/* Copyright 2019-2020 David Grote * * This file is part of WarpX. * * License: BSD-3-Clause-LBNL */ #include "PsatdAlgorithmRZ.H" #include "Utils/WarpXConst.H" #include "Utils/WarpXProfilerWrapper.H" #include "WarpX.H" #include using amrex::operator""_rt; /* \brief Initialize coefficients for the update equation */ PsatdAlgorithmRZ::PsatdAlgorithmRZ (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, amrex::Real const dt, bool const update_with_rho, const bool time_averaging, const bool J_linear_in_time, const bool dive_cleaning, const bool divb_cleaning) // Initialize members of base class : SpectralBaseAlgorithmRZ(spectral_kspace, dm, spectral_index, norder_z, nodal), m_spectral_index(spectral_index), m_dt(dt), m_update_with_rho(update_with_rho), m_time_averaging(time_averaging), m_J_linear_in_time(J_linear_in_time), m_dive_cleaning(dive_cleaning), m_divb_cleaning(divb_cleaning) { // 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 = SpectralRealCoefficients(ba, dm, n_rz_azimuthal_modes, 0); X2_coef = SpectralRealCoefficients(ba, dm, n_rz_azimuthal_modes, 0); X3_coef = SpectralRealCoefficients(ba, dm, n_rz_azimuthal_modes, 0); coefficients_initialized = false; // TODO Implement time averaging and remove this amrex::ignore_unused(m_time_averaging); } /* Advance the E and B field in spectral space (stored in `f`) * over one time step */ void PsatdAlgorithmRZ::pushSpectralFields(SpectralFieldDataRZ & f) { bool const update_with_rho = m_update_with_rho; const bool J_linear_in_time = m_J_linear_in_time; const bool dive_cleaning = m_dive_cleaning; const bool divb_cleaning = m_divb_cleaning; 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 const& fields = f.fields[mfi].array(); // Extract arrays for the coefficients amrex::Array4 const& C_arr = C_coef[mfi].array(); amrex::Array4 const& S_ck_arr = S_ck_coef[mfi].array(); amrex::Array4 const& X1_arr = X1_coef[mfi].array(); amrex::Array4 const& X2_arr = X2_coef[mfi].array(); amrex::Array4 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); amrex::Real const dt = m_dt; // 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 int const Ep_m = Idx.Ex + Idx.n_fields*mode; int const Em_m = Idx.Ey + Idx.n_fields*mode; int const Ez_m = Idx.Ez + Idx.n_fields*mode; int const Bp_m = Idx.Bx + Idx.n_fields*mode; int const Bm_m = Idx.By + Idx.n_fields*mode; int const Bz_m = Idx.Bz + Idx.n_fields*mode; int const Jp_m = Idx.Jx + Idx.n_fields*mode; int const Jm_m = Idx.Jy + Idx.n_fields*mode; int const Jz_m = Idx.Jz + Idx.n_fields*mode; int const rho_old_m = Idx.rho_old + Idx.n_fields*mode; int 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); Complex rho_diff; if (update_with_rho) { rho_diff = X2*rho_new - 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; rho_diff = (X2 - X3)*PhysConst::ep0*divE - X2*dt*divJ; } // 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) + 0.5_rt*kr*rho_diff; 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) - 0.5_rt*kr*rho_diff; 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*rho_diff; // 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); int F_m; Complex F_old; if (dive_cleaning) { F_m = Idx.F + Idx.n_fields*mode; F_old = fields(i,j,k,F_m); } int G_m; Complex G_old; if (divb_cleaning) { G_m = Idx.G + Idx.n_fields*mode; G_old = fields(i,j,k,G_m); } if (J_linear_in_time) { const int Jp_m_new = Idx.Jx_new + Idx.n_fields*mode; const int Jm_m_new = Idx.Jy_new + Idx.n_fields*mode; const int Jz_m_new = Idx.Jz_new + Idx.n_fields*mode; const Complex Jp_new = fields(i,j,k,Jp_m_new); const Complex Jm_new = fields(i,j,k,Jm_m_new); const Complex Jz_new = fields(i,j,k,Jz_m_new); fields(i,j,k,Ep_m) += -X1 * (Jp_new - Jp) / dt; fields(i,j,k,Em_m) += -X1 * (Jm_new - Jm) / dt; fields(i,j,k,Ez_m) += -X1 * (Jz_new - Jz) / dt; fields(i,j,k,Bp_m) += X2/c2 * (kz * (Jp_new - Jp) - I * kr * 0.5_rt * (Jz_new - Jz)); fields(i,j,k,Bm_m) += -X2/c2 * (kz * (Jm_new - Jm) + I * kr * 0.5_rt * (Jz_new - Jz)); fields(i,j,k,Bz_m) += I * X2/c2 * (kr * (Jp_new - Jp) + kr * (Jm_new - Jm)); if (dive_cleaning) { const Complex k_dot_J = -I * (kr * (Jp - Jm) + I * kz * Jz); const Complex k_dot_dJ = -I * (kr * ((Jp_new - Jp) - (Jm_new - Jm)) + I * kz * (Jz_new - Jz)); const Complex k_dot_E = -I * (kr * (Ep_old - Em_old) + I * kz * Ez_old); fields(i,j,k,Ep_m) += -c2 * kr * 0.5_rt * S_ck * F_old; fields(i,j,k,Em_m) += c2 * kr * 0.5_rt * S_ck * F_old; fields(i,j,k,Ez_m) += I * c2 * kz * S_ck * F_old; fields(i,j,k,F_m) = C * F_old + S_ck * (I * k_dot_E - inv_ep0 * rho_old) - X1 * ((rho_new - rho_old) / dt + I * k_dot_J) - I * X2/c2 * k_dot_dJ; } if (divb_cleaning) { const Complex k_dot_B = -I * (kr * (Bp_old - Bm_old) + I * kz * Bz_old); fields(i,j,k,Bp_m) += -c2 * kr * 0.5_rt * S_ck * G_old; fields(i,j,k,Bm_m) += c2 * kr * 0.5_rt * S_ck * G_old; fields(i,j,k,Bz_m) += I * c2 * kz * S_ck * G_old; fields(i,j,k,G_m) = C * G_old + I * S_ck * k_dot_B; } } }); } } 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 const& C = C_coef[mfi].array(); amrex::Array4 const& S_ck = S_ck_coef[mfi].array(); amrex::Array4 const& X1 = X1_coef[mfi].array(); amrex::Array4 const& X2 = X2_coef[mfi].array(); amrex::Array4 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 = 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 { // 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); S_ck(i,j,k,mode) = std::sin(c*k_norm*dt)/(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)/(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); } 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); } }); } } void PsatdAlgorithmRZ::CurrentCorrection (const int lev, SpectralFieldDataRZ& field_data, std::array,3>& current, const std::unique_ptr& rho) { // Profiling WARPX_PROFILE( "PsatdAlgorithmRZ::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 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 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 F = - ((rho_new - rho_old)/dt + 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 PsatdAlgorithmRZ::VayDeposition (const int /* lev */, SpectralFieldDataRZ& /*field_data*/, std::array,3>& /*current*/) { amrex::Abort("Vay deposition not implemented in RZ geometry"); }