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pml.c
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/*
* pml.c
*
* Created by Bernard Giroux on 11-02-11.
*
*/
/*
* 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 "pml.h"
void pml_v(double *vx_x, double *vx_z,
double *vz_x, double *vz_z,
const double *txx_x, const double *txx_z,
const double *tzz_x, const double *tzz_z,
const double *txz_x, const double *txz_z,
const double d[], const double dh[], const double dH[],
const double *txx, const double *tzz, const double *txz,
const double *b, const double *bm,
const size_t nx, const size_t nz, const size_t Npml,
const double dt, const double h)
{
register double c1, c2, txx1, txx2, txz1, txz2, tzz1, tzz2;
// Vx - upper left corner
//
size_t off1 = 0;
for (size_t j=0; j<Npml; ++j) {
txx1 = txx_x[off1 + j] + txx_z[off1 + j];
txx2 = 0.;
c1 = (2.*dt) / ( 2. + dt*d[0] );
c2 = ( 2. - dt*d[0] ) / (2.*dt);
vx_x[ off1 + j ] *= c2;
vx_x[ off1 + j ] += b[0] * (txx1 - txx2) / h;
vx_x[ off1 + j ] *= c1;
}
for (size_t i=1; i<Npml; ++i) {
for (size_t j=0; j<Npml; ++j) {
txx1 = txx_x[off1 + i*Npml+j] + txx_z[off1 + i*Npml+j];
txx2 = txx_x[off1 + (i-1)*Npml+j] + txx_z[off1 + (i-1)*Npml+j];
c1 = (2.*dt) / ( 2. + dt*d[i] );
c2 = ( 2. - dt*d[i] ) / (2.*dt);
vx_x[ off1 + i*Npml+j ] *= c2;
vx_x[ off1 + i*Npml+j ] += b[0] * (txx1 - txx2) / h;
vx_x[ off1 + i*Npml+j ] *= c1;
}
}
for (size_t i=0; i<Npml; ++i) {
txz1 = txz_x[off1 + i*Npml] + txz_z[off1 + i*Npml];
// txz2 = -txz1;
txz2 = 0.;
c1 = (2.*dt) / ( 2. + dt*d[0] );
c2 = ( 2. - dt*d[0] ) / (2.*dt);
vx_z[ off1 + i*Npml ] *= c2;
vx_z[ off1 + i*Npml ] += b[0] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml ] *= c1;
for (size_t j=1; j<Npml; ++j) {
txz1 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
txz2 = txz_x[off1 + i*Npml+j-1] + txz_z[off1 + i*Npml+j-1];
c1 = (2.*dt) / ( 2. + dt*d[j] );
c2 = ( 2. - dt*d[j] ) / (2.*dt);
vx_z[ off1 + i*Npml+j ] *= c2;
vx_z[ off1 + i*Npml+j ] += b[0] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml+j ] *= c1;
}
}
// Vx - left strip
//
off1 += Npml*Npml;
for (size_t j=0; j<nz; ++j) {
txx1 = txx_x[off1 + j] + txx_z[off1 + j];
txx2 = 0.;
c1 = (2.*dt) / ( 2. + dt*d[0] );
c2 = ( 2. - dt*d[0] ) / (2.*dt);
vx_x[ off1 + j ] *= c2;
vx_x[ off1 + j ] += b[j] * (txx1 - txx2) / h;
vx_x[ off1 + j ] *= c1;
}
for (size_t i=1; i<Npml; ++i) {
for (size_t j=0; j<nz; ++j) {
txx1 = txx_x[off1 + i*nz+j] + txx_z[off1 + i*nz+j];
txx2 = txx_x[off1 + (i-1)*nz+j] + txx_z[off1 + (i-1)*nz+j];
c1 = (2.*dt) / ( 2. + dt*d[i] );
c2 = ( 2. - dt*d[i] ) / (2.*dt);
vx_x[ off1 + i*nz+j ] *= c2;
vx_x[ off1 + i*nz+j ] += b[j] * (txx1 - txx2) / h;
vx_x[ off1 + i*nz+j ] *= c1;
}
}
size_t off2 = 0;
for (size_t i=0; i<Npml; ++i) {
txz1 = txz_x[off1 + i*nz] + txz_z[off1 + i*nz];
txz2 = txz_x[off2 + i*Npml+Npml-1] + txz_z[off2 + i*Npml+Npml-1];
vx_z[ off1 + i*nz ] += dt * b[0] * (txz1 - txz2) / h;
for (size_t j=1; j<nz; ++j) {
txz1 = txz_x[off1 + i*nz+j] + txz_z[off1 + i*nz+j];
txz2 = txz_x[off1 + i*nz+j-1] + txz_z[off1 + i*nz+j-1];
vx_z[ off1 + i*nz+j ] += dt * b[j] * (txz1 - txz2) / h;
}
}
// Vx - lower left corner
//
off1 += Npml*nz;
for (size_t j=0; j<Npml; ++j) {
txx1 = txx_x[off1 + j] + txx_z[off1 + j];
txx2 = 0.;
c1 = (2.*dt) / ( 2. + dt*d[0] );
c2 = ( 2. - dt*d[0] ) / (2.*dt);
vx_x[ off1 + j ] *= c2;
vx_x[ off1 + j ] += b[nz-1] * (txx1 - txx2) / h;
vx_x[ off1 + j ] *= c1;
}
for (size_t i=1; i<Npml; ++i) {
for (size_t j=0; j<Npml; ++j) {
txx1 = txx_x[off1 + i*Npml+j] + txx_z[off1 + i*Npml+j];
txx2 = txx_x[off1 + (i-1)*Npml+j] + txx_z[off1 + (i-1)*Npml+j];
c1 = (2.*dt) / ( 2. + dt*d[i] );
c2 = ( 2. - dt*d[i] ) / (2.*dt);
vx_x[ off1 + i*Npml+j ] *= c2;
vx_x[ off1 + i*Npml+j ] += b[nz-1] * (txx1 - txx2) / h;
vx_x[ off1 + i*Npml+j ] *= c1;
}
}
off2 = Npml*Npml;
for (size_t i=0; i<Npml; ++i) {
txz1 = txz_x[off1 + i*Npml] + txz_z[off1 + i*Npml];
txz2 = txz_x[off2 + i*nz+nz-1] + txz_z[off2 + i*nz+nz-1];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1] );
c2 = ( 2. - dt*d[Npml-1] ) / (2.*dt);
vx_z[ off1 + i*Npml ] *= c2;
vx_z[ off1 + i*Npml ] += b[nz-1] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml ] *= c1;
for (size_t j=1; j<Npml; ++j) {
txz1 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
txz2 = txz_x[off1 + i*Npml+j-1] + txz_z[off1 + i*Npml+j-1];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1-j] );
c2 = ( 2. - dt*d[Npml-1-j] ) / (2.*dt);
vx_z[ off1 + i*Npml+j ] *= c2;
vx_z[ off1 + i*Npml+j ] += b[nz-1] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml+j ] *= c1;
}
}
// Vx - upper strip
//
off2 = 0;
off1 += Npml*Npml;
for (size_t j=0; j<Npml; ++j) {
txx1 = txx_x[off1 + j] + txx_z[off1 + j];
txx2 = txx_x[off2 + (Npml-1)*Npml+j] + txx_z[off2 + (Npml-1)*Npml+j];
vx_x[ off1 + j ] += dt * b[0] * (txx1 - txx2) / h;
}
for (size_t i=1; i<nx; ++i) {
for (size_t j=0; j<Npml; ++j) {
txx1 = txx_x[off1 + i*Npml+j] + txx_z[off1 + i*Npml+j];
txx2 = txx_x[off1 + (i-1)*Npml+j] + txx_z[off1 + (i-1)*Npml+j];
vx_x[ off1 + i*Npml+j ] += dt * b[i*nz] * (txx1 - txx2) / h;
}
}
for (size_t i=0; i<nx; ++i) {
txz1 = txz_x[off1 + i*Npml] + txz_z[off1 + i*Npml];
// txz2 = -txz1;
txz2 = 0.;
c1 = (2.*dt) / ( 2. + dt*d[0] );
c2 = ( 2. - dt*d[0] ) / (2.*dt);
vx_z[ off1 + i*Npml ] *= c2;
vx_z[ off1 + i*Npml ] += b[i*nz] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml ] *= c1;
for (size_t j=1; j<Npml; ++j) {
txz1 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
txz2 = txz_x[off1 + i*Npml+j-1] + txz_z[off1 + i*Npml+j-1];
c1 = (2.*dt) / ( 2. + dt*d[j] );
c2 = ( 2. - dt*d[j] ) / (2.*dt);
vx_z[ off1 + i*Npml+j ] *= c2;
vx_z[ off1 + i*Npml+j ] += b[i*nz] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml+j ] *= c1;
}
}
// Vx - lower strip
//
off2 = Npml*Npml + Npml*nz;
off1 += Npml*nx;
for (size_t j=0; j<Npml; ++j) {
txx1 = txx_x[off1 + j] + txx_z[off1 + j];
txx2 = txx_x[off2 + (Npml-1)*Npml+j] + txx_z[off2 + (Npml-1)*Npml+j];
vx_x[ off1 + j ] += dt * b[nz-1] * (txx1 - txx2) / h;
}
for (size_t i=1; i<nx; ++i) {
for (size_t j=0; j<Npml; ++j) {
txx1 = txx_x[off1 + i*Npml+j] + txx_z[off1 + i*Npml+j];
txx2 = txx_x[off1 + (i-1)*Npml+j] + txx_z[off1 + (i-1)*Npml+j];
vx_x[ off1 + i*Npml+j ] += dt * b[i*nz+nz-1] * (txx1 - txx2) / h;
}
}
for (size_t i=0; i<nx; ++i) {
txz1 = txz_x[off1 + i*Npml] + txz_z[off1 + i*Npml];
txz2 = txz[i*nz+nz-1];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1] );
c2 = ( 2. - dt*d[Npml-1] ) / (2.*dt);
vx_z[ off1 + i*Npml ] *= c2;
vx_z[ off1 + i*Npml ] += b[i*nz+nz-1] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml ] *= c1;
for (size_t j=1; j<Npml; ++j) {
txz1 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
txz2 = txz_x[off1 + i*Npml+j-1] + txz_z[off1 + i*Npml+j-1];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1-j] );
c2 = ( 2. - dt*d[Npml-1-j] ) / (2.*dt);
vx_z[ off1 + i*Npml+j ] *= c2;
vx_z[ off1 + i*Npml+j ] += b[i*nz+nz-1] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml+j ] *= c1;
}
}
// Vx - upper right corner
//
off2 = 2*Npml*Npml + Npml*nz;
off1 += Npml*nx;
for (size_t j=0; j<Npml; ++j) { // i=0
txx1 = txx_x[off1 + j] + txx_z[off1 + j];
txx2 = txx_x[off2 + (nx-1)*Npml+j] + txx_z[off2 + (nx-1)*Npml+j];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1] );
c2 = ( 2. - dt*d[Npml-1] ) / (2.*dt);
vx_x[ off1 + j ] *= c2;
vx_x[ off1 + j ] += b[(nx-1)*nz] * (txx1 - txx2) / h;
vx_x[ off1 + j ] *= c1;
}
for (size_t i=1; i<Npml; ++i) {
for (size_t j=0; j<Npml; ++j) {
txx1 = txx_x[off1 + i*Npml+j] + txx_z[off1 + i*Npml+j];
txx2 = txx_x[off1 + (i-1)*Npml+j] + txx_z[off1 + (i-1)*Npml+j];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1-i] );
c2 = ( 2. - dt*d[Npml-1-i] ) / (2.*dt);
vx_x[ off1 + i*Npml+j ] *= c2;
vx_x[ off1 + i*Npml+j ] += b[(nx-1)*nz] * (txx1 - txx2) / h;
vx_x[ off1 + i*Npml+j ] *= c1;
}
}
for (size_t i=0; i<Npml; ++i) {
txz1 = txz_x[off1 + i*Npml] + txz_z[off1 + i*Npml];
// txz2 = -txz1;
txz2 = 0.;
c1 = (2.*dt) / ( 2. + dt*d[0] );
c2 = ( 2. - dt*d[0] ) / (2.*dt);
vx_z[ off1 + i*Npml ] *= c2;
vx_z[ off1 + i*Npml ] += b[(nx-1)*nz] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml ] *= c1;
for (size_t j=1; j<Npml; ++j) {
txz1 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
txz2 = txz_x[off1 + i*Npml+j-1] + txz_z[off1 + i*Npml+j-1];
c1 = (2.*dt) / ( 2. + dt*d[j] );
c2 = ( 2. - dt*d[j] ) / (2.*dt);
vx_z[ off1 + i*Npml+j ] *= c2;
vx_z[ off1 + i*Npml+j ] += b[(nx-1)*nz] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml+j ] *= c1;
}
}
// Vx - right strip
//
off1 += Npml*Npml;
for (size_t j=0; j<nz; ++j) { // i=0
txx1 = txx_x[off1 + j] + txx_z[off1 + j];
txx2 = txx[(nx-1)*nz+j];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1] );
c2 = ( 2. - dt*d[Npml-1] ) / (2.*dt);
vx_x[ off1 + j ] *= c2;
vx_x[ off1 + j ] += b[(nx-1)*nz+j] * (txx1 - txx2) / h;
vx_x[ off1 + j ] *= c1;
}
for (size_t i=1; i<Npml; ++i) {
for (size_t j=0; j<nz; ++j) {
txx1 = txx_x[off1 + i*nz+j] + txx_z[off1 + i*nz+j];
txx2 = txx_x[off1 + (i-1)*nz+j] + txx_z[off1 + (i-1)*nz+j];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1-i] );
c2 = ( 2. - dt*d[Npml-1-i] ) / (2.*dt);
vx_x[ off1 + i*nz+j ] *= c2;
vx_x[ off1 + i*nz+j ] += b[(nx-1)*nz+j] * (txx1 - txx2) / h;
vx_x[ off1 + i*nz+j ] *= c1;
}
}
off2 = 2*Npml*Npml + Npml*nz + 2*Npml*nx;
for (size_t i=0; i<Npml; ++i) {
txz1 = txz_x[off1 + i*nz] + txz_z[off1 + i*nz];
txz2 = txz_x[off2 + i*Npml+Npml-1] + txz_z[off2 + i*Npml+Npml-1];
vx_z[ off1 + i*nz ] += dt * b[(nx-1)*nz] * (txz1 - txz2) / h;
for (size_t j=1; j<nz; ++j) {
txz1 = txz_x[off1 + i*nz+j] + txz_z[off1 + i*nz+j];
txz2 = txz_x[off1 + i*nz+j-1] + txz_z[off1 + i*nz+j-1];
vx_z[ off1 + i*nz+j ] += dt * b[(nx-1)*nz+j] * (txz1 - txz2) / h;
}
}
// Vx - lower right corner
//
off2 = 2*Npml*Npml + Npml*nz + Npml*nx;
off1 += Npml*nz;
for (size_t j=0; j<Npml; ++j) { // i=0
txx1 = txx_x[off1 + j] + txx_z[off1 + j];
txx2 = txx_x[off2 + (nx-1)*Npml+j] + txx_z[off2 + (nx-1)*Npml+j];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1] );
c2 = ( 2. - dt*d[Npml-1] ) / (2.*dt);
vx_x[ off1 + j ] *= c2;
vx_x[ off1 + j ] += b[nx*nz-1] * (txx1 - txx2) / h;
vx_x[ off1 + j ] *= c1;
}
for (size_t i=1; i<Npml; ++i) {
for (size_t j=0; j<Npml; ++j) {
txx1 = txx_x[off1 + i*Npml+j] + txx_z[off1 + i*Npml+j];
txx2 = txx_x[off1 + (i-1)*Npml+j] + txx_z[off1 + (i-1)*Npml+j];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1-i] );
c2 = ( 2. - dt*d[Npml-1-i] ) / (2.*dt);
vx_x[ off1 + i*Npml+j ] *= c2;
vx_x[ off1 + i*Npml+j ] += b[nx*nz-1] * (txx1 - txx2) / h;
vx_x[ off1 + i*Npml+j ] *= c1;
}
}
off2 = 3*Npml*Npml + Npml*nz + 2*Npml*nx;
for (size_t i=0; i<Npml; ++i) {
txz1 = txz_x[off1 + i*Npml] + txz_z[off1 + i*Npml];
txz2 = txz_x[off2 + i*nz+nz-1] + txz_z[off2 + i*nz+nz-1];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1] );
c2 = ( 2. - dt*d[Npml-1] ) / (2.*dt);
vx_z[ off1 + i*Npml ] *= c2;
vx_z[ off1 + i*Npml ] += b[nx*nz-1] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml ] *= c1;
for (size_t j=1; j<Npml; ++j) {
txz1 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
txz2 = txz_x[off1 + i*Npml+j-1] + txz_z[off1 + i*Npml+j-1];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1-j] );
c2 = ( 2. - dt*d[Npml-1-j] ) / (2.*dt);
vx_z[ off1 + i*Npml+j ] *= c2;
vx_z[ off1 + i*Npml+j ] += b[nx*nz-1] * (txz1 - txz2) / h;
vx_z[ off1 + i*Npml+j ] *= c1;
}
}
// Vz - upper left corner
//
off1 = 0;
for (size_t i=0; i<Npml-1; ++i) {
for (size_t j=0; j<Npml; ++j) {
txz1 = txz_x[off1 + (i+1)*Npml+j] + txz_z[off1 + (i+1)*Npml+j];
txz2 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dh[i] );
c2 = ( 2. - dt*dh[i] ) / (2.*dt);
vz_x[ off1 + i*Npml+j ] *= c2;
vz_x[ off1 + i*Npml+j ] += bm[0] * (txz1 - txz2) / h;
vz_x[ off1 + i*Npml+j ] *= c1;
}
}
off2 = 2*Npml*Npml + Npml*nz;
for (size_t j=0; j<Npml; ++j) {
txz1 = txz_x[off2 + j] + txz_z[off2 + j];
txz2 = txz_x[off1 + (Npml-1)*Npml+j] + txz_z[off1 + (Npml-1)*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dh[Npml-1] );
c2 = ( 2. - dt*dh[Npml-1] ) / (2.*dt);
vz_x[ off1 + (Npml-1)*Npml+j ] *= c2;
vz_x[ off1 + (Npml-1)*Npml+j ] += bm[0] * (txz1 - txz2) / h;
vz_x[ off1 + (Npml-1)*Npml+j ] *= c1;
}
off2 = Npml*Npml;
for (size_t i=0; i<Npml; ++i) {
for (size_t j=0; j<Npml-1; ++j) {
tzz1 = tzz_x[ off1 + i*Npml+j+1 ] + tzz_z[ off1 + i*Npml+j+1 ];
tzz2 = tzz_x[ off1 + i*Npml+j ] + tzz_z[ off1 + i*Npml+j ];
c1 = (2.*dt) / ( 2. + dt*dh[j] );
c2 = ( 2. - dt*dh[j] ) / (2.*dt);
vz_z[ off1 + i*Npml+j ] *= c2;
vz_z[ off1 + i*Npml+j ] += bm[0] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+j ] *= c1;
}
tzz1 = tzz_x[ off2 + i*nz ] + tzz_z[ off2 + i*nz ];
tzz2 = tzz_x[ off1 + i*Npml+Npml-1 ] + tzz_z[ off1 + i*Npml+Npml-1 ];
c1 = (2.*dt) / ( 2. + dt*dh[Npml-1] );
c2 = ( 2. - dt*dh[Npml-1] ) / (2.*dt);
vz_z[ off1 + i*Npml+Npml-1 ] *= c2;
vz_z[ off1 + i*Npml+Npml-1 ] += bm[0] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+Npml-1 ] *= c1;
}
// Vz - left strip
//
off1 += Npml*Npml;
for (size_t i=0; i<Npml-1; ++i) {
for (size_t j=0; j<nz; ++j) {
txz1 = txz_x[off1 + (i+1)*nz+j] + txz_z[off1 + (i+1)*nz+j];
txz2 = txz_x[off1 + i*nz+j] + txz_z[off1 + i*nz+j];
c1 = (2.*dt) / ( 2. + dt*dh[i] );
c2 = ( 2. - dt*dh[i] ) / (2.*dt);
vz_x[ off1 + i*nz+j ] *= c2;
vz_x[ off1 + i*nz+j ] += bm[j] * (txz1 - txz2) / h;
vz_x[ off1 + i*nz+j ] *= c1;
}
}
for (size_t j=0; j<nz; ++j) {
txz1 = txz[j];
txz2 = txz_x[off1 + (Npml-1)*nz+j] + txz_z[off1 + (Npml-1)*nz+j];
c1 = (2.*dt) / ( 2. + dt*dh[(Npml-1)] );
c2 = ( 2. - dt*dh[(Npml-1)] ) / (2.*dt);
vz_x[ off1 + (Npml-1)*nz+j ] *= c2;
vz_x[ off1 + (Npml-1)*nz+j ] += bm[j] * (txz1 - txz2) / h;
vz_x[ off1 + (Npml-1)*nz+j ] *= c1;
}
off2 = Npml*Npml + Npml*nz;
for (size_t i=0; i<Npml; ++i) {
for (size_t j=0; j<nz-1; ++j) {
tzz1 = tzz_x[ off1 + i*nz+j+1 ] + tzz_z[ off1 + i*nz+j+1 ];
tzz2 = tzz_x[ off1 + i*nz+j ] + tzz_z[ off1 + i*nz+j ];
vz_z[ off1 + i*nz+j ] += dt * bm[j] * (tzz1 - tzz2) / h;
}
tzz1 = tzz_x[ off2 + i*Npml ] + tzz_z[ off2 + i*Npml ];
tzz2 = tzz_x[ off1 + i*nz+nz-1 ] + tzz_z[ off1 + i*nz+nz-1 ];
vz_z[ off1 + i*nz+nz-1 ] += dt * bm[nz-1] * (tzz1 - tzz2) / h;
}
// Vz - lower left corner
//
off1 += Npml*nz;
for (size_t i=0; i<Npml-1; ++i) {
for (size_t j=0; j<Npml; ++j) {
txz1 = txz_x[off1 + (i+1)*Npml+j] + txz_z[off1 + (i+1)*Npml+j];
txz2 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dh[i] );
c2 = ( 2. - dt*dh[i] ) / (2.*dt);
vz_x[ off1 + i*Npml+j ] *= c2;
vz_x[ off1 + i*Npml+j ] += bm[nz-1] * (txz1 - txz2) / h;
vz_x[ off1 + i*Npml+j ] *= c1;
}
}
off2 = 2*Npml*Npml + Npml*nz + Npml*nx;
for (size_t j=0; j<Npml; ++j) {
txz1 = txz_x[off2 + j] + txz_z[off2 + j];
txz2 = txz_x[off1 + (Npml-1)*Npml+j] + txz_z[off1 + (Npml-1)*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dh[Npml-1] );
c2 = ( 2. - dt*dh[Npml-1] ) / (2.*dt);
vz_x[ off1 + (Npml-1)*Npml+j ] *= c2;
vz_x[ off1 + (Npml-1)*Npml+j ] += bm[nz-1] * (txz1 - txz2) / h;
vz_x[ off1 + (Npml-1)*Npml+j ] *= c1;
}
for (size_t i=0; i<Npml; ++i) {
for (size_t j=0; j<Npml-1; ++j) {
tzz1 = tzz_x[ off1 + i*Npml+j+1 ] + tzz_z[ off1 + i*Npml+j+1 ];
tzz2 = tzz_x[ off1 + i*Npml+j ] + tzz_z[ off1 + i*Npml+j ];
c1 = (2.*dt) / ( 2. + dt*dH[Npml-1-j] );
c2 = ( 2. - dt*dH[Npml-1-j] ) / (2.*dt);
vz_z[ off1 + i*Npml+j ] *= c2;
vz_z[ off1 + i*Npml+j ] += bm[nz-1] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+j ] *= c1;
}
tzz1 = 0.;
tzz2 = tzz_x[ off1 + i*Npml+Npml-1 ] + tzz_z[ off1 + i*Npml+Npml-1 ];
c1 = (2.*dt) / ( 2. + dt*dH[0] );
c2 = ( 2. - dt*dH[0] ) / (2.*dt);
vz_z[ off1 + i*Npml+Npml-1 ] *= c2;
vz_z[ off1 + i*Npml+Npml-1 ] += bm[nz-1] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+Npml-1 ] *= c1;
}
// Vz - upper strip
//
off1 += Npml*Npml;
for (size_t i=0; i<nx-1; ++i) {
for (size_t j=0; j<Npml; ++j) {
txz1 = txz_x[off1 + (i+1)*Npml+j] + txz_z[off1 + (i+1)*Npml+j];
txz2 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
vz_x[ off1 + i*Npml+j ] += dt * bm[i*nz] * (txz1 - txz2) / h;
}
}
off2 = 2*Npml*Npml + Npml*nz + 2*Npml*nx;
for (size_t j=0; j<Npml; ++j) {
txz1 = txz_x[off2 + j] + txz_z[off2 + j];
txz2 = txz_x[off1 + (nx-1)*Npml+j] + txz_z[off1 + (nx-1)*Npml+j];
vz_x[ off1 + (nx-1)*Npml+j ] += dt * bm[(nx-1)*nz] * (txz1 - txz2) / h;
}
for (size_t i=0; i<nx; ++i) {
for (size_t j=0; j<Npml-1; ++j) {
tzz1 = tzz_x[ off1 + i*Npml+j+1 ] + tzz_z[ off1 + i*Npml+j+1 ];
tzz2 = tzz_x[ off1 + i*Npml+j ] + tzz_z[ off1 + i*Npml+j ];
c1 = (2.*dt) / ( 2. + dt*dh[j] );
c2 = ( 2. - dt*dh[j] ) / (2.*dt);
vz_z[ off1 + i*Npml+j ] *= c2;
vz_z[ off1 + i*Npml+j ] += bm[i*nz] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+j ] *= c1;
}
tzz1 = tzz[ i*nz ];
tzz2 = tzz_x[ off1 + i*Npml+Npml-1 ] + tzz_z[ off1 + i*Npml+Npml-1 ];
c1 = (2.*dt) / ( 2. + dt*dh[Npml-1] );
c2 = ( 2. - dt*dh[Npml-1] ) / (2.*dt);
vz_z[ off1 + i*Npml+Npml-1 ] *= c2;
vz_z[ off1 + i*Npml+Npml-1 ] += bm[i*nz] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+Npml-1 ] *= c1;
}
// Vz - lower strip
//
off1 += Npml*nx;
for (size_t i=0; i<nx-1; ++i) {
for (size_t j=0; j<Npml; ++j) {
txz1 = txz_x[off1 + (i+1)*Npml+j] + txz_z[off1 + (i+1)*Npml+j];
txz2 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
vz_x[ off1 + i*Npml+j ] += dt * bm[i*nz+nz-1] * (txz1 - txz2) / h;
}
}
off2 = 3*Npml*Npml + 2*Npml*nz + 2*Npml*nx;
for (size_t j=0; j<Npml; ++j) {
txz1 = txz_x[off2 + j] + txz_z[off2 + j];
txz2 = txz_x[off1 + (nx-1)*Npml+j] + txz_z[off1 + (nx-1)*Npml+j];
vz_x[ off1 + (nx-1)*Npml+j ] += dt * bm[(nx-1)*nz+nz-1] * (txz1 - txz2) / h;
}
for (size_t i=0; i<nx; ++i) {
for (size_t j=0; j<Npml-1; ++j) {
tzz1 = tzz_x[ off1 + i*Npml+j+1 ] + tzz_z[ off1 + i*Npml+j+1 ];
tzz2 = tzz_x[ off1 + i*Npml+j ] + tzz_z[ off1 + i*Npml+j ];
c1 = (2.*dt) / ( 2. + dt*dH[Npml-1-j] );
c2 = ( 2. - dt*dH[Npml-1-j] ) / (2.*dt);
vz_z[ off1 + i*Npml+j ] *= c2;
vz_z[ off1 + i*Npml+j ] += bm[i*nz+nz-1] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+j ] *= c1;
}
tzz1 = 0.;
tzz2 = tzz_x[ off1 + i*Npml+Npml-1 ] + tzz_z[ off1 + i*Npml+Npml-1 ];
c1 = (2.*dt) / ( 2. + dt*dH[0] );
c2 = ( 2. - dt*dH[0] ) / (2.*dt);
vz_z[ off1 + i*Npml+Npml-1 ] *= c2;
vz_z[ off1 + i*Npml+Npml-1 ] += bm[i*nz+nz-1] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+Npml-1 ] *= c1;
}
// Vz - upper right corner
//
off1 += Npml*nx;
for (size_t i=0; i<Npml-1; ++i) {
for (size_t j=0; j<Npml; ++j) {
txz1 = txz_x[off1 + (i+1)*Npml+j] + txz_z[off1 + (i+1)*Npml+j];
txz2 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dH[Npml-1-i] );
c2 = ( 2. - dt*dH[Npml-1-i] ) / (2.*dt);
vz_x[ off1 + i*Npml+j ] *= c2;
vz_x[ off1 + i*Npml+j ] += bm[(nx-1)*nz] * (txz1 - txz2) / h;
vz_x[ off1 + i*Npml+j ] *= c1;
}
}
for (size_t j=0; j<Npml; ++j) {
txz1 = 0.;
txz2 = txz_x[off1 + (Npml-1)*Npml+j] + txz_z[off1 + (Npml-1)*Npml+j];
// txz1 = -txz2;
c1 = (2.*dt) / ( 2. + dt*dH[0] );
c2 = ( 2. - dt*dH[0] ) / (2.*dt);
vz_x[ off1 + (Npml-1)*Npml+j ] *= c2;
vz_x[ off1 + (Npml-1)*Npml+j ] += bm[(nx-1)*nz] * (txz1 - txz2) / h;
vz_x[ off1 + (Npml-1)*Npml+j ] *= c1;
}
off2 = 3*Npml*Npml + Npml*nz + 2*Npml*nx;
for (size_t i=0; i<Npml; ++i) {
for (size_t j=0; j<Npml-1; ++j) {
tzz1 = tzz_x[ off1 + i*Npml+j+1 ] + tzz_z[ off1 + i*Npml+j+1 ];
tzz2 = tzz_x[ off1 + i*Npml+j ] + tzz_z[ off1 + i*Npml+j ];
c1 = (2.*dt) / ( 2. + dt*dh[j] );
c2 = ( 2. - dt*dh[j] ) / (2.*dt);
vz_z[ off1 + i*Npml+j ] *= c2;
vz_z[ off1 + i*Npml+j ] += bm[(nx-1)*nz] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+j ] *= c1;
}
tzz1 = tzz_x[ off2 + i*nz ] + tzz_z[ off2 + i*nz ];
tzz2 = tzz_x[ off1 + i*Npml+Npml-1 ] + tzz_z[ off1 + i*Npml+Npml-1 ];
c1 = (2.*dt) / ( 2. + dt*dh[Npml-1] );
c2 = ( 2. - dt*dh[Npml-1] ) / (2.*dt);
vz_z[ off1 + i*Npml+Npml-1 ] *= c2;
vz_z[ off1 + i*Npml+Npml-1 ] += bm[(nx-1)*nz] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+Npml-1 ] *= c1;
}
// Vz - right strip
//
off1 += Npml*Npml;
for (size_t i=0; i<Npml-1; ++i) {
for (size_t j=0; j<nz; ++j) {
txz1 = txz_x[off1 + (i+1)*nz+j] + txz_z[off1 + (i+1)*nz+j];
txz2 = txz_x[off1 + i*nz+j] + txz_z[off1 + i*nz+j];
c1 = (2.*dt) / ( 2. + dt*dH[Npml-1-i] );
c2 = ( 2. - dt*dH[Npml-1-i] ) / (2.*dt);
vz_x[ off1 + i*nz+j ] *= c2;
vz_x[ off1 + i*nz+j ] += bm[(nx-1)*nz+j] * (txz1 - txz2) / h;
vz_x[ off1 + i*nz+j ] *= c1;
}
}
for (size_t j=0; j<nz; ++j) {
txz1 = 0.;
txz2 = txz_x[off1 + (Npml-1)*nz+j] + txz_z[off1 + (Npml-1)*nz+j];
// txz1 = -txz2;
c1 = (2.*dt) / ( 2. + dt*dH[0] );
c2 = ( 2. - dt*dH[0] ) / (2.*dt);
vz_x[ off1 + (Npml-1)*nz+j ] *= c2;
vz_x[ off1 + (Npml-1)*nz+j ] += bm[(nx-1)*nz+j] * (txz1 - txz2) / h;
vz_x[ off1 + (Npml-1)*nz+j ] *= c1;
}
off2 = 3*Npml*Npml + 2*Npml*nz + 2*Npml*nx;
for (size_t i=0; i<Npml; ++i) {
for (size_t j=0; j<nz-1; ++j) {
tzz1 = tzz_x[ off1 + i*nz+j+1 ] + tzz_z[ off1 + i*nz+j+1 ];
tzz2 = tzz_x[ off1 + i*nz+j ] + tzz_z[ off1 + i*nz+j ];
vz_z[ off1 + i*nz+j ] += dt * bm[(nx-1)*nz+j] * (tzz1 - tzz2) / h;
}
tzz1 = tzz_x[ off2 + i*Npml ] + tzz_z[ off2 + i*Npml ];
tzz2 = tzz_x[ off1 + i*nz+nz-1 ] + tzz_z[ off1 + i*nz+nz-1 ];
vz_z[ off1 + i*nz+nz-1 ] += dt * bm[nx*nz-1] * (tzz1 - tzz2) / h;
}
// Vz - lower right corner
//
off1 += Npml*nz;
for (size_t i=0; i<Npml-1; ++i) {
for (size_t j=0; j<Npml; ++j) {
txz1 = txz_x[off1 + (i+1)*Npml+j] + txz_z[off1 + (i+1)*Npml+j];
txz2 = txz_x[off1 + i*Npml+j] + txz_z[off1 + i*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dH[Npml-1-i] );
c2 = ( 2. - dt*dH[Npml-1-i] ) / (2.*dt);
vz_x[ off1 + i*Npml+j ] *= c2;
vz_x[ off1 + i*Npml+j ] += bm[nx*nz-1] * (txz1 - txz2) / h;
vz_x[ off1 + i*Npml+j ] *= c1;
}
}
for (size_t j=0; j<Npml; ++j) {
txz1 = 0.;
txz2 = txz_x[off1 + (Npml-1)*Npml+j] + txz_z[off1 + (Npml-1)*Npml+j];
// txz1 = -txz2;
c1 = (2.*dt) / ( 2. + dt*dH[0] );
c2 = ( 2. - dt*dH[0] ) / (2.*dt);
vz_x[ off1 + (Npml-1)*Npml+j ] *= c2;
vz_x[ off1 + (Npml-1)*Npml+j ] += bm[nx*nz-1] * (txz1 - txz2) / h;
vz_x[ off1 + (Npml-1)*Npml+j ] *= c1;
}
for (size_t i=0; i<Npml; ++i) {
for (size_t j=0; j<Npml-1; ++j) {
tzz1 = tzz_x[ off1 + i*Npml+j+1 ] + tzz_z[ off1 + i*Npml+j+1 ];
tzz2 = tzz_x[ off1 + i*Npml+j ] + tzz_z[ off1 + i*Npml+j ];
c1 = (2.*dt) / ( 2. + dt*dH[Npml-1-j] );
c2 = ( 2. - dt*dH[Npml-1-j] ) / (2.*dt);
vz_z[ off1 + i*Npml+j ] *= c2;
vz_z[ off1 + i*Npml+j ] += bm[nx*nz-1] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+j ] *= c1;
}
tzz1 = 0.;
tzz2 = tzz_x[ off1 + i*Npml+Npml-1 ] + tzz_z[ off1 + i*Npml+Npml-1 ];
c1 = (2.*dt) / ( 2. + dt*dH[0] );
c2 = ( 2. - dt*dH[0] ) / (2.*dt);
vz_z[ off1 + i*Npml+Npml-1 ] *= c2;
vz_z[ off1 + i*Npml+Npml-1 ] += bm[nx*nz-1] * (tzz1 - tzz2) / h;
vz_z[ off1 + i*Npml+Npml-1 ] *= c1;
}
}
void pml_t(const double *vx_x, const double *vx_z,
const double *vz_x, const double *vz_z,
double *txx_x, double *txx_z,
double *tzz_x, double *tzz_z,
double *txz_x, double *txz_z,
const double d[], const double dh[], const double dH[],
const double *vx, const double *vz,
const double *la, const double *l2m, const double *mu,
const size_t nx, const size_t nz, const size_t Npml,
const double dt, const double h)
{
register double c1, c2, vx1, vx2, vz1, vz2;
// txx & tzz - upper left corner
//
size_t off1 = 0;
for (size_t i=0; i<Npml-1; ++i) {
for (size_t j=0; j<Npml; ++j) {
vx1 = vx_x[off1 + (i+1)*Npml+j] + vx_z[off1 + (i+1)*Npml+j];
vx2 = vx_x[off1 + i*Npml+j] + vx_z[off1 + i*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dh[i] );
c2 = ( 2. - dt*dh[i] ) / (2.*dt);
txx_x[ off1 + i*Npml+j ] *= c2;
txx_x[ off1 + i*Npml+j ] += l2m[0] * (vx1 - vx2) / h;
txx_x[ off1 + i*Npml+j ] *= c1;
tzz_x[ off1 + i*Npml+j ] *= c2;
tzz_x[ off1 + i*Npml+j ] += la[0] * (vx1 - vx2) / h;
tzz_x[ off1 + i*Npml+j ] *= c1;
}
}
size_t off2 = 2*Npml*Npml + Npml*nz;
for (size_t j=0; j<Npml; ++j) {
vx1 = vx_x[off2 + j] + vx_z[off2 + j];
vx2 = vx_x[off1 + (Npml-1)*Npml+j] + vx_z[off1 + (Npml-1)*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dh[(Npml-1)] );
c2 = ( 2. - dt*dh[(Npml-1)] ) / (2.*dt);
txx_x[ off1 + (Npml-1)*Npml+j ] *= c2;
txx_x[ off1 + (Npml-1)*Npml+j ] += l2m[0] * (vx1 - vx2) / h;
txx_x[ off1 + (Npml-1)*Npml+j ] *= c1;
tzz_x[ off1 + (Npml-1)*Npml+j ] *= c2;
tzz_x[ off1 + (Npml-1)*Npml+j ] += la[0] * (vx1 - vx2) / h;
tzz_x[ off1 + (Npml-1)*Npml+j ] *= c1;
}
for (size_t i=0; i<Npml; ++i) {
vz1 = vz_x[off1 + i*Npml] + vz_z[off1 + i*Npml];
vz2 = 0.;
c1 = (2.*dt) / ( 2. + dt*d[0] );
c2 = ( 2. - dt*d[0] ) / (2.*dt);
txx_z[ off1 + i*Npml ] *= c2;
txx_z[ off1 + i*Npml ] += la[0] * (vz1 - vz2) / h;
txx_z[ off1 + i*Npml ] *= c1;
tzz_z[ off1 + i*Npml ] *= c2;
tzz_z[ off1 + i*Npml ] += l2m[0] * (vz1 - vz2) / h;
tzz_z[ off1 + i*Npml ] *= c1;
for (size_t j=1; j<Npml; ++j) {
vz1 = vz_x[off1 + i*Npml+j] + vz_z[off1 + i*Npml+j];
vz2 = vz_x[off1 + i*Npml+j-1] + vz_z[off1 + i*Npml+j-1];
c1 = (2.*dt) / ( 2. + dt*d[j] );
c2 = ( 2. - dt*d[j] ) / (2.*dt);
txx_z[ off1 + i*Npml+j ] *= c2;
txx_z[ off1 + i*Npml+j ] += la[0] * (vz1 - vz2) / h;
txx_z[ off1 + i*Npml+j ] *= c1;
tzz_z[ off1 + i*Npml+j ] *= c2;
tzz_z[ off1 + i*Npml+j ] += l2m[0] * (vz1 - vz2) / h;
tzz_z[ off1 + i*Npml+j ] *= c1;
}
}
// txx & tzz - left strip
//
off1 += Npml*Npml;
for (size_t i=0; i<Npml-1; ++i) {
for (size_t j=0; j<nz; ++j) {
vx1 = vx_x[off1 + (i+1)*nz+j] + vx_z[off1 + (i+1)*nz+j];
vx2 = vx_x[off1 + i*nz+j] + vx_z[off1 + i*nz+j];
c1 = (2.*dt) / ( 2. + dt*dh[i] );
c2 = ( 2. - dt*dh[i] ) / (2.*dt);
txx_x[ off1 + i*nz+j ] *= c2;
txx_x[ off1 + i*nz+j ] += l2m[j] * (vx1 - vx2) / h;
txx_x[ off1 + i*nz+j ] *= c1;
tzz_x[ off1 + i*nz+j ] *= c2;
tzz_x[ off1 + i*nz+j ] += la[j] * (vx1 - vx2) / h;
tzz_x[ off1 + i*nz+j ] *= c1;
}
}
for (size_t j=0; j<nz; ++j) {
vx1 = vx[j];
vx2 = vx_x[off1 + (Npml-1)*nz+j] + vx_z[off1 + (Npml-1)*nz+j];
c1 = (2.*dt) / ( 2. + dt*dh[(Npml-1)] );
c2 = ( 2. - dt*dh[(Npml-1)] ) / (2.*dt);
txx_x[ off1 + (Npml-1)*nz+j ] *= c2;
txx_x[ off1 + (Npml-1)*nz+j ] += l2m[j] * (vx1 - vx2) / h;
txx_x[ off1 + (Npml-1)*nz+j ] *= c1;
tzz_x[ off1 + (Npml-1)*nz+j ] *= c2;
tzz_x[ off1 + (Npml-1)*nz+j ] += la[j] * (vx1 - vx2) / h;
tzz_x[ off1 + (Npml-1)*nz+j ] *= c1;
}
off2 = 0;
for (size_t i=0; i<Npml; ++i) {
vz1 = vz_x[off1 + i*nz] + vz_z[off1 + i*nz];
vz2 = vz_x[off2 + i*Npml+Npml-1] + vz_z[off2 + i*Npml+Npml-1];
txx_z[ off1 + i*nz ] += dt * la[0] * (vz1 - vz2) / h;
tzz_z[ off1 + i*nz ] += dt * l2m[0] * (vz1 - vz2) / h;
for (size_t j=1; j<nz; ++j) {
vz1 = vz_x[off1 + i*nz+j] + vz_z[off1 + i*nz+j];
vz2 = vz_x[off1 + i*nz+j-1] + vz_z[off1 + i*nz+j-1];
txx_z[ off1 + i*nz+j ] += dt * la[j] * (vz1 - vz2) / h;
tzz_z[ off1 + i*nz+j ] += dt * l2m[j] * (vz1 - vz2) / h;
}
}
// txx & tzz - lower left corner
//
off1 += Npml*nz;
for (size_t i=0; i<Npml-1; ++i) {
for (size_t j=0; j<Npml; ++j) {
vx1 = vx_x[off1 + (i+1)*Npml+j] + vx_z[off1 + (i+1)*Npml+j];
vx2 = vx_x[off1 + i*Npml+j] + vx_z[off1 + i*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dh[i] );
c2 = ( 2. - dt*dh[i] ) / (2.*dt);
txx_x[ off1 + i*Npml+j ] *= c2;
txx_x[ off1 + i*Npml+j ] += l2m[nz-1] * (vx1 - vx2) / h;
txx_x[ off1 + i*Npml+j ] *= c1;
tzz_x[ off1 + i*Npml+j ] *= c2;
tzz_x[ off1 + i*Npml+j ] += la[nz-1] * (vx1 - vx2) / h;
tzz_x[ off1 + i*Npml+j ] *= c1;
}
}
off2 = 2*Npml*Npml + Npml*nz + Npml*nx;
for (size_t j=0; j<Npml; ++j) {
vx1 = vx_x[off2 + j] + vx_z[off2 + j];
vx2 = vx_x[off1 + (Npml-1)*Npml+j] + vx_z[off1 + (Npml-1)*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dh[(Npml-1)] );
c2 = ( 2. - dt*dh[(Npml-1)] ) / (2.*dt);
txx_x[ off1 + (Npml-1)*Npml+j ] *= c2;
txx_x[ off1 + (Npml-1)*Npml+j ] += l2m[nz-1] * (vx1 - vx2) / h;
txx_x[ off1 + (Npml-1)*Npml+j ] *= c1;
tzz_x[ off1 + (Npml-1)*Npml+j ] *= c2;
tzz_x[ off1 + (Npml-1)*Npml+j ] += la[nz-1] * (vx1 - vx2) / h;
tzz_x[ off1 + (Npml-1)*Npml+j ] *= c1;
}
off2 = Npml*Npml;
for (size_t i=0; i<Npml; ++i) {
vz1 = vz_x[off1 + i*Npml] + vz_z[off1 + i*Npml];
vz2 = vz_x[off2 + i*nz+nz-1] + vz_z[off2 + i*nz+nz-1];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1] );
c2 = ( 2. - dt*d[Npml-1] ) / (2.*dt);
txx_z[ off1 + i*Npml ] *= c2;
txx_z[ off1 + i*Npml ] += la[nz-1] * (vz1 - vz2) / h;
txx_z[ off1 + i*Npml ] *= c1;
tzz_z[ off1 + i*Npml ] *= c2;
tzz_z[ off1 + i*Npml ] += l2m[nz-1] * (vz1 - vz2) / h;
tzz_z[ off1 + i*Npml ] *= c1;
for (size_t j=1; j<Npml; ++j) {
vz1 = vz_x[off1 + i*Npml+j] + vz_z[off1 + i*Npml+j];
vz2 = vz_x[off1 + i*Npml+j-1] + vz_z[off1 + i*Npml+j-1];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1-j] );
c2 = ( 2. - dt*d[Npml-1-j] ) / (2.*dt);
txx_z[ off1 + i*Npml+j ] *= c2;
txx_z[ off1 + i*Npml+j ] += la[nz-1] * (vz1 - vz2) / h;
txx_z[ off1 + i*Npml+j ] *= c1;
tzz_z[ off1 + i*Npml+j ] *= c2;
tzz_z[ off1 + i*Npml+j ] += l2m[nz-1] * (vz1 - vz2) / h;
tzz_z[ off1 + i*Npml+j ] *= c1;
}
}
// txx & tzz - upper strip
//
off1 += Npml*Npml;
for (size_t i=0; i<nx-1; ++i) {
for (size_t j=0; j<Npml; ++j) {
vx1 = vx_x[off1 + (i+1)*Npml+j] + vx_z[off1 + (i+1)*Npml+j];
vx2 = vx_x[off1 + i*Npml+j] + vx_z[off1 + i*Npml+j];
txx_x[ off1 + i*Npml+j ] += dt * l2m[i*nz] * (vx1 - vx2) / h;
tzz_x[ off1 + i*Npml+j ] += dt * la[i*nz] * (vx1 - vx2) / h;
}
}
off2 = 2*Npml*Npml + Npml*nz + 2*Npml*nx;
for (size_t j=0; j<Npml; ++j) {
vx1 = vx_x[off2 + j] + vx_z[off2 + j];
vx2 = vx_x[off1 + (nx-1)*Npml+j] + vx_z[off1 + (nx-1)*Npml+j];
txx_x[ off1 + (nx-1)*Npml+j ] += dt * l2m[(nx-1)*nz] * (vx1 - vx2) / h;
tzz_x[ off1 + (nx-1)*Npml+j ] += dt * la[(nx-1)*nz] * (vx1 - vx2) / h;
}
for (size_t i=0; i<nx; ++i) {
vz1 = vz_x[off1 + i*Npml] + vz_z[off1 + i*Npml];
vz2 = 0.;
c1 = (2.*dt) / ( 2. + dt*d[0] );
c2 = ( 2. - dt*d[0] ) / (2.*dt);
txx_z[ off1 + i*Npml ] *= c2;
txx_z[ off1 + i*Npml ] += la[i*nz] * (vz1 - vz2) / h;
txx_z[ off1 + i*Npml ] *= c1;
tzz_z[ off1 + i*Npml ] *= c2;
tzz_z[ off1 + i*Npml ] += l2m[i*nz] * (vz1 - vz2) / h;
tzz_z[ off1 + i*Npml ] *= c1;
for (size_t j=1; j<Npml; ++j) {
vz1 = vz_x[off1 + i*Npml+j] + vz_z[off1 + i*Npml+j];
vz2 = vz_x[off1 + i*Npml+j-1] + vz_z[off1 + i*Npml+j-1];
c1 = (2.*dt) / ( 2. + dt*d[j] );
c2 = ( 2. - dt*d[j] ) / (2.*dt);
txx_z[ off1 + i*Npml+j ] *= c2;
txx_z[ off1 + i*Npml+j ] += la[i*nz] * (vz1 - vz2) / h;
txx_z[ off1 + i*Npml+j ] *= c1;
tzz_z[ off1 + i*Npml+j ] *= c2;
tzz_z[ off1 + i*Npml+j ] += l2m[i*nz] * (vz1 - vz2) / h;
tzz_z[ off1 + i*Npml+j ] *= c1;
}
}
// txx & tzz - lower strip
//
off1 += Npml*nx;
for (size_t i=0; i<nx-1; ++i) {
for (size_t j=0; j<Npml; ++j) {
vx1 = vx_x[off1 + (i+1)*Npml+j] + vx_z[off1 + (i+1)*Npml+j];
vx2 = vx_x[off1 + i*Npml+j] + vx_z[off1 + i*Npml+j];
txx_x[ off1 + i*Npml+j ] += dt * l2m[i*nz+nz-1] * (vx1 - vx2) / h;
tzz_x[ off1 + i*Npml+j ] += dt * la[i*nz+nz-1] * (vx1 - vx2) / h;
}
}
off2 = 3*Npml*Npml + 2*Npml*nz + 2*Npml*nx;
for (size_t j=0; j<Npml; ++j) {
vx1 = vx_x[off2 + j] + vx_z[off2 + j];
vx2 = vx_x[off1 + (nx-1)*Npml+j] + vx_z[off1 + (nx-1)*Npml+j];
txx_x[ off1 + (nx-1)*Npml+j ] += dt * l2m[nx*nz-1] * (vx1 - vx2) / h;
tzz_x[ off1 + (nx-1)*Npml+j ] += dt * la[nx*nz-1] * (vx1 - vx2) / h;
}
for (size_t i=0; i<nx; ++i) {
vz1 = vz_x[off1 + i*Npml] + vz_z[off1 + i*Npml];
vz2 = vz[i*nz+nz-1];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1] );
c2 = ( 2. - dt*d[Npml-1] ) / (2.*dt);
txx_z[ off1 + i*Npml ] *= c2;
txx_z[ off1 + i*Npml ] += la[i*nz+nz-1] * (vz1 - vz2) / h;
txx_z[ off1 + i*Npml ] *= c1;
tzz_z[ off1 + i*Npml ] *= c2;
tzz_z[ off1 + i*Npml ] += l2m[i*nz+nz-1] * (vz1 - vz2) / h;
tzz_z[ off1 + i*Npml ] *= c1;
for (size_t j=1; j<Npml; ++j) {
vz1 = vz_x[off1 + i*Npml+j] + vz_z[off1 + i*Npml+j];
vz2 = vz_x[off1 + i*Npml+j-1] + vz_z[off1 + i*Npml+j-1];
c1 = (2.*dt) / ( 2. + dt*d[Npml-1-j] );
c2 = ( 2. - dt*d[Npml-1-j] ) / (2.*dt);
txx_z[ off1 + i*Npml+j ] *= c2;
txx_z[ off1 + i*Npml+j ] += la[i*nz+nz-1] * (vz1 - vz2) / h;
txx_z[ off1 + i*Npml+j ] *= c1;
tzz_z[ off1 + i*Npml+j ] *= c2;
tzz_z[ off1 + i*Npml+j ] += l2m[i*nz+nz-1] * (vz1 - vz2) / h;
tzz_z[ off1 + i*Npml+j ] *= c1;
}
}
// txx & tzz - upper right corner
//
off1 += Npml*nx;
for (size_t i=0; i<Npml-1; ++i) {
for (size_t j=0; j<Npml; ++j) {
vx1 = vx_x[off1 + (i+1)*Npml+j] + vx_z[off1 + (i+1)*Npml+j];
vx2 = vx_x[off1 + i*Npml+j] + vx_z[off1 + i*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dH[Npml-1-i] );
c2 = ( 2. - dt*dH[Npml-1-i] ) / (2.*dt);
txx_x[ off1 + i*Npml+j ] *= c2;
txx_x[ off1 + i*Npml+j ] += l2m[(nx-1)*nz] * (vx1 - vx2) / h;
txx_x[ off1 + i*Npml+j ] *= c1;
tzz_x[ off1 + i*Npml+j ] *= c2;
tzz_x[ off1 + i*Npml+j ] += la[(nx-1)*nz] * (vx1 - vx2) / h;
tzz_x[ off1 + i*Npml+j ] *= c1;
}
}
for (size_t j=0; j<Npml; ++j) {
vx1 = 0.;
vx2 = vx_x[off1 + (Npml-1)*Npml+j] + vx_z[off1 + (Npml-1)*Npml+j];
c1 = (2.*dt) / ( 2. + dt*dH[0] );
c2 = ( 2. - dt*dH[0] ) / (2.*dt);
txx_x[ off1 + (Npml-1)*Npml+j ] *= c2;
txx_x[ off1 + (Npml-1)*Npml+j ] += l2m[(nx-1)*nz] * (vx1 - vx2) / h;
txx_x[ off1 + (Npml-1)*Npml+j ] *= c1;
tzz_x[ off1 + (Npml-1)*Npml+j ] *= c2;
tzz_x[ off1 + (Npml-1)*Npml+j ] += la[(nx-1)*nz] * (vx1 - vx2) / h;
tzz_x[ off1 + (Npml-1)*Npml+j ] *= c1;
}
for (size_t i=0; i<Npml; ++i) {
vz1 = vz_x[off1 + i*Npml] + vz_z[off1 + i*Npml];
vz2 = 0.;
c1 = (2.*dt) / ( 2. + dt*d[0] );
c2 = ( 2. - dt*d[0] ) / (2.*dt);
txx_z[ off1 + i*Npml ] *= c2;
txx_z[ off1 + i*Npml ] += la[(nx-1)*nz] * (vz1 - vz2) / h;
txx_z[ off1 + i*Npml ] *= c1;
tzz_z[ off1 + i*Npml ] *= c2;
tzz_z[ off1 + i*Npml ] += l2m[(nx-1)*nz] * (vz1 - vz2) / h;
tzz_z[ off1 + i*Npml ] *= c1;
for (size_t j=1; j<Npml; ++j) {
vz1 = vz_x[off1 + i*Npml+j] + vz_z[off1 + i*Npml+j];
vz2 = vz_x[off1 + i*Npml+j-1] + vz_z[off1 + i*Npml+j-1];
c1 = (2.*dt) / ( 2. + dt*d[j] );
c2 = ( 2. - dt*d[j] ) / (2.*dt);
txx_z[ off1 + i*Npml+j ] *= c2;
txx_z[ off1 + i*Npml+j ] += la[(nx-1)*nz] * (vz1 - vz2) / h;
txx_z[ off1 + i*Npml+j ] *= c1;
tzz_z[ off1 + i*Npml+j ] *= c2;
tzz_z[ off1 + i*Npml+j ] += l2m[(nx-1)*nz] * (vz1 - vz2) / h;
tzz_z[ off1 + i*Npml+j ] *= c1;
}
}
// txx & tzz - right strip
//
off1 += Npml*Npml;
for (size_t i=0; i<Npml-1; ++i) {
for (size_t j=0; j<nz; ++j) {
vx1 = vx_x[off1 + (i+1)*nz+j] + vx_z[off1 + (i+1)*nz+j];
vx2 = vx_x[off1 + i*nz+j] + vx_z[off1 + i*nz+j];
c1 = (2.*dt) / ( 2. + dt*dH[Npml-1-i] );
c2 = ( 2. - dt*dH[Npml-1-i] ) / (2.*dt);
txx_x[ off1 + i*nz+j ] *= c2;