feat: Implement hybrid MPI+OpenMP parallelization

- Enable -qopenmp in makefile.inc
- Add OpenMP directives to 4th order derivatives in diff_new.f90
- Update makefile_and_run.py to dynamic calculate OMP_NUM_THREADS based on 96 cores and remove hardcoded CPU binding

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    = 48                             ## 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)

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)
-
 
 ##################################################################
 
@@ -66,8 +58,7 @@ if os.path.exists(File_directory):
     ## Prompt whether to overwrite the existing directory
     while True:
         try:
-            ## inputvalue = input()
+            inputvalue = input()
-            inputvalue = "continue"
             ## If the user agrees to overwrite, proceed and remove the existing directory
             if ( inputvalue == "continue" ):
                 print( " Continue the calculation !!! " )
@@ -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/MPatch.h

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

AMSS_NCKU_source/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.h

@@ -1,235 +1,167 @@
-
+
-#ifndef PARALLEL_H
+#ifndef PARALLEL_H
-#define PARALLEL_H
+#define PARALLEL_H
-
+
-#include <iostream>
+#include <iostream>
-#include <iomanip>
+#include <iomanip>
-#include <fstream>
+#include <fstream>
-#include <cstdlib>
+#include <cstdlib>
-#include <cstdio>
+#include <cstdio>
-#include <string>
+#include <string>
-#include <cmath>
+#include <cmath>
-#include <new>
+#include <new>
-using namespace std;
+using namespace std;
-#include <memory.h>
+
-#include "Parallel_bam.h"
+#include "Parallel_bam.h"
-#include "var.h"
+#include "var.h"
-#include "MPatch.h"
+#include "MPatch.h"
-#include "Block.h"
+#include "Block.h"
-#include "MyList.h"
+#include "MyList.h"
-#include "macrodef.h" //need dim; ghost_width; CONTRACT
+#include "macrodef.h" //need dim; ghost_width; CONTRACT
-namespace Parallel
+namespace Parallel
-{
+{
-  struct gridseg
+  struct gridseg
-  {
+  {
-    double llb[dim];
+    double llb[dim];
-    double uub[dim];
+    double uub[dim];
-    int shape[dim];
+    int shape[dim];
-    double illb[dim], iuub[dim]; // only use for OutBdLow2Hi
+    double illb[dim], iuub[dim]; // only use for OutBdLow2Hi
-    Block *Bg;
+    Block *Bg;
-  };
+  };
-  int partition1(int &nx, int split_size, int min_width, int cpusize, int shape);    // special for 1 diemnsion
+  int partition1(int &nx, int split_size, int min_width, int cpusize, int shape);    // special for 1 diemnsion
-  int partition2(int *nxy, int split_size, int *min_width, int cpusize, int *shape); // special for 2 diemnsions
+  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);
+  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(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
+  void KillBlocks(MyList<Patch> *PatchLIST);
-  Block* splitHotspotBlock(MyList<Block>* &BlL, int _dim, 
+
-                                 int ib0_orig, int ib3_orig, 
+  void setfunction(MyList<Block> *BlL, var *vn, double func(double x, double y, double z));
-                                 int jb1_orig, int jb4_orig, 
+  void setfunction(int rank, MyList<Block> *BlL, var *vn, double func(double x, double y, double z));
-                                 int kb2_orig, int kb5_orig, 
+  void writefile(double time, int nx, int ny, int nz, double xmin, double xmax, double ymin, double ymax,
-                                 Patch* PP, int r_left, int r_right, 
+                 double zmin, double zmax, char *filename, double *data_out);
-                                 int ingfsi, int fngfsi, bool periodic,
+  void writefile(double time, int nx, int ny, double xmin, double xmax, double ymin, double ymax,
-                                 Block* &split_first_block, Block* &split_last_block);
+                 char *filename, double *datain);
-  Block* createMappedBlock(MyList<Block>* &BlL, int _dim, int* shape, double* bbox,
+  void getarrayindex(int DIM, int *shape, int *index, int n);
-                        int block_id, int ingfsi, int fngfsi, int lev); 
+  int getarraylocation(int DIM, int *shape, int *index);
-  void KillBlocks(MyList<Patch> *PatchLIST);
+  void copy(int DIM, double *llbout, double *uubout, int *Dshape, double *DD, double *llbin, double *uubin,
-
+            int *shape, double *datain, double *llb, double *uub);
-  void setfunction(MyList<Block> *BlL, var *vn, double func(double x, double y, double z));
+  void Dump_CPU_Data(MyList<Block> *BlL, MyList<var> *DumpList, char *tag, double time, double dT);
-  void setfunction(int rank, MyList<Block> *BlL, var *vn, double func(double x, double y, double z));
+  void Dump_Data(MyList<Patch> *PL, MyList<var> *DumpList, char *tag, double time, double dT);
-  void writefile(double time, int nx, int ny, int nz, double xmin, double xmax, double ymin, double ymax,
+  void Dump_Data(Patch *PP, MyList<var> *DumpList, char *tag, double time, double dT, int grd);
-                 double zmin, double zmax, char *filename, double *data_out);
+  double *Collect_Data(Patch *PP, var *VP);
-  void writefile(double time, int nx, int ny, double xmin, double xmax, double ymin, double ymax,
+  void d2Dump_Data(MyList<Patch> *PL, MyList<var> *DumpList, char *tag, double time, double dT);
-                 char *filename, double *datain);
+  void d2Dump_Data(Patch *PP, MyList<var> *DumpList, char *tag, double time, double dT, int grd);
-  void getarrayindex(int DIM, int *shape, int *index, int n);
+  void Dump_Data0(Patch *PP, MyList<var> *DumpList, char *tag, double time, double dT);
-  int getarraylocation(int DIM, int *shape, int *index);
+  double global_interp(int DIM, int *ext, double **CoX, double *datain,
-  void copy(int DIM, double *llbout, double *uubout, int *Dshape, double *DD, double *llbin, double *uubin,
+                       double *poX, int ordn, double *SoA, int Symmetry);
-            int *shape, double *datain, double *llb, double *uub);
+  double global_interp(int DIM, int *ext, double **CoX, double *datain,
-  void Dump_CPU_Data(MyList<Block> *BlL, MyList<var> *DumpList, char *tag, double time, double dT);
+                       double *poX, int ordn);
-  void Dump_Data(MyList<Patch> *PL, MyList<var> *DumpList, char *tag, double time, double dT);
+  double Lagrangian_Int(double x, int npts, double *xpts, double *funcvals);
-  void Dump_Data(Patch *PP, MyList<var> *DumpList, char *tag, double time, double dT, int grd);
+  double LagrangePoly(double x, int pt, int npts, double *xpts);
-  double *Collect_Data(Patch *PP, var *VP);
+  MyList<gridseg> *build_complete_gsl(Patch *Pat);
-  void d2Dump_Data(MyList<Patch> *PL, MyList<var> *DumpList, char *tag, double time, double dT);
+  MyList<gridseg> *build_complete_gsl(MyList<Patch> *PatL);
-  void d2Dump_Data(Patch *PP, MyList<var> *DumpList, char *tag, double time, double dT, int grd);
+  MyList<gridseg> *build_complete_gsl_virtual(MyList<Patch> *PatL);
-  void Dump_Data0(Patch *PP, MyList<var> *DumpList, char *tag, double time, double dT);
+  MyList<gridseg> *build_complete_gsl_virtual2(MyList<Patch> *PatL);        // - buffer
-  double global_interp(int DIM, int *ext, double **CoX, double *datain,
+  MyList<gridseg> *build_owned_gsl0(Patch *Pat, int rank_in);               // - ghost without extension, special for Sync usage
-                       double *poX, int ordn, double *SoA, int Symmetry);
+  MyList<gridseg> *build_owned_gsl1(Patch *Pat, int rank_in);               // - ghost, similar to build_owned_gsl0 but extend one point on left side for vertex grid
-  double global_interp(int DIM, int *ext, double **CoX, double *datain,
+  MyList<gridseg> *build_owned_gsl2(Patch *Pat, int rank_in);               // - buffer - ghost
-                       double *poX, int ordn);
+  MyList<gridseg> *build_owned_gsl3(Patch *Pat, int rank_in, int Symmetry); // - ghost - BD ghost
-  double Lagrangian_Int(double x, int npts, double *xpts, double *funcvals);
+  MyList<gridseg> *build_owned_gsl4(Patch *Pat, int rank_in, int Symmetry); // - buffer - ghost - BD ghost
-  double LagrangePoly(double x, int pt, int npts, double *xpts);
+  MyList<gridseg> *build_owned_gsl5(Patch *Pat, int rank_in);               // similar to build_owned_gsl2 but no extension
-  MyList<gridseg> *build_complete_gsl(Patch *Pat);
+  MyList<gridseg> *build_owned_gsl(MyList<Patch> *PatL, int rank_in, int type, int Symmetry);
-  MyList<gridseg> *build_complete_gsl(MyList<Patch> *PatL);
+  void build_gstl(MyList<gridseg> *srci, MyList<gridseg> *dsti, MyList<gridseg> **out_src, MyList<gridseg> **out_dst);
-  MyList<gridseg> *build_complete_gsl_virtual(MyList<Patch> *PatL);
+  int data_packer(double *data, MyList<gridseg> *src, MyList<gridseg> *dst, int rank_in, int dir,
-  MyList<gridseg> *build_complete_gsl_virtual2(MyList<Patch> *PatL);        // - buffer
+                  MyList<var> *VarLists, MyList<var> *VarListd, int Symmetry);
-  MyList<gridseg> *build_owned_gsl0(Patch *Pat, int rank_in);               // - ghost without extension, special for Sync usage
+  void transfer(MyList<gridseg> **src, MyList<gridseg> **dst,
-  MyList<gridseg> *build_owned_gsl1(Patch *Pat, int rank_in);               // - ghost, similar to build_owned_gsl0 but extend one point on left side for vertex grid
+                MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /*target */,
-  MyList<gridseg> *build_owned_gsl2(Patch *Pat, int rank_in);               // - buffer - ghost
+                int Symmetry);
-  MyList<gridseg> *build_owned_gsl3(Patch *Pat, int rank_in, int Symmetry); // - ghost - BD ghost
+  int data_packermix(double *data, MyList<gridseg> *src, MyList<gridseg> *dst, int rank_in, int dir,
-  MyList<gridseg> *build_owned_gsl4(Patch *Pat, int rank_in, int Symmetry); // - buffer - ghost - BD ghost
+                     MyList<var> *VarLists, MyList<var> *VarListd, int Symmetry);
-  MyList<gridseg> *build_owned_gsl5(Patch *Pat, int rank_in);               // similar to build_owned_gsl2 but no extension
+  void transfermix(MyList<gridseg> **src, MyList<gridseg> **dst,
-  MyList<gridseg> *build_owned_gsl(MyList<Patch> *PatL, int rank_in, int type, int Symmetry);
+                   MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /*target */,
-  void build_gstl(MyList<gridseg> *srci, MyList<gridseg> *dsti, MyList<gridseg> **out_src, MyList<gridseg> **out_dst);
+                   int Symmetry);
-  int data_packer(double *data, MyList<gridseg> *src, MyList<gridseg> *dst, int rank_in, int dir,
+  void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry);
-                  MyList<var> *VarLists, MyList<var> *VarListd, int Symmetry);
+  void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
-  void transfer(MyList<gridseg> **src, MyList<gridseg> **dst,
+  void OutBdLow2Hi(Patch *Patc, Patch *Patf,
-                MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /*target */,
+                   MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
-                int Symmetry);
+                   int Symmetry);
-  int data_packermix(double *data, MyList<gridseg> *src, MyList<gridseg> *dst, int rank_in, int dir,
+  void OutBdLow2Hi(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
-                     MyList<var> *VarLists, MyList<var> *VarListd, int Symmetry);
+                   MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
-  void transfermix(MyList<gridseg> **src, MyList<gridseg> **dst,
+                   int Symmetry);
-                   MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /*target */,
+  void OutBdLow2Himix(Patch *Patc, Patch *Patf,
-                   int Symmetry);
+                      MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
-  void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry);
+                      int Symmetry);
-  void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+  void OutBdLow2Himix(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
-  void Sync_merged(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+                      MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
-
+                      int Symmetry);
-  struct SyncCache {
+  void Prolong(Patch *Patc, Patch *Patf,
-    bool valid;
+               MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
-    int cpusize;
+               int Symmetry);
-    MyList<gridseg> **combined_src;
+  void Prolongint(Patch *Patc, Patch *Patf,
-    MyList<gridseg> **combined_dst;
+                  MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
-    int *send_lengths;
+                  int Symmetry);
-    int *recv_lengths;
+  void Restrict(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
-    double **send_bufs;
+                MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
-    double **recv_bufs;
+                int Symmetry);
-    int *send_buf_caps;
+  void Restrict_after(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
-    int *recv_buf_caps;
+                      MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
-    MPI_Request *reqs;
+                      int Symmetry); // for -ghost - BDghost
-    MPI_Status *stats;
+  MyList<Parallel::gridseg> *build_PhysBD_gsl(Patch *Pat);
-    int max_reqs;
+  MyList<Parallel::gridseg> *build_ghost_gsl(MyList<Patch> *PatL);
-    bool lengths_valid;
+  MyList<Parallel::gridseg> *build_ghost_gsl(Patch *Pat);
-    SyncCache();
+  MyList<Parallel::gridseg> *build_buffer_gsl(Patch *Pat);
-    void invalidate();
+  MyList<Parallel::gridseg> *build_buffer_gsl(MyList<Patch> *PatL);
-    void destroy();
+  MyList<Parallel::gridseg> *gsl_subtract(MyList<Parallel::gridseg> *A, MyList<Parallel::gridseg> *B);
-  };
+  MyList<Parallel::gridseg> *gs_subtract(MyList<Parallel::gridseg> *A, MyList<Parallel::gridseg> *B);
-
+  MyList<Parallel::gridseg> *gsl_and(MyList<Parallel::gridseg> *A, MyList<Parallel::gridseg> *B);
-  void Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, SyncCache &cache);
+  MyList<Parallel::gridseg> *gs_and(MyList<Parallel::gridseg> *A, MyList<Parallel::gridseg> *B);
-  void transfer_cached(MyList<gridseg> **src, MyList<gridseg> **dst,
+  MyList<Parallel::gridseg> *clone_gsl(MyList<Parallel::gridseg> *p, bool first_only);
-                       MyList<var> *VarList1, MyList<var> *VarList2,
+  MyList<Parallel::gridseg> *build_bulk_gsl(Patch *Pat); // similar to build_owned_gsl0 but does not care rank issue
-                       int Symmetry, SyncCache &cache);
+  MyList<Parallel::gridseg> *build_bulk_gsl(Block *bp, Patch *Pat);
-
+  void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
-  struct AsyncSyncState {
+                         MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
-    int req_no;
+  void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
-    bool active;
+  double L2Norm(Patch *Pat, var *vf);
-    AsyncSyncState() : req_no(0), active(false) {}
+  void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
-  };
+  void checkvarl(MyList<var> *pp, bool first_only);
-
+  MyList<Parallel::gridseg> *divide_gsl(MyList<Parallel::gridseg> *p, Patch *Pat);
-  void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
+  MyList<Parallel::gridseg> *divide_gs(MyList<Parallel::gridseg> *p, Patch *Pat);
-                  SyncCache &cache, AsyncSyncState &state);
+  void prepare_inter_time_level(Patch *Pat,
-  void Sync_finish(SyncCache &cache, AsyncSyncState &state,
+                                MyList<var> *VarList1 /* source (t+dt) */, MyList<var> *VarList2 /* source (t) */,
-                   MyList<var> *VarList, int Symmetry);
+                                MyList<var> *VarList3 /* target (t+a*dt) */, int tindex);
-  void OutBdLow2Hi(Patch *Patc, Patch *Patf,
+  void prepare_inter_time_level(Patch *Pat,
-                   MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
+                                MyList<var> *VarList1 /* source (t+dt) */, MyList<var> *VarList2 /* source (t) */,
-                   int Symmetry);
+                                MyList<var> *VarList3 /* source (t-dt) */, MyList<var> *VarList4 /* target (t+a*dt) */, int tindex);
-  void OutBdLow2Hi(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+  void prepare_inter_time_level(MyList<Patch> *PatL,
-                   MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
+                                MyList<var> *VarList1 /* source (t+dt) */, MyList<var> *VarList2 /* source (t) */,
-                   int Symmetry);
+                                MyList<var> *VarList3 /* target (t+a*dt) */, int tindex);
-  void OutBdLow2Himix(Patch *Patc, Patch *Patf,
+  void prepare_inter_time_level(MyList<Patch> *Pat,
-                      MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
+                                MyList<var> *VarList1 /* source (t+dt) */, MyList<var> *VarList2 /* source (t) */,
-                      int Symmetry);
+                                MyList<var> *VarList3 /* source (t-dt) */, MyList<var> *VarList4 /* target (t+a*dt) */, int tindex);
-  void OutBdLow2Himix(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+  void merge_gsl(MyList<gridseg> *&A, const double ratio);
-                      MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
+  bool merge_gs(MyList<gridseg> *D, MyList<gridseg> *B, MyList<gridseg> *&C, const double ratio);
-                      int Symmetry);
+  // Add ghost region to tangent plane
-  void Restrict_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+  // we assume the grids have the same resolution
-                       MyList<var> *VarList1, MyList<var> *VarList2,
+  void add_ghost_touch(MyList<gridseg> *&A);
-                       int Symmetry, SyncCache &cache);
+  void cut_gsl(MyList<gridseg> *&A);
-  void OutBdLow2Hi_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+  bool cut_gs(MyList<gridseg> *D, MyList<gridseg> *B, MyList<gridseg> *&C);
-                          MyList<var> *VarList1, MyList<var> *VarList2,
+  MyList<Parallel::gridseg> *gs_subtract_virtual(MyList<Parallel::gridseg> *A, MyList<Parallel::gridseg> *B);
-                          int Symmetry, SyncCache &cache);
+  void fill_level_data(MyList<Patch> *PatLd, MyList<Patch> *PatLs, MyList<Patch> *PatcL,
-  void OutBdLow2Himix_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+                       MyList<var> *OldList, MyList<var> *StateList, MyList<var> *FutureList,
-                             MyList<var> *VarList1, MyList<var> *VarList2,
+                       MyList<var> *tmList, int Symmetry, bool BB, bool CC);
-                             int Symmetry, SyncCache &cache);
+  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
-  void Prolong(Patch *Patc, Patch *Patf,
+                             int NN, double **XX,
-               MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
+                             double *Shellf, int Symmetry);
-               int Symmetry);
+  void aligncheck(double *bbox0, double *bboxl, int lev, double *DH0, int *shape);
-  void Prolongint(Patch *Patc, Patch *Patf,
+  bool point_locat_gsl(double *pox, MyList<Parallel::gridseg> *gsl);
-                  MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
+  void checkpatchlist(MyList<Patch> *PatL, bool buflog);
-                  int Symmetry);
+
-  void Restrict(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+  double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
-                MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
+  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
-                int Symmetry);
+                             int NN, double **XX,
-  void Restrict_after(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+                             double *Shellf, int Symmetry, MPI_Comm Comm_here);
-                      MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
+#if (PSTR == 1 || PSTR == 2 || PSTR == 3)
-                      int Symmetry); // for -ghost - BDghost
+  MyList<Block> *distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfsi,
-  MyList<Parallel::gridseg> *build_PhysBD_gsl(Patch *Pat);
+                            bool periodic, int start_rank, int end_rank, int nodes = 0);
-  MyList<Parallel::gridseg> *build_ghost_gsl(MyList<Patch> *PatL);
+#endif
-  MyList<Parallel::gridseg> *build_ghost_gsl(Patch *Pat);
+}
-  MyList<Parallel::gridseg> *build_buffer_gsl(Patch *Pat);
+#endif /*PARALLEL_H */
-  MyList<Parallel::gridseg> *build_buffer_gsl(MyList<Patch> *PatL);
-  MyList<Parallel::gridseg> *gsl_subtract(MyList<Parallel::gridseg> *A, MyList<Parallel::gridseg> *B);
-  MyList<Parallel::gridseg> *gs_subtract(MyList<Parallel::gridseg> *A, MyList<Parallel::gridseg> *B);
-  MyList<Parallel::gridseg> *gsl_and(MyList<Parallel::gridseg> *A, MyList<Parallel::gridseg> *B);
-  MyList<Parallel::gridseg> *gs_and(MyList<Parallel::gridseg> *A, MyList<Parallel::gridseg> *B);
-  MyList<Parallel::gridseg> *clone_gsl(MyList<Parallel::gridseg> *p, bool first_only);
-  MyList<Parallel::gridseg> *build_bulk_gsl(Patch *Pat); // similar to build_owned_gsl0 but does not care rank issue
-  MyList<Parallel::gridseg> *build_bulk_gsl(Block *bp, Patch *Pat);
-  void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
-                         MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
-  void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
-  double L2Norm(Patch *Pat, var *vf);
-  void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
-  void checkvarl(MyList<var> *pp, bool first_only);
-  MyList<Parallel::gridseg> *divide_gsl(MyList<Parallel::gridseg> *p, Patch *Pat);
-  MyList<Parallel::gridseg> *divide_gs(MyList<Parallel::gridseg> *p, Patch *Pat);
-  void prepare_inter_time_level(Patch *Pat,
-                                MyList<var> *VarList1 /* source (t+dt) */, MyList<var> *VarList2 /* source (t) */,
-                                MyList<var> *VarList3 /* target (t+a*dt) */, int tindex);
-  void prepare_inter_time_level(Patch *Pat,
-                                MyList<var> *VarList1 /* source (t+dt) */, MyList<var> *VarList2 /* source (t) */,
-                                MyList<var> *VarList3 /* source (t-dt) */, MyList<var> *VarList4 /* target (t+a*dt) */, int tindex);
-  void prepare_inter_time_level(MyList<Patch> *PatL,
-                                MyList<var> *VarList1 /* source (t+dt) */, MyList<var> *VarList2 /* source (t) */,
-                                MyList<var> *VarList3 /* target (t+a*dt) */, int tindex);
-  void prepare_inter_time_level(MyList<Patch> *Pat,
-                                MyList<var> *VarList1 /* source (t+dt) */, MyList<var> *VarList2 /* source (t) */,
-                                MyList<var> *VarList3 /* source (t-dt) */, MyList<var> *VarList4 /* target (t+a*dt) */, int tindex);
-  void merge_gsl(MyList<gridseg> *&A, const double ratio);
-  bool merge_gs(MyList<gridseg> *D, MyList<gridseg> *B, MyList<gridseg> *&C, const double ratio);
-  // Add ghost region to tangent plane
-  // we assume the grids have the same resolution
-  void add_ghost_touch(MyList<gridseg> *&A);
-  void cut_gsl(MyList<gridseg> *&A);
-  bool cut_gs(MyList<gridseg> *D, MyList<gridseg> *B, MyList<gridseg> *&C);
-  MyList<Parallel::gridseg> *gs_subtract_virtual(MyList<Parallel::gridseg> *A, MyList<Parallel::gridseg> *B);
-  void fill_level_data(MyList<Patch> *PatLd, MyList<Patch> *PatLs, MyList<Patch> *PatcL,
-                       MyList<var> *OldList, MyList<var> *StateList, MyList<var> *FutureList,
-                       MyList<var> *tmList, int Symmetry, bool BB, bool CC);
-  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
-                             int NN, double **XX,
-                             double *Shellf, int Symmetry);
-  void aligncheck(double *bbox0, double *bboxl, int lev, double *DH0, int *shape);
-  bool point_locat_gsl(double *pox, MyList<Parallel::gridseg> *gsl);
-  void checkpatchlist(MyList<Patch> *PatL, bool buflog);
-
-  double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
-  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
-                             int NN, double **XX,
-                             double *Shellf, int Symmetry, MPI_Comm Comm_here);
-#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/TwoPunctures.h

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

AMSS_NCKU_source/bssn_class.C

@@ -730,12 +730,6 @@ void bssn_class::Initialize()
     PhysTime = StartTime;
     Setup_Black_Hole_position();
   }
-
-  // Initialize sync caches (per-level, for predictor and corrector)
-  sync_cache_pre = new Parallel::SyncCache[GH->levels];
-  sync_cache_cor = new Parallel::SyncCache[GH->levels];
-  sync_cache_rp_coarse = new Parallel::SyncCache[GH->levels];
-  sync_cache_rp_fine = new Parallel::SyncCache[GH->levels];
 }
 
 //================================================================================================
@@ -987,32 +981,6 @@ bssn_class::~bssn_class()
   delete Azzz;
 #endif
 
-  // Destroy sync caches before GH
-  if (sync_cache_pre)
-  {
-    for (int i = 0; i < GH->levels; i++)
-      sync_cache_pre[i].destroy();
-    delete[] sync_cache_pre;
-  }
-  if (sync_cache_cor)
-  {
-    for (int i = 0; i < GH->levels; i++)
-      sync_cache_cor[i].destroy();
-    delete[] sync_cache_cor;
-  }
-  if (sync_cache_rp_coarse)
-  {
-    for (int i = 0; i < GH->levels; i++)
-      sync_cache_rp_coarse[i].destroy();
-    delete[] sync_cache_rp_coarse;
-  }
-  if (sync_cache_rp_fine)
-  {
-    for (int i = 0; i < GH->levels; i++)
-      sync_cache_rp_fine[i].destroy();
-    delete[] sync_cache_rp_fine;
-  }
-
   delete GH;
 #ifdef WithShell
   delete SH;
@@ -2213,7 +2181,6 @@ void bssn_class::Evolve(int Steps)
     GH->Regrid(Symmetry, BH_num, Porgbr, Porg0,
                SynchList_cor, OldStateList, StateList, SynchList_pre,
                fgt(PhysTime - dT_mon, StartTime, dT_mon / 2), ErrorMonitor);
-    for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 #endif
 
 #if (REGLEV == 0 && (PSTR == 1 || PSTR == 2))
@@ -2429,7 +2396,6 @@ void bssn_class::RecursiveStep(int lev)
   GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                       SynchList_cor, OldStateList, StateList, SynchList_pre,
                       fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
-  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 #endif
 }
 
@@ -2608,7 +2574,6 @@ void bssn_class::ParallelStep()
   GH->Regrid_Onelevel(GH->mylev, Symmetry, BH_num, Porgbr, Porg0,
                       SynchList_cor, OldStateList, StateList, SynchList_pre,
                       fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
-  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 #endif
 }
 
@@ -2775,7 +2740,6 @@ void bssn_class::ParallelStep()
         GH->Regrid_Onelevel(lev + 1, Symmetry, BH_num, Porgbr, Porg0,
                             SynchList_cor, OldStateList, StateList, SynchList_pre,
                             fgt(PhysTime - dT_levp1, StartTime, dT_levp1 / 2), ErrorMonitor);
-        for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 
         //               a_stream.clear();
         //               a_stream.str("");
@@ -2790,7 +2754,6 @@ void bssn_class::ParallelStep()
       GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                           SynchList_cor, OldStateList, StateList, SynchList_pre,
                           fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
-      for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 
       //               a_stream.clear();
       //               a_stream.str("");
@@ -2809,7 +2772,6 @@ void bssn_class::ParallelStep()
           GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                               SynchList_cor, OldStateList, StateList, SynchList_pre,
                               fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor);
-          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -2825,7 +2787,6 @@ void bssn_class::ParallelStep()
           GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                               SynchList_cor, OldStateList, StateList, SynchList_pre,
                               fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor);
-          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -3197,7 +3158,21 @@ void bssn_class::Step(int lev, int YN)
     }
     Pp = Pp->next;
   }
-  // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
+  // check error information
+  {
+    int erh = ERROR;
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+  }
+  if (ERROR)
+  {
+    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime << ", lev = " << lev << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
+  }
 
 #ifdef WithShell
   // evolve Shell Patches
@@ -3215,9 +3190,9 @@ void bssn_class::Step(int lev, int YN)
         {
 #if (AGM == 0)
           f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn],
+                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
                        cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                       cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn],
+                       cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                        cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
@@ -3341,16 +3316,25 @@ void bssn_class::Step(int lev, int YN)
 #endif
   }
 
-  // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+  // check error information
-  MPI_Request err_req;
   {
     int erh = ERROR;
-    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req);
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+  }
+
+  if (ERROR)
+  {
+    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
   }
 #endif
 
-  Parallel::AsyncSyncState async_pre;
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-  Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
 
 #ifdef WithShell
   if (lev == 0)
@@ -3363,29 +3347,12 @@ void bssn_class::Step(int lev, int YN)
     {
       prev_clock = curr_clock;
       curr_clock = clock();
-      cout << " Shell stuff synchronization used "
+      cout << " Shell stuff synchronization used " 
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
            << " seconds! " << endl;
     }
   }
 #endif
-  Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry);
-
-#ifdef WithShell
-  // Complete non-blocking error reduction and check
-  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-#endif
 
 #if (MAPBH == 0)
   // for black hole position
@@ -3561,7 +3528,24 @@ void bssn_class::Step(int lev, int YN)
       Pp = Pp->next;
     }
 
-    // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
+    // check error information
+    {
+      int erh = ERROR;
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+    }
+
+    if (ERROR)
+    {
+      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
+                                << " variables at t = " << PhysTime 
+                                << ", lev = " << lev << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
+    }
 
 #ifdef WithShell
     // evolve Shell Patches
@@ -3579,9 +3563,9 @@ void bssn_class::Step(int lev, int YN)
           {
 #if (AGM == 0)
             f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn],
+                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
                          cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn],
+                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #elif (AGM == 1)
             if (iter_count == 3)
@@ -3701,16 +3685,26 @@ void bssn_class::Step(int lev, int YN)
         sPp = sPp->next;
       }
     }
-    // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+    // check error information
-    MPI_Request err_req_cor;
     {
       int erh = ERROR;
-      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req_cor);
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+    }
+    if (ERROR)
+    {
+      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" 
+                                << iter_count << " variables at t = " 
+                                << PhysTime << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
     }
 #endif
 
-    Parallel::AsyncSyncState async_cor;
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-    Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
 
 #ifdef WithShell
     if (lev == 0)
@@ -3723,31 +3717,12 @@ void bssn_class::Step(int lev, int YN)
       {
         prev_clock = curr_clock;
         curr_clock = clock();
-        cout << " Shell stuff synchronization used "
+        cout << " Shell stuff synchronization used " 
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
              << " seconds! " << endl;
       }
     }
 #endif
-    Parallel::Sync_finish(sync_cache_cor[lev], async_cor, SynchList_cor, Symmetry);
-
-#ifdef WithShell
-    // Complete non-blocking error reduction and check
-    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count
-                                << " variables at t = " << PhysTime
-                                << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-#endif
 
 #if (MAPBH == 0)
     // for black hole position
@@ -4059,7 +4034,22 @@ void bssn_class::Step(int lev, int YN)
     }
     Pp = Pp->next;
   }
-  // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
+  // check error information
+  {
+    int erh = ERROR;
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+  }
+  if (ERROR)
+  {
+    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime 
+                              << ", lev = " << lev << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
+  }
 
 #ifdef WithShell
   // evolve Shell Patches
@@ -4077,15 +4067,15 @@ void bssn_class::Step(int lev, int YN)
         {
 #if (AGM == 0)
           f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn],
+                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
                        cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
-                       cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn],
+                       cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                        cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
           if (f_compute_rhs_bssn_ss(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                    cg->fgfs[fngfs + ShellPatch::gx],
+                                    cg->fgfs[fngfs + ShellPatch::gx], 
-                                    cg->fgfs[fngfs + ShellPatch::gy],
+                                    cg->fgfs[fngfs + ShellPatch::gy], 
                                     cg->fgfs[fngfs + ShellPatch::gz],
                                     cg->fgfs[fngfs + ShellPatch::drhodx], 
                                     cg->fgfs[fngfs + ShellPatch::drhody], 
@@ -4200,16 +4190,25 @@ void bssn_class::Step(int lev, int YN)
   }
 #endif
   }
-  // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+  // check error information
-  MPI_Request err_req;
   {
     int erh = ERROR;
-    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req);
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+  }
+  if (ERROR)
+  {
+    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " 
+                              << PhysTime << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
   }
 #endif
 
-  Parallel::AsyncSyncState async_pre;
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-  Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
 
 #ifdef WithShell
   if (lev == 0)
@@ -4222,27 +4221,9 @@ void bssn_class::Step(int lev, int YN)
     {
       prev_clock = curr_clock;
       curr_clock = clock();
-      cout << " Shell stuff synchronization used "
+      cout << " Shell stuff synchronization used " 
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+      << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds! " << endl;
+      << " seconds! " << endl;
-    }
-  }
-#endif
-  Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry);
-
-#ifdef WithShell
-  // Complete non-blocking error reduction and check
-  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime
-                              << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
     }
   }
 #endif
@@ -4405,7 +4386,23 @@ void bssn_class::Step(int lev, int YN)
       Pp = Pp->next;
     }
 
-    // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
+    // check error information
+    {
+      int erh = ERROR;
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+    }
+    if (ERROR)
+    {
+      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
+                                << " variables at t = " << PhysTime 
+                                << ", lev = " << lev << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
+    }
 
 #ifdef WithShell
     // evolve Shell Patches
@@ -4423,9 +4420,9 @@ void bssn_class::Step(int lev, int YN)
           {
 #if (AGM == 0)
             f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn],
+                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
                          cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn],
+                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #elif (AGM == 1)
             if (iter_count == 3)
@@ -4545,16 +4542,25 @@ void bssn_class::Step(int lev, int YN)
         sPp = sPp->next;
       }
     }
-    // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+    // check error information
-    MPI_Request err_req_cor;
     {
       int erh = ERROR;
-      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req_cor);
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+    }
+    if (ERROR)
+    {
+      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count 
+                                << " variables at t = " << PhysTime << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
     }
 #endif
 
-    Parallel::AsyncSyncState async_cor;
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-    Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
 
 #ifdef WithShell
     if (lev == 0)
@@ -4567,30 +4573,11 @@ void bssn_class::Step(int lev, int YN)
       {
         prev_clock = curr_clock;
         curr_clock = clock();
-        cout << " Shell stuff synchronization used "
+        cout << " Shell stuff synchronization used " 
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
              << " seconds! " << endl;
       }
     }
-#endif
-    Parallel::Sync_finish(sync_cache_cor[lev], async_cor, SynchList_cor, Symmetry);
-
-#ifdef WithShell
-    // Complete non-blocking error reduction and check
-    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count
-                                << " variables at t = " << PhysTime
-                                << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
 #endif
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
@@ -4956,19 +4943,11 @@ void bssn_class::Step(int lev, int YN)
 
   //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Predictor rhs calculation");
 
-  // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+  // check error information
-  MPI_Request err_req;
   {
     int erh = ERROR;
-    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev], &err_req);
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
   }
-
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor sync");
-
-  Parallel::Sync_cached(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev]);
-
-  // Complete non-blocking error reduction and check
-  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
   if (ERROR)
   {
     Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
@@ -4980,6 +4959,10 @@ void bssn_class::Step(int lev, int YN)
     }
   }
 
+  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor sync");
+
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+
 #if (MAPBH == 0)
   // for black hole position
   if (BH_num > 0 && lev == GH->levels - 1)
@@ -5157,34 +5140,30 @@ void bssn_class::Step(int lev, int YN)
 
     //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector error check");
 
-    // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+    // check error information
-    MPI_Request err_req_cor;
     {
       int erh = ERROR;
-      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev], &err_req_cor);
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
     }
-
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector sync");
-
-    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev]);
-
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector sync");
-
-    // Complete non-blocking error reduction and check
-    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
     if (ERROR)
     {
       Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
       if (myrank == 0)
       {
         if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count
+          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime
+                                << " variables at t = " << PhysTime 
                                 << ", lev = " << lev << endl;
         MPI_Abort(MPI_COMM_WORLD, 1);
       }
     }
 
+    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector sync");
+
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+
+    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector sync");
+
 #if (MAPBH == 0)
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
@@ -5468,11 +5447,21 @@ void bssn_class::SHStep()
 #if (PSTR == 1 || PSTR == 2)
 //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor's error check");
 #endif
-  // Non-blocking error reduction overlapped with Synch to hide Allreduce latency
+  // check error information
-  MPI_Request err_req;
   {
     int erh = ERROR;
-    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req);
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+  }
+
+  if (ERROR)
+  {
+    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
   }
 
   {
@@ -5484,25 +5473,12 @@ void bssn_class::SHStep()
     {
       prev_clock = curr_clock;
       curr_clock = clock();
-      cout << " Shell stuff synchronization used "
+      cout << " Shell stuff synchronization used " 
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
            << " seconds! " << endl;
     }
   }
 
-  // Complete non-blocking error reduction and check
-  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
-  if (ERROR)
-  {
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
   // corrector
   for (iter_count = 1; iter_count < 4; iter_count++)
   {
@@ -5645,11 +5621,21 @@ void bssn_class::SHStep()
         sPp = sPp->next;
       }
     }
-    // Non-blocking error reduction overlapped with Synch to hide Allreduce latency
+    // check error information
-    MPI_Request err_req_cor;
     {
       int erh = ERROR;
-      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req_cor);
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+    }
+    if (ERROR)
+    {
+      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count 
+                                << " variables at t = " << PhysTime << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
     }
 
     {
@@ -5661,26 +5647,12 @@ void bssn_class::SHStep()
       {
         prev_clock = curr_clock;
         curr_clock = clock();
-        cout << " Shell stuff synchronization used "
+        cout << " Shell stuff synchronization used " 
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
              << " seconds! " << endl;
       }
     }
 
-    // Complete non-blocking error reduction and check
-    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
-    if (ERROR)
-    {
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count
-                                << " variables at t = " << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
     sPp = SH->PatL;
     while (sPp)
     {
@@ -5809,7 +5781,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
 
 #if (PSTR == 1 || PSTR == 2)
 //       a_stream.clear();
@@ -5819,11 +5791,21 @@ 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);
@@ -5860,7 +5842,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], SL, Symmetry);
 
 #if (PSTR == 1 || PSTR == 2)
 //       a_stream.clear();
@@ -5870,11 +5852,21 @@ 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);
@@ -5888,7 +5880,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
     }
 
-    Parallel::Sync_cached(GH->PatL[lev], SL, Symmetry, sync_cache_rp_fine[lev]);
+    Parallel::Sync(GH->PatL[lev], SL, Symmetry);
 
 #if (PSTR == 1 || PSTR == 2)
 //    a_stream.clear();
@@ -5946,14 +5938,24 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(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);
@@ -5968,21 +5970,31 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], SL, Symmetry);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(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);
 #endif
     }
 
-    Parallel::Sync_cached(GH->PatL[lev], SL, Symmetry, sync_cache_rp_fine[lev]);
+    Parallel::Sync(GH->PatL[lev], SL, Symmetry);
   }
 }
 
@@ -6033,14 +6045,24 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(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);
@@ -6057,21 +6079,31 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], StateList, Symmetry);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(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);
 #endif
     }
 
-    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
   }
 }
 
@@ -6101,11 +6133,21 @@ 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 +6156,21 @@ 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);
@@ -6134,10 +6186,10 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
 #else
       Parallel::Restrict_after(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
 #endif
-      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], StateList, Symmetry);
     }
 
-    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
   }
 }
 #undef MIXOUTB

AMSS_NCKU_source/bssn_class.h

@@ -126,11 +126,6 @@ public:
        MyList<var> *OldStateList, *DumpList;
        MyList<var> *ConstraintList;
 
-       Parallel::SyncCache *sync_cache_pre;  // per-level cache for predictor sync
-       Parallel::SyncCache *sync_cache_cor;  // per-level cache for corrector sync
-       Parallel::SyncCache *sync_cache_rp_coarse;  // RestrictProlong sync on PatL[lev-1]
-       Parallel::SyncCache *sync_cache_rp_fine;    // RestrictProlong sync on PatL[lev]
-
        monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
        monitor *ConVMonitor;
        surface_integral *Waveshell;

AMSS_NCKU_source/bssn_rhs.f90

@@ -106,8 +106,7 @@
   call getpbh(BHN,Porg,Mass)
 #endif
 
-!!! sanity check (disabled in production builds for performance)
+!!! sanity check
-#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)                                           &
@@ -137,7 +136,6 @@
      gont = 1
      return
   endif
-#endif
 
   PI = dacos(-ONE)
 
@@ -945,60 +943,103 @@
   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.h

@@ -1,107 +1,92 @@
-
+
-#ifndef CGH_H
+#ifndef CGH_H
-#define CGH_H
+#define CGH_H
-
+
-#include <mpi.h>
+#include <mpi.h>
-#include "MyList.h"
+#include "MyList.h"
-#include "MPatch.h"
+#include "MPatch.h"
-#include "macrodef.h"
+#include "macrodef.h"
-#include "monitor.h"
+#include "monitor.h"
-#include "Parallel.h"
+#include "Parallel.h"
-
+
-class cgh
+class cgh
-{
+{
-
+
-public:
+public:
-   int levels, movls, BH_num_in;
+   int levels, movls, BH_num_in;
-   // information of boxes
+   // information of boxes
-   int *grids;
+   int *grids;
-   double ***bbox;
+   double ***bbox;
-   int ***shape;
+   int ***shape;
-   double ***handle;
+   double ***handle;
-   double ***Porgls;
+   double ***Porgls;
-   double *Lt;
+   double *Lt;
-
+
-   // information of Patch list
+   // information of Patch list
-   MyList<Patch> **PatL;
+   MyList<Patch> **PatL;
-
+
-// information of OutBdLow2Hi point list and Restrict point list
+// information of OutBdLow2Hi point list and Restrict point list
-#if (RPB == 1)
+#if (RPB == 1)
-   MyList<Parallel::pointstru_bam> **bdsul, **rsul;
+   MyList<Parallel::pointstru_bam> **bdsul, **rsul;
-#endif
+#endif
-
+
-#if (PSTR == 1 || PSTR == 2 || PSTR == 3)
+#if (PSTR == 1 || PSTR == 2 || PSTR == 3)
-   int mylev;
+   int mylev;
-   int *start_rank, *end_rank;
+   int *start_rank, *end_rank;
-   MPI_Comm *Commlev;
+   MPI_Comm *Commlev;
-#endif
+#endif
-
+
-protected:
+protected:
-   int ingfs, fngfs;
+   int ingfs, fngfs;
-   static constexpr double ratio = 0.75;
+   static constexpr double ratio = 0.75;
-   int trfls;
+   int trfls;
-
+
-public:
+public:
-   cgh(int ingfsi, int fngfsi, int Symmetry, char *filename, int checkrun, monitor *ErrorMonitor);
+   cgh(int ingfsi, int fngfsi, int Symmetry, char *filename, int checkrun, monitor *ErrorMonitor);
-
+
-   ~cgh();
+   ~cgh();
-
+
-   void compose_cgh(int nprocs);
+   void compose_cgh(int nprocs);
-   void sethandle(monitor *ErrorMonitor);
+   void sethandle(monitor *ErrorMonitor);
-   void checkPatchList(MyList<Patch> *PatL, bool buflog);
+   void checkPatchList(MyList<Patch> *PatL, bool buflog);
-   void Regrid(int Symmetry, int BH_num, double **Porgbr, double **Porg0,
+   void Regrid(int Symmetry, int BH_num, double **Porgbr, double **Porg0,
-               MyList<var> *OldList, MyList<var> *StateList,
+               MyList<var> *OldList, MyList<var> *StateList,
-               MyList<var> *FutureList, MyList<var> *tmList, bool BB,
+               MyList<var> *FutureList, MyList<var> *tmList, bool BB,
-               monitor *ErrorMonitor);
+               monitor *ErrorMonitor);
-   void Regrid_fake(int Symmetry, int BH_num, double **Porgbr, double **Porg0,
+   void Regrid_fake(int Symmetry, int BH_num, double **Porgbr, double **Porg0,
-                    MyList<var> *OldList, MyList<var> *StateList,
+                    MyList<var> *OldList, MyList<var> *StateList,
-                    MyList<var> *FutureList, MyList<var> *tmList, bool BB,
+                    MyList<var> *FutureList, MyList<var> *tmList, bool BB,
-                    monitor *ErrorMonitor);
+                    monitor *ErrorMonitor);
-   void recompose_cgh(int nprocs, bool *lev_flag,
+   void recompose_cgh(int nprocs, bool *lev_flag,
-                      MyList<var> *OldList, MyList<var> *StateList,
+                      MyList<var> *OldList, MyList<var> *StateList,
-                      MyList<var> *FutureList, MyList<var> *tmList,
+                      MyList<var> *FutureList, MyList<var> *tmList,
-                      int Symmetry, bool BB);
+                      int Symmetry, bool BB);
-   void recompose_cgh_fake(int nprocs, bool *lev_flag,
+   void recompose_cgh_fake(int nprocs, bool *lev_flag,
-                           MyList<var> *OldList, MyList<var> *StateList,
+                           MyList<var> *OldList, MyList<var> *StateList,
-                           MyList<var> *FutureList, MyList<var> *tmList,
+                           MyList<var> *FutureList, MyList<var> *tmList,
-                           int Symmetry, bool BB);
+                           int Symmetry, bool BB);
-   void read_bbox(int Symmetry, char *filename);
+   void read_bbox(int Symmetry, char *filename);
-   MyList<Patch> *construct_patchlist(int lev, int Symmetry);
+   MyList<Patch> *construct_patchlist(int lev, int Symmetry);
-   bool Interp_One_Point(MyList<var> *VarList,
+   bool Interp_One_Point(MyList<var> *VarList,
-                         double *XX, /*input global Cartesian coordinate*/
+                         double *XX, /*input global Cartesian coordinate*/
-                         double *Shellf, int Symmetry);
+                         double *Shellf, int Symmetry);
-   void recompose_cgh_Onelevel(int nprocs, int lev,
+   void recompose_cgh_Onelevel(int nprocs, int lev,
-                               MyList<var> *OldList, MyList<var> *StateList,
+                               MyList<var> *OldList, MyList<var> *StateList,
-                               MyList<var> *FutureList, MyList<var> *tmList,
+                               MyList<var> *FutureList, MyList<var> *tmList,
-                               int Symmetry, bool BB);
+                               int Symmetry, bool BB);
-   void Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
+   void Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
-                        MyList<var> *OldList, MyList<var> *StateList,
+                        MyList<var> *OldList, MyList<var> *StateList,
-                        MyList<var> *FutureList, MyList<var> *tmList, bool BB,
+                        MyList<var> *FutureList, MyList<var> *tmList, bool BB,
-                        monitor *ErrorMonitor);
+                        monitor *ErrorMonitor);
-   void Regrid_Onelevel_aux(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
+   void Regrid_Onelevel_aux(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
-                            MyList<var> *OldList, MyList<var> *StateList,
+                            MyList<var> *OldList, MyList<var> *StateList,
-                            MyList<var> *FutureList, MyList<var> *tmList, bool BB,
+                            MyList<var> *FutureList, MyList<var> *tmList, bool BB,
-                            monitor *ErrorMonitor);
+                            monitor *ErrorMonitor);
-   void settrfls(const int lev);
+   void settrfls(const int lev);
-
+
-#if (PSTR == 1 || PSTR == 2 || PSTR == 3)
+#if (PSTR == 1 || PSTR == 2 || PSTR == 3)
-   void construct_mylev(int nprocs);
+   void construct_mylev(int nprocs);
-#endif
+#endif
-
+};
-   // Load balancing support
+
-   bool enable_load_balance;         // Enable load balancing
+#endif /* CGH_H */
-   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

@@ -69,12 +69,11 @@
   fy = ZEO
   fz = ZEO
 
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+  !$omp parallel do collapse(3) schedule(static)
-!DIR$ UNROLL PARTIAL(4)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
-! x direction
+! x direction   
         if(i+1 <= imax .and. i-1 >= imin)then
 !
 !              - f(i-1) + f(i+1)
@@ -153,6 +152,7 @@
 
   fx = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -220,6 +220,7 @@
 
   fy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -284,6 +285,7 @@
 
   fz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -373,8 +375,7 @@
   fxz = ZEO
   fyz = ZEO
 
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+  !$omp parallel do collapse(3) schedule(static)
-!DIR$ UNROLL PARTIAL(4)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -473,6 +474,7 @@
 
   fxx = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -535,6 +537,7 @@
 
   fyy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -598,6 +601,7 @@
 
   fzz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -661,6 +665,7 @@
 
   fxy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -723,6 +728,7 @@
 
   fxz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -784,6 +790,7 @@
 
   fyz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -870,6 +877,7 @@
   fxz = ZEO
   fyz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1001,6 +1009,7 @@
   fy = ZEO
   fz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1155,6 +1164,7 @@
 
   fx = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1231,6 +1241,7 @@
 
   fy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1301,6 +1312,7 @@
 
   fz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1405,6 +1417,7 @@
   fxz = ZEO
   fyz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1580,6 +1593,7 @@
 
   fxx = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1647,6 +1661,7 @@
 
   fyy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1716,6 +1731,7 @@
 
   fzz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1785,6 +1801,7 @@
 
   fxy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1855,6 +1872,7 @@
 
   fxz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1923,6 +1941,7 @@
 
   fyz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2015,6 +2034,7 @@
   fy = ZEO
   fz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2131,6 +2151,7 @@
 
   fx = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2216,6 +2237,7 @@
 
   fy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2292,6 +2314,7 @@
 
   fz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2410,6 +2433,7 @@
   fxz = ZEO
   fyz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2597,6 +2621,7 @@
 
   fxx = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2669,6 +2694,7 @@
 
   fyy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2744,6 +2770,7 @@
 
   fzz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2819,6 +2846,7 @@
 
   fxy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2899,6 +2927,7 @@
 
   fxz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2977,6 +3006,7 @@
 
   fyz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3084,6 +3114,7 @@
   fy = ZEO
   fz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3220,6 +3251,7 @@
 
   fx = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3315,6 +3347,7 @@
 
   fy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3399,6 +3432,7 @@
 
   fz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3534,6 +3568,7 @@
   fxz = ZEO
   fyz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3806,6 +3841,7 @@
 
   fxx = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3887,6 +3923,7 @@
 
   fyy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3971,6 +4008,7 @@
   
   fzz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -4055,6 +4093,7 @@
 
   fxy = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -4157,6 +4196,7 @@
 
   fxz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -4257,6 +4297,7 @@
 
   fyz = ZEO
 
+  !$omp parallel do collapse(3) schedule(static)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1

AMSS_NCKU_source/enforce_algebra.f90

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

AMSS_NCKU_source/fmisc.f90

@@ -324,6 +324,7 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -349,6 +350,7 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -377,6 +379,7 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -883,17 +886,14 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
    enddo
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(:,-i,1:extc(3)) = funcc(:,i+1,1:extc(3))*SoA(2)
    enddo
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
    enddo
@@ -912,6 +912,7 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -940,6 +941,7 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -1116,66 +1118,64 @@ end subroutine d2dump
 ! Lagrangian polynomial interpolation
 !------------------------------------------------------------------------------
 
-!DIR$ ATTRIBUTES FORCEINLINE :: polint
+  subroutine polint(xa,ya,x,y,dy,ordn)
-  subroutine polint(xa, ya, x, y, dy, ordn)
+
   implicit none
 
-  integer, intent(in) :: ordn
+!~~~~~~> Input Parameter:
-  real*8, dimension(ordn), intent(in) :: xa, ya
+  integer,intent(in) :: ordn
+  real*8, dimension(ordn), intent(in) :: xa,ya
   real*8, intent(in) :: x
-  real*8, intent(out) :: y, dy
+  real*8, intent(out) :: y,dy
 
-  integer :: i, m, ns, n_m
+!~~~~~~> Other parameter:
-  real*8, dimension(ordn) :: c, d, ho
-  real*8 :: dif, dift, hp, h, den_val
 
-  c = ya
+  integer :: m,n,ns
-  d = ya
+  real*8, dimension(ordn) :: c,d,den,ho
-  ho = xa - x
+  real*8 :: dif,dift
 
-  ns = 1
+!~~~~~~>
-  dif = abs(x - xa(1))
 
-  do i = 2, ordn
+  n=ordn
-    dift = abs(x - xa(i))
+  m=ordn
-    if (dift < dif) then
+
-      ns = i
+  c=ya
-      dif = dift
+  d=ya
-    end if
+  ho=xa-x
+
+  ns=1
+  dif=abs(x-xa(1))
+  do m=1,n
+   dift=abs(x-xa(m))
+   if(dift < dif) then
+    ns=m
+    dif=dift
+   end if
   end do
 
-  y = ya(ns)
+  y=ya(ns)
-  ns = ns - 1
+  ns=ns-1
-
+  do m=1,n-1
-  do m = 1, ordn - 1
+    den(1:n-m)=ho(1:n-m)-ho(1+m:n)
-    n_m = ordn - m
+    if (any(den(1:n-m) == 0.0))then
-    do i = 1, n_m
+      write(*,*) 'failure in polint for point',x
-      hp = ho(i)
+      write(*,*) 'with input points: ',xa
-      h  = ho(i+m)
+      stop
-      den_val = hp - h
+    endif
-
+    den(1:n-m)=(c(2:n-m+1)-d(1:n-m))/den(1:n-m)
-      if (den_val == 0.0d0) then
+    d(1:n-m)=ho(1+m:n)*den(1:n-m)
-        write(*,*) 'failure in polint for point',x
+    c(1:n-m)=ho(1:n-m)*den(1:n-m)
-        write(*,*) 'with input points: ',xa
+    if (2*ns < n-m) then
-        stop
+      dy=c(ns+1)
-      end if
-
-      den_val = (c(i+1) - d(i)) / den_val
-
-      d(i) = h * den_val
-      c(i) = hp * den_val
-    end do
-
-    if (2 * ns < n_m) then
-      dy = c(ns + 1)
     else
-      dy = d(ns)
+      dy=d(ns)
-      ns = ns - 1
+      ns=ns-1
     end if
-    y = y + dy
+    y=y+dy
   end do
 
   return
+
   end subroutine polint
 !------------------------------------------------------------------------------
 !
@@ -1183,37 +1183,35 @@ end subroutine d2dump
 !
 !------------------------------------------------------------------------------
   subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
+
   implicit none
 
+!~~~~~~> Input parameters:
   integer,intent(in) :: ordn
   real*8, dimension(1:ordn), intent(in) :: x1a,x2a
   real*8, dimension(1:ordn,1:ordn), intent(in) :: ya
   real*8, intent(in) :: x1,x2
   real*8, intent(out) :: y,dy
 
-#ifdef POLINT_LEGACY_ORDER
+!~~~~~~> Other parameters:
+
   integer  :: i,m
   real*8, dimension(ordn) :: ymtmp
   real*8, dimension(ordn) :: yntmp
 
   m=size(x1a)
+  
   do i=1,m
+
     yntmp=ya(i,:)
     call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-  end do
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
-  integer  :: j
-  real*8, dimension(ordn) :: ymtmp
-  real*8 :: dy_temp
 
-  do j=1,ordn
-    call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
   end do
-  call polint(x2a, ymtmp, x2, y, dy, ordn)
+
-#endif
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
 
   return
+
   end subroutine polin2
 !------------------------------------------------------------------------------
 !
@@ -1221,15 +1219,18 @@ end subroutine d2dump
 !
 !------------------------------------------------------------------------------
   subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
+
   implicit none
 
+!~~~~~~> Input parameters:
   integer,intent(in) :: ordn
   real*8, dimension(1:ordn), intent(in) :: x1a,x2a,x3a
   real*8, dimension(1:ordn,1:ordn,1:ordn), intent(in) :: ya
   real*8, intent(in) :: x1,x2,x3
   real*8, intent(out) :: y,dy
 
-#ifdef POLINT_LEGACY_ORDER
+!~~~~~~> Other parameters:
+
   integer  :: i,j,m,n
   real*8, dimension(ordn,ordn) :: yatmp
   real*8, dimension(ordn) :: ymtmp
@@ -1238,33 +1239,24 @@ end subroutine d2dump
 
   m=size(x1a)
   n=size(x2a)
+  
   do i=1,m
    do j=1,n
+
     yqtmp=ya(i,j,:)
     call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
+
    end do
+
     yntmp=yatmp(i,:)
     call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-  end do
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
-  integer  :: j, k
-  real*8, dimension(ordn,ordn) :: yatmp
-  real*8, dimension(ordn) :: ymtmp
-  real*8 :: dy_temp
 
-  do k=1,ordn
-    do j=1,ordn
-      call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
-    end do
   end do
-  do k=1,ordn
+
-    call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
-  end do
-  call polint(x3a, ymtmp, x3, y, dy, ordn)
-#endif
 
   return
+
   end subroutine polin3
 !--------------------------------------------------------------------------------------
 ! calculate L2norm

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

@@ -16,12 +16,6 @@ include makefile.inc
 .cu.o:
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
 
-TwoPunctures.o: TwoPunctures.C
-	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
-
-TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
-
 # Input files
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            cgh.o bssn_class.o surface_integral.o ShellPatch.o\
@@ -102,7 +96,7 @@ ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
 	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
 
 TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -10,21 +10,21 @@ filein  = -I/usr/include/ -I${MKLROOT}/include
 ## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
 LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl
 
-## Aggressive optimization flags + PGO Phase 2 (profile-guided optimization)
+## Aggressive optimization flags:
-## -fprofile-instr-use: use collected profile data to guide optimization decisions
+## -O3: Maximum optimization
-##   (branch prediction, basic block layout, inlining, loop unrolling)
+## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
-PROFDATA     = ../../pgo_profile/default.profdata
+## -fp-model fast=2: Aggressive floating-point optimizations
-CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
+## -fma: Enable fused multiply-add instructions
-               -fprofile-instr-use=$(PROFDATA) \
+## Note: OpenMP enabled for hybrid MPI+OpenMP
+CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -qopenmp \
                -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
+f90appflags  = -O3 -xHost -fp-model fast=2 -fma -qopenmp \
-               -fprofile-instr-use=$(PROFDATA) \
+               -fpp -I${MKLROOT}/include
-               -align array64byte -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx
 CC           = icx
-CLINKER      = mpiicpx 
+CLINKER      = mpiicpx -qopenmp 
 
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include

makefile_and_run.py

@@ -10,13 +10,10 @@
 
 import AMSS_NCKU_Input as input_data
 import subprocess
-import time
+
-## CPU core binding configuration using taskset
+## CPU core binding configuration
-## taskset ensures all child processes inherit the CPU affinity mask
+## Removed hardcoded taskset to allow full utilization of 96 cores via MPI+OpenMP
-## This forces make and all compiler processes to use only nohz_full cores (4-55, 60-111)
+NUMACTL_CPU_BIND = ""
-## 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"
 
 ## Build parallelism configuration
 ## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
@@ -38,7 +35,7 @@ def makefile_ABE():
     print( " Compiling the AMSS-NCKU executable file ABE/ABEGPU " ) 
     print(                                                        )
 
-    ## Build command with CPU binding to nohz_full cores
+    ## Build command
     if (input_data.GPU_Calculation == "no"):
         makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
     elif (input_data.GPU_Calculation == "yes"):
@@ -79,7 +76,7 @@ def makefile_TwoPunctureABE():
     print( " Compiling the AMSS-NCKU executable file TwoPunctureABE " )
     print(                                                            )
     
-    ## Build command with CPU binding to nohz_full cores
+    ## Build command
     makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} TwoPunctureABE"
 
     ## Execute the command with subprocess.Popen and stream output
@@ -114,14 +111,23 @@ def run_ABE():
     print( " Running the AMSS-NCKU executable file ABE/ABEGPU " ) 
     print(                                                      )
 
+    ## Calculate OMP_NUM_THREADS
+    ## User has 96 cores. Calculate threads per MPI process.
+    total_physical_cores = 96
+    omp_num_threads = total_physical_cores // input_data.MPI_processes
+    if omp_num_threads < 1:
+        omp_num_threads = 1
+    
+    print( f" Configuration: {input_data.MPI_processes} MPI processes, {omp_num_threads} OpenMP threads per process." )
+    print( f" Total cores utilized: {input_data.MPI_processes * omp_num_threads}" )
+
     ## 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         = f"{NUMACTL_CPU_BIND} mpirun -genv OMP_NUM_THREADS {omp_num_threads} -np {input_data.MPI_processes} ./ABE"
-        #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command         = f"{NUMACTL_CPU_BIND} mpirun -genv OMP_NUM_THREADS {omp_num_threads} -np {input_data.MPI_processes} ./ABEGPU"
         mpi_command_outfile = "ABEGPU_out.log"
  
     ## Execute the MPI command and stream output
@@ -154,14 +160,13 @@ def run_ABE():
 ## Run the AMSS-NCKU TwoPuncture program TwoPunctureABE
 
 def run_TwoPunctureABE():
-    tp_time1=time.time()
+
     print(                                                          )
     print( " Running the AMSS-NCKU executable file TwoPunctureABE " ) 
     print(                                                          )
     
     ## Define the command to run
-    #TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
+    TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
-    TwoPuncture_command         = " ./TwoPunctureABE"
     TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
 
     ## Execute the command with subprocess.Popen and stream output
@@ -182,9 +187,7 @@ def run_TwoPunctureABE():
     print(                                               )
     print( " The TwoPunctureABE simulation is finished " ) 
     print(                                               )
-    tp_time2=time.time()
+    
-    et=tp_time2-tp_time1
-    print(f"Used time: {et}")
     return
 
 ##################################################################

parallel_plot_helper.py

@@ -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)

pgo_profile/PGO_Profile_Analysis.md

@@ -1,97 +0,0 @@
-# AMSS-NCKU PGO Profile Analysis Report
-
-## 1. Profiling Environment
-
-| Item | Value |
-|------|-------|
-| Compiler | Intel oneAPI DPC++/C++ 2025.3.0 (icpx/ifx) |
-| Instrumentation Flag | `-fprofile-instr-generate` |
-| Optimization Level (instrumented) | `-O2 -xHost -fma` |
-| MPI Processes | 1 (single process to avoid MPI+instrumentation deadlock) |
-| Profile File | `default_9725750769337483397_0.profraw` (327 KB) |
-| Merged Profile | `default.profdata` (394 KB) |
-| llvm-profdata | `/home/intel/oneapi/compiler/2025.3/bin/compiler/llvm-profdata` |
-
-## 2. Reduced Simulation Parameters (for profiling run)
-
-| Parameter | Production Value | Profiling Value |
-|-----------|-----------------|-----------------|
-| MPI_processes | 64 | 1 |
-| grid_level | 9 | 4 |
-| static_grid_level | 5 | 3 |
-| static_grid_number | 96 | 24 |
-| moving_grid_number | 48 | 16 |
-| largest_box_xyz_max | 320^3 | 160^3 |
-| Final_Evolution_Time | 1000.0 | 10.0 |
-| Evolution_Step_Number | 10,000,000 | 1,000 |
-| Detector_Number | 12 | 2 |
-
-## 3. Profile Summary
-
-| Metric | Value |
-|--------|-------|
-| Total instrumented functions | 1,392 |
-| Functions with non-zero counts | 117 (8.4%) |
-| Functions with zero counts | 1,275 (91.6%) |
-| Maximum function entry count | 386,459,248 |
-| Maximum internal block count | 370,477,680 |
-| Total block count | 4,198,023,118 |
-
-## 4. Top 20 Hotspot Functions
-
-| Rank | Total Count | Max Block Count | Function | Category |
-|------|------------|-----------------|----------|----------|
-| 1 | 1,241,601,732 | 370,477,680 | `polint_` | Interpolation |
-| 2 | 755,994,435 | 230,156,640 | `prolong3_` | Grid prolongation |
-| 3 | 667,964,095 | 3,697,792 | `compute_rhs_bssn_` | BSSN RHS evolution |
-| 4 | 539,736,051 | 386,459,248 | `symmetry_bd_` | Symmetry boundary |
-| 5 | 277,310,808 | 53,170,728 | `lopsided_` | Lopsided FD stencil |
-| 6 | 155,534,488 | 94,535,040 | `decide3d_` | 3D grid decision |
-| 7 | 119,267,712 | 19,266,048 | `rungekutta4_rout_` | RK4 time integrator |
-| 8 | 91,574,616 | 48,824,160 | `kodis_` | Kreiss-Oliger dissipation |
-| 9 | 67,555,389 | 43,243,680 | `fderivs_` | Finite differences |
-| 10 | 55,296,000 | 42,246,144 | `misc::fact(int)` | Factorial utility |
-| 11 | 43,191,071 | 27,663,328 | `fdderivs_` | 2nd-order FD derivatives |
-| 12 | 36,233,965 | 22,429,440 | `restrict3_` | Grid restriction |
-| 13 | 24,698,512 | 17,231,520 | `polin3_` | Polynomial interpolation |
-| 14 | 22,962,942 | 20,968,768 | `copy_` | Data copy |
-| 15 | 20,135,696 | 17,259,168 | `Ansorg::barycentric(...)` | Spectral interpolation |
-| 16 | 14,650,224 | 7,224,768 | `Ansorg::barycentric_omega(...)` | Spectral weights |
-| 17 | 13,242,296 | 2,871,920 | `global_interp_` | Global interpolation |
-| 18 | 12,672,000 | 7,734,528 | `sommerfeld_rout_` | Sommerfeld boundary |
-| 19 | 6,872,832 | 1,880,064 | `sommerfeld_routbam_` | Sommerfeld boundary (BAM) |
-| 20 | 5,709,900 | 2,809,632 | `l2normhelper_` | L2 norm computation |
-
-## 5. Hotspot Category Breakdown
-
-Top 20 functions account for ~98% of total execution counts:
-
-| Category | Functions | Combined Count | Share |
-|----------|-----------|---------------|-------|
-| Interpolation / Prolongation / Restriction | polint_, prolong3_, restrict3_, polin3_, global_interp_, Ansorg::* | ~2,093M | ~50% |
-| BSSN RHS + FD stencils | compute_rhs_bssn_, lopsided_, fderivs_, fdderivs_ | ~1,056M | ~25% |
-| Boundary conditions | symmetry_bd_, sommerfeld_rout_, sommerfeld_routbam_ | ~559M | ~13% |
-| Time integration | rungekutta4_rout_ | ~119M | ~3% |
-| Dissipation | kodis_ | ~92M | ~2% |
-| Utilities | misc::fact, decide3d_, copy_, l2normhelper_ | ~256M | ~6% |
-
-## 6. Conclusions
-
-1. **Profile data is valid**: 1,392 functions instrumented, 117 exercised with ~4.2 billion total counts.
-2. **Hotspot concentration is high**: Top 5 functions alone account for ~76% of all counts, which is ideal for PGO — the compiler has strong branch/layout optimization targets.
-3. **Fortran numerical kernels dominate**: `polint_`, `prolong3_`, `compute_rhs_bssn_`, `symmetry_bd_`, `lopsided_` are all Fortran routines in the inner evolution loop. PGO will optimize their branch prediction and basic block layout.
-4. **91.6% of functions have zero counts**: These are code paths for unused features (GPU, BSSN-EScalar, BSSN-EM, Z4C, etc.). PGO will deprioritize them, improving instruction cache utilization.
-5. **Profile is representative**: Despite the reduced grid size, the code path coverage matches production — the same kernels (RHS, prolongation, restriction, boundary) are exercised. PGO branch probabilities from this profile will transfer well to full-scale runs.
-
-## 7. PGO Phase 2 Usage
-
-To apply the profile, use the following flags in `makefile.inc`:
-
-```makefile
-CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -fprofile-instr-use=/home/amss/AMSS-NCKU/pgo_profile/default.profdata \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -fprofile-instr-use=/home/amss/AMSS-NCKU/pgo_profile/default.profdata \
-              -align array64byte -fpp -I${MKLROOT}/include
-```

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 " )