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|
/* Copyright 2019
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#include "PsatdAlgorithmFirstOrder.H"
#include "Utils/TextMsg.H"
#include "Utils/WarpXAlgorithmSelection.H"
#include "Utils/WarpXConst.H"
#include "Utils/WarpX_Complex.H"
#include <AMReX_Array4.H>
#include <AMReX_BLProfiler.H>
#include <AMReX_BaseFab.H>
#include <AMReX_BoxArray.H>
#include <AMReX_GpuComplex.H>
#include <AMReX_GpuLaunch.H>
#include <AMReX_GpuQualifiers.H>
#include <AMReX_IntVect.H>
#include <AMReX_MFIter.H>
#include <AMReX_PODVector.H>
#include <cmath>
#if WARPX_USE_PSATD
using namespace amrex::literals;
PsatdAlgorithmFirstOrder::PsatdAlgorithmFirstOrder(
const SpectralKSpace& spectral_kspace,
const amrex::DistributionMapping& dm,
const SpectralFieldIndex& spectral_index,
const int norder_x,
const int norder_y,
const int norder_z,
const short grid_type,
const amrex::Real dt,
const bool div_cleaning,
const int J_in_time,
const int rho_in_time)
// Initializer list
: SpectralBaseAlgorithm(spectral_kspace, dm, spectral_index, norder_x, norder_y, norder_z, grid_type),
m_spectral_index(spectral_index),
m_dt(dt),
m_div_cleaning(div_cleaning),
m_J_in_time(J_in_time),
m_rho_in_time(rho_in_time)
{}
void
PsatdAlgorithmFirstOrder::pushSpectralFields (SpectralFieldData& f) const
{
const bool div_cleaning = m_div_cleaning;
const bool J_constant = (m_J_in_time == JInTime::Constant) ? true : false;
const bool J_linear = (m_J_in_time == JInTime::Linear ) ? true : false;
const bool rho_constant = (m_rho_in_time == RhoInTime::Constant) ? true : false;
const bool rho_linear = (m_rho_in_time == RhoInTime::Linear ) ? true : false;
const amrex::Real dt = m_dt;
const amrex::Real dt2 = dt*dt;
const SpectralFieldIndex& Idx = m_spectral_index;
// Loop over boxes
for (amrex::MFIter mfi(f.fields); mfi.isValid(); ++mfi)
{
const amrex::Box& bx = f.fields[mfi].box();
// Extract arrays for the fields to be updated
amrex::Array4<Complex> fields = f.fields[mfi].array();
// Extract pointers for the k vectors
const amrex::Real* modified_kx_arr = modified_kx_vec[mfi].dataPtr();
#if defined(WARPX_DIM_3D)
const amrex::Real* modified_ky_arr = modified_ky_vec[mfi].dataPtr();
#endif
const amrex::Real* modified_kz_arr = modified_kz_vec[mfi].dataPtr();
// Loop over indices within one box
amrex::ParallelFor(bx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
{
// Record old values of the fields to be updated
const Complex Ex_old = fields(i,j,k,Idx.Ex);
const Complex Ey_old = fields(i,j,k,Idx.Ey);
const Complex Ez_old = fields(i,j,k,Idx.Ez);
const Complex Bx_old = fields(i,j,k,Idx.Bx);
const Complex By_old = fields(i,j,k,Idx.By);
const Complex Bz_old = fields(i,j,k,Idx.Bz);
// Shortcuts for the values of J and rho
const Complex Jx_mid = (J_constant) ? fields(i,j,k,Idx.Jx_mid) : 0._rt;
const Complex Jy_mid = (J_constant) ? fields(i,j,k,Idx.Jy_mid) : 0._rt;
const Complex Jz_mid = (J_constant) ? fields(i,j,k,Idx.Jz_mid) : 0._rt;
const Complex Jx_old = (J_linear ) ? fields(i,j,k,Idx.Jx_old) : 0._rt;
const Complex Jy_old = (J_linear ) ? fields(i,j,k,Idx.Jy_old) : 0._rt;
const Complex Jz_old = (J_linear ) ? fields(i,j,k,Idx.Jz_old) : 0._rt;
const Complex Jx_new = (J_linear ) ? fields(i,j,k,Idx.Jx_new) : 0._rt;
const Complex Jy_new = (J_linear ) ? fields(i,j,k,Idx.Jy_new) : 0._rt;
const Complex Jz_new = (J_linear ) ? fields(i,j,k,Idx.Jz_new) : 0._rt;
const Complex Jx_c0 = (J_constant) ? Jx_mid : Jx_old;
const Complex Jy_c0 = (J_constant) ? Jy_mid : Jy_old;
const Complex Jz_c0 = (J_constant) ? Jz_mid : Jz_old;
const Complex Jx_c1 = (J_linear ) ? (Jx_new-Jx_old)/dt : 0._rt;
const Complex Jy_c1 = (J_linear ) ? (Jy_new-Jy_old)/dt : 0._rt;
const Complex Jz_c1 = (J_linear ) ? (Jz_new-Jz_old)/dt : 0._rt;
Complex rho_mid, rho_old, rho_new, F_old, G_old;
Complex rho_c0, rho_c1;
if (div_cleaning)
{
rho_mid = (rho_constant) ? fields(i,j,k,Idx.rho_mid) : 0._rt;
rho_old = (rho_linear ) ? fields(i,j,k,Idx.rho_old) : 0._rt;
rho_new = (rho_linear ) ? fields(i,j,k,Idx.rho_new) : 0._rt;
F_old = fields(i,j,k,Idx.F);
G_old = fields(i,j,k,Idx.G);
rho_c0 = (rho_constant) ? rho_mid : rho_old;
rho_c1 = (rho_linear ) ? (rho_new-rho_old)/dt : 0._rt;
}
// k vector values
const amrex::Real kx = modified_kx_arr[i];
#if defined(WARPX_DIM_3D)
const amrex::Real ky = modified_ky_arr[j];
const amrex::Real kz = modified_kz_arr[k];
#else
constexpr amrex::Real ky = 0._rt;
const amrex::Real kz = modified_kz_arr[j];
#endif
// Physical constants and imaginary unit
constexpr amrex::Real c = PhysConst::c;
constexpr amrex::Real c2 = c*c;
constexpr amrex::Real inv_c = 1._rt/c;
constexpr amrex::Real mu0 = PhysConst::mu0;
constexpr Complex I = Complex{0._rt, 1._rt};
const amrex::Real kx2 = kx*kx;
const amrex::Real ky2 = ky*ky;
const amrex::Real kz2 = kz*kz;
const amrex::Real knorm = std::sqrt(kx2 + ky2 + kz2);
const amrex::Real knorm2 = knorm*knorm;
const amrex::Real knorm4 = knorm2*knorm2;
// Auxiliary variables
const amrex::Real inv_knorm = 1._rt/knorm;
const amrex::Real inv_knorm2 = 1._rt/knorm2;
const amrex::Real inv_knorm4 = 1._rt/knorm4;
const amrex::Real C = std::cos(c*knorm*dt);
const amrex::Real S = std::sin(c*knorm*dt);
// Update equations
if (knorm == 0._rt)
{
fields(i,j,k,Idx.Ex) = Ex_old - mu0*c2*dt*Jx_c0 - 0.5_rt*mu0*c2*dt2*Jx_c1;
fields(i,j,k,Idx.Ey) = Ey_old - mu0*c2*dt*Jy_c0 - 0.5_rt*mu0*c2*dt2*Jy_c1;
fields(i,j,k,Idx.Ez) = Ez_old - mu0*c2*dt*Jz_c0 - 0.5_rt*mu0*c2*dt2*Jz_c1;
if (div_cleaning)
{
fields(i,j,k,Idx.F) = F_old - mu0*c2*dt*rho_c0 - 0.5_rt*mu0*c2*dt2*rho_c1;
}
}
else // knorm != 0
{
Complex C01, C02, C03, C04, C05, C06, C07, C08,
C09, C10, C11, C12, C13, C14, C15, C16;
// Ex
C01 = (div_cleaning) ? C : (kx2+ky2*C+kz2*C)*inv_knorm2;
C02 = (div_cleaning) ? 0._rt : kx*ky*(1._rt-C)*inv_knorm2;
C03 = (div_cleaning) ? 0._rt : kx*kz*(1._rt-C)*inv_knorm2;
C04 = 0._rt;
C05 = -I*c*kz*S*inv_knorm;
C06 = I*c*ky*S*inv_knorm;
C07 = (div_cleaning) ? I*c*kx*S*inv_knorm : 0._rt;
C09 = (div_cleaning) ? -mu0*c*S*inv_knorm : -mu0*c*(dt*c*kx2*knorm2+ky2*knorm*S+kz2*knorm*S)*inv_knorm4;
C10 = (div_cleaning) ? 0._rt : mu0*c*kx*ky*(knorm*S-dt*c*knorm2)*inv_knorm4;
C11 = (div_cleaning) ? 0._rt : mu0*c*kx*kz*(knorm*S-dt*c*knorm2)*inv_knorm4;
C12 = 0._rt; // This is not redundant, do not remove this
if (J_linear) C12 = (div_cleaning) ? mu0*(C-1._rt)*inv_knorm2 : mu0*(2._rt*ky2*(C-1._rt)+2._rt*kz2*(C-1._rt)-dt2*c2*kx2*knorm2)*inv_knorm4*0.5_rt;
C13 = (J_linear && !div_cleaning) ? mu0*kx*ky*(2._rt*(1._rt-C)-dt2*c2*knorm2)*inv_knorm4*0.5_rt : 0._rt;
C14 = (J_linear && !div_cleaning) ? mu0*kx*kz*(2._rt*(1._rt-C)-dt2*c2*knorm2)*inv_knorm4*0.5_rt : 0._rt;
C15 = (div_cleaning) ? I*mu0*c2*kx*(C-1._rt)*inv_knorm2 : 0._rt;
C16 = (div_cleaning && rho_linear) ? I*mu0*c*kx*(knorm*S-dt*c*knorm2)*inv_knorm4 : 0._rt;
fields(i,j,k,Idx.Ex) = C01*Ex_old + C02*Ey_old + C03*Ez_old
+ C04*Bx_old + C05*By_old + C06*Bz_old
+ C07*F_old // only with div cleaning
+ C09*Jx_c0 + C10*Jy_c0 + C11*Jz_c0
+ C12*Jx_c1 + C13*Jy_c1 + C14*Jz_c1 // only with J linear in time
+ C15*rho_c0 // only with div cleaning
+ C16*rho_c1; // only with div cleaning and rho linear in time
// Ey
C01 = (div_cleaning) ? 0._rt : kx*ky*(1._rt-C)*inv_knorm2;
C02 = (div_cleaning) ? C : (kx2*C+ky2+kz2*C)*inv_knorm2;
C03 = (div_cleaning) ? 0._rt : ky*kz*(1._rt-C)*inv_knorm2;
C04 = I*c*kz*S*inv_knorm;
C05 = 0._rt;
C06 = -I*c*kx*S*inv_knorm;
C07 = (div_cleaning) ? I*c*ky*S*inv_knorm : 0._rt;
C09 = (div_cleaning) ? 0._rt : mu0*c*kx*ky*(knorm*S-dt*c*knorm2)*inv_knorm4;
C10 = (div_cleaning) ? -mu0*c*S*inv_knorm : -mu0*c*(dt*c*ky2*knorm2+kx2*knorm*S+kz2*knorm*S)*inv_knorm4;
C11 = (div_cleaning) ? 0._rt : mu0*c*ky*kz*(knorm*S-dt*c*knorm2)*inv_knorm4;
C12 = (J_linear && !div_cleaning) ? mu0*kx*ky*(2._rt*(1._rt-C)-dt2*c2*knorm2)*inv_knorm4*0.5_rt : 0._rt;
C13 = 0._rt; // This is not redundant, do not remove this
if (J_linear) C13 = (div_cleaning) ? mu0*(C-1._rt)*inv_knorm2 : mu0*(2._rt*kx2*(C-1._rt)+2._rt*kz2*(C-1._rt)-dt2*c2*ky2*knorm2)*inv_knorm4*0.5_rt;
C14 = (J_linear && !div_cleaning) ? mu0*ky*kz*(2._rt*(1._rt-C)-dt2*c2*knorm2)*inv_knorm4*0.5_rt : 0._rt;
C15 = (div_cleaning) ? I*mu0*c2*ky*(C-1._rt)*inv_knorm2 : 0._rt;
C16 = (div_cleaning && rho_linear) ? I*mu0*c*ky*(knorm*S-dt*c*knorm2)*inv_knorm4 : 0._rt;
fields(i,j,k,Idx.Ey) = C01*Ex_old + C02*Ey_old + C03*Ez_old
+ C04*Bx_old + C05*By_old + C06*Bz_old
+ C07*F_old // only with div cleaning
+ C09*Jx_c0 + C10*Jy_c0 + C11*Jz_c0
+ C12*Jx_c1 + C13*Jy_c1 + C14*Jz_c1 // only with J linear in time
+ C15*rho_c0 // only with div cleaning
+ C16*rho_c1; // only with div cleaning and rho linear in time
// Ez
C01 = (div_cleaning) ? 0._rt : kx*kz*(1._rt-C)*inv_knorm2;
C02 = (div_cleaning) ? 0._rt : ky*kz*(1._rt-C)*inv_knorm2;
C03 = (div_cleaning) ? C : (kx2*C+ky2*C+kz2)*inv_knorm2;
C04 = -I*c*ky*S*inv_knorm;
C05 = I*c*kx*S*inv_knorm;
C06 = 0._rt;
C07 = (div_cleaning) ? I*c*kz*S*inv_knorm : 0._rt;
C09 = (div_cleaning) ? 0._rt : mu0*c*kx*kz*(knorm*S-dt*c*knorm2)*inv_knorm4;
C10 = (div_cleaning) ? 0._rt : mu0*c*ky*kz*(knorm*S-dt*c*knorm2)*inv_knorm4;
C11 = (div_cleaning) ? -mu0*c*S*inv_knorm : -mu0*c*(dt*c*kz2*knorm2+kx2*knorm*S+ky2*knorm*S)*inv_knorm4;
C12 = (J_linear && !div_cleaning) ? mu0*kx*kz*(2._rt*(1._rt-C)-dt2*c2*knorm2)*inv_knorm4*0.5_rt : 0._rt;
C13 = (J_linear && !div_cleaning) ? mu0*ky*kz*(2._rt*(1._rt-C)-dt2*c2*knorm2)*inv_knorm4*0.5_rt : 0._rt;
C14 = 0._rt; // This is not redundant, do not remove this
if (J_linear) C14 = (div_cleaning) ? mu0*(C-1._rt)*inv_knorm2 : mu0*(2._rt*kx2*(C-1._rt)+2._rt*ky2*(C-1._rt)-dt2*c2*kz2*knorm2)*inv_knorm4*0.5_rt;
C15 = (div_cleaning) ? I*mu0*c2*kz*(C-1._rt)*inv_knorm2 : 0._rt;
C16 = (div_cleaning && rho_linear) ? I*mu0*c*kz*(knorm*S-dt*c*knorm2)*inv_knorm4 : 0._rt;
fields(i,j,k,Idx.Ez) = C01*Ex_old + C02*Ey_old + C03*Ez_old
+ C04*Bx_old + C05*By_old + C06*Bz_old
+ C07*F_old // only with div cleaning
+ C09*Jx_c0 + C10*Jy_c0 + C11*Jz_c0
+ C12*Jx_c1 + C13*Jy_c1 + C14*Jz_c1 // only with J linear in time
+ C15*rho_c0 // only with div cleaning
+ C16*rho_c1; // only with div cleaning and rho linear in time
// Bx
C01 = 0._rt;
C02 = I*kz*S*inv_knorm*inv_c;
C03 = -I*ky*S*inv_knorm*inv_c;
C04 = (div_cleaning) ? C : (kx2+ky2*C+kz2*C)*inv_knorm2;
C05 = (div_cleaning) ? 0._rt : kx*ky*(1._rt-C)*inv_knorm2;
C06 = (div_cleaning) ? 0._rt : kx*kz*(1._rt-C)*inv_knorm2;
C08 = (div_cleaning) ? I*kx*S*inv_knorm*inv_c : 0._rt;
C09 = 0._rt;
C10 = I*mu0*kz*(C-1._rt)*inv_knorm2;
C11 = -I*mu0*ky*(C-1._rt)*inv_knorm2;
C12 = 0._rt;
C13 = (J_linear) ? I*mu0*kz*(knorm*S-dt*c*knorm2)*inv_knorm4*inv_c : 0._rt;
C14 = (J_linear) ? -I*mu0*ky*(knorm*S-dt*c*knorm2)*inv_knorm4*inv_c : 0._rt;
fields(i,j,k,Idx.Bx) = C01*Ex_old + C02*Ey_old + C03*Ez_old
+ C04*Bx_old + C05*By_old + C06*Bz_old
+ C08*G_old // only with div cleaning
+ C09*Jx_c0 + C10*Jy_c0 + C11*Jz_c0
+ C12*Jx_c1 + C13*Jy_c1 + C14*Jz_c1; // only with J linear in time
// By
C01 = -I*kz*S*inv_knorm*inv_c;
C02 = 0._rt;
C03 = I*kx*S*inv_knorm*inv_c;
C04 = (div_cleaning) ? 0._rt : kx*ky*(1._rt-C)*inv_knorm2;
C05 = (div_cleaning) ? C : (kx2*C+ky2+kz2*C)*inv_knorm2;
C06 = (div_cleaning) ? 0._rt : ky*kz*(1._rt-C)*inv_knorm2;
C08 = (div_cleaning) ? I*ky*S*inv_knorm*inv_c : 0._rt;
C09 = -I*mu0*kz*(C-1._rt)*inv_knorm2;
C10 = 0._rt;
C11 = I*mu0*kx*(C-1._rt)*inv_knorm2;
C12 = (J_linear) ? -I*mu0*kz*(knorm*S-dt*c*knorm2)*inv_knorm4*inv_c : 0._rt;
C13 = 0._rt;
C14 = (J_linear) ? I*mu0*kx*(knorm*S-dt*c*knorm2)*inv_knorm4*inv_c : 0._rt;
fields(i,j,k,Idx.By) = C01*Ex_old + C02*Ey_old + C03*Ez_old
+ C04*Bx_old + C05*By_old + C06*Bz_old
+ C08*G_old // only with div cleaning
+ C09*Jx_c0 + C10*Jy_c0 + C11*Jz_c0
+ C12*Jx_c1 + C13*Jy_c1 + C14*Jz_c1; // only with J linear in time
// Bz
C01 = I*ky*S*inv_knorm*inv_c;
C02 = -I*kx*S*inv_knorm*inv_c;
C03 = 0._rt;
C04 = (div_cleaning) ? 0._rt : kx*kz*(1._rt-C)*inv_knorm2;
C05 = (div_cleaning) ? 0._rt : ky*kz*(1._rt-C)*inv_knorm2;
C06 = (div_cleaning) ? C : (kx2*C+ky2*C+kz2)*inv_knorm2;
C08 = (div_cleaning) ? I*kz*S*inv_knorm*inv_c : 0._rt;
C09 = I*mu0*ky*(C-1._rt)*inv_knorm2;
C10 = -I*mu0*kx*(C-1._rt)*inv_knorm2;
C11 = 0._rt;
C12 = (J_linear) ? I*mu0*ky*(knorm*S-dt*c*knorm2)*inv_knorm4*inv_c : 0._rt;
C13 = (J_linear) ? -I*mu0*kx*(knorm*S-dt*c*knorm2)*inv_knorm4*inv_c : 0._rt;
C14 = 0._rt;
fields(i,j,k,Idx.Bz) = C01*Ex_old + C02*Ey_old + C03*Ez_old
+ C04*Bx_old + C05*By_old + C06*Bz_old
+ C08*G_old // only with div cleaning
+ C09*Jx_c0 + C10*Jy_c0 + C11*Jz_c0
+ C12*Jx_c1 + C13*Jy_c1 + C14*Jz_c1; // only with J linear in time
if (div_cleaning)
{
// F
C01 = I*kx*S*inv_knorm*inv_c;
C02 = I*ky*S*inv_knorm*inv_c;
C03 = I*kz*S*inv_knorm*inv_c;
C07 = C;
C09 = I*mu0*kx*(C-1._rt)*inv_knorm2;
C10 = I*mu0*ky*(C-1._rt)*inv_knorm2;
C11 = I*mu0*kz*(C-1._rt)*inv_knorm2;
C12 = (J_linear) ? I*mu0*kx*(knorm*S-dt*c*knorm2)*inv_knorm4*inv_c : 0._rt;
C13 = (J_linear) ? I*mu0*ky*(knorm*S-dt*c*knorm2)*inv_knorm4*inv_c : 0._rt;
C14 = (J_linear) ? I*mu0*kz*(knorm*S-dt*c*knorm2)*inv_knorm4*inv_c : 0._rt;
C15 = -mu0*c*S*inv_knorm;
C16 = (rho_linear) ? mu0*(C-1._rt)*inv_knorm2 : 0._rt;
fields(i,j,k,Idx.F) = C01*Ex_old + C02*Ey_old + C03*Ez_old
+ C07*F_old
+ C09*Jx_c0 + C10*Jy_c0 + C11*Jz_c0
+ C12*Jx_c1 + C13*Jy_c1 + C14*Jz_c1 // only with J linear in time
+ C15*rho_c0
+ C16*rho_c1; // only with rho linear in time
// G
C04 = I*c*kx*S*inv_knorm;
C05 = I*c*ky*S*inv_knorm;
C06 = I*c*kz*S*inv_knorm;
C08 = C;
fields(i,j,k,Idx.G) = C04*Bx_old + C05*By_old + C06*Bz_old
+ C08*G_old;
}
}
});
}
}
void PsatdAlgorithmFirstOrder::CurrentCorrection (SpectralFieldData& field_data)
{
// Profiling
BL_PROFILE("PsatdAlgorithmFirstOrder::CurrentCorrection");
amrex::ignore_unused(field_data);
amrex::Abort(Utils::TextMsg::Err(
"Current correction not implemented for first-order PSATD equations"));
}
void
PsatdAlgorithmFirstOrder::VayDeposition (SpectralFieldData& field_data)
{
// Profiling
BL_PROFILE("PsatdAlgorithmFirstOrder::VayDeposition()");
amrex::ignore_unused(field_data);
amrex::Abort(Utils::TextMsg::Err(
"Vay deposition not implemented for first-order PSATD equations"));
}
#endif // WARPX_USE_PSATD
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