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solver.cpp
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solver.cpp
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//
// solver.cpp
// PDE
//
// Created by Ali Dorostkar on 3/24/12.
// Copyright (c) 2012 Uppsala. All rights reserved.
//
// SOLVER class solves 2D PDE
#include "solver.h"
// Compute index of the block with respect to placement
#define idx(i,j,k) (i) + (j)*LN_X + (k)*LN_X*LN_Y
// Compute index of the PML block with respect to placement
#define PML_idx(i,k) (i) + (k)*LN_X
/* ----======== Base class ========----- */
FDM::baseSolver::baseSolver(double _h, double _dt, int _order){
h = _h;
dt = _dt;
order = _order;
tEnd = 2;
X_layers = vector<double>(2);
Y_layers = vector<double>(2);
Z_layers = vector<double>(2);
speeds = vector<double>(1);
X_layers[0] = 0;
X_layers[1] = 1;
Y_layers[0] = 0;
Y_layers[1] = 1;
Z_layers[0] = 0;
Z_layers[1] = 1;
speeds[0] = 1;
LN_X = 1;
LN_Y = 1;
LN_Z = 1;
totalBlocks = LN_X*LN_Y*LN_Z;
Ta_0 = 5;
SPP = 10;
init_args = NULL;
initializer = NULL;
fource_args = NULL;
Fource = NULL;
plot_args = NULL;
plotter = NULL;
finilizer = NULL;
finilizer_args = NULL;
Set_H_INV();
}
void FDM::baseSolver::Set_FourceFunction(void (*SF)(Vdata &, Vdata &, baseSolver &, const Vdata&, int, double, void *), void * args){
if(SF != NULL){
Fource = SF;
fource_args = args;
}
}
void FDM::baseSolver::Set_Initializer(void (*SI)(Vdata &, baseSolver &, void *), void * args){
if(SI != NULL){
initializer = SI;
init_args = args;
}
}
void FDM::baseSolver::Set_Plotter(void (*SP)(const Vdata &, baseSolver&,int, double , void *),void * args){
plotter = SP;
plot_args = args;
}
void FDM::baseSolver::Set_Finilizer(void (*FI)(Vdata &, baseSolver &, double, void *), void * args){
finilizer = FI;
finilizer_args = args;
}
void FDM::baseSolver::X_Interfc_L(const myData & u1, const myData & u1x,const double c1 ,const myData & u2, const myData & u2x,const double c2,myData & I2){
int Nx1 = u1.Nx();
int Ny = u2.Ny();
int Nz = u2.Nz();
double Ta_n = 0.5;
myData I_u2_0(1,Ny,Nz);
myData I_u2x_0(1,Ny,Nz);
for (int k = 0; k < Nz; k++) {
for (int j = 0; j < Ny; j++) {
// I_u2_0(0,j,k) = Ta_0/h*(c1+c2)*(u2(0,j,k) - u1(Nx1-1,j,k));
I_u2_0(0,j,k) = Ta_0/h*(c1+c2)*(u2(0,j,k) - u1(Nx1-1,j,k));
I_u2x_0(0,j,k) = -Ta_n*(c2*u2x(0,j,k) - c1*u1x(Nx1-1,j,k));
}
}
for (int k = 0; k < Nz; k++) {
for (int j = 0; j < Ny; j++) {
I2(0,j,k) = I_u2_0(0,j,k) + I_u2x_0(0,j,k);
}
}
}
void FDM::baseSolver::X_Interfc_R(const myData & u1, const myData & u1x,const double c1,myData & I1 ,const myData & u2, const myData & u2x,const double c2){
int Nx1 = u1.Nx();
int Ny = u1.Ny();
int Nz = u1.Nz();
double Ta_n = 0.5;
myData I_u1_n(1,Ny,Nz);
myData I_u1x_n(1,Ny,Nz);
for (int k = 0; k < Nz; k++) {
for (int j = 0; j < Ny; j++) {
// I_u1_n(0,j,k) = Ta_0/h*(c1+c2)*(u1(Nx1-1,j,k) - u2(0,j,k));
I_u1_n(0,j,k) = Ta_0/h*(c1+c2)*(u1(Nx1-1,j,k) - u2(0,j,k));
I_u1x_n(0,j,k) = Ta_n*(c1*u1x(Nx1-1,j,k) - c2*u2x(0,j,k));
}
}
for (int k = 0; k < Nz; k++) {
for (int j = 0; j < Ny; j++) {
I1(Nx1-1,j,k) = I_u1_n(0,j,k) + I_u1x_n(0,j,k);
}
}
}
void FDM::baseSolver::Y_Interfc_L(const myData & u1, const myData & u1y,const double c1 ,const myData & u2, const myData & u2y,const double c2,myData & I2){
int Nx = u1.Nx();
int Ny1 = u1.Ny();
int Nz = u1.Nz();
double Ta_n = 0.5;
myData I_u2_0(Nx,1,Nz);
myData I_u2y_0(Nx,1,Nz);
for (int k = 0; k < Nz; k++) {
for (int i = 0; i < Nx; i++) {
// I_u2_0(i,0,k) = Ta_0/h*(c1+c2)*(u2(i,0,k) - u1(i,Ny1-1,k));
I_u2_0(i,0,k) = Ta_0/h*(c1+c2)*(u2(i,0,k) - u1(i,Ny1-1,k));
I_u2y_0(i,0,k) = -Ta_n*(c2*u2y(i,0,k) - c1*u1y(i,Ny1-1,k));
}
}
for (int k = 0; k < Nz; k++) {
for (int i = 0; i < Nx; i++) {
I2(i,0,k) = I_u2_0(i,0,k) + I_u2y_0(i,0,k);
}
}
}
void FDM::baseSolver::Y_Interfc_R(const myData & u1, const myData & u1y,const double c1,myData & I1 ,const myData & u2, const myData & u2y,const double c2){
int Nx = u1.Nx();
int Ny1 = u1.Ny();
int Nz = u1.Nz();
double Ta_n = 0.5;
myData I_u1_n(Nx,1,Nz);
myData I_u1y_n(Nx,1,Nz);
for (int k = 0; k < Nz; k++) {
for (int i = 0; i < Nx; i++) {
// I_u1_n(i,0,k) = Ta_0/h*(c1+c2)*(u1(i,Ny1-1,k) - u2(i,0,k));
I_u1_n(i,0,k) = Ta_0/h*(c1+c2)*(u1(i,Ny1-1,k) - u2(i,0,k));
I_u1y_n(i,0,k) = Ta_n*(c1*u1y(i,Ny1-1,k) - c2*u2y(i,0,k));
}
}
for (int k = 0; k < Nz; k++) {
for (int i = 0; i < Nx; i++) {
I1(i,Ny1-1,k) = I_u1_n(i,0,k) + I_u1y_n(i,0,k);
}
}
}
void FDM::baseSolver::Z_Interfc_L(const myData & u1, const myData & u1z,const double c1 ,const myData & u2, const myData & u2z,const double c2,myData & I2){
int Nx = u1.Nx();
int Ny = u1.Ny();
int Nz1 = u1.Nz();
double Ta_n = 0.5;
myData I_u2_0(Nx,Ny,1);
myData I_u2z_0(Nx,Ny,1);
for (int j = 0; j < Ny; j++) {
for (int i = 0; i < Nx; i++) {
// I_u2_0(i,j,0) = Ta_0/h*(c1+c2)*(u2(i,j,0) - u1(i,j,Nz1-1));
I_u2_0(i,j,0) = Ta_0/h*(c1+c2)*(u2(i,j,0) - u1(i,j,Nz1-1));
I_u2z_0(i,j,0) = -Ta_n*(c2*u2z(i,j,0) - c1*u1z(i,j,Nz1-1));
}
}
for (int j = 0; j < Ny; j++) {
for (int i = 0; i<Nx; i++) {
I2(i,j,0) = I_u2_0(i,j,0) + I_u2z_0(i,j,0);
}
}
}
void FDM::baseSolver::Z_Interfc_R(const myData & u1, const myData & u1z,const double c1,myData & I1 ,const myData & u2, const myData & u2z,const double c2){
int Nx = u1.Nx();
int Ny = u1.Ny();
int Nz1 = u1.Nz();
double Ta_n = 0.5;
myData I_u1_n(Nx,Ny,1);
myData I_u1z_n(Nx,Ny,1);
for (int j = 0; j < Ny; j++) {
for (int i = 0; i < Nx; i++) {
// I_u1_n(i,j,0) = Ta_0/h*(c1+c2)*(u1(i,j,Nz1-1) - u2(i,j,0));
I_u1_n(i,j,0) = Ta_0/h*(c1+c2)*(u1(i,j,Nz1-1) - u2(i,j,0));
I_u1z_n(i,j,0) = Ta_n*(c1*u1z(i,j,Nz1-1) - c2*u2z(i,j,0));
}
}
for (int j = 0; j < Ny; j++) {
for (int i = 0; i<Nx; i++) {
I1(i,j,Nz1-1) = I_u1_n(i,j,0) + I_u1z_n(i,j,0);
}
}
}
void FDM::baseSolver::Set_H_INV(){
double a;
switch (order) {
case 2:
a = 0.5;
break;
case 4:
a = 4567./14400.;
break;
case 6:
a = 7493827./25401600.;
break;
default:
a = 0.5;
break;
}
H1 = 1/(a*h);
}
/* ----======== Solver class ========----- */
FDM::solver::solver(double _h, double _dt, int _order) : FDM::baseSolver::baseSolver(_h, _dt, _order){}
Vdata FDM::solver::run(){
///// INITIALIZE /////
Vdata u(totalBlocks);
Vdata u0(totalBlocks);
Vdata ut0(totalBlocks);
Vdata u_out(totalBlocks);
int Nz = 0;
int Nx = 0;
int Ny = 0;
for (int lz = 0; lz < LN_Z; lz++) {
Nz = static_cast<int>( (Z_layers[lz + 1] - Z_layers[lz])/h + 1 );
for (int ly = 0; ly < LN_Y; ly++) {
Ny = static_cast<int>( (Y_layers[ly + 1] - Y_layers[ly])/h + 1 );
for (int lx = 0; lx < LN_X; lx++) {
Nx = static_cast<int>( (X_layers[lx+1] - X_layers[lx])/h + 1 );
int index = idx(lx,ly,lz);
u[index] = myData(Nx,Ny,Nz);
u0[index] = myData(Nx,Ny,Nz);
ut0[index] = myData(Nx,Ny,Nz);
u_out[index] = myData(Nx,Ny,Nz);
}
}
}
if (initializer != NULL)
initializer(u, *this, init_args);
if(plotter != NULL)
plotter(u,*this,0,0, plot_args);
///// TIME MARCH /////
double t = 0;
int iterNr = static_cast<int>( tEnd/dt );
for (int k = 0; k < iterNr; k++) {
t = k*dt;
Tstep(u_out, u, u0, ut0, k, t);
u0 = u;
u = u_out;
///// PLOT /////
if(k%SPP == 0 && plotter != NULL)
plotter(u,*this,k+1,t+dt, plot_args);
}
if(finilizer != NULL)
finilizer(u,*this,tEnd, finilizer_args);
return u;
}
void FDM::solver::Tstep(Vdata & u_out,const Vdata & u, const Vdata & u0,const Vdata & ut0, int k,double t){
Vdata rhs4(totalBlocks);
Vdata F(totalBlocks);
Vdata Ftt(totalBlocks);
Vdata F4(totalBlocks);
for (int ln = 0; ln < totalBlocks; ln++){
int Nx = u[ln].Nx();
int Ny = u[ln].Ny();
int Nz = u[ln].Nz();
F[ln] = myData(Nx,Ny,Nz);
Ftt[ln] = myData(Nx,Ny,Nz);
F4[ln] = myData(Nx,Ny,Nz);
rhs4[ln] = myData(Nx,Ny,Nz);
}
Fource(F, Ftt, *this, u, k, t, fource_args);
Vdata rhs = RHS(u);
if(order > 2){
rhs4 = RHS(rhs);
F4 = RHS(F);
for (int ln = 0; ln < totalBlocks; ln++)
F4[ln] += Ftt[ln];
}
for (int ln = 0; ln < totalBlocks; ln++) {
switch (k) {
case 0:
u_out[ln] = u[ln] + dt*ut0[ln] + (dt*dt/2)*(rhs[ln] + (dt*dt/12)*(rhs4[ln] + F4[ln]) + F[ln]);
break;
default:
// u_out[ln] = (2*u[ln] - u0[ln] + dt*dt*(rhs[ln] + (dt*dt/12)*(rhs4[ln] + F4[ln]) + F[ln]));
u_out[ln] = rhs4[ln];
u_out[ln] += F4[ln];
u_out[ln] *= (dt*dt/12);
u_out[ln] += F[ln];
u_out[ln] += rhs[ln];
u_out[ln] *= dt*dt;
u_out[ln] -= u0[ln];
u_out[ln] += 2*u[ln];
break;
}
}
}
Vdata FDM::solver::RHS(const Vdata & u){
Vdata rhs(totalBlocks);
Vdata ux(totalBlocks);
Vdata uy(totalBlocks);
Vdata uz(totalBlocks);
for (int ln = 0; ln < totalBlocks;ln++){
int Nx = u[ln].Nx();
int Ny = u[ln].Ny();
int Nz = u[ln].Nz();
rhs[ln] = myData(Nx,Ny,Nz);
ux[ln] = u[ln].D1(h, order, X_DIR);
uy[ln] = u[ln].D1(h, order, Y_DIR);
uz[ln] = u[ln].D1(h, order, Z_DIR);
}
for (int lz = 0; lz < LN_Z;lz++){
for (int ly = 0; ly < LN_Y; ly++) {
for (int lx = 0; lx < LN_X; lx++) {
int index = idx(lx, ly, lz);
int Nx = u[index].Nx();
int Ny = u[index].Ny();
int Nz = u[index].Nz();
myData Bux(Nx,Ny,Nz);
myData Buy(Nx,Ny,Nz);
myData Buz(Nx,Ny,Nz);
myData X_Iu1(Nx,Ny,Nz);
myData X_Iu2(Nx,Ny,Nz);
myData Y_Iu1(Nx,Ny,Nz);
myData Y_Iu2(Nx,Ny,Nz);
myData Z_Iu1(Nx,Ny,Nz);
myData Z_Iu2(Nx,Ny,Nz);
//Bux setup
if(lx == 0){
for (int k = 0; k < Nz; k++) {
for (int j = 0; j < Ny; j++) {
Bux(0,j,k) = -1;
}
}
}
if(lx == LN_X - 1){
for (int k = 0; k < Nz; k++) {
for (int j = 0; j < Ny; j++) {
Bux(Nx - 1,j,k) = 1;
}
}
}
//
//Buy setup
if(ly == 0){
for (int k = 0; k < Nz; k++) {
for (int i = 0; i < Nx; i++) {
Buy(i,0,k) = -1;
}
}
}
if(ly == LN_Y - 1){
for (int k = 0; k < Nz; k++) {
for (int i = 0; i < Nx; i++) {
Buy(i,Ny - 1,k) = 1;
}
}
}
//
//Buz setup
if(lz == 0){
for (int j = 0; j < Ny; j++) {
for (int i = 0; i < Nx; i++) {
Buz(i,j,0) = -1;
}
}
}
if(lz == LN_Z - 1){
for (int j = 0; j < Ny; j++) {
for (int i = 0; i < Nx; i++) {
Buz(i,j,Nz - 1) = 1;
}
}
}
//
///// interface
// x direction
if (lx != 0) {
int index2 = idx(lx - 1, ly, lz);
X_Interfc_L(u[index2], ux[index2], speeds[index2], u[index], ux[index], speeds[index], X_Iu1);
}
if (lx != LN_X - 1) {
int index2 = idx(lx + 1, ly, lz);
X_Interfc_R(u[index], ux[index], speeds[index], X_Iu2, u[index2], ux[index2], speeds[index2]);
}
// y direction
if (ly != 0) {
int index2 = idx(lx, ly - 1, lz);
Y_Interfc_L(u[index2],uy[index2],speeds[index2],u[index], uy[index], speeds[index], Y_Iu1);
}
if (ly != LN_Y - 1) {
int index2 = idx(lx, ly + 1, lz);
Y_Interfc_R(u[index],uy[index],speeds[index],Y_Iu2,u[index2], uy[index2], speeds[index2]);
}
// z direction
if (lz != 0) {
int index2 = idx(lx, ly, lz - 1);
Z_Interfc_L(u[index2],uz[index2],speeds[index2],u[index], uz[index], speeds[index], Z_Iu1);
}
if (lz != LN_Z - 1) {
int index2 = idx(lx, ly, lz + 1);
Z_Interfc_R(u[index],uz[index],speeds[index],Z_Iu2,u[index2], uz[index2], speeds[index2]);
}
myData Dxxu = u[index].D2(h, order, X_DIR);
myData Dyyu = u[index].D2(h, order, Y_DIR);
myData Dzzu = u[index].D2(h, order, Z_DIR);
// rhs[index] = speeds[index]*(Dxxu + Dyyu + Dzzu) - H1*(speeds[index]*Bux*ux[index] + speeds[index]*Buy*uy[index] + speeds[index]*Buz*uz[index] + X_Iu1 + X_Iu2 + Y_Iu1 + Y_Iu2+ Z_Iu1 + Z_Iu2);
rhs[index] += Dxxu;
rhs[index] += Dyyu;
rhs[index] += Dzzu;
rhs[index] *= speeds[index];
Bux *= ux[index];
Bux *= speeds[index];
Buy *= uy[index];
Buy *= speeds[index];
Buz *= uz[index];
Buz *= speeds[index];
Bux += Buy;
Bux += Buz;
Bux += X_Iu1;
Bux += X_Iu2;
Bux += Y_Iu1;
Bux += Y_Iu2;
Bux += Z_Iu1;
Bux += Z_Iu2;
Bux *= H1;
rhs[index] -= Bux;
}
}
}
return rhs;
}
void FDM::solver::Set_Domain(vector<double> & _X_layers, vector<double> & _Y_layers, vector<double> & _Z_layers,vector<double> & _speeds){
LN_X = (int)_X_layers.size() - 1;
LN_Y = (int)_Y_layers.size() - 1;
LN_Z = (int)_Z_layers.size() - 1;
totalBlocks = LN_X*LN_Y*LN_Z;
if (_speeds.size() != totalBlocks) {
exit(EXIT_FAILURE);
}
speeds = _speeds;
X_layers = _X_layers;
Y_layers = _Y_layers;
Z_layers = _Z_layers;
}
/* ----======== PML class ========----- */
FDM::pmlSolver::pmlSolver(double _h, double _dt, int _order) : FDM::baseSolver::baseSolver(_h, _dt, _order){
// Set options to defaults
LN_X = 1;
LN_Y = 2; // one layer and PML
LN_Z = 1;
Ta_0 = 5;
SPP = 10;
PML_Polinomial_Degree = 3;
PML_Length = 0.5;
maxSpeed = 1;
totalBlocks = LN_X*LN_Y*LN_Z;
PML_Blocks = LN_X*LN_Z;
X_layers = vector<double>(LN_X + 1);
Y_layers = vector<double>(LN_Y + 1);
Z_layers = vector<double>(LN_Z + 1);
speeds = vector<double>(totalBlocks);
X_layers[0] = 0;
X_layers[1] = 1;
Y_layers[0] = 0;
Y_layers[1] = 1;
Y_layers[2] = 1 + PML_Length;
Z_layers[0] = 0;
Z_layers[1] = 1;
speeds[0] = 1;
speeds[1] = 1;
// Compute Damping coeff
Set_DampingCoeff();
}
Vdata FDM::pmlSolver::run(){
///// INITIALIZE /////
Vdata u(totalBlocks);
Vdata u0(totalBlocks);
Vdata ut0(totalBlocks);
Vdata u_out(totalBlocks);
Vdata v(PML_Blocks);
Vdata v_out(PML_Blocks);
Vdata w(PML_Blocks);
Vdata w_out(PML_Blocks);
Vdata p(PML_Blocks);
Vdata p_out(PML_Blocks);
Vdata sigma(PML_Blocks);
Vdata a_u(PML_Blocks);
Vdata b_u(PML_Blocks);
int Nz = 0;
int Nx = 0;
int Ny = 0;
for (int lz = 0; lz < LN_Z; lz++) {
Nz = static_cast<int>( (Z_layers[lz + 1] - Z_layers[lz])/h + 1 );
for (int ly = 0; ly < LN_Y; ly++) {
Ny = static_cast<int>( (Y_layers[ly + 1] - Y_layers[ly])/h + 1 );
for (int lx = 0; lx < LN_X; lx++) {
Nx = static_cast<int>( (X_layers[lx + 1] - X_layers[lx])/h + 1 );
int index = idx(lx,ly,lz);
u[index] = myData(Nx,Ny,Nz);
u0[index] = myData(Nx,Ny,Nz);
ut0[index] = myData(Nx,Ny,Nz);
u_out[index] = myData(Nx,Ny,Nz);
}
}
}
//initializing PML
int PML_Ny = static_cast<int>( PML_Length/h + 1);
for (int lz = 0; lz < LN_Z; lz++) {
Nz = static_cast<int>( (Z_layers[lz + 1] - Z_layers[lz])/h + 1 );
for (int lx = 0; lx < LN_X; lx++) {
Nx = static_cast<int>( (X_layers[lx + 1] - X_layers[lx])/h + 1 );
int index = idx(lx,LN_Y-1,lz);
int PML_index = PML_idx(lx,lz);
u[index] = myData(Nx,PML_Ny,Nz);
u0[index] = myData(Nx,PML_Ny,Nz);
ut0[index] = myData(Nx,PML_Ny,Nz);
u_out[index] = myData(Nx,PML_Ny,Nz);
v[PML_index] = myData(Nx,PML_Ny,Nz);
v_out[PML_index] = myData(Nx,PML_Ny,Nz);
w[PML_index] = myData(Nx,PML_Ny,Nz);
w_out[PML_index] = myData(Nx,PML_Ny,Nz);
p[PML_index] = myData(Nx,PML_Ny,Nz);
p_out[PML_index] = myData(Nx,PML_Ny,Nz);
sigma[PML_index] = sigmaY(u[index]);
a_u[PML_index] = 1/(1 + 0.5*dt*sigma[PML_index]);
b_u[PML_index] = 1 - 0.5*dt*sigma[PML_index];
}
}
if (initializer != NULL)
initializer(u, *this, init_args);
if(plotter != NULL)
plotter(u,*this,0,0, plot_args);
///// TIME MARCH /////
double t = 0;
int iterNr = static_cast<int>( tEnd/dt );
for (int k = 0; k < iterNr; k++) {
t = k*dt;
Tstep(u_out, u, u0, ut0, v_out, v, w_out, w, p_out, p, sigma, a_u, b_u, k, t);
u0 = u;
u = u_out;
v = v_out;
w = w_out;
p = p_out;
///// PLOT /////
if(k%SPP == 0 && plotter != NULL)
plotter(u,*this,k+1,t+dt, plot_args);
}
if(finilizer != NULL)
finilizer(u,*this,tEnd, finilizer_args);
return u;
}
void FDM::pmlSolver::Tstep(Vdata & u_out,const Vdata & u, const Vdata & u0,const Vdata & ut0, Vdata & v_out,const Vdata & v, Vdata & w_out,const Vdata & w, Vdata & p_out,const Vdata & p, const Vdata & sigma, const Vdata & a_u, const Vdata & b_u, int k,double t){
Vdata rhs4(totalBlocks);
Vdata F(totalBlocks);
Vdata Ftt(totalBlocks);
Vdata F4(totalBlocks);
Vdata sigma4(PML_Blocks);
for (int ln = 0; ln < totalBlocks; ln++){
int Nx = u[ln].Nx();
int Ny = u[ln].Ny();
int Nz = u[ln].Nz();
F[ln] = myData(Nx,Ny,Nz);
Ftt[ln] = myData(Nx,Ny,Nz);
F4[ln] = myData(Nx,Ny,Nz);
rhs4[ln] = myData(Nx,Ny,Nz);
}
for (int lz = 0; lz < LN_Z; lz++) {
for (int lx = 0; lx < LN_X; lx++) {
int index = idx(lx,LN_Y-1,lz);
int PML_index = PML_idx(lx,lz);
int Nx = u[index].Nx();
int Ny = u[index].Ny();
int Nz = u[index].Nz();
sigma4[PML_index] = myData(Nx,Ny,Nz);
}
}
Fource(F, Ftt, *this, u, k, t, fource_args);
Vdata rhs = RHS(u, sigma, w, p);
if(order > 2){
rhs4 = RHS(rhs, sigma4, w, p);
F4 = RHS(F,sigma4, w, p);
for (int ln = 0; ln < totalBlocks; ln++)
F4[ln] += Ftt[ln];
}
for (int lz = 0; lz < LN_Z; lz++) {
for (int ly = 0; ly < LN_Y - 1; ly++) {
for (int lx = 0; lx < LN_X; lx++) {
int ln = idx(lx, ly, lz);
switch (k) {
case 0:
u_out[ln] = u[ln] + dt*ut0[ln] + (dt*dt/2)*(rhs[ln] + (dt*dt/12)*(rhs4[ln] + F4[ln]) + F[ln]);
break;
default:
// u_out[ln] = (2*u[ln] - u0[ln] + dt*dt*(rhs[ln] + (dt*dt/12)*(rhs4[ln] + F4[ln]) + F[ln]));
u_out[ln] = rhs4[ln];
u_out[ln] += F4[ln];
u_out[ln] *= (dt*dt/12);
u_out[ln] += F[ln];
u_out[ln] += rhs[ln];
u_out[ln] *= dt*dt;
u_out[ln] -= u0[ln];
u_out[ln] += 2*u[ln];
break;
}
}
}
}
for (int lz = 0; lz < LN_Z; lz++) {
for (int lx = 0; lx < LN_X; lx++) {
int ln = idx(lx,LN_Y-1,lz);
int PML_ln = PML_idx(lx,lz);
switch (k) {
case 0:
u_out[ln] = u[ln] + dt*ut0[ln] + (dt*dt/2)*(rhs[ln] + (dt*dt/12)*(rhs4[ln] + F4[ln]) + F[ln]);
break;
default:
// u_out[ln] = (2*u[ln] - u0[ln] + dt*dt*(rhs[ln] + (dt*dt/12)*(rhs4[ln] + F4[ln]) + F[ln]));
u_out[ln] = rhs4[ln];
u_out[ln] += F4[ln];
u_out[ln] *= (dt*dt/12);
u_out[ln] -= speeds[ln]*(sigma[PML_ln]*v[PML_ln]).D1(h,order, Y_DIR);
u_out[ln] += speeds[ln]*(sigma[PML_ln]*w[PML_ln]).D1(h,order, X_DIR);
u_out[ln] += speeds[ln]*(sigma[PML_ln]*p[PML_ln]).D1(h,order, Z_DIR);
u_out[ln] += F[ln];
u_out[ln] += rhs[ln];
u_out[ln] *= dt*dt;
u_out[ln] -= b_u[PML_ln]*u0[ln];
u_out[ln] += 2*u[ln];
u_out[ln] *= (a_u[PML_ln]);
break;
}
v_out[PML_ln] = a_u[PML_ln]*(b_u[PML_ln]*v[PML_ln] + (dt/2)*(u_out[ln] + u[ln]).D1(h,order, Y_DIR));
w_out[PML_ln] = (u_out[ln] + u[ln]).D1(h,order, X_DIR);
w_out[PML_ln] *= (dt/2);
w_out[PML_ln] += w[PML_ln];
p_out[PML_ln] = (u_out[ln] + u[ln]).D1(h,order, Z_DIR);
p_out[PML_ln] *= (dt/2);
p_out[PML_ln] += p[PML_ln];
}
}
}
Vdata FDM::pmlSolver::RHS(const Vdata & u, const Vdata & sigma, const Vdata & w, const Vdata & p){
Vdata rhs(totalBlocks);
Vdata ux(totalBlocks);
Vdata uy(totalBlocks);
Vdata uz(totalBlocks);
for (int ln = 0; ln < totalBlocks;ln++){
int Nx = u[ln].Nx();
int Ny = u[ln].Ny();
int Nz = u[ln].Nz();
rhs[ln] = myData(Nx,Ny,Nz);
ux[ln] = u[ln].D1(h, order, X_DIR);
uy[ln] = u[ln].D1(h, order, Y_DIR);
uz[ln] = u[ln].D1(h, order, Z_DIR);
}
for (int lz = 0; lz < LN_Z;lz++){
for (int ly = 0; ly < LN_Y - 1; ly++) {
for (int lx = 0; lx < LN_X; lx++) {
int index = idx(lx, ly, lz);
int Nx = u[index].Nx();
int Ny = u[index].Ny();
int Nz = u[index].Nz();
myData Bux(Nx,Ny,Nz);
myData Buy(Nx,Ny,Nz);
myData Buz(Nx,Ny,Nz);
myData X_Iu1(Nx,Ny,Nz);
myData X_Iu2(Nx,Ny,Nz);
myData Y_Iu1(Nx,Ny,Nz);
myData Y_Iu2(Nx,Ny,Nz);
myData Z_Iu1(Nx,Ny,Nz);
myData Z_Iu2(Nx,Ny,Nz);
//Bux setup
if(lx == 0){
for (int k = 0; k < Nz; k++) {
for (int j = 0; j < Ny; j++) {
Bux(0,j,k) = -1;
}
}
}
if(lx == LN_X - 1){
for (int k = 0; k < Nz; k++) {
for (int j = 0; j < Ny; j++) {
Bux(Nx - 1,j,k) = 1;
}
}
}
//
//Buy setup
if(ly == 0){
for (int k = 0; k < Nz; k++) {
for (int i = 0; i < Nx; i++) {
Buy(i,0,k) = -1;
}
}
}
//
//Buz setup
if(lz == 0){
for (int j = 0; j < Ny; j++) {
for (int i = 0; i < Nx; i++) {
Buz(i,j,0) = -1;
}
}
}
if(lz == LN_Z - 1){
for (int j = 0; j < Ny; j++) {
for (int i = 0; i < Nx; i++) {
Buz(i,j,Nz - 1) = 1;
}
}
}
//
///// interface
// x direction
if (lx != 0) {
int index2 = idx(lx - 1, ly, lz);
X_Interfc_L(u[index2], ux[index2], speeds[index2], u[index], ux[index], speeds[index], X_Iu1);
}
if (lx != LN_X - 1) {
int index2 = idx(lx + 1, ly, lz);
X_Interfc_R(u[index], ux[index], speeds[index], X_Iu2, u[index2], ux[index2], speeds[index2]);
}
// y direction
if (ly != 0) {
int index2 = idx(lx, ly - 1, lz);
Y_Interfc_L(u[index2],uy[index2],speeds[index2],u[index], uy[index], speeds[index], Y_Iu1);
}
// if (ly != LN_Y - 1) { //always happens in this loop
int index2 = idx(lx, ly + 1, lz);
Y_Interfc_R(u[index],uy[index],speeds[index],Y_Iu2,u[index2], uy[index2], speeds[index2]);
// }
// z direction
if (lz != 0) {
int index2 = idx(lx, ly, lz - 1);
Z_Interfc_L(u[index2],uz[index2],speeds[index2],u[index], uz[index], speeds[index], Z_Iu1);
}
if (lz != LN_Z - 1) {
int index2 = idx(lx, ly, lz + 1);
Z_Interfc_R(u[index],uz[index],speeds[index],Z_Iu2,u[index2], uz[index2], speeds[index2]);
}
myData Dxxu = u[index].D2(h, order, X_DIR);
myData Dyyu = u[index].D2(h, order, Y_DIR);
myData Dzzu = u[index].D2(h, order, Z_DIR);
// rhs[index] = speeds[index]*(Dxxu + Dyyu + Dzzu) - H1*(speeds[index]*Bux*ux[index] + speeds[index]*Buy*uy[index] + speeds[index]*Buz*uz[index] + X_Iu1 + X_Iu2 + Y_Iu1 + Y_Iu2+ Z_Iu1 + Z_Iu2);
rhs[index] += Dxxu;
rhs[index] += Dyyu;
rhs[index] += Dzzu;
rhs[index] *= speeds[index];
ux[index] *= speeds[index];
uy[index] *= speeds[index];
uz[index] *= speeds[index];
Bux *= ux[index];
Buy *= uy[index];
Buz *= uz[index];
Bux += Buy;
Bux += Buz;
Bux += X_Iu1;
Bux += X_Iu2;
Bux += Y_Iu1;
Bux += Y_Iu2;
Bux += Z_Iu1;
Bux += Z_Iu2;
Bux *= H1;
rhs[index] -= Bux;
}
}
}
for (int lz = 0; lz < LN_Z;lz++){
for (int lx = 0; lx < LN_X; lx++) {
int ly = LN_Y - 1;
int index = idx(lx, ly, lz);
int Nx = u[index].Nx();
int Ny = u[index].Ny();
int Nz = u[index].Nz();
myData Bux(Nx,Ny,Nz);
myData Buy(Nx,Ny,Nz);
myData Buz(Nx,Ny,Nz);
myData X_Iu1(Nx,Ny,Nz);
myData X_Iu2(Nx,Ny,Nz);
myData Y_Iu1(Nx,Ny,Nz);
myData Y_Iu2(Nx,Ny,Nz);
myData Z_Iu1(Nx,Ny,Nz);
myData Z_Iu2(Nx,Ny,Nz);
//Bux setup
if(lx == 0){
for (int k = 0; k < Nz; k++) {
for (int j = 0; j < Ny; j++) {
Bux(0,j,k) = -1;
}
}
}
if(lx == LN_X - 1){
for (int k = 0; k < Nz; k++) {
for (int j = 0; j < Ny; j++) {
Bux(Nx - 1,j,k) = 1;
}
}
}
//
// if(ly == LN_Y - 1){ //always happens
for (int k = 0; k < Nz; k++) {
for (int i = 0; i < Nx; i++) {
Buy(i,Ny - 1,k) = 1;
}
}
// }
//
//Buz setup
if(lz == 0){
for (int j = 0; j < Ny; j++) {
for (int i = 0; i < Nx; i++) {
Buz(i,j,0) = -1;
}
}
}
if(lz == LN_Z - 1){
for (int j = 0; j < Ny; j++) {
for (int i = 0; i < Nx; i++) {
Buz(i,j,Nz - 1) = 1;
}
}
}
//
///// interface
// x direction
if (lx != 0) {
int index2 = idx(lx - 1, ly, lz);