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