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/* Copyright 2020 Remi Lehe
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#include "WarpX.H"
#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 <AMReX_Gpu.H>
using namespace amrex;
/**
* \brief Update the B field, over one timestep
*/
void FiniteDifferenceSolver::EvolveB (
std::array< std::unique_ptr<amrex::MultiFab>, 3 >& Bfield,
std::array< std::unique_ptr<amrex::MultiFab>, 3 > const& Efield,
int lev, 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){
EvolveBCylindrical <CylindricalYeeAlgorithm> ( Bfield, Efield, lev, dt );
#else
if (m_do_nodal) {
EvolveBCartesian <CartesianNodalAlgorithm> ( Bfield, Efield, lev, dt );
} else if (m_fdtd_algo == MaxwellSolverAlgo::Yee) {
EvolveBCartesian <CartesianYeeAlgorithm> ( Bfield, Efield, lev, dt );
} else if (m_fdtd_algo == MaxwellSolverAlgo::CKC) {
EvolveBCartesian <CartesianCKCAlgorithm> ( Bfield, Efield, lev, dt );
#endif
} else {
amrex::Abort("EvolveB: Unknown algorithm");
}
}
#ifndef WARPX_DIM_RZ
template<typename T_Algo>
void FiniteDifferenceSolver::EvolveBCartesian (
std::array< std::unique_ptr<amrex::MultiFab>, 3 >& Bfield,
std::array< std::unique_ptr<amrex::MultiFab>, 3 > const& Efield,
int lev, amrex::Real const dt ) {
amrex::LayoutData<amrex::Real>* cost = WarpX::getCosts(lev);
// 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(*Bfield[0], TilingIfNotGPU()); mfi.isValid(); ++mfi ) {
if (cost && WarpX::load_balance_costs_update_algo == LoadBalanceCostsUpdateAlgo::Timers)
{
amrex::Gpu::synchronize();
}
Real wt = amrex::second();
// Extract field data for this grid/tile
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& Ex = Efield[0]->array(mfi);
Array4<Real> const& Ey = Efield[1]->array(mfi);
Array4<Real> const& Ez = Efield[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& tbx = mfi.tilebox(Bfield[0]->ixType().toIntVect());
Box const& tby = mfi.tilebox(Bfield[1]->ixType().toIntVect());
Box const& tbz = mfi.tilebox(Bfield[2]->ixType().toIntVect());
// Loop over the cells and update the fields
amrex::ParallelFor(tbx, tby, tbz,
[=] AMREX_GPU_DEVICE (int i, int j, int k){
Bx(i, j, k) += dt * T_Algo::UpwardDz(Ey, coefs_z, n_coefs_z, i, j, k)
- dt * T_Algo::UpwardDy(Ez, coefs_y, n_coefs_y, i, j, k);
},
[=] AMREX_GPU_DEVICE (int i, int j, int k){
By(i, j, k) += dt * T_Algo::UpwardDx(Ez, coefs_x, n_coefs_x, i, j, k)
- dt * T_Algo::UpwardDz(Ex, coefs_z, n_coefs_z, i, j, k);
},
[=] AMREX_GPU_DEVICE (int i, int j, int k){
Bz(i, j, k) += dt * T_Algo::UpwardDy(Ex, coefs_y, n_coefs_y, i, j, k)
- dt * T_Algo::UpwardDx(Ey, coefs_x, n_coefs_x, i, j, k);
}
);
if (cost && WarpX::load_balance_costs_update_algo == LoadBalanceCostsUpdateAlgo::Timers)
{
amrex::Gpu::synchronize();
wt = amrex::second() - wt;
amrex::HostDevice::Atomic::Add( &(*cost)[mfi.index()], wt);
}
}
}
#else // corresponds to ifndef WARPX_DIM_RZ
template<typename T_Algo>
void FiniteDifferenceSolver::EvolveBCylindrical (
std::array< std::unique_ptr<amrex::MultiFab>, 3 >& Bfield,
std::array< std::unique_ptr<amrex::MultiFab>, 3 > const& Efield,
int lev, amrex::Real const dt ) {
amrex::LayoutData<amrex::Real>* cost = WarpX::getCosts(lev);
// 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(*Bfield[0], TilingIfNotGPU()); mfi.isValid(); ++mfi ) {
if (cost && WarpX::load_balance_costs_update_algo == LoadBalanceCostsUpdateAlgo::Timers)
{
amrex::Gpu::synchronize();
}
Real wt = amrex::second();
// Extract field data for this grid/tile
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& Er = Efield[0]->array(mfi);
Array4<Real> const& Et = Efield[1]->array(mfi);
Array4<Real> const& Ez = Efield[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& tbr = mfi.tilebox(Bfield[0]->ixType().toIntVect());
Box const& tbt = mfi.tilebox(Bfield[1]->ixType().toIntVect());
Box const& tbz = mfi.tilebox(Bfield[2]->ixType().toIntVect());
// Loop over the cells and update the fields
amrex::ParallelFor(tbr, tbt, tbz,
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
Real const r = rmin + i*dr; // r on nodal point (Br is nodal in r)
if (r != 0) { // Off-axis, regular Maxwell equations
Br(i, j, 0, 0) += dt * T_Algo::UpwardDz(Et, coefs_z, n_coefs_z, i, j, 0, 0); // Mode m=0
for (int m=1; m<nmodes; m++) { // Higher-order modes
Br(i, j, 0, 2*m-1) += dt*(
T_Algo::UpwardDz(Et, coefs_z, n_coefs_z, i, j, 0, 2*m-1)
- m * Ez(i, j, 0, 2*m )/r ); // Real part
Br(i, j, 0, 2*m ) += dt*(
T_Algo::UpwardDz(Et, coefs_z, n_coefs_z, i, j, 0, 2*m )
+ m * Ez(i, j, 0, 2*m-1)/r ); // Imaginary part
}
} else { // r==0: On-axis corrections
// Ensure that Br remains 0 on axis (except for m=1)
Br(i, j, 0, 0) = 0.; // Mode m=0
for (int m=1; m<nmodes; m++) { // Higher-order modes
if (m == 1){
// For m==1, Ez is linear in r, for small r
// Therefore, the formula below regularizes the singularity
Br(i, j, 0, 2*m-1) += dt*(
T_Algo::UpwardDz(Et, coefs_z, n_coefs_z, i, j, 0, 2*m-1)
- m * Ez(i+1, j, 0, 2*m )/dr ); // Real part
Br(i, j, 0, 2*m ) += dt*(
T_Algo::UpwardDz(Et, coefs_z, n_coefs_z, i, j, 0, 2*m )
+ m * Ez(i+1, j, 0, 2*m-1)/dr ); // Imaginary part
} else {
Br(i, j, 0, 2*m-1) = 0.;
Br(i, j, 0, 2*m ) = 0.;
}
}
}
},
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
Bt(i, j, 0, 0) += dt*(
T_Algo::UpwardDr(Ez, coefs_r, n_coefs_r, i, j, 0, 0)
- T_Algo::UpwardDz(Er, coefs_z, n_coefs_z, i, j, 0, 0)); // Mode m=0
for (int m=1 ; m<nmodes ; m++) { // Higher-order modes
Bt(i, j, 0, 2*m-1) += dt*(
T_Algo::UpwardDr(Ez, coefs_r, n_coefs_r, i, j, 0, 2*m-1)
- T_Algo::UpwardDz(Er, coefs_z, n_coefs_z, i, j, 0, 2*m-1)); // Real part
Bt(i, j, 0, 2*m ) += dt*(
T_Algo::UpwardDr(Ez, coefs_r, n_coefs_r, i, j, 0, 2*m )
- T_Algo::UpwardDz(Er, coefs_z, n_coefs_z, i, j, 0, 2*m )); // Imaginary part
}
},
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
Real const r = rmin + (i + 0.5)*dr; // r on a cell-centered grid (Bz is cell-centered in r)
Bz(i, j, 0, 0) += dt*( - T_Algo::UpwardDrr_over_r(Et, r, dr, coefs_r, n_coefs_r, i, j, 0, 0));
for (int m=1 ; m<nmodes ; m++) { // Higher-order modes
Bz(i, j, 0, 2*m-1) += dt*( m * Er(i, j, 0, 2*m )/r
- T_Algo::UpwardDrr_over_r(Et, r, dr, coefs_r, n_coefs_r, i, j, 0, 2*m-1)); // Real part
Bz(i, j, 0, 2*m ) += dt*(-m * Er(i, j, 0, 2*m-1)/r
- T_Algo::UpwardDrr_over_r(Et, r, dr, coefs_r, n_coefs_r, i, j, 0, 2*m )); // Imaginary part
}
}
);
if (cost && WarpX::load_balance_costs_update_algo == LoadBalanceCostsUpdateAlgo::Timers)
{
amrex::Gpu::synchronize();
wt = amrex::second() - wt;
amrex::HostDevice::Atomic::Add( &(*cost)[mfi.index()], wt);
}
}
}
#endif // corresponds to ifndef WARPX_DIM_RZ
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