ex4: init

This commit is contained in:
2025-10-06 14:30:33 +02:00
parent 4627b0b522
commit dbd6259ac7
9 changed files with 903 additions and 0 deletions

3
exercise4/.gitignore vendored Normal file
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data/
data_sequential/
images/

38
exercise4/Makefile Normal file
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CC=gcc
PARALLEL_CC=mpicc
CFLAGS+= -std=c99 -O2 -Wall -Wextra
LDLIBS+= -lm
SEQUENTIAL_SRC_FILES=wave_2d_sequential.c argument_utils.c
PARALLEL_SRC_FILES=wave_2d_parallel.c argument_utils.c
IMAGES=$(shell find data -type f | sed s/\\.dat/.png/g | sed s/data/images/g )
.PHONY: all clean dirs plot movie
all: dirs ${TARGETS}
dirs:
mkdir -p data images
sequential: ${SEQUENTIAL_SRC_FILES}
$(CC) $^ $(CFLAGS) -o $@ $(LDLIBS)
parallel: ${PARALLEL_SRC_FILES}
$(PARALLEL_CC) $^ $(CFLAGS) -o $@ $(LDLIBS)
plot: ${IMAGES}
images/%.png: data/%.dat
./plot_image.sh $<
movie: ${IMAGES}
ffmpeg -y -an -i images/%5d.png -vcodec libx264 -pix_fmt yuv420p -profile:v baseline -level 3 -r 12 wave.mp4
check: dirs sequential parallel
mkdir -p data_sequential
./sequential
cp -rf ./data/* ./data_sequential
mpiexec -n 1 --oversubscribe ./parallel
./compare.sh
rm ./data/*
mpiexec -n 4 --oversubscribe ./parallel
./compare.sh
rm ./data/*
rm ./data_sequential/*
./sequential -m 2048 -n 512
cp -rf ./data/* ./data_sequential
mpiexec -n 16 --oversubscribe ./parallel -m 2048 -n 512
./compare.sh
rm -rf data_sequential
clean:
-rm -fr sequential parallel data images wave.mp4

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exercise4/README.md Normal file
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* make : builds the executable 'wave_1d'
* ./wave\_2d : fills the 'data/' directory with stored time steps
* make plot : converts saved time steps to png files under 'images/', using gnuplot. Runs faster if launched with e.g. 4 threads (make -j4 plot).
* make movie : converts collection of png files under 'images' into an mp4 movie file, using ffmpeg
* make check : builds both executeables and compares their output

127
exercise4/argument_utils.c Normal file
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#include "argument_utils.h"
#include <getopt.h>
#include <stddef.h>
#include <stdio.h>
#include <memory.h>
#include <stdlib.h>
OPTIONS *parse_args ( int argc, char **argv )
{
/*
* Argument parsing: don't change this!
*/
int_t M = 1024;
int_t N = 1024;
int_t max_iteration = 10000;
int_t snapshot_frequency = 10;
static struct option const long_options[] = {
{"help", no_argument, 0, 'h'},
{"y_size", required_argument, 0, 'm'},
{"x_size", required_argument, 0, 'n'},
{"max_iteration", required_argument, 0, 'i'},
{"snapshot_frequency", required_argument, 0, 's'},
{0, 0, 0, 0}
};
static char const * short_options = "hm:n:i:s:";
{
char *endptr;
int c;
int option_index = 0;
while ( (c = getopt_long( argc, argv, short_options, long_options, &option_index )) != -1 )
{
switch (c)
{
case 'h':
help( argv[0], 0, NULL );
exit(0);
break;
case 'm':
M = strtol(optarg, &endptr, 10);
if ( endptr == optarg || M < 0 )
{
help( argv[0], c, optarg );
return NULL;
}
break;
case 'n':
N = strtol(optarg, &endptr, 10);
if ( endptr == optarg || N < 0 )
{
help( argv[0], c, optarg );
return NULL;
}
break;
case 'i':
max_iteration = strtol(optarg, &endptr, 10);
if ( endptr == optarg || max_iteration < 0 )
{
help( argv[0], c, optarg);
return NULL;
}
break;
case 's':
snapshot_frequency = strtol(optarg, &endptr, 10);
if ( endptr == optarg || snapshot_frequency < 0 )
{
help( argv[0], c, optarg );
return NULL;
}
break;
default:
abort();
}
}
}
if ( argc < (optind) )
{
printf("argc/optind: %d/%d\n", argc, optind);
help( argv[0], ' ', "Not enough arugments" );
return NULL;
}
OPTIONS *args_parsed = malloc( sizeof(OPTIONS) );
args_parsed->M = M;
args_parsed->N = N;
args_parsed->max_iteration = max_iteration;
args_parsed->snapshot_frequency = snapshot_frequency;
return args_parsed;
}
void help ( char const *exec, char const opt, char const *optarg )
{
FILE *out = stdout;
if ( opt != 0 )
{
out = stderr;
if ( optarg )
{
fprintf(out, "Invalid parameter - %c %s\n", opt, optarg);
}
else
{
fprintf(out, "Invalid parameter - %c\n", opt);
}
}
fprintf(out, "%s [options]\n", exec);
fprintf(out, "\n");
fprintf(out, "Options Description Restriction Default\n");
fprintf(out, " -m, --y_size size of the y dimension n>0 256\n" );
fprintf(out, " -n, --x_size size of the x dimension n>0 256\n" );
fprintf(out, " -i, --max_iteration number of iterations i>0 100000\n" );
fprintf(out, " -s, --snapshot_freq snapshot frequency s>0 1000\n" );
fprintf(out, "\n");
fprintf(out, "Example: %s -m 256 -n 256 -i 100000 -s 1000\n", exec);
}

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#ifndef _ARGUMENT_UTILS_H_
#define _ARGUMENT_UTILS_H_
#include <stdint.h>
typedef int64_t int_t;
typedef struct options_struct {
int_t M;
int_t N;
int_t max_iteration;
int_t snapshot_frequency;
} OPTIONS;
OPTIONS *parse_args ( int argc, char **argv );
void help ( char const *exec, char const opt, char const *optarg );
#endif

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exercise4/compare.sh Executable file
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#! /usr/bin/env bash
GREEN=$(tput setaf 2)
RED=$(tput setaf 1)
RESET=$(tput sgr0)
DIR1="data"
DIR2="data_sequential"
if [ ! -d "$DIR1" ]; then
echo "Directory $DIR1 does not exist."
exit 1
fi
if [ ! -d "$DIR2" ]; then
echo "Directory $DIR2 does not exist."
exit 1
fi
found_difference=1
for file in "$DIR1"/*.dat; do
# Extract the file name (basename)
filename=$(basename "$file")
# Check if the corresponding file exists in DIR2
if [ -f "$DIR2/$filename" ]; then
# Compare the two files using diff
diff_output=$(diff "$file" "$DIR2/$filename")
if [ -n "$diff_output" ]; then
echo "$diff_output"
found_difference=0
fi
else
echo "File $filename does not exist in $DIR2"
fi
done
if [ $found_difference -eq 1 ]; then
echo
echo
echo "${GREEN}The sequential and parallel version produced mathcing output!${RESET}"
echo
echo
else
echo
echo
echo "${RED}There were mismatches between the sequential and the parallel output.${RESET}"
echo
echo
fi

100
exercise4/plot_image.sh Executable file
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#! /usr/bin/env bash
help()
{
echo
echo "Plot 2D Wave Equation"
echo
echo "Syntax"
echo "--------------------------------------------------------"
echo "./plot_results.sh [-m|n|h] [data_folder] "
echo
echo "Option Description Arguments Default"
echo "--------------------------------------------------------"
echo "m x size Optional 1024 "
echo "n y size Optional 1024 "
echo "h Help None "
echo
echo "Example"
echo "--------------------------------------------------------"
echo "./plot_image.sh -m 1024 -n 1024"
echo
}
#-----------------------------------------------------------------
set -e
M=1024
N=1024
# Check if the data folder is provided
if [ $# -lt 1 ]; then
echo "Error: No data folder provided."
help
exit 1
fi
# Parse options and arguments
while getopts ":m:n:h" opt; do
case $opt in
m)
M=$OPTARG;;
n)
N=$OPTARG;;
h)
help
exit;;
\?)
echo "Invalid option"
help
exit;;
esac
done
# Shift parsed options so that the remaining arguments start at $1
shift $((OPTIND - 1))
# Ensure that the data folder is provided and exists
DATAFOLDER=./data
if [ ! -d "$DATAFOLDER" ]; then
echo "Error: Data folder $DATAFOLDER does not exist."
exit 1
fi
#-----------------------------------------------------------------
# Set up the size of the grid based on the options passed
SIZE_M=`echo $M | bc`
SIZE_N=`echo $N | bc`
# Ensure the output directory exists
mkdir -p images
# Loop through all .dat files in the data folder
for DATAFILE in "$DATAFOLDER"/*.dat; do
# Skip if no .dat files are found
if [ ! -f "$DATAFILE" ]; then
echo "No .dat files found in the folder."
exit 1
fi
# Create the corresponding output image file name
IMAGEFILE=`echo $DATAFILE | sed 's/dat$/png/' | sed 's/data/images/'`
# Run the gnuplot command to create the plot in the background
(
cat <<END_OF_SCRIPT | gnuplot -
set term png
set output "$IMAGEFILE"
set zrange[-1:1]
splot "$DATAFILE" binary array=${SIZE_N}x${SIZE_M} format='%double' with pm3d
END_OF_SCRIPT
echo "Plot saved to $IMAGEFILE"
) & # Run in the background
done
# Wait for all background processes to finish
wait
echo "All plots have been generated."

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#define _XOPEN_SOURCE 600
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
#include <math.h>
#include <sys/time.h>
#include <sys/stat.h>
#include <errno.h>
#include <inttypes.h>
#include "argument_utils.h"
// TASK: T1a
// Include the MPI headerfile
// BEGIN: T1a
;
// END: T1a
// Convert 'struct timeval' into seconds in double prec. floating point
#define WALLTIME(t) ((double)(t).tv_sec + 1e-6 * (double)(t).tv_usec)
// Option to change numerical precision
typedef int64_t int_t;
typedef double real_t;
// Buffers for three time steps, indexed with 2 ghost points for the boundary
real_t
*buffers[3] = { NULL, NULL, NULL };
// TASK: T1b
// Declare variables each MPI process will need
// BEGIN: T1b
#define U_prv(i,j) buffers[0][((i)+1)*(N+2)+(j)+1]
#define U(i,j) buffers[1][((i)+1)*(N+2)+(j)+1]
#define U_nxt(i,j) buffers[2][((i)+1)*(N+2)+(j)+1]
// END: T1b
// Simulation parameters: size, step count, and how often to save the state
int_t
M = 256, // rows
N = 256, // cols
max_iteration = 4000,
snapshot_freq = 20;
// Wave equation parameters, time step is derived from the space step
const real_t
c = 1.0,
dx = 1.0,
dy = 1.0;
real_t
dt;
// Rotate the time step buffers.
void move_buffer_window ( void )
{
real_t *temp = buffers[0];
buffers[0] = buffers[1];
buffers[1] = buffers[2];
buffers[2] = temp;
}
// TASK: T8
// Save the present time step in a numbered file under 'data/'
void domain_save ( int_t step )
{
// BEGIN: T8
char filename[256];
// Ensure output directory exists (ignore error if it already exists)
if (mkdir("data", 0755) != 0 && errno != EEXIST) {
perror("mkdir data");
exit(EXIT_FAILURE);
}
snprintf(filename, sizeof(filename), "data/%05" PRId64 ".dat", step);
FILE *out = fopen(filename, "wb");
if (out == NULL) {
perror("fopen output file");
fprintf(stderr, "Failed to open '%s' for writing.\n", filename);
exit(EXIT_FAILURE);
}
for ( int_t i = 0; i < M; ++i ) {
size_t written = fwrite ( &U(i,0), sizeof(real_t), (size_t)N, out );
if ( written != (size_t)N ) {
perror("fwrite");
fclose(out);
exit(EXIT_FAILURE);
}
}
if ( fclose(out) != 0 ) {
perror("fclose");
exit(EXIT_FAILURE);
}
// END: T8
}
// TASK: T7
// Neumann (reflective) boundary condition
void boundary_condition ( void )
{
// BEGIN: T7
// Vertical ghost layers (bottom and top)
for (int_t i=0; i<M; i++) {
U(i,-1) = U(i,1); // bottom ghost row <- mirror of row 1
U(i,N) = U(i,N-2); // top ghost row <- mirror of row N-2
}
// Horizontal ghost layers (left and right)
for (int_t j=0; j<N; j++) {
U(-1,j) = U(1,j); // left ghost col <- mirror of col 1
U(M,j) = U(M-2,j); // right ghost col <- mirror of col M-2
}
// Corner ghost cells (use ghost indices)
U(-1,-1) = U(1,1); // bottom-left
U(-1,N) = U(1,N-2); // top-left
U(M,-1) = U(M-2,1); // bottom-right
U(M,N) = U(M-2,N-2); // top-right
// END: T7
}
// TASK: T4
// Set up our three buffers, and fill two with an initial perturbation
// and set the time step.
void domain_initialize ( void )
{
// BEGIN: T4
buffers[0] = malloc ( (M+2)*(N+2)*sizeof(real_t) );
buffers[1] = malloc ( (M+2)*(N+2)*sizeof(real_t) );
buffers[2] = malloc ( (M+2)*(N+2)*sizeof(real_t) );
if ( !buffers[0] || !buffers[1] || !buffers[2] ) {
perror("malloc");
exit(EXIT_FAILURE);
}
// initialize interior (physical cells)
for ( int_t i=0; i<M; i++ )
{
for ( int_t j=0; j<N; j++ )
{
real_t dx_i = (i - M/2.0);
real_t dy_j = (j - N/2.0);
real_t delta = sqrt( (dx_i*dx_i) / (real_t)M + (dy_j*dy_j) / (real_t)N );
U_prv(i,j) = U(i,j) = exp ( -4.0*delta*delta );
}
}
// Set the time step (CFL) with a safety factor
dt = 1.0 / ( c * sqrt( 1.0/(dx*dx) + 1.0/(dy*dy) ) );
dt *= 0.9; // safety factor
// Fill ghost cells once so they are valid before the first step
boundary_condition();
// END: T4
}
// Get rid of all the memory allocations
void domain_finalize ( void )
{
free ( buffers[0] );
free ( buffers[1] );
free ( buffers[2] );
}
// TASK: T5
// Integration formula
void time_step ( void )
{
// BEGIN: T5
double coef_x = (c * dt) * (c * dt) / (dx * dx);
double coef_y = (c * dt) * (c * dt) / (dy * dy);
double coef_xy = (c * dt) * (c * dt) / (6.0 * dx * dy);
// Only iterate over physical domain cells i = 0..M-1, j = 0..N-1
for (int i = 0; i < M; i++)
{
for (int j = 0; j < N; j++)
{
U_nxt(i,j) = 2.0*U(i,j) - U_prv(i,j)
+ coef_x * (U(i+1,j) - 2.0*U(i,j) + U(i-1,j))
+ coef_y * (U(i,j+1) - 2.0*U(i,j) + U(i,j-1))
+ coef_xy * (U(i+1,j+1) + U(i+1,j-1) +
U(i-1,j+1) + U(i-1,j-1) - 4.0*U(i,j));
}
}
// END: T5
}
void get_corner_procs(void) {
int neighbor_coords[2];
neighbor_coords[0] = coordinates[0] - 1;
neighbor_coords[1] = coordinates[1] - 1;
if (neighbor_coords[0] >= 0 && neighbor_coords[1] >= 0) {
MPI_Cart_rank(cartesian_comm, neighbor_coords, &up_left);
} else {
up_left = MPI_PROC_NULL;
}
neighbor_coords[0] = coordinates[0] - 1;
neighbor_coords[1] = coordinates[1] + 1;
if (neighbor_coords[0] >= 0 && neighbor_coords[1] < dims[1]) {
MPI_Cart_rank(cartesian_comm, neighbor_coords, &up_right);
} else {
up_right = MPI_PROC_NULL;
}
neighbor_coords[0] = coordinates[0] + 1;
neighbor_coords[1] = coordinates[1] - 1;
if (neighbor_coords[0] < dims[0] && neighbor_coords[1] >= 0) {
MPI_Cart_rank(cartesian_comm, neighbor_coords, &down_left);
} else {
down_left = MPI_PROC_NULL;
}
neighbor_coords[0] = coordinates[0] + 1;
neighbor_coords[1] = coordinates[1] + 1;
if (neighbor_coords[0] < dims[0] && neighbor_coords[1] < dims[1]) {
MPI_Cart_rank(cartesian_comm, neighbor_coords, &down_right);
} else {
down_right = MPI_PROC_NULL;
}
}
// TASK: T6
// Communicate the border between processes.
void border_exchange ( void )
{
// BEGIN: T6
;
// END: T6
}
// Main time integration.
void simulate( void )
{
// Go through each time step
for ( int_t iteration=0; iteration<=max_iteration; iteration++ )
{
if ( (iteration % snapshot_freq)==0 )
{
domain_save ( iteration / snapshot_freq );
}
// Derive step t+1 from steps t and t-1
border_exchange();
boundary_condition();
time_step();
// Rotate the time step buffers
move_buffer_window();
}
}
int main ( int argc, char **argv )
{
// TASK: T1c
// Initialise MPI
// BEGIN: T1c
;
// END: T1c
// TASK: T3
// Distribute the user arguments to all the processes
// BEGIN: T3
OPTIONS *options = parse_args( argc, argv );
if ( !options )
{
fprintf( stderr, "Argument parsing failed\n" );
exit( EXIT_FAILURE );
}
M = options->M;
N = options->N;
max_iteration = options->max_iteration;
snapshot_freq = options->snapshot_frequency;
// END: T3
// Set up the initial state of the domain
domain_initialize();
struct timeval t_start, t_end;
// TASK: T2
// Time your code
// BEGIN: T2
simulate();
// END: T2
// Clean up and shut down
domain_finalize();
// TASK: T1d
// Finalise MPI
// BEGIN: T1d
;
// END: T1d
exit ( EXIT_SUCCESS );
}

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#define _XOPEN_SOURCE 600
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
#include <math.h>
#include <sys/time.h>
#include <sys/stat.h>
#include <errno.h>
#include <inttypes.h>
#include "argument_utils.h"
// Convert 'struct timeval' into seconds in double prec. floating point
#define WALLTIME(t) ((double)(t).tv_sec + 1e-6 * (double)(t).tv_usec)
// Option to change numerical precision
typedef int64_t int_t;
typedef double real_t;
// Simulation parameters: size, step count, and how often to save the state
int_t
N = 256,
M = 256,
max_iteration = 4000,
snapshot_freq = 20;
// Wave equation parameters, time step is derived from the space step
const real_t
c = 1.0,
dx = 1.0,
dy = 1.0;
real_t
dt;
// Buffers for three time steps, indexed with 2 ghost points for the boundary
real_t
*buffers[3] = { NULL, NULL, NULL };
#define U_prv(i,j) buffers[0][((i)+1)*(N+2)+(j)+1]
#define U(i,j) buffers[1][((i)+1)*(N+2)+(j)+1]
#define U_nxt(i,j) buffers[2][((i)+1)*(N+2)+(j)+1]
// Rotate the time step buffers.
void move_buffer_window ( void )
{
real_t *temp = buffers[0];
buffers[0] = buffers[1];
buffers[1] = buffers[2];
buffers[2] = temp;
}
// Save the present time step in a numbered file under 'data/'
void domain_save ( int_t step )
{
char filename[256];
// Ensure output directory exists (ignore error if it already exists)
if (mkdir("data", 0755) != 0 && errno != EEXIST) {
perror("mkdir data");
exit(EXIT_FAILURE);
}
snprintf(filename, sizeof(filename), "data/%05" PRId64 ".dat", step);
FILE *out = fopen(filename, "wb");
if (out == NULL) {
perror("fopen output file");
fprintf(stderr, "Failed to open '%s' for writing.\n", filename);
exit(EXIT_FAILURE);
}
for ( int_t i = 0; i < M; ++i ) {
size_t written = fwrite ( &U(i,0), sizeof(real_t), (size_t)N, out );
if ( written != (size_t)N ) {
perror("fwrite");
fclose(out);
exit(EXIT_FAILURE);
}
}
if ( fclose(out) != 0 ) {
perror("fclose");
exit(EXIT_FAILURE);
}
}
// Neumann (reflective) boundary condition
void boundary_condition ( void )
{
// Vertical ghost layers (bottom and top)
for (int_t i=0; i<M; i++) {
U(i,-1) = U(i,1); // bottom ghost row <- mirror of row 1
U(i,N) = U(i,N-2); // top ghost row <- mirror of row N-2
}
// Horizontal ghost layers (left and right)
for (int_t j=0; j<N; j++) {
U(-1,j) = U(1,j); // left ghost col <- mirror of col 1
U(M,j) = U(M-2,j); // right ghost col <- mirror of col M-2
}
// Corner ghost cells (use ghost indices)
U(-1,-1) = U(1,1); // bottom-left
U(-1,N) = U(1,N-2); // top-left
U(M,-1) = U(M-2,1); // bottom-right
U(M,N) = U(M-2,N-2); // top-right
}
// Set up our three buffers, and fill two with an initial perturbation
void domain_initialize ( void )
{
buffers[0] = malloc ( (M+2)*(N+2)*sizeof(real_t) );
buffers[1] = malloc ( (M+2)*(N+2)*sizeof(real_t) );
buffers[2] = malloc ( (M+2)*(N+2)*sizeof(real_t) );
if ( !buffers[0] || !buffers[1] || !buffers[2] ) {
perror("malloc");
exit(EXIT_FAILURE);
}
// initialize interior (physical cells)
for ( int_t i=0; i<M; i++ )
{
for ( int_t j=0; j<N; j++ )
{
real_t dx_i = (i - M/2.0);
real_t dy_j = (j - N/2.0);
real_t delta = sqrt( (dx_i*dx_i) / (real_t)M + (dy_j*dy_j) / (real_t)N );
U_prv(i,j) = U(i,j) = exp ( -4.0*delta*delta );
}
}
// Set the time step (CFL) with a safety factor
dt = 1.0 / ( c * sqrt( 1.0/(dx*dx) + 1.0/(dy*dy) ) );
dt *= 0.9; // safety factor
// Fill ghost cells once so they are valid before the first step
boundary_condition();
}
// Get rid of all the memory allocations
void domain_finalize ( void )
{
free ( buffers[0] );
free ( buffers[1] );
free ( buffers[2] );
}
// Integration formula (Eq. 9 from the pdf document)
void time_step ( void )
{
double coef_x = (c * dt) * (c * dt) / (dx * dx);
double coef_y = (c * dt) * (c * dt) / (dy * dy);
double coef_xy = (c * dt) * (c * dt) / (6.0 * dx * dy);
// Only iterate over physical domain cells i = 0..M-1, j = 0..N-1
for (int i = 0; i < M; i++)
{
for (int j = 0; j < N; j++)
{
U_nxt(i,j) = 2.0*U(i,j) - U_prv(i,j)
+ coef_x * (U(i+1,j) - 2.0*U(i,j) + U(i-1,j))
+ coef_y * (U(i,j+1) - 2.0*U(i,j) + U(i,j-1))
+ coef_xy * (U(i+1,j+1) + U(i+1,j-1) +
U(i-1,j+1) + U(i-1,j-1) - 4.0*U(i,j));
}
}
}
// Main time integration.
void simulate( void )
{
// Go through each time step
for ( int_t iteration=0; iteration<=max_iteration; iteration++ )
{
if ( (iteration % snapshot_freq)==0 )
{
domain_save ( iteration / snapshot_freq );
}
// Derive step t+1 from steps t and t-1
boundary_condition();
time_step();
// Rotate the time step buffers
move_buffer_window();
}
}
int main ( int argc, char **argv )
{
OPTIONS *options = parse_args( argc, argv );
if ( !options )
{
fprintf( stderr, "Argument parsing failed\n" );
exit( EXIT_FAILURE );
}
M = options->M;
N = options->N;
max_iteration = options->max_iteration;
snapshot_freq = options->snapshot_frequency;
if (M < 2 || N < 2)
{
fprintf(stderr, "M and N must be >= 2\n");
exit(EXIT_FAILURE);
}
// Set up the initial state of the domain
domain_initialize();
struct timeval t_start, t_end;
gettimeofday ( &t_start, NULL );
simulate();
gettimeofday ( &t_end, NULL );
printf ( "Total elapsed time: %lf seconds\n",
WALLTIME(t_end) - WALLTIME(t_start)
);
// Clean up and shut down
domain_finalize();
exit ( EXIT_SUCCESS );
}