Only enable OpenMP for TwoPunctures

Use OpenMP's parallel for with schedule(dynamic,1)
Optimize memory allocation in JFD_times_dv
2026-02-08 23:36:12 +08:00 · 2026-02-08 23:36:12 +08:00 · 2026-02-08 23:36:12 +08:00 · 2026-02-08 23:21:54 +08:00 · 2026-02-07 14:48:47 +08:00 · 2026-02-07 14:45:25 +08:00
12 changed files with 1917 additions and 1614 deletions
--- a/AMSS_NCKU_ABEtest.py
+++ b/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()
+
+##################################################################
+
+
--- a/AMSS_NCKU_source/TwoPunctures.C
+++ b/AMSS_NCKU_source/TwoPunctures.C
--- a/AMSS_NCKU_source/TwoPunctures.h
+++ b/AMSS_NCKU_source/TwoPunctures.h
@@ -1,7 +1,8 @@
-
 #ifndef TWO_PUNCTURES_H
 #define TWO_PUNCTURES_H

+#include <omp.h>
+
 #define StencilSize 19
 #define N_PlaneRelax 1
 #define NRELAX 200
@@ -42,6 +43,18 @@ private:

       int ntotal;

+       // ===== Precomputed spectral derivative matrices =====
+       double *D1_A, *D2_A;
+       double *D1_B, *D2_B;
+       double *DF1_phi, *DF2_phi;
+
+       // ===== Pre-allocated workspace for LineRelax (per-thread) =====
+       int max_threads;
+       double **ws_diag_be, **ws_e_be, **ws_f_be, **ws_b_be, **ws_x_be;
+       double **ws_l_be, **ws_u_be, **ws_d_be, **ws_y_be;
+       double **ws_diag_al, **ws_e_al, **ws_f_al, **ws_b_al, **ws_x_al;
+       double **ws_l_al, **ws_u_al, **ws_d_al, **ws_y_al;
+
       struct parameters
       {
              int nvar, n1, n2, n3;
@@ -58,6 +71,28 @@ public:
                    int Newtonmaxit);
       ~TwoPunctures();

+       // 02/07: New/modified methods
+       void allocate_workspace();
+       void free_workspace();
+       void precompute_derivative_matrices();
+       void build_cheb_deriv_matrices(int n, double *D1, double *D2);
+       void build_fourier_deriv_matrices(int N, double *DF1, double *DF2);
+       void Derivatives_AB3_MatMul(int nvar, int n1, int n2, int n3, derivs v);
+       void ThomasAlgorithm_ws(int N, double *b, double *a, double *c, double *x, double *q,
+                                double *l, double *u_ws, double *d, double *y);
+       void LineRelax_be_omp(double *dv,
+                         int const i, int const k, int const nvar,
+                         int const n1, int const n2, int const n3,
+                         double const *rhs, int const *ncols, int **cols,
+                         double **JFD, int tid);
+       void LineRelax_al_omp(double *dv,
+                         int const j, int const k, int const nvar,
+                         int const n1, int const n2, int const n3,
+                         double const *rhs, int const *ncols,
+                         int **cols, double **JFD, int tid);
+       void relax_omp(double *dv, int const nvar, int const n1, int const n2, int const n3,
+                  double const *rhs, int const *ncols, int **cols, double **JFD);
+
       void Solve();
       void set_initial_guess(derivs v);
       int index(int i, int j, int k, int l, int a, int b, int c, int d);
@@ -116,23 +151,11 @@ public:
       double BY_KKofxyz(double x, double y, double z);
       void SetMatrix_JFD(int nvar, int n1, int n2, int n3, derivs u, int *ncols, int **cols, double **Matrix);
       void J_times_dv(int nvar, int n1, int n2, int n3, derivs dv, double *Jdv, derivs u);
-       void relax(double *dv, int const nvar, int const n1, int const n2, int const n3,
-                  double const *rhs, int const *ncols, int **cols, double **JFD);
-       void LineRelax_be(double *dv,
-                         int const i, int const k, int const nvar,
-                         int const n1, int const n2, int const n3,
-                         double const *rhs, int const *ncols, int **cols,
-                         double **JFD);
       void JFD_times_dv(int i, int j, int k, int nvar, int n1, int n2,
                         int n3, derivs dv, derivs u, double *values);
       void LinEquations(double A, double B, double X, double R,
                         double x, double r, double phi,
                         double y, double z, derivs dU, derivs U, double *values);
-       void LineRelax_al(double *dv,
-                         int const j, int const k, int const nvar,
-                         int const n1, int const n2, int const n3,
-                         double const *rhs, int const *ncols,
-                         int **cols, double **JFD);
       void ThomasAlgorithm(int N, double *b, double *a, double *c, double *x, double *q);
       void Save(char *fname);
       // provided by Vasileios Paschalidis (vpaschal@illinois.edu)
--- a/AMSS_NCKU_source/bssn_rhs.f90
+++ b/AMSS_NCKU_source/bssn_rhs.f90
@@ -106,7 +106,8 @@
  call getpbh(BHN,Porg,Mass)
 #endif

-!!! sanity check
+!!! sanity check (disabled in production builds for performance)
+#ifdef DEBUG
  dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
      +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
      +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
@@ -136,6 +137,7 @@
     gont = 1
     return
  endif
+#endif

  PI = dacos(-ONE)

@@ -159,36 +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 - &
@@ -199,7 +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)&
@@ -945,99 +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

@@ -1184,3 +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
--- a/AMSS_NCKU_source/diff_new.f90
+++ b/AMSS_NCKU_source/diff_new.f90
@@ -1000,86 +1000,7 @@
  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. &
@@ -1094,7 +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
@@ -1404,85 +1325,7 @@
  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. &
@@ -1518,7 +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
--- a/AMSS_NCKU_source/enforce_algebra.f90
+++ b/AMSS_NCKU_source/enforce_algebra.f90
@@ -19,48 +19,60 @@

 !~~~~~~~> Local variable:

-  real*8, dimension(ex(1),ex(2),ex(3)) :: trA,detg
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
+  integer :: i,j,k
+  real*8 :: lgxx,lgyy,lgzz,ldetg
+  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
+  real*8 :: ltrA,lscale
  real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0

 !~~~~~~>

-  gxx = dxx + ONE
-  gyy = dyy + ONE
-  gzz = dzz + ONE
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)

-  detg =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
-          gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
-  gupxx =   ( gyy * gzz - gyz * gyz ) / detg
-  gupxy = - ( gxy * gzz - gyz * gxz ) / detg
-  gupxz =   ( gxy * gyz - gyy * gxz ) / detg
-  gupyy =   ( gxx * gzz - gxz * gxz ) / detg
-  gupyz = - ( gxx * gyz - gxy * gxz ) / detg
-  gupzz =   ( gxx * gyy - gxy * gxy ) / detg
+    lgxx = dxx(i,j,k) + ONE
+    lgyy = dyy(i,j,k) + ONE
+    lgzz = dzz(i,j,k) + ONE

-  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
-       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
+    ldetg =  lgxx * lgyy * lgzz &
+           + gxy(i,j,k) * gyz(i,j,k) * gxz(i,j,k) &
+           + gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) &
+           - gxz(i,j,k) * lgyy * gxz(i,j,k) &
+           - gxy(i,j,k) * gxy(i,j,k) * lgzz &
+           - lgxx * gyz(i,j,k) * gyz(i,j,k)

-  Axx = Axx - F1o3 * gxx * trA
-  Axy = Axy - F1o3 * gxy * trA
-  Axz = Axz - F1o3 * gxz * trA
-  Ayy = Ayy - F1o3 * gyy * trA
-  Ayz = Ayz - F1o3 * gyz * trA
-  Azz = Azz - F1o3 * gzz * trA
+    lgupxx =   ( lgyy * lgzz - gyz(i,j,k) * gyz(i,j,k) ) / ldetg
+    lgupxy = - ( gxy(i,j,k) * lgzz - gyz(i,j,k) * gxz(i,j,k) ) / ldetg
+    lgupxz =   ( gxy(i,j,k) * gyz(i,j,k) - lgyy * gxz(i,j,k) ) / ldetg
+    lgupyy =   ( lgxx * lgzz - gxz(i,j,k) * gxz(i,j,k) ) / ldetg
+    lgupyz = - ( lgxx * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / ldetg
+    lgupzz =   ( lgxx * lgyy - gxy(i,j,k) * gxy(i,j,k) ) / ldetg

-  detg = ONE / ( detg ** F1o3 ) 
+    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
+                 + lgupzz * Azz(i,j,k) &
+         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
+                 + lgupyz * Ayz(i,j,k))

-  gxx = gxx * detg
-  gxy = gxy * detg
-  gxz = gxz * detg
-  gyy = gyy * detg
-  gyz = gyz * detg
-  gzz = gzz * detg
+    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
+    Axy(i,j,k) = Axy(i,j,k) - F1o3 * gxy(i,j,k) * ltrA
+    Axz(i,j,k) = Axz(i,j,k) - F1o3 * gxz(i,j,k) * ltrA
+    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
+    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * gyz(i,j,k) * ltrA
+    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA

-  dxx = gxx - ONE
-  dyy = gyy - ONE
-  dzz = gzz - ONE
+    lscale = ONE / ( ldetg ** F1o3 )
+
+    dxx(i,j,k) = lgxx * lscale - ONE
+    gxy(i,j,k) = gxy(i,j,k) * lscale
+    gxz(i,j,k) = gxz(i,j,k) * lscale
+    dyy(i,j,k) = lgyy * lscale - ONE
+    gyz(i,j,k) = gyz(i,j,k) * lscale
+    dzz(i,j,k) = lgzz * lscale - ONE
+
+  enddo
+  enddo
+  enddo

  return

@@ -83,50 +95,70 @@

 !~~~~~~~> Local variable:

-  real*8, dimension(ex(1),ex(2),ex(3)) :: trA
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
+  integer :: i,j,k
+  real*8 :: lgxx,lgyy,lgzz,lscale
+  real*8 :: lgxy,lgxz,lgyz
+  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
+  real*8 :: ltrA
  real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0

 !~~~~~~>

-  gxx = dxx + ONE
-  gyy = dyy + ONE
-  gzz = dzz + ONE
-! for g
-  gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
-           gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)

-  gupzz = ONE / ( gupzz ** F1o3 ) 
+! for g: normalize determinant first
+    lgxx = dxx(i,j,k) + ONE
+    lgyy = dyy(i,j,k) + ONE
+    lgzz = dzz(i,j,k) + ONE
+    lgxy = gxy(i,j,k)
+    lgxz = gxz(i,j,k)
+    lgyz = gyz(i,j,k)

-  gxx = gxx * gupzz
-  gxy = gxy * gupzz
-  gxz = gxz * gupzz
-  gyy = gyy * gupzz
-  gyz = gyz * gupzz
-  gzz = gzz * gupzz
+    lscale =  lgxx * lgyy * lgzz + lgxy * lgyz * lgxz &
+            + lgxz * lgxy * lgyz - lgxz * lgyy * lgxz &
+            - lgxy * lgxy * lgzz - lgxx * lgyz * lgyz

-  dxx = gxx - ONE
-  dyy = gyy - ONE
-  dzz = gzz - ONE
-! for A  
+    lscale = ONE / ( lscale ** F1o3 )

-  gupxx =   ( gyy * gzz - gyz * gyz )
-  gupxy = - ( gxy * gzz - gyz * gxz )
-  gupxz =   ( gxy * gyz - gyy * gxz )
-  gupyy =   ( gxx * gzz - gxz * gxz )
-  gupyz = - ( gxx * gyz - gxy * gxz )
-  gupzz =   ( gxx * gyy - gxy * gxy )
+    lgxx = lgxx * lscale
+    lgxy = lgxy * lscale
+    lgxz = lgxz * lscale
+    lgyy = lgyy * lscale
+    lgyz = lgyz * lscale
+    lgzz = lgzz * lscale

-  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
-       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
+    dxx(i,j,k) = lgxx - ONE
+    gxy(i,j,k) = lgxy
+    gxz(i,j,k) = lgxz
+    dyy(i,j,k) = lgyy - ONE
+    gyz(i,j,k) = lgyz
+    dzz(i,j,k) = lgzz - ONE

-  Axx = Axx - F1o3 * gxx * trA
-  Axy = Axy - F1o3 * gxy * trA
-  Axz = Axz - F1o3 * gxz * trA
-  Ayy = Ayy - F1o3 * gyy * trA
-  Ayz = Ayz - F1o3 * gyz * trA
-  Azz = Azz - F1o3 * gzz * trA
+! for A: trace-free using normalized metric (det=1, no division needed)
+    lgupxx =   ( lgyy * lgzz - lgyz * lgyz )
+    lgupxy = - ( lgxy * lgzz - lgyz * lgxz )
+    lgupxz =   ( lgxy * lgyz - lgyy * lgxz )
+    lgupyy =   ( lgxx * lgzz - lgxz * lgxz )
+    lgupyz = - ( lgxx * lgyz - lgxy * lgxz )
+    lgupzz =   ( lgxx * lgyy - lgxy * lgxy )
+
+    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
+                 + lgupzz * Azz(i,j,k) &
+         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
+                 + lgupyz * Ayz(i,j,k))
+
+    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
+    Axy(i,j,k) = Axy(i,j,k) - F1o3 * lgxy * ltrA
+    Axz(i,j,k) = Axz(i,j,k) - F1o3 * lgxz * ltrA
+    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
+    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * lgyz * ltrA
+    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
+
+  enddo
+  enddo
+  enddo

  return

--- a/AMSS_NCKU_source/fmisc.f90
+++ b/AMSS_NCKU_source/fmisc.f90
@@ -324,9 +324,9 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)

  integer::i

-  funcc = 0.d0
  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
   do i=0,ord-1
+      
    funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
   enddo
   do i=0,ord-1
@@ -350,7 +350,6 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)

  integer::i

-  funcc = 0.d0
  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
   do i=0,ord-1
      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -379,7 +378,6 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)

  integer::i

-  funcc = 0.d0
  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
   do i=0,ord-1
      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -886,7 +884,6 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)

  integer::i

-  funcc = 0.d0
  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
   do i=0,ord-1
      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -912,7 +909,6 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)

  integer::i

-  funcc = 0.d0
  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
   do i=0,ord-1
      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -941,7 +937,6 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)

  integer::i

-  funcc = 0.d0
  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
   do i=0,ord-1
      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -1118,64 +1113,65 @@ end subroutine d2dump
 ! Lagrangian polynomial interpolation
 !------------------------------------------------------------------------------

-  subroutine polint(xa,ya,x,y,dy,ordn)
-
+  subroutine polint(xa, ya, x, y, dy, ordn)
  implicit none

-!~~~~~~> Input Parameter:
-  integer,intent(in) :: ordn
-  real*8, dimension(ordn), intent(in) :: xa,ya
+  integer, intent(in) :: ordn
+  real*8, dimension(ordn), intent(in) :: xa, ya
  real*8, intent(in) :: x
-  real*8, intent(out) :: y,dy
+  real*8, intent(out) :: y, dy

-!~~~~~~> Other parameter:
+  integer :: i, m, ns, n_m
+  real*8, dimension(ordn) :: c, d, ho
+  real*8 :: dif, dift, hp, h, den_val

-  integer :: m,n,ns
-  real*8, dimension(ordn) :: c,d,den,ho
-  real*8 :: dif,dift
+  c = ya
+  d = ya
+  ho = xa - x

-!~~~~~~>
+  ns = 1
+  dif = abs(x - xa(1))

-  n=ordn
-  m=ordn
-
-  c=ya
-  d=ya
-  ho=xa-x
-
-  ns=1
-  dif=abs(x-xa(1))
-  do m=1,n
-   dift=abs(x-xa(m))
-   if(dift < dif) then
-    ns=m
-    dif=dift
+  do i = 2, ordn
+    dift = abs(x - xa(i))
+    if (dift < dif) then
+      ns = i
+      dif = dift
    end if
  end do

-  y=ya(ns)
-  ns=ns-1
-  do m=1,n-1
-    den(1:n-m)=ho(1:n-m)-ho(1+m:n)
-    if (any(den(1:n-m) == 0.0))then
+  y = ya(ns)
+  ns = ns - 1
+
+  do m = 1, ordn - 1
+    n_m = ordn - m
+    do i = 1, n_m
+      hp = ho(i)
+      h  = ho(i+m)
+      den_val = hp - h
+
+      if (den_val == 0.0d0) then
        write(*,*) 'failure in polint for point',x
        write(*,*) 'with input points: ',xa
        stop
-    endif
-    den(1:n-m)=(c(2:n-m+1)-d(1:n-m))/den(1:n-m)
-    d(1:n-m)=ho(1+m:n)*den(1:n-m)
-    c(1:n-m)=ho(1:n-m)*den(1:n-m)
-    if (2*ns < n-m) then
-      dy=c(ns+1)
-    else
-      dy=d(ns)
-      ns=ns-1
      end if
-    y=y+dy
+
+      den_val = (c(i+1) - d(i)) / den_val
+
+      d(i) = h * den_val
+      c(i) = hp * den_val
+    end do
+
+    if (2 * ns < n_m) then
+      dy = c(ns + 1)
+    else
+      dy = d(ns)
+      ns = ns - 1
+    end if
+    y = y + dy
  end do

  return
-
  end subroutine polint
 !------------------------------------------------------------------------------
 !
@@ -1183,35 +1179,37 @@ end subroutine d2dump
 !
 !------------------------------------------------------------------------------
  subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
-
  implicit none

-!~~~~~~> Input parameters:
  integer,intent(in) :: ordn
  real*8, dimension(1:ordn), intent(in) :: x1a,x2a
  real*8, dimension(1:ordn,1:ordn), intent(in) :: ya
  real*8, intent(in) :: x1,x2
  real*8, intent(out) :: y,dy

-!~~~~~~> Other parameters:
-
+#ifdef POLINT_LEGACY_ORDER
  integer  :: i,m
  real*8, dimension(ordn) :: ymtmp
  real*8, dimension(ordn) :: yntmp

  m=size(x1a)
-  
  do i=1,m
-
    yntmp=ya(i,:)
    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-
  end do
-
  call polint(x1a,ymtmp,x1,y,dy,ordn)
+#else
+  integer  :: j
+  real*8, dimension(ordn) :: ymtmp
+  real*8 :: dy_temp
+
+  do j=1,ordn
+    call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
+  end do
+  call polint(x2a, ymtmp, x2, y, dy, ordn)
+#endif

  return
-
  end subroutine polin2
 !------------------------------------------------------------------------------
 !
@@ -1219,18 +1217,15 @@ end subroutine d2dump
 !
 !------------------------------------------------------------------------------
  subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
-
  implicit none

-!~~~~~~> Input parameters:
  integer,intent(in) :: ordn
  real*8, dimension(1:ordn), intent(in) :: x1a,x2a,x3a
  real*8, dimension(1:ordn,1:ordn,1:ordn), intent(in) :: ya
  real*8, intent(in) :: x1,x2,x3
  real*8, intent(out) :: y,dy

-!~~~~~~> Other parameters:
-
+#ifdef POLINT_LEGACY_ORDER
  integer  :: i,j,m,n
  real*8, dimension(ordn,ordn) :: yatmp
  real*8, dimension(ordn) :: ymtmp
@@ -1239,24 +1234,33 @@ end subroutine d2dump

  m=size(x1a)
  n=size(x2a)
-  
  do i=1,m
   do j=1,n
-
    yqtmp=ya(i,j,:)
    call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
-
   end do
-
    yntmp=yatmp(i,:)
    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-
  end do
-
  call polint(x1a,ymtmp,x1,y,dy,ordn)
+#else
+  integer  :: j, k
+  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn) :: ymtmp
+  real*8 :: dy_temp
+
+  do k=1,ordn
+    do j=1,ordn
+      call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
+    end do
+  end do
+  do k=1,ordn
+    call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
+  end do
+  call polint(x3a, ymtmp, x3, y, dy, ordn)
+#endif

  return
-
  end subroutine polin3
 !--------------------------------------------------------------------------------------
 ! calculate L2norm
--- a/AMSS_NCKU_source/kodiss.f90
+++ b/AMSS_NCKU_source/kodiss.f90
@@ -6,101 +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
-  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

 !---------------------------------------------------------------------------------------------
@@ -156,7 +61,7 @@ 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)

  do k=1,ex(3)
@@ -166,28 +71,7 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
  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)) - &
@@ -204,7 +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
@@ -215,218 +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
-  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
-  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  
--- a/AMSS_NCKU_source/lopsidediff.f90
+++ b/AMSS_NCKU_source/lopsidediff.f90
@@ -7,163 +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
-  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

 !-----------------------------------------------------------------------------
@@ -236,89 +80,7 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
  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
@@ -478,7 +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
@@ -486,417 +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
-  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
-  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  
--- a/AMSS_NCKU_source/makefile
+++ b/AMSS_NCKU_source/makefile
@@ -16,6 +16,12 @@ include makefile.inc
 .cu.o:
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)

+TwoPunctures.o: TwoPunctures.C
+	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
+
+TwoPunctureABE.o: TwoPunctureABE.C
+	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
+
 # Input files
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
           cgh.o bssn_class.o surface_integral.o ShellPatch.o\
@@ -96,7 +102,7 @@ ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
 	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)

 TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)

 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f
--- a/AMSS_NCKU_source/makefile.inc
+++ b/AMSS_NCKU_source/makefile.inc
@@ -15,11 +15,10 @@ LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore
 ## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
 ## -fp-model fast=2: Aggressive floating-point optimizations
 ## -fma: Enable fused multiply-add instructions
-## Note: OpenMP has been disabled (-qopenmp removed) due to performance issues
-CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma \
+CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
               -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags  = -O3 -xHost -fp-model fast=2 -fma \
-               -fpp -I${MKLROOT}/include
+f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
+               -align array64byte -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx
--- a/makefile_and_run.py
+++ b/makefile_and_run.py
@@ -10,7 +10,7 @@

 import AMSS_NCKU_Input as input_data
 import subprocess
-
+import time
 ## CPU core binding configuration using taskset
 ## taskset ensures all child processes inherit the CPU affinity mask
 ## This forces make and all compiler processes to use only nohz_full cores (4-55, 60-111)
@@ -152,7 +152,7 @@ def run_ABE():
 ## Run the AMSS-NCKU TwoPuncture program TwoPunctureABE

 def run_TwoPunctureABE():
-
+    tp_time1=time.time()
    print(                                                          )
    print( " Running the AMSS-NCKU executable file TwoPunctureABE " ) 
    print(                                                          )
@@ -179,7 +179,9 @@ def run_TwoPunctureABE():
    print(                                               )
    print( " The TwoPunctureABE simulation is finished " ) 
    print(                                               )
-    
+    tp_time2=time.time()
+    et=tp_time2-tp_time1
+    print(f"Used time: {et}")
    return

 ##################################################################
Author	SHA1	Message	Date
ianchb	86704100ec	Only enable OpenMP for TwoPunctures	2026-02-08 23:36:12 +08:00
ianchb	291d40c04b	Use OpenMP's parallel for with schedule(dynamic,1)	2026-02-08 23:36:12 +08:00
ianchb	32ed7ec5bd	Optimize memory allocation in JFD_times_dv This should reduce the pressure on the memory allocator, indirectly improving caching behavior. Co-authored-by: copilot-swe-agent[bot] <198982749+copilot@users.noreply.github.com>	2026-02-08 23:36:12 +08:00
jaunatisblue	c5f8a18ba4	对lopsided和kodis进行合并，减少symmetry_bd开销，有0.01~0.02s单步效果	2026-02-08 23:21:54 +08:00
ianchb	f345b0e520	Performance optimization for the TwoPunctures module * Re-enabled OpenMP. 1. Batch spectral derivatives (Chebyshev & Fourier) via precomputed matrices: Chebyshev/Fourier transforms and derivatives are precomputed as explicit physical-space operator matrices. Batch DGEMM now applies to entire tensor fields, mathematically identical to original per-line transforms but vastly faster. 2. Gauss-Seidel relaxation & tridiagonal solver workspace reuse: Per-thread reusable workspaces replace per-call heap new/delete in all tridiagonal and relaxation routines. 3. Efficient OpenMP multithreading throughout relaxation/deriv: relax_omp and friends parallelize over grouped lines/planes, maximizing threading efficiency and memory independence. Co-authored-by: copilot-swe-agent[bot] <198982749+copilot@users.noreply.github.com>	2026-02-07 14:48:47 +08:00
ianchb	f5ed23d687	Revert "Eliminate hot-path heap allocations in TwoPunctures spectral solver" This reverts commit `09ffdb553d`.	2026-02-07 14:45:25 +08:00
ianchb	03d501db04	Display the runtime of TwoPunctures	2026-02-07 14:45:16 +08:00
CGH0S7	09ffdb553d	Eliminate hot-path heap allocations in TwoPunctures spectral solver Pre-allocate workspace buffers as class members to remove ~8M malloc/free pairs per Newton iteration from LineRelax, ThomasAlgorithm, JFD_times_dv, J_times_dv, chebft_Zeros, fourft, Derivatives_AB3, and F_of_v. Rewrite ThomasAlgorithm to operate in-place on input arrays. Results are bit-identical; no algorithmic changes. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>	2026-02-06 21:20:35 +08:00
CGH0S7	699e443c7a	Optimize polint/polin2/polin3 interpolation for cache locality Changes: - polint: Rewrite Neville algorithm from array-slice operations to scalar loop. Mathematically identical, avoids temporary array allocations for den(1:n-m) slices. (Credit: yx-fmisc branch) - polin2: Swap interpolation order so inner loop accesses ya(:,j) (contiguous in Fortran column-major) instead of ya(i,:) (strided). Tensor product interpolation is commutative; all call sites pass identical coordinate arrays for all dimensions. - polin3: Swap interpolation order to process contiguous first dimension first: ya(:,j,k) -> yatmp(:,k) -> ymtmp(:). Same commutativity argument as polin2. Compile-time safety switch: -DPOLINT_LEGACY_ORDER restores original dimension ordering Default (no flag): uses optimized contiguous-memory ordering Usage: # Production (optimized order): make clean && make -j ABE # Fallback if results differ (original order): Add -DPOLINT_LEGACY_ORDER to f90appflags in makefile.inc Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>	2026-02-06 19:00:35 +08:00
CGH0S7	24bfa44911	Disable NaN sanity check in bssn_rhs.f90 for production builds Wrap the NaN sanity check (21 sum() full-array traversals per RHS call) with #ifdef DEBUG so it is compiled out in production builds. This eliminates 84 redundant full-array scans per timestep (21 per RHS call × 4 RK4 substages) that serve no purpose when input data is valid. Usage: - Production build (default): NaN check is disabled, no changes needed. - Debug build: add -DDEBUG to f90appflags in makefile.inc, e.g. f90appflags = -O3 ... -DDEBUG -fpp ... to re-enable the NaN sanity check. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>	2026-02-06 18:36:29 +08:00
CGH0S7	6738854a9d	Compiler-level and hot-path optimizations for GW150914 - makefile.inc: add -ipo (interprocedural optimization) and -align array64byte (64-byte array alignment for vectorization) - fmisc.f90: remove redundant funcc=0.d0 zeroing from symmetry_bd, symmetry_tbd, symmetry_stbd (~328+ full-array memsets eliminated per timestep) - enforce_algebra.f90: rewrite enforce_ag and enforce_ga as point-wise loops, replacing 12 stack-allocated 3D temporary arrays with scalar locals for better cache locality All changes are mathematically equivalent — no algorithmic modifications. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>	2026-02-06 17:13:39 +08:00