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#ifndef WARPX_FINITE_DIFFERENCE_ALGORITHM_CKC_H_
#define WARPX_FINITE_DIFFERENCE_ALGORITHM_CKC_H_
#include <AMReX_REAL.H>
#include <AMReX_Array4.H>
#include <AMReX_Gpu.H>
struct CKCAlgorithm {
static void InitializeStencilCoefficients(
std::array<amrex::Real,3>& cell_size,
amrex::Gpu::ManagedVector<amrex::Real>& stencil_coefs_x,
amrex::Gpu::ManagedVector<amrex::Real>& stencil_coefs_y,
amrex::Gpu::ManagedVector<amrex::Real>& stencil_coefs_z ) {
using namespace amrex;
// Compute Cole-Karkkainen-Cowan coefficients according
// to Cowan - PRST-AB 16, 041303 (2013)
Real alphax=0, alphay=0, alphaz=0;
Real betaxy=0, betaxz=0, betayx=0, betayz=0, betazx=0, betazy=0;
Real gammax=0, gammay=0, gammaz=0;
Real const inv_dx = 1./cell_size[0];
Real const inv_dy = 1./cell_size[1];
Real const inv_dz = 1./cell_size[2];
# if defined WARPX_DIM_3D
const Real delta = std::max( { inv_dx,inv_dy,inv_dz } );
const Real rx = (inv_dx/delta)*(inv_dx/delta);
const Real ry = (inv_dy/delta)*(inv_dy/delta);
const Real rz = (inv_dz/delta)*(inv_dz/delta);
const Real beta = 0.125*(1. - rx*ry*rz/(ry*rz + rz*rx + rx*ry));
betaxy = ry*beta;
betaxz = rz*beta;
betayx = rx*beta;
betayz = rz*beta;
betazx = rx*beta;
betazy = ry*beta;
gammax = ry*rz*(0.0625 - 0.125*ry*rz/(ry*rz + rz*rx + rx*ry));
gammay = rx*rz*(0.0625 - 0.125*rx*rz/(ry*rz + rz*rx + rx*ry));
gammaz = rx*ry*(0.0625 - 0.125*rx*ry/(ry*rz + rz*rx + rx*ry));
alphax = 1. - 2.*betaxy - 2.*betaxz - 4.*gammax;
alphay = 1. - 2.*betayx - 2.*betayz - 4.*gammay;
alphaz = 1. - 2.*betazx - 2.*betazy - 4.*gammaz;
betaxy *= inv_dx;
betaxz *= inv_dx;
betayx *= inv_dy;
betayz *= inv_dy;
betazx *= inv_dz;
betazy *= inv_dz;
alphax *= inv_dx;
alphay *= inv_dy;
alphaz *= inv_dz;
gammax *= inv_dx;
gammay *= inv_dy;
gammaz *= inv_dz;
# elif defined WARPX_DIM_XZ
const Real delta = std::max(inv_dx,inv_dz);
const Real rx = (inv_dx/delta)*(inv_dx/delta);
const Real rz = (inv_dz/delta)*(inv_dz/delta);
betaxz = 0.125*rz;
betazx = 0.125*rx;
alphax = 1. - 2.*betaxz;
alphaz = 1. - 2.*betazx;
betaxz *= inv_dx;
betazx *= inv_dz;
alphax *= inv_dx;
alphaz *= inv_dz;
# endif
// Store the coefficients in array `stencil_coefs`, in prescribed order
stencil_coefs_x.resize(6);
stencil_coefs_x[0] = inv_dx;
stencil_coefs_x[1] = alphax;
stencil_coefs_x[2] = betaxy;
stencil_coefs_x[3] = betaxz;
stencil_coefs_x[4] = gammax;
stencil_coefs_y.resize(6);
stencil_coefs_y[0] = inv_dy;
stencil_coefs_y[1] = alphay;
stencil_coefs_y[2] = betayz;
stencil_coefs_y[3] = betayx;
stencil_coefs_y[4] = gammay;
stencil_coefs_z.resize(6);
stencil_coefs_z[0] = inv_dz;
stencil_coefs_z[1] = alphaz;
stencil_coefs_z[2] = betazx;
stencil_coefs_z[3] = betazy;
stencil_coefs_z[4] = gammaz;
}
/**
/* Perform derivative along x on a cell-centered grid, from a nodal field `F`*/
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real UpwardDx(
amrex::Array4<amrex::Real> const& F,
amrex::Real const* coefs_x, int const n_coefs_x,
int const i, int const j, int const k ) {
amrex::Real alphax = coefs_x[1];
amrex::Real betaxy = coefs_x[2];
amrex::Real betaxz = coefs_x[3];
amrex::Real gammax = coefs_x[4];
# if defined WARPX_DIM_3D
return alphax * (F(i+1,j ,k ) - F(i, j, k ))
+ betaxy * (F(i+1,j+1,k ) - F(i ,j+1,k )
+ F(i+1,j-1,k ) - F(i ,j-1,k ))
+ betaxz * (F(i+1,j ,k+1) - F(i ,j ,k+1)
+ F(i+1,j ,k-1) - F(i ,j ,k-1))
+ gammax * (F(i+1,j+1,k+1) - F(i ,j+1,k+1)
+ F(i+1,j-1,k+1) - F(i ,j-1,k+1)
+ F(i+1,j+1,k-1) - F(i ,j+1,k-1)
+ F(i+1,j-1,k-1) - F(i ,j-1,k-1));
# elif (defined WARPX_DIM_XZ)
return alphax * (F(i+1,j ,k ) - F(i, j, k ))
+ betaxz * (F(i+1,j+1,k ) - F(i ,j+1,k )
+ F(i+1,j-1,k ) - F(i ,j-1,k ));
# endif
};
/**
/* Perform derivative along x on a nodal grid, from a cell-centered field `F`*/
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real Downwardx(
amrex::Array4<amrex::Real> const& F,
amrex::Real const* coefs_x, int const n_coefs_x,
int const i, int const j, int const k ) {
amrex::Real inv_dx = coefs_x[0];
return inv_dx*( F(i,j,k) - F(i-1,j,k) );
};
/**
/* Perform derivative along y on a cell-centered grid, from a nodal field `F`*/
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real UpwardDy(
amrex::Array4<amrex::Real> const& F,
amrex::Real const* coefs_y, int const n_coefs_y,
int const i, int const j, int const k ) {
# if defined WARPX_DIM_3D
amrex::Real alphay = coefs_y[1];
amrex::Real betayz = coefs_y[2];
amrex::Real betayx = coefs_y[3];
amrex::Real gammay = coefs_y[4];
return alphay * (F(i ,j+1,k ) - F(i ,j ,k ))
+ betayx * (F(i+1,j+1,k ) - F(i+1,j ,k )
+ F(i-1,j+1,k ) - F(i-1,j ,k ))
+ betayz * (F(i ,j+1,k+1) - F(i ,j ,k+1)
+ F(i ,j+1,k-1) - F(i ,j ,k-1))
+ gammay * (F(i+1,j+1,k+1) - F(i+1,j ,k+1)
+ F(i-1,j+1,k+1) - F(i-1,j ,k+1)
+ F(i+1,j+1,k-1) - F(i+1,j ,k-1)
+ F(i-1,j+1,k-1) - F(i-1,j ,k-1));
# elif (defined WARPX_DIM_XZ)
return 0; // 2D Cartesian: derivative along y is 0
# endif
};
/**
/* Perform derivative along y on a nodal grid, from a cell-centered field `F`*/
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real Downwardy(
amrex::Array4<amrex::Real> const& F,
amrex::Real const* coefs_y, int const n_coefs_y,
int const i, int const j, int const k ) {
# if defined WARPX_DIM_3D
amrex::Real inv_dy = coefs_y[0];
return inv_dy*( F(i,j,k) - F(i,j-1,k) );
# elif (defined WARPX_DIM_XZ)
return 0; // 2D Cartesian: derivative along y is 0
# endif
};
/**
/* 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 ) {
amrex::Real alphaz = coefs_z[1];
amrex::Real betazx = coefs_z[2];
amrex::Real betazy = coefs_z[3];
amrex::Real gammaz = coefs_z[4];
# if defined WARPX_DIM_3D
return alphaz * (F(i ,j ,k+1) - F(i ,j ,k ))
+ betazx * (F(i+1,j ,k+1) - F(i+1,j ,k )
+ F(i-1,j ,k+1) - F(i-1,j ,k ))
+ betazy * (F(i ,j+1,k+1) - F(i ,j+1,k )
+ F(i ,j-1,k+1) - F(i ,j-1,k ))
+ gammaz * (F(i+1,j+1,k+1) - F(i+1,j+1,k )
+ F(i-1,j+1,k+1) - F(i-1,j+1,k )
+ F(i+1,j-1,k+1) - F(i+1,j-1,k )
+ F(i-1,j-1,k+1) - F(i-1,j-1,k ));
# elif (defined WARPX_DIM_XZ)
return alphaz * (F(i ,j+1,k ) - F(i ,j ,k ))
+ betazx * (F(i+1,j+1,k ) - F(i+1,j ,k )
+ F(i-1,j+1,k ) - F(i-1,j ,k ));
# endif
};
/**
/* Perform derivative along z on a nodal grid, from a cell-centered field `F`*/
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real Downwardz(
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 ) {
amrex::Real inv_dz = coefs_z[0];
# if defined WARPX_DIM_3D
return inv_dz*( F(i,j,k) - F(i,j,k-1) );
# elif (defined WARPX_DIM_XZ)
return inv_dz*( F(i,j,k) - F(i,j-1,k) );
# endif
};
};
#endif // WARPX_FINITE_DIFFERENCE_ALGORITHM_CKC_H_
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