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EMSolver.cpp
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EMSolver.cpp
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#include "veritas.hpp"
#include "EMSolver.hpp"
#include "Settings.hpp"
#include "Mesh.hpp"
EMFieldSolver::EMFieldSolver(Settings &settings, const std::vector<std::shared_ptr<Mesh> > &meshes) : settings(settings), x_size(settings.x_size_finest), meshes(meshes), chargeStream(NULL), ELongStream(NULL), ETransStream(NULL), potentialStream(NULL), BStream(NULL), AsqStream(NULL), timeStream(NULL), Ex0(0.0) {
n_prepad = std::max(std::floor(settings.preLength / settings.GetDx(0)), 2.0);
n_postpad = std::max(std::floor(settings.postLength / settings.GetDx(0)), 2.0);
charge.resize(x_size, 0);
J.resize(x_size, 0);
neutralizationCharge.resize(x_size, 0.0);
charges.resize(settings.q.size(),charge);
for (unsigned int i=0; i<settings.p_size.size();i++) {
energies.push_back({0.0});
energies[i].resize(settings.p_size_finest[i],0.0);
}
By.resize((x_size + n_prepad + n_postpad) * 8, 0.0);
Bz.resize((x_size + n_prepad + n_postpad) * 8, 0.0);
Ey.resize((x_size + n_prepad + n_postpad) * 8, 0.0);
Ez.resize((x_size + n_prepad + n_postpad) * 8, 0.0);
Ay.resize((x_size + n_prepad + n_postpad) * 8, 0.0);
Az.resize((x_size + n_prepad + n_postpad) * 8, 0.0);
a_squared.resize(x_size + 1, 0.0);
double w1(-16.0 / 30.0 / 0.4), w2(1.0 / 30.0 / 0.4), w3(1 / 0.4);
PHI = new double[x_size];
pM = new double[x_size * x_size];
for (unsigned int i = 0; i < x_size; i++) {
PHI[i] = 0.0;
}
for (unsigned int i = 0; i < x_size * x_size; i++) {
pM[i] = 0.0;
}
for (unsigned int i = 2; i < x_size - 2; i++) {
pM[i * x_size + i] = w3;
pM[i * x_size + i + 1] = w1;
pM[i * x_size + i - 1] = w1;
pM[i * x_size + i + 2] = w2;
pM[i * x_size + i - 2] = w2;
}
pM[0] = 1.0;
pM[x_size + 1] = w3;
pM[x_size + 2] = w1;
pM[x_size + 0] = w1;
pM[x_size + 3] = w2;
pM[2 * x_size - 1] = w2;
pM[(x_size - 2) * x_size + x_size - 2] = w3;
pM[(x_size - 2) * x_size + x_size - 1] = w1;
pM[(x_size - 2) * x_size + x_size - 3] = w1;
pM[(x_size - 2) * x_size + 0] = w2;
pM[(x_size - 2) * x_size + x_size - 4] = w2;
pM[(x_size - 1) * x_size + (x_size - 1)] = w3;
pM[(x_size - 1) * x_size + 0] = w1;
pM[(x_size - 1) * x_size + (x_size - 2)] = w1;
pM[(x_size - 1) * x_size + 1] = w2;
pM[(x_size - 1) * x_size + (x_size - 3)] = w2;
#if defined(USINGMKL)
lapack_int INFO = 3;
lapack_int LDA = x_size;
lapack_int N = x_size;
IPIV = new lapack_int[x_size];
INFO = LAPACKE_dgetrf(LAPACK_COL_MAJOR, N, N, pM, LDA, IPIV);
if (INFO != 0) std::cerr << "WARNING: Illegal parameter or singular result from dgetrf" << std::endl;
#else
int INFO = 3;
int LDA = x_size;
int N = x_size;
IPIV = new int[x_size];
dgetrf_(&N, &N, pM, &LDA, IPIV, &INFO);
#endif
fieldCoef = (1.0 / (12 * settings.GetDx(0)));
}
EMFieldSolver::~EMFieldSolver() {
delete[] PHI;
delete[] pM;
delete[] IPIV;
delete chargeStream;
delete ELongStream;
delete ETransStream;
delete potentialStream;
delete BStream;
delete AsqStream;
delete timeStream;
}
void EMFieldSolver::AssembleRhoAndJ() {
std::fill(charge.begin(), charge.end(), 0.0);
std::fill(J.begin(), J.end(), 0.0);
for (unsigned int i=0; i<meshes.size();i++) {
std::fill(charges[i].begin(), charges[i].end(),0.0);
}
for (unsigned int i=0; i<meshes.size();i++) {
meshes[i]->InterpolateRhoAndJToFinestMesh(charges[i], J);
}
for (unsigned int i=0; i<meshes.size();i++) {
#pragma ivdep
for (unsigned int j=0; j<x_size; j++) {
charge[j]+=charges[i][j];
}
}
}
void EMFieldSolver::AssembleEnergy() {
for (unsigned int i=0; i<meshes.size();i++) {
std::fill(energies[i].begin(), energies[i].end(),0.0);
}
for (unsigned int i=0; i<meshes.size();i++) {
meshes[i]->InterpolateEnergyToFinestMesh(energies[i]);
}
}
double EMFieldSolver::GetASquared(int i) {
return a_squared[std::min(std::max(i, 0), (int)x_size)];
}
double EMFieldSolver::GetEfield(int i) {
int ip1 = i + 1;
int im1 = i - 1;
int ip2 = i + 2;
int im2 = i - 2;
ip1 = (ip1 > -1) ? ip1 : (ip1 + x_size);
im1 = (im1 > -1) ? im1 : (im1 + x_size);
ip2 = (ip2 > -1) ? ip2 : (ip2 + x_size);
im2 = (im2 > -1) ? im2 : (im2 + x_size);
ip1 = (ip1 < (int)x_size) ? ip1 : (ip1 - x_size);
im1 = (im1 < (int)x_size) ? im1 : (im1 - x_size);
ip2 = (ip2 < (int)x_size) ? ip2 : (ip2 - x_size);
im2 = (im2 < (int)x_size) ? im2 : (im2 - x_size);
return -fieldCoef * (8 * (PHI[ip1] - PHI[im1]) - PHI[ip2] + PHI[im2]) + Ex0;
}
void EMFieldSolver::UpdatePotential() {
double te = eps0_inv;
for (unsigned int i = 0; i < x_size; i++) {
PHI[i] = te * (charge[i] + neutralizationCharge[i]);
}
double w = std::pow(settings.GetDx(0), 2.0);
for (unsigned int i = 0; i < x_size; i++) {
PHI[i] *= w;
}
char TRANS = 'N';
#if defined(USINGMKL)
lapack_int INFO = 3;
lapack_int LDA = x_size;
lapack_int LDB = x_size;
lapack_int N = x_size;
lapack_int NRHS = 1;
INFO = LAPACKE_dgetrs(LAPACK_COL_MAJOR, TRANS, N, NRHS, pM, LDA, IPIV, PHI, LDB);
if (INFO != 0) std::cerr << "WARNING: Illegal parameter or singular result from dgetrs" << std::endl;
#else
int INFO = 3;
int LDA = x_size;
int LDB = x_size;
int N = x_size;
int NRHS = 1;
dgetrs_(&TRANS, &N, &NRHS, pM, &LDA, IPIV, PHI, &LDB, &INFO);
#endif
Ex0 += -(GetEfield(-1) + GetEfield(0)) * 0.5;
}
void EMFieldSolver::RGKStep(int step, double timestep) {
RGKCalculateRHS(step);
RGKUpdateIntermediateSolution(step, timestep);
InterpolateToFaces();
}
void EMFieldSolver::RGKUpdateIntermediateSolution(int step, double timestep) {
unsigned int iloop = x_size + n_prepad + n_postpad;
if (step == -1) {
} else if (step == 0) {
double a0 = 0.5 * timestep;
#pragma ivdep
for (unsigned int i = 0; i < iloop; i++) {
int idx0 = Index(i, 0);
int idx1 = Index(i, 1);
int idx2 = Index(i, 2);
By[idx1] = By[idx0] + a0 * By[idx2];
Bz[idx1] = Bz[idx0] + a0 * Bz[idx2];
Ey[idx1] = Ey[idx0] + a0 * Ey[idx2];
Ez[idx1] = Ez[idx0] + a0 * Ez[idx2];
Ay[idx1] = Ay[idx0] + a0 * Ay[idx2];
Az[idx1] = Az[idx0] + a0 * Az[idx2];
}
} else if (step == 1) {
double a0 = 0.221776 * timestep;
double a1 = 0.110224 * timestep;
#pragma ivdep
for (unsigned int i = 0; i < iloop; i++) {
int idx0 = Index(i, 0);
int idx1 = Index(i, 1);
int idx2 = Index(i, 2);
int idx3 = Index(i, 3);
By[idx1] = By[idx0] + a0 * By[idx2] + a1 * By[idx3];
Bz[idx1] = Bz[idx0] + a0 * Bz[idx2] + a1 * Bz[idx3];
Ey[idx1] = Ey[idx0] + a0 * Ey[idx2] + a1 * Ey[idx3];
Ez[idx1] = Ez[idx0] + a0 * Ez[idx2] + a1 * Ez[idx3];
Ay[idx1] = Ay[idx0] + a0 * Ay[idx2] + a1 * Ay[idx3];
Az[idx1] = Az[idx0] + a0 * Az[idx2] + a1 * Az[idx3];
}
} else if (step == 2) {
double a0 = -0.04884659515311857 * timestep;
double a1 = -0.17772065232640102 * timestep;
double a2 = 0.8465672474795197 * timestep;
#pragma ivdep
for (unsigned int i = 0; i < iloop; i++) {
int idx0 = Index(i, 0);
int idx1 = Index(i, 1);
int idx2 = Index(i, 2);
int idx3 = Index(i, 3);
int idx4 = Index(i, 4);
By[idx1] = By[idx0] + a0 * By[idx2] + a1 * By[idx3] + a2 * By[idx4];
Bz[idx1] = Bz[idx0] + a0 * Bz[idx2] + a1 * Bz[idx3] + a2 * Bz[idx4];
Ey[idx1] = Ey[idx0] + a0 * Ey[idx2] + a1 * Ey[idx3] + a2 * Ey[idx4];
Ez[idx1] = Ez[idx0] + a0 * Ez[idx2] + a1 * Ez[idx3] + a2 * Ez[idx4];
Ay[idx1] = Ay[idx0] + a0 * Ay[idx2] + a1 * Ay[idx3] + a2 * Ay[idx4];
Az[idx1] = Az[idx0] + a0 * Az[idx2] + a1 * Az[idx3] + a2 * Az[idx4];
}
} else if (step == 3) {
double a0 = -0.15541685842491548 * timestep;
double a1 = -0.3567050098221991 * timestep;
double a2 = 1.0587258798684427 * timestep;
double a3 = 0.30339598837867193 * timestep;
#pragma ivdep
for (unsigned int i = 0; i < iloop; i++) {
int idx0 = Index(i, 0);
int idx1 = Index(i, 1);
int idx2 = Index(i, 2);
int idx3 = Index(i, 3);
int idx4 = Index(i, 4);
int idx5 = Index(i, 5);
By[idx1] = By[idx0] + a0 * By[idx2] + a1 * By[idx3] + a2 * By[idx4] + a3 * By[idx5];
Bz[idx1] = Bz[idx0] + a0 * Bz[idx2] + a1 * Bz[idx3] + a2 * Bz[idx4] + a3 * Bz[idx5];
Ey[idx1] = Ey[idx0] + a0 * Ey[idx2] + a1 * Ey[idx3] + a2 * Ey[idx4] + a3 * Ey[idx5];
Ez[idx1] = Ez[idx0] + a0 * Ez[idx2] + a1 * Ez[idx3] + a2 * Ez[idx4] + a3 * Ez[idx5];
Ay[idx1] = Ay[idx0] + a0 * Ay[idx2] + a1 * Ay[idx3] + a2 * Ay[idx4] + a3 * Ay[idx5];
Az[idx1] = Az[idx0] + a0 * Az[idx2] + a1 * Az[idx3] + a2 * Az[idx4] + a3 * Az[idx5];
}
} else if (step == 4) {
double a0 = 0.2014243506726763 * timestep;
double a1 = 0.008742057842904185 * timestep;
double a2 = 0.15993995707168115 * timestep;
double a3 = 0.4038290605220775 * timestep;
double a4 = 0.22606457389066084 * timestep;
#pragma ivdep
for (unsigned int i = 0; i < iloop; i++) {
int idx0 = Index(i, 0);
int idx1 = Index(i, 1);
int idx2 = Index(i, 2);
int idx3 = Index(i, 3);
int idx4 = Index(i, 4);
int idx5 = Index(i, 5);
int idx6 = Index(i, 6);
By[idx1] = By[idx0] + a0 * By[idx2] + a1 * By[idx3] + a2 * By[idx4] + a3 * By[idx5] + a4 * By[idx6];
Bz[idx1] = Bz[idx0] + a0 * Bz[idx2] + a1 * Bz[idx3] + a2 * Bz[idx4] + a3 * Bz[idx5] + a4 * Bz[idx6];
Ey[idx1] = Ey[idx0] + a0 * Ey[idx2] + a1 * Ey[idx3] + a2 * Ey[idx4] + a3 * Ey[idx5] + a4 * Ey[idx6];
Ez[idx1] = Ez[idx0] + a0 * Ez[idx2] + a1 * Ez[idx3] + a2 * Ez[idx4] + a3 * Ez[idx5] + a4 * Ez[idx6];
Ay[idx1] = Ay[idx0] + a0 * Ay[idx2] + a1 * Ay[idx3] + a2 * Ay[idx4] + a3 * Ay[idx5] + a4 * Ay[idx6];
Az[idx1] = Az[idx0] + a0 * Az[idx2] + a1 * Az[idx3] + a2 * Az[idx4] + a3 * Az[idx5] + a4 * Az[idx6];
}
} else if (step==5) {
double a0 = 0.2014243506726763 * timestep;
double a1 = 0.008742057842904185 * timestep;
double a2 = 0.15993995707168115 * timestep;
double a3 = 0.4038290605220775 * timestep;
double a4 = 0.22606457389066084 * timestep;
double a5 = 0;
double b0 = 0.15791629516167136 * timestep - a0;
double b1 = 0.0 * timestep - a1;
double b2 = 0.18675894052400077 * timestep - a2;
double b3 = 0.6805652953093346 * timestep - a3;
double b4 = -0.27524053099500667 * timestep - a4;
double b5 = 0.25 * timestep - a5;
#pragma ivdep
for (unsigned int i = 0; i < iloop; i++) {
int idx0 = Index(i, 0);
int idx1 = Index(i, 1);
int idx2 = Index(i, 2);
int idx3 = Index(i, 3);
int idx4 = Index(i, 4);
int idx5 = Index(i, 5);
int idx6 = Index(i, 6);
int idx7 = Index(i, 7);
By[idx0] = By[idx1] + b0 * By[idx2] + b1 * By[idx3] + b2 * By[idx4] + b3 * By[idx5] + b4 * By[idx6] + b5 * By[idx7];
Bz[idx0] = Bz[idx1] + b0 * Bz[idx2] + b1 * Bz[idx3] + b2 * Bz[idx4] + b3 * Bz[idx5] + b4 * Bz[idx6] + b5 * Bz[idx7];
Ey[idx0] = Ey[idx1] + b0 * Ey[idx2] + b1 * Ey[idx3] + b2 * Ey[idx4] + b3 * Ey[idx5] + b4 * Ey[idx6] + b5 * Ey[idx7];
Ez[idx0] = Ez[idx1] + b0 * Ez[idx2] + b1 * Ez[idx3] + b2 * Ez[idx4] + b3 * Ez[idx5] + b4 * Ez[idx6] + b5 * Ez[idx7];
Ay[idx0] = Ay[idx1] + b0 * Ay[idx2] + b1 * Ay[idx3] + b2 * Ay[idx4] + b3 * Ay[idx5] + b4 * Ay[idx6] + b5 * Ay[idx7];
Az[idx0] = Az[idx1] + b0 * Az[idx2] + b1 * Az[idx3] + b2 * Az[idx4] + b3 * Az[idx5] + b4 * Az[idx6] + b5 * Az[idx7];
By[idx1] = By[idx0];
Bz[idx1] = Bz[idx0];
Ey[idx1] = Ey[idx0];
Ez[idx1] = Ez[idx0];
Ay[idx1] = Ay[idx0];
Az[idx1] = Az[idx0];
}
}
}
void EMFieldSolver::DumpCharge() {
if (chargeStream == NULL) {
std::string fileName = "output/charge.txt";
chargeStream = new std::ofstream(fileName);
(*chargeStream) << std::scientific << std::setprecision(settings.output.precision);
DumpCharge();
} else {
for (unsigned int k=0; k<settings.q.size(); k++) {
for (unsigned int i = 0; i < charge.size(); i++) {
(*chargeStream) << charges[k][i] << " ";
}
(*chargeStream) << std::endl;
}
}
}
void EMFieldSolver::DumpEnergy() {
if (energyStreams.size() == 0) {
for (unsigned int i=0; i<settings.q.size(); i++) {
std::stringstream fileName;
fileName << "output/dNdP_" << i << ".txt";
energyStreams.push_back(std::make_unique<std::ofstream>(fileName.str()));
(*energyStreams[i]) << std::scientific << std::setprecision(settings.output.precision);
}
DumpEnergy();
} else {
for (unsigned int k=0; k<settings.q.size(); k++) {
for (unsigned int i = 0; i < energies[k].size(); i++) {
(*energyStreams[k]) << energies[k][i] << " ";
}
(*energyStreams[k]) << std::endl;
}
}
}
void EMFieldSolver::DumpEFieldLongitudinal() {
if (ELongStream == NULL) {
std::string fileName = "output/EFieldLong.txt";
ELongStream = new std::ofstream(fileName);
(*ELongStream) << std::scientific << std::setprecision(settings.output.precision);
DumpEFieldLongitudinal();
} else {
for (unsigned int i = 0; i < charge.size(); i++) {
(*ELongStream) << GetEfield(i) << " ";
}
(*ELongStream) << std::endl;
}
}
void EMFieldSolver::DumpEFieldTransverse() {
if (ETransStream == NULL) {
std::string fileName = "output/EFieldTrans.txt";
ETransStream = new std::ofstream(fileName);
(*ETransStream) << std::scientific << std::setprecision(settings.output.precision);
DumpEFieldTransverse();
} else {
for (unsigned int i = 0; i < n_prepad + x_size + n_postpad; i++) {
(*ETransStream) << Ey[i] << " ";
}
(*ETransStream) << std::endl;
for (unsigned int i = 0; i < n_prepad + x_size + n_postpad; i++) {
(*ETransStream) << Ez[i] << " ";
}
(*ETransStream) << std::endl;
}
}
void EMFieldSolver::DumpPotential() {
if (potentialStream == NULL) {
std::string fileName = "output/potential.txt";
potentialStream = new std::ofstream(fileName);
(*potentialStream) << std::scientific << std::setprecision(settings.output.precision);
DumpPotential();
} else {
for (unsigned int i = 0; i < x_size; i++) {
(*potentialStream) << PHI[i] << " ";
}
(*potentialStream) << std::endl;
}
}
void EMFieldSolver::DumpBFieldTransverse() {
if (BStream == NULL) {
std::string fileName = "output/BFieldTrans.txt";
BStream = new std::ofstream(fileName);
(*BStream) << std::scientific << std::setprecision(settings.output.precision);
DumpBFieldTransverse();
} else {
for (unsigned int i = 0; i < n_prepad + x_size + n_postpad; i++) {
(*BStream) << By[i] << " ";
}
(*BStream) << std::endl;
for (unsigned int i = 0; i < n_prepad + x_size + n_postpad; i++) {
(*BStream) << Bz[i] << " ";
}
(*BStream) << std::endl;
}
}
void EMFieldSolver::DumpAsqField() {
if (AsqStream == NULL) {
std::string fileName = "output/ASquared.txt";
AsqStream = new std::ofstream(fileName);
(*AsqStream) << std::scientific << std::setprecision(settings.output.precision);
DumpAsqField();
} else {
for (unsigned int i = 0; i < x_size; i++) {
(*AsqStream) << GetASquared(i) << " ";
}
(*AsqStream) << std::endl;
}
}
void EMFieldSolver::DumpTime(double time) {
if (timeStream == NULL) {
std::string fileName = "output/time.txt";
timeStream = new std::ofstream(fileName);
(*timeStream) << std::scientific << std::setprecision(settings.output.precision);
DumpTime(time);
} else {
(*timeStream) << time << std::endl; //Have to flush this one..
}
}
void EMFieldSolver::RGKCalculateRHS(int step) {
unsigned int iloop = x_size + n_prepad + n_postpad;
#pragma ivdep
for (unsigned int i = 0; i < iloop; i++) {
int idxs2 = Index(i, step + 2);
By[idxs2] = 0;
Bz[idxs2] = 0;
Ey[idxs2] = 0;
Ez[idxs2] = 0;
Ay[idxs2] = 0;
Az[idxs2] = 0;
}
double dx_inv = 1 / settings.GetDx(0);
{
int i = 0;
int idxs2 = Index(i, step + 2);
int idx1 = Index(i, 1);
int idxp1 = Index(i + 1, 1);
By[idxs2] = dx_inv * (Ez[idxp1] - Ez[idx1]);
Bz[idxs2] = -dx_inv * (Ey[idxp1] - Ey[idx1]);
Ey[idxs2] = -dx_inv * (Bz[idx1] - settings.GetBZ(0, settings.time)) * eps0_inv * mu_inv;
Ez[idxs2] = dx_inv * (By[idx1] - settings.GetBY(0, settings.time)) * eps0_inv * mu_inv;
Ay[idxs2] = -Ey[idx1];
Az[idxs2] = -Ez[idx1];
}
int imax = n_prepad;
#pragma ivdep
for (int i = 1; i < imax; i++) {
int idxs2 = Index(i, step + 2);
int idx1 = Index(i, 1);
int idxp1 = Index(i + 1, 1);
int idxn1 = Index(i - 1, 1);
By[idxs2] = dx_inv * (Ez[idxp1] - Ez[idx1]);
Bz[idxs2] = -dx_inv * (Ey[idxp1] - Ey[idx1]);
Ey[idxs2] = -dx_inv * (Bz[idx1] - Bz[idxn1]) * eps0_inv * mu_inv;
Ez[idxs2] = dx_inv * (By[idx1] - By[idxn1]) * eps0_inv * mu_inv;
Ay[idxs2] = -Ey[idx1];
Az[idxs2] = -Ez[idx1];
}
double c1 = -1.0 / 24;
double c2 = 9.0 / 8.0;
imax = n_prepad + (int)x_size;
#pragma ivdep
for (int i = n_prepad; i < imax; i++) {
int idxs2 = Index(i, step + 2);
int idx1 = Index(i, 1);
int idxp1 = Index(i + 1, 1);
int idxn1 = Index(i - 1, 1);
int idxp2 = Index(i + 2, 1);
int idxn2 = Index(i - 2, 1);
By[idxs2] = dx_inv * (c1 * (Ez[idxp2] - Ez[idxn1]) + c2 * (Ez[idxp1] - Ez[idx1]));
Bz[idxs2] = -dx_inv * (c1 * (Ey[idxp2] - Ey[idxn1]) + c2 * (Ey[idxp1] - Ey[idx1]));
Ey[idxs2] = -dx_inv * (c1 * (Bz[idxp1] - Bz[idxn2]) + c2 * (Bz[idx1] - Bz[idxn1])) * eps0_inv * mu_inv - eps0_inv * J[i - n_prepad] * Ay[idx1];
Ez[idxs2] = dx_inv * (c1 * (By[idxp1] - By[idxn2]) + c2 * (By[idx1] - By[idxn1])) * eps0_inv * mu_inv - eps0_inv * J[i - n_prepad] * Az[idx1];
Ay[idxs2] = -Ey[idx1];
Az[idxs2] = -Ez[idx1];
}
imax = n_prepad + (int)x_size + n_postpad - 2;
#pragma ivdep
for (int i = n_prepad + (int)x_size; i < imax; i++) {
int idxs2 = Index(i, step + 2);
int idx1 = Index(i, 1);
int idxp1 = Index(i + 1, 1);
int idxn1 = Index(i - 1, 1);
By[idxs2] = dx_inv * (Ez[idxp1] - Ez[idx1]);
Bz[idxs2] = -dx_inv * (Ey[idxp1] - Ey[idx1]);
Ey[idxs2] = -dx_inv * (Bz[idx1] - Bz[idxn1]) * eps0_inv * mu_inv;
Ez[idxs2] = dx_inv * (By[idx1] - By[idxn1]) * eps0_inv * mu_inv;
Ay[idxs2] = -Ey[idx1];
Az[idxs2] = -Ez[idx1];
}
}
void EMFieldSolver::InterpolateToFaces() {
#pragma simd
for (unsigned int i = 0; i < x_size; i++) {
double a_y = 0.0;
{
double f1 = Ay[Index(n_prepad + i - 2, 1)];
double f2 = Ay[Index(n_prepad + i - 1, 1)];
double f3 = Ay[Index(n_prepad + i, 1)];
double f4 = Ay[Index(n_prepad + i + 1, 1)];
double fL = (1.0 / 6) * (-f1 + 5 * f2 + 2 * f3);
double fR = (1.0 / 6) * (2 * f2 + 5 * f3 - f4);
double AL = f1 - 2 * f2 + f3;
double BL = f3 - f1;
double AR = f2 - 2 * f3 + f4;
double BR = f4 - f2;
double bL = 4.0 / 3 * (AL * AL) + 0.5 * AL * BL + 0.25 * (BL * BL);
double bR = 4.0 / 3 * (AR * AR) - 0.5 * AR * BR + 0.25 * (BR * BR);
double mm(1.0e-10);
double oL = 0.5 / ((mm + bL) * (mm + bL));
double oR = 0.5 / ((mm + bR) * (mm + bR));
double wL = oL / (oL + oR);
double wR = oR / (oL + oR);
a_y = wL * fL + wR * fR;
}
double a_z = 0.0;
{
double f1 = Az[Index(n_prepad + i - 2, 1)];
double f2 = Az[Index(n_prepad + i - 1, 1)];
double f3 = Az[Index(n_prepad + i, 1)];
double f4 = Az[Index(n_prepad + i + 1, 1)];
double fL = (1.0 / 6) * (-f1 + 5 * f2 + 2 * f3);
double fR = (1.0 / 6) * (2 * f2 + 5 * f3 - f4);
double AL = f1 - 2 * f2 + f3;
double BL = f3 - f1;
double AR = f2 - 2 * f3 + f4;
double BR = f4 - f2;
double bL = 4.0 / 3 * (AL * AL) + 0.5 * AL * BL + 0.25 * (BL * BL);
double bR = 4.0 / 3 * (AR * AR) - 0.5 * AR * BR + 0.25 * (BR * BR);
double mm(1.0e-10);
double oL = 0.5 / ((mm + bL) * (mm + bL));
double oR = 0.5 / ((mm + bR) * (mm + bR));
double wL = oL / (oL + oR);
double wR = oR / (oL + oR);
a_z = wL * fL + wR * fR;
}
a_squared[i] = (a_y * a_y) + (a_z * a_z);
}
}
void EMFieldSolver::EnforceChargeNeutralization() {
AssembleRhoAndJ();
std::fill(J.begin(), J.end(), 0.0);
for (unsigned int i = 0; i < charge.size(); i++) {
neutralizationCharge[i] = -charge[i];
}
}
double EMFieldSolver::EstimateCFLBound() {
int n = meshes.size();
std::vector<double> &m = settings.m;
std::vector<double> &q = settings.q;
std::vector<double> dps;
dps.assign(n, 0.0);
double dpsMax(0.0);
for (int i = 0; i < n; i++) {
dps[i] = 1 / settings.GetDp(0, i);
dpsMax = std::max(dpsMax, std::fabs(q[i]) * dps[i]);
}
double pc(0.0);
for (unsigned int i = 0; i < x_size; i++) {
double Azv = Az[i];
double Ayv = Ay[i];
double As = Ayv * Ayv + Azv * Azv;
double temp(0.0);
#pragma novector
for (int j = 0; j < n; j++) {
temp = std::max(temp, std::fabs(q[j]) / m[j] / std::sqrt(1 + As / ((m[j] * cs) * (m[j] * cs))) * dps[j]);
}
pc = std::max(pc, temp * std::fabs(Ayv * Bz[i] - Azv * By[i]) + dpsMax * std::fabs(GetEfield(i)));
}
return 1.0 / std::max((cs / settings.GetDx(0) + pc), 1e-40);
}
double EMFieldSolver::GetMagneticForce(int i) {
i+=n_prepad;
i=i>-1?i:0;
i=i<(x_size+n_prepad+n_postpad)?i:(x_size+n_prepad+n_postpad-1);
return Az[Index(i,1)]*By[Index(i,1)]-Ay[Index(i,1)]*Bz[Index(i,1)];
}