wave_1d_sequential.c

#define _XOPEN_SOURCE 600
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
#include <math.h>
#include <sys/time.h>


// 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.
const int_t
    N = 65536,
    max_iteration = 100000,
    snapshot_freq = 500;

// Wave equation parameters, time step is derived from the space step.
const real_t
    c  = 1.0,
    dx = 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) buffers[0][(i)+1]
#define U(i)     buffers[1][(i)+1]
#define U_nxt(i) buffers[2][(i)+1]


// Convert 'struct timeval' into seconds in double prec. floating point
#define WALLTIME(t) ((double)(t).tv_sec + 1e-6 * (double)(t).tv_usec)


// Save the present time step in a numbered file under 'data/'.
void domain_save ( int_t step )
{
    char filename[256];
    sprintf ( filename, "data/%.5ld.dat", step );
    FILE *out = fopen ( filename, "wb" );
    fwrite ( &U(0), sizeof(real_t), N, out );
    fclose ( out );
}


// Set up our three buffers, fill two with an initial cosine wave,
// and set the time step.
void domain_initialize ( void )
{
    buffers[0] = malloc ( (N+2)*sizeof(real_t) );
    buffers[1] = malloc ( (N+2)*sizeof(real_t) );
    buffers[2] = malloc ( (N+2)*sizeof(real_t) );

    for ( int_t i=0; i<N; i++ )
    {
        U_prv(i) = U(i) = cos ( M_PI*i / (real_t)N );
    }

    // Set the time step for 1D case.
    dt = dx / c;
}


// Return the memory to the OS.
void domain_finalize ( void )
{
    free ( buffers[0] );
    free ( buffers[1] );
    free ( buffers[2] );
}


// 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;
}


// Derive step t+1 from steps t and t-1.
void time_step ( void )
{
    for ( int_t i=0; i<N; i++ )
    {
        U_nxt(i) = -U_prv(i) + 2.0*U(i)
                 + (dt*dt*c*c)/(dx*dx) * (U(i-1)+U(i+1)-2.0*U(i));
    }
}


// Neumann (reflective) boundary condition.
void boundary_condition ( void )
{
    U(-1) = U(1);
    U(N)  = U(N-2);
}


// 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();

        move_buffer_window();
    }
}


int main ( void )
{
    struct timeval t_start, t_end;

    domain_initialize();

    gettimeofday ( &t_start, NULL );
    simulate();
    gettimeofday ( &t_end, NULL );

    printf ( "Total elapsed time: %lf seconds\n",
        WALLTIME(t_end) - WALLTIME(t_start)
    );

    domain_finalize();

    exit ( EXIT_SUCCESS );
}