CartesianYeeAlgorithm.H

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/* Copyright 2020 Remi Lehe
 *
 * This file is part of WarpX.
 *
 * License: BSD-3-Clause-LBNL
 */
 
#ifndef WARPX_FINITE_DIFFERENCE_ALGORITHM_CARTESIAN_YEE_H_
#define WARPX_FINITE_DIFFERENCE_ALGORITHM_CARTESIAN_YEE_H_
 
#include "FieldAccessorFunctors.H"
#include "Utils/WarpXConst.H"
 
#include <AMReX.H>
#include <AMReX_Array4.H>
#include <AMReX_Gpu.H>
#include <AMReX_REAL.H>
#include "Utils/WarpXUtil.H"
#include "WarpX.H"
#include "FieldSolver/FiniteDifferenceSolver/MacroscopicProperties/MacroscopicProperties.H"
 
#include <array>
#include <cmath>
 
 
struct CartesianYeeAlgorithm {
 
    static void InitializeStencilCoefficients (
        std::array<amrex::Real,3>& cell_size,
        amrex::Vector<amrex::Real>& stencil_coefs_x,
        amrex::Vector<amrex::Real>& stencil_coefs_y,
        amrex::Vector<amrex::Real>& stencil_coefs_z ) {
 
        using namespace amrex;
        // Store the inverse cell size along each direction in the coefficients
        stencil_coefs_x.resize(1);
        stencil_coefs_x[0] = 1._rt/cell_size[0];
        stencil_coefs_y.resize(1);
        stencil_coefs_y[0] = 1._rt/cell_size[1];
        stencil_coefs_z.resize(1);
        stencil_coefs_z[0] = 1._rt/cell_size[2];
    }
 
    static amrex::Real ComputeMaxDt ( amrex::Real const * const dx ) {
        using namespace amrex::literals;
        amrex::Real const delta_t  = 1._rt / ( std::sqrt( AMREX_D_TERM(
                                           1._rt / (dx[0]*dx[0]),
                                         + 1._rt / (dx[1]*dx[1]),
                                         + 1._rt / (dx[2]*dx[2])
                                     ) ) * PhysConst::c );
        return delta_t;
    }
 
    static amrex::IntVect GetMaxGuardCell () {
        // The yee solver requires one guard cell in each dimension
        return (amrex::IntVect(AMREX_D_DECL(1,1,1)));
    }
 
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real UpwardDx (
        amrex::Array4<amrex::Real> const& F,
        amrex::Real const * const coefs_x, int const /*n_coefs_x*/,
        int const i, int const j, int const k, int const ncomp=0 ) {
 
        using namespace amrex;
#if (defined WARPX_DIM_1D_Z)
        amrex::ignore_unused(F, coefs_x, i, j, k, ncomp);
        return 0._rt; // 1D Cartesian: derivative along x is 0
#else
        amrex::Real const inv_dx = coefs_x[0];
        return inv_dx*( F(i+1,j,k,ncomp) - F(i,j,k,ncomp) );
#endif
    }
 
    template< typename T_Field>
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real DownwardDx (
        T_Field const& F,
        amrex::Real const * const coefs_x, int const /*n_coefs_x*/,
        int const i, int const j, int const k, int const ncomp=0 ) {
 
        using namespace amrex;
#if (defined WARPX_DIM_1D_Z)
        amrex::ignore_unused(F, coefs_x, i, j, k, ncomp);
        return 0._rt; // 1D Cartesian: derivative along x is 0
#else
        amrex::Real const inv_dx = coefs_x[0];
        return inv_dx*( F(i,j,k,ncomp) - F(i-1,j,k,ncomp) );
#endif
    }
 
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real UpwardDy (
        amrex::Array4<amrex::Real> const& F,
        amrex::Real const * const coefs_y, int const n_coefs_y,
        int const i, int const j, int const k, int const ncomp=0 ) {
 
        using namespace amrex;
#if defined WARPX_DIM_3D
        Real const inv_dy = coefs_y[0];
        amrex::ignore_unused(n_coefs_y);
        return inv_dy*( F(i,j+1,k,ncomp) - F(i,j,k,ncomp) );
#elif (defined WARPX_DIM_XZ || WARPX_DIM_1D_Z)
        amrex::ignore_unused(F, coefs_y, n_coefs_y,
            i, j, k, ncomp);
        return 0._rt; // 1D and 2D Cartesian: derivative along y is 0
#else
        amrex::ignore_unused(F, coefs_y, n_coefs_y,
            i, j, k, ncomp);
        return 0._rt;
#endif
    }
 
    template< typename T_Field>
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real DownwardDy (
        T_Field const& F,
        amrex::Real const * const coefs_y, int const n_coefs_y,
        int const i, int const j, int const k, int const ncomp=0 ) {
 
        using namespace amrex;
#if defined WARPX_DIM_3D
        Real const inv_dy = coefs_y[0];
        amrex::ignore_unused(n_coefs_y);
        return inv_dy*( F(i,j,k,ncomp) - F(i,j-1,k,ncomp) );
#elif (defined WARPX_DIM_XZ || WARPX_DIM_1D_Z)
        amrex::ignore_unused(F, coefs_y, n_coefs_y,
            i, j, k, ncomp);
        return 0._rt; // 1D and 2D Cartesian: derivative along y is 0
#else
        amrex::ignore_unused(F, coefs_y, n_coefs_y,
            i, j, k, ncomp);
        return 0._rt;
#endif
    }
 
   AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real UpwardDz (
        amrex::Array4<amrex::Real> const& F,
        amrex::Real const * const coefs_z, int const /*n_coefs_z*/,
        int const i, int const j, int const k, int const ncomp=0 ) {
 
        using namespace amrex;
        Real const inv_dz = coefs_z[0];
#if defined WARPX_DIM_3D
        return inv_dz*( F(i,j,k+1,ncomp) - F(i,j,k,ncomp) );
#elif (defined WARPX_DIM_XZ)
        return inv_dz*( F(i,j+1,k,ncomp) - F(i,j,k,ncomp) );
#elif (defined WARPX_DIM_1D_Z)
        return inv_dz*( F(i+1,j,k,ncomp) - F(i,j,k,ncomp) );
#endif
    }
 
    template< typename T_Field>
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real DownwardDz (
        T_Field const& F,
        amrex::Real const * const coefs_z, int const /*n_coefs_z*/,
        int const i, int const j, int const k, int const ncomp=0 ) {
 
        using namespace amrex;
        Real const inv_dz = coefs_z[0];
#if defined WARPX_DIM_3D
        return inv_dz*( F(i,j,k,ncomp) - F(i,j,k-1,ncomp) );
#elif (defined WARPX_DIM_XZ)
        return inv_dz*( F(i,j,k,ncomp) - F(i,j-1,k,ncomp) );
#elif (defined WARPX_DIM_1D_Z)
        return inv_dz*( F(i,j,k,ncomp) - F(i-1,j,k,ncomp) );
#endif
    }
 
#ifdef WARPX_MAG_LLG
 
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real LaplacianDx (
        amrex::Array4<amrex::Real> const& F,
        amrex::Real const * const coefs_x,
        int const i, int const j, int const k, int const ncomp=0 ) {
 
        amrex::Real const inv_dx = coefs_x[0];
        return inv_dx*inv_dx*( F(i+1,j,k,ncomp) - 2.0*F(i,j,k,ncomp) + F(i-1,j,k,ncomp));
    }
 
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real LaplacianDy (
        amrex::Array4<amrex::Real> const& F,
        amrex::Real const * const coefs_y,
        int const i, int const j, int const k, int const ncomp=0 ) {
 
        amrex::Real const inv_dy = coefs_y[0];
        return inv_dy*inv_dy*( F(i,j+1,k,ncomp) - 2.0*F(i,j,k,ncomp) + F(i,j-1,k,ncomp));
    }
 
   AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real LaplacianDz (
        amrex::Array4<amrex::Real> const& F,
        amrex::Real const * const coefs_z,
        int const i, int const j, int const k, int const ncomp=0 ) {
 
        amrex::Real const inv_dz = coefs_z[0];
        return inv_dz*inv_dz*( F(i,j,k+1,ncomp) - 2.0*F(i,j,k,ncomp) + F(i,j,k-1,ncomp));
    }
 
   AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real Laplacian (
        amrex::Array4<amrex::Real> const& F,
        amrex::Real const * const coefs_x, amrex::Real const * const coefs_y, amrex::Real const * const coefs_z,
        int const i, int const j, int const k, int const ncomp=0 ) {
 
        return LaplacianDx(F, coefs_x, i, j, k, ncomp) + LaplacianDy(F, coefs_y, i, j, k, ncomp) + LaplacianDz(F, coefs_z, i, j, k, ncomp);
    }
 
#endif
 
#ifdef WARPX_MAG_LLG
 
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real LaplacianDx_Mag (
        amrex::Array4<amrex::Real> const& F,
        amrex::Real const * const coefs_x, int const n_coefs_x, amrex::Real const Ms_lo_x, amrex::Real const Ms_hi_x,
        int const i, int const j, int const k, int const ncomp=0, int const nodality=0) {
 
        amrex::Real const inv_dx = coefs_x[0];
        if (nodality == 0){ // at x face (normal face). dM/dx = 0
           if (Ms_hi_x == 0.){
               return 0.5 * inv_dx * inv_dx * (8. * F(i-1, j, k, ncomp) - F(i-2, j, k, ncomp) - 7. * F(i, j, k, ncomp));
           } else if (Ms_lo_x == 0){
               return 0.5 * inv_dx * inv_dx * (8. * F(i+1, j, k, ncomp) - F(i+2, j, k, ncomp) - 7. * F(i, j, k, ncomp));
           } else {
               return inv_dx*(UpwardDx(F, coefs_x, n_coefs_x, i, j, k, ncomp) - DownwardDx(F, coefs_x, n_coefs_x, i, j, k, ncomp));
           }
        } else { // at y or z faces
           if (Ms_hi_x == 0.){
               return inv_dx*(0. - DownwardDx(F, coefs_x, n_coefs_x, i, j, k, ncomp));
           } else if (Ms_lo_x == 0.){
               return inv_dx*(UpwardDx(F, coefs_x, n_coefs_x, i, j, k, ncomp) - 0.);
           } else {
               return inv_dx*(UpwardDx(F, coefs_x, n_coefs_x, i, j, k, ncomp) - DownwardDx(F, coefs_x, n_coefs_x, i, j, k, ncomp));
           }
        }
    }
 
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real LaplacianDy_Mag (
        amrex::Array4<amrex::Real> const& F,
        amrex::Real const * const coefs_y, int const n_coefs_y, amrex::Real const Ms_lo_y, amrex::Real const Ms_hi_y,
        int const i, int const j, int const k, int const ncomp=0, int const nodality=0) {
 
        amrex::Real const inv_dy = coefs_y[0];
        if (nodality == 1){ // y face (normal face), dM/dy = 0
           if (Ms_hi_y == 0.){
               return 0.5 * inv_dy * inv_dy * (8. * F(i, j-1, k, ncomp) - F(i, j-2, k, ncomp) - 7. * F(i, j, k, ncomp));
           } else if (Ms_lo_y == 0.) {
               return 0.5 * inv_dy * inv_dy * (8. * F(i, j+1, k, ncomp) - F(i, j+2, k, ncomp) - 7. * F(i, j, k, ncomp));
           } else {
               return inv_dy*(UpwardDy(F, coefs_y, n_coefs_y, i, j, k, ncomp) - DownwardDy(F, coefs_y, n_coefs_y, i, j, k, ncomp));
           }
 
        } else { // x or z faces
           if (Ms_hi_y == 0.){
               return inv_dy*(0. - DownwardDy(F, coefs_y, n_coefs_y, i, j, k, ncomp));
           } else if (Ms_lo_y == 0.) {
               return inv_dy*(UpwardDy(F, coefs_y, n_coefs_y, i, j, k, ncomp) - 0.);
           } else {
               return inv_dy*(UpwardDy(F, coefs_y, n_coefs_y, i, j, k, ncomp) - DownwardDy(F, coefs_y, n_coefs_y, i, j, k, ncomp));
           }
        }
    }
 
   AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real LaplacianDz_Mag (
        amrex::Array4<amrex::Real> const& F,
        amrex::Real const * const coefs_z, int const n_coefs_z, amrex::Real const Ms_lo_z, amrex::Real const Ms_hi_z,
        int const i, int const j, int const k, int const ncomp=0, int const nodality=0) {
 
        amrex::Real const inv_dz = coefs_z[0];
        if (nodality == 2){ // z face (normal face) dM/dz = 0
           if ( Ms_hi_z == 0.) {
               return 0.5 * inv_dz * inv_dz * (8. * F(i, j, k-1, ncomp) - F(i, j, k-2, ncomp) - 7. * F(i, j, k, ncomp));
           } else if ( Ms_lo_z == 0.){
               return 0.5 * inv_dz * inv_dz * (8. * F(i, j, k+1, ncomp) - F(i, j, k+2, ncomp) - 7. * F(i, j, k, ncomp));
           } else {
               return inv_dz*(UpwardDz(F, coefs_z, n_coefs_z, i, j, k, ncomp) - DownwardDz(F, coefs_z, n_coefs_z, i, j, k, ncomp));
           }
 
        } else { // x or y face
           if ( Ms_hi_z == 0.) {
               return inv_dz*(0. - DownwardDz(F, coefs_z, n_coefs_z, i, j, k, ncomp));
           } else if ( Ms_lo_z == 0.){
               return inv_dz*(UpwardDz(F, coefs_z, n_coefs_z, i, j, k, ncomp) - 0.);
           } else {
               return inv_dz*(UpwardDz(F, coefs_z, n_coefs_z, i, j, k, ncomp) - DownwardDz(F, coefs_z, n_coefs_z, i, j, k, ncomp));
           }
        }
    }
 
   AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real Laplacian_Mag (
        amrex::Array4<amrex::Real> const& F,
        amrex::Real const * const coefs_x, amrex::Real const * const coefs_y, amrex::Real const * const coefs_z,
        int const n_coefs_x, int const n_coefs_y, int const n_coefs_z,
        amrex::Real const Ms_lo_x, amrex::Real const Ms_hi_x, amrex::Real const Ms_lo_y, amrex::Real const Ms_hi_y, amrex::Real const Ms_lo_z, amrex::Real const Ms_hi_z,
        int const i, int const j, int const k, int const ncomp=0, int const nodality=0) {
 
        return LaplacianDx_Mag(F, coefs_x, n_coefs_x, Ms_lo_x, Ms_hi_x, i, j, k, ncomp, nodality) + LaplacianDy_Mag(F, coefs_y, n_coefs_y, Ms_lo_y, Ms_hi_y, i, j, k, ncomp, nodality) + LaplacianDz_Mag(F, coefs_z, n_coefs_z, Ms_lo_z, Ms_hi_z, i, j, k, ncomp, nodality);
    }
 
#endif
 
};
 
#endif // WARPX_FINITE_DIFFERENCE_ALGORITHM_CARTESIAN_YEE_H_