1. Pass 1（357-395行）：遍历所有 Patch，对每个 block 计算含ghost zone 的实际体积，存入 block_volumes

2. Greedy LPT（397-414行）：按体积从大到小排序，依次分配给当前负载最小的 rank
  3. Pass 2（416-555行）：原来的 block创建循环，但用 assigned_ranks[block_idx++] 替代 n_rank++，Block
  构造时直接拿到正确的 rank，内存分配在对的进程上

AMSS_NCKU_ABEtest.py

@@ -0,0 +1,447 @@
+
+##################################################################
+##
+## AMSS-NCKU ABE Test Program (Skip TwoPuncture if data exists)
+## Modified from AMSS_NCKU_Program.py
+## Author: Xiaoqu
+## Modified: 2026/02/01
+##
+##################################################################
+
+
+##################################################################
+
+## Print program introduction
+
+import print_information
+
+print_information.print_program_introduction()
+
+##################################################################
+
+import AMSS_NCKU_Input as input_data
+
+##################################################################
+
+## Create directories to store program run data
+
+import os
+import shutil
+import sys
+import time
+
+## Set the output directory according to the input file
+File_directory = os.path.join(input_data.File_directory)
+
+## Check if output directory exists and if TwoPuncture data is available
+#skip_twopuncture = False
+skip_twopuncture = True
+output_directory = os.path.join(File_directory, "AMSS_NCKU_output")
+binary_results_directory = os.path.join(output_directory, input_data.Output_directory)
+
+if os.path.exists(File_directory):
+    print( " Output directory already exists." )
+    print()
+    '''
+    # Check if TwoPuncture initial data files exist
+    if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture"):
+        twopuncture_output = os.path.join(output_directory, "TwoPunctureABE")
+        input_par = os.path.join(output_directory, "input.par")
+
+        if os.path.exists(twopuncture_output) and os.path.exists(input_par):
+            print( " Found existing TwoPuncture initial data." )
+            print( " Do you want to skip TwoPuncture phase and reuse existing data?" )
+            print( " Input 'skip' to skip TwoPuncture and start ABE directly" )
+            print( " Input 'regenerate' to regenerate everything from scratch" )
+            print()
+            
+            while True:
+                try:
+                    inputvalue = input()
+                    if ( inputvalue == "skip" ):
+                        print( " Skipping TwoPuncture phase, will reuse existing initial data." )
+                        print()
+                        skip_twopuncture = True
+                        break
+                    elif ( inputvalue == "regenerate" ):
+                        print( " Regenerating everything from scratch." )
+                        print()
+                        skip_twopuncture = False
+                        break
+                    else:
+                        print( " Please input 'skip' or 'regenerate'." )
+                except ValueError:
+                    print( " Please input 'skip' or 'regenerate'." )
+            
+        else:
+            print( " TwoPuncture initial data not found, will regenerate everything." )
+            print()
+'''
+    # If not skipping, remove and recreate directory
+    if not skip_twopuncture:
+        shutil.rmtree(File_directory, ignore_errors=True)
+        os.mkdir(File_directory)
+        os.mkdir(output_directory)
+        os.mkdir(binary_results_directory)
+        figure_directory = os.path.join(File_directory, "figure")
+        os.mkdir(figure_directory)
+        shutil.copy("AMSS_NCKU_Input.py", File_directory)
+        print( " Output directory has been regenerated." )
+        print()
+else:
+    # Create fresh directory structure
+    os.mkdir(File_directory)
+    shutil.copy("AMSS_NCKU_Input.py", File_directory)
+    os.mkdir(output_directory)
+    os.mkdir(binary_results_directory)
+    figure_directory = os.path.join(File_directory, "figure")
+    os.mkdir(figure_directory)
+    print( " Output directory has been generated." )
+    print()
+
+# Ensure figure directory exists
+figure_directory = os.path.join(File_directory, "figure")
+if not os.path.exists(figure_directory):
+    os.mkdir(figure_directory)
+
+##################################################################
+
+## Output related parameter information
+
+import setup
+
+## Print and save input parameter information
+setup.print_input_data( File_directory )
+
+if not skip_twopuncture:
+    setup.generate_AMSSNCKU_input()
+
+setup.print_puncture_information()
+
+
+##################################################################
+
+## Generate AMSS-NCKU program input files based on the configured parameters
+
+if not skip_twopuncture:
+    print()
+    print( " Generating the AMSS-NCKU input parfile for the ABE executable." )
+    print()
+
+    ## Generate cgh-related input files from the grid information
+
+    import numerical_grid
+
+    numerical_grid.append_AMSSNCKU_cgh_input()
+
+    print()
+    print( " The input parfile for AMSS-NCKU C++ executable file ABE has been generated." )
+    print( " However, the input relevant to TwoPuncture need to be appended later." )
+    print()
+
+
+##################################################################
+
+## Plot the initial grid configuration
+
+if not skip_twopuncture:
+    print()
+    print( " Schematically plot the numerical grid structure." )
+    print()
+
+    import numerical_grid
+    numerical_grid.plot_initial_grid()
+
+
+##################################################################
+
+## Generate AMSS-NCKU macro files according to the numerical scheme and parameters
+
+if not skip_twopuncture:
+    print()
+    print( " Automatically generating the macro file for AMSS-NCKU C++ executable file ABE " )
+    print( " (Based on the finite-difference numerical scheme) " )
+    print()
+
+    import generate_macrodef
+
+    generate_macrodef.generate_macrodef_h()
+    print( " AMSS-NCKU macro file macrodef.h has been generated. " )
+
+    generate_macrodef.generate_macrodef_fh()
+    print( " AMSS-NCKU macro file macrodef.fh has been generated. " )
+
+
+##################################################################
+
+# Compile the AMSS-NCKU program according to user requirements
+# NOTE: ABE compilation is always performed, even when skipping TwoPuncture
+
+print()
+print( " Preparing to compile and run the AMSS-NCKU code as requested " )
+print( " Compiling the AMSS-NCKU code based on the generated macro files " )
+print()
+
+AMSS_NCKU_source_path = "AMSS_NCKU_source"
+AMSS_NCKU_source_copy = os.path.join(File_directory, "AMSS_NCKU_source_copy")
+
+## If AMSS_NCKU source folder is missing, create it and prompt the user
+if not os.path.exists(AMSS_NCKU_source_path):
+    os.makedirs(AMSS_NCKU_source_path)
+    print( " The AMSS-NCKU source files are incomplete; copy all source files into ./AMSS_NCKU_source. " )
+    print( " Press Enter to continue. " )
+    inputvalue = input()
+
+# Copy AMSS-NCKU source files to prepare for compilation
+# If skipping TwoPuncture and source_copy already exists, remove it first
+if skip_twopuncture and os.path.exists(AMSS_NCKU_source_copy):
+    shutil.rmtree(AMSS_NCKU_source_copy)
+
+shutil.copytree(AMSS_NCKU_source_path, AMSS_NCKU_source_copy)
+
+# Copy the generated macro files into the AMSS_NCKU source folder
+if not skip_twopuncture:
+    macrodef_h_path  = os.path.join(File_directory, "macrodef.h")
+    macrodef_fh_path = os.path.join(File_directory, "macrodef.fh")
+else:
+    # When skipping TwoPuncture, use existing macro files from previous run
+    macrodef_h_path  = os.path.join(File_directory, "macrodef.h")
+    macrodef_fh_path = os.path.join(File_directory, "macrodef.fh")
+
+shutil.copy2(macrodef_h_path,  AMSS_NCKU_source_copy)
+shutil.copy2(macrodef_fh_path, AMSS_NCKU_source_copy)
+
+# Compile related programs
+import makefile_and_run
+
+## Change working directory to the target source copy
+os.chdir(AMSS_NCKU_source_copy)
+
+## Build the main AMSS-NCKU executable (ABE or ABEGPU)
+makefile_and_run.makefile_ABE()
+
+## If the initial-data method is Ansorg-TwoPuncture, build the TwoPunctureABE executable
+## Only build TwoPunctureABE if not skipping TwoPuncture phase
+if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
+    makefile_and_run.makefile_TwoPunctureABE()
+
+## Change current working directory back up two levels
+os.chdir('..')
+os.chdir('..')
+
+print()
+
+##################################################################
+
+## Copy the AMSS-NCKU executable (ABE/ABEGPU) to the run directory
+
+if (input_data.GPU_Calculation == "no"):
+    ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABE")
+elif (input_data.GPU_Calculation == "yes"):
+    ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABEGPU")
+
+if not os.path.exists( ABE_file ):
+    print()
+    print( " Lack of AMSS-NCKU executable file ABE/ABEGPU; recompile AMSS_NCKU_source manually. " )
+    print( " When recompilation is finished, press Enter to continue. " )
+    inputvalue = input()
+
+## Copy the executable ABE (or ABEGPU) into the run directory
+shutil.copy2(ABE_file, output_directory)
+
+## If the initial-data method is TwoPuncture, copy the TwoPunctureABE executable to the run directory
+## Only copy TwoPunctureABE if not skipping TwoPuncture phase
+if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
+    TwoPuncture_file = os.path.join(AMSS_NCKU_source_copy, "TwoPunctureABE")
+
+    if not os.path.exists( TwoPuncture_file ):
+        print()
+        print( " Lack of AMSS-NCKU executable file TwoPunctureABE; recompile TwoPunctureABE in AMSS_NCKU_source. " )
+        print( " When recompilation is finished, press Enter to continue. " )
+        inputvalue = input()
+
+    ## Copy the TwoPunctureABE executable into the run directory
+    shutil.copy2(TwoPuncture_file, output_directory)
+
+##################################################################
+
+## If the initial-data method is TwoPuncture, generate the TwoPuncture input files
+
+if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
+
+    print()
+    print( " Initial data is chosen as Ansorg-TwoPuncture" )
+    print()
+    
+    print()
+    print( " Automatically generating the input parfile for the TwoPunctureABE executable " )
+    print()
+    
+    import generate_TwoPuncture_input
+    
+    generate_TwoPuncture_input.generate_AMSSNCKU_TwoPuncture_input()
+    
+    print()
+    print( " The input parfile for the TwoPunctureABE executable has been generated. " )
+    print()
+    
+    ## Generated AMSS-NCKU TwoPuncture input filename
+    AMSS_NCKU_TwoPuncture_inputfile      = 'AMSS-NCKU-TwoPuncture.input'
+    AMSS_NCKU_TwoPuncture_inputfile_path = os.path.join( File_directory, AMSS_NCKU_TwoPuncture_inputfile )
+ 
+    ## Copy and rename the file
+    shutil.copy2( AMSS_NCKU_TwoPuncture_inputfile_path, os.path.join(output_directory, 'TwoPunctureinput.par') )
+    
+    ## Run TwoPuncture to generate initial-data files
+    
+    start_time = time.time()  # Record start time
+
+    print()
+    print()
+    
+    ## Change to the output (run) directory
+    os.chdir(output_directory)
+
+    ## Run the TwoPuncture executable
+    import makefile_and_run
+    makefile_and_run.run_TwoPunctureABE()
+    
+    ## Change current working directory back up two levels
+    os.chdir('..')
+    os.chdir('..')
+
+elif (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and skip_twopuncture:
+    print()
+    print( " Skipping TwoPuncture execution, using existing initial data." )
+    print()
+    start_time = time.time()  # Record start time for ABE only
+else:
+    start_time = time.time()  # Record start time
+    
+##################################################################
+    
+## Update puncture data based on TwoPuncture run results
+
+if not skip_twopuncture:
+    import renew_puncture_parameter
+    renew_puncture_parameter.append_AMSSNCKU_BSSN_input(File_directory, output_directory)
+
+    ## Generated AMSS-NCKU input filename
+    AMSS_NCKU_inputfile      = 'AMSS-NCKU.input'
+    AMSS_NCKU_inputfile_path = os.path.join(File_directory, AMSS_NCKU_inputfile)
+ 
+    ## Copy and rename the file
+    shutil.copy2( AMSS_NCKU_inputfile_path, os.path.join(output_directory, 'input.par') )
+
+    print()
+    print( " Successfully copy all AMSS-NCKU input parfile to target dictionary. " )
+    print()
+else:
+    print()
+    print( " Using existing input.par file from previous run." )
+    print()
+
+##################################################################
+
+## Launch the AMSS-NCKU program
+
+print()
+print()
+
+## Change to the run directory
+os.chdir( output_directory )
+
+import makefile_and_run
+makefile_and_run.run_ABE()
+
+## Change current working directory back up two levels
+os.chdir('..')
+os.chdir('..')
+
+end_time = time.time()
+elapsed_time = end_time - start_time
+
+##################################################################
+
+## Copy some basic input and log files out to facilitate debugging
+
+## Path to the file that stores calculation settings
+AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "setting.par")
+## Copy and rename the file for easier inspection
+shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "AMSSNCKU_setting_parameter") )
+
+## Path to the error log file
+AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "Error.log")
+## Copy and rename the error log
+shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "Error.log") )
+
+## Primary program outputs
+AMSS_NCKU_BH_data         = os.path.join(binary_results_directory, "bssn_BH.dat"        )
+AMSS_NCKU_ADM_data        = os.path.join(binary_results_directory, "bssn_ADMQs.dat"     )
+AMSS_NCKU_psi4_data       = os.path.join(binary_results_directory, "bssn_psi4.dat"      )
+AMSS_NCKU_constraint_data = os.path.join(binary_results_directory, "bssn_constraint.dat")
+## copy and rename the file
+shutil.copy( AMSS_NCKU_BH_data,         os.path.join(output_directory, "bssn_BH.dat"        ) )
+shutil.copy( AMSS_NCKU_ADM_data,        os.path.join(output_directory, "bssn_ADMQs.dat"     ) )
+shutil.copy( AMSS_NCKU_psi4_data,       os.path.join(output_directory, "bssn_psi4.dat"      ) )
+shutil.copy( AMSS_NCKU_constraint_data, os.path.join(output_directory, "bssn_constraint.dat") )
+
+## Additional program outputs
+if (input_data.Equation_Class == "BSSN-EM"):
+    AMSS_NCKU_phi1_data = os.path.join(binary_results_directory, "bssn_phi1.dat" )
+    AMSS_NCKU_phi2_data = os.path.join(binary_results_directory, "bssn_phi2.dat" )
+    shutil.copy( AMSS_NCKU_phi1_data, os.path.join(output_directory, "bssn_phi1.dat" ) )
+    shutil.copy( AMSS_NCKU_phi2_data, os.path.join(output_directory, "bssn_phi2.dat" ) )
+elif (input_data.Equation_Class == "BSSN-EScalar"):
+    AMSS_NCKU_maxs_data = os.path.join(binary_results_directory, "bssn_maxs.dat" )
+    shutil.copy( AMSS_NCKU_maxs_data, os.path.join(output_directory, "bssn_maxs.dat" ) )
+
+##################################################################
+
+## Plot the AMSS-NCKU program results
+
+print()
+print( " Plotting the txt and binary results data from the AMSS-NCKU simulation " )
+print()
+
+
+import plot_xiaoqu
+import plot_GW_strain_amplitude_xiaoqu
+
+## Plot black hole trajectory
+plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
+plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
+
+## Plot black hole separation vs. time
+plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
+
+## Plot gravitational waveforms (psi4 and strain amplitude)
+for i in range(input_data.Detector_Number):
+    plot_xiaoqu.generate_gravitational_wave_psi4_plot( binary_results_directory, figure_directory, i )
+    plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot( binary_results_directory, figure_directory, i )
+
+## Plot ADM mass evolution
+for i in range(input_data.Detector_Number):
+    plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
+
+## Plot Hamiltonian constraint violation over time
+for i in range(input_data.grid_level):
+    plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
+
+## Plot stored binary data
+plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )
+
+print()
+print( f" This Program Cost = {elapsed_time} Seconds " )
+print()
+
+
+##################################################################
+
+print()
+print( " The AMSS-NCKU-Python simulation is successfully finished, thanks for using !!! " )
+print()
+
+##################################################################
+
+

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    = 1                              ## number of processes (MPI removed, single-process mode)
+MPI_processes    = 64                             ## 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_source/ABE.C

@@ -20,11 +20,7 @@ using namespace std;
 #include <map.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "misc.h"
 #include "macrodef.h"

AMSS_NCKU_source/Ansorg.h

@@ -19,11 +19,7 @@ using namespace std;
 #include <math.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #define PI M_PI
 

AMSS_NCKU_source/Block.h

@@ -2,11 +2,7 @@
 #ifndef BLOCK_H
 #define BLOCK_H
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 #include "macrodef.h" //need dim here; Vertex or Cell
 #include "var.h"
 #include "MyList.h"

AMSS_NCKU_source/IntPnts0.C

@@ -4,11 +4,7 @@
 #include <stdarg.h>
 #include <string.h>
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "myglobal.h"
 

AMSS_NCKU_source/MPatch.C

@@ -341,9 +341,8 @@ void Patch::Interp_Points(MyList<var> *VarList,
                           double *Shellf, int Symmetry)
 {
   // NOTE: we do not Synchnize variables here, make sure of that before calling this routine
-  int myrank, nprocs;
+  int myrank;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
 
   int ordn = 2 * ghost_width;
   MyList<var> *varl;
@@ -355,18 +354,24 @@ void Patch::Interp_Points(MyList<var> *VarList,
     varl = varl->next;
   }
 
-  memset(Shellf, 0, sizeof(double) * NN * num_var);
+  double *shellf;
+  shellf = new double[NN * num_var];
+  memset(shellf, 0, sizeof(double) * NN * num_var);
 
-  // owner_rank[j] records which MPI rank owns point j
-  // All ranks traverse the same block list so they all agree on ownership
-  int *owner_rank;
-  owner_rank = new int[NN];
-  for (int j = 0; j < NN; j++)
-    owner_rank[j] = -1;
+  // we use weight to monitor code, later some day we can move it for optimization
+  int *weight;
+  weight = new int[NN];
+  memset(weight, 0, sizeof(int) * NN);
+
+  double *DH, *llb, *uub;
+  DH = new double[dim];
 
-  double DH[dim], llb[dim], uub[dim];
   for (int i = 0; i < dim; i++)
+  {
     DH[i] = getdX(i);
+  }
+  llb = new double[dim];
+  uub = new double[dim];
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -398,6 +403,12 @@ void Patch::Interp_Points(MyList<var> *VarList,
       bool flag = true;
       for (int i = 0; i < dim; i++)
       {
+// NOTE: our dividing structure is (exclude ghost)
+// -1 0
+//       1  2
+// so (0,1) does not belong to any part for vertex structure
+// here we put (0,0.5) to left part and (0.5,1) to right part
+// BUT for cell structure the bbox is (-1.5,0.5) and (0.5,2.5), there is no missing region at all
 #ifdef Vertex
 #ifdef Cell
 #error Both Cell and Vertex are defined
@@ -422,7 +433,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
       if (flag)
       {
         notfind = false;
-        owner_rank[j] = BP->rank;
         if (myrank == BP->rank)
         {
           //---> interpolation
@@ -430,11 +440,14 @@ void Patch::Interp_Points(MyList<var> *VarList,
           int k = 0;
           while (varl) // run along variables
           {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+            //              shellf[j*num_var+k] = Parallel::global_interp(dim,BP->shape,BP->X,BP->fgfs[varl->data->sgfn],
+            //	  		                                    pox,ordn,varl->data->SoA,Symmetry);
+            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[j * num_var + k],
                             pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
             varl = varl->next;
             k++;
           }
+          weight[j] = 1;
         }
       }
       if (Bp == ble)
@@ -443,327 +456,103 @@ void Patch::Interp_Points(MyList<var> *VarList,
     }
   }
 
-  // Replace MPI_Allreduce with per-owner MPI_Bcast:
-  // Group consecutive points by owner rank and broadcast each group.
-  // Since each point's data is non-zero only on the owner rank,
-  // Bcast from owner is equivalent to Allreduce(MPI_SUM) but much cheaper.
+  MPI_Allreduce(shellf, Shellf, NN * num_var, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  int *Weight;
+  Weight = new int[NN];
+  MPI_Allreduce(weight, Weight, NN, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+
+  //  misc::tillherecheck("print me");
+
+  for (int i = 0; i < NN; i++)
   {
-    int j = 0;
-    while (j < NN)
+    if (Weight[i] > 1)
     {
-      int cur_owner = owner_rank[j];
-      if (cur_owner < 0)
-      {
-        if (myrank == 0)
-        {
-          cout << "ERROR: Patch::Interp_Points fails to find point (";
-          for (int d = 0; d < dim; d++)
-          {
-            cout << XX[d][j];
-            if (d < dim - 1)
-              cout << ",";
-            else
-              cout << ")";
-          }
-          cout << " on Patch (";
-          for (int d = 0; d < dim; d++)
-          {
-            cout << bbox[d] << "+" << lli[d] * DH[d];
-            if (d < dim - 1)
-              cout << ",";
-            else
-              cout << ")--";
-          }
-          cout << "(";
-          for (int d = 0; d < dim; d++)
-          {
-            cout << bbox[dim + d] << "-" << uui[d] * DH[d];
-            if (d < dim - 1)
-              cout << ",";
-            else
-              cout << ")" << endl;
-          }
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        j++;
-        continue;
-      }
-      // Find contiguous run of points with the same owner
-      int jstart = j;
-      while (j < NN && owner_rank[j] == cur_owner)
-        j++;
-      int count = (j - jstart) * num_var;
-      MPI_Bcast(Shellf + jstart * num_var, count, MPI_DOUBLE, cur_owner, MPI_COMM_WORLD);
+      if (myrank == 0)
+        cout << "WARNING: Patch::Interp_Points meets multiple weight" << endl;
+      for (int j = 0; j < num_var; j++)
+        Shellf[j + i * num_var] = Shellf[j + i * num_var] / Weight[i];
     }
-  }
-
-  delete[] owner_rank;
-}
-void Patch::Interp_Points(MyList<var> *VarList,
-                          int NN, double **XX,
-                          double *Shellf, int Symmetry,
-                          int Nmin_consumer, int Nmax_consumer)
-{
-  // Targeted point-to-point overload: each owner sends each point only to
-  // the one rank that needs it for integration (consumer), reducing
-  // communication volume by ~nprocs times compared to the Bcast version.
-  int myrank, nprocs;
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
-
-  int ordn = 2 * ghost_width;
-  MyList<var> *varl;
-  int num_var = 0;
-  varl = VarList;
-  while (varl)
-  {
-    num_var++;
-    varl = varl->next;
-  }
-
-  memset(Shellf, 0, sizeof(double) * NN * num_var);
-
-  // owner_rank[j] records which MPI rank owns point j
-  int *owner_rank;
-  owner_rank = new int[NN];
-  for (int j = 0; j < NN; j++)
-    owner_rank[j] = -1;
-
-  double DH[dim], llb[dim], uub[dim];
-  for (int i = 0; i < dim; i++)
-    DH[i] = getdX(i);
-
-  // --- Interpolation phase (identical to original) ---
-  for (int j = 0; j < NN; j++)
-  {
-    double pox[dim];
-    for (int i = 0; i < dim; i++)
-    {
-      pox[i] = XX[i][j];
-      if (myrank == 0 && (XX[i][j] < bbox[i] + lli[i] * DH[i] || XX[i][j] > bbox[dim + i] - uui[i] * DH[i]))
-      {
-        cout << "Patch::Interp_Points: point (";
-        for (int k = 0; k < dim; k++)
-        {
-          cout << XX[k][j];
-          if (k < dim - 1)
-            cout << ",";
-          else
-            cout << ") is out of current Patch." << endl;
-        }
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
-    MyList<Block> *Bp = blb;
-    bool notfind = true;
-    while (notfind && Bp)
-    {
-      Block *BP = Bp->data;
-
-      bool flag = true;
-      for (int i = 0; i < dim; i++)
-      {
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
-        {
-          flag = false;
-          break;
-        }
-      }
-
-      if (flag)
-      {
-        notfind = false;
-        owner_rank[j] = BP->rank;
-        if (myrank == BP->rank)
-        {
-          varl = VarList;
-          int k = 0;
-          while (varl)
-          {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-        }
-      }
-      if (Bp == ble)
-        break;
-      Bp = Bp->next;
-    }
-  }
-
-  // --- Error check for unfound points ---
-  for (int j = 0; j < NN; j++)
-  {
-    if (owner_rank[j] < 0 && myrank == 0)
+    else if (Weight[i] == 0 && myrank == 0)
     {
       cout << "ERROR: Patch::Interp_Points fails to find point (";
-      for (int d = 0; d < dim; d++)
+      for (int j = 0; j < dim; j++)
       {
-        cout << XX[d][j];
-        if (d < dim - 1)
+        cout << XX[j][i];
+        if (j < dim - 1)
           cout << ",";
         else
           cout << ")";
       }
       cout << " on Patch (";
-      for (int d = 0; d < dim; d++)
+      for (int j = 0; j < dim; j++)
       {
-        cout << bbox[d] << "+" << lli[d] * DH[d];
-        if (d < dim - 1)
+        cout << bbox[j] << "+" << lli[j] * getdX(j);
+        if (j < dim - 1)
           cout << ",";
         else
           cout << ")--";
       }
       cout << "(";
-      for (int d = 0; d < dim; d++)
+      for (int j = 0; j < dim; j++)
       {
-        cout << bbox[dim + d] << "-" << uui[d] * DH[d];
-        if (d < dim - 1)
+        cout << bbox[dim + j] << "-" << uui[j] * getdX(j);
+        if (j < dim - 1)
           cout << ",";
         else
           cout << ")" << endl;
       }
+#if 0
+       checkBlock();
+#else
+      cout << "splited domains:" << endl;
+      {
+        MyList<Block> *Bp = blb;
+        while (Bp)
+        {
+          Block *BP = Bp->data;
+
+          for (int i = 0; i < dim; i++)
+          {
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif
+            llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
+            uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
+#else
+#ifdef Cell
+            llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
+            uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif
+          }
+          cout << "(";
+          for (int j = 0; j < dim; j++)
+          {
+            cout << llb[j] << ":" << uub[j];
+            if (j < dim - 1)
+              cout << ",";
+            else
+              cout << ")" << endl;
+          }
+          if (Bp == ble)
+            break;
+          Bp = Bp->next;
+        }
+      }
+#endif
       MPI_Abort(MPI_COMM_WORLD, 1);
     }
   }
 
-  // --- Targeted point-to-point communication phase ---
-  // Compute consumer_rank[j] using the same deterministic formula as surface_integral
-  int *consumer_rank = new int[NN];
-  {
-    int mp = NN / nprocs;
-    int Lp = NN - nprocs * mp;
-    for (int j = 0; j < NN; j++)
-    {
-      if (j < Lp * (mp + 1))
-        consumer_rank[j] = j / (mp + 1);
-      else
-        consumer_rank[j] = Lp + (j - Lp * (mp + 1)) / mp;
-    }
-  }
-
-  // Count sends and recvs per rank
-  int *send_count = new int[nprocs];
-  int *recv_count = new int[nprocs];
-  memset(send_count, 0, sizeof(int) * nprocs);
-  memset(recv_count, 0, sizeof(int) * nprocs);
-
-  for (int j = 0; j < NN; j++)
-  {
-    int own = owner_rank[j];
-    int con = consumer_rank[j];
-    if (own == con)
-      continue; // local — no communication needed
-    if (own == myrank)
-      send_count[con]++;
-    if (con == myrank)
-      recv_count[own]++;
-  }
-
-  // Build send buffers: for each destination rank, pack (index, data) pairs
-  // Each entry: 1 int (point index j) + num_var doubles
-  int total_send = 0, total_recv = 0;
-  int *send_offset = new int[nprocs];
-  int *recv_offset = new int[nprocs];
-  for (int r = 0; r < nprocs; r++)
-  {
-    send_offset[r] = total_send;
-    total_send += send_count[r];
-    recv_offset[r] = total_recv;
-    total_recv += recv_count[r];
-  }
-
-  // Pack send buffers: each message contains (j, data[0..num_var-1]) per point
-  int stride = 1 + num_var; // 1 double for index + num_var doubles for data
-  double *sendbuf = new double[total_send * stride];
-  double *recvbuf = new double[total_recv * stride];
-
-  // Temporary counters for packing
-  int *pack_pos = new int[nprocs];
-  memset(pack_pos, 0, sizeof(int) * nprocs);
-
-  for (int j = 0; j < NN; j++)
-  {
-    int own = owner_rank[j];
-    int con = consumer_rank[j];
-    if (own != myrank || con == myrank)
-      continue;
-    int pos = (send_offset[con] + pack_pos[con]) * stride;
-    sendbuf[pos] = (double)j; // point index
-    for (int v = 0; v < num_var; v++)
-      sendbuf[pos + 1 + v] = Shellf[j * num_var + v];
-    pack_pos[con]++;
-  }
-
-  // Post non-blocking recvs and sends
-  int n_req = 0;
-  for (int r = 0; r < nprocs; r++)
-  {
-    if (recv_count[r] > 0) n_req++;
-    if (send_count[r] > 0) n_req++;
-  }
-
-  MPI_Request *reqs = new MPI_Request[n_req];
-  int req_idx = 0;
-
-  for (int r = 0; r < nprocs; r++)
-  {
-    if (recv_count[r] > 0)
-    {
-      MPI_Irecv(recvbuf + recv_offset[r] * stride,
-                recv_count[r] * stride, MPI_DOUBLE,
-                r, 0, MPI_COMM_WORLD, &reqs[req_idx++]);
-    }
-  }
-  for (int r = 0; r < nprocs; r++)
-  {
-    if (send_count[r] > 0)
-    {
-      MPI_Isend(sendbuf + send_offset[r] * stride,
-                send_count[r] * stride, MPI_DOUBLE,
-                r, 0, MPI_COMM_WORLD, &reqs[req_idx++]);
-    }
-  }
-
-  if (n_req > 0)
-    MPI_Waitall(n_req, reqs, MPI_STATUSES_IGNORE);
-
-  // Unpack recv buffers into Shellf
-  for (int i = 0; i < total_recv; i++)
-  {
-    int pos = i * stride;
-    int j = (int)recvbuf[pos];
-    for (int v = 0; v < num_var; v++)
-      Shellf[j * num_var + v] = recvbuf[pos + 1 + v];
-  }
-
-  delete[] reqs;
-  delete[] sendbuf;
-  delete[] recvbuf;
-  delete[] pack_pos;
-  delete[] send_offset;
-  delete[] recv_offset;
-  delete[] send_count;
-  delete[] recv_count;
-  delete[] consumer_rank;
-  delete[] owner_rank;
+  delete[] shellf;
+  delete[] weight;
+  delete[] Weight;
+  delete[] DH;
+  delete[] llb;
+  delete[] uub;
 }
 void Patch::Interp_Points(MyList<var> *VarList,
                           int NN, double **XX,
@@ -784,22 +573,24 @@ void Patch::Interp_Points(MyList<var> *VarList,
     varl = varl->next;
   }
 
-  memset(Shellf, 0, sizeof(double) * NN * num_var);
+  double *shellf;
+  shellf = new double[NN * num_var];
+  memset(shellf, 0, sizeof(double) * NN * num_var);
 
-  // owner_rank[j] stores the global rank that owns point j
-  int *owner_rank;
-  owner_rank = new int[NN];
-  for (int j = 0; j < NN; j++)
-    owner_rank[j] = -1;
+  // we use weight to monitor code, later some day we can move it for optimization
+  int *weight;
+  weight = new int[NN];
+  memset(weight, 0, sizeof(int) * NN);
 
-  // Build global-to-local rank translation for Comm_here
-  MPI_Group world_group, local_group;
-  MPI_Comm_group(MPI_COMM_WORLD, &world_group);
-  MPI_Comm_group(Comm_here, &local_group);
+  double *DH, *llb, *uub;
+  DH = new double[dim];
 
-  double DH[dim], llb[dim], uub[dim];
   for (int i = 0; i < dim; i++)
+  {
     DH[i] = getdX(i);
+  }
+  llb = new double[dim];
+  uub = new double[dim];
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -831,6 +622,12 @@ void Patch::Interp_Points(MyList<var> *VarList,
       bool flag = true;
       for (int i = 0; i < dim; i++)
       {
+// NOTE: our dividing structure is (exclude ghost)
+// -1 0
+//       1  2
+// so (0,1) does not belong to any part for vertex structure
+// here we put (0,0.5) to left part and (0.5,1) to right part
+// BUT for cell structure the bbox is (-1.5,0.5) and (0.5,2.5), there is no missing region at all
 #ifdef Vertex
 #ifdef Cell
 #error Both Cell and Vertex are defined
@@ -855,7 +652,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
       if (flag)
       {
         notfind = false;
-        owner_rank[j] = BP->rank;
         if (myrank == BP->rank)
         {
           //---> interpolation
@@ -863,11 +659,14 @@ void Patch::Interp_Points(MyList<var> *VarList,
           int k = 0;
           while (varl) // run along variables
           {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+            //              shellf[j*num_var+k] = Parallel::global_interp(dim,BP->shape,BP->X,BP->fgfs[varl->data->sgfn],
+            //	  		                                    pox,ordn,varl->data->SoA,Symmetry);
+            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[j * num_var + k],
                             pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
             varl = varl->next;
             k++;
           }
+          weight[j] = 1;
         }
       }
       if (Bp == ble)
@@ -876,35 +675,97 @@ void Patch::Interp_Points(MyList<var> *VarList,
     }
   }
 
-  // Collect unique global owner ranks and translate to local ranks in Comm_here
-  // Then broadcast each owner's points via MPI_Bcast on Comm_here
-  {
-    int j = 0;
-    while (j < NN)
-    {
-      int cur_owner_global = owner_rank[j];
-      if (cur_owner_global < 0)
-      {
-        // Point not found — skip (error check disabled for sub-communicator levels)
-        j++;
-        continue;
-      }
-      // Translate global rank to local rank in Comm_here
-      int cur_owner_local;
-      MPI_Group_translate_ranks(world_group, 1, &cur_owner_global, local_group, &cur_owner_local);
+  MPI_Allreduce(shellf, Shellf, NN * num_var, MPI_DOUBLE, MPI_SUM, Comm_here);
+  int *Weight;
+  Weight = new int[NN];
+  MPI_Allreduce(weight, Weight, NN, MPI_INT, MPI_SUM, Comm_here);
 
-      // Find contiguous run of points with the same owner
-      int jstart = j;
-      while (j < NN && owner_rank[j] == cur_owner_global)
-        j++;
-      int count = (j - jstart) * num_var;
-      MPI_Bcast(Shellf + jstart * num_var, count, MPI_DOUBLE, cur_owner_local, Comm_here);
+  //  misc::tillherecheck("print me");
+  //  if(lmyrank == 0) cout<<"myrank = "<<myrank<<"print me"<<endl;
+
+  for (int i = 0; i < NN; i++)
+  {
+    if (Weight[i] > 1)
+    {
+      if (lmyrank == 0)
+        cout << "WARNING: Patch::Interp_Points meets multiple weight" << endl;
+      for (int j = 0; j < num_var; j++)
+        Shellf[j + i * num_var] = Shellf[j + i * num_var] / Weight[i];
     }
+#if 0 // for not involved levels, this may fail     
+     else if(Weight[i] == 0 && lmyrank == 0)
+     {
+       cout<<"ERROR: Patch::Interp_Points fails to find point (";
+       for(int j=0;j<dim;j++)
+       {
+	  cout<<XX[j][i];
+	  if(j<dim-1) cout<<",";
+	  else        cout<<")";
+       }
+       cout<<" on Patch (";
+       for(int j=0;j<dim;j++)
+       {
+	  cout<<bbox[j]<<"+"<<lli[j]*getdX(j);
+	  if(j<dim-1) cout<<",";
+	  else        cout<<")--";
+       }
+       cout<<"(";
+       for(int j=0;j<dim;j++)
+       {
+	  cout<<bbox[dim+j]<<"-"<<uui[j]*getdX(j);
+	  if(j<dim-1) cout<<",";
+	  else        cout<<")"<<endl;
+       }
+#if 0
+       checkBlock();
+#else
+  cout<<"splited domains:"<<endl;
+  {
+     MyList<Block> *Bp=blb;
+     while(Bp)
+     {
+	Block *BP=Bp->data;
+
+	for(int i=0;i<dim;i++)
+	{
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif    
+          llb[i] = (feq(BP->bbox[i]    ,bbox[i]    ,DH[i]/2)) ? BP->bbox[i]+lli[i]*DH[i]     : BP->bbox[i]    +(ghost_width-0.5)*DH[i];
+          uub[i] = (feq(BP->bbox[dim+i],bbox[dim+i],DH[i]/2)) ? BP->bbox[dim+i]-uui[i]*DH[i] : BP->bbox[dim+i]-(ghost_width-0.5)*DH[i];
+#else
+#ifdef Cell
+          llb[i] = (feq(BP->bbox[i]    ,bbox[i]    ,DH[i]/2)) ? BP->bbox[i]+lli[i]*DH[i]     : BP->bbox[i]    +ghost_width*DH[i];
+          uub[i] = (feq(BP->bbox[dim+i],bbox[dim+i],DH[i]/2)) ? BP->bbox[dim+i]-uui[i]*DH[i] : BP->bbox[dim+i]-ghost_width*DH[i];
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif 
+	}       
+       cout<<"(";
+       for(int j=0;j<dim;j++)
+       {
+	  cout<<llb[j]<<":"<<uub[j];
+	  if(j<dim-1) cout<<",";
+	  else        cout<<")"<<endl;
+       }
+	if(Bp == ble) break;
+	Bp=Bp->next;
+     }
+  }
+#endif       
+       MPI_Abort(MPI_COMM_WORLD,1);
+     }
+#endif
   }
 
-  MPI_Group_free(&world_group);
-  MPI_Group_free(&local_group);
-  delete[] owner_rank;
+  delete[] shellf;
+  delete[] weight;
+  delete[] Weight;
+  delete[] DH;
+  delete[] llb;
+  delete[] uub;
 }
 void Patch::checkBlock()
 {

AMSS_NCKU_source/MPatch.h

@@ -2,11 +2,7 @@
 #ifndef PATCH_H
 #define PATCH_H
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 #include "MyList.h"
 #include "Block.h"
 #include "var.h"
@@ -43,10 +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/Newton.C

@@ -8,11 +8,7 @@
 #include <limits.h>
 #include <float.h>
 #include <math.h>
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "util_Table.h"
 #include "cctk.h"

AMSS_NCKU_source/NullShellPatch.h

@@ -23,11 +23,7 @@ using namespace std;
 #include <complex.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 #include "MyList.h"
 #include "Block.h"
 #include "Parallel.h"

AMSS_NCKU_source/NullShellPatch2.h

@@ -23,11 +23,7 @@ using namespace std;
 #include <complex.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 #include "MyList.h"
 #include "Block.h"
 #include "Parallel.h"

AMSS_NCKU_source/Parallel.C

@@ -4,6 +4,8 @@
 #include "prolongrestrict.h"
 #include "misc.h"
 #include "parameters.h"
+#include <vector>
+#include <algorithm>
 
 int Parallel::partition1(int &nx, int split_size, int min_width, int cpusize, int shape) // special for 1 diemnsion
 {
@@ -72,14 +74,14 @@ int Parallel::partition3(int *nxyz, int split_size, int *min_width, int cpusize,
   int n;
 
   block_size = shape[0] * shape[1] * shape[2];
-  n = Mymax(1, (block_size + split_size / 2) / split_size);
+  n =  Mymax(1, (block_size + split_size / 2) / split_size);
 
   maxnx = Mymax(1, shape[0] / min_width[0]);
-  maxnx = Mymin(cpusize, maxnx);
+  maxnx =  Mymin(cpusize, maxnx);
   maxny = Mymax(1, shape[1] / min_width[1]);
-  maxny = Mymin(cpusize, maxny);
+  maxny =  Mymin(cpusize, maxny);
   maxnz = Mymax(1, shape[2] / min_width[2]);
-  maxnz = Mymin(cpusize, maxnz);
+  maxnz =  Mymin(cpusize, maxnz);
   fx = (double)shape[0] / (shape[0] + shape[1] + shape[2]);
   fy = (double)shape[1] / (shape[0] + shape[1] + shape[2]);
   fz = (double)shape[2] / (shape[0] + shape[1] + shape[2]);
@@ -352,14 +354,73 @@ MyList<Block> *Parallel::distribute(MyList<Patch> *PatchLIST, int cpusize, int i
   split_size = Mymax(min_size, block_size / nodes);
   split_size = Mymax(1, split_size);
 
-  int n_rank = 0;
+  // Pass 1: compute block volumes for greedy rank assignment
+  std::vector<long> block_volumes;
   PLi = PatchLIST;
   int reacpu = 0;
   while (PLi)
   {
     Patch *PP = PLi->data;
-
     reacpu += partition3(nxyz, split_size, mmin_width, nodes, PP->shape);
+    int ibbox_here[2 * dim];
+    for (int i = 0; i < nxyz[0]; i++)
+      for (int j = 0; j < nxyz[1]; j++)
+        for (int k = 0; k < nxyz[2]; k++)
+        {
+          ibbox_here[0] = (PP->shape[0] * i) / nxyz[0];
+          ibbox_here[3] = (PP->shape[0] * (i + 1)) / nxyz[0] - 1;
+          ibbox_here[1] = (PP->shape[1] * j) / nxyz[1];
+          ibbox_here[4] = (PP->shape[1] * (j + 1)) / nxyz[1] - 1;
+          ibbox_here[2] = (PP->shape[2] * k) / nxyz[2];
+          ibbox_here[5] = (PP->shape[2] * (k + 1)) / nxyz[2] - 1;
+          if (periodic)
+          {
+            for (int d = 0; d < dim; d++) { ibbox_here[d] -= ghost_width; ibbox_here[dim + d] += ghost_width; }
+          }
+          else
+          {
+            ibbox_here[0] = Mymax(0, ibbox_here[0] - ghost_width);
+            ibbox_here[3] = Mymin(PP->shape[0] - 1, ibbox_here[3] + ghost_width);
+            ibbox_here[1] = Mymax(0, ibbox_here[1] - ghost_width);
+            ibbox_here[4] = Mymin(PP->shape[1] - 1, ibbox_here[4] + ghost_width);
+            ibbox_here[2] = Mymax(0, ibbox_here[2] - ghost_width);
+            ibbox_here[5] = Mymin(PP->shape[2] - 1, ibbox_here[5] + ghost_width);
+          }
+          long vol = 1;
+          for (int d = 0; d < dim; d++)
+            vol *= (ibbox_here[dim + d] - ibbox_here[d] + 1);
+          block_volumes.push_back(vol);
+        }
+    PLi = PLi->next;
+  }
+
+  // Greedy LPT: sort by volume descending, assign each to least-loaded rank
+  std::vector<int> assigned_ranks(block_volumes.size());
+  {
+    std::vector<int> order(block_volumes.size());
+    for (int i = 0; i < (int)order.size(); i++) order[i] = i;
+    std::sort(order.begin(), order.end(), [&](int a, int b) {
+      return block_volumes[a] > block_volumes[b];
+    });
+    std::vector<long> load(cpusize, 0);
+    for (int idx : order)
+    {
+      int min_r = 0;
+      for (int r = 1; r < cpusize; r++)
+        if (load[r] < load[min_r]) min_r = r;
+      assigned_ranks[idx] = min_r;
+      load[min_r] += block_volumes[idx];
+    }
+  }
+
+  // Pass 2: create blocks with pre-assigned ranks
+  int block_idx = 0;
+  PLi = PatchLIST;
+  while (PLi)
+  {
+    Patch *PP = PLi->data;
+
+    partition3(nxyz, split_size, mmin_width, nodes, PP->shape);
 
     Block *ng0, *ng;
     int shape_here[dim], ibbox_here[2 * dim];
@@ -443,10 +504,7 @@ MyList<Block> *Parallel::distribute(MyList<Patch> *PatchLIST, int cpusize, int i
             int shape_res[dim * pices];
             double bbox_res[2 * dim * pices];
             misc::dividBlock(dim, shape_here, bbox_here, pices, picef, shape_res, bbox_res, min_width);
-            ng = ng0 = new Block(dim, shape_res, bbox_res, n_rank++, ingfsi, fngfsi, PP->lev, 0); // delete through KillBlocks
-
-            //	       if(n_rank==cpusize) {n_rank=0; cerr<<"place one!!"<<endl;}
-
+            ng = ng0 = new Block(dim, shape_res, bbox_res, assigned_ranks[block_idx++], ingfsi, fngfsi, PP->lev, 0); // delete through KillBlocks
             //	       ng->checkBlock();
             if (BlL)
               BlL->insert(ng);
@@ -455,22 +513,19 @@ MyList<Block> *Parallel::distribute(MyList<Patch> *PatchLIST, int cpusize, int i
 
             for (int i = 1; i < pices; i++)
             {
-              ng = new Block(dim, shape_res + i * dim, bbox_res + i * 2 * dim, n_rank++, ingfsi, fngfsi, PP->lev, i); // delete through KillBlocks
-              //	        if(n_rank==cpusize) {n_rank=0; cerr<<"place two!! "<<i<<endl;}
+              ng = new Block(dim, shape_res + i * dim, bbox_res + i * 2 * dim, assigned_ranks[block_idx++], ingfsi, fngfsi, PP->lev, i); // delete through KillBlocks
               //	        ng->checkBlock();
               BlL->insert(ng);
             }
           }
 #else
-          ng = ng0 = new Block(dim, shape_here, bbox_here, n_rank++, ingfsi, fngfsi, PP->lev); // delete through KillBlocks
+          ng = ng0 = new Block(dim, shape_here, bbox_here, assigned_ranks[block_idx++], ingfsi, fngfsi, PP->lev); // delete through KillBlocks
           //	    ng->checkBlock();
           if (BlL)
             BlL->insert(ng);
           else
             BlL = new MyList<Block>(ng); // delete through KillBlocks
 #endif
-          if (n_rank == cpusize)
-            n_rank = 0;
 
           // set PP->blb
           if (i == 0 && j == 0 && k == 0)
@@ -3504,7 +3559,7 @@ int Parallel::data_packermix(double *data, MyList<Parallel::gridseg> *src, MyLis
 
   return size_out;
 }
-//
+
 void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridseg> **dst,
                         MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /*target */,
                         int Symmetry)
@@ -3512,13 +3567,20 @@ void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridse
   int myrank, cpusize;
   MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-
+/*
+  // Early exit: if no gridseg pairs exist for any node, skip all work
+  {
+    bool has_segs = false;
+    for (int n = 0; n < cpusize; n++) {
+      if (src[n] && dst[n]) { has_segs = true; break; }
+    }
+    if (!has_segs) return;
+  }
+*/
   int node;
 
-  MPI_Request *reqs;
-  MPI_Status *stats;
-  reqs = new MPI_Request[2 * cpusize];
-  stats = new MPI_Status[2 * cpusize];
+  MPI_Request *reqs = new MPI_Request[2 * cpusize];
+  MPI_Status *stats = new MPI_Status[2 * cpusize];
   int req_no = 0;
 
   double **send_data, **rec_data;
@@ -3527,49 +3589,41 @@ void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridse
   int length;
 
   for (node = 0; node < cpusize; node++)
-  {
     send_data[node] = rec_data[node] = 0;
+
+  // 第1步: 本地拷贝 + 所有 Irecv
+  for (node = 0; node < cpusize; node++)
+  {
     if (node == myrank)
     {
       if (length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry))
       {
         rec_data[node] = new double[length];
-        if (!rec_data[node])
-        {
-          cout << "out of memory when new in short transfer, place 1" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
         data_packer(rec_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
       }
     }
     else
     {
-      // send from this cpu to cpu#node
-      if (length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry))
-      {
-        send_data[node] = new double[length];
-        if (!send_data[node])
-        {
-          cout << "out of memory when new in short transfer, place 2" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        data_packer(send_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-        MPI_Isend((void *)send_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no++);
-      }
-      // receive from cpu#node to this cpu
       if (length = data_packer(0, src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry))
       {
         rec_data[node] = new double[length];
-        if (!rec_data[node])
-        {
-          cout << "out of memory when new in short transfer, place 3" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
         MPI_Irecv((void *)rec_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no++);
       }
     }
   }
-  // wait for all requests to complete
+
+  // 第2步: pack + Isend
+  for (node = 0; node < cpusize; node++)
+  {
+    if (node == myrank) continue;
+    if (length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry))
+    {
+      send_data[node] = new double[length];
+      data_packer(send_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+      MPI_Isend((void *)send_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no++);
+    }
+  }
+
   MPI_Waitall(req_no, reqs, stats);
 
   for (node = 0; node < cpusize; node++)
@@ -3756,484 +3810,6 @@ void Parallel::Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry)
   delete[] transfer_src;
   delete[] transfer_dst;
 }
-// Merged Sync: collect all intra-patch and inter-patch grid segment lists,
-// then issue a single transfer() call instead of N+1 separate ones.
-void Parallel::Sync_merged(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry)
-{
-  int cpusize;
-  MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
-
-  MyList<Parallel::gridseg> **combined_src = new MyList<Parallel::gridseg> *[cpusize];
-  MyList<Parallel::gridseg> **combined_dst = new MyList<Parallel::gridseg> *[cpusize];
-  for (int node = 0; node < cpusize; node++)
-    combined_src[node] = combined_dst[node] = 0;
-
-  // Phase A: Intra-patch ghost exchange segments
-  MyList<Patch> *Pp = PatL;
-  while (Pp)
-  {
-    Patch *Pat = Pp->data;
-    MyList<Parallel::gridseg> *dst_ghost = build_ghost_gsl(Pat);
-
-    for (int node = 0; node < cpusize; node++)
-    {
-      MyList<Parallel::gridseg> *src_owned = build_owned_gsl0(Pat, node);
-      MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
-      build_gstl(src_owned, dst_ghost, &tsrc, &tdst);
-
-      if (tsrc)
-      {
-        if (combined_src[node])
-          combined_src[node]->catList(tsrc);
-        else
-          combined_src[node] = tsrc;
-      }
-      if (tdst)
-      {
-        if (combined_dst[node])
-          combined_dst[node]->catList(tdst);
-        else
-          combined_dst[node] = tdst;
-      }
-
-      if (src_owned)
-        src_owned->destroyList();
-    }
-
-    if (dst_ghost)
-      dst_ghost->destroyList();
-
-    Pp = Pp->next;
-  }
-
-  // Phase B: Inter-patch buffer exchange segments
-  MyList<Parallel::gridseg> *dst_buffer = build_buffer_gsl(PatL);
-  for (int node = 0; node < cpusize; node++)
-  {
-    MyList<Parallel::gridseg> *src_owned = build_owned_gsl(PatL, node, 5, Symmetry);
-    MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
-    build_gstl(src_owned, dst_buffer, &tsrc, &tdst);
-
-    if (tsrc)
-    {
-      if (combined_src[node])
-        combined_src[node]->catList(tsrc);
-      else
-        combined_src[node] = tsrc;
-    }
-    if (tdst)
-    {
-      if (combined_dst[node])
-        combined_dst[node]->catList(tdst);
-      else
-        combined_dst[node] = tdst;
-    }
-
-    if (src_owned)
-      src_owned->destroyList();
-  }
-  if (dst_buffer)
-    dst_buffer->destroyList();
-
-  // Phase C: Single transfer
-  transfer(combined_src, combined_dst, VarList, VarList, Symmetry);
-
-  // Phase D: Cleanup
-  for (int node = 0; node < cpusize; node++)
-  {
-    if (combined_src[node])
-      combined_src[node]->destroyList();
-    if (combined_dst[node])
-      combined_dst[node]->destroyList();
-  }
-  delete[] combined_src;
-  delete[] combined_dst;
-}
-// SyncCache constructor
-Parallel::SyncCache::SyncCache()
-    : valid(false), cpusize(0), combined_src(0), combined_dst(0),
-      send_lengths(0), recv_lengths(0), send_bufs(0), recv_bufs(0),
-      send_buf_caps(0), recv_buf_caps(0), reqs(0), stats(0), max_reqs(0)
-{
-}
-// SyncCache invalidate: free grid segment lists but keep buffers
-void Parallel::SyncCache::invalidate()
-{
-  if (!valid)
-    return;
-  for (int i = 0; i < cpusize; i++)
-  {
-    if (combined_src[i])
-      combined_src[i]->destroyList();
-    if (combined_dst[i])
-      combined_dst[i]->destroyList();
-    combined_src[i] = combined_dst[i] = 0;
-    send_lengths[i] = recv_lengths[i] = 0;
-  }
-  valid = false;
-}
-// SyncCache destroy: free everything
-void Parallel::SyncCache::destroy()
-{
-  invalidate();
-  if (combined_src) delete[] combined_src;
-  if (combined_dst) delete[] combined_dst;
-  if (send_lengths) delete[] send_lengths;
-  if (recv_lengths) delete[] recv_lengths;
-  if (send_buf_caps) delete[] send_buf_caps;
-  if (recv_buf_caps) delete[] recv_buf_caps;
-  for (int i = 0; i < cpusize; i++)
-  {
-    if (send_bufs && send_bufs[i]) delete[] send_bufs[i];
-    if (recv_bufs && recv_bufs[i]) delete[] recv_bufs[i];
-  }
-  if (send_bufs) delete[] send_bufs;
-  if (recv_bufs) delete[] recv_bufs;
-  if (reqs) delete[] reqs;
-  if (stats) delete[] stats;
-  combined_src = combined_dst = 0;
-  send_lengths = recv_lengths = 0;
-  send_buf_caps = recv_buf_caps = 0;
-  send_bufs = recv_bufs = 0;
-  reqs = 0; stats = 0;
-  cpusize = 0; max_reqs = 0;
-}
-// transfer_cached: reuse pre-allocated buffers from SyncCache
-void Parallel::transfer_cached(MyList<Parallel::gridseg> **src, MyList<Parallel::gridseg> **dst,
-                               MyList<var> *VarList1, MyList<var> *VarList2,
-                               int Symmetry, SyncCache &cache)
-{
-  int myrank;
-  MPI_Comm_size(MPI_COMM_WORLD, &cache.cpusize);
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-  int cpusize = cache.cpusize;
-
-  int req_no = 0;
-  int node;
-
-  for (node = 0; node < cpusize; node++)
-  {
-    if (node == myrank)
-    {
-      int length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-      cache.recv_lengths[node] = length;
-      if (length > 0)
-      {
-        if (length > cache.recv_buf_caps[node])
-        {
-          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
-          cache.recv_bufs[node] = new double[length];
-          cache.recv_buf_caps[node] = length;
-        }
-        data_packer(cache.recv_bufs[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-      }
-    }
-    else
-    {
-      // send
-      int slength = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-      cache.send_lengths[node] = slength;
-      if (slength > 0)
-      {
-        if (slength > cache.send_buf_caps[node])
-        {
-          if (cache.send_bufs[node]) delete[] cache.send_bufs[node];
-          cache.send_bufs[node] = new double[slength];
-          cache.send_buf_caps[node] = slength;
-        }
-        data_packer(cache.send_bufs[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-        MPI_Isend((void *)cache.send_bufs[node], slength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no++);
-      }
-      // recv
-      int rlength = data_packer(0, src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
-      cache.recv_lengths[node] = rlength;
-      if (rlength > 0)
-      {
-        if (rlength > cache.recv_buf_caps[node])
-        {
-          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
-          cache.recv_bufs[node] = new double[rlength];
-          cache.recv_buf_caps[node] = rlength;
-        }
-        MPI_Irecv((void *)cache.recv_bufs[node], rlength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no++);
-      }
-    }
-  }
-
-  MPI_Waitall(req_no, cache.reqs, cache.stats);
-
-  for (node = 0; node < cpusize; node++)
-    if (cache.recv_bufs[node] && cache.recv_lengths[node] > 0)
-      data_packer(cache.recv_bufs[node], src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
-}
-// Sync_cached: build grid segment lists on first call, reuse on subsequent calls
-void Parallel::Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, SyncCache &cache)
-{
-  if (!cache.valid)
-  {
-    int cpusize;
-    MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
-    cache.cpusize = cpusize;
-
-    // Allocate cache arrays if needed
-    if (!cache.combined_src)
-    {
-      cache.combined_src = new MyList<Parallel::gridseg> *[cpusize];
-      cache.combined_dst = new MyList<Parallel::gridseg> *[cpusize];
-      cache.send_lengths = new int[cpusize];
-      cache.recv_lengths = new int[cpusize];
-      cache.send_bufs = new double *[cpusize];
-      cache.recv_bufs = new double *[cpusize];
-      cache.send_buf_caps = new int[cpusize];
-      cache.recv_buf_caps = new int[cpusize];
-      for (int i = 0; i < cpusize; i++)
-      {
-        cache.send_bufs[i] = cache.recv_bufs[i] = 0;
-        cache.send_buf_caps[i] = cache.recv_buf_caps[i] = 0;
-      }
-      cache.max_reqs = 2 * cpusize;
-      cache.reqs = new MPI_Request[cache.max_reqs];
-      cache.stats = new MPI_Status[cache.max_reqs];
-    }
-
-    for (int node = 0; node < cpusize; node++)
-    {
-      cache.combined_src[node] = cache.combined_dst[node] = 0;
-      cache.send_lengths[node] = cache.recv_lengths[node] = 0;
-    }
-
-    // Build intra-patch segments (same as Sync_merged Phase A)
-    MyList<Patch> *Pp = PatL;
-    while (Pp)
-    {
-      Patch *Pat = Pp->data;
-      MyList<Parallel::gridseg> *dst_ghost = build_ghost_gsl(Pat);
-      for (int node = 0; node < cpusize; node++)
-      {
-        MyList<Parallel::gridseg> *src_owned = build_owned_gsl0(Pat, node);
-        MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
-        build_gstl(src_owned, dst_ghost, &tsrc, &tdst);
-        if (tsrc)
-        {
-          if (cache.combined_src[node])
-            cache.combined_src[node]->catList(tsrc);
-          else
-            cache.combined_src[node] = tsrc;
-        }
-        if (tdst)
-        {
-          if (cache.combined_dst[node])
-            cache.combined_dst[node]->catList(tdst);
-          else
-            cache.combined_dst[node] = tdst;
-        }
-        if (src_owned) src_owned->destroyList();
-      }
-      if (dst_ghost) dst_ghost->destroyList();
-      Pp = Pp->next;
-    }
-
-    // Build inter-patch segments (same as Sync_merged Phase B)
-    MyList<Parallel::gridseg> *dst_buffer = build_buffer_gsl(PatL);
-    for (int node = 0; node < cpusize; node++)
-    {
-      MyList<Parallel::gridseg> *src_owned = build_owned_gsl(PatL, node, 5, Symmetry);
-      MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
-      build_gstl(src_owned, dst_buffer, &tsrc, &tdst);
-      if (tsrc)
-      {
-        if (cache.combined_src[node])
-          cache.combined_src[node]->catList(tsrc);
-        else
-          cache.combined_src[node] = tsrc;
-      }
-      if (tdst)
-      {
-        if (cache.combined_dst[node])
-          cache.combined_dst[node]->catList(tdst);
-        else
-          cache.combined_dst[node] = tdst;
-      }
-      if (src_owned) src_owned->destroyList();
-    }
-    if (dst_buffer) dst_buffer->destroyList();
-
-    cache.valid = true;
-  }
-
-  // Use cached lists with buffer-reusing transfer
-  transfer_cached(cache.combined_src, cache.combined_dst, VarList, VarList, Symmetry, cache);
-}
-// Sync_start: pack and post MPI_Isend/Irecv, return immediately
-void Parallel::Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
-                          SyncCache &cache, AsyncSyncState &state)
-{
-  // Ensure cache is built
-  if (!cache.valid)
-  {
-    // Build cache (same logic as Sync_cached)
-    int cpusize;
-    MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
-    cache.cpusize = cpusize;
-
-    if (!cache.combined_src)
-    {
-      cache.combined_src = new MyList<Parallel::gridseg> *[cpusize];
-      cache.combined_dst = new MyList<Parallel::gridseg> *[cpusize];
-      cache.send_lengths = new int[cpusize];
-      cache.recv_lengths = new int[cpusize];
-      cache.send_bufs = new double *[cpusize];
-      cache.recv_bufs = new double *[cpusize];
-      cache.send_buf_caps = new int[cpusize];
-      cache.recv_buf_caps = new int[cpusize];
-      for (int i = 0; i < cpusize; i++)
-      {
-        cache.send_bufs[i] = cache.recv_bufs[i] = 0;
-        cache.send_buf_caps[i] = cache.recv_buf_caps[i] = 0;
-      }
-      cache.max_reqs = 2 * cpusize;
-      cache.reqs = new MPI_Request[cache.max_reqs];
-      cache.stats = new MPI_Status[cache.max_reqs];
-    }
-
-    for (int node = 0; node < cpusize; node++)
-    {
-      cache.combined_src[node] = cache.combined_dst[node] = 0;
-      cache.send_lengths[node] = cache.recv_lengths[node] = 0;
-    }
-
-    MyList<Patch> *Pp = PatL;
-    while (Pp)
-    {
-      Patch *Pat = Pp->data;
-      MyList<Parallel::gridseg> *dst_ghost = build_ghost_gsl(Pat);
-      for (int node = 0; node < cpusize; node++)
-      {
-        MyList<Parallel::gridseg> *src_owned = build_owned_gsl0(Pat, node);
-        MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
-        build_gstl(src_owned, dst_ghost, &tsrc, &tdst);
-        if (tsrc)
-        {
-          if (cache.combined_src[node])
-            cache.combined_src[node]->catList(tsrc);
-          else
-            cache.combined_src[node] = tsrc;
-        }
-        if (tdst)
-        {
-          if (cache.combined_dst[node])
-            cache.combined_dst[node]->catList(tdst);
-          else
-            cache.combined_dst[node] = tdst;
-        }
-        if (src_owned) src_owned->destroyList();
-      }
-      if (dst_ghost) dst_ghost->destroyList();
-      Pp = Pp->next;
-    }
-
-    MyList<Parallel::gridseg> *dst_buffer = build_buffer_gsl(PatL);
-    for (int node = 0; node < cpusize; node++)
-    {
-      MyList<Parallel::gridseg> *src_owned = build_owned_gsl(PatL, node, 5, Symmetry);
-      MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
-      build_gstl(src_owned, dst_buffer, &tsrc, &tdst);
-      if (tsrc)
-      {
-        if (cache.combined_src[node])
-          cache.combined_src[node]->catList(tsrc);
-        else
-          cache.combined_src[node] = tsrc;
-      }
-      if (tdst)
-      {
-        if (cache.combined_dst[node])
-          cache.combined_dst[node]->catList(tdst);
-        else
-          cache.combined_dst[node] = tdst;
-      }
-      if (src_owned) src_owned->destroyList();
-    }
-    if (dst_buffer) dst_buffer->destroyList();
-    cache.valid = true;
-  }
-
-  // Now pack and post async MPI operations
-  int myrank;
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-  int cpusize = cache.cpusize;
-  state.req_no = 0;
-  state.active = true;
-
-  MyList<Parallel::gridseg> **src = cache.combined_src;
-  MyList<Parallel::gridseg> **dst = cache.combined_dst;
-
-  for (int node = 0; node < cpusize; node++)
-  {
-    if (node == myrank)
-    {
-      int length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList, VarList, Symmetry);
-      cache.recv_lengths[node] = length;
-      if (length > 0)
-      {
-        if (length > cache.recv_buf_caps[node])
-        {
-          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
-          cache.recv_bufs[node] = new double[length];
-          cache.recv_buf_caps[node] = length;
-        }
-        data_packer(cache.recv_bufs[node], src[myrank], dst[myrank], node, PACK, VarList, VarList, Symmetry);
-      }
-    }
-    else
-    {
-      int slength = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList, VarList, Symmetry);
-      cache.send_lengths[node] = slength;
-      if (slength > 0)
-      {
-        if (slength > cache.send_buf_caps[node])
-        {
-          if (cache.send_bufs[node]) delete[] cache.send_bufs[node];
-          cache.send_bufs[node] = new double[slength];
-          cache.send_buf_caps[node] = slength;
-        }
-        data_packer(cache.send_bufs[node], src[myrank], dst[myrank], node, PACK, VarList, VarList, Symmetry);
-        MPI_Isend((void *)cache.send_bufs[node], slength, MPI_DOUBLE, node, 2, MPI_COMM_WORLD, cache.reqs + state.req_no++);
-      }
-      int rlength = data_packer(0, src[node], dst[node], node, UNPACK, VarList, VarList, Symmetry);
-      cache.recv_lengths[node] = rlength;
-      if (rlength > 0)
-      {
-        if (rlength > cache.recv_buf_caps[node])
-        {
-          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
-          cache.recv_bufs[node] = new double[rlength];
-          cache.recv_buf_caps[node] = rlength;
-        }
-        MPI_Irecv((void *)cache.recv_bufs[node], rlength, MPI_DOUBLE, node, 2, MPI_COMM_WORLD, cache.reqs + state.req_no++);
-      }
-    }
-  }
-}
-// Sync_finish: wait for async MPI operations and unpack
-void Parallel::Sync_finish(SyncCache &cache, AsyncSyncState &state,
-                           MyList<var> *VarList, int Symmetry)
-{
-  if (!state.active)
-    return;
-
-  MPI_Waitall(state.req_no, cache.reqs, cache.stats);
-
-  int cpusize = cache.cpusize;
-  MyList<Parallel::gridseg> **src = cache.combined_src;
-  MyList<Parallel::gridseg> **dst = cache.combined_dst;
-
-  for (int node = 0; node < cpusize; node++)
-    if (cache.recv_bufs[node] && cache.recv_lengths[node] > 0)
-      data_packer(cache.recv_bufs[node], src[node], dst[node], node, UNPACK, VarList, VarList, Symmetry);
-
-  state.active = false;
-}
 // collect buffer grid segments or blocks for the periodic boundary condition of given patch
 // ---------------------------------------------------
 // |con |                                       |con |

AMSS_NCKU_source/Parallel.h

@@ -81,42 +81,6 @@ namespace Parallel
                    int Symmetry);
   void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry);
   void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
-  void Sync_merged(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
-
-  struct SyncCache {
-    bool valid;
-    int cpusize;
-    MyList<gridseg> **combined_src;
-    MyList<gridseg> **combined_dst;
-    int *send_lengths;
-    int *recv_lengths;
-    double **send_bufs;
-    double **recv_bufs;
-    int *send_buf_caps;
-    int *recv_buf_caps;
-    MPI_Request *reqs;
-    MPI_Status *stats;
-    int max_reqs;
-    SyncCache();
-    void invalidate();
-    void destroy();
-  };
-
-  void Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, SyncCache &cache);
-  void transfer_cached(MyList<gridseg> **src, MyList<gridseg> **dst,
-                       MyList<var> *VarList1, MyList<var> *VarList2,
-                       int Symmetry, SyncCache &cache);
-
-  struct AsyncSyncState {
-    int req_no;
-    bool active;
-    AsyncSyncState() : req_no(0), active(false) {}
-  };
-
-  void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
-                  SyncCache &cache, AsyncSyncState &state);
-  void Sync_finish(SyncCache &cache, AsyncSyncState &state,
-                   MyList<var> *VarList, int Symmetry);
   void OutBdLow2Hi(Patch *Patc, Patch *Patf,
                    MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                    int Symmetry);

AMSS_NCKU_source/ShellPatch.h

@@ -2,11 +2,7 @@
 #ifndef SHELLPATCH_H
 #define SHELLPATCH_H
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 #include "MyList.h"
 #include "Block.h"
 #include "Parallel.h"

AMSS_NCKU_source/Z4c_class.h

@@ -19,11 +19,7 @@ using namespace std;
 #include <math.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "cgh.h"
 #include "ShellPatch.h"

AMSS_NCKU_source/bssnEM_class.h

@@ -19,11 +19,7 @@ using namespace std;
 #include <math.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "cgh.h"
 #include "ShellPatch.h"

AMSS_NCKU_source/bssnEScalar_class.h

@@ -19,11 +19,7 @@ using namespace std;
 #include <math.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "cgh.h"
 #include "ShellPatch.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
-  MPI_Request err_req;
+  // check error information
   {
     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_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
 
 #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 "
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+      cout << " Shell stuff synchronization used " 
+           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
            << " seconds! " << endl;
     }
   }
 #endif
-  Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry);
-
-#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
-    MPI_Request err_req_cor;
+    // check error information
     {
       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_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
 
 #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 "
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+        cout << " Shell stuff synchronization used " 
+             << (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::gy],
+                                    cg->fgfs[fngfs + ShellPatch::gx], 
+                                    cg->fgfs[fngfs + ShellPatch::gy], 
                                     cg->fgfs[fngfs + ShellPatch::gz],
                                     cg->fgfs[fngfs + ShellPatch::drhodx], 
                                     cg->fgfs[fngfs + ShellPatch::drhody], 
@@ -4200,16 +4190,25 @@ void bssn_class::Step(int lev, int YN)
   }
 #endif
   }
-  // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
-  MPI_Request err_req;
+  // check error information
   {
     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_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
 
 #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 "
-           << (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);
+      cout << " Shell stuff synchronization used " 
+      << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
+      << " seconds! " << endl;
     }
   }
 #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
-    MPI_Request err_req_cor;
+    // check error information
     {
       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_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
 
 #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 "
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+        cout << " Shell stuff synchronization used " 
+             << (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
-  MPI_Request err_req;
+  // check error information
   {
     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
-    MPI_Request err_req_cor;
+    // check error information
     {
       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
-                                << " variables at t = " << PhysTime
+          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
+                                << " variables at t = " << PhysTime 
                                 << ", lev = " << lev << endl;
         MPI_Abort(MPI_COMM_WORLD, 1);
       }
     }
 
+    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector sync");
+
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+
+    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector sync");
+
 #if (MAPBH == 0)
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
@@ -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
-  MPI_Request err_req;
+  // check error information
   {
     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 "
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+      cout << " Shell stuff synchronization used " 
+           << (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
-    MPI_Request err_req_cor;
+    // check error information
     {
       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 "
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+        cout << " Shell stuff synchronization used " 
+             << (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();
@@ -5870,7 +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();
@@ -5908,7 +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();
@@ -5966,7 +5938,7 @@ 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];
@@ -5998,7 +5970,7 @@ 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];
@@ -6022,7 +5994,7 @@ void bssn_class::RestrictProlong_aux(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);
   }
 }
 
@@ -6073,7 +6045,7 @@ 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];
@@ -6107,7 +6079,7 @@ 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];
@@ -6131,7 +6103,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
 #endif
     }
 
-    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
   }
 }
 
@@ -6214,10 +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

@@ -19,11 +19,7 @@ using namespace std;
 #include <math.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "macrodef.h"
 #include "cgh.h"
@@ -130,11 +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_gpu_class.h

@@ -19,11 +19,7 @@ using namespace std;
 #include <math.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "macrodef.h"
 #include "cgh.h"

AMSS_NCKU_source/bssn_rhs.f90

@@ -161,36 +161,8 @@
 
   chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
 
-  call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
-  call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
-  call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
-  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
 
-  gxx_rhs = - TWO * alpn1 * Axx    -  F2o3 * gxx * div_beta          + &
-              TWO *(  gxx * betaxx +   gxy * betayx +   gxz * betazx)
 
-  gyy_rhs = - TWO * alpn1 * Ayy    -  F2o3 * gyy * div_beta          + &
-              TWO *(  gxy * betaxy +   gyy * betayy +   gyz * betazy)
-
-  gzz_rhs = - TWO * alpn1 * Azz    -  F2o3 * gzz * div_beta          + &
-              TWO *(  gxz * betaxz +   gyz * betayz +   gzz * betazz)
-
-  gxy_rhs = - TWO * alpn1 * Axy    +  F1o3 * gxy    * div_beta       + &
-                      gxx * betaxy                  +   gxz * betazy + &
-                                       gyy * betayx +   gyz * betazx   &
-                                                    -   gxy * betazz
-
-  gyz_rhs = - TWO * alpn1 * Ayz    +  F1o3 * gyz    * div_beta       + &
-                      gxy * betaxz +   gyy * betayz                  + &
-                      gxz * betaxy                  +   gzz * betazy   &
-                                                    -   gyz * betaxx
- 
-  gxz_rhs = - TWO * alpn1 * Axz    +  F1o3 * gxz    * div_beta       + &
-                      gxx * betaxz +   gxy * betayz                  + &
-                                       gyz * betayx +   gzz * betazx   &
-                                                    -   gxz * betayy     !rhs for gij
 
 ! invert tilted metric
   gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
@@ -201,7 +173,12 @@
   gupyy =   ( gxx * gzz - gxz * gxz ) / gupzz
   gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
   gupzz =   ( gxx * gyy - gxy * gxy ) / gupzz
-
+  call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
+  call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
+  call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
+  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
   if(co == 0)then
 ! Gam^i_Res = Gam^i + gup^ij_,j
   Gmx_Res = Gamx - (gupxx*(gupxx*gxxx+gupxy*gxyx+gupxz*gxzx)&
@@ -947,99 +924,99 @@
 
 !!!!!!!!!advection term part
 
+  gxx_rhs = - TWO * alpn1 * Axx    -  F2o3 * gxx * div_beta          + &
+              TWO *(  gxx * betaxx +   gxy * betayx +   gxz * betazx)
+
+  gyy_rhs = - TWO * alpn1 * Ayy    -  F2o3 * gyy * div_beta          + &
+              TWO *(  gxy * betaxy +   gyy * betayy +   gyz * betazy)
+
+  gzz_rhs = - TWO * alpn1 * Azz    -  F2o3 * gzz * div_beta          + &
+              TWO *(  gxz * betaxz +   gyz * betayz +   gzz * betazz)
+
+  gxy_rhs = - TWO * alpn1 * Axy    +  F1o3 * gxy    * div_beta       + &
+                      gxx * betaxy                  +   gxz * betazy + &
+                                        gyy * betayx +   gyz * betazx   &
+                                                    -   gxy * betazz
+
+  gyz_rhs = - TWO * alpn1 * Ayz    +  F1o3 * gyz    * div_beta       + &
+                      gxy * betaxz +   gyy * betayz                  + &
+                      gxz * betaxy                  +   gzz * betazy   &
+                                                    -   gyz * betaxx
+
+  gxz_rhs = - TWO * alpn1 * Axz    +  F1o3 * gxz    * div_beta       + &
+                      gxx * betaxz +   gxy * betayz                  + &
+                                        gyz * betayx +   gzz * betazx   &
+                                                    -   gxz * betayy     !rhs for gij
+
+
+
+
+
+  if(eps>0)then 
+! usual Kreiss-Oliger dissipation     
+  call merge_lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps) 
+  call merge_lopsided_kodis(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
+
+
+
+
+
+
+
+
+
+
+
+
+  else 
   call lopsided(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS)
   call lopsided(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA)
   call lopsided(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA)
   call lopsided(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS)
-
   call lopsided(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS)
   call lopsided(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA)
   call lopsided(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA)
   call lopsided(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS)
-
   call lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS)
-
   call lopsided(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS)
   call lopsided(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS)
   call lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA)
-!!
   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
 
@@ -1186,3 +1163,265 @@ endif
   return
 
   end function compute_rhs_bssn
+
+
+
+
+  subroutine merge_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
+
+  !~~~~~~> 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_lopsided,jmin_lopsided,kmin_lopsided,imin_kodis,jmin_kodis,kmin_kodis,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
+    real*8, parameter :: SIX=6.d0,FIT=1.5d1,TWT=2.d1
+    real*8,parameter::cof=6.4d1   ! 2^6
+    real*8,intent(in) :: eps
+    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_lopsided = 1
+    jmin_lopsided = 1
+    kmin_lopsided = 1
+    if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin_lopsided = -2
+    if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin_lopsided = -2
+    if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin_lopsided = -2
+
+    imin_kodis = 1
+    jmin_kodis = 1
+    kmin_kodis = 1
+
+    if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin_kodis = -2
+    if(Symmetry == OCTANT .and. dabs(X(1)) < dX) imin_kodis = -2
+    if(Symmetry == OCTANT .and. dabs(Y(1)) < dY) jmin_kodis = -2
+
+
+    call symmetry_bd(3,ex,f,fh,SoA)
+
+  ! 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
+
+  !! new code, 2012dec27, based on bam
+  ! x direction   
+      if(Sfx(i,j,k) > ZEO)then
+        if(i+3 <= imax)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      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(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      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
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      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))
+  ! set imax and imin_lopsided 0
+      endif
+    elseif(Sfx(i,j,k) < ZEO)then
+        if(i-3 >= imin_lopsided)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      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_lopsided)then
+  !
+  !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      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_lopsided)then
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      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))
+  ! set imax and imin_lopsided 0
+      endif
+    endif
+
+  ! y direction   
+      if(Sfy(i,j,k) > ZEO)then
+        if(j+3 <= jmax)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      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(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      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
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      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))
+  ! set imax and imin_lopsided 0
+      endif
+    elseif(Sfy(i,j,k) < ZEO)then
+        if(j-3 >= jmin_lopsided)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      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_lopsided)then
+  !
+  !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      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_lopsided)then
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      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))
+  ! set jmax and jmin_lopsided 0
+      endif
+    endif
+
+  ! z direction   
+      if(Sfz(i,j,k) > ZEO)then
+        if(k+3 <= kmax)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      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(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      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
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      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))
+  ! set imax and imin_lopsided 0
+      endif
+    elseif(Sfz(i,j,k) < ZEO)then
+        if(k-3 >= kmin_lopsided)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      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_lopsided)then
+  !
+  !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      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_lopsided)then
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      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))
+  ! set kmax and kmin_lopsided 0
+      endif
+    endif
+
+
+    if(i-3 >= imin_kodis .and. i+3 <= imax .and. &
+      j-3 >= jmin_kodis .and. j+3 <= jmax .and. &
+      k-3 >= kmin_kodis .and. k+3 <= kmax) then
+
+  ! calculation order if important ?
+    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
+
+    return
+
+
+
+  end subroutine merge_lopsided_kodis

AMSS_NCKU_source/cgh.C

@@ -20,11 +20,7 @@ using namespace std;
 #include <map.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "macrodef.h"
 #include "misc.h"

AMSS_NCKU_source/cgh.h

@@ -2,11 +2,7 @@
 #ifndef CGH_H
 #define CGH_H
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 #include "MyList.h"
 #include "MPatch.h"
 #include "macrodef.h"

AMSS_NCKU_source/checkpoint.h

@@ -19,11 +19,7 @@ using namespace std;
 #include <time.h>
 #include <stdlib.h>
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "var.h"
 #include "MyList.h"

AMSS_NCKU_source/diff_new.f90

@@ -69,7 +69,6 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -152,7 +151,6 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -220,7 +218,6 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -285,7 +282,6 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -375,7 +371,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -474,7 +469,6 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -537,7 +531,6 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -601,7 +594,6 @@
 
   fzz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -665,7 +657,6 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -728,7 +719,6 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -790,7 +780,6 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -877,7 +866,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1009,90 +997,10 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
-#if 0  
-! x direction   
-        if(i+2 <= imax .and. i-2 >= imin)then
-!
-!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
-!  fx(i) = ---------------------------------------------
-!                             12 dx
-      fx(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 .and. i-1 >= imin)then
-!
-!              - f(i-1) + f(i+1)
-!  fx(i) = --------------------------------
-!                     2 dx
-      fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
-
-! set imax and imin 0
-    endif
-! y direction   
-        if(j+2 <= jmax .and. j-2 >= jmin)then
-
-      fy(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 .and. j-1 >= jmin)then
-
-     fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
-
-! set jmax and jmin 0
-    endif
-! z direction   
-        if(k+2 <= kmax .and. k-2 >= kmin)then
-
-      fz(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 .and. k-1 >= kmin)then
-
-      fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
-
-! set kmax and kmin 0
-    endif
-#elif 0
-! x direction   
-        if(i+2 <= imax .and. i-2 >= imin)then
-!
-!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
-!  fx(i) = ---------------------------------------------
-!                             12 dx
-      fx(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+3 <= imax .and. i-1 >= imin)then
-      fx(i,j,k)=d12dx*(-3.d0*fh(i-1,j,k)-1.d1*fh(i,j,k)+1.8d1*fh(i+1,j,k)-6.d0*fh(i+2,j,k)+fh(i+3,j,k))
-    elseif(i+1 <= imax .and. i-3 >= imin)then
-      fx(i,j,k)=d12dx*( 3.d0*fh(i+1,j,k)+1.d1*fh(i,j,k)-1.8d1*fh(i-1,j,k)+6.d0*fh(i-2,j,k)-fh(i-3,j,k))
-! set imax and imin 0
-    endif
-! y direction   
-        if(j+2 <= jmax .and. j-2 >= jmin)then
-
-      fy(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+3 <= jmax .and. j-1 >= jmin)then
-      fy(i,j,k)=d12dy*(-3.d0*fh(i,j-1,k)-1.d1*fh(i,j,k)+1.8d1*fh(i,j+1,k)-6.d0*fh(i,j+2,k)+fh(i,j+3,k))
-    elseif(j+1 <= jmax .and. j-3 >= jmin)then
-      fy(i,j,k)=d12dy*( 3.d0*fh(i,j+1,k)+1.d1*fh(i,j,k)-1.8d1*fh(i,j-1,k)+6.d0*fh(i,j-2,k)-fh(i,j-3,k))
-
-! set jmax and jmin 0
-    endif
-! z direction   
-        if(k+2 <= kmax .and. k-2 >= kmin)then
-
-      fz(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+3 <= kmax .and. k-1 >= kmin)then
-      fz(i,j,k)=d12dz*(-3.d0*fh(i,j,k-1)-1.d1*fh(i,j,k)+1.8d1*fh(i,j,k+1)-6.d0*fh(i,j,k+2)+fh(i,j,k+3))
-    elseif(k+1 <= kmax .and. k-3 >= kmin)then
-      fz(i,j,k)=d12dz*( 3.d0*fh(i,j,k+1)+1.d1*fh(i,j,k)-1.8d1*fh(i,j,k-1)+6.d0*fh(i,j,k-2)-fh(i,j,k-3))
-
-! set kmax and kmin 0
-    endif
-#else
 ! for bam comparison
    if(i+2 <= imax .and. i-2 >= imin .and. &
       j+2 <= jmax .and. j-2 >= jmin .and. &
@@ -1107,7 +1015,7 @@
       fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
       fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
    endif
-#endif
+
   enddo
   enddo
   enddo
@@ -1164,7 +1072,6 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1241,7 +1148,6 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1312,7 +1218,6 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1417,89 +1322,10 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
-#if 0  
-!~~~~~~ fxx
-        if(i+2 <= imax .and. i-2 >= imin)then
-!
-!               - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
-!  fxx(i) = ----------------------------------------------------------
-!                                  12 dx^2 
-   fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
-                       -fh(i+2,j,k)+F16*fh(i+1,j,k)              )
-   elseif(i+1 <= imax .and. i-1 >= imin)then
-!
-!               f(i-1) - 2 f(i) + f(i+1)
-!  fxx(i) = --------------------------------
-!                         dx^2 
-   fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
-                      +fh(i+1,j,k)              )
-   endif
 
-
-!~~~~~~ fyy
-        if(j+2 <= jmax .and. j-2 >= jmin)then
-
-   fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
-                       -fh(i,j+2,k)+F16*fh(i,j+1,k)              )
-   elseif(j+1 <= jmax .and. j-1 >= jmin)then
-
-   fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
-                      +fh(i,j+1,k)              )
-   endif
-
-!~~~~~~ fzz
-        if(k+2 <= kmax .and. k-2 >= kmin)then
-
-   fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
-                       -fh(i,j,k+2)+F16*fh(i,j,k+1)              )
-   elseif(k+1 <= kmax .and. k-1 >= kmin)then
-
-   fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
-                      +fh(i,j,k+1)              )
-   endif
-!~~~~~~ fxy
-       if(i+2 <= imax .and. i-2 >= imin .and. j+2 <= jmax .and. j-2 >= jmin)then
-!
-!                 ( f(i-2,j-2) - 8 f(i-1,j-2) + 8 f(i+1,j-2) - f(i+2,j-2) )
-!             - 8 ( f(i-2,j-1) - 8 f(i-1,j-1) + 8 f(i+1,j-1) - f(i+2,j-1) )
-!             + 8 ( f(i-2,j+1) - 8 f(i-1,j+1) + 8 f(i+1,j+1) - f(i+2,j+1) )
-!             -   ( f(i-2,j+2) - 8 f(i-1,j+2) + 8 f(i+1,j+2) - f(i+2,j+2) )
-!  fxy(i,j) = ----------------------------------------------------------------
-!                                  144 dx dy
-   fxy(i,j,k) = Fdxdy*(     (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k))  &
-                       -F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k))  &
-                       +F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k))  &
-                       -    (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
-
-   elseif(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
-!                 f(i-1,j-1) - f(i+1,j-1) - f(i-1,j+1) + f(i+1,j+1) 
-!  fxy(i,j) = -----------------------------------------------------------
-!                                      4 dx dy
-   fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
-   endif
-!~~~~~~ fxz
-       if(i+2 <= imax .and. i-2 >= imin .and. k+2 <= kmax .and. k-2 >= kmin)then
-   fxz(i,j,k) = Fdxdz*(     (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2))  &
-                       -F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1))  &
-                       +F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1))  &
-                       -    (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
-   elseif(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
-   fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
-   endif
-!~~~~~~ fyz
-       if(j+2 <= jmax .and. j-2 >= jmin .and. k+2 <= kmax .and. k-2 >= kmin)then
-   fyz(i,j,k) = Fdydz*(     (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2))  &
-                       -F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1))  &
-                       +F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1))  &
-                       -    (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
-   elseif(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
-   fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
-   endif 
-#else
 ! for bam comparison
    if(i+2 <= imax .and. i-2 >= imin .and. &
       j+2 <= jmax .and. j-2 >= jmin .and. &
@@ -1535,7 +1361,7 @@
    fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
    fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
    endif
-#endif
+
    enddo
    enddo
    enddo
@@ -1593,7 +1419,6 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1661,7 +1486,6 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1731,7 +1555,6 @@
 
   fzz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1801,7 +1624,6 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1872,7 +1694,6 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1941,7 +1762,6 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2034,7 +1854,6 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2151,7 +1970,6 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2237,7 +2055,6 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2314,7 +2131,6 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2433,7 +2249,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2621,7 +2436,6 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2694,7 +2508,6 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2770,7 +2583,6 @@
 
   fzz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2846,7 +2658,6 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -2927,7 +2738,6 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3006,7 +2816,6 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3114,7 +2923,6 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3251,7 +3059,6 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3347,7 +3154,6 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3432,7 +3238,6 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3568,7 +3373,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3841,7 +3645,6 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -3923,7 +3726,6 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -4008,7 +3810,6 @@
   
   fzz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -4093,7 +3894,6 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -4196,7 +3996,6 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -4297,7 +4096,6 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1

AMSS_NCKU_source/diff_new_sh.f90

@@ -81,7 +81,6 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -180,7 +179,6 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -264,7 +262,6 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -345,7 +342,6 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -447,7 +443,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -558,7 +553,6 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -633,7 +627,6 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -709,7 +702,6 @@
 
   fzz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -785,7 +777,6 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -860,7 +851,6 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -934,7 +924,6 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1030,7 +1019,6 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1146,7 +1134,6 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1240,7 +1227,6 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1328,7 +1314,6 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1445,7 +1430,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1596,7 +1580,6 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1676,7 +1659,6 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1758,7 +1740,6 @@
 
   fzz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1840,7 +1821,6 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -1923,7 +1903,6 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2004,7 +1983,6 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2109,7 +2087,6 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2242,7 +2219,6 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2345,7 +2321,6 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2439,7 +2414,6 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2570,7 +2544,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2770,7 +2743,6 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2855,7 +2827,6 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -2943,7 +2914,6 @@
 
   fzz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -3031,7 +3001,6 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -3124,7 +3093,6 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -3215,7 +3183,6 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -3335,7 +3302,6 @@
   fy = ZEO
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -3488,7 +3454,6 @@
 
   fx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -3601,7 +3566,6 @@
 
   fy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -3703,7 +3667,6 @@
 
   fz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -3851,7 +3814,6 @@
   fxz = ZEO
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -4136,7 +4098,6 @@
 
   fxx = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -4230,7 +4191,6 @@
 
   fyy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -4327,7 +4287,6 @@
   
   fzz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -4424,7 +4383,6 @@
 
   fxy = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -4539,7 +4497,6 @@
 
   fxz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -4652,7 +4609,6 @@
 
   fyz = ZEO
 
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -4723,7 +4679,6 @@ subroutine fderivs_shc(ex,f,fx,fy,fz,crho,sigma,R,SYM1,SYM2,SYM3,Symmetry,Lev,ss
 #if 0  
   integer :: i,j,k
   
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -4774,7 +4729,6 @@ subroutine fdderivs_shc(ex,f,fxx,fxy,fxz,fyy,fyz,fzz,crho,sigma,R,SYM1,SYM2,SYM3
 #if 0  
   integer :: i,j,k
   
-  !$omp parallel do collapse(2) private(i,j,k)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)

AMSS_NCKU_source/enforce_algebra.f90

@@ -27,7 +27,6 @@
 
 !~~~~~~>
 
-  !$omp parallel do collapse(2) private(i,j,k,lgxx,lgyy,lgzz,ldetg,lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz,ltrA,lscale)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
@@ -105,7 +104,6 @@
 
 !~~~~~~>
 
-  !$omp parallel do collapse(2) private(i,j,k,lgxx,lgyy,lgzz,lscale,lgxy,lgxz,lgyz,lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz,ltrA)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)

AMSS_NCKU_source/expansion.C

@@ -6,11 +6,7 @@
 #include <stdio.h>
 #include <assert.h>
 #include <math.h>
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "util_Table.h"
 #include "cctk.h"

AMSS_NCKU_source/find_horizons.C

@@ -6,11 +6,7 @@
 #include <stdio.h>
 #include <assert.h>
 #include <math.h>
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "cctk.h"
 

AMSS_NCKU_source/fmisc.f90

@@ -326,7 +326,8 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   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)
+      
+    funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
    enddo
    do i=0,ord-1
       funcc(:,-i,1:extc(3)) = funcc(:,i+2,1:extc(3))*SoA(2)

AMSS_NCKU_source/kodiss.f90

@@ -6,102 +6,6 @@
 ! Vertex or Cell is distinguished in routine symmetry_bd which locates in
 ! file "fmisc.f90"
 
-#if (ghost_width == 2)
-! second order code
-
-!------------------------------------------------------------------------------------------------------------------------------
-!usual type Kreiss-Oliger type numerical dissipation
-!We support cell center only
-!  (D_+D_-)^2 =
-!   f(i-2) - 4 f(i-1) + 6 f(i) - 4 f(i+1) + f(i+2)
-! ------------------------------------------------------
-!                       dx^4
-!------------------------------------------------------------------------------------------------------------------------------
-! do not add dissipation near boundary
-subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
-
-implicit none
-! argument variables
-integer,intent(in) :: Symmetry
-integer,dimension(3),intent(in)::ex
-real*8, dimension(1:3), intent(in) :: SoA
-double precision,intent(in),dimension(ex(1))::X
-double precision,intent(in),dimension(ex(2))::Y
-double precision,intent(in),dimension(ex(3))::Z
-double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
-double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
-real*8,intent(in) :: eps
-
-!~~~~~~ other variables
-
-  real*8 :: dX,dY,dZ
-  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-  real*8,parameter   :: cof = 1.6d1 ! 2^4
-  real*8,  parameter :: F4=4.d0,F6=6.d0
-  integer::i,j,k
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-
-  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 = -1
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
-
-  call symmetry_bd(2,ex,f,fh,SoA)
-
-!   f(i-2) - 4 f(i-1) + 6 f(i) - 4 f(i+1) + f(i+2)
-! ------------------------------------------------------
-!                       dx^4
-
-!  note the sign (-1)^r-1, now r=2
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-
-  if(i-2 >= imin .and. i+2 <= imax .and. &
-     j-2 >= jmin .and. j+2 <= jmax .and. &
-     k-2 >= kmin .and. k+2 <= kmax) then
-! x direction
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dX/cof * (     &
-                                (fh(i-2,j,k)+fh(i+2,j,k)) &
-                         - F4 * (fh(i-1,j,k)+fh(i+1,j,k)) &
-                         + F6 *  fh(i,j,k) )
-! y direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dY/cof * (     &
-                                (fh(i,j-2,k)+fh(i,j+2,k)) &
-                         - F4 * (fh(i,j-1,k)+fh(i,j+1,k)) &
-                         + F6 *  fh(i,j,k) )
-! z direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dZ/cof * (     &
-                                (fh(i,j,k-2)+fh(i,j,k+2)) &
-                         - F4 * (fh(i,j,k-1)+fh(i,j,k+1)) &
-                         + F6 *  fh(i,j,k) )
-
-  endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-end subroutine kodis
-
-#elif (ghost_width == 3)
 ! fourth order code
 
 !---------------------------------------------------------------------------------------------
@@ -157,39 +61,17 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
   if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
   if(Symmetry == OCTANT .and. dabs(X(1)) < dX) imin = -2
   if(Symmetry == OCTANT .and. dabs(Y(1)) < dY) jmin = -2
-
+  !print*,'imin,jmin,kmin=',imin,jmin,kmin
   call symmetry_bd(3,ex,f,fh,SoA)
 
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
+  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
-#if 0     
-! x direction
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dX/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)            )
-! y direction
 
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dY/cof * (     &
-                              (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)            )
-! z direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dZ/cof * (     &
-                              (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)            )
-#else
 ! calculation order if important ?
    f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/cof *( (     &
                               (fh(i-3,j,k)+fh(i+3,j,k)) - &
@@ -206,7 +88,7 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
                           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
+
   endif
 
   enddo
@@ -217,220 +99,6 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
 
   end subroutine kodis
 
-#elif (ghost_width == 4)
-! sixth order code
-!------------------------------------------------------------------------------------------------------------------------------
-!usual type Kreiss-Oliger type numerical dissipation
-!We support cell center only
-!  (D_+D_-)^4 =
-!   f(i-4) - 8 f(i-3) + 28 f(i-2) - 56 f(i-1) + 70 f(i) - 56 f(i+1) + 28 f(i+2) - 8 f(i+3) + f(i+4)
-! ----------------------------------------------------------------------------------------------------------
-!                                              dx^8
-!------------------------------------------------------------------------------------------------------------------------------
-! do not add dissipation near boundary
-subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
 
-implicit none
-! argument variables
-integer,intent(in) :: Symmetry
-integer,dimension(3),intent(in)::ex
-real*8, dimension(1:3), intent(in) :: SoA
-double precision,intent(in),dimension(ex(1))::X
-double precision,intent(in),dimension(ex(2))::Y
-double precision,intent(in),dimension(ex(3))::Z
-double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
-double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
-real*8,intent(in) :: eps
 
-!~~~~~~ other variables
 
-  real*8 :: dX,dY,dZ
-  real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-  real*8,parameter   :: cof = 2.56d2 ! 2^8
-  real*8,  parameter :: F8=8.d0,F28=2.8d1,F56=5.6d1,F70=7.d1
-  integer::i,j,k
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-  
-  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 = -3
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
-
-  call symmetry_bd(4,ex,f,fh,SoA)
-
-!   f(i-4) - 8 f(i-3) + 28 f(i-2) - 56 f(i-1) + 70 f(i) - 56 f(i+1) + 28 f(i+2) - 8 f(i+3) + f(i+4)
-! ----------------------------------------------------------------------------------------------------------
-!                                              dx^8
-
-!  note the sign (-1)^r-1, now r=4
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-
-  if(i>imin+3 .and. i < imax-3 .and. &
-     j>jmin+3 .and. j < jmax-3 .and. &
-     k>kmin+3 .and. k < kmax-3) then
-! x direction
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dX/cof * (     &
-                                (fh(i-4,j,k)+fh(i+4,j,k)) &
-                         - F8 * (fh(i-3,j,k)+fh(i+3,j,k)) &
-                         +F28 * (fh(i-2,j,k)+fh(i+2,j,k)) &
-                         -F56 * (fh(i-1,j,k)+fh(i+1,j,k)) &
-                         +F70 *  fh(i,j,k) )
-! y direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dY/cof * (     &
-                                (fh(i,j-4,k)+fh(i,j+4,k)) &
-                         - F8 * (fh(i,j-3,k)+fh(i,j+3,k)) &
-                         +F28 * (fh(i,j-2,k)+fh(i,j+2,k)) &
-                         -F56 * (fh(i,j-1,k)+fh(i,j+1,k)) &
-                         +F70 *  fh(i,j,k) )
-! z direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dZ/cof * (     &
-                                (fh(i,j,k-4)+fh(i,j,k+4)) &
-                         - F8 * (fh(i,j,k-3)+fh(i,j,k+3)) &
-                         +F28 * (fh(i,j,k-2)+fh(i,j,k+2)) &
-                         -F56 * (fh(i,j,k-1)+fh(i,j,k+1)) &
-                         +F70 *  fh(i,j,k) )
-
-  endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-end subroutine kodis
-
-#elif (ghost_width == 5)
-! eighth order code
-!------------------------------------------------------------------------------------------------------------------------------
-!usual type Kreiss-Oliger type numerical dissipation
-!We support cell center only
-! Note the notation D_+ and D_- [P240 of B. Gustafsson, H.-O. Kreiss, and J. Oliger, Time
-! Dependent Problems and Difference Methods (Wiley, New York, 1995).]
-! D_+ = (f(i+1) - f(i))/h
-! D_- = (f(i) - f(i-1))/h
-! then we have D_+D_- = D_-D_+ = (f(i+1) - 2f(i) + f(i-1))/h^2
-! for nth order accurate finite difference code, we need r =n/2+1
-!              D_+^rD_-^r = (D_+D_-)^r 
-! following the tradiation of PRD 77, 024027 (BB's calibration paper, Eq.(64),
-!  correct some typo according to above book) :
-! + eps*(-1)^(r-1)*h^(2r-1)/2^(2r)*(D_+D_-)^r 
-!
-!
-! this is for 8th order accurate finite difference scheme
-!  (D_+D_-)^5 =
-!  f(i-5) - 10 f(i-4) + 45 f(i-3) - 120 f(i-2) + 210 f(i-1) - 252 f(i) + 210 f(i+1) - 120 f(i+2) + 45 f(i+3) - 10 f(i+4) + f(i+5)
-! -------------------------------------------------------------------------------------------------------------------------------
-!                                                              dx^10
-!---------------------------------------------------------------------------------------------------------------------------------
-! do not add dissipation near boundary
-subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
-
-implicit none
-! argument variables
-integer,intent(in) :: Symmetry
-integer,dimension(3),intent(in)::ex
-real*8, dimension(1:3), intent(in) :: SoA
-double precision,intent(in),dimension(ex(1))::X
-double precision,intent(in),dimension(ex(2))::Y
-double precision,intent(in),dimension(ex(3))::Z
-double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
-double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
-real*8,intent(in) :: eps
-
-!~~~~~~ other variables
-
-  real*8 :: dX,dY,dZ
-  real*8,dimension(-4:ex(1),-4:ex(2),-4:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-  real*8,parameter   :: cof = 1.024d3 ! 2^2r = 2^10
-  real*8,  parameter :: F10=1.d1,F45=4.5d1,F120=1.2d2,F210=2.1d2,F252=2.52d2
-  integer::i,j,k
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-  
-  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 = -4
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -4
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -4
-
-  call symmetry_bd(5,ex,f,fh,SoA)
-
-!  f(i-5) - 10 f(i-4) + 45 f(i-3) - 120 f(i-2) + 210 f(i-1) - 252 f(i) + 210 f(i+1) - 120 f(i+2) + 45 f(i+3) - 10 f(i+4) + f(i+5)
-! -------------------------------------------------------------------------------------------------------------------------------
-!                                                              dx^10
-
-!  note the sign (-1)^r-1, now r=5
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-
-  if(i>imin+4 .and. i < imax-4 .and. &
-     j>jmin+4 .and. j < jmax-4 .and. &
-     k>kmin+4 .and. k < kmax-4) then
-! x direction
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dX/cof * (      &
-                                 (fh(i-5,j,k)+fh(i+5,j,k)) &
-                         - F10 * (fh(i-4,j,k)+fh(i+4,j,k)) &
-                         + F45 * (fh(i-3,j,k)+fh(i+3,j,k)) &
-                         - F120* (fh(i-2,j,k)+fh(i+2,j,k)) &
-                         + F210* (fh(i-1,j,k)+fh(i+1,j,k)) &
-                         - F252 * fh(i,j,k) )
-! y direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dY/cof * (      &
-                                 (fh(i,j-5,k)+fh(i,j+5,k)) &
-                         - F10 * (fh(i,j-4,k)+fh(i,j+4,k)) &
-                         + F45 * (fh(i,j-3,k)+fh(i,j+3,k)) &
-                         - F120* (fh(i,j-2,k)+fh(i,j+2,k)) &
-                         + F210* (fh(i,j-1,k)+fh(i,j+1,k)) &
-                         - F252 * fh(i,j,k) )
-! z direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dZ/cof * (      &
-                                 (fh(i,j,k-5)+fh(i,j,k+5)) &
-                         - F10 * (fh(i,j,k-4)+fh(i,j,k+4)) &
-                         + F45 * (fh(i,j,k-3)+fh(i,j,k+3)) &
-                         - F120* (fh(i,j,k-2)+fh(i,j,k+2)) &
-                         + F210* (fh(i,j,k-1)+fh(i,j,k+1)) &
-                         - F252 * fh(i,j,k) )
-
-  endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-end subroutine kodis
-
-#endif  

AMSS_NCKU_source/kodiss_sh.f90

@@ -80,8 +80,7 @@ real*8,intent(in) :: eps
 !                       dx^4
 
 !  note the sign (-1)^r-1, now r=2
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
+  do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
 
@@ -179,8 +178,7 @@ real*8,intent(in) :: eps
 !                       dx^4
 
 !  note the sign (-1)^r-1, now r=2
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
+  do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
 
@@ -275,8 +273,7 @@ integer, parameter :: NO_SYMM=0, EQ_SYMM=1, OCTANT=2
 
   call symmetry_stbd(2,ex,f,fh,SoA)
 
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
+  do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
 
@@ -372,8 +369,7 @@ integer, parameter :: NO_SYMM=0, EQ_SYMM=1, OCTANT=2
 
   call symmetry_stbd(3,ex,f,fh,SoA)
 
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
+  do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
 
@@ -514,8 +510,7 @@ integer, parameter :: NO_SYMM=0, EQ_SYMM=1, OCTANT=2
 
   call symmetry_stbd(3,ex,f,fh,SoA)
 
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
+  do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
 
@@ -603,8 +598,7 @@ integer, parameter :: NO_SYMM=0, EQ_SYMM=1, OCTANT=2
 
   call symmetry_stbd(3,ex,f,fh,SoA)
 
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
+  do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
 
@@ -700,8 +694,7 @@ real*8,intent(in) :: eps
 !                                              dx^8
 
 !  note the sign (-1)^r-1, now r=4
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
+  do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
 
@@ -801,8 +794,7 @@ integer, parameter :: NO_SYMM=0, EQ_SYMM=1, OCTANT=2
 
   call symmetry_stbd(4,ex,f,fh,SoA)
 
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
+  do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
 
@@ -911,8 +903,7 @@ real*8,intent(in) :: eps
 !                                                              dx^10
 
 !  note the sign (-1)^r-1, now r=5
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
+  do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
 
@@ -1015,8 +1006,7 @@ integer, parameter :: NO_SYMM=0, EQ_SYMM=1, OCTANT=2
 
   call symmetry_stbd(5,ex,f,fh,SoA)
 
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)
+  do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)
 

AMSS_NCKU_source/lopsidediff.f90

@@ -7,164 +7,7 @@
 ! Vertex or Cell is distinguished in routine symmetry_bd which locates in
 ! file "fmisc.f90"
 
-#if (ghost_width == 2)
-! second order code
 
-!-----------------------------------------------------------------------------
-!         v
-! D f = ------[ - 3 f  + 4 f   - f     ]
-!  i     2dx         i      i+v   i+2v
-!
-! where
-!
-!        i
-!      |B |
-! v = -----
-!        i
-!       B
-!
-!-----------------------------------------------------------------------------
-subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
-  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
-
-!~~~~~~> local variables:
-! note index -1,0, so we have 2 extra points
-  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8 :: dX,dY,dZ
-  real*8 :: d2dx,d2dy,d2dz
-  real*8,  parameter :: ZEO=0.d0,ONE=1.d0,TWO=2.d0,THR=3.d0,FOUR=4.d0
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-
-  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 = -1
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
-
-  call symmetry_bd(2,ex,f,fh,SoA)
-
-! upper bound set ex-1 only for efficiency, 
-! the loop body will set ex 0 also
-  !$omp parallel do collapse(2) private(i,j,k)
-  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+2 <= imax .and. i >= imin)then
-!         v
-! D f = ------[ - 3 f  + 4 f   - f     ]
-!  i     2dx         i      i+v   i+2v
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
-                  Sfx(i,j,k)*d2dx*(-THR*fh(i,j,k)+FOUR*fh(i+1,j,k)-fh(i+2,j,k))
-       elseif(i+1 <= imax .and. i >= imin)then
-!         v
-! D f = ------[ - f  + f   ]
-!  i      dx       i    i+v
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
-                  Sfx(i,j,k)*d2dx*(-fh(i,j,k)+fh(i+1,j,k))
-
-       endif
-
-    elseif(Sfx(i,j,k) <= ZEO)then
-      if( i-2 >= imin .and. i <= imax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
-                  Sfx(i,j,k)*d2dx*(-THR*fh(i,j,k)+FOUR*fh(i-1,j,k)-fh(i-2,j,k))
-      elseif(i-1 >= imin .and. i <= imax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
-                  Sfx(i,j,k)*d2dx*(-fh(i,j,k)+fh(i-1,j,k))
-      endif
-
-! set imax and imin 0
-    endif
-
-! y direction   
-    if(Sfy(i,j,k) >= ZEO)then
-       if( j+2 <= jmax .and. j >= jmin)then
-!         v
-! D f = ------[ - 3 f  + 4 f   - f     ]
-!  i     2dx         i      i+v   i+2v
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
-                  Sfy(i,j,k)*d2dy*(-THR*fh(i,j,k)+FOUR*fh(i,j+1,k)-fh(i,j+2,k))
-       elseif(j+1 <= jmax .and. j >= jmin)then
-!         v
-! D f = ------[ - f  + f   ]
-!  i      dx       i    i+v
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
-                  Sfy(i,j,k)*d2dy*(-fh(i,j,k)+fh(i,j+1,k))
-       endif
-
-    elseif(Sfy(i,j,k) <= ZEO)then
-      if( j-2 >= jmin .and. j <= jmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
-                  Sfy(i,j,k)*d2dy*(-THR*fh(i,j,k)+FOUR*fh(i,j-1,k)-fh(i,j-2,k))
-      elseif(j-1 >= jmin .and. j <= jmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
-                  Sfy(i,j,k)*d2dy*(-fh(i,j,k)+fh(i,j-1,k))
-      endif
-
-! set jmin and jmax 0
-     endif
-!! z direction   
-    if(Sfz(i,j,k) >= ZEO)then
-      if( k+2 <= kmax .and. k >= kmin)then
-!         v
-! D f = ------[ - 3 f  + 4 f   - f     ]
-!  i     2dx         i      i+v   i+2v
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
-                  Sfz(i,j,k)*d2dz*(-THR*fh(i,j,k)+FOUR*fh(i,j,k+1)-fh(i,j,k+2))
-       elseif(k+1 <= kmax .and. k >= kmin)then
-!         v
-! D f = ------[ - f  + f   ]
-!  i      dx       i    i+v
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
-                  Sfz(i,j,k)*d2dz*(-fh(i,j,k)+fh(i,j,k+1))
-       endif
-
-    elseif(Sfz(i,j,k) <= ZEO)then
-      if( k-2 >= kmin .and. k <= kmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
-                  Sfz(i,j,k)*d2dz*(-THR*fh(i,j,k)+FOUR*fh(i,j,k-1)-fh(i,j,k-2))
-      elseif(k-1 >= kmin .and. k <= kmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
-                  Sfz(i,j,k)*d2dz*(-fh(i,j,k)+fh(i,j,k-1))
-      endif
-
-! set kmin and kmax 0
-     endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-  end subroutine lopsided
-
-#elif (ghost_width == 3)
 ! fourth order code
 
 !-----------------------------------------------------------------------------
@@ -234,93 +77,10 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
 
 ! upper bound set ex-1 only for efficiency, 
 ! the loop body will set ex 0 also
-  !$omp parallel do collapse(2) private(i,j,k)
-  do k=1,ex(3)-1
+  do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
-#if 0  
-!! old code
-! x direction   
-    if(Sfx(i,j,k) >= ZEO .and. i+3 <= imax .and. i-1 >= imin)then
-!         v
-! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
-!  i     12dx       i-v      i      i+v     i+2v    i+3v
-     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(Sfx(i,j,k) <= ZEO .and. i-3 >= imin .and. 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))
-
-     elseif(i+2 <= imax .and. i-2 >= imin)then
-!
-!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
-!  fx(i) = ---------------------------------------------
-!                             12 dx
-     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 .and. i-1 >= imin)then
-!
-!              - f(i-1) + f(i+1)
-!  fx(i) = --------------------------------
-!                     2 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
-
-! set imax and imin 0
-    endif
-
-! y direction   
-    if(Sfy(i,j,k) >= ZEO .and. j+3 <= jmax .and. j-1 >= jmin)then
-!         v
-! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
-!  i     12dx       i-v      i      i+v     i+2v    i+3v
-     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(Sfy(i,j,k) <= ZEO .and. j-3 >= jmin .and. 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))
-
-     elseif(j+2 <= jmax .and. 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 <= jmax .and. j-1 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
-! set jmin and jmax 0
-     endif
-!! z direction   
-    if(Sfz(i,j,k) >= ZEO .and. k+3 <= kmax .and. k-1 >= kmin)then
-!         v
-! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
-!  i     12dx       i-v      i      i+v     i+2v    i+3v
-     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(Sfz(i,j,k) <= ZEO .and. k-3 >= kmin .and. 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))
-
-     elseif(k+2 <= kmax .and. 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 <= kmax .and. k-1 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
-! set kmin and kmax 0
-     endif
-#else
 !! new code, 2012dec27, based on bam
 ! x direction   
     if(Sfx(i,j,k) > ZEO)then
@@ -480,7 +240,6 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
 ! set kmax and kmin 0
      endif
    endif
-#endif
   enddo
   enddo
   enddo
@@ -488,419 +247,3 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
   return
 
   end subroutine lopsided
-
-#elif (ghost_width == 4)
-! sixth order code
-! Compute advection terms in right hand sides of field equations
-!         v
-! D f = ------[ 2f     - 24f    - 35f  + 80f    - 30f     + 8f     - f    ]
-!  i     60dx     i-2v      i-v      i      i+v      i+2v     i+3v    i+4v
-!
-! where
-!
-!        i
-!      |B |
-! v = -----
-!        i
-!       B
-!
-!-----------------------------------------------------------------------------
-subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
-  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
-
-!~~~~~~> local variables:
-
-  real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8 :: dX,dY,dZ
-  real*8 :: d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
-  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
-  real*8,  parameter :: TWO=2.d0,F24=2.4d1,F35=3.5d1,F80=8.d1,F30=3.d1,EIT=8.d0
-  real*8,  parameter ::  F9=9.d0,F45=4.5d1,F12=1.2d1
-  real*8,  parameter ::  F10=1.d1,F77=7.7d1,F150=1.5d2,F100=1.d2,F50=5.d1,F15=1.5d1
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-
-  d60dx = ONE/F60/dX
-  d60dy = ONE/F60/dY
-  d60dz = ONE/F60/dZ
-
-  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 = -3
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
-
-  call symmetry_bd(4,ex,f,fh,SoA)
-
-! upper bound set ex-1 only for efficiency, 
-! the loop body will set ex 0 also
-  !$omp parallel do collapse(2) private(i,j,k)
-  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 .and. i+4 <= imax .and. i-2 >= imin)then
-!         v
-! D f = ------[ 2f     - 24f    - 35f  + 80f    - 30f     + 8f     - f    ]
-!  i     60dx     i-2v      i-v      i      i+v      i+2v     i+3v    i+4v
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                             &
-                  Sfx(i,j,k)*d60dx*(TWO*fh(i-2,j,k)-F24*fh(i-1,j,k)-F35*fh(i,j,k)+F80*fh(i+1,j,k) &
-                                   -F30*fh(i+2,j,k)+EIT*fh(i+3,j,k)-    fh(i+4,j,k))
-    elseif(Sfx(i,j,k) >= ZEO .and. i+5 <= imax .and. i-1 >= imin)then
-!         v
-! D f = ------[-10f    - 77f  + 150f    - 100f     + 50f     -15f     + 2f    ]
-!  i     60dx      i-v      i       i+v       i+2v      i+3v     i+4v    i+5v
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
-                  Sfx(i,j,k)*d60dx*(-F10*fh(i-1,j,k)-F77*fh(i  ,j,k)+F150*fh(i+1,j,k)-F100*fh(i+2,j,k) &
-                                    +F50*fh(i+3,j,k)-F15*fh(i+4,j,k)+ TWO*fh(i+5,j,k))
-
-    elseif(Sfx(i,j,k) <= ZEO .and. i-4 >= imin .and. i+2 <= imax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
-                  Sfx(i,j,k)*d60dx*(TWO*fh(i+2,j,k)-F24*fh(i+1,j,k)-F35*fh(i,j,k)+F80*fh(i-1,j,k) &
-                                   -F30*fh(i-2,j,k)+EIT*fh(i-3,j,k)-    fh(i-4,j,k))
-    elseif(Sfx(i,j,k) <= ZEO .and. i-5 >= imin .and. i+1 <= imax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
-                  Sfx(i,j,k)*d60dx*(-F10*fh(i+1,j,k)-F77*fh(i  ,j,k)+F150*fh(i-1,j,k)-F100*fh(i-2,j,k) &
-                                    +F50*fh(i-3,j,k)-F15*fh(i-4,j,k)+ TWO*fh(i-5,j,k))
-
-     elseif(i+3 <= imax .and. i-3 >= imin)then
-!           - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
-!  fx(i) = -----------------------------------------------------------------
-!                                        60 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
-                  Sfx(i,j,k)*d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
-
-     elseif(i+2 <= imax .and. i-2 >= imin)then
-!
-!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
-!  fx(i) = ---------------------------------------------
-!                             12 dx
-     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 .and. i-1 >= imin)then
-!
-!              - f(i-1) + f(i+1)
-!  fx(i) = --------------------------------
-!                     2 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
-
-! set imax and imin 0
-    endif
-
-! y direction   
-     if(Sfy(i,j,k) >= ZEO .and. j+4 <= jmax .and. j-2 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                   &
-                  Sfy(i,j,k)*d60dy*(TWO*fh(i,j-2,k)-F24*fh(i,j-1,k)-F35*fh(i,j,k)+F80*fh(i,j+1,k) &
-                                   -F30*fh(i,j+2,k)+EIT*fh(i,j+3,k)-    fh(i,j+4,k))
-     elseif(Sfy(i,j,k) >= ZEO .and. j+5 <= jmax .and. j-1 >= jmin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
-                  Sfy(i,j,k)*d60dy*(-F10*fh(i,j-1,k)-F77*fh(i,j  ,k)+F150*fh(i,j+1,k)-F100*fh(i,j+2,k) &
-                                    +F50*fh(i,j+3,k)-F15*fh(i,j+4,k)+ TWO*fh(i,j+5,k))
-
-     elseif(Sfy(i,j,k) <= ZEO .and. j-4 >= jmin .and. j+2 <= jmax)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
-                  Sfy(i,j,k)*d60dy*(TWO*fh(i,j+2,k)-F24*fh(i,j+1,k)-F35*fh(i,j,k)+F80*fh(i,j-1,k) &
-                                   -F30*fh(i,j-2,k)+EIT*fh(i,j-3,k)-    fh(i,j-4,k))
-
-     elseif(Sfy(i,j,k) <= ZEO .and. j-5 >= jmin .and. j+1 <= jmax)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
-                  Sfy(i,j,k)*d60dy*(-F10*fh(i,j+1,k)-F77*fh(i,j  ,k)+F150*fh(i,j-1,k)-F100*fh(i,j-2,k) &
-                                    +F50*fh(i,j-3,k)-F15*fh(i,j-4,k)+ TWO*fh(i,j-5,k))
-
-     elseif(j+3 <= jmax .and. j-3 >= jmin)then
-          
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
-                  Sfy(i,j,k)*d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
-
-     elseif(j+2 <= jmax .and. 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 <= jmax .and. j-1 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
-! set jmin and jmax 0
-     endif
-!! z direction   
-     if(Sfz(i,j,k) >= ZEO .and. k+4 <= kmax .and. k-2 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                   &
-                  Sfz(i,j,k)*d60dz*(TWO*fh(i,j,k-2)-F24*fh(i,j,k-1)-F35*fh(i,j,k)+F80*fh(i,j,k+1) &
-                                   -F30*fh(i,j,k+2)+EIT*fh(i,j,k+3)-    fh(i,j,k+4))
-     elseif(Sfz(i,j,k) >= ZEO .and. k+5 <= kmax .and. k-1 >= kmin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
-                  Sfz(i,j,k)*d60dz*(-F10*fh(i,j,k-1)-F77*fh(i,j,k  )+F150*fh(i,j,k+1)-F100*fh(i,j,k+2) &
-                                    +F50*fh(i,j,k+3)-F15*fh(i,j,k+4)+ TWO*fh(i,j,k+5))
-
-     elseif(Sfz(i,j,k) <= ZEO .and. k-4 >= kmin .and. k+2 <= kmax)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
-                  Sfz(i,j,k)*d60dz*(TWO*fh(i,j,k+2)-F24*fh(i,j,k+1)-F35*fh(i,j,k)+F80*fh(i,j,k-1) &
-                                   -F30*fh(i,j,k-2)+EIT*fh(i,j,k-3)-    fh(i,j,k-4))
-
-     elseif(Sfz(i,j,k) <= ZEO .and. k-5 >= kmin .and. k+1 <= kmax)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
-                  Sfz(i,j,k)*d60dz*(-F10*fh(i,j,k+1)-F77*fh(i,j,k  )+F150*fh(i,j,k-1)-F100*fh(i,j,k-2) &
-                                    +F50*fh(i,j,k-3)-F15*fh(i,j,k-4)+ TWO*fh(i,j,k-5))
-     
-     elseif(k+3 <= kmax .and. k-3 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
-                  Sfz(i,j,k)*d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
-
-     elseif(k+2 <= kmax .and. 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 <= kmax .and. k-1 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
-! set kmin and kmax 0
-     endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-  end subroutine lopsided
-
-#elif (ghost_width == 5)
-! eighth order code
-!-----------------------------------------------------------------------------
-! PRD 77, 024034 (2008)
-! Compute advection terms in right hand sides of field equations
-!        v [ - 5 f(i-3v) + 60 f(i-2v) - 420 f(i-v) - 378 f(i) + 1050 f(i+v) - 420 f(i+2v) + 140 f(i+3v) - 30 f(i+4v) + 3 f(i+5v)]
-! D f = --------------------------------------------------------------------------------------------------------------------------
-!  i                                                             840 dx           
-!
-! where
-!
-!        i
-!      |B |
-! v = -----
-!        i
-!       B
-!
-!-----------------------------------------------------------------------------
-subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
-  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
-
-!~~~~~~> local variables:
-
-  real*8,dimension(-4:ex(1),-4:ex(2),-4:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8 :: dX,dY,dZ
-  real*8 :: d840dx,d840dy,d840dz,d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
-  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
-  real*8,  parameter :: TWO=2.d0,F30=3.d1,EIT=8.d0
-  real*8,  parameter ::  F9=9.d0,F45=4.5d1,F12=1.2d1,F140=1.4d2,THR=3.d0
-  real*8,  parameter :: F840=8.4d2,F5=5.d0,F420=4.2d2,F378=3.78d2,F1050=1.05d3
-  real*8,  parameter :: F32=3.2d1,F168=1.68d2,F672=6.72d2
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-
-  d840dx = ONE/F840/dX
-  d840dy = ONE/F840/dY
-  d840dz = ONE/F840/dZ
-
-  d60dx = ONE/F60/dX
-  d60dy = ONE/F60/dY
-  d60dz = ONE/F60/dZ
-
-  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 = -4
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -4
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -4
-
-  call symmetry_bd(5,ex,f,fh,SoA)
-
-! upper bound set ex-1 only for efficiency, 
-! the loop body will set ex 0 also
-  !$omp parallel do collapse(2) private(i,j,k)
-  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 .and. i+5 <= imax .and. i-3 >= imin)then
-!        v [ - 5 f(i-3v) + 60 f(i-2v) - 420 f(i-v) - 378 f(i) + 1050 f(i+v) - 420 f(i+2v) + 140 f(i+3v) - 30 f(i+4v) + 3 f(i+5v)]
-! D f = --------------------------------------------------------------------------------------------------------------------------
-!  i                                                             840 dx    
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
-                  Sfx(i,j,k)*d840dx*(-F5*fh(i-3,j,k)+F60 *fh(i-2,j,k)-F420*fh(i-1,j,k)-F378*fh(i  ,j,k) &
-                                  +F1050*fh(i+1,j,k)-F420*fh(i+2,j,k)+F140*fh(i+3,j,k)-F30 *fh(i+4,j,k)+THR*fh(i+5,j,k))
-
-    elseif(Sfx(i,j,k) <= ZEO .and. i-5 >= imin .and. i+3 <= imax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                          &
-                  Sfx(i,j,k)*d840dx*(-F5*fh(i+3,j,k)+F60 *fh(i+2,j,k)-F420*fh(i+1,j,k)-F378*fh(i   ,j,k) &
-                                  +F1050*fh(i-1,j,k)-F420*fh(i-2,j,k)+F140*fh(i-3,j,k)- F30*fh(i-4,j,k)+THR*fh(i-5,j,k))
-
-    elseif(i+4 <= imax .and. i-4 >= imin)then
-!           3 f(i-4) - 32 f(i-3) + 168 f(i-2) - 672 f(i-1) + 672 f(i+1) - 168 f(i+2) + 32 f(i+3) - 3 f(i+4)
-!  fx(i) = -------------------------------------------------------------------------------------------------
-!                                                        840 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
-                  Sfx(i,j,k)*d840dx*( THR*fh(i-4,j,k)-F32 *fh(i-3,j,k)+F168*fh(i-2,j,k)-F672*fh(i-1,j,k)+    &
-                                     F672*fh(i+1,j,k)-F168*fh(i+2,j,k)+F32 *fh(i+3,j,k)-THR *fh(i+4,j,k))
-
-     elseif(i+3 <= imax .and. i-3 >= imin)then
-!           - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
-!  fx(i) = -----------------------------------------------------------------
-!                                        60 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
-                  Sfx(i,j,k)*d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
-
-     elseif(i+2 <= imax .and. i-2 >= imin)then
-!
-!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
-!  fx(i) = ---------------------------------------------
-!                             12 dx
-     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 .and. i-1 >= imin)then
-!
-!              - f(i-1) + f(i+1)
-!  fx(i) = --------------------------------
-!                     2 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
-
-! set imax and imin 0
-    endif
-
-! y direction   
-    if(Sfy(i,j,k) >= ZEO .and. j+5 <= jmax .and. j-3 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
-                  Sfy(i,j,k)*d840dy*(-F5*fh(i,j-3,k)+F60 *fh(i,j-2,k)-F420*fh(i,j-1,k)-F378*fh(i,j  ,k) &
-                                  +F1050*fh(i,j+1,k)-F420*fh(i,j+2,k)+F140*fh(i,j+3,k)-F30 *fh(i,j+4,k)+THR*fh(i,j+5,k))
-
-    elseif(Sfy(i,j,k) <= ZEO .and. j-5 >= jmin .and. j+3 <= jmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                         &
-                  Sfy(i,j,k)*d840dy*(-F5*fh(i,j+3,k)+F60 *fh(i,j+2,k)-F420*fh(i,j+1,k)-F378*fh(i,j  ,k) &
-                                  +F1050*fh(i,j-1,k)-F420*fh(i,j-2,k)+F140*fh(i,j-3,k)- F30*fh(i,j-4,k)+THR*fh(i,j-5,k))
-
-    elseif(j+4 <= jmax .and. j-4 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
-                  Sfy(i,j,k)*d840dy*( THR*fh(i,j-4,k)-F32 *fh(i,j-3,k)+F168*fh(i,j-2,k)-F672*fh(i,j-1,k)+    &
-                                     F672*fh(i,j+1,k)-F168*fh(i,j+2,k)+F32 *fh(i,j+3,k)-THR *fh(i,j+4,k))
-
-     elseif(j+3 <= jmax .and. j-3 >= jmin)then
-          
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
-                  Sfy(i,j,k)*d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
-
-     elseif(j+2 <= jmax .and. 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 <= jmax .and. j-1 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
-! set jmin and jmax 0
-     endif
-!! z direction   
-    if(Sfz(i,j,k) >= ZEO .and. k+5 <= kmax .and. k-3 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
-                  Sfz(i,j,k)*d840dz*(-F5*fh(i,j,k-3)+F60 *fh(i,j,k-2)-F420*fh(i,j,k-1)-F378*fh(i,j,k  ) &
-                                  +F1050*fh(i,j,k+1)-F420*fh(i,j,k+2)+F140*fh(i,j,k+3)-F30 *fh(i,j,k+4)+THR*fh(i,j,k+5))
-
-    elseif(Sfz(i,j,k) <= ZEO .and. k-5 >= kmin .and. k+3 <= kmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                         &
-                  Sfz(i,j,k)*d840dz*(-F5*fh(i,j,k+3)+F60 *fh(i,j,k+2)-F420*fh(i,j,k+1)-F378*fh(i,j,k  ) &
-                                  +F1050*fh(i,j,k-1)-F420*fh(i,j,k-2)+F140*fh(i,j,k-3)- F30*fh(i,j,k-4)+THR*fh(i,j,k-5))
-
-    elseif(k+4 <= kmax .and. k-4 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
-                  Sfz(i,j,k)*d840dz*( THR*fh(i,j,k-4)-F32 *fh(i,j,k-3)+F168*fh(i,j,k-2)-F672*fh(i,j,k-1)+    &
-                                     F672*fh(i,j,k+1)-F168*fh(i,j,k+2)+F32 *fh(i,j,k+3)-THR *fh(i,j,k+4))
-     
-     elseif(k+3 <= kmax .and. k-3 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
-                  Sfz(i,j,k)*d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
-
-     elseif(k+2 <= kmax .and. 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 <= kmax .and. k-1 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
-! set kmin and kmax 0
-     endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-  end subroutine lopsided
-
-#endif  

AMSS_NCKU_source/makefile

@@ -95,8 +95,8 @@ $(CUDAFILES): bssn_gpu.h gpu_mem.h gpu_rhsSS_mem.h
 misc.o : zbesh.o
 
 # projects
-ABE: $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -qopenmp -o $@ $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
+ABE: $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) 
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
 	
 ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
 	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)

AMSS_NCKU_source/makefile.inc

@@ -6,23 +6,24 @@
 ## Intel oneAPI version with oneMKL (Optimized for performance)
 filein  = -I/usr/include/ -I${MKLROOT}/include
 
-## Using OpenMP-threaded MKL for parallel performance
+## Using sequential MKL (OpenMP disabled for better single-threaded performance)
 ## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_intel_thread -lmkl_core -liomp5 -lifcore -limf -lpthread -lm -ldl
+LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl
 
-## Aggressive optimization flags + PGO Phase 2 (profile-guided optimization)
-## -fprofile-instr-use: use collected profile data to guide optimization decisions
-##   (branch prediction, basic block layout, inlining, loop unrolling)
-PROFDATA     = /home/amss/AMSS-NCKU/pgo_profile/default.profdata
-CXXAPPFLAGS  = -O3 -march=native -fp-model fast=2 -fma -ipo -qopenmp \
-               -DMPI_STUB -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags  = -O3 -march=native -fp-model fast=2 -fma -ipo -qopenmp \
+## Aggressive optimization flags:
+## -O3: Maximum optimization
+## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
+## -fp-model fast=2: Aggressive floating-point optimizations
+## -fma: Enable fused multiply-add instructions
+CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
+               -Dfortran3 -Dnewc -I${MKLROOT}/include
+f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
                -align array64byte -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx
 CC           = icx
-CLINKER      = icpx
+CLINKER      = mpiicpx 
 
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include

AMSS_NCKU_source/misc.C

@@ -14,11 +14,7 @@ using namespace std;
 #include <string.h>
 #include <math.h>
 #endif
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "misc.h"
 #include "macrodef.h"

AMSS_NCKU_source/misc.h

@@ -24,11 +24,7 @@ using namespace std;
 #include <complex.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 namespace misc
 {

AMSS_NCKU_source/monitor.h

@@ -20,11 +20,7 @@ using namespace std;
 #endif
 #include <time.h>
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 class monitor
 {

AMSS_NCKU_source/mpi_stub.h

@@ -1,153 +0,0 @@
-#ifndef MPI_STUB_H
-#define MPI_STUB_H
-
-/*
- * MPI Stub Header — single-process shim for AMSS-NCKU ABE solver.
- * Provides all MPI types, constants, and functions used in the codebase
- * as no-ops or trivial implementations for nprocs=1, myrank=0.
- */
-
-#include <cstring>
-#include <cstdlib>
-#include <cstdio>
-#include <time.h>
-
-/* ── Types ─────────────────────────────────────────────────────────── */
-
-typedef int MPI_Comm;
-typedef int MPI_Datatype;
-typedef int MPI_Op;
-typedef int MPI_Request;
-typedef int MPI_Group;
-
-typedef struct MPI_Status {
-    int MPI_SOURCE;
-    int MPI_TAG;
-    int MPI_ERROR;
-} MPI_Status;
-
-/* ── Constants ─────────────────────────────────────────────────────── */
-
-#define MPI_COMM_WORLD  0
-
-#define MPI_INT              1
-#define MPI_DOUBLE           2
-#define MPI_DOUBLE_PRECISION 2
-#define MPI_DOUBLE_INT       3
-
-#define MPI_SUM    1
-#define MPI_MAX    2
-#define MPI_MAXLOC 3
-
-#define MPI_STATUS_IGNORE   ((MPI_Status *)0)
-#define MPI_STATUSES_IGNORE ((MPI_Status *)0)
-
-#define MPI_MAX_PROCESSOR_NAME 256
-
-/* ── Helper: sizeof for MPI_Datatype ──────────────────────────────── */
-
-static inline size_t mpi_stub_sizeof(MPI_Datatype type) {
-    switch (type) {
-        case MPI_INT:        return sizeof(int);
-        case MPI_DOUBLE:     return sizeof(double);
-        case MPI_DOUBLE_INT: return sizeof(double) + sizeof(int);
-        default:             return 0;
-    }
-}
-
-/* ── Init / Finalize ──────────────────────────────────────────────── */
-
-static inline int MPI_Init(int *, char ***) { return 0; }
-static inline int MPI_Finalize() { return 0; }
-
-/* ── Communicator queries ─────────────────────────────────────────── */
-
-static inline int MPI_Comm_rank(MPI_Comm, int *rank) { *rank = 0; return 0; }
-static inline int MPI_Comm_size(MPI_Comm, int *size) { *size = 1; return 0; }
-static inline int MPI_Comm_split(MPI_Comm comm, int, int, MPI_Comm *newcomm) {
-    *newcomm = comm;
-    return 0;
-}
-static inline int MPI_Comm_free(MPI_Comm *) { return 0; }
-
-/* ── Group operations ─────────────────────────────────────────────── */
-
-static inline int MPI_Comm_group(MPI_Comm, MPI_Group *group) {
-    *group = 0;
-    return 0;
-}
-static inline int MPI_Group_translate_ranks(MPI_Group, int n,
-        const int *ranks1, MPI_Group, int *ranks2) {
-    for (int i = 0; i < n; ++i) ranks2[i] = ranks1[i];
-    return 0;
-}
-static inline int MPI_Group_free(MPI_Group *) { return 0; }
-
-/* ── Collective operations ────────────────────────────────────────── */
-
-static inline int MPI_Allreduce(const void *sendbuf, void *recvbuf,
-        int count, MPI_Datatype datatype, MPI_Op, MPI_Comm) {
-    std::memcpy(recvbuf, sendbuf, count * mpi_stub_sizeof(datatype));
-    return 0;
-}
-
-static inline int MPI_Iallreduce(const void *sendbuf, void *recvbuf,
-        int count, MPI_Datatype datatype, MPI_Op, MPI_Comm,
-        MPI_Request *request) {
-    std::memcpy(recvbuf, sendbuf, count * mpi_stub_sizeof(datatype));
-    *request = 0;
-    return 0;
-}
-
-static inline int MPI_Bcast(void *, int, MPI_Datatype, int, MPI_Comm) {
-    return 0;
-}
-
-static inline int MPI_Barrier(MPI_Comm) { return 0; }
-
-/* ── Point-to-point (never reached with nprocs=1) ─────────────────── */
-
-static inline int MPI_Send(const void *, int, MPI_Datatype, int, int, MPI_Comm) {
-    return 0;
-}
-static inline int MPI_Recv(void *, int, MPI_Datatype, int, int, MPI_Comm, MPI_Status *) {
-    return 0;
-}
-static inline int MPI_Isend(const void *, int, MPI_Datatype, int, int, MPI_Comm,
-        MPI_Request *req) {
-    *req = 0;
-    return 0;
-}
-static inline int MPI_Irecv(void *, int, MPI_Datatype, int, int, MPI_Comm,
-        MPI_Request *req) {
-    *req = 0;
-    return 0;
-}
-
-/* ── Completion ───────────────────────────────────────────────────── */
-
-static inline int MPI_Wait(MPI_Request *, MPI_Status *) { return 0; }
-static inline int MPI_Waitall(int, MPI_Request *, MPI_Status *) { return 0; }
-
-/* ── Utility ──────────────────────────────────────────────────────── */
-
-static inline int MPI_Abort(MPI_Comm, int error_code) {
-    std::fprintf(stderr, "MPI_Abort called with error code %d\n", error_code);
-    std::exit(error_code);
-    return 0;
-}
-
-static inline double MPI_Wtime() {
-    struct timespec ts;
-    clock_gettime(CLOCK_MONOTONIC, &ts);
-    return (double)ts.tv_sec + (double)ts.tv_nsec * 1.0e-9;
-}
-
-static inline int MPI_Get_processor_name(char *name, int *resultlen) {
-    const char *stub_name = "localhost";
-    std::strcpy(name, stub_name);
-    *resultlen = (int)std::strlen(stub_name);
-    return 0;
-}
-
-#endif /* MPI_STUB_H */

AMSS_NCKU_source/parameters.h

@@ -24,11 +24,7 @@ using namespace std;
 #include <map.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 namespace parameters
 {

AMSS_NCKU_source/perf.h

@@ -30,11 +30,7 @@ using namespace std;
 #include <sys/time.h>
 #include <sys/resource.h>
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 /* Real time */
 #define TimerSignal SIGALRM

AMSS_NCKU_source/rungekutta4_rout.f90

@@ -109,33 +109,23 @@
 
   if( RK4 == 0 ) then
 
-   !$omp parallel workshare
    f1 = f0 + HLF * dT * f_rhs
-   !$omp end parallel workshare
 
   elseif(RK4 == 1 ) then
 
-   !$omp parallel workshare
    f_rhs = f_rhs + TWO * f1
-   !$omp end parallel workshare
-   !$omp parallel workshare
+
    f1 = f0 + HLF * dT * f1
-   !$omp end parallel workshare
 
   elseif(RK4 == 2 ) then
 
-   !$omp parallel workshare
    f_rhs = f_rhs + TWO * f1
-   !$omp end parallel workshare
-   !$omp parallel workshare
+
    f1 = f0 +       dT * f1
-   !$omp end parallel workshare
 
   elseif( RK4 == 3 ) then
-
-   !$omp parallel workshare
+ 
    f1 = f0 +F1o6 * dT *(f1 + f_rhs)
-   !$omp end parallel workshare
 
   else
 
@@ -144,7 +134,7 @@
 
   endif
 
-  return
+  return   
 
   end subroutine rungekutta4_rout
 !-----------------------------------------------------------------------------
@@ -225,19 +215,15 @@
 
   if( RK4 == 0 ) then
 
-   !$omp parallel workshare
    f1 = f0 + dT * f_rhs
-   !$omp end parallel workshare
 
   else
 
-   !$omp parallel workshare
    f1 = f0 + HLF * dT * (f1+f_rhs)
-   !$omp end parallel workshare
 
   endif
 
-  return
+  return   
 
   end subroutine icn_rout
 !~~~~~~~~~~~~~~~~~~  
@@ -253,10 +239,8 @@
   real*8, dimension(ex(1),ex(2),ex(3)),intent(in) ::f_rhs
   real*8, dimension(ex(1),ex(2),ex(3)),intent(out) ::f1
 
-  !$omp parallel workshare
    f1 = f0 + dT * f_rhs
-  !$omp end parallel workshare
 
-  return
+  return   
 
   end subroutine euler_rout

AMSS_NCKU_source/scalar_class.h

@@ -19,11 +19,7 @@ using namespace std;
 #include <math.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "cgh.h"
 #include "ShellPatch.h"

AMSS_NCKU_source/scalarwaves.C

@@ -18,11 +18,7 @@ using namespace std;
 #include <math.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "misc.h"
 #include "microdef.h"

AMSS_NCKU_source/setup.C

@@ -3,11 +3,7 @@
 #include <math.h>
 #include <string.h>
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "util_Table.h"
 #include "cctk.h"

AMSS_NCKU_source/surface_integral.C

@@ -20,11 +20,7 @@ using namespace std;
 #include <math.h>
 #include <map.h>
 #endif
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "misc.h"
 #include "cgh.h"
@@ -224,9 +220,16 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
     pox[2][n] = rex * nz_g[n];
   }
 
+  double *shellf;
+  shellf = new double[n_tot * InList];
+
+  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry);
+
   int mp, Lp, Nmin, Nmax;
+
   mp = n_tot / cpusize;
   Lp = n_tot - cpusize * mp;
+
   if (Lp > myrank)
   {
     Nmin = myrank * mp + myrank;
@@ -238,11 +241,6 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
     Nmax = Nmin + mp - 1;
   }
 
-  double *shellf;
-  shellf = new double[n_tot * InList];
-
-  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Nmin, Nmax);
-
   //|~~~~~> Integrate the dot product of Dphi with the surface normal.
 
   double *RP_out, *IP_out;
@@ -365,17 +363,8 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -567,17 +556,8 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, Comm_here);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, Comm_here);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, Comm_here);
 
   //|------= Free memory.
 
@@ -755,17 +735,8 @@ void surface_integral::surf_Wave(double rex, int lev, ShellPatch *GH, var *Rpsi4
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -1013,17 +984,8 @@ void surface_integral::surf_Wave(double rex, int lev, ShellPatch *GH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -1457,17 +1419,8 @@ void surface_integral::surf_Wave(double rex, int lev, ShellPatch *GH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -1901,17 +1854,8 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -2096,17 +2040,8 @@ void surface_integral::surf_Wave(double rex, int lev, NullShellPatch2 *GH, var *
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -2291,17 +2226,8 @@ void surface_integral::surf_Wave(double rex, int lev, NullShellPatch *GH, var *R
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -2388,9 +2314,25 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     pox[2][n] = rex * nz_g[n];
   }
 
+  double *shellf;
+  shellf = new double[n_tot * InList];
+
+  // we have assumed there is only one box on this level,
+  // so we do not need loop boxes
+  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry);
+
+  double Mass_out = 0;
+  double ang_outx, ang_outy, ang_outz;
+  double p_outx, p_outy, p_outz;
+  ang_outx = ang_outy = ang_outz = 0.0;
+  p_outx = p_outy = p_outz = 0.0;
+  const double f1o8 = 0.125;
+
   int mp, Lp, Nmin, Nmax;
+
   mp = n_tot / cpusize;
   Lp = n_tot - cpusize * mp;
+
   if (Lp > myrank)
   {
     Nmin = myrank * mp + myrank;
@@ -2402,20 +2344,6 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     Nmax = Nmin + mp - 1;
   }
 
-  double *shellf;
-  shellf = new double[n_tot * InList];
-
-  // we have assumed there is only one box on this level,
-  // so we do not need loop boxes
-  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Nmin, Nmax);
-
-  double Mass_out = 0;
-  double ang_outx, ang_outy, ang_outz;
-  double p_outx, p_outy, p_outz;
-  ang_outx = ang_outy = ang_outz = 0.0;
-  p_outx = p_outy = p_outz = 0.0;
-  const double f1o8 = 0.125;
-
   double Chi, Psi;
   double Gxx, Gxy, Gxz, Gyy, Gyz, Gzz;
   double gupxx, gupxy, gupxz, gupyy, gupyz, gupzz;
@@ -2536,13 +2464,15 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     }
   }
 
-  {
-    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
-    double scalar_in[7];
-    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    mass = scalar_in[0]; sx = scalar_in[1]; sy = scalar_in[2]; sz = scalar_in[3];
-    px = scalar_in[4]; py = scalar_in[5]; pz = scalar_in[6];
-  }
+  MPI_Allreduce(&Mass_out, &mass, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&ang_outz, &sz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  MPI_Allreduce(&p_outx, &px, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&p_outy, &py, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&p_outz, &pz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
 #ifdef GaussInt
   mass = mass * rex * rex * dphi * factor;
@@ -2805,13 +2735,15 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     }
   }
 
-  {
-    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
-    double scalar_in[7];
-    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, Comm_here);
-    mass = scalar_in[0]; sx = scalar_in[1]; sy = scalar_in[2]; sz = scalar_in[3];
-    px = scalar_in[4]; py = scalar_in[5]; pz = scalar_in[6];
-  }
+  MPI_Allreduce(&Mass_out, &mass, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+
+  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+  MPI_Allreduce(&ang_outz, &sz, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+
+  MPI_Allreduce(&p_outx, &px, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+  MPI_Allreduce(&p_outy, &py, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+  MPI_Allreduce(&p_outz, &pz, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
 
 #ifdef GaussInt
   mass = mass * rex * rex * dphi * factor;
@@ -3088,13 +3020,15 @@ void surface_integral::surf_MassPAng(double rex, int lev, ShellPatch *GH, var *c
     }
   }
 
-  {
-    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
-    double scalar_in[7];
-    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    mass = scalar_in[0]; sx = scalar_in[1]; sy = scalar_in[2]; sz = scalar_in[3];
-    px = scalar_in[4]; py = scalar_in[5]; pz = scalar_in[6];
-  }
+  MPI_Allreduce(&Mass_out, &mass, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&ang_outz, &sz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  MPI_Allreduce(&p_outx, &px, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&p_outy, &py, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&p_outz, &pz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
 #ifdef GaussInt
   mass = mass * rex * rex * dphi * factor;
@@ -3673,17 +3607,8 @@ void surface_integral::surf_Wave(double rex, cgh *GH, ShellPatch *SH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 

AMSS_NCKU_source/testNull.C

@@ -18,11 +18,7 @@ using namespace std;
 #include <math.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "misc.h"
 #include "macrodef.h"

AMSS_NCKU_source/testNull2.C

@@ -20,11 +20,7 @@ using namespace std;
 #include <map.h>
 #endif
 
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "misc.h"
 #include "macrodef.h"

AMSS_NCKU_source/var.C

@@ -9,11 +9,7 @@
 using namespace std;
 
 #include <time.h>
-#ifdef MPI_STUB
-#include "mpi_stub.h"
-#else
 #include <mpi.h>
-#endif
 
 #include "var.h"
 

makefile_and_run.py

@@ -11,30 +11,16 @@
 import AMSS_NCKU_Input as input_data
 import subprocess
 import time
-import os
-
-## OpenMP configuration for threaded Fortran kernels
-## OMP_NUM_THREADS: set to number of physical cores (not hyperthreads)
-## OMP_PROC_BIND: bind threads to cores to avoid migration overhead
-## OMP_STACKSIZE: each thread needs stack space for fh arrays (~3.6MB)
-if "OMP_NUM_THREADS" not in os.environ:
-    os.environ["OMP_NUM_THREADS"] = "96"
-os.environ["OMP_STACKSIZE"] = "16M"
-os.environ["OMP_PROC_BIND"] = "close"
-os.environ["OMP_PLACES"] = "cores"
 ## CPU core binding configuration using taskset
 ## taskset ensures all child processes inherit the CPU affinity mask
 ## This forces make and all compiler processes to use only nohz_full cores (4-55, 60-111)
 ## Format: taskset -c 4-55,60-111 ensures processes only run on these cores
-#NUMACTL_CPU_BIND = "taskset -c 0-111"
-#NUMACTL_CPU_BIND = "taskset -c 16-47,64-95"
-#NUMACTL_CPU_BIND = "taskset -c 8-15"
-NUMACTL_CPU_BIND = ""
+NUMACTL_CPU_BIND = "taskset -c 0-111"
 
 ## Build parallelism configuration
 ## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
 ## Set make -j to utilize available cores for faster builds
-BUILD_JOBS = 16
+BUILD_JOBS = 104
 
 
 ##################################################################
@@ -128,28 +114,28 @@ def run_ABE():
     print(                                                      )
 
     ## Define the command to run; cast other values to strings as needed
-
+    
     if (input_data.GPU_Calculation == "no"):
-        run_command         = NUMACTL_CPU_BIND + " ./ABE"
-        run_command_outfile = "ABE_out.log"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        run_command         = NUMACTL_CPU_BIND + " ./ABEGPU"
-        run_command_outfile = "ABEGPU_out.log"
-
-    ## Execute the command and stream output
-    run_process = subprocess.Popen(run_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command_outfile = "ABEGPU_out.log"
+ 
+    ## Execute the MPI command and stream output
+    mpi_process = subprocess.Popen(mpi_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
 
     ## Write ABE run output to file while printing to stdout
-    with open(run_command_outfile, 'w') as file0:
+    with open(mpi_command_outfile, 'w') as file0:  
         ## Read and print output lines; also write each line to file
-        for line in run_process.stdout:
+        for line in mpi_process.stdout:
             print(line, end='')  # stream output in real time
             file0.write(line)    # write the line to file
             file0.flush()        # flush to ensure each line is written immediately (optional)            
     file0.close()
 
     ## Wait for the process to finish
-    run_return_code = run_process.wait()
+    mpi_return_code = mpi_process.wait()
     
     print(                                           )
     print( " The ABE/ABEGPU simulation is finished " ) 
@@ -172,8 +158,7 @@ def run_TwoPunctureABE():
     print(                                                          )
     
     ## Define the command to run
-    #TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
-    TwoPuncture_command         = " ./TwoPunctureABE"
+    TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
     TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
 
     ## Execute the command with subprocess.Popen and stream output

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
-```