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diff --git a/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmGalileanRZ.cpp b/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmGalileanRZ.cpp new file mode 100644 index 000000000..2faf48c04 --- /dev/null +++ b/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithmGalileanRZ.cpp @@ -0,0 +1,385 @@ +/* Copyright 2019-2020 David Grote + * + * This file is part of WarpX. + * + * License: BSD-3-Clause-LBNL + */ +#include "PsatdAlgorithmGalileanRZ.H" +#include "Utils/WarpXConst.H" +#include "Utils/WarpXProfilerWrapper.H" +#include "WarpX.H" + +#include <cmath> + +using namespace amrex::literals; + + +/* \brief Initialize coefficients for the update equation */ +PsatdAlgorithmGalileanRZ::PsatdAlgorithmGalileanRZ (SpectralKSpaceRZ const & spectral_kspace, + amrex::DistributionMapping const & dm, + const SpectralFieldIndex& spectral_index, + int const n_rz_azimuthal_modes, int const norder_z, + bool const nodal, + const amrex::Vector<amrex::Real>& v_galilean, + amrex::Real const dt, + bool const update_with_rho) + // Initialize members of base class + : SpectralBaseAlgorithmRZ(spectral_kspace, dm, spectral_index, norder_z, nodal), + m_spectral_index(spectral_index), + m_dt(dt), + m_v_galilean(v_galilean), + m_update_with_rho(update_with_rho) +{ + + // Allocate the arrays of coefficients + amrex::BoxArray const & ba = spectral_kspace.spectralspace_ba; + C_coef = SpectralRealCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + S_ck_coef = SpectralRealCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + X1_coef = SpectralComplexCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + X2_coef = SpectralComplexCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + X3_coef = SpectralComplexCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + X4_coef = SpectralComplexCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + Theta2_coef = SpectralComplexCoefficients(ba, dm, n_rz_azimuthal_modes, 0); + T_rho_coef = SpectralComplexCoefficients(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 + * The algorithm is described in https://doi.org/10.1103/PhysRevE.94.053305 + * */ +void +PsatdAlgorithmGalileanRZ::pushSpectralFields (SpectralFieldDataRZ & f) +{ + + bool const update_with_rho = m_update_with_rho; + + 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; + } + + const SpectralFieldIndex& Idx = m_spectral_index; + + // 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 Complex> const& X1_arr = X1_coef[mfi].array(); + amrex::Array4<const Complex> const& X2_arr = X2_coef[mfi].array(); + amrex::Array4<const Complex> const& X3_arr = X3_coef[mfi].array(); + amrex::Array4<const Complex> const& X4_arr = X4_coef[mfi].array(); + amrex::Array4<const Complex> const& Theta2_arr = Theta2_coef[mfi].array(); + amrex::Array4<const Complex> const& T_rho_arr = T_rho_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 + 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; + 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); + Complex const X1 = X1_arr(i,j,k,mode); + Complex const X2 = X2_arr(i,j,k,mode); + Complex const X3 = X3_arr(i,j,k,mode); + Complex const X4 = X4_arr(i,j,k,mode); + Complex const T2 = Theta2_arr(i,j,k,mode); + Complex const T_rho = T_rho_arr(i,j,k,mode); + + Complex rho_diff; + if (update_with_rho) { + rho_diff = X2*rho_new - T2*X3*rho_old; + } else { + Complex const divE = kr*(Ep_old - Em_old) + I*kz*Ez_old; + Complex const divJ = kr*(Jp - Jm) + I*kz*Jz; + + auto const myeps0 = PhysConst::ep0; // temporary for NVCC + rho_diff = T2*(X2 - X3)*myeps0*divE + T_rho*X2*divJ; + } + + // Update E (see WarpX online documentation: theory section) + fields(i,j,k,Ep_m) = T2*C*Ep_old + + T2*S_ck*(-c2*I*kr/2._rt*Bz_old + c2*kz*Bp_old) + + X4*Jp + 0.5_rt*kr*rho_diff; + fields(i,j,k,Em_m) = T2*C*Em_old + + T2*S_ck*(-c2*I*kr/2._rt*Bz_old - c2*kz*Bm_old) + + X4*Jm - 0.5_rt*kr*rho_diff; + fields(i,j,k,Ez_m) = T2*C*Ez_old + + T2*S_ck*(c2*I*kr*Bp_old + c2*I*kr*Bm_old) + + X4*Jz - I*kz*rho_diff; + // Update B (see WarpX online documentation: theory section) + // Note: here X1 is T2*x1/(ep0*c*c*k_norm*k_norm), where + // x1 has the same definition as in the original paper + fields(i,j,k,Bp_m) = T2*C*Bp_old + - T2*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) = T2*C*Bm_old + - T2*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) = T2*C*Bz_old + - T2*S_ck*I*(kr*Ep_old + kr*Em_old) + + X1*I*(kr*Jp + kr*Jm); + }); + } +} + +void PsatdAlgorithmGalileanRZ::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<Complex> const& X1 = X1_coef[mfi].array(); + amrex::Array4<Complex> const& X2 = X2_coef[mfi].array(); + amrex::Array4<Complex> const& X3 = X3_coef[mfi].array(); + amrex::Array4<Complex> const& X4 = X4_coef[mfi].array(); + amrex::Array4<Complex> const& Theta2 = Theta2_coef[mfi].array(); + amrex::Array4<Complex> const& T_rho = T_rho_coef[mfi].array(); + + // Extract real (for portability on GPU) + amrex::Real vz = m_v_galilean[2]; + + 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 = m_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 + { + constexpr amrex::Real c = PhysConst::c; + constexpr amrex::Real ep0 = PhysConst::ep0; + Complex const I = Complex{0._rt,1._rt}; + + // 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 + if (k_norm != 0._rt){ + + C(i,j,k,mode) = std::cos(c*k_norm*dt); + S_ck(i,j,k,mode) = std::sin(c*k_norm*dt)/(c*k_norm); + + // Calculate dot product with galilean velocity + amrex::Real const kv = kz*vz; + + amrex::Real const nu = kv/(k_norm*c); + Complex const theta = amrex::exp( 0.5_rt*I*kv*dt ); + Complex const theta_star = amrex::exp( -0.5_rt*I*kv*dt ); + Complex const e_theta = amrex::exp( I*c*k_norm*dt ); + + Theta2(i,j,k,mode) = theta*theta; + + if (kz == 0._rt) { + T_rho(i,j,k,mode) = -dt; + } else { + T_rho(i,j,k,mode) = (1._rt - theta*theta)/(I*kz*vz); + } + + if ( (nu != 1._rt) && (nu != 0._rt) ) { + + // Note: the coefficients X1, X2, X do not correspond + // exactly to the original Galilean paper, but the + // update equation have been modified accordingly so that + // the expressions below (with the update equations) + // are mathematically equivalent to those of the paper. + Complex x1 = 1._rt/(1._rt-nu*nu) * + (theta_star - C(i,j,k,mode)*theta + I*kv*S_ck(i,j,k,mode)*theta); + // x1, above, is identical to the original paper + X1(i,j,k,mode) = theta*x1/(ep0*c*c*k_norm*k_norm); + // The difference betwen X2 and X3 below, and those + // from the original paper is the factor ep0*k_norm*k_norm + X2(i,j,k,mode) = (x1 - theta*(1._rt - C(i,j,k,mode))) + /(theta_star-theta)/(ep0*k_norm*k_norm); + X3(i,j,k,mode) = (x1 - theta_star*(1._rt - C(i,j,k,mode))) + /(theta_star-theta)/(ep0*k_norm*k_norm); + X4(i,j,k,mode) = I*kv*X1(i,j,k,mode) - theta*theta*S_ck(i,j,k,mode)/ep0; + + } else if (nu == 0._rt) { + + 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)/(ep0 * k_norm*k_norm); + X3(i,j,k,mode) = (C(i,j,k,mode) - S_ck(i,j,k,mode)/dt)/(ep0 * k_norm*k_norm); + X4(i,j,k,mode) = -S_ck(i,j,k,mode)/ep0; + + } else if ( nu == 1._rt) { + X1(i,j,k,mode) = (1._rt - e_theta*e_theta + 2._rt*I*c*k_norm*dt) / (4._rt*c*c*ep0*k_norm*k_norm); + X2(i,j,k,mode) = (3._rt - 4._rt*e_theta + e_theta*e_theta + 2._rt*I*c*k_norm*dt) / (4._rt*ep0*k_norm*k_norm*(1._rt - e_theta)); + X3(i,j,k,mode) = (3._rt - 2._rt/e_theta - 2._rt*e_theta + e_theta*e_theta - 2._rt*I*c*k_norm*dt) / (4._rt*ep0*(e_theta - 1._rt)*k_norm*k_norm); + X4(i,j,k,mode) = I*(-1._rt + e_theta*e_theta + 2._rt*I*c*k_norm*dt) / (4._rt*ep0*c*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; + X1(i,j,k,mode) = 0.5_rt * dt*dt / ep0; + X2(i,j,k,mode) = c*c * dt*dt / (6._rt*ep0); + X3(i,j,k,mode) = - c*c * dt*dt / (3._rt*ep0); + X4(i,j,k,mode) = -dt/ep0; + Theta2(i,j,k,mode) = 1._rt; + } + }); + } +} + +void +PsatdAlgorithmGalileanRZ::CurrentCorrection (const int lev, + SpectralFieldDataRZ& field_data, + std::array<std::unique_ptr<amrex::MultiFab>,3>& current, + const std::unique_ptr<amrex::MultiFab>& rho ) +{ + // Profiling + WARPX_PROFILE( "PsatdAlgorithmGalileanRZ::CurrentCorrection" ); + + const SpectralFieldIndex& Idx = m_spectral_index; + + // Forward Fourier transform of J and rho + field_data.ForwardTransform( lev, *current[0], Idx.Jx, + *current[1], Idx.Jy); + field_data.ForwardTransform( lev, *current[2], Idx.Jz, 0); + field_data.ForwardTransform( lev, *rho, Idx.rho_old, 0 ); + field_data.ForwardTransform( lev, *rho, Idx.rho_new, 1 ); + + // Loop over boxes + for (amrex::MFIter mfi(field_data.fields); mfi.isValid(); ++mfi){ + + amrex::Box const & bx = field_data.fields[mfi].box(); + + // Extract arrays for the fields to be updated + amrex::Array4<Complex> fields = field_data.fields[mfi].array(); + + // Extract pointers for the k vectors + auto const & kr_modes = field_data.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); + + // Local copy of member variables before GPU loop + amrex::Real vz = m_v_galilean[2]; + amrex::Real const dt = m_dt; + + // Loop over indices within one box + int const modes = field_data.n_rz_azimuthal_modes; + 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 + 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; + + // Shortcuts 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]; + amrex::Real const k_norm2 = kr*kr + kz*kz; + + constexpr Complex I = Complex{0._rt,1._rt}; + + // Correct J + if ( k_norm2 != 0._rt ) + { + Complex const theta2 = amrex::exp(I*kz*vz*dt); + Complex const inv_1_T2 = 1._rt/(kz*vz == 0._rt ? 1._rt : 1._rt - theta2); + Complex const j_corr_coef = (kz == 0._rt ? 1._rt/dt : -I*kz*vz*inv_1_T2); + Complex const F = - (j_corr_coef*(rho_new - rho_old*theta2) + I*kz*Jz + kr*(Jp - Jm))/k_norm2; + + fields(i,j,k,Jp_m) += +0.5_rt*kr*F; + fields(i,j,k,Jm_m) += -0.5_rt*kr*F; + fields(i,j,k,Jz_m) += -I*kz*F; + } + }); + } + + // Backward Fourier transform of J + field_data.BackwardTransform( lev, + *current[0], Idx.Jx, + *current[1], Idx.Jy); + field_data.BackwardTransform( lev, *current[2], Idx.Jz, 0 ); + +} + +void +PsatdAlgorithmGalileanRZ::VayDeposition (const int /*lev*/, + SpectralFieldDataRZ& /*field_data*/, + std::array<std::unique_ptr<amrex::MultiFab>,3>& /*current*/) +{ + amrex::Abort("Vay deposition not implemented in RZ geometry"); +} |