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/* Copyright 2020 Remi Lehe
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#ifndef WARPX_FINITE_DIFFERENCE_ALGORITHM_CYLINDRICAL_YEE_H_
#define WARPX_FINITE_DIFFERENCE_ALGORITHM_CYLINDRICAL_YEE_H_
#include <AMReX_REAL.H>
#include <AMReX_Array4.H>
#include <AMReX_Gpu.H>
struct CylindricalYeeAlgorithm {
static void InitializeStencilCoefficients(
std::array<amrex::Real,3>& cell_size,
amrex::Gpu::ManagedVector<amrex::Real>& stencil_coefs_r,
amrex::Gpu::ManagedVector<amrex::Real>& stencil_coefs_z ) {
// Store the inverse cell size along each direction in the coefficients
stencil_coefs_r.resize(1);
stencil_coefs_r[0] = 1./cell_size[0]; // 1./dr
stencil_coefs_z.resize(1);
stencil_coefs_z[0] = 1./cell_size[2]; // 1./dz
}
/** Applies the differential operator `1/r * d(rF)/dr`,
* where `F` is on a *nodal* grid in `r`
* and the differential operator is evaluated on *cell-centered* grid.
* The input parameter `r` is given at the cell-centered position */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real UpwardDrr_over_r(
amrex::Array4<amrex::Real> const& F,
amrex::Real const r, amrex::Real const dr,
amrex::Real const* coefs_r, int const n_coefs_r,
int const i, int const j, int const k, int const comp ) {
amrex::Real const inv_dr = coefs_r[0];
return 1./r * inv_dr*( (r+0.5*dr)*F(i+1,j,k,comp) - (r-0.5*dr)*F(i,j,k,comp) );
};
/**
/* Perform derivative along r on a cell-centered grid, from a nodal field `F`*/
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real UpwardDr(
amrex::Array4<amrex::Real> const& F,
amrex::Real const* coefs_r, int const n_coefs_r,
int const i, int const j, int const k, int const comp ) {
amrex::Real const inv_dr = coefs_r[0];
return inv_dr*( F(i+1,j,k,comp) - F(i,j,k,comp) );
};
/**
/* Perform derivative along r on a nodal grid, from a cell-centered field `F`*/
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real DownwardDr(
amrex::Array4<amrex::Real> const& F,
amrex::Real const* coefs_r, int const n_coefs_r,
int const i, int const j, int const k, int const comp ) {
amrex::Real const inv_dr = coefs_r[0];
return inv_dr*( F(i,j,k,comp) - F(i-1,j,k,comp) );
};
/**
/* Perform derivative along z on a cell-centered grid, from a nodal field `F`*/
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real UpwardDz(
amrex::Array4<amrex::Real> const& F,
amrex::Real const* coefs_z, int const n_coefs_z,
int const i, int const j, int const k, int const comp ) {
amrex::Real const inv_dz = coefs_z[0];
return inv_dz*( F(i,j+1,k,comp) - F(i,j,k,comp) );
};
/**
/* Perform derivative along z on a nodal grid, from a cell-centered field `F`*/
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real DownwardDz(
amrex::Array4<amrex::Real> const& F,
amrex::Real const* coefs_z, int const n_coefs_z,
int const i, int const j, int const k, int const comp ) {
amrex::Real const inv_dz = coefs_z[0];
return inv_dz*( F(i,j,k,comp) - F(i,j-1,k,comp) );
};
/** Divide by the radius `r` and avoid potential singularities */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real DivideByR(
amrex::Array4<amrex::Real> const& F,
amrex::Real const r, amrex::Real const dr, int const m,
int const i, int const j, int const k, int const comp) {
if (r != 0) {
return F(i,j,k,comp)/r;
} else { // r==0 ; singularity when dividing by r
if (m==1) {
// For m==1, F is linear in r, for small r
// Therefore, the formula below regularizes the singularity
return F(i+1,j,k,comp)/dr;
} else {
return 0;
}
}
};
};
#endif // WARPX_FINITE_DIFFERENCE_ALGORITHM_CYLINDRICAL_YEE_H_
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