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propagate.c
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propagate.c
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/*
* propagate.c
*
* Created by Bernard Giroux on 10-08-29.
*
*/
/*
* Copyright (c) 2011, Bernard Giroux
* All rights reserved.
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of the University of California, Berkeley nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE REGENTS AND CONTRIBUTORS BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include <math.h>
#include <stddef.h>
#include <stdlib.h>
#include <unistd.h>
#ifdef _OPENMP
#include <omp.h>
#endif
#include "propagate.h"
extern int verbose;
void init_fftw_data(double *W, struct fftw_data *d, const struct grid *g) {
size_t nnodes = g->nx2 * g->nz2;
size_t nx = g->nx2;
size_t nz = g->nz2;
double *tau_xx = &(W[0]);
double *tau_zz = &(W[nnodes]);
double *tau_xz = &(W[2*nnodes]);
double *p = &(W[3*nnodes]);
double *v_x = &(W[4*nnodes]);
double *v_z = &(W[5*nnodes]);
double *q_x = &(W[6*nnodes]);
double *q_z = &(W[7*nnodes]);
#ifdef _OPENMP
if ( verbose >= 1 ) {
fprintf(stdout, "Initializing fftw data - using %d threads (this may take some time) ... ", omp_get_max_threads());
fflush(stdout);
}
fftw_init_threads();
fftw_plan_with_nthreads( omp_get_max_threads() );
#else
if ( verbose >= 1 ) {
fprintf(stdout, "Initializing fftw data (this may take some time) ... ");
fflush(stdout);
}
#endif
if ( NULL == ( d->o_x = (fftw_complex*) fftw_malloc((nx/2+1)*nz*sizeof(fftw_complex)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->o_z = (fftw_complex*) fftw_malloc(nx*(nz/2+1)*sizeof(fftw_complex)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->t1 = (double *) fftw_malloc(nnodes * sizeof(double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->t2 = (double *) fftw_malloc(nnodes * sizeof(double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->t3 = (double *) fftw_malloc(nnodes * sizeof(double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kx_f = (complex double *) fftw_malloc( (nx/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kx_b = (complex double *) fftw_malloc( (nx/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kz_f = (complex double *) fftw_malloc( (nz/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kz_b = (complex double *) fftw_malloc( (nz/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
double dn = 8.0*atan(1.0) / (g->dx*nx*nx);
for (size_t n=0; n<nx/2+1; ++n) {
double k = n*dn;
d->kx_f[n] = I*k*cexp( 0.5*I*k*g->dx*nx );
d->kx_b[n] = I*k*cexp( -0.5*I*k*g->dx*nx );
}
dn = 8.0*atan(1.0) / (g->dz*nz*nz);
for (size_t n=0; n<nz/2+1; ++n) {
double k = n*dn;
d->kz_f[n] = I*k*cexp( 0.5*I*k*g->dz*nz );
d->kz_b[n] = I*k*cexp( -0.5*I*k*g->dz*nz );
}
char hostname[100], wisdomfile[200];
gethostname( hostname, 100 );
sprintf(wisdomfile, "%s/.fftw/%s.wisdom", getenv("HOME"), hostname);
FILE *wfile = fopen(wisdomfile, "r");
if ( wfile != NULL ) {
fftw_import_wisdom_from_file( wfile );
fclose( wfile );
}
int n[] = { (int)nx };
int howmany = (int)nz;
int inembed[] = { (int)nnodes };
int istride = (int)nz;
int idist = 1;
int onembed[] = { (int)((nx/2+1)*nz) };
int ostride = 1;
int odist = nx/2+1;
if ( NULL == (
d->tauxx_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
tau_xx, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauxz_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
tau_xz, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->p_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
p, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vx_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
v_x, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vz_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
v_z, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->qx_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
q_x, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauxx_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t1, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauxz_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t1, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->p_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t2, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vx_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t1, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vz_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t2, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->qx_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t3, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
n[0] = (int)nz;
howmany = (int)nx;
inembed[0] = (int)nnodes;
istride = 1;
idist = (int)nz;
onembed[0] = (int)(nx*(nz/2+1));
ostride = 1;
odist = nz/2+1;
if ( NULL == (
d->tauxz_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
tau_xz, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauzz_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
tau_zz, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->p_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
p, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vx_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
v_x, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vz_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
v_z, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->qz_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
q_z, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauxz_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t2, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauzz_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t2, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->p_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t2, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vx_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t1, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vz_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t2, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->qz_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t3, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( (wfile = fopen(wisdomfile, "w")) != NULL ) {
fftw_export_wisdom_to_file( wfile );
fclose( wfile );
}
}
void free_fftw_data(struct fftw_data *d) {
fftw_destroy_plan( d->tauxx_x_f );
fftw_destroy_plan( d->tauzz_z_f );
fftw_destroy_plan( d->tauxz_x_f );
fftw_destroy_plan( d->tauxz_z_f );
fftw_destroy_plan( d->p_x_f );
fftw_destroy_plan( d->p_z_f );
fftw_destroy_plan( d->vx_x_f );
fftw_destroy_plan( d->vx_z_f );
fftw_destroy_plan( d->vz_x_f );
fftw_destroy_plan( d->vz_z_f );
fftw_destroy_plan( d->qx_x_f );
fftw_destroy_plan( d->qz_z_f );
fftw_destroy_plan( d->tauxx_x_i );
fftw_destroy_plan( d->tauzz_z_i );
fftw_destroy_plan( d->tauxz_x_i );
fftw_destroy_plan( d->tauxz_z_i );
fftw_destroy_plan( d->p_x_i );
fftw_destroy_plan( d->p_z_i );
fftw_destroy_plan( d->vx_x_i );
fftw_destroy_plan( d->vx_z_i );
fftw_destroy_plan( d->vz_x_i );
fftw_destroy_plan( d->vz_z_i );
fftw_destroy_plan( d->qx_x_i );
fftw_destroy_plan( d->qz_z_i );
fftw_free( d->o_x );
fftw_free( d->o_z );
fftw_free( d->t1 );
fftw_free( d->t2 );
fftw_free( d->t3 );
fftw_free( d->kx_f );
fftw_free( d->kx_b );
fftw_free( d->kz_f );
fftw_free( d->kz_b );
}
void init_fftw_data_ve(double *W, struct fftw_data *d, const struct grid *g) {
size_t nnodes = g->nx2 * g->nz2;
size_t nx = g->nx2;
size_t nz = g->nz2;
double *tau_xx = &(W[0]);
double *tau_zz = &(W[nnodes]);
double *tau_xz = &(W[2*nnodes]);
double *v_x = &(W[3*nnodes]);
double *v_z = &(W[4*nnodes]);
#ifdef _OPENMP
if ( verbose >= 1 ) {
fprintf(stdout, "Initializing fftw data - using %d threads (this may take some time) ... ", omp_get_max_threads());
fflush(stdout);
}
fftw_init_threads();
fftw_plan_with_nthreads( omp_get_max_threads() );
#else
if ( verbose >= 1 ) {
fprintf(stdout, "Initializing fftw data (this may take some time) ... ");
fflush(stdout);
}
#endif
if ( NULL == ( d->o_x = (fftw_complex*) fftw_malloc((nx/2+1)*nz*sizeof(fftw_complex)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->o_z = (fftw_complex*) fftw_malloc(nx*(nz/2+1)*sizeof(fftw_complex)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->t1 = (double *) fftw_malloc(nnodes * sizeof(double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->t2 = (double *) fftw_malloc(nnodes * sizeof(double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kx_f = (complex double *) fftw_malloc( (nx/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kx_b = (complex double *) fftw_malloc( (nx/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kz_f = (complex double *) fftw_malloc( (nz/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kz_b = (complex double *) fftw_malloc( (nz/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
double dn = 8.0*atan(1.0) / (g->dx*nx*nx);
for (size_t n=0; n<nx/2+1; ++n) {
double k = n*dn;
d->kx_f[n] = I*k*cexp( 0.5*I*k*g->dx*nx );
d->kx_b[n] = I*k*cexp( -0.5*I*k*g->dx*nx );
}
dn = 8.0*atan(1.0) / (g->dz*nz*nz);
for (size_t n=0; n<nz/2+1; ++n) {
double k = n*dn;
d->kz_f[n] = I*k*cexp( 0.5*I*k*g->dz*nz );
d->kz_b[n] = I*k*cexp( -0.5*I*k*g->dz*nz );
}
char hostname[100], wisdomfile[200];
gethostname( hostname, 100 );
sprintf(wisdomfile, "%s/.fftw/%s.wisdom", getenv("HOME"), hostname);
FILE *wfile = fopen(wisdomfile, "r");
if ( wfile != NULL ) {
fftw_import_wisdom_from_file( wfile );
fclose( wfile );
}
int n[] = { (int)nx };
int howmany = (int)nz;
int inembed[] = { (int)nnodes };
int istride = (int)nz;
int idist = 1;
int onembed[] = { (int)((nx/2+1)*nz) };
int ostride = 1;
int odist = nx/2+1;
if ( NULL == (
d->tauxx_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
tau_xx, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauxz_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
tau_xz, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vx_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
v_x, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vz_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
v_z, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauxx_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t1, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauxz_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t1, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vx_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t1, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vz_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t2, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
n[0] = (int)nz;
howmany = (int)nx;
inembed[0] = (int)nnodes;
istride = 1;
idist = (int)nz;
onembed[0] = (int)(nx*(nz/2+1));
ostride = 1;
odist = nz/2+1;
if ( NULL == (
d->tauxz_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
tau_xz, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauzz_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
tau_zz, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vx_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
v_x, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vz_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
v_z, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauxz_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t2, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauzz_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t2, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vx_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t1, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vz_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t2, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( (wfile = fopen(wisdomfile, "w")) != NULL ) {
fftw_export_wisdom_to_file( wfile );
fclose( wfile );
}
}
void free_fftw_data_ve(struct fftw_data *d) {
fftw_destroy_plan( d->tauxx_x_f );
fftw_destroy_plan( d->tauzz_z_f );
fftw_destroy_plan( d->tauxz_x_f );
fftw_destroy_plan( d->tauxz_z_f );
fftw_destroy_plan( d->vx_x_f );
fftw_destroy_plan( d->vx_z_f );
fftw_destroy_plan( d->vz_x_f );
fftw_destroy_plan( d->vz_z_f );
fftw_destroy_plan( d->tauxx_x_i );
fftw_destroy_plan( d->tauzz_z_i );
fftw_destroy_plan( d->tauxz_x_i );
fftw_destroy_plan( d->tauxz_z_i );
fftw_destroy_plan( d->vx_x_i );
fftw_destroy_plan( d->vx_z_i );
fftw_destroy_plan( d->vz_x_i );
fftw_destroy_plan( d->vz_z_i );
fftw_free( d->o_x );
fftw_free( d->o_z );
fftw_free( d->t1 );
fftw_free( d->t2 );
fftw_free( d->kx_f );
fftw_free( d->kx_b );
fftw_free( d->kz_f );
fftw_free( d->kz_b );
}
void init_fftw_data_ve_sh(double *W, struct fftw_data_ve_sh *d, const struct grid *g) {
size_t nnodes = g->nx2 * g->nz2;
size_t nx = g->nx2;
size_t nz = g->nz2;
double *tau_xy = &(W[0]);
double *tau_yz = &(W[nnodes]);
double *v_y = &(W[2*nnodes]);
#ifdef _OPENMP
if ( verbose >= 1 ) {
fprintf(stdout, "Initializing fftw data - using %d threads (this may take some time) ... ", omp_get_max_threads());
fflush(stdout);
}
fftw_init_threads();
fftw_plan_with_nthreads( omp_get_max_threads() );
#else
if ( verbose >= 1 ) {
fprintf(stdout, "Initializing fftw data (this may take some time) ... ");
fflush(stdout);
}
#endif
if ( NULL == ( d->o_x = (fftw_complex*) fftw_malloc((nx/2+1)*nz*sizeof(fftw_complex)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->o_z = (fftw_complex*) fftw_malloc(nx*(nz/2+1)*sizeof(fftw_complex)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->t1 = (double *) fftw_malloc(nnodes * sizeof(double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->t2 = (double *) fftw_malloc(nnodes * sizeof(double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kx_f = (complex double *) fftw_malloc( (nx/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kx_b = (complex double *) fftw_malloc( (nx/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kz_f = (complex double *) fftw_malloc( (nz/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == ( d->kz_b = (complex double *) fftw_malloc( (nz/2+1)*sizeof(complex double)))) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
double dn = 8.0*atan(1.0) / (g->dx*nx*nx);
for (size_t n=0; n<nx/2+1; ++n) {
double k = n*dn;
d->kx_f[n] = I*k*cexp( 0.5*I*k*g->dx*nx );
d->kx_b[n] = I*k*cexp( -0.5*I*k*g->dx*nx );
}
dn = 8.0*atan(1.0) / (g->dz*nz*nz);
for (size_t n=0; n<nz/2+1; ++n) {
double k = n*dn;
d->kz_f[n] = I*k*cexp( 0.5*I*k*g->dz*nz );
d->kz_b[n] = I*k*cexp( -0.5*I*k*g->dz*nz );
}
char hostname[100], wisdomfile[200];
gethostname( hostname, 100 );
sprintf(wisdomfile, "%s/.fftw/%s.wisdom", getenv("HOME"), hostname);
FILE *wfile = fopen(wisdomfile, "r");
if ( wfile != NULL ) {
fftw_import_wisdom_from_file( wfile );
fclose( wfile );
}
int n[] = { (int)nx };
int howmany = (int)nz;
int inembed[] = { (int)nnodes };
int istride = (int)nz;
int idist = 1;
int onembed[] = { (int)((nx/2+1)*nz) };
int ostride = 1;
int odist = nx/2+1;
if ( NULL == (
d->tauxy_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
tau_xy, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vy_x_f = fftw_plan_many_dft_r2c( 1, n, howmany,
v_y, inembed, istride, idist,
d->o_x, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauxy_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t1, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vy_x_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_x, onembed, ostride, odist,
d->t1, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
n[0] = (int)nz;
howmany = (int)nx;
inembed[0] = (int)nnodes;
istride = 1;
idist = (int)nz;
onembed[0] = (int)(nx*(nz/2+1));
ostride = 1;
odist = nz/2+1;
if ( NULL == (
d->tauyz_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
tau_yz, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vy_z_f = fftw_plan_many_dft_r2c( 1, n, howmany,
v_y, inembed, istride, idist,
d->o_z, onembed, ostride, odist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->tauyz_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t2, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( NULL == (
d->vy_z_i = fftw_plan_many_dft_c2r( 1, n, howmany,
d->o_z, onembed, ostride, odist,
d->t1, inembed, istride, idist,
FFTW_PATIENT)
)) { fprintf(stderr, "Error: cannot allocate memory\n"); abort(); }
if ( (wfile = fopen(wisdomfile, "w")) != NULL ) {
fftw_export_wisdom_to_file( wfile );
fclose( wfile );
}
}
void free_fftw_data_ve_sh(struct fftw_data_ve_sh *d) {
fftw_destroy_plan( d->tauxy_x_f );
fftw_destroy_plan( d->tauyz_z_f );
fftw_destroy_plan( d->vy_x_f );
fftw_destroy_plan( d->vy_z_f );
fftw_destroy_plan( d->tauxy_x_i );
fftw_destroy_plan( d->tauyz_z_i );
fftw_destroy_plan( d->vy_x_i );
fftw_destroy_plan( d->vy_z_i );
fftw_free( d->o_x );
fftw_free( d->o_z );
fftw_free( d->t1 );
fftw_free( d->t2 );
fftw_free( d->kx_f );
fftw_free( d->kx_b );
fftw_free( d->kz_f );
fftw_free( d->kz_b );
}
void propagate(double *W, double *delta, const struct grid *g,
const struct computationVariables *c, struct fftw_data *d) {
size_t nnodes = g->nx2 * g->nz2;
//double *q_x = &(W[6*nnodes]);
//double *q_z = &(W[7*nnodes]);
double *e = &(W[8*nnodes]);
double *tau2_xx = &(delta[0]);
double *tau2_zz = &(delta[nnodes]);
double *tau2_xz = &(delta[2*nnodes]);
double *p2 = &(delta[3*nnodes]);
double *v2_x = &(delta[4*nnodes]);
double *v2_z = &(delta[5*nnodes]);
double *q2_x = &(delta[6*nnodes]);
double *q2_z = &(delta[7*nnodes]);
double *e2 = &(delta[8*nnodes]);
//
// Solving system (26) in Carcione and Helle (1999)
//
// -------------------------------------------------------------------------
//
// Solve for
//
// D_x^+\tau_{xx} + D_z^-\tau_{xz} = \rho\frac{\partial v_x}{\partial t} + \rho_f\frac{\partial q_x}{\partial t}
// and
// -D_x^+p = \rho_f\frac{\partial v_x}{\partial t} + m\frac{\partial q_x}{\partial t} + \frac{\eta}{\kappa}q_x
//
// Note:
// rho_f^2/rho - m is stored into m
// rho_f/rho is stored into rho_f
// 1/rho is stored into rho
// D_x+ tau_xx
fftw_execute( d->tauxx_x_f );
partial_x_forward(d, g);
fftw_execute( d->tauxx_x_i ); // d->t1 now holds D_x tau_xx
// Dz- tau_xz
fftw_execute( d->tauxz_z_f );
partial_z_backward(d, g);
fftw_execute( d->tauxz_z_i ); // d->t2 now holds D_z tau_xz
for ( size_t n=0; n<nnodes; ++n )
d->t1[n] += d->t2[n]; // d->t1 now holds D_x tau_xx + D_z tau_xz
// D_x+ p
fftw_execute( d->p_x_f );
partial_x_forward(d, g);
fftw_execute( d->p_x_i ); // d->t2 now holds D_x p
for ( size_t n=0; n<nnodes; ++n ) {
// q2_x[n] = (d->t2[n] + c->rho_f_i[n]*d->t1[n] + c->nk_i[n]*q_x[n]) / c->m_i[n];
q2_x[n] = (d->t2[n] + c->rho_f_i[n]*d->t1[n]) / c->m_i[n];
v2_x[n] = c->rho_i[n]*d->t1[n] - c->rho_f_i[n]*q2_x[n];
}
// -------------------------------------------------------------------------
//
// Solve for
//
// D_x^+\tau_{xz} + D_z^-\tau_{zz} = \rho\frac{\partial v_z}{\partial t} + \rho_f\frac{\partial q_z}{\partial t}
// and
// -D_z^+p = \rho_f\frac{\partial v_z}{\partial t} + m\frac{\partial q_z}{\partial t} + \frac{\eta}{\kappa}q_z
// D_x- tau_xz
fftw_execute( d->tauxz_x_f );
partial_x_backward(d, g);
fftw_execute( d->tauxz_x_i ); // d->t1 now holds D_x tau_xz
// D_z+ tau_zz
fftw_execute( d->tauzz_z_f );
partial_z_forward(d, g);
fftw_execute( d->tauzz_z_i ); // d->t2 now holds D_z tau_zz
for ( size_t n=0; n<nnodes; ++n )
d->t1[n] += d->t2[n]; // d->t1 now holds D_x tau_xz + D_z tau_zz
// D_z+ p
fftw_execute( d->p_z_f );
partial_z_forward(d, g);
fftw_execute( d->p_z_i ); // d->t2 now holds D_z p
for ( size_t n=0; n<nnodes; ++n ) {
// q2_z[n] = (d->t2[n] + c->rho_f_j[n]*d->t1[n] + c->nk_j[n]*q_z[n]) / c->m_j[n];
q2_z[n] = (d->t2[n] + c->rho_f_j[n]*d->t1[n]) / c->m_j[n];
v2_z[n] = c->rho_j[n]*d->t1[n] - c->rho_f_j[n]*q2_z[n];
}
// -------------------------------------------------------------------------
// \epsilon = \alpha\left(D_x^-v_x + D_z^-v_z\right) + D_x^-q_x + D_z^-q_z
//
// D_x- v_x
fftw_execute( d->vx_x_f );
partial_x_backward(d, g);
fftw_execute( d->vx_x_i ); // d->t1 now holds D_xv_x
// D_z- v_z
fftw_execute( d->vz_z_f );
partial_z_backward(d, g);
fftw_execute( d->vz_z_i ); // d->t2 now holds D_zv_z
for ( size_t n=0; n<nnodes; ++n )
c->epsilon[n] = c->alpha[n] * ( d->t1[n]+d->t2[n] );
// D_x- q_x
fftw_execute( d->qx_x_f );
partial_x_backward(d, g);
fftw_execute( d->qx_x_i ); // d->t3 now holds D_xq_x
for ( size_t n=0; n<nnodes; ++n )
c->epsilon[n] += d->t3[n];
// D_z- q_z
fftw_execute( d->qz_z_f );
partial_z_backward(d, g);
fftw_execute( d->qz_z_i ); // d->t3 now holds D_zq_z
for ( size_t n=0; n<nnodes; ++n )
c->epsilon[n] += d->t3[n];
// -------------------------------------------------------------------------
//
// \frac{\partial e}{\partial t} = -\frac{1}{\tau_\sigma}\left[M\left(L+\varphi\right)^{-1}\varphi\epsilon+e\right]
//
// 1/tau_s is stored into tau_s
// M*varphi/(1+varphi) is stored into varphi
for ( size_t n=0; n<nnodes; ++n ) {
e2[n] = -c->tau_s[n] * (c->varphi[n]*c->epsilon[n] + e[n]);
// store M*epsilon + e in epsilon
c->epsilon[n] = c->M[n]*c->epsilon[n] + e[n];
}
// -------------------------------------------------------------------------
//
// \frac{\partial p}{\partial t} = -\left(M\epsilon+e\right)+s_f
//
for ( size_t n=0; n<nnodes; ++n )
p2[n] = - c->epsilon[n];
// -------------------------------------------------------------------------
//
// \frac{\partial \tau_{xx}}{\partial t} = E D_x^-v_x + (E-2\mu)D_z^-v_z+\alpha(M\epsilon+e)+s_{x}
//
// c->E holds in fact E
// c->mu holds in fact (E-2mu)
for ( size_t n=0; n<nnodes; ++n )
tau2_xx[n] = c->E[n]*d->t1[n] + c->mu[n]*d->t2[n] + c->alpha[n]*c->epsilon[n];
// -------------------------------------------------------------------------
//
// \frac{\partial \tau_{zz}}{\partial t} = (E-2\mu) D_x^-v_x + E D_z^-v_z+\alpha(M\epsilon+e)+s_{z}
//
for ( size_t n=0; n<nnodes; ++n )
tau2_zz[n] = c->mu[n]*d->t1[n] + c->E[n]*d->t2[n] + c->alpha[n]*c->epsilon[n];
// -------------------------------------------------------------------------
//
// \frac{\partial \tau_{xz}}{\partial t} = \mu\left(D_z^+v_x + D_x^+v_z\right)+s_{xz}
//
// with \mu interpolated at (i+1/2,j+1/2)
// D_z+ v_x
fftw_execute( d->vx_z_f );
partial_z_forward(d, g);
fftw_execute( d->vx_z_i ); // d->t1 now holds D_zv_x
// D_x+ v_z
fftw_execute( d->vz_x_f );
partial_x_forward(d, g);
fftw_execute( d->vz_x_i ); // d->t2 now holds D_xv_z
for ( size_t n=0; n<nnodes; ++n )
tau2_xz[n] = c->mu_ij[n] * ( d->t1[n]+d->t2[n] );
}
void propagateCPML(double *W, double *delta, const struct grid *g,
const struct computationVariables *c, struct fftw_data *d,
struct mem_pml *m, struct fac_pml *p) {
size_t nnodes = g->nx2 * g->nz2;
size_t npml = g->ab.np;
// double *q_x = &(W[6*nnodes]);
// double *q_z = &(W[7*nnodes]);
double *e = &(W[8*nnodes]);
double *tau2_xx = &(delta[0]);
double *tau2_zz = &(delta[nnodes]);
double *tau2_xz = &(delta[2*nnodes]);
double *p2 = &(delta[3*nnodes]);
double *v2_x = &(delta[4*nnodes]);
double *v2_z = &(delta[5*nnodes]);
double *q2_x = &(delta[6*nnodes]);
double *q2_z = &(delta[7*nnodes]);
double *e2 = &(delta[8*nnodes]);
//
// Solving system (26) in Carcione and Helle (1999)
//
// -------------------------------------------------------------------------
//
// Solve for
//
// D_x^+\tau_{xx} + D_z^-\tau_{xz} = \rho\frac{\partial v_x}{\partial t} + \rho_f\frac{\partial q_x}{\partial t}
// and
// -D_x^+p = \rho_f\frac{\partial v_x}{\partial t} + m\frac{\partial q_x}{\partial t} + \frac{\eta}{\kappa}q_x
//
// Note:
// rho_f^2/rho - m is stored into m
// rho_f/rho is stored into rho_f
// 1/rho is stored into rho
// D_x+ tau_xx
fftw_execute( d->tauxx_x_f );
partial_x_forward(d, g);
fftw_execute( d->tauxx_x_i ); // d->t1 now holds D_x tau_xx
// Dz- tau_xz
fftw_execute( d->tauxz_z_f );
partial_z_backward(d, g);
fftw_execute( d->tauxz_z_i ); // d->t2 now holds D_z tau_xz
// update memory variables and replace spatial derivative in PML region
// derivative evaluated at i+1/2,j
size_t ipml = 0;
for ( size_t nl=0; nl<npml; ++nl ) { // left
for ( size_t j=0; j<g->nz2; ++j, ++ipml ) {
size_t ind = nl*g->nz2 + j;
m[1].dx_txx[ipml] = p->bh_x[nl]*m[0].dx_txx[ipml] + p->ch_x[nl]*d->t1[ind]; // eq 32 of Martin et al. 2010, with sign corrected before c_x
d->t1[ind] = d->t1[ind]/p->kh_x[nl] + m[2].dx_txx[ipml];
}
}
for ( size_t nl=0; nl<npml+1; ++nl ) { // right
for ( size_t j=0; j<g->nz2; ++j, ++ipml ) {
size_t ind = (g->nx2-1-nl)*g->nz2 + j;
m[1].dx_txx[ipml] = p->bH_x[nl]*m[0].dx_txx[ipml] + p->cH_x[nl] *d->t1[ind];
d->t1[ind] = d->t1[ind]/p->kH_x[nl] + m[2].dx_txx[ipml];
}
}
// derivative evaluated at i+1/2,j
ipml=0;
for ( size_t nl=0; nl<npml; ++nl ) { // top
for ( size_t i=0; i<g->nx2; ++i, ++ipml ) {
size_t ind = i*g->nz2+nl;
m[1].dz_txz[ipml] = p->b_z[nl]*m[0].dz_txz[ipml] + p->c_z[nl]*d->t2[ind];
d->t2[ind] = d->t2[ind]/p->k_z[nl] + m[2].dz_txz[ipml];
}
}
for ( size_t nl=0; nl<npml; ++nl ) { // bottom
for ( size_t i=0; i<g->nx2; ++i, ++ipml ) {
size_t ind = i*g->nz2 + g->nz2-1-nl;
m[1].dz_txz[ipml] = p->b_z[nl]*m[0].dz_txz[ipml] + p->c_z[nl]*d->t2[ind];
d->t2[ind] = d->t2[ind]/p->k_z[nl] + m[2].dz_txz[ipml];
}
}
for ( size_t n=0; n<nnodes; ++n )
d->t1[n] += d->t2[n]; // d->t1 now holds D_x tau_xx + D_z tau_xz
// D_x+ p
fftw_execute( d->p_x_f );
partial_x_forward(d, g);
fftw_execute( d->p_x_i ); // d->t2 now holds D_x p
// update memory variables and replace spatial derivative in PML region
// derivative evaluated at i+1/2,j
ipml=0;
for ( size_t nl=0; nl<npml; ++nl ) { // left
for ( size_t j=0; j<g->nz2; ++j, ++ipml ) {
size_t ind = nl*g->nz2 + j;
m[1].dx_p[ipml] = p->bh_x[nl]*m[0].dx_p[ipml] + p->ch_x[nl]*d->t2[ind];
d->t2[ind] = d->t2[ind]/p->kh_x[nl] + m[2].dx_p[ipml];
}
}
for ( size_t nl=0; nl<npml+1; ++nl ) { // right
for ( size_t j=0; j<g->nz2; ++j, ++ipml ) {
size_t ind = (g->nx2-1-nl)*g->nz2 + j;
m[1].dx_p[ipml] = p->bH_x[nl]*m[0].dx_p[ipml] + p->cH_x[nl]*d->t2[ind];
d->t2[ind] = d->t2[ind]/p->kH_x[nl] + m[2].dx_p[ipml];
}
}
for (size_t i=1; i<g->nx2-1; ++i) {
for ( size_t j=1; j<g->nz2-1; ++j) {
size_t n = i*g->nz2+j;