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
|
/* Copyright 2019 Remi Lehe
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#include <PMLPsatdAlgorithm.H>
#include <WarpXConst.H>
#include <cmath>
using namespace amrex;
/* \brief Initialize coefficients for the update equation */
PMLPsatdAlgorithm::PMLPsatdAlgorithm(
const SpectralKSpace& spectral_kspace,
const DistributionMapping& dm,
const int norder_x, const int norder_y,
const int norder_z, const bool nodal, const Real dt)
// Initialize members of base class
: SpectralBaseAlgorithm( spectral_kspace, dm,
norder_x, norder_y, norder_z, nodal )
{
const BoxArray& ba = spectral_kspace.spectralspace_ba;
// Allocate the arrays of coefficients
C_coef = SpectralRealCoefficients(ba, dm, 1, 0);
S_ck_coef = SpectralRealCoefficients(ba, dm, 1, 0);
InitializeSpectralCoefficients(spectral_kspace, dm, dt);
}
/* Advance the E and B field in spectral space (stored in `f`)
* over one time step */
void
PMLPsatdAlgorithm::pushSpectralFields(SpectralFieldData& f) const{
// Loop over boxes
for (MFIter mfi(f.fields); mfi.isValid(); ++mfi){
const Box& bx = f.fields[mfi].box();
// Extract arrays for the fields to be updated
Array4<Complex> fields = f.fields[mfi].array();
// Extract arrays for the coefficients
Array4<const Real> C_arr = C_coef[mfi].array();
Array4<const Real> S_ck_arr = S_ck_coef[mfi].array();
// Extract pointers for the k vectors
const Real* modified_kx_arr = modified_kx_vec[mfi].dataPtr();
#if (AMREX_SPACEDIM==3)
const Real* modified_ky_arr = modified_ky_vec[mfi].dataPtr();
#endif
const Real* modified_kz_arr = modified_kz_vec[mfi].dataPtr();
// Loop over indices within one box
ParallelFor(bx,
[=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
{
// Record old values of the fields to be updated
using Idx = SpectralPMLIndex;
const Complex Ex_old = fields(i,j,k,Idx::Exy) \
+ fields(i,j,k,Idx::Exz);
const Complex Ey_old = fields(i,j,k,Idx::Eyx) \
+ fields(i,j,k,Idx::Eyz);
const Complex Ez_old = fields(i,j,k,Idx::Ezx) \
+ fields(i,j,k,Idx::Ezy);
const Complex Bx_old = fields(i,j,k,Idx::Bxy) \
+ fields(i,j,k,Idx::Bxz);
const Complex By_old = fields(i,j,k,Idx::Byx) \
+ fields(i,j,k,Idx::Byz);
const Complex Bz_old = fields(i,j,k,Idx::Bzx) \
+ fields(i,j,k,Idx::Bzy);
// k vector values, and coefficients
const Real kx = modified_kx_arr[i];
#if (AMREX_SPACEDIM==3)
const Real ky = modified_ky_arr[j];
const Real kz = modified_kz_arr[k];
#else
constexpr Real ky = 0;
const Real kz = modified_kz_arr[j];
#endif
constexpr Real c2 = PhysConst::c*PhysConst::c;
const Complex I = Complex{0,1};
const Real C = C_arr(i,j,k);
const Real S_ck = S_ck_arr(i,j,k);
// Update E
fields(i,j,k,Idx::Exy) = C*fields(i,j,k,Idx::Exy) + S_ck*c2*I*ky*Bz_old;
fields(i,j,k,Idx::Exz) = C*fields(i,j,k,Idx::Exz) - S_ck*c2*I*kz*By_old;
fields(i,j,k,Idx::Eyz) = C*fields(i,j,k,Idx::Eyz) + S_ck*c2*I*kz*Bx_old;
fields(i,j,k,Idx::Eyx) = C*fields(i,j,k,Idx::Eyx) - S_ck*c2*I*kx*Bz_old;
fields(i,j,k,Idx::Ezx) = C*fields(i,j,k,Idx::Ezx) + S_ck*c2*I*kx*By_old;
fields(i,j,k,Idx::Ezy) = C*fields(i,j,k,Idx::Ezy) - S_ck*c2*I*ky*Bx_old;
// Update B
fields(i,j,k,Idx::Bxy) = C*fields(i,j,k,Idx::Bxy) - S_ck*I*ky*Ez_old;
fields(i,j,k,Idx::Bxz) = C*fields(i,j,k,Idx::Bxz) + S_ck*I*kz*Ey_old;
fields(i,j,k,Idx::Byz) = C*fields(i,j,k,Idx::Byz) - S_ck*I*kz*Ex_old;
fields(i,j,k,Idx::Byx) = C*fields(i,j,k,Idx::Byx) + S_ck*I*kx*Ez_old;
fields(i,j,k,Idx::Bzx) = C*fields(i,j,k,Idx::Bzx) - S_ck*I*kx*Ey_old;
fields(i,j,k,Idx::Bzy) = C*fields(i,j,k,Idx::Bzy) + S_ck*I*ky*Ex_old;
});
}
};
void PMLPsatdAlgorithm::InitializeSpectralCoefficients (
const SpectralKSpace& spectral_kspace,
const amrex::DistributionMapping& dm,
const amrex::Real dt)
{
const BoxArray& ba = spectral_kspace.spectralspace_ba;
// Fill them with the right values:
// Loop over boxes and allocate the corresponding coefficients
// for each box owned by the local MPI proc
for (MFIter mfi(ba, dm); mfi.isValid(); ++mfi){
const Box& bx = ba[mfi];
// Extract pointers for the k vectors
const Real* modified_kx = modified_kx_vec[mfi].dataPtr();
#if (AMREX_SPACEDIM==3)
const Real* modified_ky = modified_ky_vec[mfi].dataPtr();
#endif
const Real* modified_kz = modified_kz_vec[mfi].dataPtr();
// Extract arrays for the coefficients
Array4<Real> C = C_coef[mfi].array();
Array4<Real> S_ck = S_ck_coef[mfi].array();
// Loop over indices within one box
ParallelFor(bx,
[=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
{
// Calculate norm of vector
const Real k_norm = std::sqrt(
std::pow(modified_kx[i], 2) +
#if (AMREX_SPACEDIM==3)
std::pow(modified_ky[j], 2) +
std::pow(modified_kz[k], 2));
#else
std::pow(modified_kz[j], 2));
#endif
// Calculate coefficients
constexpr Real c = PhysConst::c;
if (k_norm != 0){
C(i,j,k) = std::cos(c*k_norm*dt);
S_ck(i,j,k) = std::sin(c*k_norm*dt)/(c*k_norm);
} else { // Handle k_norm = 0, by using the analytical limit
C(i,j,k) = 1.;
S_ck(i,j,k) = dt;
}
});
}
};
|
