PSATD: More Options for Time Dependency of J, Rho (#3242)

* Rename PsatdAlgorithm as PsatdAlgorithmJConstantInTime

* Add New Inputs: psatd.J_in_time, psatd.rho_in_time

* Update PSATD Classes

* Fix Bug for FDTD Build

* Fix Warning for RZ PSATD Build

* Fix Multi-J Loop w/ J Constant in Time

* Clean up

* Fix Error Message

* Fix Time of Charge Deposition for Rho Linear

* Add 3D Langmuir CI Tests w/ Multi-J Algo

* Fix Checksums of New CI Tests

* Remove Extra CI Tests (added in #3363)

* Fix CI Tests w/ Multi-J PSATD

* Add Docs for New Input Parameters

* Galilean/Comoving PSATD Not Compatible w/ J Linear

1 files changed, 0 insertions, 897 deletions

diff --git a/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithm.cpp b/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithm.cpp
deleted file mode 100644
index 1cbc27f0b..000000000
--- a/Source/FieldSolver/SpectralSolver/SpectralAlgorithms/PsatdAlgorithm.cpp
+++ /dev/null
@@ -1,897 +0,0 @@
-/* Copyright 2019
- *
- * This file is part of WarpX.
- *
- * License: BSD-3-Clause-LBNL
- */
-#include "PsatdAlgorithm.H"
-
-#include "Utils/TextMsg.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;
-
-PsatdAlgorithm::PsatdAlgorithm(
-    const SpectralKSpace& spectral_kspace,
-    const DistributionMapping& dm,
-    const SpectralFieldIndex& spectral_index,
-    const int norder_x,
-    const int norder_y,
-    const int norder_z,
-    const bool nodal,
-    const amrex::Vector<amrex::Real>& v_galilean,
-    const amrex::Real dt,
-    const bool update_with_rho,
-    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),
-    // Initialize the centered finite-order modified k vectors:
-    // these are computed always with the assumption of centered grids
-    // (argument nodal = true), for both nodal and staggered simulations
-    modified_kx_vec_centered(spectral_kspace.getModifiedKComponent(dm, 0, norder_x, true)),
-#if defined(WARPX_DIM_3D)
-    modified_ky_vec_centered(spectral_kspace.getModifiedKComponent(dm, 1, norder_y, true)),
-    modified_kz_vec_centered(spectral_kspace.getModifiedKComponent(dm, 2, norder_z, true)),
-#else
-    modified_kz_vec_centered(spectral_kspace.getModifiedKComponent(dm, 1, norder_z, true)),
-#endif
-    m_v_galilean(v_galilean),
-    m_dt(dt),
-    m_update_with_rho(update_with_rho),
-    m_time_averaging(time_averaging),
-    m_dive_cleaning(dive_cleaning),
-    m_divb_cleaning(divb_cleaning)
-{
-    const amrex::BoxArray& ba = spectral_kspace.spectralspace_ba;
-
-    m_is_galilean = (v_galilean[0] != 0.) || (v_galilean[1] != 0.) || (v_galilean[2] != 0.);
-
-    // Always allocate these coefficients
-    C_coef = SpectralRealCoefficients(ba, dm, 1, 0);
-    S_ck_coef = SpectralRealCoefficients(ba, dm, 1, 0);
-    X1_coef = SpectralComplexCoefficients(ba, dm, 1, 0);
-    X2_coef = SpectralComplexCoefficients(ba, dm, 1, 0);
-    X3_coef = SpectralComplexCoefficients(ba, dm, 1, 0);
-
-    // Allocate these coefficients only with Galilean PSATD
-    if (m_is_galilean)
-    {
-        X4_coef = SpectralComplexCoefficients(ba, dm, 1, 0);
-        T2_coef = SpectralComplexCoefficients(ba, dm, 1, 0);
-    }
-
-    InitializeSpectralCoefficients(spectral_kspace, dm, dt);
-
-    // Allocate these coefficients only with time averaging
-    if (time_averaging)
-    {
-        Psi1_coef = SpectralComplexCoefficients(ba, dm, 1, 0);
-        Psi2_coef = SpectralComplexCoefficients(ba, dm, 1, 0);
-        Y1_coef = SpectralComplexCoefficients(ba, dm, 1, 0);
-        Y3_coef = SpectralComplexCoefficients(ba, dm, 1, 0);
-        Y2_coef = SpectralComplexCoefficients(ba, dm, 1, 0);
-        Y4_coef = SpectralComplexCoefficients(ba, dm, 1, 0);
-        InitializeSpectralCoefficientsAveraging(spectral_kspace, dm, dt);
-    }
-
-    WARPX_ALWAYS_ASSERT_WITH_MESSAGE(
-        !dive_cleaning || !m_is_galilean,
-        "warpx.do_dive_cleaning = 1 not implemented for Galilean PSATD algorithms"
-    );
-
-    WARPX_ALWAYS_ASSERT_WITH_MESSAGE(
-        !divb_cleaning || !m_is_galilean,
-        "warpx.do_divb_cleaning = 1 not implemented for Galilean PSATD algorithms"
-    );
-
-    WARPX_ALWAYS_ASSERT_WITH_MESSAGE(
-        !time_averaging || update_with_rho,
-        "PSATD: psatd.time_averaging = 1 implemented only with psatd.update_with_rho = 1"
-    );
-}
-
-void
-PsatdAlgorithm::pushSpectralFields (SpectralFieldData& f) const
-{
-    const bool update_with_rho = m_update_with_rho;
-    const bool time_averaging  = m_time_averaging;
-    const bool dive_cleaning   = m_dive_cleaning;
-    const bool divb_cleaning   = m_divb_cleaning;
-    const bool is_galilean     = m_is_galilean;
-
-    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 Complex> X1_arr = X1_coef[mfi].array();
-        amrex::Array4<const Complex> X2_arr = X2_coef[mfi].array();
-        amrex::Array4<const Complex> X3_arr = X3_coef[mfi].array();
-
-        amrex::Array4<const Complex> X4_arr;
-        amrex::Array4<const Complex> T2_arr;
-        if (is_galilean)
-        {
-            X4_arr = X4_coef[mfi].array();
-            T2_arr = T2_coef[mfi].array();
-        }
-
-        // These coefficients are allocated only with averaged Galilean PSATD
-        amrex::Array4<const Complex> Psi1_arr;
-        amrex::Array4<const Complex> Psi2_arr;
-        amrex::Array4<const Complex> Y1_arr;
-        amrex::Array4<const Complex> Y2_arr;
-        amrex::Array4<const Complex> Y3_arr;
-        amrex::Array4<const Complex> Y4_arr;
-
-        if (time_averaging)
-        {
-            Psi1_arr = Psi1_coef[mfi].array();
-            Psi2_arr = Psi2_coef[mfi].array();
-            Y1_arr = Y1_coef[mfi].array();
-            Y2_arr = Y2_coef[mfi].array();
-            Y3_arr = Y3_coef[mfi].array();
-            Y4_arr = Y4_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
-        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 = fields(i,j,k,Idx.Jx);
-            const Complex Jy = fields(i,j,k,Idx.Jy);
-            const Complex Jz = fields(i,j,k,Idx.Jz);
-            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;
-            if (dive_cleaning)
-            {
-                F_old = fields(i,j,k,Idx.F);
-            }
-
-            Complex G_old;
-            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 Real c2 = PhysConst::c * PhysConst::c;
-            constexpr 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 Complex X1 = X1_arr(i,j,k);
-            const Complex X2 = X2_arr(i,j,k);
-            const Complex X3 = X3_arr(i,j,k);
-            const Complex X4 = (is_galilean) ? X4_arr(i,j,k) : - S_ck / PhysConst::ep0;
-            const Complex T2 = (is_galilean) ? T2_arr(i,j,k) : 1.0_rt;
-
-            // Update equations for E in the formulation with rho
-            // T2 = 1 always with standard PSATD (zero Galilean velocity)
-
-            if (update_with_rho)
-            {
-                fields(i,j,k,Idx.Ex) = T2 * C * Ex_old
-                                       + I * c2 * T2 * S_ck * (ky * Bz_old - kz * By_old)
-                                       + X4 * Jx - I * (X2 * rho_new - T2 * X3 * rho_old) * kx;
-
-                fields(i,j,k,Idx.Ey) = T2 * C * Ey_old
-                                       + I * c2 * T2 * S_ck * (kz * Bx_old - kx * Bz_old)
-                                       + X4 * Jy - I * (X2 * rho_new - T2 * X3 * rho_old) * ky;
-
-                fields(i,j,k,Idx.Ez) = T2 * C * Ez_old
-                                       + I * c2 * T2 * S_ck * (kx * By_old - ky * Bx_old)
-                                       + X4 * Jz - I * (X2 * rho_new - T2 * X3 * rho_old) * kz;
-            }
-
-            // Update equations for E in the formulation without rho
-            // T2 = 1 always with standard PSATD (zero Galilean velocity)
-
-            else {
-
-                Complex k_dot_J = kx * Jx + ky * Jy + kz * Jz;
-                Complex k_dot_E = kx * Ex_old + ky * Ey_old + kz * Ez_old;
-
-                fields(i,j,k,Idx.Ex) = T2 * C * Ex_old
-                                       + I * c2 * T2 * S_ck * (ky * Bz_old - kz * By_old)
-                                       + X4 * Jx + X2 * k_dot_E * kx + X3 * k_dot_J * kx;
-
-                fields(i,j,k,Idx.Ey) = T2 * C * Ey_old
-                                       + I * c2 * T2 * S_ck * (kz * Bx_old - kx * Bz_old)
-                                       + X4 * Jy + X2 * k_dot_E * ky + X3 * k_dot_J * ky;
-
-                fields(i,j,k,Idx.Ez) = T2 * C * Ez_old
-                                       + I * c2 * T2 * S_ck * (kx * By_old - ky * Bx_old)
-                                       + X4 * Jz + X2 * k_dot_E * kz + X3 * k_dot_J * kz;
-            }
-
-            // Update equations for B
-            // T2 = 1 always with standard PSATD (zero Galilean velocity)
-
-            fields(i,j,k,Idx.Bx) = T2 * C * Bx_old
-                                   - I * T2 * S_ck * (ky * Ez_old - kz * Ey_old)
-                                   + I * X1 * (ky * Jz - kz * Jy);
-
-            fields(i,j,k,Idx.By) = T2 * C * By_old
-                                   - I * T2 * S_ck * (kz * Ex_old - kx * Ez_old)
-                                   + I * X1 * (kz * Jx - kx * Jz);
-
-            fields(i,j,k,Idx.Bz) = T2 * C * Bz_old
-                                   - I * T2 * S_ck * (kx * Ey_old - ky * Ex_old)
-                                   + I * X1 * (kx * Jy - ky * Jx);
-
-            if (dive_cleaning)
-            {
-                const Complex k_dot_J  = kx * Jx + ky * Jy + kz * Jz;
-                const Complex k_dot_E = kx * Ex_old + ky * Ey_old + kz * Ez_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);
-            }
-
-            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;
-            }
-
-            // Additional update equations for averaged Galilean algorithm
-            if (time_averaging)
-            {
-                // These coefficients are initialized in the function InitializeSpectralCoefficients below
-                const Complex Psi1 = Psi1_arr(i,j,k);
-                const Complex Psi2 = Psi2_arr(i,j,k);
-                const Complex Y1 = Y1_arr(i,j,k);
-                const Complex Y3 = Y3_arr(i,j,k);
-                const Complex Y2 = Y2_arr(i,j,k);
-                const Complex Y4 = Y4_arr(i,j,k);
-
-                fields(i,j,k,Idx.Ex_avg) = Psi1 * Ex_old
-                                           - I * c2 * Psi2 * (ky * Bz_old - kz * By_old)
-                                           + Y4 * Jx + (Y2 * rho_new + Y3 * rho_old) * kx;
-
-                fields(i,j,k,Idx.Ey_avg) = Psi1 * Ey_old
-                                           - I * c2 * Psi2 * (kz * Bx_old - kx * Bz_old)
-                                           + Y4 * Jy + (Y2 * rho_new + Y3 * rho_old) * ky;
-
-                fields(i,j,k,Idx.Ez_avg) = Psi1 * Ez_old
-                                           - I * c2 * Psi2 * (kx * By_old - ky * Bx_old)
-                                           + Y4 * Jz + (Y2 * rho_new + Y3 * rho_old) * kz;
-
-                fields(i,j,k,Idx.Bx_avg) = Psi1 * Bx_old
-                                           + I * Psi2 * (ky * Ez_old - kz * Ey_old)
-                                           + I * Y1 * (ky * Jz - kz * Jy);
-
-                fields(i,j,k,Idx.By_avg) = Psi1 * By_old
-                                           + I * Psi2 * (kz * Ex_old - kx * Ez_old)
-                                           + I * Y1 * (kz * Jx - kx * Jz);
-
-                fields(i,j,k,Idx.Bz_avg) = Psi1 * Bz_old
-                                           + I * Psi2 * (kx * Ey_old - ky * Ex_old)
-                                           + I * Y1 * (kx * Jy - ky * Jx);
-            }
-        });
-    }
-}
-
-void PsatdAlgorithm::InitializeSpectralCoefficients (
-    const SpectralKSpace& spectral_kspace,
-    const amrex::DistributionMapping& dm,
-    const amrex::Real dt)
-{
-    const bool update_with_rho = m_update_with_rho;
-    const bool is_galilean     = m_is_galilean;
-
-    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();
-        const amrex::Real* kx_c = modified_kx_vec_centered[mfi].dataPtr();
-#if defined(WARPX_DIM_3D)
-        const amrex::Real* ky_s = modified_ky_vec[mfi].dataPtr();
-        const amrex::Real* ky_c = modified_ky_vec_centered[mfi].dataPtr();
-#endif
-        const amrex::Real* kz_s = modified_kz_vec[mfi].dataPtr();
-        const amrex::Real* kz_c = modified_kz_vec_centered[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<Complex> X1 = X1_coef[mfi].array();
-        amrex::Array4<Complex> X2 = X2_coef[mfi].array();
-        amrex::Array4<Complex> X3 = X3_coef[mfi].array();
-
-        amrex::Array4<Complex> X4;
-        amrex::Array4<Complex> T2;
-        if (is_galilean)
-        {
-            X4 = X4_coef[mfi].array();
-            T2 = T2_coef[mfi].array();
-        }
-
-        // Extract Galilean velocity
-        amrex::Real vg_x = m_v_galilean[0];
-#if defined(WARPX_DIM_3D)
-        amrex::Real vg_y = m_v_galilean[1];
-#endif
-        amrex::Real vg_z = m_v_galilean[2];
-
-        // Loop over indices within one box
-        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;
-            constexpr Complex I = Complex{0._rt, 1._rt};
-
-            const amrex::Real c2 = std::pow(c, 2);
-            const amrex::Real dt2 = std::pow(dt, 2);
-            const amrex::Real dt3 = std::pow(dt, 3);
-
-            // Calculate the dot product of the k vector with the Galilean velocity.
-            // This has to be computed always with the centered (that is, nodal) finite-order
-            // modified k vectors, to work correctly for both nodal and staggered simulations.
-            // w_c = 0 always with standard PSATD (zero Galilean velocity).
-            const amrex::Real w_c = kx_c[i]*vg_x +
-#if defined(WARPX_DIM_3D)
-                ky_c[j]*vg_y + kz_c[k]*vg_z;
-#else
-                kz_c[j]*vg_z;
-#endif
-            const amrex::Real w2_c = std::pow(w_c, 2);
-
-            const amrex::Real om_s = c * knorm_s;
-            const amrex::Real om2_s = std::pow(om_s, 2);
-
-            const Complex theta_c      = amrex::exp( I * w_c * dt * 0.5_rt);
-            const Complex theta2_c     = amrex::exp( I * w_c * dt);
-            const Complex theta_c_star = amrex::exp(-I * w_c * dt * 0.5_rt);
-
-            // 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;
-            }
-
-            // Auxiliary variable
-            amrex::Real tmp;
-            if (om_s != 0.)
-            {
-                tmp = (1._rt - C(i,j,k)) / (ep0 * om2_s);
-            }
-            else // om_s = 0
-            {
-                tmp = 0.5_rt * dt2 / ep0;
-            }
-
-            // T2
-            if (is_galilean)
-            {
-                T2(i,j,k) = theta_c * theta_c;
-            }
-
-            // X1 (multiplies i*([k] \times J) in the update equation for update B)
-            if ((om_s != 0.) || (w_c != 0.))
-            {
-                X1(i,j,k) = (1._rt - theta2_c * C(i,j,k) + I * w_c * theta2_c * S_ck(i,j,k))
-                            / (ep0 * (om2_s - w2_c));
-            }
-            else // om_s = 0 and w_c = 0
-            {
-                X1(i,j,k) = 0.5_rt * dt2 / ep0;
-            }
-
-            // X2 (multiplies rho_new      if update_with_rho = 1 in the update equation for E)
-            // X2 (multiplies ([k] \dot E) if update_with_rho = 0 in the update equation for E)
-            if (update_with_rho)
-            {
-                if (w_c != 0.)
-                {
-                    X2(i,j,k) = c2 * (theta_c_star * X1(i,j,k) - theta_c * tmp)
-                                / (theta_c_star - theta_c);
-                }
-                else // w_c = 0
-                {
-                    if (om_s != 0.)
-                    {
-                        X2(i,j,k) = c2 * (dt - S_ck(i,j,k)) / (ep0 * dt * om2_s);
-                    }
-                    else // om_s = 0 and w_c = 0
-                    {
-                        X2(i,j,k) = c2 * dt2 / (6._rt * ep0);
-                    }
-                }
-            }
-            else // update_with_rho = 0
-            {
-                X2(i,j,k) = c2 * ep0 * theta2_c * tmp;
-            }
-
-            // X3 (multiplies rho_old      if update_with_rho = 1 in the update equation for E)
-            // X3 (multiplies ([k] \dot J) if update_with_rho = 0 in the update equation for E)
-            if (update_with_rho)
-            {
-                if (w_c != 0.)
-                {
-                    X3(i,j,k) = c2 * (theta_c_star * X1(i,j,k) - theta_c_star * tmp)
-                                / (theta_c_star - theta_c);
-                }
-                else // w_c = 0
-                {
-                    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 and w_c = 0
-                    {
-                        X3(i,j,k) = - c2 * dt2 / (3._rt * ep0);
-                    }
-                }
-            }
-            else // update_with_rho = 0
-            {
-                if (w_c != 0.)
-                {
-                    X3(i,j,k) = I * c2 * (theta2_c * tmp - X1(i,j,k)) / w_c;
-                }
-                else // w_c = 0
-                {
-                    if (om_s != 0.)
-                    {
-                        X3(i,j,k) = c2 * (S_ck(i,j,k) - dt) / (ep0 * om2_s);
-                    }
-                    else // om_s = 0 and w_c = 0
-                    {
-                        X3(i,j,k) = - c2 * dt3 / (6._rt * ep0);
-                    }
-                }
-            }
-
-            // X4 (multiplies J in the update equation for E)
-            if (is_galilean)
-            {
-                X4(i,j,k) = I * w_c * X1(i,j,k) - theta2_c * S_ck(i,j,k) / ep0;
-            }
-        });
-    }
-}
-
-void PsatdAlgorithm::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();
-        const amrex::Real* kx_c = modified_kx_vec_centered[mfi].dataPtr();
-#if defined(WARPX_DIM_3D)
-        const amrex::Real* ky_s = modified_ky_vec[mfi].dataPtr();
-        const amrex::Real* ky_c = modified_ky_vec_centered[mfi].dataPtr();
-#endif
-        const amrex::Real* kz_s = modified_kz_vec[mfi].dataPtr();
-        const amrex::Real* kz_c = modified_kz_vec_centered[mfi].dataPtr();
-
-        // Coefficients allocated only with averaged Galilean PSATD
-        amrex::Array4<Complex> Psi1 = Psi1_coef[mfi].array();
-        amrex::Array4<Complex> Psi2 = Psi2_coef[mfi].array();
-        amrex::Array4<Complex> Y1 = Y1_coef[mfi].array();
-        amrex::Array4<Complex> Y3 = Y3_coef[mfi].array();
-        amrex::Array4<Complex> Y2 = Y2_coef[mfi].array();
-        amrex::Array4<Complex> Y4 = Y4_coef[mfi].array();
-
-        // Extract Galilean velocity
-        amrex::Real vg_x = m_v_galilean[0];
-#if defined(WARPX_DIM_3D)
-        amrex::Real vg_y = m_v_galilean[1];
-#endif
-        amrex::Real vg_z = m_v_galilean[2];
-
-        // Loop over indices within one box
-        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;
-            constexpr Complex I = Complex{0._rt, 1._rt};
-
-            const amrex::Real c2 = std::pow(c, 2);
-            const amrex::Real dt2 = std::pow(dt, 2);
-
-            // Calculate the dot product of the k vector with the Galilean velocity.
-            // This has to be computed always with the centered (that is, nodal) finite-order
-            // modified k vectors, to work correctly for both nodal and staggered simulations.
-            // w_c = 0 always with standard PSATD (zero Galilean velocity).
-            const amrex::Real w_c = kx_c[i]*vg_x +
-#if defined(WARPX_DIM_3D)
-                ky_c[j]*vg_y + kz_c[k]*vg_z;
-#else
-                kz_c[j]*vg_z;
-#endif
-            const amrex::Real w2_c = std::pow(w_c, 2);
-            const amrex::Real w3_c = std::pow(w_c, 3);
-
-            const amrex::Real om_s = c * knorm_s;
-            const amrex::Real om2_s = std::pow(om_s, 2);
-            const amrex::Real om4_s = std::pow(om_s, 4);
-
-            const Complex theta_c  = amrex::exp(I * w_c * dt * 0.5_rt);
-            const Complex theta2_c = amrex::exp(I * w_c * dt);
-            const Complex theta3_c = amrex::exp(I * w_c * dt * 1.5_rt);
-            const Complex theta5_c = amrex::exp(I * w_c * dt * 2.5_rt);
-
-            // C1,C3
-            const amrex::Real C1 = std::cos(0.5_rt * om_s * dt);
-            const amrex::Real C3 = std::cos(1.5_rt * om_s * dt);
-
-            // S1_om, S3_om
-            amrex::Real S1_om, S3_om;
-            if (om_s != 0.)
-            {
-                S1_om = std::sin(0.5_rt * om_s * dt) / om_s;
-                S3_om = std::sin(1.5_rt * om_s * dt) / om_s;
-            }
-            else // om_s = 0
-            {
-                S1_om = 0.5_rt * dt;
-                S3_om = 1.5_rt * dt;
-            }
-
-            // Psi1 (multiplies E in the update equation for <E>)
-            // Psi1 (multiplies B in the update equation for <B>)
-            if ((om_s != 0.) || (w_c != 0.))
-            {
-                Psi1(i,j,k) = (theta3_c * (om2_s * S3_om + I * w_c * C3)
-                              - theta_c * (om2_s * S1_om + I * w_c * C1)) / (dt * (om2_s - w2_c));
-            }
-            else // om_s = 0 and w_c = 0
-            {
-                Psi1(i,j,k) = 1._rt;
-            }
-
-            // Psi2 (multiplies i*([k] \times B) in the update equation for <E>)
-            // Psi2 (multiplies i*([k] \times E) in the update equation for <B>)
-            if ((om_s != 0.) || (w_c != 0.))
-            {
-                Psi2(i,j,k) = (theta3_c * (C3 - I * w_c * S3_om)
-                              - theta_c * (C1 - I * w_c * S1_om)) / (dt * (om2_s - w2_c));
-            }
-            else // om_s = 0 and w_c = 0
-            {
-                Psi2(i,j,k) = - dt;
-            }
-
-            // Psi3
-            Complex Psi3;
-            if (w_c != 0.)
-            {
-                Psi3 = - I * (theta3_c - theta_c) / (dt * w_c);
-            }
-            else // w_c = 0
-            {
-                Psi3 = 1._rt;
-            }
-
-            // Y1 (multiplies i*([k] \times J) in the update equation for <B>)
-            if ((om_s != 0.) || (w_c != 0.))
-            {
-                Y1(i,j,k) = (1._rt - Psi1(i,j,k) - I * w_c * Psi2(i,j,k)) / (ep0 * (om2_s - w2_c));
-            }
-            else // om_s = 0 and w_c = 0
-            {
-                Y1(i,j,k) = 13._rt * dt2 / (24._rt * ep0);
-            }
-
-            // Y2 (multiplies rho_new in the update equation for <E>)
-            if ((om_s != 0.) && (w_c != 0.))
-            {
-                Y2(i,j,k) = I * c2 * (ep0 * om2_s * Y1(i,j,k) - Psi3 + Psi1(i,j,k))
-                            / (ep0 * om2_s * (theta2_c - 1._rt));
-            }
-            else if ((om_s != 0.) && (w_c == 0.))
-            {
-                Y2(i,j,k) = I * c2 * (C1 - C3 - dt2 * om2_s) / (ep0 * dt2 * om4_s);
-            }
-            else if ((om_s == 0.) && (w_c != 0.))
-            {
-                Y2(i,j,k) = c2 * (9._rt * dt2 * w2_c * theta3_c - dt2 * w2_c * theta_c
-                            - 24._rt * theta3_c + 24._rt * theta_c + I * 8._rt * dt * w_c
-                            + I * 24._rt * dt * w_c * theta3_c - I * 8._rt * dt * w_c * theta_c)
-                            / (8._rt * ep0 * dt * w3_c * (1._rt - theta2_c));
-            }
-            else // om_s = 0 and w_c = 0
-            {
-                Y2(i,j,k) = - I * 5._rt * c2 * dt2 / (24._rt * ep0);
-            }
-
-            // Y3 (multiplies rho_old in the update equation for <E>)
-            if ((om_s != 0.) && (w_c != 0.))
-            {
-                Y3(i,j,k) = I * c2 * (Psi3 - Psi1(i,j,k) - ep0 * theta2_c * om2_s * Y1(i,j,k))
-                            / (ep0 * om2_s * (theta2_c - 1._rt));
-            }
-            else if ((om_s != 0.) && (w_c == 0.))
-            {
-                Y3(i,j,k) = I * c2 * (C3 - C1 + dt * om2_s * (S3_om - S1_om)) / (ep0 * dt2 * om4_s);
-            }
-            else if ((om_s == 0.) && (w_c != 0.))
-            {
-                Y3(i,j,k) = c2 * (9._rt * dt2 * w2_c * theta3_c - dt2 * w2_c * theta_c
-                            - 16._rt * theta5_c + 8._rt * theta3_c + 8._rt * theta_c
-                            + I * 12._rt * dt * w_c * theta5_c + I * 8._rt * dt * w_c * theta3_c
-                            - I * 4._rt * dt * w_c * theta_c + I * 8._rt * dt * w_c * theta2_c)
-                            / (8._rt * ep0 * dt * w3_c * (theta2_c - 1._rt));
-            }
-            else // om_s = 0 and w_c = 0
-            {
-                Y3(i,j,k) = - I * c2 * dt2 / (3._rt * ep0);
-            }
-
-            // Y4 (multiplies J in the update equation for <E>)
-            Y4(i,j,k) = (Psi2(i,j,k) + I * ep0 * w_c * Y1(i,j,k)) / ep0;
-        });
-    }
-}
-
-void PsatdAlgorithm::CurrentCorrection (SpectralFieldData& field_data)
-{
-    // Profiling
-    BL_PROFILE("PsatdAlgorithm::CurrentCorrection");
-
-    const SpectralFieldIndex& Idx = m_spectral_index;
-
-    // Loop over boxes
-    for (amrex::MFIter mfi(field_data.fields); mfi.isValid(); ++mfi){
-
-        const amrex::Box& 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
-        const amrex::Real* const modified_kx_arr = modified_kx_vec[mfi].dataPtr();
-        const amrex::Real* const modified_kx_arr_c = modified_kx_vec_centered[mfi].dataPtr();
-#if defined(WARPX_DIM_3D)
-        const amrex::Real* const modified_ky_arr = modified_ky_vec[mfi].dataPtr();
-        const amrex::Real* const modified_ky_arr_c = modified_ky_vec_centered[mfi].dataPtr();
-#endif
-        const amrex::Real* const modified_kz_arr = modified_kz_vec[mfi].dataPtr();
-        const amrex::Real* const modified_kz_arr_c = modified_kz_vec_centered[mfi].dataPtr();
-
-        // Local copy of member variables before GPU loop
-        const amrex::Real dt = m_dt;
-
-        // Galilean velocity
-        const amrex::Real vgx = m_v_galilean[0];
-        const amrex::Real vgy = m_v_galilean[1];
-        const amrex::Real vgz = m_v_galilean[2];
-
-        // Loop over indices within one box
-        ParallelFor(bx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
-        {
-            // Shortcuts for the values of J and rho
-            const Complex Jx = fields(i,j,k,Idx.Jx);
-            const Complex Jy = fields(i,j,k,Idx.Jy);
-            const Complex Jz = fields(i,j,k,Idx.Jz);
-            const Complex rho_old = fields(i,j,k,Idx.rho_old);
-            const Complex rho_new = fields(i,j,k,Idx.rho_new);
-
-            // k vector values, and coefficients
-            const amrex::Real kx = modified_kx_arr[i];
-            const amrex::Real kx_c = modified_kx_arr_c[i];
-#if defined(WARPX_DIM_3D)
-            const amrex::Real ky = modified_ky_arr[j];
-            const amrex::Real kz = modified_kz_arr[k];
-            const amrex::Real ky_c = modified_ky_arr_c[j];
-            const amrex::Real kz_c = modified_kz_arr_c[k];
-#else
-            constexpr amrex::Real ky = 0._rt;
-            const     amrex::Real kz = modified_kz_arr[j];
-            constexpr amrex::Real ky_c = 0._rt;
-            const     amrex::Real kz_c = modified_kz_arr_c[j];
-#endif
-            constexpr Complex I = Complex{0._rt, 1._rt};
-
-            const amrex::Real k_norm = std::sqrt(kx * kx + ky * ky + kz * kz);
-
-            // Correct J
-            if (k_norm != 0._rt)
-            {
-                const Complex k_dot_J = kx * Jx + ky * Jy + kz * Jz;
-                const amrex::Real k_dot_vg = kx_c * vgx + ky_c * vgy + kz_c * vgz;
-
-                // k_dot_vg = 0 always with standard PSATD (zero Galilean velocity)
-                if ( k_dot_vg != 0._rt )
-                {
-                    const Complex rho_old_mod = rho_old * amrex::exp(I * k_dot_vg * dt);
-                    const Complex den = 1._rt - amrex::exp(I * k_dot_vg * dt);
-
-                    fields(i,j,k,Idx.Jx) = Jx - (k_dot_J - k_dot_vg * (rho_new - rho_old_mod) / den)
-                        * kx / (k_norm * k_norm);
-
-                    fields(i,j,k,Idx.Jy) = Jy - (k_dot_J - k_dot_vg * (rho_new - rho_old_mod) / den)
-                        * ky / (k_norm * k_norm);
-
-                    fields(i,j,k,Idx.Jz) = Jz - (k_dot_J - k_dot_vg * (rho_new - rho_old_mod) / den)
-                        * kz / (k_norm * k_norm);
-                }
-
-                else
-                {
-                    fields(i,j,k,Idx.Jx) = Jx - (k_dot_J - I * (rho_new - rho_old) / dt)
-                        * kx / (k_norm * k_norm);
-
-                    fields(i,j,k,Idx.Jy) = Jy - (k_dot_J - I * (rho_new - rho_old) / dt)
-                        * ky / (k_norm * k_norm);
-
-                    fields(i,j,k,Idx.Jz) = Jz - (k_dot_J - I * (rho_new - rho_old) / dt)
-                        * kz / (k_norm * k_norm);
-                }
-            }
-        });
-    }
-}
-
-void
-PsatdAlgorithm::VayDeposition (SpectralFieldData& field_data)
-{
-    // Profiling
-    BL_PROFILE("PsatdAlgorithm::VayDeposition()");
-
-    const SpectralFieldIndex& Idx = m_spectral_index;
-
-    // Loop over boxes
-    for (amrex::MFIter mfi(field_data.fields); mfi.isValid(); ++mfi)
-    {
-        const amrex::Box& 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 modified k vectors
-        const amrex::Real* const modified_kx_arr = modified_kx_vec[mfi].dataPtr();
-#if defined(WARPX_DIM_3D)
-        const amrex::Real* const modified_ky_arr = modified_ky_vec[mfi].dataPtr();
-#endif
-        const amrex::Real* const modified_kz_arr = modified_kz_vec[mfi].dataPtr();
-
-        // Loop over indices within one box
-        ParallelFor(bx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
-        {
-            // Shortcuts for the values of D
-            const Complex Dx = fields(i,j,k,Idx.Jx);
-#if defined(WARPX_DIM_3D)
-            const Complex Dy = fields(i,j,k,Idx.Jy);
-#endif
-            const Complex Dz = fields(i,j,k,Idx.Jz);
-
-            // Imaginary unit
-            constexpr Complex I = Complex{0._rt, 1._rt};
-
-            // Modified k vector values
-            const amrex::Real kx_mod = modified_kx_arr[i];
-#if defined(WARPX_DIM_3D)
-            const amrex::Real ky_mod = modified_ky_arr[j];
-            const amrex::Real kz_mod = modified_kz_arr[k];
-#else
-            const amrex::Real kz_mod = modified_kz_arr[j];
-#endif
-
-            // Compute Jx
-            if (kx_mod != 0._rt) fields(i,j,k,Idx.Jx) = I * Dx / kx_mod;
-            else                 fields(i,j,k,Idx.Jx) = 0._rt;
-
-#if defined(WARPX_DIM_3D)
-            // Compute Jy
-            if (ky_mod != 0._rt) fields(i,j,k,Idx.Jy) = I * Dy / ky_mod;
-            else                 fields(i,j,k,Idx.Jy) = 0._rt;
-#endif
-
-            // Compute Jz
-            if (kz_mod != 0._rt) fields(i,j,k,Idx.Jz) = I * Dz / kz_mod;
-            else                 fields(i,j,k,Idx.Jz) = 0._rt;
-        });
-    }
-}
-
-#endif // WARPX_USE_PSATD