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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_NODAL_H_
#define WARPX_FINITE_DIFFERENCE_ALGORITHM_CARTESIAN_NODAL_H_
#include "Utils/WarpXConst.H"
#include <AMReX.H>
#include <AMReX_Array4.H>
#include <AMReX_Gpu.H>
#include <AMReX_REAL.H>
#include <array>
#include <cmath>
/**
* This struct contains only static functions to initialize the stencil coefficients
* and to compute finite-difference derivatives for the Cartesian nodal algorithm.
*/
struct CartesianNodalAlgorithm {
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];
}
/**
* Compute the maximum timestep, for which the scheme remains stable
* (Courant-Friedrichs-Levy limit) */
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;
}
/**
* \brief Returns maximum number of guard cells required by the field-solve
*/
static amrex::IntVect GetMaxGuardCell () {
// The nodal solver requires one guard cell in each dimension
return (amrex::IntVect(AMREX_D_DECL(1,1,1)));
}
/**
* Perform derivative along x
* (For a solver on a staggered grid, `UpwardDx` and `DownwardDx` take into
* account the staggering; but for `CartesianNodalAlgorithm`, they are equivalent) */
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;
Real const inv_dx = coefs_x[0];
return 0.5_rt*inv_dx*( F(i+1,j,k,ncomp) - F(i-1,j,k,ncomp) );
}
/**
* Perform derivative along x
* (For a solver on a staggered grid, `UpwardDx` and `DownwardDx` take into
* account the staggering; but for `CartesianNodalAlgorithm`, they are equivalent) */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real DownwardDx (
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 ) {
return UpwardDx( F, coefs_x, n_coefs_x, i, j, k ,ncomp);
// For CartesianNodalAlgorithm, UpwardDx and DownwardDx are equivalent
}
/**
* Perform derivative along y
* (For a solver on a staggered grid, `UpwardDy` and `DownwardDy` take into
* account the staggering; but for `CartesianNodalAlgorithm`, they are equivalent) */
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];
return 0.5_rt*inv_dy*( F(i,j+1,k,ncomp) - F(i,j-1,k,ncomp) );
#elif (defined WARPX_DIM_XZ)
ignore_unused(i, j, k, coefs_y, ncomp, F);
return 0._rt; // 2D Cartesian: derivative along y is 0
#endif
}
/**
* Perform derivative along y
* (For a solver on a staggered grid, `UpwardDy` and `DownwardDy` take into
* account the staggering; but for `CartesianNodalAlgorithm`, they are equivalent) */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real DownwardDy (
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 ) {
return UpwardDy( F, coefs_y, n_coefs_y, i, j, k ,ncomp);
// For CartesianNodalAlgorithm, UpwardDy and DownwardDy are equivalent
}
/**
* Perform derivative along z
* (For a solver on a staggered grid, `UpwardDz` and `DownwardDz` take into
* account the staggering; but for `CartesianNodalAlgorithm`, they are equivalent) */
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 0.5_rt*inv_dz*( F(i,j,k+1,ncomp) - F(i,j,k-1,ncomp) );
#elif (defined WARPX_DIM_XZ)
return 0.5_rt*inv_dz*( F(i,j+1,k,ncomp) - F(i,j-1,k,ncomp) );
#endif
}
/**
* Perform derivative along z
* (For a solver on a staggered grid, `UpwardDz` and `DownwardDz` take into
* account the staggering; but for `CartesianNodalAlgorithm`, they are equivalent) */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real DownwardDz (
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 ) {
return UpwardDz( F, coefs_z, n_coefs_z, i, j, k ,ncomp);
// For CartesianNodalAlgorithm, UpwardDz and DownwardDz are equivalent
}
};
#endif // WARPX_FINITE_DIFFERENCE_ALGORITHM_CARTESIAN_NODAL_H_
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