黄老板逆天重写

AMSS_NCKU_Input.py

@@ -16,7 +16,7 @@ import numpy
 File_directory   = "GW150914"                    ## output file directory
 Output_directory = "binary_output"               ## binary data file directory
                                                  ## The file directory name should not be too long
-MPI_processes    = 64                             ## number of mpi processes used in the simulation
+MPI_processes    = 2                          ## number of mpi processes used in the simulation
 
 GPU_Calculation  = "no"                          ## Use GPU or not 
                                                  ## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)
@@ -50,7 +50,7 @@ Check_Time               = 100.0
 Dump_Time                = 100.0                  ## time inteval dT for dumping binary data
 D2_Dump_Time             = 100.0                  ## dump the ascii data for 2d surface after dT'
 Analysis_Time            = 0.1                    ## dump the puncture position and GW psi4 after dT"
-Evolution_Step_Number    = 10000000               ## stop the calculation after the maximal step number
+Evolution_Step_Number    = 6               ## stop the calculation after the maximal step number
 Courant_Factor           = 0.5                    ## Courant Factor
 Dissipation              = 0.15                   ## Kreiss-Oliger Dissipation Strength
 

AMSS_NCKU_Program.py

@@ -8,14 +8,6 @@
 ##
 ##################################################################
 
-## 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)
-
 
 ##################################################################
 
@@ -57,33 +49,32 @@ import time
 File_directory = os.path.join(input_data.File_directory)   
 
 ## If the specified output directory exists, ask the user whether to continue
-if os.path.exists(File_directory):
+# if os.path.exists(File_directory):
-    print( " Output dictionary has been existed !!!  "                                                              )
+#     print( " Output dictionary has been existed !!!  "                                                              )
-    print( " If you want to overwrite the existing file directory, please input 'continue' in the terminal !! "     ) 
+#     print( " If you want to overwrite the existing file directory, please input 'continue' in the terminal !! "     ) 
-    print( " If you want to retain the existing file directory, please input 'stop' in the terminal to stop the "   ) 
+#     print( " If you want to retain the existing file directory, please input 'stop' in the terminal to stop the "   ) 
-    print( " simulation. Then you can reset the output dictionary in the input script file AMSS_NCKU_Input.py !!! " )
+#     print( " simulation. Then you can reset the output dictionary in the input script file AMSS_NCKU_Input.py !!! " )
-    print(                                                                                                          )
+#     print(                                                                                                          )
-    ## Prompt whether to overwrite the existing directory
+#     ## Prompt whether to overwrite the existing directory
-    while True:
+#     while True:
-        try:
+#         try:
-            ## inputvalue = input()
+#             inputvalue = input()
-            inputvalue = "continue"
+#             ## If the user agrees to overwrite, proceed and remove the existing directory
-            ## If the user agrees to overwrite, proceed and remove the existing directory
+#             if ( inputvalue == "continue" ):
-            if ( inputvalue == "continue" ):
+#                 print( " Continue the calculation !!! " )
-                print( " Continue the calculation !!! " )
+#                 print(                                  )
-                print(                                  )
+#                 break  
-                break  
+#             ## If the user chooses not to overwrite, exit and keep the existing directory
-            ## If the user chooses not to overwrite, exit and keep the existing directory
+#             elif ( inputvalue == "stop" ):
-            elif ( inputvalue == "stop" ):
+#                 print( " Stop the calculation !!! "    )
-                print( " Stop the calculation !!! "    )
+#                 sys.exit() 
-                sys.exit() 
+#             ## If the user input is invalid, prompt again
-            ## If the user input is invalid, prompt again
+#             else:
-            else:
+#                 print( " Please input your choice !!! "                   )
-                print( " Please input your choice !!! "                   )
+#                 print( " Input 'continue' or 'stop' in the terminal !!! " )
-                print( " Input 'continue' or 'stop' in the terminal !!! " )
+#         except ValueError:
-        except ValueError:
+#             print( " Please input your choice !!! "                   )
-            print( " Please input your choice !!! "                   )
+#             print( " Input 'continue' or 'stop' in the terminal !!! " )
-            print( " Input 'continue' or 'stop' in the terminal !!! " )
         
 ## Remove the existing output directory if present
 shutil.rmtree(File_directory, ignore_errors=True)
@@ -433,31 +424,26 @@ 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_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot,   (binary_results_directory, figure_directory) ) )
+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_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
 
 ## Plot black hole separation vs. time
-plot_tasks.append( ( plot_xiaoqu.generate_puncture_distence_plot, (binary_results_directory, figure_directory) ) )
+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_tasks.append( ( plot_xiaoqu.generate_gravitational_wave_psi4_plot, (binary_results_directory, figure_directory, i) ) )
+    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_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_tasks.append( ( plot_xiaoqu.generate_ADMmass_plot, (binary_results_directory, figure_directory, i) ) )
+    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_tasks.append( ( plot_xiaoqu.generate_constraint_check_plot, (binary_results_directory, figure_directory, i) ) )
+    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_source/ABE.C

@@ -24,7 +24,7 @@ using namespace std;
 
 #include "misc.h"
 #include "macrodef.h"
-
+#include <omp.h>
 #ifndef ABEtype
 #error "not define ABEtype"
 #endif
@@ -71,6 +71,7 @@ int main(int argc, char *argv[])
       if (myrank == 0)
       {     
             Begin_clock = MPI_Wtime();
+
       }
 
       if (argc > 1)

AMSS_NCKU_source/MPatch.C

@@ -13,7 +13,7 @@ using namespace std;
 #include "MPatch.h"
 #include "Parallel.h"
 #include "fmisc.h"
-
+#include "xh_global_interp.h"
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
 {
 
@@ -394,7 +394,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
     while (notfind && Bp) // run along Blocks
     {
       Block *BP = Bp->data;
-
       bool flag = true;
       for (int i = 0; i < dim; i++)
       {
@@ -430,8 +429,10 @@ void Patch::Interp_Points(MyList<var> *VarList,
           int k = 0;
           while (varl) // run along variables
           {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+
+            xh_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++;
           }
@@ -441,7 +442,9 @@ void Patch::Interp_Points(MyList<var> *VarList,
         break;
       Bp = Bp->next;
     }
+
   }
+
   // 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,
@@ -506,13 +509,11 @@ void Patch::Interp_Points(MyList<var> *VarList,
   // 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.
-  /*
-  double t_calc_end, t_calc_total = 0;
-  double t_calc_start = MPI_Wtime();*/
   int myrank, nprocs;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
   MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
-
+// printf("here----\n");
+  // int zzz = 0;
   int ordn = 2 * ghost_width;
   MyList<var> *varl;
   int num_var = 0;
@@ -531,30 +532,35 @@ void Patch::Interp_Points(MyList<var> *VarList,
   for (int j = 0; j < NN; j++)
     owner_rank[j] = -1;
 
-  double DH[dim], llb[dim], uub[dim];
+  double DH[dim];
   for (int i = 0; i < dim; i++)
     DH[i] = getdX(i);
 
   // --- Interpolation phase (identical to original) ---
+  // printf("NN: %d, num_var = %d\n", NN, num_var);
+  #pragma omp parallel
+  {
+  #pragma omp for
   for (int j = 0; j < NN; j++)
   {
-    double pox[dim];
+    double pox[dim], llb[dim], uub[dim];
+    MyList<var> *varl1;
     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]))
+      // 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 (";
+      //   cout << "Patch::Interp_Points: point (";
-        for (int k = 0; k < dim; k++)
+      //   for (int k = 0; k < dim; k++)
-        {
+      //   {
-          cout << XX[k][j];
+      //     cout << XX[k][j];
-          if (k < dim - 1)
+      //     if (k < dim - 1)
-            cout << ",";
+      //       cout << ",";
-          else
+      //     else
-            cout << ") is out of current Patch." << endl;
+      //       cout << ") is out of current Patch." << endl;
-        }
+      //   }
-        MPI_Abort(MPI_COMM_WORLD, 1);
+      //   MPI_Abort(MPI_COMM_WORLD, 1);
-      }
+      // }
     }
 
     MyList<Block> *Bp = blb;
@@ -586,21 +592,23 @@ void Patch::Interp_Points(MyList<var> *VarList,
           break;
         }
       }
-
+      // printf("flag = %d\n", flag);
       if (flag)
       {
         notfind = false;
         owner_rank[j] = BP->rank;
         if (myrank == BP->rank)
         {
-          varl = VarList;
+          varl1 = VarList;
           int k = 0;
-          while (varl)
+          while (varl1)
           {
-            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);
+            xh_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl1->data->sgfn], Shellf[j * num_var + k],
-            varl = varl->next;
+                            pox[0], pox[1], pox[2], ordn, varl1->data->SoA, Symmetry);
+            varl1 = varl1->next;
             k++;
+            // zzz += 1;
           }
         }
       }
@@ -609,9 +617,8 @@ void Patch::Interp_Points(MyList<var> *VarList,
       Bp = Bp->next;
     }
   }
-  /*
+  }
-      t_calc_end = MPI_Wtime();
+  // printf("Interpolation done, zzz = %d\n", zzz);
-      t_calc_total = t_calc_end - t_calc_start;*/
   // --- Error check for unfound points ---
   for (int j = 0; j < NN; j++)
   {
@@ -768,63 +775,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
   delete[] recv_count;
   delete[] consumer_rank;
   delete[] owner_rank;
-  /*
-  // 4. 汇总并输出真正干活最慢的 Top 4
-  struct RankStats {
-    int rank;
-    double calc_time; // 净计算时间
-  };
-
-  // 创建当前进程的统计数据
-  RankStats local_stat;
-  local_stat.rank = myrank;
-  local_stat.calc_time = t_calc_total;
-
-  // 为所有进程的统计数据分配内存
-  RankStats *all_stats = nullptr;
-  if (myrank == 0) {
-    all_stats = new RankStats[nprocs];
-  }
-
-  // 使用MPI_Gather收集所有进程的数据到rank 0
-  MPI_Gather(&local_stat, sizeof(RankStats), MPI_BYTE,
-             all_stats, sizeof(RankStats), MPI_BYTE,
-             0, MPI_COMM_WORLD);
-
-  // 准备输出前4个rank的信息（所有rank都参与，确保广播后一致）
-  int top10_ranks[10] = { -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 };
-  double top10_times[10] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
-  int num_top10 = 0;
-
-  if (myrank == 0) {
-    // 按 calc_time（净计算时间）排序
-    std::sort(all_stats, all_stats + nprocs, [](const RankStats& a, const RankStats& b) {
-        return a.calc_time > b.calc_time;
-    });
-
-    // 取前4个
-    num_top10 = (nprocs < 10) ? nprocs : 10;
-    for (int i = 0; i < num_top10; i++) {
-      top10_ranks[i] = all_stats[i].rank;
-      top10_times[i] = all_stats[i].calc_time;
-    }
-
-    printf("\n--- Top %d Ranks by ACTIVE COMPUTATION (CPU Time) ---\n", num_top10);
-    for (int i = 0; i < num_top10; i++) {
-      printf("Rank [%4d]: Calc %.6f s\n", top10_ranks[i], top10_times[i]);
-    }
-
-    // 清理分配的内存
-    delete[] all_stats;
-  }
-
-  // 广播前4个rank的信息给所有进程
-  MPI_Bcast(&num_top10, 1, MPI_INT, 0, MPI_COMM_WORLD);
-  if (num_top10 > 0) {
-    MPI_Bcast(top10_ranks, 10, MPI_INT, 0, MPI_COMM_WORLD);
-    MPI_Bcast(top10_times, 10, MPI_DOUBLE, 0, MPI_COMM_WORLD);
-  }
-*/
 }
 void Patch::Interp_Points(MyList<var> *VarList,
                           int NN, double **XX,
@@ -834,7 +784,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
   int myrank, lmyrank;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
   MPI_Comm_rank(Comm_here, &lmyrank);
-
   int ordn = 2 * ghost_width;
   MyList<var> *varl;
   int num_var = 0;
@@ -924,7 +873,7 @@ void Patch::Interp_Points(MyList<var> *VarList,
           int k = 0;
           while (varl) // run along variables
           {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+            xh_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++;
@@ -1156,7 +1105,7 @@ bool Patch::Interp_ONE_Point(MyList<var> *VarList, double *XX,
         {
           //              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[k],
+          xh_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[k],
                           pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
           varl = varl->next;
           k++;
@@ -1398,7 +1347,7 @@ bool Patch::Interp_ONE_Point(MyList<var> *VarList, double *XX,
         {
           //              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[k],
+          xh_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[k],
                           pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
           varl = varl->next;
           k++;

AMSS_NCKU_source/NullShellPatch.h

@@ -24,7 +24,6 @@ using namespace std;
 #endif
 
 #include <mpi.h>
-#include <memory.h>
 #include "MyList.h"
 #include "Block.h"
 #include "Parallel.h"

AMSS_NCKU_source/Parallel.C

@@ -4,8 +4,7 @@
 #include "prolongrestrict.h"
 #include "misc.h"
 #include "parameters.h"
-#include <set>
+#include <omp.h>
-
 int Parallel::partition1(int &nx, int split_size, int min_width, int cpusize, int shape) // special for 1 diemnsion
 {
   nx = Mymax(1, shape / min_width);
@@ -116,7 +115,7 @@ int Parallel::partition3(int *nxyz, int split_size, int *min_width, int cpusize,
   return nx * ny * nz;
 #undef SEARCH_SIZE
 }
-#elif 0 // Zhihui's idea one on 2013-09-25
+#elif 1 // Zhihui's idea one on 2013-09-25
 {
   int nx, ny, nz;
   int hmin_width;
@@ -151,7 +150,7 @@ int Parallel::partition3(int *nxyz, int split_size, int *min_width, int cpusize,
 
   return nx * ny * nz;
 }
-#elif 0 // Zhihui's idea two on 2013-09-25
+#elif 1 // Zhihui's idea two on 2013-09-25
 {
   int nx, ny, nz;
   const int hmin_width = 8; // for example we use 8
@@ -501,428 +500,6 @@ MyList<Block> *Parallel::distribute(MyList<Patch> *PatchLIST, int cpusize, int i
 
   return BlL;
 }
-MyList<Block> *Parallel::distribute_hard(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfsi,
-                                    bool periodic, int nodes)
-{
-#ifdef USE_GPU_DIVIDE
-  double cpu_part, gpu_part;
-  map<string, double>::iterator iter;
-  iter = parameters::dou_par.find("cpu part");
-  if (iter != parameters::dou_par.end())
-  {
-    cpu_part = iter->second;
-  }
-  else
-  {
-    int myrank;
-    MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-    // read parameter from file
-    const int LEN = 256;
-    char pline[LEN];
-    string str, sgrp, skey, sval;
-    int sind;
-    char pname[50];
-    {
-      map<string, string>::iterator iter = parameters::str_par.find("inputpar");
-      if (iter != parameters::str_par.end())
-      {
-        strcpy(pname, (iter->second).c_str());
-      }
-      else
-      {
-        cout << "Error inputpar" << endl;
-        exit(0);
-      }
-    }
-    ifstream inf(pname, ifstream::in);
-    if (!inf.good() && myrank == 0)
-    {
-      cout << "Can not open parameter file " << pname << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-
-    for (int i = 1; inf.good(); i++)
-    {
-      inf.getline(pline, LEN);
-      str = pline;
-
-      int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-      if (status == -1)
-      {
-        cout << "error reading parameter file " << pname << " in line " << i << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-      else if (status == 0)
-        continue;
-
-      if (sgrp == "ABE")
-      {
-        if (skey == "cpu part")
-          cpu_part = atof(sval.c_str());
-      }
-    }
-    inf.close();
-
-    parameters::dou_par.insert(map<string, double>::value_type("cpu part", cpu_part));
-  }
-  iter = parameters::dou_par.find("gpu part");
-  if (iter != parameters::dou_par.end())
-  {
-    gpu_part = iter->second;
-  }
-  else
-  {
-    int myrank;
-    MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-    // read parameter from file
-    const int LEN = 256;
-    char pline[LEN];
-    string str, sgrp, skey, sval;
-    int sind;
-    char pname[50];
-    {
-      map<string, string>::iterator iter = parameters::str_par.find("inputpar");
-      if (iter != parameters::str_par.end())
-      {
-        strcpy(pname, (iter->second).c_str());
-      }
-      else
-      {
-        cout << "Error inputpar" << endl;
-        exit(0);
-      }
-    }
-    ifstream inf(pname, ifstream::in);
-    if (!inf.good() && myrank == 0)
-    {
-      cout << "Can not open parameter file " << pname << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-
-    for (int i = 1; inf.good(); i++)
-    {
-      inf.getline(pline, LEN);
-      str = pline;
-
-      int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-      if (status == -1)
-      {
-        cout << "error reading parameter file " << pname << " in line " << i << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-      else if (status == 0)
-        continue;
-
-      if (sgrp == "ABE")
-      {
-        if (skey == "gpu part")
-          gpu_part = atof(sval.c_str());
-      }
-    }
-    inf.close();
-
-    parameters::dou_par.insert(map<string, double>::value_type("gpu part", gpu_part));
-  }
-
-  if (nodes == 0)
-    nodes = cpusize / 2;
-#else
-  if (nodes == 0)
-    nodes = cpusize;
-#endif
-
-  if (dim != 3)
-  {
-    cout << "distrivute: now we only support 3-dimension" << endl;
-    MPI_Abort(MPI_COMM_WORLD, 1);
-  }
-
-  MyList<Block> *BlL = 0;
-  int split_size, min_size, block_size = 0;
-
-  int min_width = 2 * Mymax(ghost_width, buffer_width);
-  int nxyz[dim], mmin_width[dim], min_shape[dim];
-
-  MyList<Patch> *PLi = PatchLIST;
-  for (int i = 0; i < dim; i++)
-    min_shape[i] = PLi->data->shape[i];
-  int lev = PLi->data->lev;
-  PLi = PLi->next;
-  while (PLi)
-  {
-    Patch *PP = PLi->data;
-    for (int i = 0; i < dim; i++)
-      min_shape[i] = Mymin(min_shape[i], PP->shape[i]);
-    if (lev != PLi->data->lev)
-      cout << "Parallel::distribute CAUSTION: meet Patches for different level: " << lev << " and " << PLi->data->lev << endl;
-    PLi = PLi->next;
-  }
-
-  for (int i = 0; i < dim; i++)
-    mmin_width[i] = Mymin(min_width, min_shape[i]);
-
-  min_size = mmin_width[0];
-  for (int i = 1; i < dim; i++)
-    min_size = min_size * mmin_width[i];
-
-  PLi = PatchLIST;
-  while (PLi)
-  {
-    Patch *PP = PLi->data;
-    //    PP->checkPatch(true);
-    int bs = PP->shape[0];
-    for (int i = 1; i < dim; i++)
-      bs = bs * PP->shape[i];
-    block_size = block_size + bs;
-    PLi = PLi->next;
-  }
-  split_size = Mymax(min_size, block_size / nodes);
-  split_size = Mymax(1, split_size);
-
-  int n_rank = 0;
-  PLi = PatchLIST;
-  int reacpu = 0;
-  int current_block_id = 0;
-  while (PLi) {
-    Block *ng0, *ng;
-    bool first_block_in_patch = true; 
-    Patch *PP = PLi->data;
-    reacpu += partition3(nxyz, split_size, mmin_width, nodes, PP->shape);
-
-    for (int i = 0; i < nxyz[0]; i++)
-    for (int j = 0; j < nxyz[1]; j++)
-    for (int k = 0; k < nxyz[2]; k++)
-    {
-        // --- 1. 定义局部变量 ---
-        int ibbox_here[6], shape_here[3];
-        double bbox_here[6], dd;
-        Block *current_ng_start = nullptr; // 本次循环产生的第一个(或唯一一个)块
-
-        // --- 2. 核心逻辑分支 ---
-        if (current_block_id == 27 || current_block_id == 28 ||
-            current_block_id == 35 || current_block_id == 36)
-        {
-            // A. 计算原始索引 (不带 Ghost)
-            int ib0 = (PP->shape[0] * i) / nxyz[0];
-            int ib3 = (PP->shape[0] * (i + 1)) / nxyz[0] - 1;
-            int jb1 = (PP->shape[1] * j) / nxyz[1];
-            int jb4 = (PP->shape[1] * (j + 1)) / nxyz[1] - 1;
-            int kb2 = (PP->shape[2] * k) / nxyz[2];
-            int kb5 = (PP->shape[2] * (k + 1)) / nxyz[2] - 1;
-
-            int r_l, r_r;
-            if(current_block_id == 27)      { r_l = 26; r_r = 27; }
-            else if(current_block_id == 28) { r_l = 28; r_r = 29; }
-            else if(current_block_id == 35) { r_l = 34; r_r = 35; }
-            else                            { r_l = 36; r_r = 37; }
-            Block * split_first_block = nullptr;
-            Block * split_last_block = nullptr; 
-            // 拆分逻辑：该函数应更新类成员变量 split_first_block 和 split_last_block
-            splitHotspotBlock(BlL, dim, ib0, ib3, jb1, jb4, kb2, kb5, 
-                              PP, r_l, r_r, ingfsi, fngfsi, periodic,split_first_block,split_last_block);
-            
-            current_ng_start = split_first_block;
-            ng = split_last_block; 
-        }
-        else 
-        {
-            // B. 普通块逻辑 (含 Ghost 扩张)
-            ibbox_here[0] = (PP->shape[0] * i) / nxyz[0];
-            ibbox_here[3] = (PP->shape[0] * (i + 1)) / nxyz[0] - 1;
-            ibbox_here[1] = (PP->shape[1] * j) / nxyz[1];
-            ibbox_here[4] = (PP->shape[1] * (j + 1)) / nxyz[1] - 1;
-            ibbox_here[2] = (PP->shape[2] * k) / nxyz[2];
-            ibbox_here[5] = (PP->shape[2] * (k + 1)) / nxyz[2] - 1;
-
-            if (periodic) {
-                for(int d=0; d<3; d++) {
-                    ibbox_here[d] -= ghost_width;
-                    ibbox_here[d+3] += ghost_width;
-                }
-            } else {
-                ibbox_here[0] = Mymax(0, ibbox_here[0] - ghost_width);
-                ibbox_here[3] = Mymin(PP->shape[0] - 1, ibbox_here[3] + ghost_width);
-                ibbox_here[1] = Mymax(0, ibbox_here[1] - ghost_width);
-                ibbox_here[4] = Mymin(PP->shape[1] - 1, ibbox_here[4] + ghost_width);
-                ibbox_here[2] = Mymax(0, ibbox_here[2] - ghost_width);
-                ibbox_here[5] = Mymin(PP->shape[2] - 1, ibbox_here[5] + ghost_width);
-            }
-
-            for(int d=0; d<3; d++) shape_here[d] = ibbox_here[d+3] - ibbox_here[d] + 1;
-
-            // 物理坐标计算 (根据你的宏定义 Cell/Vertex)
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-          // 0--4, 5--10
-          dd = (PP->bbox[3] - PP->bbox[0]) / (PP->shape[0] - 1);
-          bbox_here[0] = PP->bbox[0] + ibbox_here[0] * dd;
-          bbox_here[3] = PP->bbox[0] + ibbox_here[3] * dd;
-
-          dd = (PP->bbox[4] - PP->bbox[1]) / (PP->shape[1] - 1);
-          bbox_here[1] = PP->bbox[1] + ibbox_here[1] * dd;
-          bbox_here[4] = PP->bbox[1] + ibbox_here[4] * dd;
-
-          dd = (PP->bbox[5] - PP->bbox[2]) / (PP->shape[2] - 1);
-          bbox_here[2] = PP->bbox[2] + ibbox_here[2] * dd;
-          bbox_here[5] = PP->bbox[2] + ibbox_here[5] * dd;
-#else
-#ifdef Cell
-          // 0--5, 5--10
-          dd = (PP->bbox[3] - PP->bbox[0]) / PP->shape[0];
-          bbox_here[0] = PP->bbox[0] + (ibbox_here[0]) * dd;
-          bbox_here[3] = PP->bbox[0] + (ibbox_here[3] + 1) * dd;
-
-          dd = (PP->bbox[4] - PP->bbox[1]) / PP->shape[1];
-          bbox_here[1] = PP->bbox[1] + (ibbox_here[1]) * dd;
-          bbox_here[4] = PP->bbox[1] + (ibbox_here[4] + 1) * dd;
-
-          dd = (PP->bbox[5] - PP->bbox[2]) / PP->shape[2];
-          bbox_here[2] = PP->bbox[2] + (ibbox_here[2]) * dd;
-          bbox_here[5] = PP->bbox[2] + (ibbox_here[5] + 1) * dd;
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-            ng = createMappedBlock(BlL, dim, shape_here, bbox_here, current_block_id, ingfsi, fngfsi, PP->lev);
-            current_ng_start = ng;
-        }
-
-        // --- 3. 统一处理 Patch 起始 Block 指针 ---
-        if (first_block_in_patch) {
-            ng0 = current_ng_start;
-            
-            // 立即设置 PP->blb，避免后续循环覆盖 ng0
-            MyList<Block> *Bp_start = BlL;
-            while (Bp_start && Bp_start->data != ng0) Bp_start = Bp_start->next;
-            PP->blb = Bp_start;
-            
-            first_block_in_patch = false;
-        }
-        
-        current_block_id++;
-    }
-
-    // --- 4. 设置 Patch 结束 Block 指针 ---
-    MyList<Block> *Bp_end = BlL;
-    while (Bp_end && Bp_end->data != ng) Bp_end = Bp_end->next;
-    PP->ble = Bp_end;
-
-    PLi = PLi->next;
-    first_block_in_patch = true; 
-  }
-  if (reacpu < nodes * 2 / 3)
-  {
-    int myrank;
-    MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-    if (myrank == 0)
-      cout << "Parallel::distribute CAUSTION: level#" << lev << " uses essencially " << reacpu << " processors vs " << nodes << " nodes run, your scientific computation scale is not as large as you estimate." << endl;
-  }
-
-  return BlL;
-}
-
- /**
- * @brief 将当前 Block 几何二等分并存入列表
- * @param axis 拆分轴：0-x, 1-y, 2-z (建议选最长轴)
- */
-Block* Parallel::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)
-{
-    // 1. 索引二分 (基于无 ghost 的原始索引)
-    int mid = (ib0_orig + ib3_orig) / 2;
-
-    // 左块原始索引: [ib0, mid], 右块原始索引: [mid+1, ib3]
-    int indices_L[6] = {ib0_orig, jb1_orig, kb2_orig, mid, jb4_orig, kb5_orig};
-    int indices_R[6] = {mid + 1, jb1_orig, kb2_orig, ib3_orig, jb4_orig, kb5_orig};
-
-    // 2. 内部处理逻辑 (复刻原 distribute 逻辑)
-    auto createSubBlock = [&](int* ib_raw, int target_rank) {
-        int ib_final[6];
-        int sh_here[3];
-        double bb_here[6], dd;
-
-        // --- 逻辑 A: Ghost 扩张 ---
-        if (periodic) {
-            ib_final[0] = ib_raw[0] - ghost_width;
-            ib_final[3] = ib_raw[3] + ghost_width;
-            ib_final[1] = ib_raw[1] - ghost_width;
-            ib_final[4] = ib_raw[4] + ghost_width;
-            ib_final[2] = ib_raw[2] - ghost_width;
-            ib_final[5] = ib_raw[5] + ghost_width;
-        } else {
-            ib_final[0] = Mymax(0, ib_raw[0] - ghost_width);
-            ib_final[3] = Mymin(PP->shape[0] - 1, ib_raw[3] + ghost_width);
-            ib_final[1] = Mymax(0, ib_raw[1] - ghost_width);
-            ib_final[4] = Mymin(PP->shape[1] - 1, ib_raw[4] + ghost_width);
-            ib_final[2] = Mymax(0, ib_raw[2] - ghost_width);
-            ib_final[5] = Mymin(PP->shape[2] - 1, ib_raw[5] + ghost_width);
-        }
-
-        sh_here[0] = ib_final[3] - ib_final[0] + 1;
-        sh_here[1] = ib_final[4] - ib_final[1] + 1;
-        sh_here[2] = ib_final[5] - ib_final[2] + 1;
-
-        // --- 逻辑 B: 物理坐标计算 (严格匹配 Cell 模式) ---
-        // X 方向
-        dd = (PP->bbox[3] - PP->bbox[0]) / PP->shape[0];
-        bb_here[0] = PP->bbox[0] + ib_final[0] * dd;
-        bb_here[3] = PP->bbox[0] + (ib_final[3] + 1) * dd;
-
-        // Y 方向
-        dd = (PP->bbox[4] - PP->bbox[1]) / PP->shape[1];
-        bb_here[1] = PP->bbox[1] + ib_final[1] * dd;
-        bb_here[4] = PP->bbox[1] + (ib_final[4] + 1) * dd;
-
-        // Z 方向
-        dd = (PP->bbox[5] - PP->bbox[2]) / PP->shape[2];
-        bb_here[2] = PP->bbox[2] + ib_final[2] * dd;
-        bb_here[5] = PP->bbox[2] + (ib_final[5] + 1) * dd;
-
-        Block* Bg = new Block(dim, sh_here, bb_here, target_rank, ingfsi, fngfsi, PP->lev);
-        if (BlL) BlL->insert(Bg);
-        else     BlL = new MyList<Block>(Bg);
-
-       
-        return Bg;
-    };
-
-    // 执行创建
-    split_first_block = createSubBlock(indices_L, r_left);
-    split_last_block  = createSubBlock(indices_R, r_right);
-}
-
-
-/**
- * @brief 创建映射后的 Block
- */
-  Block* Parallel::createMappedBlock(MyList<Block>* &BlL, int _dim, int* shape, double* bbox,
-                        int block_id, int ingfsi, int fngfsi, int lev)
-  {
-      // 映射表逻辑
-      int target_rank = block_id;
-      if (block_id == 26)      target_rank = 25;
-      else if (block_id == 29) target_rank = 30;
-      else if (block_id == 34) target_rank = 33;
-      else if (block_id == 37) target_rank = 38;
-
-      Block* ng = new Block(dim, shape, bbox, target_rank, ingfsi, fngfsi, lev);
-
-      if (BlL) BlL->insert(ng);
-      else     BlL = new MyList<Block>(ng);
-
-      return ng;
-  }
-
-
-
-
 #elif (PSTR == 1 || PSTR == 2 || PSTR == 3)
 MyList<Block> *Parallel::distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfsi,
                                     bool periodic, int start_rank, int end_rank, int nodes)
@@ -3761,7 +3338,7 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
 {
   int myrank;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-
+  // double time1 = omp_get_wtime();
   int DIM = dim;
 
   if (dir != PACK && dir != UNPACK)
@@ -3784,7 +3361,6 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
     varls = varls->next;
     varld = varld->next;
   }
-
   if (varls || varld)
   {
     cout << "error in short data packer, var lists does not match." << endl;
@@ -3798,7 +3374,6 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
     type = 2;
   else
     type = 3;
-
   while (src && dst)
   {
     if ((dir == PACK && dst->data->Bg->rank == rank_in && src->data->Bg->rank == myrank) ||
@@ -3808,6 +3383,7 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
       varld = VarListd;
       while (varls && varld)
       {
+
         if (data)
         {
           if (dir == PACK)
@@ -3828,6 +3404,7 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
               f_prolong3(DIM, src->data->Bg->bbox, src->data->Bg->bbox + dim, src->data->Bg->shape, src->data->Bg->fgfs[varls->data->sgfn],
                          dst->data->llb, dst->data->uub, dst->data->shape, data + size_out,
                          dst->data->llb, dst->data->uub, varls->data->SoA, Symmetry);
+
             }
           if (dir == UNPACK) // from target data to corresponding grid
             f_copy(DIM, dst->data->Bg->bbox, dst->data->Bg->bbox + dim, dst->data->Bg->shape, dst->data->Bg->fgfs[varld->data->sgfn],
@@ -3841,8 +3418,14 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
     }
     dst = dst->next;
     src = src->next;
-  }
 
+  }
+  // double time2 = omp_get_wtime();
+  // xxx += time2 - time1;
+  // if(myrank == 0){
+  // printf("prolong3 time = %lf\n", time2 - time1);
+
+  // }
   return size_out;
 }
 int Parallel::data_packermix(double *data, MyList<Parallel::gridseg> *src, MyList<Parallel::gridseg> *dst, int rank_in, int dir,
@@ -3937,7 +3520,7 @@ void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridse
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
 
   int node;
-
+  // double time1 = omp_get_wtime();
   MPI_Request *reqs;
   MPI_Status *stats;
   reqs = new MPI_Request[2 * cpusize];
@@ -4006,7 +3589,9 @@ void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridse
     if (rec_data[node])
       delete[] rec_data[node];
   }
-
+  // double time2 = omp_get_wtime();
+  // if (myrank == 0)
+  //   printf("transfer time = %lf\n", time2 - time1);
   delete[] reqs;
   delete[] stats;
   delete[] send_data;
@@ -5709,203 +5294,6 @@ void Parallel::OutBdLow2Himix(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
   delete[] transfer_src;
   delete[] transfer_dst;
 }
-
-// Restrict_cached: cache grid segment lists, reuse buffers via transfer_cached
-void Parallel::Restrict_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
-                               MyList<var> *VarList1, MyList<var> *VarList2,
-                               int Symmetry, SyncCache &cache)
-{
-  if (!cache.valid)
-  {
-    int cpusize;
-    MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
-    cache.cpusize = cpusize;
-
-    if (!cache.combined_src)
-    {
-      cache.combined_src = new MyList<Parallel::gridseg> *[cpusize];
-      cache.combined_dst = new MyList<Parallel::gridseg> *[cpusize];
-      cache.send_lengths = new int[cpusize];
-      cache.recv_lengths = new int[cpusize];
-      cache.send_bufs = new double *[cpusize];
-      cache.recv_bufs = new double *[cpusize];
-      cache.send_buf_caps = new int[cpusize];
-      cache.recv_buf_caps = new int[cpusize];
-      for (int i = 0; i < cpusize; i++)
-      {
-        cache.send_bufs[i] = cache.recv_bufs[i] = 0;
-        cache.send_buf_caps[i] = cache.recv_buf_caps[i] = 0;
-      }
-      cache.max_reqs = 2 * cpusize;
-      cache.reqs = new MPI_Request[cache.max_reqs];
-      cache.stats = new MPI_Status[cache.max_reqs];
-    }
-
-    MyList<Parallel::gridseg> *dst = build_complete_gsl(PatcL);
-    for (int node = 0; node < cpusize; node++)
-    {
-      MyList<Parallel::gridseg> *src_owned = build_owned_gsl(PatfL, node, 2, Symmetry);
-      build_gstl(src_owned, dst, &cache.combined_src[node], &cache.combined_dst[node]);
-      if (src_owned) src_owned->destroyList();
-    }
-    if (dst) dst->destroyList();
-
-    cache.valid = true;
-  }
-
-  transfer_cached(cache.combined_src, cache.combined_dst, VarList1, VarList2, Symmetry, cache);
-}
-
-// OutBdLow2Hi_cached: cache grid segment lists, reuse buffers via transfer_cached
-void Parallel::OutBdLow2Hi_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
-                                  MyList<var> *VarList1, MyList<var> *VarList2,
-                                  int Symmetry, SyncCache &cache)
-{
-  if (!cache.valid)
-  {
-    int cpusize;
-    MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
-    cache.cpusize = cpusize;
-
-    if (!cache.combined_src)
-    {
-      cache.combined_src = new MyList<Parallel::gridseg> *[cpusize];
-      cache.combined_dst = new MyList<Parallel::gridseg> *[cpusize];
-      cache.send_lengths = new int[cpusize];
-      cache.recv_lengths = new int[cpusize];
-      cache.send_bufs = new double *[cpusize];
-      cache.recv_bufs = new double *[cpusize];
-      cache.send_buf_caps = new int[cpusize];
-      cache.recv_buf_caps = new int[cpusize];
-      for (int i = 0; i < cpusize; i++)
-      {
-        cache.send_bufs[i] = cache.recv_bufs[i] = 0;
-        cache.send_buf_caps[i] = cache.recv_buf_caps[i] = 0;
-      }
-      cache.max_reqs = 2 * cpusize;
-      cache.reqs = new MPI_Request[cache.max_reqs];
-      cache.stats = new MPI_Status[cache.max_reqs];
-    }
-
-    MyList<Parallel::gridseg> *dst = build_buffer_gsl(PatfL);
-    for (int node = 0; node < cpusize; node++)
-    {
-      MyList<Parallel::gridseg> *src_owned = build_owned_gsl(PatcL, node, 4, Symmetry);
-      build_gstl(src_owned, dst, &cache.combined_src[node], &cache.combined_dst[node]);
-      if (src_owned) src_owned->destroyList();
-    }
-    if (dst) dst->destroyList();
-
-    cache.valid = true;
-  }
-
-  transfer_cached(cache.combined_src, cache.combined_dst, VarList1, VarList2, Symmetry, cache);
-}
-
-// OutBdLow2Himix_cached: same as OutBdLow2Hi_cached but uses transfermix for unpacking
-void Parallel::OutBdLow2Himix_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
-                                     MyList<var> *VarList1, MyList<var> *VarList2,
-                                     int Symmetry, SyncCache &cache)
-{
-  if (!cache.valid)
-  {
-    int cpusize;
-    MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
-    cache.cpusize = cpusize;
-
-    if (!cache.combined_src)
-    {
-      cache.combined_src = new MyList<Parallel::gridseg> *[cpusize];
-      cache.combined_dst = new MyList<Parallel::gridseg> *[cpusize];
-      cache.send_lengths = new int[cpusize];
-      cache.recv_lengths = new int[cpusize];
-      cache.send_bufs = new double *[cpusize];
-      cache.recv_bufs = new double *[cpusize];
-      cache.send_buf_caps = new int[cpusize];
-      cache.recv_buf_caps = new int[cpusize];
-      for (int i = 0; i < cpusize; i++)
-      {
-        cache.send_bufs[i] = cache.recv_bufs[i] = 0;
-        cache.send_buf_caps[i] = cache.recv_buf_caps[i] = 0;
-      }
-      cache.max_reqs = 2 * cpusize;
-      cache.reqs = new MPI_Request[cache.max_reqs];
-      cache.stats = new MPI_Status[cache.max_reqs];
-    }
-
-    MyList<Parallel::gridseg> *dst = build_buffer_gsl(PatfL);
-    for (int node = 0; node < cpusize; node++)
-    {
-      MyList<Parallel::gridseg> *src_owned = build_owned_gsl(PatcL, node, 4, Symmetry);
-      build_gstl(src_owned, dst, &cache.combined_src[node], &cache.combined_dst[node]);
-      if (src_owned) src_owned->destroyList();
-    }
-    if (dst) dst->destroyList();
-
-    cache.valid = true;
-  }
-
-  // Use transfermix instead of transfer for mix-mode interpolation
-  int myrank;
-  MPI_Comm_size(MPI_COMM_WORLD, &cache.cpusize);
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-  int cpusize = cache.cpusize;
-
-  int req_no = 0;
-  for (int node = 0; node < cpusize; node++)
-  {
-    if (node == myrank)
-    {
-      int length = data_packermix(0, cache.combined_src[myrank], cache.combined_dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-      cache.recv_lengths[node] = length;
-      if (length > 0)
-      {
-        if (length > cache.recv_buf_caps[node])
-        {
-          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
-          cache.recv_bufs[node] = new double[length];
-          cache.recv_buf_caps[node] = length;
-        }
-        data_packermix(cache.recv_bufs[node], cache.combined_src[myrank], cache.combined_dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-      }
-    }
-    else
-    {
-      int slength = data_packermix(0, cache.combined_src[myrank], cache.combined_dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-      cache.send_lengths[node] = slength;
-      if (slength > 0)
-      {
-        if (slength > cache.send_buf_caps[node])
-        {
-          if (cache.send_bufs[node]) delete[] cache.send_bufs[node];
-          cache.send_bufs[node] = new double[slength];
-          cache.send_buf_caps[node] = slength;
-        }
-        data_packermix(cache.send_bufs[node], cache.combined_src[myrank], cache.combined_dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-        MPI_Isend((void *)cache.send_bufs[node], slength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no++);
-      }
-      int rlength = data_packermix(0, cache.combined_src[node], cache.combined_dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
-      cache.recv_lengths[node] = rlength;
-      if (rlength > 0)
-      {
-        if (rlength > cache.recv_buf_caps[node])
-        {
-          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
-          cache.recv_bufs[node] = new double[rlength];
-          cache.recv_buf_caps[node] = rlength;
-        }
-        MPI_Irecv((void *)cache.recv_bufs[node], rlength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no++);
-      }
-    }
-  }
-
-  MPI_Waitall(req_no, cache.reqs, cache.stats);
-
-  for (int node = 0; node < cpusize; node++)
-    if (cache.recv_bufs[node] && cache.recv_lengths[node] > 0)
-      data_packermix(cache.recv_bufs[node], cache.combined_src[node], cache.combined_dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
-}
-
 // collect all buffer grid segments or blocks for given patch
 MyList<Parallel::gridseg> *Parallel::build_buffer_gsl(Patch *Pat)
 {
@@ -6905,224 +6293,3 @@ void Parallel::checkpatchlist(MyList<Patch> *PatL, bool buflog)
     PL = PL->next;
   }
 }
-// Check if load balancing is needed based on interpolation times
-bool Parallel::check_load_balance_need(double *rank_times, int nprocs, int &num_heavy, int *heavy_ranks)
-{
-  // Calculate average time
-  double avg_time = 0;
-  for (int r = 0; r < nprocs; r++)
-  {
-    avg_time += rank_times[r];
-  }
-  avg_time /= nprocs;
-
-  // Identify heavy ranks (time > 1.5x average)
-  std::vector<std::pair<int, double>> rank_times_vec;
-  for (int r = 0; r < nprocs; r++)
-  {
-    if (rank_times[r] > avg_time * 1.5)
-    {
-      rank_times_vec.push_back(std::make_pair(r, rank_times[r]));
-    }
-  }
-
-  // Sort by time (descending)
-  std::sort(rank_times_vec.begin(), rank_times_vec.end(),
-            [](const std::pair<int, double>& a, const std::pair<int, double>& b) {
-              return a.second > b.second;
-            });
-
-  // Take top 4 heavy ranks
-  num_heavy = std::min(4, (int)rank_times_vec.size());
-  if (num_heavy > 0)
-  {
-    for (int i = 0; i < num_heavy; i++)
-    {
-      heavy_ranks[i] = rank_times_vec[i].first;
-    }
-    return true;  // Load balancing is needed
-  }
-
-  return false;  // No load balancing needed
-}
-
-// Split blocks belonging to heavy ranks to improve load balancing
-// Strategy: Split heavy rank blocks in half, merge 8 light ranks to free 4 ranks
-void Parallel::split_heavy_blocks(MyList<Patch> *PatL, int *heavy_ranks, int num_heavy,
-                                  int split_factor, int cpusize, int ingfsi, int fngfsi)
-{
-  int myrank, nprocs;
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
-
-  if (myrank != 0) return; // Only rank 0 performs the analysis
-
-  cout << "\n=== Load Balancing Strategy ===" << endl;
-  cout << "Heavy ranks to split (in half): " << num_heavy << endl;
-  for (int i = 0; i < num_heavy; i++)
-    cout << "  Heavy rank " << heavy_ranks[i] << endl;
-
-  // Step 1: Identify all blocks and their ranks
-  std::vector<int> all_ranks;
-  std::map<int, std::vector<Block*>> rank_to_blocks;
-
-  MyList<Patch> *PL = PatL;
-  while (PL)
-  {
-    Patch *PP = PL->data;
-    MyList<Block> *BP = PP->blb;
-    while (BP)
-    {
-      Block *block = BP->data;
-      all_ranks.push_back(block->rank);
-      rank_to_blocks[block->rank].push_back(block);
-      BP = BP->next;
-    }
-    PL = PL->next;
-  }
-
-  // Step 2: Identify light ranks (not in heavy_ranks list)
-  std::set<int> heavy_set(heavy_ranks, heavy_ranks + num_heavy);
-  std::vector<int> light_ranks;
-  for (int r : all_ranks)
-  {
-    if (heavy_set.find(r) == heavy_set.end())
-    {
-      light_ranks.push_back(r);
-    }
-  }
-
-  // Remove duplicates from light_ranks
-  std::sort(light_ranks.begin(), light_ranks.end());
-  light_ranks.erase(std::unique(light_ranks.begin(), light_ranks.end()), light_ranks.end());
-
-  cout << "Found " << light_ranks.size() << " light ranks (candidates for merging)" << endl;
-
-  // Step 3: Select 8 light ranks to merge (those with smallest workload)
-  // For now, we select the first 8 light ranks
-  int num_to_merge = 8;
-  if (light_ranks.size() < num_to_merge)
-  {
-    cout << "WARNING: Not enough light ranks to merge. Found " << light_ranks.size()
-         << ", need " << num_to_merge << endl;
-    num_to_merge = light_ranks.size();
-  }
-
-  std::vector<int> ranks_to_merge(light_ranks.begin(), light_ranks.begin() + num_to_merge);
-
-  cout << "Light ranks to merge (8 -> 4 merged ranks):" << endl;
-  for (int i = 0; i < num_to_merge; i++)
-    cout << "  Rank " << ranks_to_merge[i] << endl;
-
-  // Step 4: Analyze blocks that need to be split
-  cout << "\n=== Analyzing blocks for splitting ===" << endl;
-
-  struct BlockSplitInfo {
-    Block *original_block;
-    int split_dim;
-    int split_point;
-  };
-
-  std::vector<BlockSplitInfo> blocks_to_split;
-
-  PL = PatL;
-  while (PL)
-  {
-    Patch *PP = PL->data;
-    MyList<Block> *BP = PP->blb;
-    while (BP)
-    {
-      Block *block = BP->data;
-
-      // Check if this block belongs to a heavy rank
-      for (int i = 0; i < num_heavy; i++)
-      {
-        if (block->rank == heavy_ranks[i])
-        {
-          // Find the largest dimension for splitting
-          int max_dim = 0;
-          int max_size = block->shape[0];
-          for (int d = 1; d < dim; d++)
-          {
-            if (block->shape[d] > max_size)
-            {
-              max_size = block->shape[d];
-              max_dim = d;
-            }
-          }
-
-          int split_point = max_size / 2;
-
-          BlockSplitInfo info;
-          info.original_block = block;
-          info.split_dim = max_dim;
-          info.split_point = split_point;
-          blocks_to_split.push_back(info);
-
-          cout << "Block at rank " << block->rank << " will be split" << endl;
-          cout << "  Shape: [" << block->shape[0] << ", " << block->shape[1] << ", " << block->shape[2] << "]" << endl;
-          cout << "  Split along dimension " << max_dim << " at index " << split_point << endl;
-          break;
-        }
-      }
-
-      BP = BP->next;
-    }
-    PL = PL->next;
-  }
-
-  cout << "\nTotal blocks to split: " << blocks_to_split.size() << endl;
-
-  // Step 5: Calculate new rank assignments
-  // Strategy:
-  // - For each heavy rank, its blocks are split in half
-  // - First half keeps the original rank
-  // - Second half gets a new rank (from the freed light ranks)
-  // - 8 light ranks are merged into 4 ranks, freeing up 4 ranks
-
-  std::vector<int> freed_ranks;
-  for (size_t i = 0; i < ranks_to_merge.size(); i += 2)
-  {
-    // Merge pairs of light ranks: (ranks_to_merge[i], ranks_to_merge[i+1]) -> ranks_to_merge[i]
-    // This frees up ranks_to_merge[i+1]
-    if (i + 1 < ranks_to_merge.size())
-    {
-      freed_ranks.push_back(ranks_to_merge[i + 1]);
-      cout << "Merging ranks " << ranks_to_merge[i] << " and " << ranks_to_merge[i + 1]
-           << " -> keeping rank " << ranks_to_merge[i] << ", freeing rank " << ranks_to_merge[i + 1] << endl;
-    }
-  }
-
-  cout << "\nFreed ranks available for split blocks: ";
-  for (int r : freed_ranks)
-    cout << r << " ";
-  cout << endl;
-
-  // Step 6: Assign new ranks to split blocks
-  int freed_idx = 0;
-  for (size_t i = 0; i < blocks_to_split.size(); i++)
-  {
-    BlockSplitInfo &info = blocks_to_split[i];
-    Block *original = info.original_block;
-
-    if (freed_idx < freed_ranks.size())
-    {
-      cout << "\nSplitting block at rank " << original->rank << endl;
-      cout << "  First half: keeps rank " << original->rank << endl;
-      cout << "  Second half: gets new rank " << freed_ranks[freed_idx] << endl;
-      freed_idx++;
-    }
-    else
-    {
-      cout << "WARNING: Not enough freed ranks for all split blocks!" << endl;
-      break;
-    }
-  }
-
-  cout << "\n=== Load Balancing Analysis Complete ===" << endl;
-  cout << "Next steps:" << endl;
-  cout << "  1. Recompose the grid with new rank assignments" << endl;
-  cout << "  2. Data migration will be handled by recompose_cgh" << endl;
-  cout << "  3. Ghost zone communication will be updated automatically" << endl;
-}
-

AMSS_NCKU_source/Parallel.h

@@ -11,7 +11,7 @@
 #include <cmath>
 #include <new>
 using namespace std;
-#include <memory.h>
+
 #include "Parallel_bam.h"
 #include "var.h"
 #include "MPatch.h"
@@ -32,16 +32,6 @@ 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_hard(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfs, bool periodic, int nodes = 0); // produce corresponding Blocks
-  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));
@@ -140,15 +130,6 @@ 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);
@@ -218,18 +199,6 @@ namespace Parallel
 #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);
-  
-  // Redistribute blocks with time statistics for load balancing
-  MyList<Block> *distribute(MyList<Patch> *PatchLIST, MyList<Block> *OldBlockL,
-                            int cpusize, int ingfsi, int fngfsi,
-                            bool periodic, int start_rank, int end_rank, int nodes = 0);
 #endif
-
-  // Dynamic load balancing: split blocks for heavy ranks
-    void split_heavy_blocks(MyList<Patch> *PatL, int *heavy_ranks, int num_heavy,
-                            int split_factor, int cpusize, int ingfsi, int fngfsi);
-
-    // Check if load balancing is needed based on interpolation times
-    bool check_load_balance_need(double *rank_times, int nprocs, int &num_heavy, int *heavy_ranks);
 }
 #endif /*PARALLEL_H */

AMSS_NCKU_source/bssn_class.C

@@ -40,7 +40,7 @@ using namespace std;
 
 #include "derivatives.h"
 #include "ricci_gamma.h"
-
+#include "xh_bssn_rhs_compute.h"
 //================================================================================================
 
 // define bssn_class
@@ -2029,6 +2029,7 @@ void bssn_class::Read_Ansorg()
 void bssn_class::Evolve(int Steps)
 {
   clock_t prev_clock, curr_clock;
+  double prev_time, curr_time;
   double LastDump = 0.0, LastCheck = 0.0, Last2dDump = 0.0;
   LastAnas = 0;
 #if 0
@@ -2141,8 +2142,10 @@ void bssn_class::Evolve(int Steps)
     //     if(fabs(Porg0[0][0]-Porg0[1][0])+fabs(Porg0[0][1]-Porg0[1][1])+fabs(Porg0[0][2]-Porg0[1][2])<1e-6) 
     //     { GH->levels=GH->movls; }
 
-    if (myrank == 0)
+    if (myrank == 0){
       curr_clock = clock();
+      curr_time = omp_get_wtime();
+    }
 #if (PSTR == 0)
     RecursiveStep(0);
 #elif (PSTR == 1 || PSTR == 2 || PSTR == 3)
@@ -2198,12 +2201,17 @@ void bssn_class::Evolve(int Steps)
     if (myrank == 0)
     {
       prev_clock = curr_clock;
+      prev_time = curr_time;
       curr_clock = clock();
+      curr_time = omp_get_wtime();
       cout << endl;
+      // cout << " Timestep # " << ncount << ": integrating to time: " << PhysTime << "   "
+      //      << " Computer used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
+      //      << " seconds! " << endl;
+      // // cout << endl;
       cout << " Timestep # " << ncount << ": integrating to time: " << PhysTime << "   "
-           << " Computer used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
+            << " Computer used " << (curr_time - prev_time) 
             << " seconds! " << endl;
-      // cout << endl;
     }
 
     if (PhysTime >= TotalTime)
@@ -3092,7 +3100,7 @@ void bssn_class::Step(int lev, int YN)
                      cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
-        if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+        if (f_compute_rhs_bssn_xh(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],
@@ -3292,7 +3300,7 @@ void bssn_class::Step(int lev, int YN)
                  << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
             ERROR = 1;
           }
-
+          // cout<<"....................................."<<endl;
           // rk4 substep and boundary
           {
             MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; 
@@ -3457,7 +3465,7 @@ void bssn_class::Step(int lev, int YN)
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #endif
 
-          if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+          if (f_compute_rhs_bssn_xh(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],
@@ -3970,7 +3978,7 @@ void bssn_class::Step(int lev, int YN)
                      cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
-        if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+        if (f_compute_rhs_bssn_xh(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],
@@ -4312,7 +4320,7 @@ void bssn_class::Step(int lev, int YN)
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #endif
 
-          if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+          if (f_compute_rhs_bssn_xh(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],
@@ -4848,7 +4856,7 @@ void bssn_class::Step(int lev, int YN)
                      cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
-        if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+        if (f_compute_rhs_bssn_xh(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],
@@ -5048,7 +5056,7 @@ void bssn_class::Step(int lev, int YN)
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #endif
 
-          if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+          if (f_compute_rhs_bssn_xh(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],
@@ -5819,11 +5827,21 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SL,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, GH->bdsul[lev], Symmetry);
@@ -5870,11 +5888,21 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SL, SL, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SL, SL, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->bdsul[lev], Symmetry);
@@ -5949,11 +5977,21 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SL,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, GH->bdsul[lev], Symmetry);
@@ -5971,11 +6009,21 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SL, SL, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SL, SL, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->bdsul[lev], Symmetry);
@@ -6036,11 +6084,21 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SynchList_cor,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, GH->bdsul[lev], Symmetry);
@@ -6060,11 +6118,21 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],StateList,SynchList_cor,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, GH->bdsul[lev], Symmetry);
@@ -6101,11 +6169,21 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
       }
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SynchList_cor,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, GH->bdsul[lev], Symmetry);
@@ -6114,11 +6192,21 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
     else // no time refinement levels and for all same time levels
     {
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],StateList,SynchList_cor,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, GH->bdsul[lev], Symmetry);
@@ -7263,7 +7351,7 @@ void bssn_class::Constraint_Out()
             Block *cg = BP->data;
             if (myrank == cg->rank)
             {
-              f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+              f_compute_rhs_bssn_xh(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],
@@ -7766,7 +7854,7 @@ void bssn_class::Interp_Constraint(bool infg)
             Block *cg = BP->data;
             if (myrank == cg->rank)
             {
-              f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+              f_compute_rhs_bssn_xh(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],
@@ -8024,7 +8112,7 @@ void bssn_class::Compute_Constraint()
           Block *cg = BP->data;
           if (myrank == cg->rank)
           {
-            f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+            f_compute_rhs_bssn_xh(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],

AMSS_NCKU_source/bssn_rhs.f90

@@ -106,38 +106,6 @@
   call getpbh(BHN,Porg,Mass)
 #endif
 
-!!! sanity check (disabled in production builds for performance)
-#ifdef DEBUG
-  dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
-      +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
-      +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
-      +sum(Lap)+sum(betax)+sum(betay)+sum(betaz)
-  if(dX.ne.dX) then
-     if(sum(chi).ne.sum(chi))write(*,*)"bssn.f90: find NaN in chi"
-     if(sum(trK).ne.sum(trK))write(*,*)"bssn.f90: find NaN in trk"
-     if(sum(dxx).ne.sum(dxx))write(*,*)"bssn.f90: find NaN in dxx"
-     if(sum(gxy).ne.sum(gxy))write(*,*)"bssn.f90: find NaN in gxy"
-     if(sum(gxz).ne.sum(gxz))write(*,*)"bssn.f90: find NaN in gxz"
-     if(sum(dyy).ne.sum(dyy))write(*,*)"bssn.f90: find NaN in dyy"
-     if(sum(gyz).ne.sum(gyz))write(*,*)"bssn.f90: find NaN in gyz"
-     if(sum(dzz).ne.sum(dzz))write(*,*)"bssn.f90: find NaN in dzz"
-     if(sum(Axx).ne.sum(Axx))write(*,*)"bssn.f90: find NaN in Axx"
-     if(sum(Axy).ne.sum(Axy))write(*,*)"bssn.f90: find NaN in Axy"
-     if(sum(Axz).ne.sum(Axz))write(*,*)"bssn.f90: find NaN in Axz"
-     if(sum(Ayy).ne.sum(Ayy))write(*,*)"bssn.f90: find NaN in Ayy"
-     if(sum(Ayz).ne.sum(Ayz))write(*,*)"bssn.f90: find NaN in Ayz"
-     if(sum(Azz).ne.sum(Azz))write(*,*)"bssn.f90: find NaN in Azz"
-     if(sum(Gamx).ne.sum(Gamx))write(*,*)"bssn.f90: find NaN in Gamx"
-     if(sum(Gamy).ne.sum(Gamy))write(*,*)"bssn.f90: find NaN in Gamy"
-     if(sum(Gamz).ne.sum(Gamz))write(*,*)"bssn.f90: find NaN in Gamz"
-     if(sum(Lap).ne.sum(Lap))write(*,*)"bssn.f90: find NaN in Lap"
-     if(sum(betax).ne.sum(betax))write(*,*)"bssn.f90: find NaN in betax"
-     if(sum(betay).ne.sum(betay))write(*,*)"bssn.f90: find NaN in betay"
-     if(sum(betaz).ne.sum(betaz))write(*,*)"bssn.f90: find NaN in betaz"
-     gont = 1
-     return
-  endif
-#endif
 
   PI = dacos(-ONE)
 
@@ -634,7 +602,7 @@
   gxxx = (gupxx * chix + gupxy * chiy + gupxz * chiz)/chin1
   gxxy = (gupxy * chix + gupyy * chiy + gupyz * chiz)/chin1
   gxxz = (gupxz * chix + gupyz * chiy + gupzz * chiz)/chin1
-! now get physical second kind of connection
+
   Gamxxx = Gamxxx - ( (chix + chix)/chin1 - gxx * gxxx )*HALF
   Gamyxx = Gamyxx - (                     - gxx * gxxy )*HALF
   Gamzxx = Gamzxx - (                     - gxx * gxxz )*HALF
@@ -945,60 +913,103 @@
   SSA(2)=SYM
   SSA(3)=ANTI
 
-!!!!!!!!!advection term + Kreiss-Oliger dissipation (merged for cache efficiency)
+!!!!!!!!!advection term part
-! lopsided_kodis shares the symmetry_bd buffer between advection and
-! dissipation, eliminating redundant full-grid copies. For metric variables
-! gxx/gyy/gzz (=dxx/dyy/dzz+1): kodis stencil coefficients sum to zero,
-! so the constant offset has no effect on dissipation.
 
-  call lopsided_kodis(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS)
-  call lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
+  call lopsided(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS)
-  call lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
+  call lopsided(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA)
-  call lopsided_kodis(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS)
-  call lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
+  call lopsided(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA)
-  call lopsided_kodis(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS)
 
-  call lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS)
-  call lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
+  call lopsided(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS)
-  call lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
+  call lopsided(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA)
-  call lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS)
-  call lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
+  call lopsided(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA)
-  call lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS)
 
-  call lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS)
-  call lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS)
 
-  call lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
+  call lopsided(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS)
-  call lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
+  call lopsided(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS)
-  call lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
+  call lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA)
-
+!!
-#if 1 
-!! bam does not apply dissipation on gauge variables
-  call lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-#if (GAUGE == 0 || GAUGE == 1 || GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
-  call lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps)
-  call lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps)
-  call lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
-#endif
-#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
-  call lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
-  call lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
-  call lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
-#endif
-#else
-! No dissipation on gauge variables (advection only)
   call lopsided(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS)
+
 #if (GAUGE == 0 || GAUGE == 1 || GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
   call lopsided(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS)
   call lopsided(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS)
   call lopsided(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA)
 #endif
+
 #if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
   call lopsided(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS)
   call lopsided(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS)
   call lopsided(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA)
 #endif
+
+  if(eps>0)then 
+! usual Kreiss-Oliger dissipation      
+  call kodis(ex,X,Y,Z,chi,chi_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,trK,trK_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dxx,gxx_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gxy,gxy_rhs,AAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gxz,gxz_rhs,ASA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dyy,gyy_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gyz,gyz_rhs,SAA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dzz,gzz_rhs,SSS,Symmetry,eps)
+#if 0
+#define i 42
+#define j 40
+#define k 40
+if(Lev == 1)then
+write(*,*) X(i),Y(j),Z(k)
+write(*,*) "before",Axx_rhs(i,j,k)
+endif
+#undef i
+#undef j
+#undef k
+!!stop
 #endif
+  call kodis(ex,X,Y,Z,Axx,Axx_rhs,SSS,Symmetry,eps)
+#if 0
+#define i 42
+#define j 40
+#define k 40
+if(Lev == 1)then
+write(*,*) X(i),Y(j),Z(k)
+write(*,*) "after",Axx_rhs(i,j,k)
+endif
+#undef i
+#undef j
+#undef k
+!!stop
+#endif
+  call kodis(ex,X,Y,Z,Axy,Axy_rhs,AAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Axz,Axz_rhs,ASA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Ayy,Ayy_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Ayz,Ayz_rhs,SAA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Azz,Azz_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamx,Gamx_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamy,Gamy_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamz,Gamz_rhs,SSA,Symmetry,eps)
+
+#if 1 
+!! bam does not apply dissipation on gauge variables
+  call kodis(ex,X,Y,Z,Lap,Lap_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betax,betax_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betay,betay_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betaz,betaz_rhs,SSA,Symmetry,eps)
+#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
+  call kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,SSA,Symmetry,eps)
+#endif
+#endif
+
+  endif
 
   if(co == 0)then
 ! ham_Res = trR + 2/3 * K^2 - A_ij * A^ij - 16 * PI * rho

AMSS_NCKU_source/cgh.C

@@ -43,14 +43,6 @@ cgh::cgh(int ingfsi, int fngfsi, int Symmetry, char *filename, int checkrun,
   end_rank = 0;
 #endif
 
-  // Initialize load balancing variables
-  enable_load_balance = false;
-  load_balance_check_interval = 10;  // Check every 10 time steps
-  current_time_step = 0;
-  rank_interp_times = nullptr;
-  heavy_ranks = nullptr;
-  num_heavy_ranks = 0;
-
   if (!checkrun)
   {
     read_bbox(Symmetry, filename);
@@ -121,12 +113,6 @@ cgh::~cgh()
     delete[] Porgls[lev];
   }
   delete[] Porgls;
-
-  // Clean up load balancing memory
-  if (rank_interp_times)
-    delete[] rank_interp_times;
-  if (heavy_ranks)
-    delete[] heavy_ranks;
 }
 
 //================================================================================================
@@ -144,7 +130,7 @@ void cgh::compose_cgh(int nprocs)
   for (int lev = 0; lev < levels; lev++)
   {
     checkPatchList(PatL[lev], false);
-    Parallel::distribute_hard(PatL[lev], nprocs, ingfs, fngfs, false);
+    Parallel::distribute(PatL[lev], nprocs, ingfs, fngfs, false);
 #if (RPB == 1)
     // we need distributed box of PatL[lev] and PatL[lev-1]
     if (lev > 0)
@@ -1719,121 +1705,3 @@ void cgh::settrfls(const int lev)
 {
   trfls = lev;
 }
-
-//================================================================================================
-// Load Balancing Functions
-//================================================================================================
-
-// Initialize load balancing
-void cgh::init_load_balance(int nprocs)
-{
-  if (rank_interp_times)
-    delete[] rank_interp_times;
-  if (heavy_ranks)
-    delete[] heavy_ranks;
-
-  rank_interp_times = new double[nprocs];
-  heavy_ranks = new int[4];  // Maximum 4 heavy ranks
-  num_heavy_ranks = 0;
-
-  for (int i = 0; i < nprocs; i++)
-    rank_interp_times[i] = 0.0;
-}
-
-// Update interpolation time for a rank
-void cgh::update_interp_time(int rank, double time)
-{
-  if (rank_interp_times && rank >= 0)
-  {
-    rank_interp_times[rank] = time;
-  }
-}
-
-// Check and perform load balancing if needed
-bool cgh::check_and_rebalance(int nprocs, int lev,
-                               MyList<var> *OldList, MyList<var> *StateList,
-                               MyList<var> *FutureList, MyList<var> *tmList,
-                               int Symmetry, bool BB)
-{
-  int myrank;
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-
-  // Only check at specified intervals
-  current_time_step++;
-  if (current_time_step % load_balance_check_interval != 0)
-    return false;
-
-  if (myrank == 0)
-  {
-    cout << "\n=== Checking load balance at time step " << current_time_step << " ===" << endl;
-  }
-
-  // Collect all rank times on rank 0
-  double *all_times = nullptr;
-  if (myrank == 0)
-  {
-    all_times = new double[nprocs];
-  }
-
-  MPI_Gather(rank_interp_times, 1, MPI_DOUBLE, all_times, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD);
-
-  bool need_rebalance = false;
-
-  if (myrank == 0)
-  {
-    // Check if load balancing is needed
-    need_rebalance = Parallel::check_load_balance_need(all_times, nprocs, num_heavy_ranks, heavy_ranks);
-
-    if (need_rebalance)
-    {
-      cout << "=== Load imbalance detected! Need to rebalance ===" << endl;
-      cout << "Top " << num_heavy_ranks << " heavy ranks: ";
-      for (int i = 0; i < num_heavy_ranks; i++)
-      {
-        cout << heavy_ranks[i] << " (" << all_times[heavy_ranks[i]] << " s) ";
-      }
-      cout << endl;
-
-      // Analyze blocks that need to be split
-      Parallel::split_heavy_blocks(PatL[lev], heavy_ranks, num_heavy_ranks, 2, nprocs, ingfs, fngfs);
-
-      // Set lev_flag to trigger recompose_cgh
-      cout << "=== Triggering recompose_cgh for level " << lev << " ===" << endl;
-    }
-    else
-    {
-      cout << "=== Load is balanced, no rebalancing needed ===" << endl;
-    }
-
-    delete[] all_times;
-  }
-
-  // Broadcast the decision to all ranks
-  MPI_Bcast(&need_rebalance, 1, MPI_C_BOOL, 0, MPI_COMM_WORLD);
-
-  if (need_rebalance)
-  {
-    // Broadcast heavy ranks information
-    MPI_Bcast(&num_heavy_ranks, 1, MPI_INT, 0, MPI_COMM_WORLD);
-    MPI_Bcast(heavy_ranks, num_heavy_ranks, MPI_INT, 0, MPI_COMM_WORLD);
-
-    // Perform recompose_cgh on the specified level
-    if (myrank == 0)
-    {
-      cout << "=== Performing recompose_cgh ===" << endl;
-    }
-
-    // Call recompose_cgh_Onelevel for the specified level
-    bool *lev_flag = new bool[1];
-    lev_flag[0] = true;
-    recompose_cgh_Onelevel(nprocs, lev, OldList, StateList, FutureList, tmList, Symmetry, BB);
-    delete[] lev_flag;
-
-    // Reset time counter after rebalancing
-    current_time_step = 0;
-
-    return true;
-  }
-
-  return false;
-}

AMSS_NCKU_source/cgh.h

@@ -87,21 +87,6 @@ public:
 #if (PSTR == 1 || PSTR == 2 || PSTR == 3)
    void construct_mylev(int nprocs);
 #endif
-
-   // Load balancing support
-   bool enable_load_balance;         // Enable load balancing
-   int load_balance_check_interval;  // Check interval (in time steps)
-   int current_time_step;            // Current time step counter
-   double *rank_interp_times;        // Store interpolation times for each rank
-   int *heavy_ranks;                 // Store heavy rank numbers
-   int num_heavy_ranks;              // Number of heavy ranks
-
-   void init_load_balance(int nprocs);
-   void update_interp_time(int rank, double time);
-   bool check_and_rebalance(int nprocs, int lev,
-                           MyList<var> *OldList, MyList<var> *StateList,
-                           MyList<var> *FutureList, MyList<var> *tmList,
-                           int Symmetry, bool BB);
 };
 
 #endif /* CGH_H */

AMSS_NCKU_source/diff_new.f90

@@ -69,8 +69,6 @@
   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
@@ -373,8 +371,6 @@
   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/extention/include/xh_bssn_rhs_compute.h

@@ -0,0 +1,26 @@
+#include "xh_macrodef.h"
+#include "xh_tool.h"
+int f_compute_rhs_bssn(int *ex, double &T, 
+                       double *X, double *Y, double *Z,
+                       double *chi, double *trK,
+                       double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+                       double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+                       double *Gamx, double *Gamy, double *Gamz,
+                       double *Lap, double *betax, double *betay, double *betaz,
+                       double *dtSfx, double *dtSfy, double *dtSfz,
+                       double *chi_rhs, double *trK_rhs,
+                       double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+                       double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+                       double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+                       double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+                       double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+                       double *rho, double *Sx, double *Sy, double *Sz,
+                       double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
+                       double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
+                       double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
+                       double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
+                       double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
+                       double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
+                       double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
+                       int &Symmetry, int &Lev, double &eps, int &co
+                       ); 

AMSS_NCKU_source/extention/include/xh_macrodef.h

@@ -0,0 +1,66 @@
+/* tetrad notes
+   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 tetradtype 2
+
+/* Cell center or Vertex center */
+#define Cell
+
+/* ghost_width meaning:
+   2nd order: 2
+   4th order: 3
+   6th order: 4
+   8th order: 5
+*/
+#define ghost_width 3
+
+/* use shell or not */
+#define WithShell
+
+/* use constraint preserving boundary condition or not
+   only affect Z4c
+*/
+#define CPBC
+
+/* 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
+*/
+#define GAUGE 2
+
+/* buffer points for CPBC boundary */
+#define CPBC_ghost_width (ghost_width)
+
+/* using BSSN variable for constraint violation and psi4 calculation: 0
+   using ADM variable for constraint violation and psi4 calculation: 1
+*/
+#define ABV 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 = infinity 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
+*/
+#define EScalar_CC 2

AMSS_NCKU_source/extention/include/xh_share_func.h

@@ -0,0 +1,338 @@
+#ifndef SHARE_FUNC_H
+#define SHARE_FUNC_H
+
+#include <stdlib.h>
+#include <stddef.h>
+#include <math.h>
+#include <stdio.h>
+#include <omp.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(int ord,
+                 const int extc[3],
+                 const double *func,
+                 double *funcc,
+                 const double SoA[3])
+{
+    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
+
+    // 1) funcc(1:extc1,1:extc2,1:extc3) = func
+    // Fortran 的 (iF=1..extc1) 对应 C 的 func(i0=0..extc1-1)
+    for (int k0 = 0; k0 < extc3; ++k0) {
+        for (int j0 = 0; j0 < extc2; ++j0) {
+            for (int i0 = 0; i0 < extc1; ++i0) {
+                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
+                funcc[idx_funcc_F(iF, jF, kF, ord, extc)] = func[idx_func0(i0, j0, k0, extc)];
+            }
+        }
+    }
+
+    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    for (int ii = 0; ii <= ord - 1; ++ii) {
+        const int iF_dst = -ii;       // 0, -1, -2, ...
+        const int iF_src = ii + 1;    // 1, 2, 3, ...
+        for (int kF = 1; kF <= extc3; ++kF) {
+            for (int jF = 1; jF <= extc2; ++jF) {
+                funcc[idx_funcc_F(iF_dst, jF, kF, ord, extc)] =
+                    funcc[idx_funcc_F(iF_src, jF, kF, ord, extc)] * SoA[0];
+            }
+        }
+    }
+
+    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+    for (int jj = 0; jj <= ord - 1; ++jj) {
+        const int jF_dst = -jj;
+        const int jF_src = jj + 1;
+        for (int kF = 1; kF <= extc3; ++kF) {
+            for (int iF = -ord + 1; iF <= extc1; ++iF) {
+                funcc[idx_funcc_F(iF, jF_dst, kF, ord, extc)] =
+                    funcc[idx_funcc_F(iF, jF_src, kF, ord, extc)] * SoA[1];
+            }
+        }
+    }
+
+    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+    for (int kk = 0; kk <= ord - 1; ++kk) {
+        const int kF_dst = -kk;
+        const int kF_src = kk + 1;
+        for (int jF = -ord + 1; jF <= extc2; ++jF) {
+            for (int iF = -ord + 1; iF <= extc1; ++iF) {
+                funcc[idx_funcc_F(iF, jF, kF_dst, ord, extc)] =
+                    funcc[idx_funcc_F(iF, jF, kF_src, ord, extc)] * SoA[2];
+            }
+        }
+    }
+}
+#endif
+
+/* 你已有的函数：idx_ex / idx_fh_F_ord2 以及 fh 的布局 */
+static inline void fdderivs_xh(
+    int i0, int j0, int k0,
+    const int ex[3],
+    const double *fh,
+    int iminF, int jminF, int kminF,
+    int imaxF, int jmaxF, int kmaxF,
+    double Fdxdx, double Fdydy, double Fdzdz,
+    double Fdxdy, double Fdxdz, double Fdydz,
+    double Sdxdx, double Sdydy, double Sdzdz,
+    double Sdxdy, double Sdxdz, double Sdydz,
+    double *fxx, double *fxy, double *fxz,
+    double *fyy, double *fyz, double *fzz
+){
+    const double F8  = 8.0;
+    const double F16 = 16.0;
+    const double F30 = 30.0;
+    const double TWO = 2.0;
+
+    const int iF = i0 + 1;
+    const int jF = j0 + 1;
+    const int kF = k0 + 1;
+
+    const size_t p = idx_ex(i0, j0, k0, ex);
+
+    /* 高阶分支：i±2,j±2,k±2 都在范围内 */
+    if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+        (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+        (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+    {
+        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)]
+        );
+
+        /* fxy 高阶 */
+        {
+            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 );
+        }
+
+        /* fxz 高阶 */
+        {
+            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 );
+        }
+
+        /* fyz 高阶 */
+        {
+            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 );
+        }
+    }
+    /* 二阶分支：i±1,j±1,k±1 在范围内 */
+    else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+             (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+             (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+    {
+        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)]
+        );
+    }
+    else {
+        fxx[p] = 0.0; fyy[p] = 0.0; fzz[p] = 0.0;
+        fxy[p] = 0.0; fxz[p] = 0.0; fyz[p] = 0.0;
+    }
+}

AMSS_NCKU_source/extention/include/xh_tool.h

@@ -0,0 +1,27 @@
+#include "xh_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]);

AMSS_NCKU_source/extention/src/fdderivs-fast.c

@@ -0,0 +1,311 @@
+#include "../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;
+
+
+    /* 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;
+
+    /* 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);
+
+    static thread_local double *fh = NULL;
+    static thread_local 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);
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    for (int k0 = 0; k0 < ex[2]; ++k0) {
+        for (int j0 = 0; j0 < ex[1]; ++j0) {
+            for (int i0 = 0; i0 < ex[0]; ++i0) {
+                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1; 
+                fh[idx_funcc_F(iF, jF, kF, 2, ex)] = f[idx_func0(i0, j0, k0, ex)];
+            }
+        }
+    }
+
+    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    for (int ii = 0; ii <= 2 - 1; ++ii) {
+        const int iF_dst = -ii;       // 0, -1, -2, ...
+        const int iF_src = ii + 1;    // 1, 2, 3, ...
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int jF = 1; jF <= ex[1]; ++jF) {
+                fh[idx_funcc_F(iF_dst, jF, kF, 2, ex)] = 
+                    fh[idx_funcc_F(iF_src, jF, kF, 2, ex)] * SoA[0];
+            }
+        }
+    }
+
+    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+    for (int jj = 0; jj <= 2 - 1; ++jj) {
+        const int jF_dst = -jj;
+        const int jF_src = jj + 1;
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF_dst, kF, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF_src, kF, 2, ex)] * SoA[1];
+            }
+        }
+    }
+
+    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+    for (int kk = 0; kk <= 2 - 1; ++kk) {
+        const int kF_dst = -kk;
+        const int kF_src = kk + 1;
+        for (int jF = -2 + 1; jF <= ex[1]; ++jF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF, kF_dst, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF, kF_src, 2, ex)] * SoA[2];
+            }
+        }
+    }
+    /* 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:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
+     */
+    
+    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);
+
+                /* 高阶分支：i±2,j±2,k±2 都在范围内 */
+                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+                {
+                    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)]
+                    );
+
+                    /* fxy 高阶：完全照搬 Fortran 的括号结构 */
+                    {
+                        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 );
+                    }
+
+                    /* fxz 高阶 */
+                    {
+                        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 );
+                    }
+
+                    /* fyz 高阶 */
+                    {
+                        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 );
+                    }
+                }
+                /* 二阶分支：i±1,j±1,k±1 在范围内 */
+                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+                {
+                    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)]
+                    );
+                }else{
+                    fxx[p] = 0.0;
+                    fyy[p] = 0.0;
+                    fzz[p] = 0.0;
+                    fxy[p] = 0.0;
+                    fxz[p] = 0.0;
+                    fyz[p] = 0.0;
+                }
+            }
+        }
+    }
+    // free(fh);
+}

AMSS_NCKU_source/extention/src/main.c

@@ -0,0 +1,7 @@
+#include "include/bssn_rhs_compute.h"
+
+int main() {
+    // 这里可以写一些测试代码，调用 f_compute_rhs_bssn 来验证它的正确性
+    // 例如，定义一些小的网格和初始条件，调用函数，并检查输出是否合理。
+    return 0;
+}

AMSS_NCKU_source/extention/src/new.c

@@ -0,0 +1,65 @@
+        SoA[0] = SYM, SoA[1] = SYM, SoA[2] = SYM;
+        #pragma omp for collapse(3)
+        for (int k0 = 0; k0 < ex[2]; ++k0) {
+            for (int j0 = 0; j0 < ex[1]; ++j0) {
+                for (int i0 = 0; i0 < ex[0]; ++i0) {
+                    const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1; 
+                    fh[idx_funcc_F(iF, jF, kF, 2, ex)] = Lap[idx_func0(i0, j0, k0, ex)];
+                }
+            }
+        }
+
+        // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+        #pragma omp for collapse(3)
+        for (int ii = 0; ii <= 2 - 1; ++ii) {
+            const int iF_dst = -ii;       // 0, -1, -2, ...
+            const int iF_src = ii + 1;    // 1, 2, 3, ...
+            for (int kF = 1; kF <= ex[2]; ++kF) {
+                for (int jF = 1; jF <= ex[1]; ++jF) {
+                    fh[idx_funcc_F(iF_dst, jF, kF, 2, ex)] = 
+                        fh[idx_funcc_F(iF_src, jF, kF, 2, ex)] * SoA[0];
+                }
+            }
+        }
+
+        // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+        // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+        #pragma omp for collapse(3)
+        for (int jj = 0; jj <= 2 - 1; ++jj) {
+            const int jF_dst = -jj;
+            const int jF_src = jj + 1;
+            for (int kF = 1; kF <= ex[2]; ++kF) {
+                for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                    fh[idx_funcc_F(iF, jF_dst, kF, 2, ex)] =
+                        fh[idx_funcc_F(iF, jF_src, kF, 2, ex)] * SoA[1];
+                }
+            }
+        }
+
+        // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+        #pragma omp for collapse(3)
+        for (int kk = 0; kk <= 2 - 1; ++kk) {
+            const int kF_dst = -kk;
+            const int kF_src = kk + 1;
+            for (int jF = -2 + 1; jF <= ex[1]; ++jF) {
+                for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                    fh[idx_funcc_F(iF, jF, kF_dst, 2, ex)] =
+                        fh[idx_funcc_F(iF, jF, kF_src, 2, ex)] * SoA[2];
+                }
+            }
+        }
+
+        #pragma omp for collapse(3)
+        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) {
+                    fdderivs_xh(i0, j0, k0, ex, fh, iminF, jminF, kminF, ex1, ex2, ex3, 
+                        Fdxdx, Fdydy, Fdzdz, Fdxdy, Fdxdz, Fdydz,
+                        Sdxdx, Sdydy, Sdzdz, Sdxdy, Sdxdz, Sdydz,
+                            fxx,fxy,fxz,fyy,fyz,fzz
+                    );
+                }
+            }
+        }

AMSS_NCKU_source/extention/src/xh_fdderivs.c

@@ -0,0 +1,311 @@
+#include "xh_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;
+
+
+    /* 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;
+
+    /* 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);
+
+    static thread_local double *fh = NULL;
+    static thread_local 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);
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    for (int k0 = 0; k0 < ex[2]; ++k0) {
+        for (int j0 = 0; j0 < ex[1]; ++j0) {
+            for (int i0 = 0; i0 < ex[0]; ++i0) {
+                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1; 
+                fh[idx_funcc_F(iF, jF, kF, 2, ex)] = f[idx_func0(i0, j0, k0, ex)];
+            }
+        }
+    }
+
+    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    for (int ii = 0; ii <= 2 - 1; ++ii) {
+        const int iF_dst = -ii;       // 0, -1, -2, ...
+        const int iF_src = ii + 1;    // 1, 2, 3, ...
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int jF = 1; jF <= ex[1]; ++jF) {
+                fh[idx_funcc_F(iF_dst, jF, kF, 2, ex)] = 
+                    fh[idx_funcc_F(iF_src, jF, kF, 2, ex)] * SoA[0];
+            }
+        }
+    }
+
+    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+    for (int jj = 0; jj <= 2 - 1; ++jj) {
+        const int jF_dst = -jj;
+        const int jF_src = jj + 1;
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF_dst, kF, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF_src, kF, 2, ex)] * SoA[1];
+            }
+        }
+    }
+
+    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+    for (int kk = 0; kk <= 2 - 1; ++kk) {
+        const int kF_dst = -kk;
+        const int kF_src = kk + 1;
+        for (int jF = -2 + 1; jF <= ex[1]; ++jF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF, kF_dst, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF, kF_src, 2, ex)] * SoA[2];
+            }
+        }
+    }
+    /* 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:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
+     */
+    
+    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);
+
+                /* 高阶分支：i±2,j±2,k±2 都在范围内 */
+                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+                {
+                    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)]
+                    );
+
+                    /* fxy 高阶：完全照搬 Fortran 的括号结构 */
+                    {
+                        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 );
+                    }
+
+                    /* fxz 高阶 */
+                    {
+                        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 );
+                    }
+
+                    /* fyz 高阶 */
+                    {
+                        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 );
+                    }
+                }
+                /* 二阶分支：i±1,j±1,k±1 在范围内 */
+                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+                {
+                    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)]
+                    );
+                }else{
+                    fxx[p] = 0.0;
+                    fyy[p] = 0.0;
+                    fzz[p] = 0.0;
+                    fxy[p] = 0.0;
+                    fxz[p] = 0.0;
+                    fyz[p] = 0.0;
+                }
+            }
+        }
+    }
+    // free(fh);
+}

AMSS_NCKU_source/extention/src/xh_fderivs.c

@@ -0,0 +1,145 @@
+#include "xh_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];
+
+    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 thread_local double *fh = NULL;
+    static thread_local 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;
+    }
+
+    /*
+     * Fortran loops:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
+     *
+     * C: k0=0..ex3-2, j0=0..ex2-2, i0=0..ex1-2
+     */
+    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);
+
+                // if(i+2 <= imax .and. i-2 >= imin ... )  (全是 Fortran 索引)
+                if ((iF + 2) <= ex1 && (iF - 2) >= iminF &&
+                    (jF + 2) <= ex2 && (jF - 2) >= jminF &&
+                    (kF + 2) <= ex3 && (kF - 2) >= kminF)
+                {
+                    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)]
+                    );
+                }
+                // elseif(i+1 <= imax .and. i-1 >= imin ...)
+                else if ((iF + 1) <= ex1 && (iF - 1) >= iminF &&
+                         (jF + 1) <= ex2 && (jF - 1) >= jminF &&
+                         (kF + 1) <= ex3 && (kF - 1) >= kminF)
+                {
+                    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)]
+                    );
+                }
+            }
+        }
+    }
+
+    // free(fh);
+}

AMSS_NCKU_source/extention/src/xh_kodiss.c

@@ -0,0 +1,116 @@
+#include "xh_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;
+
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    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, ...
+     */
+    for (int k0 = 0; k0 < ex3; ++k0) {
+        const int kF = k0 + 1;
+        for (int j0 = 0; j0 < ex2; ++j0) {
+            const int jF = j0 + 1;
+            for (int i0 = 0; i0 < ex1; ++i0) {
+                const int iF = i0 + 1;
+
+                // Fortran if 条件：
+                // i-3 >= imin .and. i+3 <= imax  等（都是 Fortran 索引）
+                if ((iF - 3) >= iminF && (iF + 3) <= imaxF &&
+                    (jF - 3) >= jminF && (jF + 3) <= jmaxF &&
+                    (kF - 3) >= kminF && (kF + 3) <= kmaxF)
+                {
+                    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/extention/src/xh_lopsided.c

@@ -0,0 +1,262 @@
+#include "xh_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;
+
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    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/fmisc.f90

@@ -883,17 +883,13 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-!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
@@ -1116,7 +1112,6 @@ end subroutine d2dump
 ! Lagrangian polynomial interpolation
 !------------------------------------------------------------------------------
 
-!DIR$ ATTRIBUTES FORCEINLINE :: polint
   subroutine polint(xa, ya, x, y, dy, ordn)
   implicit none
 

AMSS_NCKU_source/kodiss.f90

@@ -65,8 +65,6 @@ 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/lopsidediff.f90

@@ -487,201 +487,6 @@ 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/makefile

@@ -8,7 +8,7 @@ include makefile.inc
 	$(f90) $(f90appflags) -c $< -o $@
 
 .C.o:
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< $(filein) -o $@
 
 .for.o:
 	$(f77) -c $< -o $@
@@ -28,7 +28,8 @@ C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.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
+	   NullShellPatch2_Evo.o writefile_f.o xh_bssn_rhs.o xh_fdderivs.o xh_fderivs.o xh_kodiss.o xh_lopsided.o \
+	   xh_global_interp.o xh_polint3.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\
@@ -72,7 +73,7 @@ $(C++FILES): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.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 
+             initial_null2.h NullShellPatch2.h xh_bssn_rhs_compute.h xh_global_interp.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\
@@ -96,7 +97,7 @@ misc.o : zbesh.o
 
 # projects
 ABE: $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) 
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -qopenmp -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)

AMSS_NCKU_source/makefile.inc

@@ -13,7 +13,7 @@ LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore
 ## Aggressive optimization flags + PGO Phase 2 (profile-guided optimization)
 ## -fprofile-instr-use: use collected profile data to guide optimization decisions
 ##   (branch prediction, basic block layout, inlining, loop unrolling)
-PROFDATA     = ../../pgo_profile/default.profdata
+PROFDATA     = /home/hxh/AMSS-NCKU/pgo_profile/default.profdata
 CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
                -fprofile-instr-use=$(PROFDATA) \
                -Dfortran3 -Dnewc -I${MKLROOT}/include

AMSS_NCKU_source/surface_integral.C

@@ -11,8 +11,6 @@
 #include <strstream>
 #include <cmath>
 #include <map>
-#include <vector>
-#include <algorithm>
 using namespace std;
 #else
 #include <iostream.h>
@@ -240,6 +238,9 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
   shellf = new double[n_tot * InList];
 
   GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Nmin, Nmax);
+
+  //|~~~~~> Integrate the dot product of Dphi with the surface normal.
+
   double *RP_out, *IP_out;
   RP_out = new double[NN];
   IP_out = new double[NN];
@@ -2652,6 +2653,7 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
 
   // we have assumed there is only one box on this level,
   // so we do not need loop boxes
+
   GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Comm_here);
 
   double Mass_out = 0;

AMSS_NCKU_source/xh_bssn_rhs_compute.h

@@ -0,0 +1,30 @@
+#include "xh_tool.h"
+
+
+extern "C"
+{
+int f_compute_rhs_bssn_xh(int *ex, double &T, 
+                       double *X, double *Y, double *Z,
+                       double *chi, double *trK,
+                       double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+                       double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+                       double *Gamx, double *Gamy, double *Gamz,
+                       double *Lap, double *betax, double *betay, double *betaz,
+                       double *dtSfx, double *dtSfy, double *dtSfz,
+                       double *chi_rhs, double *trK_rhs,
+                       double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+                       double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+                       double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+                       double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+                       double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+                       double *rho, double *Sx, double *Sy, double *Sz,
+                       double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
+                       double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
+                       double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
+                       double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
+                       double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
+                       double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
+                       double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
+                       int &Symmetry, int &Lev, double &eps, int &co
+                       ); 
+}

AMSS_NCKU_source/xh_fdderivs.C

@@ -0,0 +1,311 @@
+#include "xh_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;
+
+
+    /* 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;
+
+    /* 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);
+
+    static thread_local double *fh = NULL;
+    static thread_local 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);
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    for (int k0 = 0; k0 < ex[2]; ++k0) {
+        for (int j0 = 0; j0 < ex[1]; ++j0) {
+            for (int i0 = 0; i0 < ex[0]; ++i0) {
+                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1; 
+                fh[idx_funcc_F(iF, jF, kF, 2, ex)] = f[idx_func0(i0, j0, k0, ex)];
+            }
+        }
+    }
+
+    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    for (int ii = 0; ii <= 2 - 1; ++ii) {
+        const int iF_dst = -ii;       // 0, -1, -2, ...
+        const int iF_src = ii + 1;    // 1, 2, 3, ...
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int jF = 1; jF <= ex[1]; ++jF) {
+                fh[idx_funcc_F(iF_dst, jF, kF, 2, ex)] = 
+                    fh[idx_funcc_F(iF_src, jF, kF, 2, ex)] * SoA[0];
+            }
+        }
+    }
+
+    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+    for (int jj = 0; jj <= 2 - 1; ++jj) {
+        const int jF_dst = -jj;
+        const int jF_src = jj + 1;
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF_dst, kF, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF_src, kF, 2, ex)] * SoA[1];
+            }
+        }
+    }
+
+    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+    for (int kk = 0; kk <= 2 - 1; ++kk) {
+        const int kF_dst = -kk;
+        const int kF_src = kk + 1;
+        for (int jF = -2 + 1; jF <= ex[1]; ++jF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF, kF_dst, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF, kF_src, 2, ex)] * SoA[2];
+            }
+        }
+    }
+    /* 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:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
+     */
+    
+    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);
+
+                /* 高阶分支：i±2,j±2,k±2 都在范围内 */
+                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+                {
+                    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)]
+                    );
+
+                    /* fxy 高阶：完全照搬 Fortran 的括号结构 */
+                    {
+                        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 );
+                    }
+
+                    /* fxz 高阶 */
+                    {
+                        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 );
+                    }
+
+                    /* fyz 高阶 */
+                    {
+                        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 );
+                    }
+                }
+                /* 二阶分支：i±1,j±1,k±1 在范围内 */
+                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+                {
+                    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)]
+                    );
+                }else{
+                    fxx[p] = 0.0;
+                    fyy[p] = 0.0;
+                    fzz[p] = 0.0;
+                    fxy[p] = 0.0;
+                    fxz[p] = 0.0;
+                    fyz[p] = 0.0;
+                }
+            }
+        }
+    }
+    // free(fh);
+}

AMSS_NCKU_source/xh_fderivs.C

@@ -0,0 +1,145 @@
+#include "xh_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];
+
+    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 thread_local double *fh = NULL;
+    static thread_local 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;
+    }
+
+    /*
+     * Fortran loops:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
+     *
+     * C: k0=0..ex3-2, j0=0..ex2-2, i0=0..ex1-2
+     */
+    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);
+
+                // if(i+2 <= imax .and. i-2 >= imin ... )  (全是 Fortran 索引)
+                if ((iF + 2) <= ex1 && (iF - 2) >= iminF &&
+                    (jF + 2) <= ex2 && (jF - 2) >= jminF &&
+                    (kF + 2) <= ex3 && (kF - 2) >= kminF)
+                {
+                    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)]
+                    );
+                }
+                // elseif(i+1 <= imax .and. i-1 >= imin ...)
+                else if ((iF + 1) <= ex1 && (iF - 1) >= iminF &&
+                         (jF + 1) <= ex2 && (jF - 1) >= jminF &&
+                         (kF + 1) <= ex3 && (kF - 1) >= kminF)
+                {
+                    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)]
+                    );
+                }
+            }
+        }
+    }
+
+    // free(fh);
+}

AMSS_NCKU_source/xh_global_interp.C

@@ -0,0 +1,143 @@
+#include "xh_global_interp.h"
+
+/* 你已有的 polin3（由前面 Fortran->C 翻译得到） */
+// void polin3(const double *x1a, const double *x2a, const double *x3a,
+//             const double *ya, double x1, double x2, double x3,
+//             double *y, double *dy, int ordn);
+
+/*
+  你需要提供 decide3d 的实现（这里仅声明）。
+  Fortran: decide3d(ex,f,f,cxB,cxT,SoA,ya,ORDN,Symmetry)
+  - ex: [3]
+  - f: 三维场（列主序）
+  - cxB/cxT: 3 维窗口起止（Fortran 1-based，且可能 <=0）
+  - SoA: [3]
+  - ya: 输出 ORDN^3 的采样块（列主序）
+  - return: 0 表示正常；非 0 表示错误（对应 Fortran logical = .true.）
+*/
+// int xh_decide3d(const int ex[3],
+//              const double *f_in,
+//              const double *f_in2,   /* Fortran 里传了 f,f；按原样保留 */
+//              const int cxB[3],
+//              const int cxT[3],
+//              const double SoA[3],
+//              double *ya,
+//              int ordn,
+//              int symmetry);
+
+/* 把 Fortran 1-based 下标 idxF (可为负/0) 映射到 C 的 X[idx] 访问（只用于 X(2-cxB) 这种表达式） */
+static inline double X_at_FortranIndex(const double *X, int idxF) {
+    /* Fortran: X(1) 对应 C: X[0] */
+    return X[idxF - 1];
+}
+
+/* Fortran 整数截断：idint 在这里可用 (int) 实现（对正数等价于 floor） */
+static inline int idint_like(double a) {
+    return (int)a;  /* trunc toward zero */
+}
+
+/* global_interp 的 C 版 */
+void xh_global_interp(const int ex[3],
+                   const double *X, const double *Y, const double *Z,
+                   const double *f,                 /* f(ex1,ex2,ex3) column-major */
+                   double &f_int,
+                   double x1, double y1, double z1,
+                   int ORDN,
+                   const double SoA[3],
+                   int symmetry)
+{
+    // double time1, time2;
+    // time1 = omp_get_wtime();
+    enum { NO_SYMM = 0, EQUATORIAL = 1, OCTANT = 2 };
+
+    int j, m;
+    int imin, jmin, kmin;
+    int cxB[3], cxT[3], cxI[3], cmin[3], cmax[3];
+    double cx[3];
+    double dX, dY, dZ, ddy;
+
+    /* Fortran: imin=lbound(f,1) ... 通常是 1；这里按 1 处理 */
+    imin = 1; jmin = 1; kmin = 1;
+
+    dX = X_at_FortranIndex(X, imin + 1) - X_at_FortranIndex(X, imin);
+    dY = X_at_FortranIndex(Y, jmin + 1) - X_at_FortranIndex(Y, jmin);
+    dZ = X_at_FortranIndex(Z, kmin + 1) - X_at_FortranIndex(Z, kmin);
+
+    /* x1a(j) = (j-1)*1.0  (j=1..ORDN) */
+    double *x1a = (double*)malloc((size_t)ORDN * sizeof(double));
+    double *ya  = (double*)malloc((size_t)ORDN * (size_t)ORDN * (size_t)ORDN * sizeof(double));
+    if (!x1a || !ya) {
+        fprintf(stderr, "global_interp: malloc failed\n");
+        exit(1);
+    }
+    for (j = 0; j < ORDN; j++) x1a[j] = (double)j;
+
+    /* cxI(m) = idint((p - P(1))/dP + 0.4) + 1  (Fortran 1-based) */
+    cxI[0] = idint_like((x1 - X_at_FortranIndex(X, 1)) / dX + 0.4) + 1;
+    cxI[1] = idint_like((y1 - X_at_FortranIndex(Y, 1)) / dY + 0.4) + 1;
+    cxI[2] = idint_like((z1 - X_at_FortranIndex(Z, 1)) / dZ + 0.4) + 1;
+
+    /* cxB = cxI - ORDN/2 + 1 ; cxT = cxB + ORDN - 1 */
+    int half = ORDN / 2;  /* Fortran 整数除法 */
+    for (m = 0; m < 3; m++) {
+        cxB[m] = cxI[m] - half + 1;
+        cxT[m] = cxB[m] + ORDN - 1;
+    }
+
+    /* cmin=1; cmax=ex */
+    cmin[0] = cmin[1] = cmin[2] = 1;
+    cmax[0] = ex[0];
+    cmax[1] = ex[1];
+    cmax[2] = ex[2];
+
+    /* 对称边界时允许 cxB 为负/0（与 Fortran 一致） */
+    if (symmetry == OCTANT && fabs(X_at_FortranIndex(X, 1)) < dX) cmin[0] = -half + 2;
+    if (symmetry == OCTANT && fabs(X_at_FortranIndex(Y, 1)) < dY) cmin[1] = -half + 2;
+    if (symmetry != NO_SYMM && fabs(X_at_FortranIndex(Z, 1)) < dZ) cmin[2] = -half + 2;
+
+    /* 夹紧窗口 [cxB,cxT] 到 [cmin,cmax] */
+    for (m = 0; m < 3; m++) {
+        if (cxB[m] < cmin[m]) {
+            cxB[m] = cmin[m];
+            cxT[m] = cxB[m] + ORDN - 1;
+        }
+        if (cxT[m] > cmax[m]) {
+            cxT[m] = cmax[m];
+            cxB[m] = cxT[m] + 1 - ORDN;
+        }
+    }
+
+    /*
+      cx(m) 的计算：如果 cxB>0:
+        cx = (p - P(cxB))/dP
+      else:
+        cx = (p + P(2 - cxB))/dP
+      注意这里的 cxB 是 Fortran 1-based 语义下的整数，可能 <=0。
+    */
+    if (cxB[0] > 0) cx[0] = (x1 - X_at_FortranIndex(X, cxB[0])) / dX;
+    else           cx[0] = (x1 + X_at_FortranIndex(X, 2 - cxB[0])) / dX;
+
+    if (cxB[1] > 0) cx[1] = (y1 - X_at_FortranIndex(Y, cxB[1])) / dY;
+    else           cx[1] = (y1 + X_at_FortranIndex(Y, 2 - cxB[1])) / dY;
+
+    if (cxB[2] > 0) cx[2] = (z1 - X_at_FortranIndex(Z, cxB[2])) / dZ;
+    else           cx[2] = (z1 + X_at_FortranIndex(Z, 2 - cxB[2])) / dZ;
+
+    /* decide3d: 填充 ya(1:ORDN,1:ORDN,1:ORDN) */
+    if (xh_decide3d(ex, f, f, cxB, cxT, SoA, ya, ORDN, symmetry)) {
+        printf("global_interp position: %g %g %g\n", x1, y1, z1);
+        printf("data range: %g %g   %g %g   %g %g\n",
+               X_at_FortranIndex(X, 1), X_at_FortranIndex(X, ex[0]),
+               X_at_FortranIndex(Y, 1), X_at_FortranIndex(Y, ex[1]),
+               X_at_FortranIndex(Z, 1), X_at_FortranIndex(Z, ex[2]));
+        exit(1);
+    }
+
+    /* polin3(x1a,x1a,x1a,ya,cx(1),cx(2),cx(3),f_int,ddy,ORDN) */
+    xh_polin3(x1a, x1a, x1a, ya, cx[0], cx[1], cx[2], f_int, &ddy, ORDN);
+ 
+    free(x1a);
+    free(ya);
+    // time2 = omp_get_wtime();
+    // printf("Time for global_interp: %lf seconds\n", time2 - time1);
+}

AMSS_NCKU_source/xh_global_interp.h

@@ -0,0 +1,12 @@
+#include "xh_po.h"
+
+extern "C"{
+    void xh_global_interp(const int ex[3],
+                    const double *X, const double *Y, const double *Z,
+                    const double *f,                 /* f(ex1,ex2,ex3) column-major */
+                    double &f_int,
+                    double x1, double y1, double z1,
+                    int ORDN,
+                    const double SoA[3],
+                    int symmetry);
+}

AMSS_NCKU_source/xh_kodiss.C

@@ -0,0 +1,116 @@
+#include "xh_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;
+
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    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, ...
+     */
+    for (int k0 = 0; k0 < ex3; ++k0) {
+        const int kF = k0 + 1;
+        for (int j0 = 0; j0 < ex2; ++j0) {
+            const int jF = j0 + 1;
+            for (int i0 = 0; i0 < ex1; ++i0) {
+                const int iF = i0 + 1;
+
+                // Fortran if 条件：
+                // i-3 >= imin .and. i+3 <= imax  等（都是 Fortran 索引）
+                if ((iF - 3) >= iminF && (iF + 3) <= imaxF &&
+                    (jF - 3) >= jminF && (jF + 3) <= jmaxF &&
+                    (kF - 3) >= kminF && (kF + 3) <= kmaxF)
+                {
+                    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/xh_lopsided.C

@@ -0,0 +1,262 @@
+#include "xh_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;
+
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    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/xh_po.h

@@ -0,0 +1,19 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <omp.h>
+int xh_decide3d(const int ex[3],
+             const double *f,
+             const double *fpi,   /* 这里未用，Fortran 也没用到 */
+             const int cxB[3],
+             const int cxT[3],
+             const double SoA[3],
+             double *ya,
+             int ordn,
+             int Symmetry);
+void xh_polint(const double *xa, const double *ya, double x,
+                   double *y, double *dy, int ordn);
+
+void xh_polin3(const double *x1a, const double *x2a, const double *x3a,
+                   const double *ya, double x1, double x2, double x3,
+                   double &y, double *dy, int ordn);

AMSS_NCKU_source/xh_polint3.C

@@ -0,0 +1,258 @@
+#include "xh_po.h"
+/*
+  ex[0..2]  == Fortran ex(1:3)
+  cxB/cxT   == Fortran cxB(1:3), cxT(1:3)  (可能 <=0)
+  SoA[0..2] == Fortran SoA(1:3)
+  f, fpi    == Fortran f(ex1,ex2,ex3) column-major (1-based in formulas)
+  ya        == 连续内存，尺寸为 ORDN^3，对应 Fortran ya(cxB1:cxT1, cxB2:cxT2, cxB3:cxT3)
+              但注意：我们用 offset 映射把 Fortran 的 i/j/k 坐标写进去。
+*/
+
+static inline int imax(int a, int b) { return a > b ? a : b; }
+static inline int imin(int a, int b) { return a < b ? a : b; }
+
+/* f(i,j,k): Fortran column-major, i/j/k are Fortran 1-based in [1..ex] */
+#define F(i,j,k) f[((i)-1) + ex1 * (((j)-1) + ex2 * ((k)-1))]
+
+/*
+  ya(i,j,k): i in [cxB1..cxT1], j in [cxB2..cxT2], k in [cxB3..cxT3]
+  我们把它映射到 C 的 0..ORDN-1 立方体：
+    ii = i - cxB1
+    jj = j - cxB2
+    kk = k - cxB3
+  并按 column-major 存储（与 Fortran 一致，方便直接喂给你的 polin3）
+*/
+#define YA(i,j,k) ya[((i)-cxB1) + ordn * (((j)-cxB2) + ordn * ((k)-cxB3))]
+
+int xh_decide3d(const int ex[3],
+             const double *f,
+             const double *fpi,   /* 这里未用，Fortran 也没用到 */
+             const int cxB[3],
+             const int cxT[3],
+             const double SoA[3],
+             double *ya,
+             int ordn,
+             int Symmetry)         /* Symmetry 在 decide3d 里也没直接用 */
+{
+    (void)fpi;
+    (void)Symmetry;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    int fmin1[3], fmin2[3], fmax1[3], fmax2[3];
+    int i, j, k, m;
+
+    int gont = 0;
+
+    /* 方便 YA 宏使用 */
+    const int cxB1 = cxB[0], cxB2 = cxB[1], cxB3 = cxB[2];
+
+    for (m = 0; m < 3; m++) {
+        /* Fortran 的 “NaN 检查” 在整数上基本无意义，这里不额外处理 */
+
+        fmin1[m] = imax(1, cxB[m]);
+        fmax1[m] = cxT[m];
+
+        fmin2[m] = cxB[m];
+        fmax2[m] = imin(0, cxT[m]);
+
+        /* if((fmin1<=fmax1) and (fmin1<1 or fmax1>ex)) gont=true */
+        if ((fmin1[m] <= fmax1[m]) && (fmin1[m] < 1 || fmax1[m] > ex[m])) gont = 1;
+
+        /* if((fmin2<=fmax2) and (2-fmax2<1 or 2-fmin2>ex)) gont=true */
+        if ((fmin2[m] <= fmax2[m]) && (2 - fmax2[m] < 1 || 2 - fmin2[m] > ex[m])) gont = 1;
+    }
+
+    if (gont) {
+        printf("error in decide3d\n");
+        printf("cxB: %d %d %d   cxT: %d %d %d   ex: %d %d %d\n",
+               cxB[0], cxB[1], cxB[2], cxT[0], cxT[1], cxT[2], ex[0], ex[1], ex[2]);
+        printf("fmin1: %d %d %d  fmax1: %d %d %d\n",
+               fmin1[0], fmin1[1], fmin1[2], fmax1[0], fmax1[1], fmax1[2]);
+        printf("fmin2: %d %d %d  fmax2: %d %d %d\n",
+               fmin2[0], fmin2[1], fmin2[2], fmax2[0], fmax2[1], fmax2[2]);
+        return 1;
+    }
+
+    /* ---- 填充 ya：完全照 Fortran 两大块循环写 ---- */
+
+    /* k in [fmin1(3)..fmax1(3)] */
+    for (k = fmin1[2]; k <= fmax1[2]; k++) {
+
+        /* j in [fmin1(2)..fmax1(2)] */
+        for (j = fmin1[1]; j <= fmax1[1]; j++) {
+
+            /* i in [fmin1(1)..fmax1(1)] : ya(i,j,k)=f(i,j,k) */
+            for (i = fmin1[0]; i <= fmax1[0]; i++) {
+                YA(i, j, k) = F(i, j, k);
+            }
+
+            /* i in [fmin2(1)..fmax2(1)] : ya(i,j,k)=f(2-i,j,k)*SoA(1) */
+            for (i = fmin2[0]; i <= fmax2[0]; i++) {
+                YA(i, j, k) = F(2 - i, j, k) * SoA[0];
+            }
+        }
+
+        /* j in [fmin2(2)..fmax2(2)] */
+        for (j = fmin2[1]; j <= fmax2[1]; j++) {
+
+            /* i in [fmin1(1)..fmax1(1)] : ya(i,j,k)=f(i,2-j,k)*SoA(2) */
+            for (i = fmin1[0]; i <= fmax1[0]; i++) {
+                YA(i, j, k) = F(i, 2 - j, k) * SoA[1];
+            }
+
+            /* i in [fmin2(1)..fmax2(1)] : ya=f(2-i,2-j,k)*SoA(1)*SoA(2) */
+            for (i = fmin2[0]; i <= fmax2[0]; i++) {
+                YA(i, j, k) = F(2 - i, 2 - j, k) * SoA[0] * SoA[1];
+            }
+        }
+    }
+
+    /* k in [fmin2(3)..fmax2(3)] */
+    for (k = fmin2[2]; k <= fmax2[2]; k++) {
+
+        /* j in [fmin1(2)..fmax1(2)] */
+        for (j = fmin1[1]; j <= fmax1[1]; j++) {
+
+            /* i in [fmin1(1)..fmax1(1)] : ya=f(i,j,2-k)*SoA(3) */
+            for (i = fmin1[0]; i <= fmax1[0]; i++) {
+                YA(i, j, k) = F(i, j, 2 - k) * SoA[2];
+            }
+
+            /* i in [fmin2(1)..fmax2(1)] : ya=f(2-i,j,2-k)*SoA(1)*SoA(3) */
+            for (i = fmin2[0]; i <= fmax2[0]; i++) {
+                YA(i, j, k) = F(2 - i, j, 2 - k) * SoA[0] * SoA[2];
+            }
+        }
+
+        /* j in [fmin2(2)..fmax2(2)] */
+        for (j = fmin2[1]; j <= fmax2[1]; j++) {
+
+            /* i in [fmin1(1)..fmax1(1)] : ya=f(i,2-j,2-k)*SoA(2)*SoA(3) */
+            for (i = fmin1[0]; i <= fmax1[0]; i++) {
+                YA(i, j, k) = F(i, 2 - j, 2 - k) * SoA[1] * SoA[2];
+            }
+
+            /* i in [fmin2(1)..fmax2(1)] : ya=f(2-i,2-j,2-k)*SoA1*SoA2*SoA3 */
+            for (i = fmin2[0]; i <= fmax2[0]; i++) {
+                YA(i, j, k) = F(2 - i, 2 - j, 2 - k) * SoA[0] * SoA[1] * SoA[2];
+            }
+        }
+    }
+
+    return 0;
+}
+
+#undef F
+#undef YA
+
+void xh_polint(const double *xa, const double *ya, double x,
+                   double *y, double *dy, int ordn)
+{
+    int i, m, ns, n_m;
+    double dif, dift, hp, h, den_val;
+
+    double *c  = (double*)malloc((size_t)ordn * sizeof(double));
+    double *d  = (double*)malloc((size_t)ordn * sizeof(double));
+    double *ho = (double*)malloc((size_t)ordn * sizeof(double));
+    if (!c || !d || !ho) {
+        fprintf(stderr, "polint: malloc failed\n");
+        exit(1);
+    }
+
+    for (i = 0; i < ordn; i++) {
+        c[i]  = ya[i];
+        d[i]  = ya[i];
+        ho[i] = xa[i] - x;
+    }
+
+    ns  = 0;                      // Fortran ns=1 -> C ns=0
+    dif = fabs(x - xa[0]);
+
+    for (i = 1; i < ordn; i++) {
+        dift = fabs(x - xa[i]);
+        if (dift < dif) {
+            ns  = i;
+            dif = dift;
+        }
+    }
+
+    *y  = ya[ns];
+    ns -= 1;                      // Fortran ns=ns-1
+
+    for (m = 1; m <= ordn - 1; m++) {
+        n_m = ordn - m;           // number of active points this round
+        for (i = 0; i < n_m; i++) {
+            hp      = ho[i];
+            h       = ho[i + m];
+            den_val = hp - h;
+
+            if (den_val == 0.0) {
+                fprintf(stderr, "failure in polint for point %g\n", x);
+                fprintf(stderr, "with input points xa: ");
+                for (int t = 0; t < ordn; t++) fprintf(stderr, "%g ", xa[t]);
+                fprintf(stderr, "\n");
+                exit(1);
+            }
+
+            den_val = (c[i + 1] - d[i]) / den_val;
+            d[i]    = h  * den_val;
+            c[i]    = hp * den_val;
+        }
+
+        // Fortran: if (2*ns < n_m) then dy=c(ns+1) else dy=d(ns); ns=ns-1
+        // Here ns is C-indexed and can be -1; logic still matches.
+        if (2 * ns < n_m) {
+            *dy = c[ns + 1];
+        } else {
+            *dy = d[ns];
+            ns -= 1;
+        }
+        *y += *dy;
+    }
+
+    free(c);
+    free(d);
+    free(ho);
+}
+
+void xh_polin3(const double *x1a, const double *x2a, const double *x3a,
+                   const double *ya, double x1, double x2, double x3,
+                   double &y, double *dy, int ordn)
+{
+    // ya is ordn x ordn x ordn in Fortran layout (column-major)
+    #define YA3(i,j,k) ya[(i) + ordn*((j) + ordn*(k))]  // i,j,k: 0..ordn-1
+
+    int j, k;
+    double dy_temp;
+
+    // yatmp(j,k) in Fortran code is ordn x ordn, treat column-major:
+    // yatmp(j,k) -> yatmp[j + ordn*k]
+    double *yatmp = (double*)malloc((size_t)ordn * (size_t)ordn * sizeof(double));
+    double *ymtmp = (double*)malloc((size_t)ordn * sizeof(double));
+    if (!yatmp || !ymtmp) {
+        fprintf(stderr, "polin3: malloc failed\n");
+        exit(1);
+    }
+    #define YAT(j,k) yatmp[(j) + ordn*(k)]
+
+    for (k = 0; k < ordn; k++) {
+        for (j = 0; j < ordn; j++) {
+            // call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp)
+            // ya(:,j,k) contiguous: base is &YA3(0,j,k)
+            xh_polint(x1a, &YA3(0, j, k), x1, &YAT(j, k), &dy_temp, ordn);
+        }
+    }
+
+    for (k = 0; k < ordn; k++) {
+        // call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp)
+        xh_polint(x2a, &YAT(0, k), x2, &ymtmp[k], &dy_temp, ordn);
+    }
+
+    xh_polint(x3a, ymtmp, x3, &y, dy, ordn);
+
+    #undef YAT
+    free(yatmp);
+    free(ymtmp);
+    #undef YA3
+}

AMSS_NCKU_source/xh_share_func.h

@@ -0,0 +1,338 @@
+#ifndef SHARE_FUNC_H
+#define SHARE_FUNC_H
+
+#include <stdlib.h>
+#include <stddef.h>
+#include <math.h>
+#include <stdio.h>
+#include <omp.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(int ord,
+                 const int extc[3],
+                 const double *func,
+                 double *funcc,
+                 const double SoA[3])
+{
+    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
+
+    // 1) funcc(1:extc1,1:extc2,1:extc3) = func
+    // Fortran 的 (iF=1..extc1) 对应 C 的 func(i0=0..extc1-1)
+    for (int k0 = 0; k0 < extc3; ++k0) {
+        for (int j0 = 0; j0 < extc2; ++j0) {
+            for (int i0 = 0; i0 < extc1; ++i0) {
+                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
+                funcc[idx_funcc_F(iF, jF, kF, ord, extc)] = func[idx_func0(i0, j0, k0, extc)];
+            }
+        }
+    }
+
+    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    for (int ii = 0; ii <= ord - 1; ++ii) {
+        const int iF_dst = -ii;       // 0, -1, -2, ...
+        const int iF_src = ii + 1;    // 1, 2, 3, ...
+        for (int kF = 1; kF <= extc3; ++kF) {
+            for (int jF = 1; jF <= extc2; ++jF) {
+                funcc[idx_funcc_F(iF_dst, jF, kF, ord, extc)] =
+                    funcc[idx_funcc_F(iF_src, jF, kF, ord, extc)] * SoA[0];
+            }
+        }
+    }
+
+    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+    for (int jj = 0; jj <= ord - 1; ++jj) {
+        const int jF_dst = -jj;
+        const int jF_src = jj + 1;
+        for (int kF = 1; kF <= extc3; ++kF) {
+            for (int iF = -ord + 1; iF <= extc1; ++iF) {
+                funcc[idx_funcc_F(iF, jF_dst, kF, ord, extc)] =
+                    funcc[idx_funcc_F(iF, jF_src, kF, ord, extc)] * SoA[1];
+            }
+        }
+    }
+
+    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+    for (int kk = 0; kk <= ord - 1; ++kk) {
+        const int kF_dst = -kk;
+        const int kF_src = kk + 1;
+        for (int jF = -ord + 1; jF <= extc2; ++jF) {
+            for (int iF = -ord + 1; iF <= extc1; ++iF) {
+                funcc[idx_funcc_F(iF, jF, kF_dst, ord, extc)] =
+                    funcc[idx_funcc_F(iF, jF, kF_src, ord, extc)] * SoA[2];
+            }
+        }
+    }
+}
+#endif
+
+/* 你已有的函数：idx_ex / idx_fh_F_ord2 以及 fh 的布局 */
+static inline void fdderivs_xh(
+    int i0, int j0, int k0,
+    const int ex[3],
+    const double *fh,
+    int iminF, int jminF, int kminF,
+    int imaxF, int jmaxF, int kmaxF,
+    double Fdxdx, double Fdydy, double Fdzdz,
+    double Fdxdy, double Fdxdz, double Fdydz,
+    double Sdxdx, double Sdydy, double Sdzdz,
+    double Sdxdy, double Sdxdz, double Sdydz,
+    double *fxx, double *fxy, double *fxz,
+    double *fyy, double *fyz, double *fzz
+){
+    const double F8  = 8.0;
+    const double F16 = 16.0;
+    const double F30 = 30.0;
+    const double TWO = 2.0;
+
+    const int iF = i0 + 1;
+    const int jF = j0 + 1;
+    const int kF = k0 + 1;
+
+    const size_t p = idx_ex(i0, j0, k0, ex);
+
+    /* 高阶分支：i±2,j±2,k±2 都在范围内 */
+    if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+        (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+        (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+    {
+        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)]
+        );
+
+        /* fxy 高阶 */
+        {
+            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 );
+        }
+
+        /* fxz 高阶 */
+        {
+            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 );
+        }
+
+        /* fyz 高阶 */
+        {
+            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 );
+        }
+    }
+    /* 二阶分支：i±1,j±1,k±1 在范围内 */
+    else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+             (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+             (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+    {
+        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)]
+        );
+    }
+    else {
+        fxx[p] = 0.0; fyy[p] = 0.0; fzz[p] = 0.0;
+        fxy[p] = 0.0; fxz[p] = 0.0; fyz[p] = 0.0;
+    }
+}

AMSS_NCKU_source/xh_tool.h

@@ -0,0 +1,27 @@
+#include "xh_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]);

makefile_and_run.py

@@ -16,18 +16,18 @@ import time
 ## 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"
-NUMACTL_CPU_BIND = "taskset -c 16-47,64-95"
+NUMACTL_CPU_BIND = "taskset -c 0-47"
-
+NUMACTL_CPU_BIND2 = "OMP_NUM_THREADS=48 OMP_PROC_BIND=close OMP_PLACES={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47} taskset -c 0-47"
+#NUMACTL_CPU_BIND2 = "taskset -c 0-1"
 ## 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 = 96
+BUILD_JOBS = 32
 
 
 ##################################################################
 
 
-
 ##################################################################
 
 ## Compile the AMSS-NCKU main program ABE
@@ -117,11 +117,12 @@ def run_ABE():
     ## Define the command to run; cast other values to strings as needed
     
     if (input_data.GPU_Calculation == "no"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        #mpi_command         = NUMACTL_CPU_BIND2 + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        mpi_command = """ OMP_NUM_THREADS=48 OMP_PROC_BIND=close OMP_PLACES=cores mpirun -np 1 --cpu-bind=sockets  ./ABE """
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command         = NUMACTL_CPU_BIND2 + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
         mpi_command_outfile = "ABEGPU_out.log"
  
     ## Execute the MPI command and stream output

parallel_plot_helper.py

@@ -1,29 +0,0 @@
-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

@@ -11,8 +11,6 @@
 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

@@ -8,23 +8,16 @@
 ##
 #################################################
 
-## 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
+
 
 #########################################################################################
 
@@ -199,19 +192,3 @@ 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

@@ -8,8 +8,6 @@
 #################################################
 
 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
@@ -17,9 +15,6 @@ 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
 
@@ -55,40 +50,10 @@ def generate_binary_data_plot( binary_outdir, figure_outdir ):
         file_list.append(x)
         print(x)
 
-    ## Plot each file in parallel using subprocesses.
+    ## Plot each file in the list
-    ## 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)
-        proc = subprocess.Popen(
+        plot_binary_data.plot_binary_data(filename, binary_outdir, figure_outdir)
-            [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 " )