACHE)
+endif
+
+ifeq ($(USE_CXX_ESCALAR_KERNEL),1)
+ifeq ($(ABE_TYPE),1)
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 1
+else
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 0
+endif
+else
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 0
+endif
+
+TRANSFER_CACHE_FLAG = -DBSSN_USE_TRANSFER_CACHE=$(EFFECTIVE_USE_TRANSFER_CACHE)
+ESCALAR_KERNEL_FLAG = -DBSSN_USE_ESCALAR_C_KERNEL=$(EFFECTIVE_USE_CXX_ESCALAR_KERNEL)
+```
+
+Only add `bssn_escalar_rhs_c.o` when the effective EScalar C kernel switch is
+enabled:
+
+```make
+ifeq ($(EFFECTIVE_USE_CXX_ESCALAR_KERNEL),1)
+CFILES += bssn_escalar_rhs_c.o
+endif
+```
+
+### 6. Use safe transfer-cache default
+
+In `AMSS_NCKU_source/makefile.inc`, keep:
+
+```make
+USE_TRANSFER_CACHE ?= auto
+```
+
+With the effective switch logic above, this enables cached transfer for BSSN
+vacuum while keeping non-BSSN paths on the uncached path by default.
+
+## Verification Checklist
+
+Run these checks after migrating:
+
+```bash
+python3 -c "import generate_macrodef; generate_macrodef.generate_build_config()"
+cat GW150914/AMSS_NCKU_build.mk
+```
+
+For BSSN, the generated file should contain:
+
+```make
+ABE_TYPE := 0
+```
+
+Dry-run the copied or source makefile:
+
+```bash
+make -n -B INTERP_LB_MODE=off ABE | grep -E 'BSSN_USE_TRANSFER_CACHE|BSSN_USE_ESCALAR_C_KERNEL|bssn_escalar_rhs_c'
+```
+
+Expected BSSN result:
+
+```text
+-DBSSN_USE_TRANSFER_CACHE=1 -DBSSN_USE_ESCALAR_C_KERNEL=0
+```
+
+and no `bssn_escalar_rhs_c.o` in the final link command.
+
+Run the full workflow:
+
+```bash
+python3 AMSS_NCKU_Program.py
+```
+
+For the 10-step BSSN test, compare coordinate output:
+
+```bash
+python3 - <<'PY'
+from pathlib import Path
+old = Path('../GW150914-06457/AMSS_NCKU_output/bssn_BH.dat')
+new = Path('GW150914/AMSS_NCKU_output/bssn_BH.dat')
+
+def rows(path):
+    out = []
+    for line in path.read_text().splitlines():
+        if not line.strip() or line.lstrip().startswith('#'):
+            continue
+        out.append([float(x) for x in line.split()])
+    return out
+
+ro, rn = rows(old), rows(new)
+n = min(len(ro), len(rn))
+max_abs = 0.0
+for i in range(n):
+    for a, b in zip(ro[i], rn[i]):
+        max_abs = max(max_abs, abs(a - b))
+print(f"old_rows={len(ro)} new_rows={len(rn)} compared_rows={n}")
+print(f"max_abs_diff={max_abs:.17g}")
+PY
+```
+
+For the validated migration, the first 10 rows matched exactly:
+
+```text
+max_abs_diff=0
+```

generate_interp_lb_header.py

@@ -0,0 +1,72 @@
+#!/usr/bin/env python3
+"""Convert interp_lb_profile.bin to a C header for compile-time embedding."""
+import struct, sys
+
+if len(sys.argv) < 3:
+    print(f"Usage: {sys.argv[0]} <profile.bin> <output.h>")
+    sys.exit(1)
+
+with open(sys.argv[1], 'rb') as f:
+    magic, version, nprocs, num_heavy = struct.unpack('IIii', f.read(16))
+    threshold = struct.unpack('d', f.read(8))[0]
+    times = list(struct.unpack(f'{nprocs}d', f.read(nprocs * 8)))
+    heavy = list(struct.unpack(f'{num_heavy}i', f.read(num_heavy * 4)))
+
+# For each heavy rank, compute split: left half -> lighter neighbor, right half -> heavy rank
+# (or vice versa depending on which neighbor is lighter)
+splits = []
+for hr in heavy:
+    prev_t = times[hr - 1] if hr > 0 else 1e30
+    next_t = times[hr + 1] if hr < nprocs - 1 else 1e30
+    if prev_t <= next_t:
+        splits.append((hr, hr - 1, hr))  # (block_id, r_left, r_right)
+    else:
+        splits.append((hr, hr, hr + 1))
+
+# Also remap the displaced neighbor blocks
+remaps = {}
+for hr, r_l, r_r in splits:
+    if r_l != hr:
+        # We took r_l's slot, so remap block r_l to its other neighbor
+        displaced = r_l
+        if displaced > 0 and displaced - 1 not in [s[0] for s in splits]:
+            remaps[displaced] = displaced - 1
+        elif displaced < nprocs - 1:
+            remaps[displaced] = displaced + 1
+    else:
+        displaced = r_r
+        if displaced < nprocs - 1 and displaced + 1 not in [s[0] for s in splits]:
+            remaps[displaced] = displaced + 1
+        elif displaced > 0:
+            remaps[displaced] = displaced - 1
+
+with open(sys.argv[2], 'w') as out:
+    out.write("/* Auto-generated from interp_lb_profile.bin — do not edit */\n")
+    out.write("#ifndef INTERP_LB_PROFILE_DATA_H\n")
+    out.write("#define INTERP_LB_PROFILE_DATA_H\n\n")
+    out.write(f"#define INTERP_LB_NPROCS {nprocs}\n")
+    out.write(f"#define INTERP_LB_NUM_HEAVY {num_heavy}\n\n")
+    out.write(f"static const int interp_lb_heavy_blocks[{num_heavy}] = {{")
+    out.write(", ".join(str(h) for h in heavy))
+    out.write("};\n\n")
+    out.write("/* Split table: {block_id, r_left, r_right} */\n")
+    out.write(f"static const int interp_lb_splits[{num_heavy}][3] = {{\n")
+    for bid, rl, rr in splits:
+        out.write(f"    {{{bid}, {rl}, {rr}}},\n")
+    out.write("};\n\n")
+    out.write("/* Rank remap for displaced neighbor blocks */\n")
+    out.write(f"static const int interp_lb_num_remaps = {len(remaps)};\n")
+    out.write(f"static const int interp_lb_remaps[][2] = {{\n")
+    for src, dst in sorted(remaps.items()):
+        out.write(f"    {{{src}, {dst}}},\n")
+    if not remaps:
+        out.write("    {-1, -1},\n")
+    out.write("};\n\n")
+    out.write("#endif /* INTERP_LB_PROFILE_DATA_H */\n")
+
+print(f"Generated {sys.argv[2]}:")
+print(f"  {num_heavy} heavy blocks to split: {heavy}")
+for bid, rl, rr in splits:
+    print(f"    block {bid}: split -> rank {rl} (left), rank {rr} (right)")
+for src, dst in sorted(remaps.items()):
+    print(f"    block {src}: remap -> rank {dst}")

generate_macrodef.py

@@ -12,6 +12,37 @@ import os
 import AMSS_NCKU_Input as input_data          ## import program input file
 
 
+##################################################################
+
+def get_abe_type():
+    if ( input_data.Equation_Class == "BSSN" ):
+        return 0
+    elif ( input_data.Equation_Class == "BSSN-EScalar" ):
+        return 1
+    elif ( input_data.Equation_Class == "BSSN-EM" ):
+        return 3
+    elif ( input_data.Equation_Class == "Z4C" ):
+        return 2
+    else:
+        raise ValueError("Equation_Class setting error!!!")
+
+
+##################################################################
+
+## Generate the makefile fragment used by the copied source tree.
+## The source-tree macrodef.h is not authoritative because macro files
+## are regenerated under File_directory for each run.
+
+def generate_build_config():
+
+    file1 = open( os.path.join(input_data.File_directory, "AMSS_NCKU_build.mk"), "w")
+
+    print( "# Generated by generate_macrodef.py; do not edit manually.", file=file1 )
+    print( f"ABE_TYPE := {get_abe_type()}",                             file=file1 )
+
+    file1.close()
+
+
 ##################################################################
 
 ## Generate the macro file macrodef.h according to user settings
@@ -58,19 +89,10 @@ def generate_macrodef_h():
     # 2: Z4c vacuum
     # 3: coupled to Maxwell field
 
-    if ( input_data.Equation_Class == "BSSN" ):
-        print( "#define ABEtype 0", file=file1 )
-        print(                      file=file1 )
-    elif ( input_data.Equation_Class == "BSSN-EScalar" ):
-        print( "#define ABEtype 1", file=file1 )
-        print(                      file=file1 )
-    elif ( input_data.Equation_Class == "BSSN-EM" ):
-        print( "#define ABEtype 3", file=file1 )
-        print(                      file=file1 )
-    elif ( input_data.Equation_Class == "Z4C" ):
-        print( "#define ABEtype 2", file=file1 )
-        print(                      file=file1 )
-    else:
+    try:
+        print( f"#define ABEtype {get_abe_type()}", file=file1 )
+        print(                                      file=file1 )
+    except ValueError:
         print( "Equation_Class setting error!!!"                )
         print()
         print( "# Equation type #define ABEtype setting error!!!", file=file1 )
@@ -144,6 +166,62 @@ def generate_macrodef_h():
     print( "#define REGLEV 0",      file=file1 )
     print(                          file=file1 )
 
+    # Define fine-grained timing/debug macros.
+    # All of them default to OFF so production builds do not pay profiling overhead.
+
+    fine_timing = getattr(input_data, "Fine_Timing",
+                  getattr(input_data, "Finegrained_Timing", "no"))
+    kernel_fine_timing = getattr(input_data, "Kernel_Fine_Timing",
+                          getattr(input_data, "BSSN_Kernel_Fine_Timing", "no"))
+    stdin_abort_poll = getattr(input_data, "Enable_Stdin_Abort_Poll",
+                       getattr(input_data, "Stdin_Abort_Poll", "no"))
+    timing_report_every = max(1, int(getattr(
+        input_data, "Timing_Every_Steps",
+        getattr(input_data, "Timing_Report_Every", 1))))
+    timing_top_hotspots = max(1, int(getattr(
+        input_data, "Timing_Top_Hotspots", 8)))
+
+    if ( fine_timing == "yes" ):
+        print( "#define BSSN_FINE_TIMING 1", file=file1 )
+        print(                               file=file1 )
+    elif ( fine_timing == "no" ):
+        print( "#define BSSN_FINE_TIMING 0", file=file1 )
+        print(                               file=file1 )
+    else:
+        print( "Fine_Timing setting error!!!" )
+        print()
+        print( "# Fine_Timing setting error!!!", file=file1 )
+        print(                                   file=file1 )
+
+    print( f"#define BSSN_FINE_TIMING_EVERY {timing_report_every}", file=file1 )
+    print(                                                          file=file1 )
+    print( f"#define BSSN_FINE_TIMING_TOPN {timing_top_hotspots}",  file=file1 )
+    print(                                                          file=file1 )
+
+    if ( kernel_fine_timing == "yes" ):
+        print( "#define BSSN_KERNEL_FINE_TIMING 1", file=file1 )
+        print(                                      file=file1 )
+    elif ( kernel_fine_timing == "no" ):
+        print( "#define BSSN_KERNEL_FINE_TIMING 0", file=file1 )
+        print(                                      file=file1 )
+    else:
+        print( "Kernel_Fine_Timing setting error!!!" )
+        print()
+        print( "# Kernel_Fine_Timing setting error!!!", file=file1 )
+        print(                                          file=file1 )
+
+    if ( stdin_abort_poll == "yes" ):
+        print( "#define BSSN_ENABLE_STDIN_ABORT_POLL 1", file=file1 )
+        print(                                           file=file1 )
+    elif ( stdin_abort_poll == "no" ):
+        print( "#define BSSN_ENABLE_STDIN_ABORT_POLL 0", file=file1 )
+        print(                                           file=file1 )
+    else:
+        print( "Enable_Stdin_Abort_Poll setting error!!!" )
+        print()
+        print( "# Enable_Stdin_Abort_Poll setting error!!!", file=file1 )
+        print(                                               file=file1 )
+
     # Define macro USE_GPU
     # use GPU or not
     
@@ -224,6 +302,21 @@ def generate_macrodef_h():
     print( "//     0: for every level;",                                                 file=file1 ) 
     print( "//     1: for all",                                                          file=file1 )
     print( "//",                                                                         file=file1 )
+    print( "// define BSSN_FINE_TIMING",                                                 file=file1 )
+    print( "//     enable fine-grained per-timestep timing monitor",                     file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_FINE_TIMING_EVERY",                                           file=file1 )
+    print( "//     report timing every N coarse timesteps",                              file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_FINE_TIMING_TOPN",                                            file=file1 )
+    print( "//     number of hottest timing buckets shown in stdout",                    file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_KERNEL_FINE_TIMING",                                          file=file1 )
+    print( "//     enable split timing inside compute_rhs_bssn",                         file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_ENABLE_STDIN_ABORT_POLL",                                     file=file1 )
+    print( "//     poll stdin and broadcast abort flag every coarse step",               file=file1 )
+    print( "//",                                                                         file=file1 )
     print( "// define USE_GPU",                                                          file=file1 )
     print( "//     use gpu or not",                                                      file=file1 )
     print( "//",                                                                         file=file1 )

makefile_and_run.py

@@ -10,17 +10,48 @@
 
 import AMSS_NCKU_Input as input_data
 import subprocess
+import time
 
-## CPU core binding configuration using taskset
-## taskset ensures all child processes inherit the CPU affinity mask
-## This forces make and all compiler processes to use only nohz_full cores (4-55, 60-111)
-## Format: taskset -c 4-55,60-111 ensures processes only run on these cores
-NUMACTL_CPU_BIND = "taskset -c 0-111"
 
-## Build parallelism configuration
-## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
-## Set make -j to utilize available cores for faster builds
-BUILD_JOBS = 104
+def get_last_n_cores_per_socket(n=32):
+    """
+    Read CPU topology via lscpu and return a taskset -c string
+    selecting the last `n` cores of each NUMA node (socket).
+
+    Example: 2 sockets x 56 cores each, n=32 -> node0: 24-55, node1: 80-111
+    -> "taskset -c 24-55,80-111"
+    """
+    result = subprocess.run(["lscpu", "--parse=NODE,CPU"], capture_output=True, text=True)
+
+    # Build a dict: node_id -> sorted list of CPU ids
+    node_cpus = {}
+    for line in result.stdout.splitlines():
+        if line.startswith("#") or not line.strip():
+            continue
+        parts = line.split(",")
+        if len(parts) < 2:
+            continue
+        node_id, cpu_id = int(parts[0]), int(parts[1])
+        node_cpus.setdefault(node_id, []).append(cpu_id)
+
+    segments = []
+    for node_id in sorted(node_cpus):
+        cpus = sorted(node_cpus[node_id])
+        selected = cpus[-n:]          # last n cores of this socket
+        segments.append(f"{selected[0]}-{selected[-1]}")
+
+    cpu_str = ",".join(segments)
+    total = len(segments) * n
+    print(f" CPU binding: taskset -c {cpu_str}  ({total} cores, last {n} per socket)")
+    #return f"taskset -c {cpu_str}"
+    return f""
+
+
+## CPU core binding: dynamically select the last 32 cores of each socket (64 cores total)
+NUMACTL_CPU_BIND = get_last_n_cores_per_socket(n=32)
+
+## Build parallelism: match the number of bound cores
+BUILD_JOBS = 64
 
 
 ##################################################################
@@ -39,7 +70,7 @@ def makefile_ABE():
 
     ## Build command with CPU binding to nohz_full cores
     if (input_data.GPU_Calculation == "no"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
+        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"
     else:
@@ -117,6 +148,7 @@ def run_ABE():
     
     if (input_data.GPU_Calculation == "no"):
         mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./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"
@@ -152,13 +184,14 @@ def run_ABE():
 ## Run the AMSS-NCKU TwoPuncture program TwoPunctureABE
 
 def run_TwoPunctureABE():
-
+    tp_time1=time.time()
     print(                                                          )
     print( " Running the AMSS-NCKU executable file TwoPunctureABE " ) 
     print(                                                          )
     
     ## Define the command to run
-    TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
+    #TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
+    TwoPuncture_command         = " ./TwoPunctureABE"
     TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
 
     ## Execute the command with subprocess.Popen and stream output
@@ -179,7 +212,9 @@ def run_TwoPunctureABE():
     print(                                               )
     print( " The TwoPunctureABE simulation is finished " ) 
     print(                                               )
-    
+    tp_time2=time.time()
+    et=tp_time2-tp_time1
+    print(f"Used time: {et}")
     return
 
 ##################################################################

parallel_plot_helper.py

@@ -0,0 +1,29 @@
+import multiprocessing
+
+def run_plot_task(task):
+    """Execute a single plotting task.
+    
+    Parameters
+    ----------
+    task : tuple
+        A tuple of (function, args_tuple) where function is a callable
+        plotting function and args_tuple contains its arguments.
+    """
+    func, args = task
+    return func(*args)
+
+
+def run_plot_tasks_parallel(plot_tasks):
+    """Execute a list of independent plotting tasks in parallel.
+
+    Uses the 'fork' context to create worker processes so that the main
+    script is NOT re-imported/re-executed in child processes.
+
+    Parameters
+    ----------
+    plot_tasks : list of tuples
+        Each element is (function, args_tuple).
+    """
+    ctx = multiprocessing.get_context('fork')
+    with ctx.Pool() as pool:
+        pool.map(run_plot_task, plot_tasks)

plot_GW_strain_amplitude_xiaoqu.py

@@ -11,6 +11,8 @@
 import numpy                               ## numpy for array operations
 import scipy                               ## scipy for interpolation and signal processing
 import math
+import matplotlib
+matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt     ## matplotlib for plotting
 import os                                  ## os for system/file operations
 

plot_binary_data.py

@@ -8,16 +8,23 @@
 ##
 #################################################
 
+## Restrict OpenMP to one thread per process so that running
+## many workers in parallel does not create an O(workers * BLAS_threads)
+## thread explosion.  The variable MUST be set before numpy/scipy
+## are imported, because the BLAS library reads them only at load time.
+import os
+os.environ.setdefault("OMP_NUM_THREADS",        "1")
+
 import numpy
 import scipy
+import matplotlib
+matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt
 from   matplotlib.colors    import LogNorm
 from   mpl_toolkits.mplot3d import Axes3D
 ## import torch
 import AMSS_NCKU_Input      as input_data
 
-import os
-
 
 #########################################################################################
 
@@ -192,3 +199,19 @@ def get_data_xy( Rmin, Rmax, n, data0, time, figure_title, figure_outdir ):
 
 ####################################################################################
 
+
+####################################################################################
+## Allow this module to be run as a standalone script so that each
+## binary-data plot can be executed in a fresh subprocess whose BLAS
+## environment variables (set above) take effect before numpy loads.
+##
+## Usage:  python3 plot_binary_data.py <filename> <binary_outdir> <figure_outdir>
+####################################################################################
+
+if __name__ == '__main__':
+    import sys
+    if len(sys.argv) != 4:
+        print(f"Usage: {sys.argv[0]} <filename> <binary_outdir> <figure_outdir>")
+        sys.exit(1)
+    plot_binary_data(sys.argv[1], sys.argv[2], sys.argv[3])
+

plot_xiaoqu.py

@@ -8,6 +8,8 @@
 #################################################
 
 import numpy                               ## numpy for array operations
+import matplotlib
+matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt     ## matplotlib for plotting
 from   mpl_toolkits.mplot3d import Axes3D  ## needed for 3D plots
 import glob
@@ -15,6 +17,9 @@ import os                                  ## operating system utilities
 
 import plot_binary_data
 import AMSS_NCKU_Input as input_data
+import subprocess
+import sys
+import multiprocessing
 
 # plt.rcParams['text.usetex'] = True  ## enable LaTeX fonts in plots
 
@@ -50,10 +55,40 @@ def generate_binary_data_plot( binary_outdir, figure_outdir ):
         file_list.append(x)
         print(x)
 
-    ## Plot each file in the list
+    ## Plot each file in parallel using subprocesses.
+    ## Each subprocess is a fresh Python process where the BLAS thread-count
+    ## environment variables (set at the top of plot_binary_data.py) take
+    ## effect before numpy is imported.  This avoids the thread explosion
+    ## that occurs when multiprocessing.Pool with 'fork' context inherits
+    ## already-initialized multi-threaded BLAS from the parent.
+    script = os.path.join( os.path.dirname(__file__), "plot_binary_data.py" )
+    max_workers = min( multiprocessing.cpu_count(), len(file_list) ) if file_list else 0
+
+    running = []
+    failed  = []
     for filename in file_list:
         print(filename)
-        plot_binary_data.plot_binary_data(filename, binary_outdir, figure_outdir)
+        proc = subprocess.Popen(
+            [sys.executable, script, filename, binary_outdir, figure_outdir],
+        )
+        running.append( (proc, filename) )
+        ## Keep at most max_workers subprocesses active at a time
+        if len(running) >= max_workers:
+            p, fn = running.pop(0)
+            p.wait()
+            if p.returncode != 0:
+                failed.append(fn)
+
+    ## Wait for all remaining subprocesses to finish
+    for p, fn in running:
+        p.wait()
+        if p.returncode != 0:
+            failed.append(fn)
+
+    if failed:
+        print( " WARNING: the following binary data plots failed:" )
+        for fn in failed:
+            print( "   ", fn )
 
     print(                        )
     print( " Binary Data Plot Has been Finished " )