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
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
|
#include <SpectralFieldData.H>
using namespace amrex;
/* \brief Initialize fields in spectral space, and FFT plans */
SpectralFieldData::SpectralFieldData( const BoxArray& realspace_ba,
const SpectralKSpace& k_space,
const DistributionMapping& dm )
{
const BoxArray& spectralspace_ba = k_space.spectralspace_ba;
// Allocate the arrays that contain the fields in spectral space
Ex = SpectralField(spectralspace_ba, dm, 1, 0);
Ey = SpectralField(spectralspace_ba, dm, 1, 0);
Ez = SpectralField(spectralspace_ba, dm, 1, 0);
Bx = SpectralField(spectralspace_ba, dm, 1, 0);
By = SpectralField(spectralspace_ba, dm, 1, 0);
Bz = SpectralField(spectralspace_ba, dm, 1, 0);
Jx = SpectralField(spectralspace_ba, dm, 1, 0);
Jy = SpectralField(spectralspace_ba, dm, 1, 0);
Jz = SpectralField(spectralspace_ba, dm, 1, 0);
rho_old = SpectralField(spectralspace_ba, dm, 1, 0);
rho_new = SpectralField(spectralspace_ba, dm, 1, 0);
// Allocate temporary arrays - in real space and spectral space
// These arrays will store the data just before/after the FFT
tmpRealField = SpectralField(realspace_ba, dm, 1, 0);
tmpSpectralField = SpectralField(spectralspace_ba, dm, 1, 0);
// By default, we assume the FFT is done from/to a nodal grid in real space
// It the FFT is performed from/to a cell-centered grid in real space,
// a correcting "shift" factor must be applied in spectral space.
xshift_FFTfromCell = k_space.getSpectralShiftFactor(dm, 0,
ShiftType::TransformFromCellCentered);
xshift_FFTtoCell = k_space.getSpectralShiftFactor(dm, 0,
ShiftType::TransformToCellCentered);
#if (AMREX_SPACEDIM == 3)
yshift_FFTfromCell = k_space.getSpectralShiftFactor(dm, 1,
ShiftType::TransformFromCellCentered);
yshift_FFTtoCell = k_space.getSpectralShiftFactor(dm, 1,
ShiftType::TransformToCellCentered);
zshift_FFTfromCell = k_space.getSpectralShiftFactor(dm, 2,
ShiftType::TransformFromCellCentered);
zshift_FFTtoCell = k_space.getSpectralShiftFactor(dm, 2,
ShiftType::TransformToCellCentered);
#else
zshift_FFTfromCell = k_space.getSpectralShiftFactor(dm, 1,
ShiftType::TransformFromCellCentered);
zshift_FFTtoCell = k_space.getSpectralShiftFactor(dm, 1,
ShiftType::TransformToCellCentered);
#endif
// Allocate and initialize the FFT plans
forward_plan = FFTplans(spectralspace_ba, dm);
backward_plan = FFTplans(spectralspace_ba, dm);
// Loop over boxes and allocate the corresponding plan
// for each box owned by the local MPI proc
for ( MFIter mfi(spectralspace_ba, dm); mfi.isValid(); ++mfi ){
Box bx = spectralspace_ba[mfi];
#ifdef AMREX_USE_GPU
// Add cuFFT-specific code
#else
// Create FFTW plans
forward_plan[mfi] =
// Swap dimensions: AMReX FAB are Fortran-order but FFTW is C-order
#if (AMREX_SPACEDIM == 3)
fftw_plan_dft_3d( bx.length(2), bx.length(1), bx.length(0),
#else
fftw_plan_dft_2d( bx.length(1), bx.length(0),
#endif
reinterpret_cast<fftw_complex*>( tmpRealField[mfi].dataPtr() ),
reinterpret_cast<fftw_complex*>( tmpSpectralField[mfi].dataPtr() ),
FFTW_FORWARD, FFTW_ESTIMATE );
backward_plan[mfi] =
// Swap dimensions: AMReX FAB are Fortran-order but FFTW is C-order
#if (AMREX_SPACEDIM == 3)
fftw_plan_dft_3d( bx.length(2), bx.length(1), bx.length(0),
#else
fftw_plan_dft_2d( bx.length(1), bx.length(0),
#endif
reinterpret_cast<fftw_complex*>( tmpSpectralField[mfi].dataPtr() ),
reinterpret_cast<fftw_complex*>( tmpRealField[mfi].dataPtr() ),
FFTW_BACKWARD, FFTW_ESTIMATE );
#endif
}
}
SpectralFieldData::~SpectralFieldData()
{
if (tmpRealField.size() > 0){
for ( MFIter mfi(tmpRealField); mfi.isValid(); ++mfi ){
#ifdef AMREX_USE_GPU
// Add cuFFT-specific code
#else
// Destroy FFTW plans
fftw_destroy_plan( forward_plan[mfi] );
fftw_destroy_plan( backward_plan[mfi] );
#endif
}
}
}
/* \brief Transform the component `i_comp` of MultiFab `mf`
* to spectral space, and store the corresponding result internally
* (in the spectral field specified by `field_index`) */
void
SpectralFieldData::ForwardTransform( const MultiFab& mf,
const int field_index,
const int i_comp )
{
// Check field index type, in order to apply proper shift in spectral space
const bool is_nodal_x = mf.is_nodal(0);
#if (AMREX_SPACEDIM == 3)
const bool is_nodal_y = mf.is_nodal(1);
const bool is_nodal_z = mf.is_nodal(2);
#else
const bool is_nodal_z = mf.is_nodal(1);
#endif
// Loop over boxes
for ( MFIter mfi(mf); mfi.isValid(); ++mfi ){
// Copy the real-space field `mf` to the temporary field `tmpRealField`
// This ensures that all fields have the same number of points
// before the Fourier transform.
// As a consequence, the copy discards the *last* point of `mf`
// in any direction that has *nodal* index type.
{
Box realspace_bx = mf[mfi].box(); // Copy the box
realspace_bx.enclosedCells(); // Discard last point in nodal direction
AMREX_ALWAYS_ASSERT( realspace_bx == tmpRealField[mfi].box() );
Array4<const Real> mf_arr = mf[mfi].array();
Array4<Complex> tmp_arr = tmpRealField[mfi].array();
ParallelFor( realspace_bx,
[=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept {
tmp_arr(i,j,k) = mf_arr(i,j,k,i_comp);
});
}
// Perform Fourier transform from `tmpRealField` to `tmpSpectralField`
#ifdef AMREX_USE_GPU
// Add cuFFT-specific code ; make sure that this is done on the same
// GPU stream as the above copy
#else
fftw_execute( forward_plan[mfi] );
#endif
// Copy the spectral-space field `tmpSpectralField` to the appropriate
// field (specified by the input argument field_index )
// and apply correcting shift factor if the real space data comes
// from a cell-centered grid in real space instead of a nodal grid.
{
SpectralField& field = getSpectralField( field_index );
Array4<Complex> field_arr = field[mfi].array();
Array4<const Complex> tmp_arr = tmpSpectralField[mfi].array();
const Complex* xshift_arr = xshift_FFTfromCell[mfi].dataPtr();
#if (AMREX_SPACEDIM == 3)
const Complex* yshift_arr = yshift_FFTfromCell[mfi].dataPtr();
#endif
const Complex* zshift_arr = zshift_FFTfromCell[mfi].dataPtr();
// Loop over indices within one box
const Box spectralspace_bx = tmpSpectralField[mfi].box();
ParallelFor( spectralspace_bx,
[=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept {
Complex spectral_field_value = tmp_arr(i,j,k);
// Apply proper shift in each dimension
if (is_nodal_x==false) spectral_field_value *= xshift_arr[i];
#if (AMREX_SPACEDIM == 3)
if (is_nodal_y==false) spectral_field_value *= yshift_arr[j];
if (is_nodal_z==false) spectral_field_value *= zshift_arr[k];
#elif (AMREX_SPACEDIM == 2)
if (is_nodal_z==false) spectral_field_value *= zshift_arr[j];
#endif
// Copy field into temporary array
field_arr(i,j,k) = spectral_field_value;
});
}
}
}
/* \brief Transform spectral field specified by `field_index` back to
* real space, and store it in the component `i_comp` of `mf` */
void
SpectralFieldData::BackwardTransform( MultiFab& mf,
const int field_index, const int i_comp )
{
// Check field index type, in order to apply proper shift in spectral space
const bool is_nodal_x = mf.is_nodal(0);
#if (AMREX_SPACEDIM == 3)
const bool is_nodal_y = mf.is_nodal(1);
const bool is_nodal_z = mf.is_nodal(2);
#else
const bool is_nodal_z = mf.is_nodal(1);
#endif
// Loop over boxes
for ( MFIter mfi(mf); mfi.isValid(); ++mfi ){
// Copy the spectral-space field `tmpSpectralField` to the appropriate
// field (specified by the input argument field_index)
// and apply correcting shift factor if the field is to be transformed
// to a cell-centered grid in real space instead of a nodal grid.
// Normalize (divide by 1/N) since the FFT+IFFT results in a factor N
{
SpectralField& field = getSpectralField( field_index );
Array4<const Complex> field_arr = field[mfi].array();
Array4<Complex> tmp_arr = tmpSpectralField[mfi].array();
const Complex* xshift_arr = xshift_FFTtoCell[mfi].dataPtr();
#if (AMREX_SPACEDIM == 3)
const Complex* yshift_arr = yshift_FFTtoCell[mfi].dataPtr();
#endif
const Complex* zshift_arr = zshift_FFTtoCell[mfi].dataPtr();
// Loop over indices within one box
const Box spectralspace_bx = tmpSpectralField[mfi].box();
// For normalization: divide by the number of points in the box
const Real inv_N = 1./spectralspace_bx.numPts();
ParallelFor( spectralspace_bx,
[=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept {
Complex spectral_field_value = field_arr(i,j,k);
// Apply proper shift in each dimension
if (is_nodal_x==false) spectral_field_value *= xshift_arr[i];
#if (AMREX_SPACEDIM == 3)
if (is_nodal_y==false) spectral_field_value *= yshift_arr[j];
if (is_nodal_z==false) spectral_field_value *= zshift_arr[k];
#elif (AMREX_SPACEDIM == 2)
if (is_nodal_z==false) spectral_field_value *= zshift_arr[j];
#endif
// Copy field into temporary array (after normalization)
tmp_arr(i,j,k) = inv_N*spectral_field_value;
});
}
// Perform Fourier transform from `tmpSpectralField` to `tmpRealField`
#ifdef AMREX_USE_GPU
// Add cuFFT-specific code ; make sure that this is done on the same
// GPU stream as the above copy
#else
fftw_execute( backward_plan[mfi] );
#endif
// Copy the temporary field `tmpRealField` to the real-space field `mf`
{
const Box realspace_bx = tmpRealField[mfi].box();
Array4<Real> mf_arr = mf[mfi].array();
Array4<const Complex> tmp_arr = tmpRealField[mfi].array();
ParallelFor( realspace_bx,
[=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept {
mf_arr(i,j,k,i_comp) = tmp_arr(i,j,k).real();
});
}
}
}
SpectralField&
SpectralFieldData::getSpectralField( const int field_index )
{
switch(field_index)
{
case SpectralFieldIndex::Ex : return Ex; break;
case SpectralFieldIndex::Ey : return Ey; break;
case SpectralFieldIndex::Ez : return Ez; break;
case SpectralFieldIndex::Bx : return Bx; break;
case SpectralFieldIndex::By : return By; break;
case SpectralFieldIndex::Bz : return Bz; break;
case SpectralFieldIndex::Jx : return Jx; break;
case SpectralFieldIndex::Jy : return Jy; break;
case SpectralFieldIndex::Jz : return Jz; break;
case SpectralFieldIndex::rho_old : return rho_old; break;
case SpectralFieldIndex::rho_new : return rho_new; break;
default : return tmpSpectralField; // For synthax; should not occur in practice
}
}
|
