/* Copyright 2019 * * This file is part of WarpX. * * License: BSD-3-Clause-LBNL */ #include "PsatdAlgorithmJLinearInTime.H" #include "Utils/TextMsg.H" #include "Utils/WarpXConst.H" #include "Utils/WarpX_Complex.H" #include #include #include #include #include #include #include #include #include #include #include #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::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), 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 fields = f.fields[mfi].array(); // These coefficients are always allocated amrex::Array4 C_arr = C_coef[mfi].array(); amrex::Array4 S_ck_arr = S_ck_coef[mfi].array(); amrex::Array4 X1_arr = X1_coef[mfi].array(); amrex::Array4 X2_arr = X2_coef[mfi].array(); amrex::Array4 X3_arr = X3_coef[mfi].array(); amrex::Array4 X5_arr; amrex::Array4 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 C = C_coef[mfi].array(); amrex::Array4 S_ck = S_ck_coef[mfi].array(); amrex::Array4 X1 = X1_coef[mfi].array(); amrex::Array4 X2 = X2_coef[mfi].array(); amrex::Array4 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 C = C_coef[mfi].array(); amrex::Array4 S_ck = S_ck_coef[mfi].array(); amrex::Array4 X5 = X5_coef[mfi].array(); amrex::Array4 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 (SpectralFieldData& field_data) { // Profiling BL_PROFILE("PsatdAlgorithmJLinearInTime::CurrentCorrection"); amrex::ignore_unused(field_data); amrex::Abort(Utils::TextMsg::Err( "Current correction not implemented for multi-J PSATD algorithm")); } void PsatdAlgorithmJLinearInTime::VayDeposition (SpectralFieldData& field_data) { // Profiling BL_PROFILE("PsatdAlgorithmJLinearInTime::VayDeposition()"); amrex::ignore_unused(field_data); amrex::Abort(Utils::TextMsg::Err( "Vay deposition not implemented for multi-J PSATD algorithm")); } #endif // WARPX_USE_PSATD