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Algrthm.cpp
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Algrthm.cpp
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#include "PML.h"
void PML::Match(){
int i, j;
long long it;
double c0, c1, c2; // temporary parameters
double ct, cx, cy;
for (it = 1; it < Nt; it++)
{
GetSource(flag, it); // for simulation
//BondValue(it); // use for test
for (i = 0; i < Nx - 1; i++)
{
for (j = 0; j < Ny - 1; j++)
{
// loop for E
// (1) in paper, point of eqn : (i + 1 / 2, j + 1 / 2, n + 1 / 2)
if ((i != Nxf)|(j >= Nyf1)|(j <= Nyf0)) // do not update source
{
ct = pt(it) - 0.5*dt;
cx = 0.5*(px[i] + px[i + 1]);
cy = 0.5*(py[j] + py[j + 1]);
reg = WhichReg(cx, cy);
c0 = 1 / (e0(cx, cy) / dt + 0.5*e0(cx, cy)*(sgmx(cx) + sgmy(cy)));
c1 = e0(cx, cy) / dt - 0.5*e0(cx, cy)*(sgmx(cx) + sgmy(cy));
E[j][i][flag] = c0*((Hy[j][i + 1][!flag] - Hy[j][i][!flag]) / (0.5*dx[i]+0.5*dx[i+1]) - (Hx[j + 1][i][!flag] - Hx[j][i][!flag]) / (0.5*dy[j]+0.5*dy[j+1]) \
- J[j][i][!flag] + c1*E[j][i][!flag] + g3_fcn(cx, cy, ct));
}
// loop for J
// (2) in paper, point of eqn : (i + 1 / 2, j + 1 / 2, n + 1)
ct = pt(it);
cx = 0.5*(px[i] + px[i + 1]);
cy = 0.5*(py[j] + py[j + 1]);
reg = WhichReg(cx, cy);
c0 = 1 / (1 / dt + 0.5*pJ(cx, cy));
c1 = e0(cx, cy)*pJE(cx, cy);
c2 = 1 / dt - 0.5*pJ(cx, cy);
J[j][i][flag] = c0*(c1*E[j][i][flag] + c2*J[j][i][!flag] + g4_fcn(cx, cy, ct));
if (j != 0)
{
// loop for Kx
// (3) in paper, point of eqn : (i + 1 / 2, j, n + 1 / 2)
ct = pt(it) - 0.5*dt;
cx = 0.5*(px[i] + px[i + 1]);
cy = py[j];
reg = WhichReg(cx, cy);
c0 = 1 / (1 / dt + 0.5*pKx(cx, cy));
c1 = mu0(cx, cy)*pKxHx(cx, cy);
c2 = 1 / dt - 0.5*pKx(cx, cy);
Kx[j][i][flag] = c0*(c1*Hx[j][i][!flag] + c2*Kx[j][i][!flag] + g5_fcn(cx, cy, ct));
}
if (i != 0)
{
// loop for Ky
// (4) in paper, point of eqn : (i, j + 1 / 2, n + 1 / 2)
ct = pt(it) - 0.5*dt;
cx = px[i];
cy = 0.5*(py[j] + py[j + 1]);
reg = WhichReg(cx, cy);
c0 = 1 / (1 / dt + 0.5*pKy(cx, cy));
c1 = mu0(cx, cy)*pKyHy(cx, cy);
c2 = 1 / dt - 0.5*pKy(cx, cy);
Ky[j][i][flag] = c0*(c1*Hy[j][i][!flag] + c2*Ky[j][i][!flag] + g6_fcn(cx, cy, ct));
}
}
}
for (i = 0; i < Nx - 1; i++)
{
for (j = 0; j < Ny - 1; j++)
{
if (j != 0)
{
// loop for Hx
// (5) in paper, point of eqn : (i + 1 / 2, j, n + 1)
ct = pt(it);
cx = 0.5*(px[i] + px[i + 1]);
cy = py[j];
reg = WhichReg(cx, cy);
c0 = 1 / (mu0(cx, cy) / dt - 0.5*mu0(cx, cy)*(sgmx(cx) - sgmy(cy)));
c1 = mu0(cx, cy) / dt + 0.5*mu0(cx, cy)*(sgmx(cx) - sgmy(cy));
Hx[j][i][flag] = c0*(-(E[j][i][flag] - E[j - 1][i][flag]) / dy[j - 1] - Kx[j][i][flag] + c1*Hx[j][i][!flag] + g1_fcn(cx, cy, ct));
}
if (i != 0)
{
// loop for Hy
// (6) in paper, point of eqn : (i, j + 1 / 2, n + 1)
ct = pt(it);
cx = px[i];
cy = 0.5*(py[j] + py[j + 1]);
reg = WhichReg(cx, cy);
c0 = 1 / (mu0(cx, cy) / dt + 0.5*mu0(cx, cy)*(sgmx(cx) - sgmy(cy)));
c1 = mu0(cx, cy) / dt - 0.5*mu0(cx, cy)*(sgmx(cx) - sgmy(cy));
Hy[j][i][flag] = c0*((E[j][i][flag] - E[j][i - 1][flag]) / dx[i - 1] - Ky[j][i][flag] + c1*Hy[j][i][!flag] + g2_fcn(cx, cy, ct));
}
}
}
for (i = nPML; i < Npx + nPML - 1; i++) // copy the solution E to Em
for (j = nPML; j < Npy + nPML - 1; j++)
Em[j - nPML][i - nPML] = E[j][i][flag];
if (it % lapse == 0)
{
WriteFile();
}
flag = !flag; // iterate
//Iterate();
/*test();
int aaaaaaaaaaaaaa = 1;*/
if (it % 10 == 0)
cout << "time " << it << endl;
}
}
void PML::Iterate(){
for (int i = 0; i < Nx; i++)
for (int j = 0; j < Ny; j++)
{
if (i != Nx - 1) {
Hx[j][i][0] = Hx[j][i][1];
Hx[j][i][1] = 0.0;
Kx[j][i][0] = Kx[j][i][1];
Kx[j][i][1] = 0.0;
if (j != Ny - 1){
E[j][i][0] = E[j][i][1];
E[j][i][1] = 0.0;
J[j][i][0] = J[j][i][1];
J[j][i][1] = 0.0;
}
}
if (j != Ny - 1)
{
Hy[j][i][0] = Hy[j][i][1];
Hy[j][i][1] = 0.0;
Ky[j][i][0] = Ky[j][i][1];
Ky[j][i][1] = 0.0;
}
}
}
void PML::InitValue() // write initial value, use for test
{
double cx, cy;
for (int i = 0; i < Nx; i++)
for (int j = 0; j < Ny; j++)
{
if (i != Nx - 1) {
cx = 0.5*(px[i] + px[i + 1]);
cy = py[j];
Hx[j][i][0] = Hx_fcn(cx, cy, at + 0.5*dt);
Kx[j][i][0] = Kx_fcn(cx,cy,at);
if (j != Ny - 1){
cx = 0.5*(px[i] + px[i + 1]);
cy = 0.5*(py[j] + py[j + 1]);
E[j][i][0] = E_fcn(cx,cy,at);
J[j][i][0] = J_fcn(cx, cy, at + 0.5*dt);
}
}
if (j != Ny - 1)
{
cx = px[i];
cy = 0.5*(py[j] + py[j + 1]);
Hy[j][i][0] = Hy_fcn(cx, cy, at + 0.5*dt);
Ky[j][i][0] = Ky_fcn(cx, cy, at);
}
}
}
void PML::BondValue(long long nt) // write boundary value, use for test
{
// always for 2nd layer variables
double cx, cy;
double ct = pt(nt);
for (int i = 0; i < Nx; i++)
for (int j = 0; j < Ny; j++)
{
if (i != Nx - 1){
cx = 0.5*(px[i] + px[i + 1]);
Hx[0][i][1] = Hx_fcn(cx, py[0], ct + 0.5*dt);
Hx[Ny - 1][i][1] = Hx_fcn(cx, py[Ny - 1], ct + 0.5*dt);
Kx[0][i][1] = Kx_fcn(cx, py[0], ct);
Kx[Ny - 1][i][1] = Kx_fcn(cx, py[Ny - 1], ct);
}
if (j != Ny - 1){
cy = 0.5*(py[j] + py[j + 1]);
Hy[j][0][1] = Hy_fcn(px[0], cy, ct + 0.5*dt);
Hy[j][Nx - 1][1] = Hy_fcn(px[Nx - 1], cy, ct + 0.5*dt);
Ky[j][0][1] = Ky_fcn(px[0], cy, ct);
Ky[j][Nx - 1][1] = Ky_fcn(px[Nx - 1], cy, ct);
}
}
}
void PML::test(){
// test soluition
double t = -1.0;
double er = 0.0;
double cx, cy, ct;
ct = bt;
// test Hx
for (int i = 0; i < Nx - 1; i++)
{
for (int j = 0; j < Ny; j++)
{
cx = 0.5*(px[i] + px[i + 1]);
cy = py[j];
er = fabs(Hx[j][i][0] - Hx_fcn(cx, cy, ct + 0.5*dt));
if (t < er)
t = er;
cout << Hx[j][i][0] << " ";
}
cout << endl;
}
//// test Kx
/*for (int i = 0; i < Nx - 1; i++)
{
for (int j = 0; j < Ny; j++)
{
cx = 0.5*(px[i] + px[i + 1]);
cy = py[j];
er = fabs(Kx[j][i][0] - Kx_fcn(cx, cy, ct));
if (t < er)
t = er;
cout << Kx[j][i][0] << " ";
}
cout << endl;
}*/
//// test E
//for (int i = 0; i < Nx - 1; i++)
//{
// for (int j = 0; j < Ny - 1; j++)
// {
// cx = 0.5*(px[i] + px[i + 1]);
// cy = 0.5*(py[j] + py[j + 1]);
// er = fabs(E[j][i][0] - E_fcn(cx, cy, ct));
// if (t < er)
// t = er;
// cout << E[j][i][0] << " ";
// }
// cout << endl;
//}
//// test J
//for (int i = 0; i < Nx - 1; i++)
//{
// for (int j = 0; j < Ny - 1; j++)
// {
// cx = 0.5*(px[i] + px[i + 1]);
// cy = 0.5*(py[j] + py[j + 1]);
// er = fabs(J[j][i][0] - J_fcn(cx, cy, ct + 0.5*dt));
// if (t < er)
// t = er;
// cout << J[j][i][0] << " ";
// }
// cout << endl;
//}
cout << "error" << " " << t << endl;
}