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/* Copyright 2021
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#include "Utils/WarpXAlgorithmSelection.H"
#include "FiniteDifferenceSolver.H"
#include "Utils/WarpXConst.H"
#include <AMReX_Gpu.H>
#ifdef WARPX_DIM_RZ
# include "FiniteDifferenceAlgorithms/CylindricalYeeAlgorithm.H"
#endif
using namespace amrex;
/**
* \brief Update the B field at the boundary, using the Silver-Mueller condition
*/
void FiniteDifferenceSolver::ApplySilverMuellerBoundary (
std::array< std::unique_ptr<amrex::MultiFab>, 3 >& Efield,
std::array< std::unique_ptr<amrex::MultiFab>, 3 >& Bfield,
amrex::Box domain_box,
amrex::Real const dt ) {
// Ensure that we are using the Yee solver
if (m_fdtd_algo != MaxwellSolverAlgo::Yee) {
amrex::Abort("The Silver-Mueller boundary conditions can only be used with the Yee solver.");
}
// Ensure that we are using the cells the domain
domain_box.enclosedCells();
#ifdef WARPX_DIM_RZ
// Calculate relevant coefficients
amrex::Real const cdt = PhysConst::c*dt;
amrex::Real const cdt_over_dr = cdt*m_h_stencil_coefs_r[0];
amrex::Real const coef1_r = (1._rt - cdt_over_dr)/(1._rt + cdt_over_dr);
amrex::Real const coef2_r = 2._rt*cdt_over_dr/(1._rt + cdt_over_dr) / PhysConst::c;
amrex::Real const coef3_r = cdt/(1._rt + cdt_over_dr) / PhysConst::c;
amrex::Real const cdt_over_dz = cdt*m_h_stencil_coefs_z[0];
amrex::Real const coef1_z = (1._rt - cdt_over_dz)/(1._rt + cdt_over_dz);
amrex::Real const coef2_z = 2._rt*cdt_over_dz/(1._rt + cdt_over_dz) / PhysConst::c;
// Extract stencil coefficients
Real const * const AMREX_RESTRICT coefs_z = m_stencil_coefs_z.dataPtr();
int const n_coefs_z = m_h_stencil_coefs_z.size();
// Extract cylindrical specific parameters
Real const dr = m_dr;
int const nmodes = m_nmodes;
Real const rmin = m_rmin;
// tiling is usually set by TilingIfNotGPU()
// but here, we set it to false because of potential race condition,
// since we grow the tiles by one guard cell after creating them.
for ( MFIter mfi(*Efield[0], false); 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);
// Extract tileboxes for which to loop
Box tbr = mfi.tilebox(Bfield[0]->ixType().toIntVect());
Box tbt = mfi.tilebox(Bfield[1]->ixType().toIntVect());
Box tbz = mfi.tilebox(Bfield[2]->ixType().toIntVect());
// We will modify the first (i.e. innermost) guard cell
// (if it is outside of the physical domain)
// Thus, the tileboxes here are grown by 1 guard cell
tbr.grow(1);
tbt.grow(1);
tbz.grow(1);
// Loop over the cells
amrex::ParallelFor(tbr, tbt, tbz,
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
// At the +z boundary (innermost guard cell)
if ( j==domain_box.bigEnd(1)+1 ){
for (int m=0; m<2*nmodes-1; m++)
Br(i,j,0,m) = coef1_z*Br(i,j,0,m) - coef2_z*Et(i,j,0,m);
}
// At the -z boundary (innermost guard cell)
if ( j==domain_box.smallEnd(1)-1 ){
for (int m=0; m<2*nmodes-1; m++)
Br(i,j,0,m) = coef1_z*Br(i,j,0,m) + coef2_z*Et(i,j+1,0,m);
}
},
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
// At the +z boundary (innermost guard cell)
if ( j==domain_box.bigEnd(1)+1 ){
for (int m=0; m<2*nmodes-1; m++)
Bt(i,j,0,m) = coef1_z*Bt(i,j,0,m) + coef2_z*Er(i,j,0,m);
}
// At the -z boundary (innermost guard cell)
if ( j==domain_box.smallEnd(1)-1 ){
for (int m=0; m<2*nmodes-1; m++)
Bt(i,j,0,m) = coef1_z*Bt(i,j,0,m) - coef2_z*Er(i,j+1,0,m);
}
// At the +r boundary (innermost guard cell)
if ( i==domain_box.bigEnd(0)+1 ){
// Mode 0
Bt(i,j,0,0) = coef1_r*Bt(i,j,0,0) - coef2_r*Ez(i,j,0,0)
+ coef3_r*CylindricalYeeAlgorithm::UpwardDz(Er, coefs_z, n_coefs_z, i, j, 0, 0);
for (int m=1; m<nmodes; m++) { // Higher-order modes
// Real part
Bt(i,j,0,2*m-1) = coef1_r*Bt(i,j,0,2*m-1) - coef2_r*Ez(i,j,0,2*m-1)
+ coef3_r*CylindricalYeeAlgorithm::UpwardDz(Er, coefs_z, n_coefs_z, i, j, 0, 2*m-1);
// Imaginary part
Bt(i,j,0,2*m) = coef1_r*Bt(i,j,0,2*m) - coef2_r*Ez(i,j,0,2*m)
+ coef3_r*CylindricalYeeAlgorithm::UpwardDz(Er, coefs_z, n_coefs_z, i, j, 0, 2*m);
}
}
},
[=] AMREX_GPU_DEVICE (int i, int j, int /*k*/){
// At the +r boundary (innermost guard cell)
if ( i==domain_box.bigEnd(0)+1 ){
Real const r = rmin + (i + 0.5_rt)*dr; // r on nodal point (Bz is cell-centered in r)
// Mode 0
Bz(i,j,0,0) = coef1_r*Bz(i,j,0,0) + coef2_r*Et(i,j,0,0) - coef3_r*Et(i,j,0,0)/r;
for (int m=1; m<nmodes; m++) { // Higher-order modes
// Real part
Bz(i,j,0,2*m-1) = coef1_r*Bz(i,j,0,2*m-1) + coef2_r*Et(i,j,0,2*m-1)
- coef3_r/r*(Et(i,j,0,2*m-1) - m*Er(i,j,0,2*m));
// Imaginary part
Bz(i,j,0,2*m) = coef1_r*Bz(i,j,0,2*m) + coef2_r*Et(i,j,0,2*m)
- coef3_r/r*(Et(i,j,0,2*m) + m*Er(i,j,0,2*m-1));
}
}
}
);
}
#else
// Calculate relevant coefficients
amrex::Real const cdt_over_dx = PhysConst::c*dt*m_h_stencil_coefs_x[0];
amrex::Real const coef1_x = (1._rt - cdt_over_dx)/(1._rt + cdt_over_dx);
amrex::Real const coef2_x = 2._rt*cdt_over_dx/(1._rt + cdt_over_dx) / PhysConst::c;
#ifdef WARPX_DIM_3D
amrex::Real const cdt_over_dy = PhysConst::c*dt*m_h_stencil_coefs_y[0];
amrex::Real const coef1_y = (1._rt - cdt_over_dy)/(1._rt + cdt_over_dy);
amrex::Real const coef2_y = 2._rt*cdt_over_dy/(1._rt + cdt_over_dy) / PhysConst::c;
#endif
amrex::Real const cdt_over_dz = PhysConst::c*dt*m_h_stencil_coefs_z[0];
amrex::Real const coef1_z = (1._rt - cdt_over_dz)/(1._rt + cdt_over_dz);
amrex::Real const coef2_z = 2._rt*cdt_over_dz/(1._rt + cdt_over_dz) / 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
// tiling is usually set by TilingIfNotGPU()
// but here, we set it to false because of potential race condition,
// since we grow the tiles by one guard cell after creating them.
for ( MFIter mfi(*Efield[0], false); 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);
// Extract the tileboxes for which to loop
Box tbx = mfi.tilebox(Bfield[0]->ixType().toIntVect());
Box tby = mfi.tilebox(Bfield[1]->ixType().toIntVect());
Box tbz = mfi.tilebox(Bfield[2]->ixType().toIntVect());
// We will modify the first (i.e. innermost) guard cell
// (if it is outside of the physical domain)
// Thus, the tileboxes here are grown by 1 guard cell
tbx.grow(1);
tby.grow(1);
tbz.grow(1);
// Loop over cells
amrex::ParallelFor(tbx, tby, tbz,
// Apply Boundary condition to Bx
[=] AMREX_GPU_DEVICE (int i, int j, int k){
#ifdef WARPX_DIM_3D
// At the +y boundary (innermost guard cell)
if ( j==domain_box.bigEnd(1)+1 )
Bx(i,j,k) = coef1_y * Bx(i,j,k) + coef2_y * Ez(i,j,k);
// At the -y boundary (innermost guard cell)
if ( j==domain_box.smallEnd(1)-1 )
Bx(i,j,k) = coef1_y * Bx(i,j,k) - coef2_y * Ez(i,j+1,k);
// At the +z boundary (innermost guard cell)
if ( k==domain_box.bigEnd(2)+1 )
Bx(i,j,k) = coef1_z * Bx(i,j,k) - coef2_z * Ey(i,j,k);
// At the -z boundary (innermost guard cell)
if ( k==domain_box.smallEnd(2)-1 )
Bx(i,j,k) = coef1_z * Bx(i,j,k) + coef2_z * Ey(i,j,k+1);
#elif WARPX_DIM_XZ
// At the +z boundary (innermost guard cell)
if ( j==domain_box.bigEnd(1)+1 )
Bx(i,j,k) = coef1_z * Bx(i,j,k) - coef2_z * Ey(i,j,k);
// At the -z boundary (innermost guard cell)
if ( j==domain_box.smallEnd(1)-1 )
Bx(i,j,k) = coef1_z * Bx(i,j,k) + coef2_z * Ey(i,j+1,k);
#endif
},
// Apply Boundary condition to By
[=] AMREX_GPU_DEVICE (int i, int j, int k){
// At the +x boundary (innermost guard cell)
if ( i==domain_box.bigEnd(0)+1 )
By(i,j,k) = coef1_x * By(i,j,k) - coef2_x * Ez(i,j,k);
// At the -x boundary (innermost guard cell)
if ( i==domain_box.smallEnd(0)-1 )
By(i,j,k) = coef1_x * By(i,j,k) + coef2_x * Ez(i+1,j,k);
#ifdef WARPX_DIM_3D
// At the +z boundary (innermost guard cell)
if ( k==domain_box.bigEnd(2)+1 )
By(i,j,k) = coef1_z * By(i,j,k) + coef2_z * Ex(i,j,k);
// At the -z boundary (innermost guard cell)
if ( k==domain_box.smallEnd(2)-1 )
By(i,j,k) = coef1_z * By(i,j,k) - coef2_z * Ex(i,j,k+1);
#elif WARPX_DIM_XZ
// At the +z boundary (innermost guard cell)
if ( j==domain_box.bigEnd(1)+1 )
By(i,j,k) = coef1_z * By(i,j,k) + coef2_z * Ex(i,j,k);
// At the -z boundary (innermost guard cell)
if ( j==domain_box.smallEnd(1)-1 )
By(i,j,k) = coef1_z * By(i,j,k) - coef2_z * Ex(i,j+1,k);
#endif
},
// Apply Boundary condition to Bz
[=] AMREX_GPU_DEVICE (int i, int j, int k){
// At the +x boundary (innermost guard cell)
if ( i==domain_box.bigEnd(0)+1 )
Bz(i,j,k) = coef1_x * Bz(i,j,k) + coef2_x * Ey(i,j,k);
// At the -x boundary (innermost guard cell)
if ( i==domain_box.smallEnd(0)-1 )
Bz(i,j,k) = coef1_x * Bz(i,j,k) - coef2_x * Ey(i+1,j,k);
#ifdef WARPX_DIM_3D
// At the +y boundary (innermost guard cell)
if ( j==domain_box.bigEnd(1)+1 )
Bz(i,j,k) = coef1_y * Bz(i,j,k) - coef2_y * Ex(i,j,k);
// At the -y boundary (innermost guard cell)
if ( j==domain_box.smallEnd(1)-1 )
Bz(i,j,k) = coef1_y * Bz(i,j,k) + coef2_y * Ex(i,j+1,k);
#endif
}
);
}
#endif // WARPX_DIM_RZ
}
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