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/* Copyright 2019 Remi Lehe
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#include "PMLPsatdAlgorithm.H"
#include "Utils/WarpXConst.H"
#include <cmath>
#if WARPX_USE_PSATD
using namespace amrex;
/* \brief Initialize coefficients for the update equation */
PMLPsatdAlgorithm::PMLPsatdAlgorithm(const SpectralKSpace& spectral_kspace,
const DistributionMapping& dm,
const int norder_x, const int norder_y,
const int norder_z, const bool nodal, const Real dt)
// Initialize members of base class
: SpectralBaseAlgorithm(spectral_kspace, dm, norder_x, norder_y, norder_z, nodal),
m_dt(dt)
{
const BoxArray& ba = spectral_kspace.spectralspace_ba;
// Allocate the arrays of coefficients
C_coef = SpectralRealCoefficients(ba, dm, 1, 0);
S_ck_coef = SpectralRealCoefficients(ba, dm, 1, 0);
inv_k2_coef = SpectralRealCoefficients(ba, dm, 1, 0);
InitializeSpectralCoefficients(spectral_kspace, dm, dt);
}
/* Advance the E and B field in spectral space (stored in `f`)
* over one time step */
void
PMLPsatdAlgorithm::pushSpectralFields(SpectralFieldData& f) const {
// Loop over boxes
for (MFIter mfi(f.fields); mfi.isValid(); ++mfi){
const Box& bx = f.fields[mfi].box();
// Extract arrays for the fields to be updated
Array4<Complex> fields = f.fields[mfi].array();
// Extract arrays for the coefficients
Array4<const Real> C_arr = C_coef[mfi].array();
Array4<const Real> S_ck_arr = S_ck_coef[mfi].array();
Array4<const Real> inv_k2_arr = inv_k2_coef[mfi].array();
// Extract pointers for the k vectors
const Real* modified_kx_arr = modified_kx_vec[mfi].dataPtr();
#if (AMREX_SPACEDIM==3)
const Real* modified_ky_arr = modified_ky_vec[mfi].dataPtr();
#endif
const Real* modified_kz_arr = modified_kz_vec[mfi].dataPtr();
const amrex::Real dt = m_dt;
// Loop over indices within one box
ParallelFor(bx,
[=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
{
// Record old values of the fields to be updated
using Idx = SpectralPMLIndex;
const Complex Exy = fields(i,j,k,Idx::Exy);
const Complex Exz = fields(i,j,k,Idx::Exz);
const Complex Eyx = fields(i,j,k,Idx::Eyx);
const Complex Eyz = fields(i,j,k,Idx::Eyz);
const Complex Ezx = fields(i,j,k,Idx::Ezx);
const Complex Ezy = fields(i,j,k,Idx::Ezy);
const Complex Bxy = fields(i,j,k,Idx::Bxy);
const Complex Bxz = fields(i,j,k,Idx::Bxz);
const Complex Byx = fields(i,j,k,Idx::Byx);
const Complex Byz = fields(i,j,k,Idx::Byz);
const Complex Bzx = fields(i,j,k,Idx::Bzx);
const Complex Bzy = fields(i,j,k,Idx::Bzy);
// k vector values, and coefficients
const Real kx = modified_kx_arr[i];
#if (AMREX_SPACEDIM==3)
const Real ky = modified_ky_arr[j];
const Real kz = modified_kz_arr[k];
#else
constexpr Real ky = 0._rt;
const Real kz = modified_kz_arr[j];
#endif
constexpr Real c2 = PhysConst::c * PhysConst::c;
const Complex I = Complex{0._rt, 1._rt};
const Real kx2 = kx*kx;
const Real ky2 = ky*ky;
const Real kz2 = kz*kz;
const Real k_norm = std::sqrt(kx2 + ky2 + kz2);
if (k_norm != 0._rt) {
const Real C = C_arr(i,j,k);
const Real S_ck = S_ck_arr(i,j,k);
const Real inv_k2 = inv_k2_arr(i,j,k);
const Real C1 = (kx2 * C + ky2 + kz2) * inv_k2;
const Real C2 = (kx2 + ky2 * C + kz2) * inv_k2;
const Real C3 = (kx2 + ky2 + kz2 * C) * inv_k2;
const Real C4 = kx2 * (C - 1._rt) * inv_k2;
const Real C5 = ky2 * (C - 1._rt) * inv_k2;
const Real C6 = kz2 * (C - 1._rt) * inv_k2;
const Real C7 = ky * kz * (1._rt - C) * inv_k2;
const Real C8 = kx * kz * (1._rt - C) * inv_k2;
const Real C9 = kx * ky * (1._rt - C) * inv_k2;
const Real C10 = c2 * kx * ky * kz * (dt - S_ck) * inv_k2;
const Real C11 = c2 * ky2 * kz * (dt - S_ck) * inv_k2;
const Real C12 = c2 * kz2 * ky * (dt - S_ck) * inv_k2;
const Real C13 = c2 * kz2 * kx * (dt - S_ck) * inv_k2;
const Real C14 = c2 * kx2 * kz * (dt - S_ck) * inv_k2;
const Real C15 = c2 * kx2 * ky * (dt - S_ck) * inv_k2;
const Real C16 = c2 * ky2 * kx * (dt - S_ck) * inv_k2;
const Real C17 = c2 * kx * (ky2 * dt + (kz2 + kx2) * S_ck) * inv_k2;
const Real C18 = c2 * kx * (kz2 * dt + (ky2 + kx2) * S_ck) * inv_k2;
const Real C19 = c2 * ky * (kz2 * dt + (kx2 + ky2) * S_ck) * inv_k2;
const Real C20 = c2 * ky * (kx2 * dt + (kz2 + ky2) * S_ck) * inv_k2;
const Real C21 = c2 * kz * (kx2 * dt + (ky2 + kz2) * S_ck) * inv_k2;
const Real C22 = c2 * kz * (ky2 * dt + (kx2 + kz2) * S_ck) * inv_k2;
// Update E
fields(i,j,k,Idx::Exy) = C2 * Exy + C5 * Exz + C9 * (Eyz + Eyx)
+ I*C10 * (Bxy + Bxz) + I*C11 * (Byz + Byx) + I*C19 * (Bzx + Bzy);
fields(i,j,k,Idx::Exz) = C6 * Exy + C3 * Exz + C8 * (Ezx + Ezy)
- I*C10 * (Bxy + Bxz) - I*C22 * (Byz + Byx) - I*C12 * (Bzx + Bzy);
fields(i,j,k,Idx::Eyz) = C3 * Eyz + C6 * Eyx + C7 * (Ezx + Ezy)
+ I*C21 * (Bxy + Bxz) + I*C10 * (Byz + Byx) + I*C13 * (Bzx + Bzy);
fields(i,j,k,Idx::Eyx) = C9 * (Exy + Exz) + C4 * Eyz + C1 * Eyx
- I*C14 * (Bxy + Bxz) - I*C10 * (Byz + Byx) - I*C18 * (Bzx + Bzy);
fields(i,j,k,Idx::Ezx) = C8 * (Exy + Exz) + C1 * Ezx + C4 * Ezy
+ I*C15 * (Bxy + Bxz) + I*C17 * (Byz + Byx) + I*C10 * (Bzx + Bzy);
fields(i,j,k,Idx::Ezy) = C7 * (Eyz + Eyx) + C5 * Ezx + C2 * Ezy
- I*C20 * (Bxy + Bxz) - I*C16 * (Byz + Byx) - I*C10 * (Bzx + Bzy);
// Update B
fields(i,j,k,Idx::Bxy) = C2 * Bxy + C5 * Bxz + C9 * (Byz + Byx)
- I*C10/c2 * (Exy + Exz) - I*C11/c2 * (Eyz + Eyx) - I*C19/c2 * (Ezx + Ezy);
fields(i,j,k,Idx::Bxz) = C6 * Bxy + C3 * Bxz + C8 * (Bzx + Bzy)
+ I*C10/c2 * (Exy + Exz) + I*C22/c2 * (Eyz + Eyx) + I*C12/c2 * (Ezx + Ezy);
fields(i,j,k,Idx::Byz) = C3 * Byz + C6 * Byx + C7 * (Bzx + Bzy)
- I*C21/c2 * (Exy + Exz) - I*C10/c2 * (Eyz + Eyx) - I*C13/c2 * (Ezx + Ezy);
fields(i,j,k,Idx::Byx) = C9 * (Bxy + Bxz) + C4 * Byz + C1 * Byx
+ I*C14/c2 * (Exy + Exz) + I*C10/c2 * (Eyz + Eyx) + I*C18/c2 * (Ezx + Ezy);
fields(i,j,k,Idx::Bzx) = C8 * (Bxy + Bxz) + C1 * Bzx + C4 * Bzy
- I*C15/c2 * (Exy + Exz) - I*C17/c2 * (Eyz + Eyx) - I*C10/c2 * (Ezx + Ezy);
fields(i,j,k,Idx::Bzy) = C7 * (Byz + Byx) + C5 * Bzx + C2 * Bzy
+ I*C20/c2 * (Exy + Exz) + I*C16/c2 * (Eyz + Eyx) + I*C10/c2 * (Ezx + Ezy);
}
});
}
}
void PMLPsatdAlgorithm::InitializeSpectralCoefficients (
const SpectralKSpace& spectral_kspace,
const amrex::DistributionMapping& dm,
const amrex::Real dt)
{
const BoxArray& ba = spectral_kspace.spectralspace_ba;
// Fill them with the right values:
// Loop over boxes and allocate the corresponding coefficients
// for each box owned by the local MPI proc
for (MFIter mfi(ba, dm); mfi.isValid(); ++mfi) {
const Box& bx = ba[mfi];
// Extract pointers for the k vectors
const Real* modified_kx = modified_kx_vec[mfi].dataPtr();
#if (AMREX_SPACEDIM==3)
const Real* modified_ky = modified_ky_vec[mfi].dataPtr();
#endif
const Real* modified_kz = modified_kz_vec[mfi].dataPtr();
// Extract arrays for the coefficients
Array4<Real> C = C_coef[mfi].array();
Array4<Real> S_ck = S_ck_coef[mfi].array();
Array4<Real> inv_k2 = inv_k2_coef[mfi].array();
// Loop over indices within one box
ParallelFor(bx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
{
const Real kx = modified_kx[i];
#if (AMREX_SPACEDIM==3)
const Real ky = modified_ky[j];
const Real kz = modified_kz[k];
#else
constexpr Real ky = 0._rt;
const Real kz = modified_kz[j];
#endif
// Calculate norm of vector
const Real k_norm = std::sqrt(kx*kx + ky*ky + kz*kz);
const Real k2 = k_norm * k_norm;
// Calculate coefficients
constexpr Real c = PhysConst::c;
// Coefficients for k_norm = 0 do not need to be set
if (k_norm != 0._rt) {
C(i,j,k) = std::cos(c * k_norm * dt);
S_ck(i,j,k) = std::sin(c * k_norm * dt) / (c * k_norm);
inv_k2(i,j,k) = 1._rt / k2;
}
});
}
}
void
PMLPsatdAlgorithm::CurrentCorrection (const int /*lev*/,
SpectralFieldData& /*field_data*/,
std::array<std::unique_ptr<amrex::MultiFab>,3>& /*current*/,
const std::unique_ptr<amrex::MultiFab>& /*rho*/)
{
amrex::Abort("Current correction not implemented for PML PSATD");
}
void
PMLPsatdAlgorithm::VayDeposition (const int /*lev*/,
SpectralFieldData& /*field_data*/,
std::array<std::unique_ptr<amrex::MultiFab>,3>& /*current*/)
{
amrex::Abort("Vay deposition not implemented for PML PSATD");
}
#endif // WARPX_USE_PSATD
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