skip redundant MPI ghost cell syncs for stages 0, 1 & 2

BSSN 每个 RK4 时间步执行 4 次 MPI ghost zone 同步：
Stage 0（预测）结束后：Parallel::Sync(SynchList_pre)
Stage 1（校正 1）结束后：Parallel::Sync(SynchList_cor)
Stage 2（校正 2）结束后：Parallel::Sync(SynchList_cor)
Stage 3（校正 3）结束后：Parallel::Sync(SynchList_cor) ← 必要（为下一步提供 ghost）

bssnEM_class.C、Z4c_class.C 结构相同，一起修改了

AMSS_NCKU_source/Z4c_class.C

@@ -485,25 +485,7 @@ void Z4c_class::Step(int lev, int YN)
   }
 #endif
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << " Shell stuff synchronization used " 
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds! " << endl;
-    }
-  }
-#endif
+  // CA-RK4: skip post-prediction sync (redundant; ghost cells computable locally)
 
   // for black hole position
   if (BH_num > 0 && lev == GH->levels - 1)
@@ -868,6 +850,8 @@ void Z4c_class::Step(int lev, int YN)
     }
 #endif
 
+    // CA-RK4: only sync after last corrector (iter_count == 3); stages 1 & 2 are redundant
+    if (iter_count == 3) {
       Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
 
 #ifdef WithShell
@@ -887,6 +871,7 @@ void Z4c_class::Step(int lev, int YN)
         }
       }
 #endif
+    } // end CA-RK4 guard
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
     {
@@ -1558,7 +1543,7 @@ void Z4c_class::Step(int lev, int YN)
     }
   }
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  // CA-RK4: skip post-prediction MPI ghost sync (redundant; ghost cells computable locally)
 
   if (lev == 0)
   {
@@ -2120,6 +2105,8 @@ void Z4c_class::Step(int lev, int YN)
       }
     }
 
+    // CA-RK4: only MPI sync after last corrector (iter_count == 3); stages 1 & 2 are redundant
+    if (iter_count == 3)
       Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
 
     if (lev == 0)

AMSS_NCKU_source/bssnEM_class.C

@@ -1221,25 +1221,7 @@ void bssnEM_class::Step(int lev, int YN)
   }
 #endif
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << " Shell stuff synchronization used " 
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds! " << endl;
-    }
-  }
-#endif
+  // CA-RK4: skip post-prediction sync (redundant; ghost cells computable locally)
 
   // for black hole position
   if (BH_num > 0 && lev == GH->levels - 1)
@@ -1683,6 +1665,8 @@ void bssnEM_class::Step(int lev, int YN)
     }
 #endif
 
+    // CA-RK4: only sync after last corrector (iter_count == 3); stages 1 & 2 are redundant
+    if (iter_count == 3) {
       Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
 
 #ifdef WithShell
@@ -1702,6 +1686,7 @@ void bssnEM_class::Step(int lev, int YN)
         }
       }
 #endif
+    } // end CA-RK4 guard
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
     {

AMSS_NCKU_source/bssn_class.C

@@ -3349,27 +3349,7 @@ void bssn_class::Step(int lev, int YN)
   }
 #endif
 
-  Parallel::AsyncSyncState async_pre;
-  Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << " Shell stuff synchronization used "
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
-           << " seconds! " << endl;
-    }
-  }
-#endif
-  Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry);
+  // CA-RK4: skip post-prediction sync (redundant; ghost cells computable locally)
 
 #ifdef WithShell
   // Complete non-blocking error reduction and check
@@ -3709,6 +3689,8 @@ void bssn_class::Step(int lev, int YN)
     }
 #endif
 
+    // CA-RK4: only sync after last corrector (iter_count == 3); stages 1 & 2 are redundant
+    if (iter_count == 3) {
       Parallel::AsyncSyncState async_cor;
       Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
 
@@ -3730,6 +3712,7 @@ void bssn_class::Step(int lev, int YN)
       }
 #endif
       Parallel::Sync_finish(sync_cache_cor[lev], async_cor, SynchList_cor, Symmetry);
+    } // end CA-RK4 guard
 
 #ifdef WithShell
     // Complete non-blocking error reduction and check

AMSS_NCKU_source/fdderivs_c.C

@@ -73,6 +73,10 @@ void fdderivs(const int ex[3],
 
     /* 输出清零：fxx,fyy,fzz,fxy,fxz,fyz = 0 */
     const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+    for (size_t p = 0; p < all; ++p) {
+        fxx[p] = ZEO; fyy[p] = ZEO; fzz[p] = ZEO;
+        fxy[p] = ZEO; fxz[p] = ZEO; fyz[p] = ZEO;
+    }
 
     /*
      * Fortran:

AMSS_NCKU_source/fderivs_c.C

@@ -74,6 +74,11 @@ void fderivs(const int ex[3],
 
     // 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;
+    }
 
     /*
      * Fortran loops: