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/* Copyright 2020 Remi Lehe
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#include "Utils/WarpXAlgorithmSelection.H"
#include "FiniteDifferenceSolver.H"
#ifdef WARPX_DIM_RZ
# include "FiniteDifferenceAlgorithms/CylindricalYeeAlgorithm.H"
#else
# include "FiniteDifferenceAlgorithms/CartesianYeeAlgorithm.H"
# include "FiniteDifferenceAlgorithms/CartesianCKCAlgorithm.H"
# include "FiniteDifferenceAlgorithms/CartesianNodalAlgorithm.H"
#endif
#include "Utils/WarpXConst.H"
#include <AMReX_Gpu.H>
using namespace amrex;
/**
* \brief Update the E field, over one timestep
*/
void FiniteDifferenceSolver::EvolveE (
std::array< std::unique_ptr<amrex::MultiFab>, 3 >& Efield,
std::array< std::unique_ptr<amrex::MultiFab>, 3 > const& Bfield,
std::array< std::unique_ptr<amrex::MultiFab>, 3 > const& Jfield,
std::unique_ptr<amrex::MultiFab> const& Ffield,
amrex::Real const dt ) {
// Select algorithm (The choice of algorithm is a runtime option,
// but we compile code for each algorithm, using templates)
#ifdef WARPX_DIM_RZ
if (m_fdtd_algo == MaxwellSolverAlgo::Yee){
EvolveECylindrical <CylindricalYeeAlgorithm> ( Efield, Bfield, Jfield, Ffield, dt );
#else
if (m_do_nodal) {
EvolveECartesian <CartesianNodalAlgorithm> ( Efield, Bfield, Jfield, Ffield, dt );
} else if (m_fdtd_algo == MaxwellSolverAlgo::Yee) {
EvolveECartesian <CartesianYeeAlgorithm> ( Efield, Bfield, Jfield, Ffield, dt );
} else if (m_fdtd_algo == MaxwellSolverAlgo::CKC) {
EvolveECartesian <CartesianCKCAlgorithm> ( Efield, Bfield, Jfield, Ffield, dt );
#endif
} else {
amrex::Abort("EvolveE: Unknown algorithm");
}
}
#ifndef WARPX_DIM_RZ
template<typename T_Algo>
void FiniteDifferenceSolver::EvolveECartesian (
std::array< std::unique_ptr<amrex::MultiFab>, 3 >& Efield,
std::array< std::unique_ptr<amrex::MultiFab>, 3 > const& Bfield,
std::array< std::unique_ptr<amrex::MultiFab>, 3 > const& Jfield,
std::unique_ptr<amrex::MultiFab> const& Ffield,
amrex::Real const dt ) {
Real constexpr c2 = PhysConst::c * PhysConst::c;
// Loop through the grids, and over the tiles within each grid
#ifdef AMREX_USE_OMP
#pragma omp parallel if (amrex::Gpu::notInLaunchRegion())
#endif
for ( MFIter mfi(*Efield[0], TilingIfNotGPU()); mfi.isValid(); ++mfi ) {
// Extract field data for this grid/tile
Array4<Real> const& Ex = Efield[0]->array(mfi);
Array4<Real> const& Ey = Efield[1]->array(mfi);
Array4<Real> const& Ez = Efield[2]->array(mfi);
Array4<Real> const& Bx = Bfield[0]->array(mfi);
Array4<Real> const& By = Bfield[1]->array(mfi);
Array4<Real> const& Bz = Bfield[2]->array(mfi);
Array4<Real> const& jx = Jfield[0]->array(mfi);
Array4<Real> const& jy = Jfield[1]->array(mfi);
Array4<Real> const& jz = Jfield[2]->array(mfi);
// Extract stencil coefficients
Real const * const AMREX_RESTRICT coefs_x = m_stencil_coefs_x.dataPtr();
int const n_coefs_x = m_stencil_coefs_x.size();
Real const * const AMREX_RESTRICT coefs_y = m_stencil_coefs_y.dataPtr();
int const n_coefs_y = m_stencil_coefs_y.size();
Real const * const AMREX_RESTRICT coefs_z = m_stencil_coefs_z.dataPtr();
int const n_coefs_z = m_stencil_coefs_z.size();
// Extract tileboxes for which to loop
Box const& tex = mfi.tilebox(Efield[0]->ixType().toIntVect());
Box const& tey = mfi.tilebox(Efield[1]->ixType().toIntVect());
Box const& tez = mfi.tilebox(Efield[2]->ixType().toIntVect());
// Loop over the cells and update the fields
amrex::ParallelFor(tex, tey, tez,
[=] AMREX_GPU_DEVICE (int i, int j, int k){
Ex(i, j, k) += c2 * dt * (
- T_Algo::DownwardDz(By, coefs_z, n_coefs_z, i, j, k)
+ T_Algo::DownwardDy(Bz, coefs_y, n_coefs_y, i, j, k)
- PhysConst::mu0 * jx(i, j, k) );
},
[=] AMREX_GPU_DEVICE (int i, int j, int k){
Ey(i, j, k) += c2 * dt * (
- T_Algo::DownwardDx(Bz, coefs_x, n_coefs_x, i, j, k)
+ T_Algo::DownwardDz(Bx, coefs_z, n_coefs_z, i, j, k)
- PhysConst::mu0 * jy(i, j, k) );
},
[=] AMREX_GPU_DEVICE (int i, int j, int k){
Ez(i, j, k) += c2 * dt * (
- T_Algo::DownwardDy(Bx, coefs_y, n_coefs_y, i, j, k)
+ T_Algo::DownwardDx(By, coefs_x, n_coefs_x, i, j, k)
- PhysConst::mu0 * jz(i, j, k) );
}
);
// If F is not a null pointer, further update E using the grad(F) term
// (hyperbolic correction for errors in charge conservation)
if (Ffield) {
// Extract field data for this grid/tile
Array4<Real> F = Ffield->array(mfi);
// Loop over the cells and update the fields
amrex::ParallelFor(tex, tey, tez,
[=] AMREX_GPU_DEVICE (int i, int j, int k){
Ex(i, j, k) += c2 * dt * T_Algo::UpwardDx(F, coefs_x, n_coefs_x, i, j, k);
},
[=] AMREX_GPU_DEVICE (int i, int j, int k){
Ey(i, j, k) += c2 * dt * T_Algo::UpwardDy(F, coefs_y, n_coefs_y, i, j, k);
},
[=] AMREX_GPU_DEVICE (int i, int j, int k){
Ez(i, j, k) += c2 * dt * T_Algo::UpwardDz(F, coefs_z, n_coefs_z, i, j, k);
}
);
}
}
}
#else // corresponds to ifndef WARPX_DIM_RZ
template<typename T_Algo>
void FiniteDifferenceSolver::EvolveECylindrical (
std::array< std::unique_ptr<amrex::MultiFab>, 3 >& Efield,
std::array< std::unique_ptr<amrex::MultiFab>, 3 > const& Bfield,
std::array< std::unique_ptr<amrex::MultiFab>, 3 > const& Jfield,
std::unique_ptr<amrex::MultiFab> const& Ffield,
amrex::Real const dt ) {
// Loop through the grids, and over the tiles within each grid
#ifdef AMREX_USE_OMP
#pragma omp parallel if (amrex::Gpu::notInLaunchRegion())
#endif
for ( MFIter mfi(*Efield[0], TilingIfNotGPU()); mfi.isValid(); ++mfi ) {
// Extract field data for this grid/tile
Array4<Real> const& Er = Efield[0]->array(mfi);
Array4<Real> const& Et = Efield[1]->array(mfi);
Array4<Real> const& Ez = Efield[2]->array(mfi);
Array4<Real> const& Br = Bfield[0]->array(mfi);
Array4<Real> const& Bt = Bfield[1]->array(mfi);
Array4<Real> const& Bz = Bfield[2]->array(mfi);
Array4<Real> const& jr = Jfield[0]->array(mfi);
Array4<Real> const& jt = Jfield[1]->array(mfi);
Array4<Real> const& jz = Jfield[2]->array(mfi);
// Extract stencil coefficients
Real const * const AMREX_RESTRICT coefs_r = m_stencil_coefs_r.dataPtr();
int const n_coefs_r = m_stencil_coefs_r.size();
Real const * const AMREX_RESTRICT coefs_z = m_stencil_coefs_z.dataPtr();
int const n_coefs_z = m_stencil_coefs_z.size();
// Extract cylindrical specific parameters
Real const dr = m_dr;
int const nmodes = m_nmodes;
Real const rmin = m_rmin;
// Extract tileboxes for which to loop
Box const& ter = mfi.tilebox(Efield[0]->ixType().toIntVect());
Box const& tet = mfi.tilebox(Efield[1]->ixType().toIntVect());
Box const& tez = mfi.tilebox(Efield[2]->ixType().toIntVect());
Real const c2 = PhysConst::c * PhysConst::c;
// Loop over the cells and update the fields
amrex::ParallelFor(ter, tet, tez,
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
Real const r = rmin + (i + 0.5)*dr; // r on cell-centered point (Er is cell-centered in r)
Er(i, j, 0, 0) += c2 * dt*(
- T_Algo::DownwardDz(Bt, coefs_z, n_coefs_z, i, j, 0, 0)
- PhysConst::mu0 * jr(i, j, 0, 0) ); // Mode m=0
for (int m=1; m<nmodes; m++) { // Higher-order modes
Er(i, j, 0, 2*m-1) += c2 * dt*(
- T_Algo::DownwardDz(Bt, coefs_z, n_coefs_z, i, j, 0, 2*m-1)
+ m * Bz(i, j, 0, 2*m )/r
- PhysConst::mu0 * jr(i, j, 0, 2*m-1) ); // Real part
Er(i, j, 0, 2*m ) += c2 * dt*(
- T_Algo::DownwardDz(Bt, coefs_z, n_coefs_z, i, j, 0, 2*m )
- m * Bz(i, j, 0, 2*m-1)/r
- PhysConst::mu0 * jr(i, j, 0, 2*m ) ); // Imaginary part
}
},
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
Real const r = rmin + i*dr; // r on a nodal grid (Et is nodal in r)
if (r != 0) { // Off-axis, regular Maxwell equations
Et(i, j, 0, 0) += c2 * dt*(
- T_Algo::DownwardDr(Bz, coefs_r, n_coefs_r, i, j, 0, 0)
+ T_Algo::DownwardDz(Br, coefs_z, n_coefs_z, i, j, 0, 0)
- PhysConst::mu0 * jt(i, j, 0, 0 ) ); // Mode m=0
for (int m=1 ; m<nmodes ; m++) { // Higher-order modes
Et(i, j, 0, 2*m-1) += c2 * dt*(
- T_Algo::DownwardDr(Bz, coefs_r, n_coefs_r, i, j, 0, 2*m-1)
+ T_Algo::DownwardDz(Br, coefs_z, n_coefs_z, i, j, 0, 2*m-1)
- PhysConst::mu0 * jt(i, j, 0, 2*m-1) ); // Real part
Et(i, j, 0, 2*m ) += c2 * dt*(
- T_Algo::DownwardDr(Bz, coefs_r, n_coefs_r, i, j, 0, 2*m )
+ T_Algo::DownwardDz(Br, coefs_z, n_coefs_z, i, j, 0, 2*m )
- PhysConst::mu0 * jt(i, j, 0, 2*m ) ); // Imaginary part
}
} else { // r==0: on-axis corrections
// Ensure that Et remains 0 on axis (except for m=1)
Et(i, j, 0, 0) = 0.; // Mode m=0
for (int m=1; m<nmodes; m++) { // Higher-order modes
if (m == 1){
// The bulk equation could in principle be used here since it does not diverge
// on axis. However, it typically gives poor results e.g. for the propagation
// of a laser pulse (the field is spuriously reduced on axis). For this reason
// a modified on-axis condition is used here: we use the fact that
// Etheta(r=0,m=1) should equal -iEr(r=0,m=1), for the fields Er and Et to be
// independent of theta at r=0. Now with linear interpolation:
// Er(r=0,m=1) = 0.5*[Er(r=dr/2,m=1) + Er(r=-dr/2,m=1)]
// And using the rule applying for the guards cells
// Er(r=-dr/2,m=1) = Er(r=dr/2,m=1). Thus: Et(i,j,m) = -i*Er(i,j,m)
Et(i,j,0,2*m-1) = Er(i,j,0,2*m );
Et(i,j,0,2*m ) = -Er(i,j,0,2*m-1);
} else {
Et(i, j, 0, 2*m-1) = 0.;
Et(i, j, 0, 2*m ) = 0.;
}
}
}
},
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
Real const r = rmin + i*dr; // r on a nodal grid (Ez is nodal in r)
if (r != 0) { // Off-axis, regular Maxwell equations
Ez(i, j, 0, 0) += c2 * dt*(
T_Algo::DownwardDrr_over_r(Bt, r, dr, coefs_r, n_coefs_r, i, j, 0, 0)
- PhysConst::mu0 * jz(i, j, 0, 0 ) ); // Mode m=0
for (int m=1 ; m<nmodes ; m++) { // Higher-order modes
Ez(i, j, 0, 2*m-1) += c2 * dt *(
- m * Br(i, j, 0, 2*m )/r
+ T_Algo::DownwardDrr_over_r(Bt, r, dr, coefs_r, n_coefs_r, i, j, 0, 2*m-1)
- PhysConst::mu0 * jz(i, j, 0, 2*m-1) ); // Real part
Ez(i, j, 0, 2*m ) += c2 * dt *(
m * Br(i, j, 0, 2*m-1)/r
+ T_Algo::DownwardDrr_over_r(Bt, r, dr, coefs_r, n_coefs_r, i, j, 0, 2*m )
- PhysConst::mu0 * jz(i, j, 0, 2*m ) ); // Imaginary part
}
} else { // r==0: on-axis corrections
// For m==0, Bt is linear in r, for small r
// Therefore, the formula below regularizes the singularity
Ez(i, j, 0, 0) += c2 * dt*(
4*Bt(i, j, 0, 0)/dr // regularization
- PhysConst::mu0 * jz(i, j, 0, 0 ) );
// Ensure that Ez remains 0 for higher-order modes
for (int m=1; m<nmodes; m++) {
Ez(i, j, 0, 2*m-1) = 0.;
Ez(i, j, 0, 2*m ) = 0.;
}
}
}
); // end of loop over cells
// If F is not a null pointer, further update E using the grad(F) term
// (hyperbolic correction for errors in charge conservation)
if (Ffield) {
// Extract field data for this grid/tile
Array4<Real> F = Ffield->array(mfi);
// Loop over the cells and update the fields
amrex::ParallelFor(ter, tet, tez,
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
Er(i, j, 0, 0) += c2 * dt * T_Algo::UpwardDr(F, coefs_r, n_coefs_r, i, j, 0, 0);
for (int m=1; m<nmodes; m++) { // Higher-order modes
Er(i, j, 0, 2*m-1) += c2 * dt * T_Algo::UpwardDr(F, coefs_r, n_coefs_r, i, j, 0, 2*m-1); // Real part
Er(i, j, 0, 2*m ) += c2 * dt * T_Algo::UpwardDr(F, coefs_r, n_coefs_r, i, j, 0, 2*m ); // Imaginary part
}
},
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
// Mode m=0: no update
Real const r = rmin + i*dr; // r on a nodal grid (Et is nodal in r)
if (r != 0){ // Off-axis, regular Maxwell equations
for (int m=1; m<nmodes; m++) { // Higher-order modes
Et(i, j, 0, 2*m-1) += c2 * dt * m * F(i, j, 0, 2*m )/r; // Real part
Et(i, j, 0, 2*m ) += c2 * dt * -m * F(i, j, 0, 2*m-1)/r; // Imaginary part
}
} else { // r==0: on-axis corrections
// For m==1, F is linear in r, for small r
// Therefore, the formula below regularizes the singularity
if (nmodes >= 2) { // needs to have at least m=0 and m=1
int const m=1;
Et(i, j, 0, 2*m-1) += c2 * dt * m * F(i+1, j, 0, 2*m )/dr; // Real part
Et(i, j, 0, 2*m ) += c2 * dt * -m * F(i+1, j, 0, 2*m-1)/dr; // Imaginary part
}
}
},
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
Ez(i, j, 0, 0) += c2 * dt * T_Algo::UpwardDz(F, coefs_z, n_coefs_z, i, j, 0, 0);
for (int m=1; m<nmodes; m++) { // Higher-order modes
Ez(i, j, 0, 2*m-1) += c2 * dt * T_Algo::UpwardDz(F, coefs_z, n_coefs_z, i, j, 0, 2*m-1); // Real part
Ez(i, j, 0, 2*m ) += c2 * dt * T_Algo::UpwardDz(F, coefs_z, n_coefs_z, i, j, 0, 2*m ); // Imaginary part
}
}
); // end of loop over cells
} // end of if condition for F
} // end of loop over grid/tiles
}
#endif // corresponds to ifndef WARPX_DIM_RZ
|
