1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
|
/* Copyright 2020 Remi Lehe
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#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 const alphax = coefs_x[1];
amrex::Real const betaxy = coefs_x[2];
amrex::Real const betaxz = coefs_x[3];
amrex::Real const 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 DownwardDx(
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 const 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 const alphay = coefs_y[1];
amrex::Real const betayz = coefs_y[2];
amrex::Real const betayx = coefs_y[3];
amrex::Real const 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 DownwardDy(
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 const 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 const alphaz = coefs_z[1];
amrex::Real const betazx = coefs_z[2];
amrex::Real const betazy = coefs_z[3];
amrex::Real const 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 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 ) {
amrex::Real const 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_
|
