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Diffstat (limited to 'Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmRZ.cpp')
| -rw-r--r-- | Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmRZ.cpp | 198 |
1 files changed, 198 insertions, 0 deletions
diff --git a/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmRZ.cpp b/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmRZ.cpp new file mode 100644 index 000000000..6ec4c523a --- /dev/null +++ b/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmRZ.cpp @@ -0,0 +1,198 @@ +/* Copyright 2019-2020 David Grote + * + * This file is part of WarpX. + * + * License: BSD-3-Clause-LBNL + */ +#include "PsatdAlgorithmRZ.H" +#include "Utils/WarpXConst.H" + +#include <cmath> + +using amrex::operator""_rt; + + +/* \brief Initialize coefficients for the update equation */ +PsatdAlgorithmRZ::PsatdAlgorithmRZ (SpectralKSpaceRZ const & spectral_kspace, + amrex::DistributionMapping const & dm, + int const n_rz_azimuthal_modes, int const norder_z, + bool const nodal, amrex::Real const dt_step) + // Initialize members of base class + : SpectralBaseAlgorithmRZ(spectral_kspace, dm, + norder_z, nodal), + dt(dt_step) +{ + + // Allocate the arrays of coefficients + amrex::BoxArray const & ba = spectral_kspace.spectralspace_ba; + C_coef = SpectralCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + S_ck_coef = SpectralCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + X1_coef = SpectralCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + X2_coef = SpectralCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + X3_coef = SpectralCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + + coefficients_initialized = false; +} + +/* Advance the E and B field in spectral space (stored in `f`) + * over one time step */ +void +PsatdAlgorithmRZ::pushSpectralFields(SpectralFieldDataRZ & f) +{ + + if (not coefficients_initialized) { + // This is called from here since it needs the kr values + // which can be obtained from the SpectralFieldDataRZ + InitializeSpectralCoefficients(f); + coefficients_initialized = true; + } + + // Loop over boxes + for (amrex::MFIter mfi(f.fields); mfi.isValid(); ++mfi){ + + amrex::Box const & bx = f.fields[mfi].box(); + + // Extract arrays for the fields to be updated + amrex::Array4<Complex> const& fields = f.fields[mfi].array(); + // Extract arrays for the coefficients + amrex::Array4<const amrex::Real> const& C_arr = C_coef[mfi].array(); + amrex::Array4<const amrex::Real> const& S_ck_arr = S_ck_coef[mfi].array(); + amrex::Array4<const amrex::Real> const& X1_arr = X1_coef[mfi].array(); + amrex::Array4<const amrex::Real> const& X2_arr = X2_coef[mfi].array(); + amrex::Array4<const amrex::Real> const& X3_arr = X3_coef[mfi].array(); + + // Extract pointers for the k vectors + auto const & kr_modes = f.getKrArray(mfi); + amrex::Real const* kr_arr = kr_modes.dataPtr(); + amrex::Real const* modified_kz_arr = modified_kz_vec[mfi].dataPtr(); + int const nr = bx.length(0); + + // Loop over indices within one box + // Note that k = 0 + int const modes = f.n_rz_azimuthal_modes; + amrex::ParallelFor(bx, modes, + [=] AMREX_GPU_DEVICE(int i, int j, int k, int mode) noexcept + { + + // All of the fields of each mode are grouped together + using Idx = SpectralFieldIndex; + auto const Ep_m = Idx::Ex + Idx::n_fields*mode; + auto const Em_m = Idx::Ey + Idx::n_fields*mode; + auto const Ez_m = Idx::Ez + Idx::n_fields*mode; + auto const Bp_m = Idx::Bx + Idx::n_fields*mode; + auto const Bm_m = Idx::By + Idx::n_fields*mode; + auto const Bz_m = Idx::Bz + Idx::n_fields*mode; + auto const Jp_m = Idx::Jx + Idx::n_fields*mode; + auto const Jm_m = Idx::Jy + Idx::n_fields*mode; + auto const Jz_m = Idx::Jz + Idx::n_fields*mode; + auto const rho_old_m = Idx::rho_old + Idx::n_fields*mode; + auto const rho_new_m = Idx::rho_new + Idx::n_fields*mode; + + // Record old values of the fields to be updated + Complex const Ep_old = fields(i,j,k,Ep_m); + Complex const Em_old = fields(i,j,k,Em_m); + Complex const Ez_old = fields(i,j,k,Ez_m); + Complex const Bp_old = fields(i,j,k,Bp_m); + Complex const Bm_old = fields(i,j,k,Bm_m); + Complex const Bz_old = fields(i,j,k,Bz_m); + // Shortcut for the values of J and rho + Complex const Jp = fields(i,j,k,Jp_m); + Complex const Jm = fields(i,j,k,Jm_m); + Complex const Jz = fields(i,j,k,Jz_m); + Complex const rho_old = fields(i,j,k,rho_old_m); + Complex const rho_new = fields(i,j,k,rho_new_m); + + // k vector values, and coefficients + // The k values for each mode are grouped together + int const ir = i + nr*mode; + amrex::Real const kr = kr_arr[ir]; + amrex::Real const kz = modified_kz_arr[j]; + + constexpr amrex::Real c2 = PhysConst::c*PhysConst::c; + constexpr amrex::Real inv_ep0 = 1._rt/PhysConst::ep0; + Complex const I = Complex{0._rt,1._rt}; + amrex::Real const C = C_arr(i,j,k,mode); + amrex::Real const S_ck = S_ck_arr(i,j,k,mode); + amrex::Real const X1 = X1_arr(i,j,k,mode); + amrex::Real const X2 = X2_arr(i,j,k,mode); + amrex::Real const X3 = X3_arr(i,j,k,mode); + + // Update E (see WarpX online documentation: theory section) + fields(i,j,k,Ep_m) = C*Ep_old + + S_ck*(-c2*I*kr/2._rt*Bz_old + c2*kz*Bp_old - inv_ep0*Jp) + + kr*(X2*rho_new - X3*rho_old); + fields(i,j,k,Em_m) = C*Em_old + + S_ck*(-c2*I*kr/2._rt*Bz_old - c2*kz*Bm_old - inv_ep0*Jm) + - kr*(X2*rho_new - X3*rho_old); + fields(i,j,k,Ez_m) = C*Ez_old + + S_ck*(c2*I*kr*Bp_old + c2*I*kr*Bm_old - inv_ep0*Jz) + - I*kz*(X2*rho_new - X3*rho_old); + // Update B (see WarpX online documentation: theory section) + fields(i,j,k,Bp_m) = C*Bp_old + - S_ck*(-I*kr/2._rt*Ez_old + kz*Ep_old) + + X1*(-I*kr/2._rt*Jz + kz*Jp); + fields(i,j,k,Bm_m) = C*Bm_old + - S_ck*(-I*kr/2._rt*Ez_old - kz*Em_old) + + X1*(-I*kr/2._rt*Jz - kz*Jm); + fields(i,j,k,Bz_m) = C*Bz_old + - S_ck*I*(kr*Ep_old + kr*Em_old) + + X1*I*(kr*Jp + kr*Jm); + }); + } +}; + +void PsatdAlgorithmRZ::InitializeSpectralCoefficients (SpectralFieldDataRZ const & f) +{ + + // Fill them with the right values: + // Loop over boxes and allocate the corresponding coefficients + // for each box owned by the local MPI proc + for (amrex::MFIter mfi(f.fields); mfi.isValid(); ++mfi){ + + amrex::Box const & bx = f.fields[mfi].box(); + + // Extract pointers for the k vectors + amrex::Real const* const modified_kz = modified_kz_vec[mfi].dataPtr(); + + // Extract arrays for the coefficients + amrex::Array4<amrex::Real> const& C = C_coef[mfi].array(); + amrex::Array4<amrex::Real> const& S_ck = S_ck_coef[mfi].array(); + amrex::Array4<amrex::Real> const& X1 = X1_coef[mfi].array(); + amrex::Array4<amrex::Real> const& X2 = X2_coef[mfi].array(); + amrex::Array4<amrex::Real> const& X3 = X3_coef[mfi].array(); + + auto const & kr_modes = f.getKrArray(mfi); + amrex::Real const* kr_arr = kr_modes.dataPtr(); + int const nr = bx.length(0); + amrex::Real const dt_temp = dt; + + // Loop over indices within one box + int const modes = f.n_rz_azimuthal_modes; + amrex::ParallelFor(bx, modes, + [=] AMREX_GPU_DEVICE(int i, int j, int k, int mode) noexcept + { + // Calculate norm of vector + int const ir = i + nr*mode; + amrex::Real const kr = kr_arr[ir]; + amrex::Real const kz = modified_kz[j]; + amrex::Real const k_norm = std::sqrt(kr*kr + kz*kz); + + // Calculate coefficients + constexpr amrex::Real c = PhysConst::c; + constexpr amrex::Real ep0 = PhysConst::ep0; + if (k_norm != 0){ + C(i,j,k,mode) = std::cos(c*k_norm*dt_temp); + S_ck(i,j,k,mode) = std::sin(c*k_norm*dt_temp)/(c*k_norm); + X1(i,j,k,mode) = (1._rt - C(i,j,k,mode))/(ep0 * c*c * k_norm*k_norm); + X2(i,j,k,mode) = (1._rt - S_ck(i,j,k,mode)/dt_temp)/(ep0 * k_norm*k_norm); + X3(i,j,k,mode) = (C(i,j,k,mode) - S_ck(i,j,k,mode)/dt_temp)/(ep0 * k_norm*k_norm); + } else { // Handle k_norm = 0, by using the analytical limit + C(i,j,k,mode) = 1._rt; + S_ck(i,j,k,mode) = dt_temp; + X1(i,j,k,mode) = 0.5_rt * dt_temp*dt_temp / ep0; + X2(i,j,k,mode) = c*c * dt_temp*dt_temp / (6._rt*ep0); + X3(i,j,k,mode) = - c*c * dt_temp*dt_temp / (3._rt*ep0); + } + }); + } +} |