64-BitBrainstorm_2026/AMSS-NCKU
8
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Compare commits

base: 64-BitBrainstorm_2026:chb-twopunctures
Branches Tags
64-BitBrainstorm_2026:main 64-BitBrainstorm_2026:chb-parallel 64-BitBrainstorm_2026:cjy-dystopia 64-BitBrainstorm_2026:yx-prolong 64-BitBrainstorm_2026:chb-rebase-wip 64-BitBrainstorm_2026:hxh-omp 64-BitBrainstorm_2026:hxh-new 64-BitBrainstorm_2026:yx_new_split 64-BitBrainstorm_2026:cjy-oneapi-opus-hotfix 64-BitBrainstorm_2026:chb-replace 64-BitBrainstorm_2026:yx-vacation 64-BitBrainstorm_2026:chb-new 64-BitBrainstorm_2026:yx-mpi 64-BitBrainstorm_2026:cjy-oneapi-opus-windfall 64-BitBrainstorm_2026:chb-copilot-test 64-BitBrainstorm_2026:chb-twopunctures 64-BitBrainstorm_2026:yx-fmisc 64-BitBrainstorm_2026:cjy-oneapi-opus-rhs-preview 64-BitBrainstorm_2026:cjy-oneapi-opus-preview 64-BitBrainstorm_2026:cjy-oneapi-opus-openmp 64-BitBrainstorm_2026:cjy-oneapi 64-BitBrainstorm_2026:cjy-oneapi-openmp 64-BitBrainstorm_2026:baseline 64-BitBrainstorm_2026:cjy-oneapi-parallel 64-BitBrainstorm_2026:chb-local 64-BitBrainstorm_2026:cjy-oneapi-laptop 64-BitBrainstorm_2026:cjy-oneapi-test 64-BitBrainstorm_2026:cjy-oneapi-preview 64-BitBrainstorm_2026:cjy
..
compare: 64-BitBrainstorm_2026:cjy-oneapi-test
Branches Tags
64-BitBrainstorm_2026:main 64-BitBrainstorm_2026:chb-parallel 64-BitBrainstorm_2026:cjy-dystopia 64-BitBrainstorm_2026:yx-prolong 64-BitBrainstorm_2026:chb-rebase-wip 64-BitBrainstorm_2026:hxh-omp 64-BitBrainstorm_2026:hxh-new 64-BitBrainstorm_2026:yx_new_split 64-BitBrainstorm_2026:cjy-oneapi-opus-hotfix 64-BitBrainstorm_2026:chb-replace 64-BitBrainstorm_2026:yx-vacation 64-BitBrainstorm_2026:chb-new 64-BitBrainstorm_2026:yx-mpi 64-BitBrainstorm_2026:cjy-oneapi-opus-windfall 64-BitBrainstorm_2026:chb-copilot-test 64-BitBrainstorm_2026:chb-twopunctures 64-BitBrainstorm_2026:yx-fmisc 64-BitBrainstorm_2026:cjy-oneapi-opus-rhs-preview 64-BitBrainstorm_2026:cjy-oneapi-opus-preview 64-BitBrainstorm_2026:cjy-oneapi-opus-openmp 64-BitBrainstorm_2026:cjy-oneapi 64-BitBrainstorm_2026:cjy-oneapi-openmp 64-BitBrainstorm_2026:baseline 64-BitBrainstorm_2026:cjy-oneapi-parallel 64-BitBrainstorm_2026:chb-local 64-BitBrainstorm_2026:cjy-oneapi-laptop 64-BitBrainstorm_2026:cjy-oneapi-test 64-BitBrainstorm_2026:cjy-oneapi-preview 64-BitBrainstorm_2026:cjy

5 Commits
chb-twopun ... cjy-oneapi

Author SHA1 Message Date
CGH0S7
ed89bc029b Fix potential division by zero in reta_val calculation and enable NaN checks 
Added a safety check for the denominator in the reta_val calculation to
prevent division by zero when chi approaches zero (e.g., at far-field
boundaries). Also enabled DEBUG_NAN_CHECK macro to catch invalid inputs early.
Initialized output arrays to zero to prevent uninitialized memory access.
 2026-01-19 20:29:48 +08:00
CGH0S7
19274e93d1 Fix boundary handling in bssn_rhs_opt.f90 to prevent NaNs 
Refactored calc_derivs and calc_dderivs to include correct boundary
handling logic matching the legacy code. Implemented fallback to 2nd
order derivatives when near boundaries where 4th order stencils cannot
be used. Added logic to initialize output arrays to zero to avoid
uninitialized memory access.
 2026-01-19 20:03:22 +08:00
CGH0S7
ae1a474cca Fix compilation errors and complete logic in BSSN RHS optimization 2026-01-19 19:22:52 +08:00
CGH0S7
cbb8fb3a87 patched last commit 2026-01-19 17:14:28 +08:00
CGH0S7
4472d89a9f Optimize bssn_rhs calculation with cache blocking and vectorization 
- Implemented cache blocking (BLK=8) in bssn_rhs_opt.f90 to improve L1/L2 cache hit rate.
- Introduced bssn_rhs_opt.f90 module with vectorized derivative and physics kernels.
- Renamed original implementation to bssn_rhs_legacy.f90 for fallback.
- Updated bssn_rhs.f90 to act as a dispatcher, using the optimized path for ghost_width=3.
- Updated makefile to include new source files.
- Added DEBUG_NAN_CHECK macro to optionally disable NaN checks in production.
 2026-01-19 16:39:24 +08:00
15 changed files with 3959 additions and 3017 deletions
Expand all files Collapse all files

447
AMSS_NCKU_ABEtest.py
View File

@@ -1,447 +0,0 @@
##################################################################
##
## 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()
##################################################################

2
AMSS_NCKU_Input.py
View File

@@ -16,7 +16,7 @@ import numpy
File_directory = "GW150914" ## output file directory
Output_directory = "binary_output" ## binary data file directory
## The file directory name should not be too long
MPI_processes = 64 ## number of mpi processes used in the simulation
MPI_processes = 48 ## number of mpi processes used in the simulation
GPU_Calculation = "no" ## Use GPU or not
## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)

1121
AMSS_NCKU_source/TwoPunctures.C
View File

File diff suppressed because it is too large Load Diff

53
AMSS_NCKU_source/TwoPunctures.h
View File

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

1544
AMSS_NCKU_source/bssn_rhs.f90
View File

File diff suppressed because it is too large Load Diff

1188
AMSS_NCKU_source/bssn_rhs_legacy.f90 Normal file
View File

File diff suppressed because it is too large Load Diff

1125
AMSS_NCKU_source/bssn_rhs_opt.f90 Normal file
View File

File diff suppressed because it is too large Load Diff

161
AMSS_NCKU_source/diff_new.f90
View File

@@ -1000,7 +1000,86 @@
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. &
@@ -1015,7 +1094,7 @@
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
@@ -1325,7 +1404,85 @@
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. &
@@ -1361,7 +1518,7 @@
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

172
AMSS_NCKU_source/enforce_algebra.f90
View File

@@ -18,61 +18,49 @@
real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
!~~~~~~~> Local variable:
integer :: i,j,k
real*8 :: lgxx,lgyy,lgzz,ldetg
real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
real*8 :: ltrA,lscale
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
real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
!~~~~~~>
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
gxx = dxx + ONE
gyy = dyy + ONE
gzz = dzz + ONE
lgxx = dxx(i,j,k) + ONE
lgyy = dyy(i,j,k) + ONE
lgzz = dzz(i,j,k) + ONE
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
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)
trA = gupxx * Axx + gupyy * Ayy + gupzz * Azz &
+ TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
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
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
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))
detg = ONE / ( detg ** F1o3 )
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
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
dxx = gxx - ONE
dyy = gyy - ONE
dzz = gzz - ONE
return
@@ -94,71 +82,51 @@
real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
!~~~~~~~> Local variable:
integer :: i,j,k
real*8 :: lgxx,lgyy,lgzz,lscale
real*8 :: lgxy,lgxz,lgyz
real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
real*8 :: ltrA
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
real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
!~~~~~~>
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
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
! 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)
gupzz = ONE / ( gupzz ** F1o3 )
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
! 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
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
return

146
AMSS_NCKU_source/fmisc.f90
View File

@@ -324,10 +324,10 @@ 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)
funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
enddo
do i=0,ord-1
funcc(:,-i,1:extc(3)) = funcc(:,i+2,1:extc(3))*SoA(2)
@@ -350,6 +350,7 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
integer::i
funcc = 0.d0
funcc(1:extc(1),1:extc(2),1:extc(3)) = func
do i=0,ord-1
funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -378,6 +379,7 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
integer::i
funcc = 0.d0
funcc(1:extc(1),1:extc(2),1:extc(3)) = func
do i=0,ord-1
funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -884,6 +886,7 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
integer::i
funcc = 0.d0
funcc(1:extc(1),1:extc(2),1:extc(3)) = func
do i=0,ord-1
funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -909,6 +912,7 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
integer::i
funcc = 0.d0
funcc(1:extc(1),1:extc(2),1:extc(3)) = func
do i=0,ord-1
funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -937,6 +941,7 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
integer::i
funcc = 0.d0
funcc(1:extc(1),1:extc(2),1:extc(3)) = func
do i=0,ord-1
funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -1113,65 +1118,64 @@ end subroutine d2dump
! Lagrangian polynomial interpolation
!------------------------------------------------------------------------------
subroutine polint(xa, ya, x, y, dy, ordn)
subroutine polint(xa,ya,x,y,dy,ordn)
implicit none
integer, intent(in) :: ordn
real*8, dimension(ordn), intent(in) :: xa, ya
!~~~~~~> Input Parameter:
integer,intent(in) :: ordn
real*8, dimension(ordn), intent(in) :: xa,ya
real*8, intent(in) :: x
real*8, intent(out) :: y, dy
real*8, intent(out) :: y,dy
integer :: i, m, ns, n_m
real*8, dimension(ordn) :: c, d, ho
real*8 :: dif, dift, hp, h, den_val
!~~~~~~> Other parameter:
c = ya
d = ya
ho = xa - x
integer :: m,n,ns
real*8, dimension(ordn) :: c,d,den,ho
real*8 :: dif,dift
ns = 1
dif = abs(x - xa(1))
!~~~~~~>
do i = 2, ordn
dift = abs(x - xa(i))
if (dift < dif) then
ns = i
dif = dift
end if
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
end if
end do
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
end if
den_val = (c(i+1) - d(i)) / den_val
d(i) = h * den_val
c(i) = hp * den_val
end do
if (2 * ns < n_m) then
dy = c(ns + 1)
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
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
dy=d(ns)
ns=ns-1
end if
y = y + dy
y=y+dy
end do
return
end subroutine polint
!------------------------------------------------------------------------------
!
@@ -1179,37 +1183,35 @@ end subroutine d2dump
!
!------------------------------------------------------------------------------
subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
implicit none
!~~~~~~> Input parameters:
integer,intent(in) :: ordn
real*8, dimension(1:ordn), intent(in) :: x1a,x2a
real*8, dimension(1:ordn,1:ordn), intent(in) :: ya
real*8, intent(in) :: x1,x2
real*8, intent(out) :: y,dy
#ifdef POLINT_LEGACY_ORDER
!~~~~~~> Other parameters:
integer :: i,m
real*8, dimension(ordn) :: ymtmp
real*8, dimension(ordn) :: yntmp
m=size(x1a)
do i=1,m
yntmp=ya(i,:)
call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
end do
call polint(x1a,ymtmp,x1,y,dy,ordn)
#else
integer :: j
real*8, dimension(ordn) :: ymtmp
real*8 :: dy_temp
do j=1,ordn
call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
end do
call polint(x2a, ymtmp, x2, y, dy, ordn)
#endif
call polint(x1a,ymtmp,x1,y,dy,ordn)
return
end subroutine polin2
!------------------------------------------------------------------------------
!
@@ -1217,15 +1219,18 @@ end subroutine d2dump
!
!------------------------------------------------------------------------------
subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
implicit none
!~~~~~~> Input parameters:
integer,intent(in) :: ordn
real*8, dimension(1:ordn), intent(in) :: x1a,x2a,x3a
real*8, dimension(1:ordn,1:ordn,1:ordn), intent(in) :: ya
real*8, intent(in) :: x1,x2,x3
real*8, intent(out) :: y,dy
#ifdef POLINT_LEGACY_ORDER
!~~~~~~> Other parameters:
integer :: i,j,m,n
real*8, dimension(ordn,ordn) :: yatmp
real*8, dimension(ordn) :: ymtmp
@@ -1234,33 +1239,24 @@ end subroutine d2dump
m=size(x1a)
n=size(x2a)
do i=1,m
do j=1,n
yqtmp=ya(i,j,:)
call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
end do
yntmp=yatmp(i,:)
call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
end do
call polint(x1a,ymtmp,x1,y,dy,ordn)
#else
integer :: j, k
real*8, dimension(ordn,ordn) :: yatmp
real*8, dimension(ordn) :: ymtmp
real*8 :: dy_temp
do k=1,ordn
do j=1,ordn
call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
end do
end do
do k=1,ordn
call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
end do
call polint(x3a, ymtmp, x3, y, dy, ordn)
#endif
call polint(x1a,ymtmp,x1,y,dy,ordn)
return
end subroutine polin3
!--------------------------------------------------------------------------------------
! calculate L2norm

332
AMSS_NCKU_source/kodiss.f90
View File

@@ -6,6 +6,101 @@
! 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
!---------------------------------------------------------------------------------------------
@@ -61,7 +156,7 @@ 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)
@@ -71,7 +166,28 @@ 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)) - &
@@ -88,7 +204,7 @@ 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
@@ -99,6 +215,218 @@ 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

653
AMSS_NCKU_source/lopsidediff.f90
View File

@@ -7,7 +7,163 @@
! 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
!-----------------------------------------------------------------------------
@@ -80,7 +236,89 @@ 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
@@ -240,6 +478,7 @@ 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
@@ -247,3 +486,417 @@ 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

10
AMSS_NCKU_source/makefile
View File

@@ -16,12 +16,6 @@ include makefile.inc
.cu.o:
$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
TwoPunctures.o: TwoPunctures.C
${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
TwoPunctureABE.o: TwoPunctureABE.C
${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
# Input files
C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
cgh.o bssn_class.o surface_integral.o ShellPatch.o\
@@ -40,7 +34,7 @@ C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o
F90FILES = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
prolongrestrict_cell.o prolongrestrict_vertex.o\
rungekutta4_rout.o bssn_rhs.o diff_new.o kodiss.o kodiss_sh.o\
rungekutta4_rout.o bssn_rhs_opt.o bssn_rhs.o bssn_rhs_legacy.o diff_new.o kodiss.o kodiss_sh.o\
lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
@@ -102,7 +96,7 @@ ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
TwoPunctureABE: $(TwoPunctureFILES)
$(CLINKER) $(CXXAPPFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
$(CLINKER) $(CXXAPPFLAGS) -o $@ $(TwoPunctureFILES) $(LDLIBS)
clean:
rm *.o ABE ABEGPU TwoPunctureABE make.log -f

12
AMSS_NCKU_source/makefile.inc
View File

@@ -7,18 +7,20 @@
filein = -I/usr/include/ -I${MKLROOT}/include
## Using sequential MKL (OpenMP disabled for better single-threaded performance)
## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
LDLIBS = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl
LDLIBS = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -lifcore -limf -lmpi \
-L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core \
-lpthread -lm -ldl
## Aggressive optimization flags:
## -O3: Maximum optimization
## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
## -fp-model fast=2: Aggressive floating-point optimizations
## -fma: Enable fused multiply-add instructions
CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
## Note: OpenMP has been disabled (-qopenmp removed) due to performance issues
CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma \
-Dfortran3 -Dnewc -I${MKLROOT}/include
f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-align array64byte -fpp -I${MKLROOT}/include
f90appflags = -O3 -xHost -fp-model fast=2 -fma \
-fpp -I${MKLROOT}/include
f90 = ifx
f77 = ifx
CXX = icpx

10
makefile_and_run.py
View File

@@ -10,12 +10,12 @@
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)
## Format: taskset -c 4-55,60-111 ensures processes only run on these cores
NUMACTL_CPU_BIND = "taskset -c 0-111"
NUMACTL_CPU_BIND = "taskset -c 4-55,60-111"
## Build parallelism configuration
## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
@@ -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( )
@@ -179,9 +179,7 @@ def run_TwoPunctureABE():
print( )
print( " The TwoPunctureABE simulation is finished " )
print( )
tp_time2=time.time()
et=tp_time2-tp_time1
print(f"Used time: {et}")
return
##################################################################