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Diffstat (limited to 'Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmJLinearInTime.cpp')
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diff --git a/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmJLinearInTime.cpp b/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmJLinearInTime.cpp new file mode 100644 index 000000000..5db997612 --- /dev/null +++ b/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmJLinearInTime.cpp @@ -0,0 +1,453 @@ +/* Copyright 2019 + * + * This file is part of WarpX. + * + * License: BSD-3-Clause-LBNL + */ +#include "PsatdAlgorithmJLinearInTime.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; + +PsatdAlgorithmJLinearInTime::PsatdAlgorithmJLinearInTime( + 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 bool nodal, + const amrex::IntVect& fill_guards, + const amrex::Real dt, + const bool time_averaging, + const bool dive_cleaning, + const bool divb_cleaning) + // Initializer list + : SpectralBaseAlgorithm(spectral_kspace, dm, spectral_index, norder_x, norder_y, norder_z, nodal, fill_guards), + m_spectral_index(spectral_index), + m_dt(dt), + m_time_averaging(time_averaging), + m_dive_cleaning(dive_cleaning), + m_divb_cleaning(divb_cleaning) +{ + const amrex::BoxArray& ba = spectral_kspace.spectralspace_ba; + + // Always allocate these coefficients + C_coef = SpectralRealCoefficients(ba, dm, 1, 0); + S_ck_coef = SpectralRealCoefficients(ba, dm, 1, 0); + X1_coef = SpectralRealCoefficients(ba, dm, 1, 0); + X2_coef = SpectralRealCoefficients(ba, dm, 1, 0); + X3_coef = SpectralRealCoefficients(ba, dm, 1, 0); + + InitializeSpectralCoefficients(spectral_kspace, dm, dt); + + // Allocate these coefficients only with time averaging + if (time_averaging) + { + X5_coef = SpectralRealCoefficients(ba, dm, 1, 0); + X6_coef = SpectralRealCoefficients(ba, dm, 1, 0); + InitializeSpectralCoefficientsAveraging(spectral_kspace, dm, dt); + } +} + +void +PsatdAlgorithmJLinearInTime::pushSpectralFields (SpectralFieldData& f) const +{ + const bool time_averaging = m_time_averaging; + const bool dive_cleaning = m_dive_cleaning; + const bool divb_cleaning = m_divb_cleaning; + + const amrex::Real dt = m_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(); + + // These coefficients are always allocated + amrex::Array4<const amrex::Real> C_arr = C_coef[mfi].array(); + amrex::Array4<const amrex::Real> S_ck_arr = S_ck_coef[mfi].array(); + amrex::Array4<const amrex::Real> X1_arr = X1_coef[mfi].array(); + amrex::Array4<const amrex::Real> X2_arr = X2_coef[mfi].array(); + amrex::Array4<const amrex::Real> X3_arr = X3_coef[mfi].array(); + + amrex::Array4<const amrex::Real> X5_arr; + amrex::Array4<const amrex::Real> X6_arr; + if (time_averaging) + { + X5_arr = X5_coef[mfi].array(); + X6_arr = X6_coef[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_old = fields(i,j,k,Idx.Jx); + const Complex Jy_old = fields(i,j,k,Idx.Jy); + const Complex Jz_old = fields(i,j,k,Idx.Jz); + const Complex Jx_new = fields(i,j,k,Idx.Jx_new); + const Complex Jy_new = fields(i,j,k,Idx.Jy_new); + const Complex Jz_new = fields(i,j,k,Idx.Jz_new); + const Complex rho_old = fields(i,j,k,Idx.rho_old); + const Complex rho_new = fields(i,j,k,Idx.rho_new); + + Complex F_old, G_old; + if (dive_cleaning) F_old = fields(i,j,k,Idx.F); + if (divb_cleaning) G_old = fields(i,j,k,Idx.G); + + // 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 c2 = PhysConst::c * PhysConst::c; + constexpr amrex::Real ep0 = PhysConst::ep0; + constexpr amrex::Real inv_ep0 = 1._rt / PhysConst::ep0; + constexpr Complex I = Complex{0._rt, 1._rt}; + + // These coefficients are initialized in the function InitializeSpectralCoefficients + const amrex::Real C = C_arr(i,j,k); + const amrex::Real S_ck = S_ck_arr(i,j,k); + const amrex::Real X1 = X1_arr(i,j,k); + const amrex::Real X2 = X2_arr(i,j,k); + const amrex::Real X3 = X3_arr(i,j,k); + const amrex::Real X4 = - S_ck / PhysConst::ep0; + + // Update equations for E in the formulation with rho + + fields(i,j,k,Idx.Ex) = C * Ex_old + + I * c2 * S_ck * (ky * Bz_old - kz * By_old) + + X4 * Jx_old - I * (X2 * rho_new - X3 * rho_old) * kx - X1 * (Jx_new - Jx_old) / dt; + + fields(i,j,k,Idx.Ey) = C * Ey_old + + I * c2 * S_ck * (kz * Bx_old - kx * Bz_old) + + X4 * Jy_old - I * (X2 * rho_new - X3 * rho_old) * ky - X1 * (Jy_new - Jy_old) / dt; + + fields(i,j,k,Idx.Ez) = C * Ez_old + + I * c2 * S_ck * (kx * By_old - ky * Bx_old) + + X4 * Jz_old - I * (X2 * rho_new - X3 * rho_old) * kz - X1 * (Jz_new - Jz_old) / dt; + + // Update equations for B + + fields(i,j,k,Idx.Bx) = C * Bx_old + - I * S_ck * (ky * Ez_old - kz * Ey_old) + I * X1 * (ky * Jz_old - kz * Jy_old) + + I * X2/c2 * (ky * (Jz_new - Jz_old) - kz * (Jy_new - Jy_old)); + + fields(i,j,k,Idx.By) = C * By_old + - I * S_ck * (kz * Ex_old - kx * Ez_old) + I * X1 * (kz * Jx_old - kx * Jz_old) + + I * X2/c2 * (kz * (Jx_new - Jx_old) - kx * (Jz_new - Jz_old)); + + fields(i,j,k,Idx.Bz) = C * Bz_old + - I * S_ck * (kx * Ey_old - ky * Ex_old) + I * X1 * (kx * Jy_old - ky * Jx_old) + + I * X2/c2 * (kx * (Jy_new - Jy_old) - ky * (Jx_new - Jx_old)); + + if (dive_cleaning) + { + const Complex k_dot_E = kx * Ex_old + ky * Ey_old + kz * Ez_old; + const Complex k_dot_J = kx * Jx_old + ky * Jy_old + kz * Jz_old; + const Complex k_dot_dJ = kx * (Jx_new - Jx_old) + ky * (Jy_new - Jy_old) + kz * (Jz_new - Jz_old); + + fields(i,j,k,Idx.Ex) += I * c2 * S_ck * F_old * kx; + fields(i,j,k,Idx.Ey) += I * c2 * S_ck * F_old * ky; + fields(i,j,k,Idx.Ez) += I * c2 * S_ck * F_old * kz; + + fields(i,j,k,Idx.F) = C * F_old + S_ck * (I * k_dot_E - rho_old * inv_ep0) + - X1 * ((rho_new - rho_old) / dt + I * k_dot_J) - I * X2/c2 * k_dot_dJ; + } + + if (divb_cleaning) + { + const Complex k_dot_B = kx * Bx_old + ky * By_old + kz * Bz_old; + + fields(i,j,k,Idx.Bx) += I * S_ck * G_old * kx; + fields(i,j,k,Idx.By) += I * S_ck * G_old * ky; + fields(i,j,k,Idx.Bz) += I * S_ck * G_old * kz; + + fields(i,j,k,Idx.G) = C * G_old + I * c2 * S_ck * k_dot_B; + } + + if (time_averaging) + { + const amrex::Real X5 = X5_arr(i,j,k); + const amrex::Real X6 = X6_arr(i,j,k); + + // TODO: Here the code is *accumulating* the average, + // because it is meant to be used with sub-cycling + // maybe this should be made more generic + + fields(i,j,k,Idx.Ex_avg) += S_ck * Ex_old + + I * c2 * ep0 * X1 * (ky * Bz_old - kz * By_old) + + I * X5 * rho_old * kx + I * X6 * rho_new * kx + X3/c2 * Jx_old - X2/c2 * Jx_new; + + fields(i,j,k,Idx.Ey_avg) += S_ck * Ey_old + + I * c2 * ep0 * X1 * (kz * Bx_old - kx * Bz_old) + + I * X5 * rho_old * ky + I * X6 * rho_new * ky + X3/c2 * Jy_old - X2/c2 * Jy_new; + + fields(i,j,k,Idx.Ez_avg) += S_ck * Ez_old + + I * c2 * ep0 * X1 * (kx * By_old - ky * Bx_old) + + I * X5 * rho_old * kz + I * X6 * rho_new * kz + X3/c2 * Jz_old - X2/c2 * Jz_new; + + fields(i,j,k,Idx.Bx_avg) += S_ck * Bx_old + - I * ep0 * X1 * (ky * Ez_old - kz * Ey_old) + - I * X5/c2 * (ky * Jz_old - kz * Jy_old) - I * X6/c2 * (ky * Jz_new - kz * Jy_new); + + fields(i,j,k,Idx.By_avg) += S_ck * By_old + - I * ep0 * X1 * (kz * Ex_old - kx * Ez_old) + - I * X5/c2 * (kz * Jx_old - kx * Jz_old) - I * X6/c2 * (kz * Jx_new - kx * Jz_new); + + fields(i,j,k,Idx.Bz_avg) += S_ck * Bz_old + - I * ep0 * X1 * (kx * Ey_old - ky * Ex_old) + - I * X5/c2 * (kx * Jy_old - ky * Jx_old) - I * X6/c2 * (kx * Jy_new - ky * Jx_new); + + if (dive_cleaning) + { + fields(i,j,k,Idx.Ex_avg) += I * c2 * ep0 * X1 * F_old * kx; + fields(i,j,k,Idx.Ey_avg) += I * c2 * ep0 * X1 * F_old * ky; + fields(i,j,k,Idx.Ez_avg) += I * c2 * ep0 * X1 * F_old * kz; + } + + if (divb_cleaning) + { + fields(i,j,k,Idx.Bx_avg) += I * ep0 * X1 * G_old * kx; + fields(i,j,k,Idx.By_avg) += I * ep0 * X1 * G_old * ky; + fields(i,j,k,Idx.Bz_avg) += I * ep0 * X1 * G_old * kz; + } + } + }); + } +} + +void PsatdAlgorithmJLinearInTime::InitializeSpectralCoefficients ( + const SpectralKSpace& spectral_kspace, + const amrex::DistributionMapping& dm, + const amrex::Real dt) +{ + const amrex::BoxArray& ba = spectral_kspace.spectralspace_ba; + + // Loop over boxes and allocate the corresponding coefficients for each box + for (amrex::MFIter mfi(ba, dm); mfi.isValid(); ++mfi) + { + const amrex::Box& bx = ba[mfi]; + + // Extract pointers for the k vectors + const amrex::Real* kx_s = modified_kx_vec[mfi].dataPtr(); +#if defined(WARPX_DIM_3D) + const amrex::Real* ky_s = modified_ky_vec[mfi].dataPtr(); +#endif + const amrex::Real* kz_s = modified_kz_vec[mfi].dataPtr(); + + // Coefficients always allocated + amrex::Array4<amrex::Real> C = C_coef[mfi].array(); + amrex::Array4<amrex::Real> S_ck = S_ck_coef[mfi].array(); + amrex::Array4<amrex::Real> X1 = X1_coef[mfi].array(); + amrex::Array4<amrex::Real> X2 = X2_coef[mfi].array(); + amrex::Array4<amrex::Real> X3 = X3_coef[mfi].array(); + + // Loop over indices within one box + amrex::ParallelFor(bx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept + { + // Calculate norm of k vector + const amrex::Real knorm_s = std::sqrt( + std::pow(kx_s[i], 2) + +#if defined(WARPX_DIM_3D) + std::pow(ky_s[j], 2) + std::pow(kz_s[k], 2)); +#else + std::pow(kz_s[j], 2)); +#endif + // Physical constants and imaginary unit + constexpr amrex::Real c = PhysConst::c; + constexpr amrex::Real ep0 = PhysConst::ep0; + + const amrex::Real c2 = std::pow(c, 2); + const amrex::Real dt2 = std::pow(dt, 2); + + const amrex::Real om_s = c * knorm_s; + const amrex::Real om2_s = std::pow(om_s, 2); + + // C + C(i,j,k) = std::cos(om_s * dt); + + // S_ck + if (om_s != 0.) + { + S_ck(i,j,k) = std::sin(om_s * dt) / om_s; + } + else // om_s = 0 + { + S_ck(i,j,k) = dt; + } + + // X1 (multiplies i*([k] \times J) in the update equation for update B) + if (om_s != 0.) + { + X1(i,j,k) = (1._rt - C(i,j,k)) / (ep0 * om2_s); + } + else // om_s = 0 + { + X1(i,j,k) = 0.5_rt * dt2 / ep0; + } + + // X2 (multiplies rho_new in the update equation for E) + if (om_s != 0.) + { + X2(i,j,k) = c2 * (dt - S_ck(i,j,k)) / (ep0 * dt * om2_s); + } + else // om_s = 0 + { + X2(i,j,k) = c2 * dt2 / (6._rt * ep0); + } + + // X3 (multiplies rho_old in the update equation for E) + if (om_s != 0.) + { + X3(i,j,k) = c2 * (dt * C(i,j,k) - S_ck(i,j,k)) / (ep0 * dt * om2_s); + } + else // om_s = 0 + { + X3(i,j,k) = - c2 * dt2 / (3._rt * ep0); + } + }); + } +} + +void PsatdAlgorithmJLinearInTime::InitializeSpectralCoefficientsAveraging ( + const SpectralKSpace& spectral_kspace, + const amrex::DistributionMapping& dm, + const amrex::Real dt) +{ + const amrex::BoxArray& ba = spectral_kspace.spectralspace_ba; + + // Loop over boxes and allocate the corresponding coefficients for each box + for (amrex::MFIter mfi(ba, dm); mfi.isValid(); ++mfi) + { + const amrex::Box& bx = ba[mfi]; + + // Extract pointers for the k vectors + const amrex::Real* kx_s = modified_kx_vec[mfi].dataPtr(); +#if defined(WARPX_DIM_3D) + const amrex::Real* ky_s = modified_ky_vec[mfi].dataPtr(); +#endif + const amrex::Real* kz_s = modified_kz_vec[mfi].dataPtr(); + + 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> X5 = X5_coef[mfi].array(); + amrex::Array4<amrex::Real> X6 = X6_coef[mfi].array(); + + // Loop over indices within one box + amrex::ParallelFor(bx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept + { + // Calculate norm of k vector + const amrex::Real knorm_s = std::sqrt( + std::pow(kx_s[i], 2) + +#if defined(WARPX_DIM_3D) + std::pow(ky_s[j], 2) + std::pow(kz_s[k], 2)); +#else + std::pow(kz_s[j], 2)); +#endif + // Physical constants and imaginary unit + constexpr amrex::Real c = PhysConst::c; + constexpr amrex::Real c2 = c*c; + constexpr amrex::Real ep0 = PhysConst::ep0; + + // Auxiliary coefficients + const amrex::Real dt3 = dt * dt * dt; + + const amrex::Real om_s = c * knorm_s; + const amrex::Real om2_s = om_s * om_s; + const amrex::Real om4_s = om2_s * om2_s; + + if (om_s != 0.) + { + X5(i,j,k) = c2 / ep0 * (S_ck(i,j,k) / om2_s - (1._rt - C(i,j,k)) / (om4_s * dt) + - 0.5_rt * dt / om2_s); + } + else + { + X5(i,j,k) = - c2 * dt3 / (8._rt * ep0); + } + + if (om_s != 0.) + { + X6(i,j,k) = c2 / ep0 * ((1._rt - C(i,j,k)) / (om4_s * dt) - 0.5_rt * dt / om2_s); + } + else + { + X6(i,j,k) = - c2 * dt3 / (24._rt * ep0); + } + }); + } +} + +void +PsatdAlgorithmJLinearInTime::CurrentCorrection ( + const int lev, + SpectralFieldData& field_data, + std::array<std::unique_ptr<amrex::MultiFab>,3>& current, + const std::unique_ptr<amrex::MultiFab>& rho) +{ + // Profiling + BL_PROFILE("PsatdAlgorithmJLinearInTime::CurrentCorrection"); + + amrex::ignore_unused(lev, field_data, current, rho); + amrex::Abort("Current correction not implemented for multi-J PSATD algorithm"); +} + +void +PsatdAlgorithmJLinearInTime::VayDeposition ( + const int lev, + SpectralFieldData& field_data, + std::array<std::unique_ptr<amrex::MultiFab>,3>& current) +{ + // Profiling + BL_PROFILE("PsatdAlgorithmJLinearInTime::VayDeposition()"); + + amrex::ignore_unused(lev, field_data, current); + amrex::Abort("Vay deposition not implemented for multi-J PSATD algorithm"); +} + +#endif // WARPX_USE_PSATD |