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
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
|
/* File produced by Kranc */
#define KRANC_C
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "GenericFD.h"
#include "Differencing.h"
#include "loopcontrol.h"
/* Define macros used in calculations */
#define INITVALUE (42)
#define INV(x) ((1.0) / (x))
#define SQR(x) ((x) * (x))
#define CUB(x) ((x) * (x) * (x))
#define QAD(x) ((x) * (x) * (x) * (x))
void ML_ADM_constraints_SelectBCs(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
CCTK_INT ierr = 0;
ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, GenericFD_GetBoundaryWidth(cctkGH), -1 /* no table */, "ML_ADM::ML_Ham","flat");
if (ierr < 0)
CCTK_WARN(1, "Failed to register flat BC for ML_ADM::ML_Ham.");
ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, GenericFD_GetBoundaryWidth(cctkGH), -1 /* no table */, "ML_ADM::ML_mom","flat");
if (ierr < 0)
CCTK_WARN(1, "Failed to register flat BC for ML_ADM::ML_mom.");
return;
}
void ML_ADM_constraints_Body(cGH const * restrict const cctkGH, int const dir, int const face, CCTK_REAL const normal[3], CCTK_REAL const tangentA[3], CCTK_REAL const tangentB[3], int const min[3], int const max[3], int const n_subblock_gfs, CCTK_REAL * restrict const subblock_gfs[])
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
/* Declare finite differencing variables */
if (verbose > 1)
{
CCTK_VInfo(CCTK_THORNSTRING,"Entering ML_ADM_constraints_Body");
}
if (cctk_iteration % ML_ADM_constraints_calc_every != ML_ADM_constraints_calc_offset)
{
return;
}
const char *groups[] = {"ML_ADM::ML_curv","ML_ADM::ML_Ham","ML_ADM::ML_metric","ML_ADM::ML_mom"};
GenericFD_AssertGroupStorage(cctkGH, "ML_ADM_constraints", 4, groups);
/* Include user-supplied include files */
/* Initialise finite differencing variables */
CCTK_REAL const dx = CCTK_DELTA_SPACE(0);
CCTK_REAL const dy = CCTK_DELTA_SPACE(1);
CCTK_REAL const dz = CCTK_DELTA_SPACE(2);
int const di = 1;
int const dj = CCTK_GFINDEX3D(cctkGH,0,1,0) - CCTK_GFINDEX3D(cctkGH,0,0,0);
int const dk = CCTK_GFINDEX3D(cctkGH,0,0,1) - CCTK_GFINDEX3D(cctkGH,0,0,0);
CCTK_REAL const dxi = 1.0 / dx;
CCTK_REAL const dyi = 1.0 / dy;
CCTK_REAL const dzi = 1.0 / dz;
CCTK_REAL const khalf = 0.5;
CCTK_REAL const kthird = 1/3.0;
CCTK_REAL const ktwothird = 2.0/3.0;
CCTK_REAL const kfourthird = 4.0/3.0;
CCTK_REAL const keightthird = 8.0/3.0;
CCTK_REAL const hdxi = 0.5 * dxi;
CCTK_REAL const hdyi = 0.5 * dyi;
CCTK_REAL const hdzi = 0.5 * dzi;
/* Initialize predefined quantities */
CCTK_REAL const p1o12dx = INV(dx)/12.;
CCTK_REAL const p1o12dy = INV(dy)/12.;
CCTK_REAL const p1o12dz = INV(dz)/12.;
CCTK_REAL const p1o144dxdy = (INV(dx)*INV(dy))/144.;
CCTK_REAL const p1o144dxdz = (INV(dx)*INV(dz))/144.;
CCTK_REAL const p1o144dydz = (INV(dy)*INV(dz))/144.;
CCTK_REAL const pm1o12dx2 = -pow(dx,-2)/12.;
CCTK_REAL const pm1o12dy2 = -pow(dy,-2)/12.;
CCTK_REAL const pm1o12dz2 = -pow(dz,-2)/12.;
/* Loop over the grid points */
#pragma omp parallel
LC_LOOP3 (ML_ADM_constraints,
i,j,k, min[0],min[1],min[2], max[0],max[1],max[2],
cctk_lsh[0],cctk_lsh[1],cctk_lsh[2])
{
// int index = INITVALUE;
int const index = CCTK_GFINDEX3D(cctkGH,i,j,k);
/* Declare derivatives */
// CCTK_REAL PDstandardNth1g11 = INITVALUE;
// CCTK_REAL PDstandardNth2g11 = INITVALUE;
// CCTK_REAL PDstandardNth3g11 = INITVALUE;
// CCTK_REAL PDstandardNth22g11 = INITVALUE;
// CCTK_REAL PDstandardNth33g11 = INITVALUE;
// CCTK_REAL PDstandardNth23g11 = INITVALUE;
// CCTK_REAL PDstandardNth1g12 = INITVALUE;
// CCTK_REAL PDstandardNth2g12 = INITVALUE;
// CCTK_REAL PDstandardNth3g12 = INITVALUE;
// CCTK_REAL PDstandardNth33g12 = INITVALUE;
// CCTK_REAL PDstandardNth12g12 = INITVALUE;
// CCTK_REAL PDstandardNth13g12 = INITVALUE;
// CCTK_REAL PDstandardNth23g12 = INITVALUE;
// CCTK_REAL PDstandardNth1g13 = INITVALUE;
// CCTK_REAL PDstandardNth2g13 = INITVALUE;
// CCTK_REAL PDstandardNth3g13 = INITVALUE;
// CCTK_REAL PDstandardNth22g13 = INITVALUE;
// CCTK_REAL PDstandardNth12g13 = INITVALUE;
// CCTK_REAL PDstandardNth13g13 = INITVALUE;
// CCTK_REAL PDstandardNth23g13 = INITVALUE;
// CCTK_REAL PDstandardNth1g22 = INITVALUE;
// CCTK_REAL PDstandardNth2g22 = INITVALUE;
// CCTK_REAL PDstandardNth3g22 = INITVALUE;
// CCTK_REAL PDstandardNth11g22 = INITVALUE;
// CCTK_REAL PDstandardNth33g22 = INITVALUE;
// CCTK_REAL PDstandardNth13g22 = INITVALUE;
// CCTK_REAL PDstandardNth1g23 = INITVALUE;
// CCTK_REAL PDstandardNth2g23 = INITVALUE;
// CCTK_REAL PDstandardNth3g23 = INITVALUE;
// CCTK_REAL PDstandardNth11g23 = INITVALUE;
// CCTK_REAL PDstandardNth12g23 = INITVALUE;
// CCTK_REAL PDstandardNth13g23 = INITVALUE;
// CCTK_REAL PDstandardNth23g23 = INITVALUE;
// CCTK_REAL PDstandardNth1g33 = INITVALUE;
// CCTK_REAL PDstandardNth2g33 = INITVALUE;
// CCTK_REAL PDstandardNth3g33 = INITVALUE;
// CCTK_REAL PDstandardNth11g33 = INITVALUE;
// CCTK_REAL PDstandardNth22g33 = INITVALUE;
// CCTK_REAL PDstandardNth12g33 = INITVALUE;
// CCTK_REAL PDstandardNth2K11 = INITVALUE;
// CCTK_REAL PDstandardNth3K11 = INITVALUE;
// CCTK_REAL PDstandardNth1K12 = INITVALUE;
// CCTK_REAL PDstandardNth2K12 = INITVALUE;
// CCTK_REAL PDstandardNth3K12 = INITVALUE;
// CCTK_REAL PDstandardNth1K13 = INITVALUE;
// CCTK_REAL PDstandardNth2K13 = INITVALUE;
// CCTK_REAL PDstandardNth3K13 = INITVALUE;
// CCTK_REAL PDstandardNth1K22 = INITVALUE;
// CCTK_REAL PDstandardNth3K22 = INITVALUE;
// CCTK_REAL PDstandardNth1K23 = INITVALUE;
// CCTK_REAL PDstandardNth2K23 = INITVALUE;
// CCTK_REAL PDstandardNth3K23 = INITVALUE;
// CCTK_REAL PDstandardNth1K33 = INITVALUE;
// CCTK_REAL PDstandardNth2K33 = INITVALUE;
/* Assign local copies of grid functions */
CCTK_REAL g11L = g11[index];
CCTK_REAL g12L = g12[index];
CCTK_REAL g13L = g13[index];
CCTK_REAL g22L = g22[index];
CCTK_REAL g23L = g23[index];
CCTK_REAL g33L = g33[index];
CCTK_REAL K11L = K11[index];
CCTK_REAL K12L = K12[index];
CCTK_REAL K13L = K13[index];
CCTK_REAL K22L = K22[index];
CCTK_REAL K23L = K23[index];
CCTK_REAL K33L = K33[index];
/* Include user supplied include files */
/* Precompute derivatives */
CCTK_REAL const PDstandardNth1g11 = PDstandardNth1(g11, i, j, k);
CCTK_REAL const PDstandardNth2g11 = PDstandardNth2(g11, i, j, k);
CCTK_REAL const PDstandardNth3g11 = PDstandardNth3(g11, i, j, k);
CCTK_REAL const PDstandardNth22g11 = PDstandardNth22(g11, i, j, k);
CCTK_REAL const PDstandardNth33g11 = PDstandardNth33(g11, i, j, k);
CCTK_REAL const PDstandardNth23g11 = PDstandardNth23(g11, i, j, k);
CCTK_REAL const PDstandardNth1g12 = PDstandardNth1(g12, i, j, k);
CCTK_REAL const PDstandardNth2g12 = PDstandardNth2(g12, i, j, k);
CCTK_REAL const PDstandardNth3g12 = PDstandardNth3(g12, i, j, k);
CCTK_REAL const PDstandardNth33g12 = PDstandardNth33(g12, i, j, k);
CCTK_REAL const PDstandardNth12g12 = PDstandardNth12(g12, i, j, k);
CCTK_REAL const PDstandardNth13g12 = PDstandardNth13(g12, i, j, k);
CCTK_REAL const PDstandardNth23g12 = PDstandardNth23(g12, i, j, k);
CCTK_REAL const PDstandardNth1g13 = PDstandardNth1(g13, i, j, k);
CCTK_REAL const PDstandardNth2g13 = PDstandardNth2(g13, i, j, k);
CCTK_REAL const PDstandardNth3g13 = PDstandardNth3(g13, i, j, k);
CCTK_REAL const PDstandardNth22g13 = PDstandardNth22(g13, i, j, k);
CCTK_REAL const PDstandardNth12g13 = PDstandardNth12(g13, i, j, k);
CCTK_REAL const PDstandardNth13g13 = PDstandardNth13(g13, i, j, k);
CCTK_REAL const PDstandardNth23g13 = PDstandardNth23(g13, i, j, k);
CCTK_REAL const PDstandardNth1g22 = PDstandardNth1(g22, i, j, k);
CCTK_REAL const PDstandardNth2g22 = PDstandardNth2(g22, i, j, k);
CCTK_REAL const PDstandardNth3g22 = PDstandardNth3(g22, i, j, k);
CCTK_REAL const PDstandardNth11g22 = PDstandardNth11(g22, i, j, k);
CCTK_REAL const PDstandardNth33g22 = PDstandardNth33(g22, i, j, k);
CCTK_REAL const PDstandardNth13g22 = PDstandardNth13(g22, i, j, k);
CCTK_REAL const PDstandardNth1g23 = PDstandardNth1(g23, i, j, k);
CCTK_REAL const PDstandardNth2g23 = PDstandardNth2(g23, i, j, k);
CCTK_REAL const PDstandardNth3g23 = PDstandardNth3(g23, i, j, k);
CCTK_REAL const PDstandardNth11g23 = PDstandardNth11(g23, i, j, k);
CCTK_REAL const PDstandardNth12g23 = PDstandardNth12(g23, i, j, k);
CCTK_REAL const PDstandardNth13g23 = PDstandardNth13(g23, i, j, k);
CCTK_REAL const PDstandardNth23g23 = PDstandardNth23(g23, i, j, k);
CCTK_REAL const PDstandardNth1g33 = PDstandardNth1(g33, i, j, k);
CCTK_REAL const PDstandardNth2g33 = PDstandardNth2(g33, i, j, k);
CCTK_REAL const PDstandardNth3g33 = PDstandardNth3(g33, i, j, k);
CCTK_REAL const PDstandardNth11g33 = PDstandardNth11(g33, i, j, k);
CCTK_REAL const PDstandardNth22g33 = PDstandardNth22(g33, i, j, k);
CCTK_REAL const PDstandardNth12g33 = PDstandardNth12(g33, i, j, k);
CCTK_REAL const PDstandardNth2K11 = PDstandardNth2(K11, i, j, k);
CCTK_REAL const PDstandardNth3K11 = PDstandardNth3(K11, i, j, k);
CCTK_REAL const PDstandardNth1K12 = PDstandardNth1(K12, i, j, k);
CCTK_REAL const PDstandardNth2K12 = PDstandardNth2(K12, i, j, k);
CCTK_REAL const PDstandardNth3K12 = PDstandardNth3(K12, i, j, k);
CCTK_REAL const PDstandardNth1K13 = PDstandardNth1(K13, i, j, k);
CCTK_REAL const PDstandardNth2K13 = PDstandardNth2(K13, i, j, k);
CCTK_REAL const PDstandardNth3K13 = PDstandardNth3(K13, i, j, k);
CCTK_REAL const PDstandardNth1K22 = PDstandardNth1(K22, i, j, k);
CCTK_REAL const PDstandardNth3K22 = PDstandardNth3(K22, i, j, k);
CCTK_REAL const PDstandardNth1K23 = PDstandardNth1(K23, i, j, k);
CCTK_REAL const PDstandardNth2K23 = PDstandardNth2(K23, i, j, k);
CCTK_REAL const PDstandardNth3K23 = PDstandardNth3(K23, i, j, k);
CCTK_REAL const PDstandardNth1K33 = PDstandardNth1(K33, i, j, k);
CCTK_REAL const PDstandardNth2K33 = PDstandardNth2(K33, i, j, k);
/* Calculate temporaries and grid functions */
CCTK_REAL detg = 2*g12L*g13L*g23L + g33L*(g11L*g22L - SQR(g12L)) -
g22L*SQR(g13L) - g11L*SQR(g23L);
CCTK_REAL gu11 = INV(detg)*(g22L*g33L - SQR(g23L));
CCTK_REAL gu12 = (g13L*g23L - g12L*g33L)*INV(detg);
CCTK_REAL gu13 = (-(g13L*g22L) + g12L*g23L)*INV(detg);
CCTK_REAL gu21 = (g13L*g23L - g12L*g33L)*INV(detg);
CCTK_REAL gu22 = INV(detg)*(g11L*g33L - SQR(g13L));
CCTK_REAL gu23 = (g12L*g13L - g11L*g23L)*INV(detg);
CCTK_REAL gu31 = (-(g13L*g22L) + g12L*g23L)*INV(detg);
CCTK_REAL gu32 = (g12L*g13L - g11L*g23L)*INV(detg);
CCTK_REAL gu33 = INV(detg)*(g11L*g22L - SQR(g12L));
CCTK_REAL G111 = khalf*(gu11*PDstandardNth1g11 +
2*(gu12*PDstandardNth1g12 + gu13*PDstandardNth1g13) -
gu12*PDstandardNth2g11 - gu13*PDstandardNth3g11);
CCTK_REAL G211 = khalf*(gu21*PDstandardNth1g11 +
2*(gu22*PDstandardNth1g12 + gu23*PDstandardNth1g13) -
gu22*PDstandardNth2g11 - gu23*PDstandardNth3g11);
CCTK_REAL G311 = khalf*(gu31*PDstandardNth1g11 +
2*(gu32*PDstandardNth1g12 + gu33*PDstandardNth1g13) -
gu32*PDstandardNth2g11 - gu33*PDstandardNth3g11);
CCTK_REAL G112 = khalf*(gu12*PDstandardNth1g22 +
gu11*PDstandardNth2g11 + gu13*(PDstandardNth1g23 + PDstandardNth2g13 -
PDstandardNth3g12));
CCTK_REAL G212 = khalf*(gu22*PDstandardNth1g22 +
gu21*PDstandardNth2g11 + gu23*(PDstandardNth1g23 + PDstandardNth2g13 -
PDstandardNth3g12));
CCTK_REAL G312 = khalf*(gu32*PDstandardNth1g22 +
gu31*PDstandardNth2g11 + gu33*(PDstandardNth1g23 + PDstandardNth2g13 -
PDstandardNth3g12));
CCTK_REAL G113 = khalf*(gu13*PDstandardNth1g33 +
gu11*PDstandardNth3g11 + gu12*(PDstandardNth1g23 - PDstandardNth2g13 +
PDstandardNth3g12));
CCTK_REAL G213 = khalf*(gu23*PDstandardNth1g33 +
gu21*PDstandardNth3g11 + gu22*(PDstandardNth1g23 - PDstandardNth2g13 +
PDstandardNth3g12));
CCTK_REAL G313 = khalf*(gu33*PDstandardNth1g33 +
gu31*PDstandardNth3g11 + gu32*(PDstandardNth1g23 - PDstandardNth2g13 +
PDstandardNth3g12));
CCTK_REAL G122 = khalf*(gu11*(-PDstandardNth1g22 +
2*PDstandardNth2g12) + gu12*PDstandardNth2g22 +
gu13*(2*PDstandardNth2g23 - PDstandardNth3g22));
CCTK_REAL G222 = khalf*(gu21*(-PDstandardNth1g22 +
2*PDstandardNth2g12) + gu22*PDstandardNth2g22 +
gu23*(2*PDstandardNth2g23 - PDstandardNth3g22));
CCTK_REAL G322 = khalf*(gu31*(-PDstandardNth1g22 +
2*PDstandardNth2g12) + gu32*PDstandardNth2g22 +
gu33*(2*PDstandardNth2g23 - PDstandardNth3g22));
CCTK_REAL G123 = khalf*(gu13*PDstandardNth2g33 +
gu11*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) +
gu12*PDstandardNth3g22);
CCTK_REAL G223 = khalf*(gu23*PDstandardNth2g33 +
gu21*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) +
gu22*PDstandardNth3g22);
CCTK_REAL G323 = khalf*(gu33*PDstandardNth2g33 +
gu31*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) +
gu32*PDstandardNth3g22);
CCTK_REAL G133 = khalf*(-(gu11*PDstandardNth1g33) -
gu12*PDstandardNth2g33 + 2*gu11*PDstandardNth3g13 +
2*gu12*PDstandardNth3g23 + gu13*PDstandardNth3g33);
CCTK_REAL G233 = khalf*(-(gu21*PDstandardNth1g33) -
gu22*PDstandardNth2g33 + 2*gu21*PDstandardNth3g13 +
2*gu22*PDstandardNth3g23 + gu23*PDstandardNth3g33);
CCTK_REAL G333 = khalf*(-(gu31*PDstandardNth1g33) -
gu32*PDstandardNth2g33 + 2*gu31*PDstandardNth3g13 +
2*gu32*PDstandardNth3g23 + gu33*PDstandardNth3g33);
CCTK_REAL R11 = -(G111*(G111 + G122 + G133)) - G211*(G211 + G222 +
G233) - G311*(G311 + G322 + G333) + khalf*(-(gu22*(PDstandardNth11g22 -
2*PDstandardNth12g12 + PDstandardNth22g11)) + gu23*(-PDstandardNth11g23
+ PDstandardNth12g13 + PDstandardNth13g12 - PDstandardNth23g11) +
gu32*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 -
PDstandardNth23g11) - gu33*(PDstandardNth11g33 - 2*PDstandardNth13g13 +
PDstandardNth33g11)) + SQR(G111) + SQR(G112) + SQR(G113) + SQR(G211) +
SQR(G212) + SQR(G213) + SQR(G311) + SQR(G312) + SQR(G313);
CCTK_REAL R12 = khalf*(2*(G113*G123 + G213*G223 + G313*G323) -
2*(G112*G133 + G212*G233 + G312*G333 + gu12*PDstandardNth12g12) -
gu32*PDstandardNth12g23 - gu33*PDstandardNth12g33 +
gu13*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12) +
gu32*PDstandardNth13g22 + gu33*PDstandardNth13g23 +
gu12*(PDstandardNth11g22 + PDstandardNth22g11) +
gu32*PDstandardNth22g13 + gu13*PDstandardNth23g11 -
gu32*PDstandardNth23g12 + gu33*PDstandardNth23g13 -
gu33*PDstandardNth33g12);
CCTK_REAL R13 = khalf*(2*(G112*G123 + G212*G223 + G312*G323) -
2*(G113*G122 + G213*G222 + G313*G322 + gu13*PDstandardNth13g13) +
gu12*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12 +
PDstandardNth23g11) + gu22*(PDstandardNth12g23 - PDstandardNth13g22 -
PDstandardNth22g13 + PDstandardNth23g12) + gu13*(PDstandardNth11g33 +
PDstandardNth33g11) + gu23*(PDstandardNth12g33 - PDstandardNth13g23 -
PDstandardNth23g13 + PDstandardNth33g12));
CCTK_REAL R22 = -(G122*(G111 + G122 + G133)) - G222*(G211 + G222 +
G233) - G322*(G311 + G322 + G333) + khalf*(-(gu11*(PDstandardNth11g22 -
2*PDstandardNth12g12 + PDstandardNth22g11)) + gu13*(PDstandardNth12g23
- PDstandardNth13g22 - PDstandardNth22g13 + PDstandardNth23g12) +
gu31*(PDstandardNth12g23 - PDstandardNth13g22 - PDstandardNth22g13 +
PDstandardNth23g12) - gu33*(PDstandardNth22g33 - 2*PDstandardNth23g23 +
PDstandardNth33g22)) + SQR(G112) + SQR(G122) + SQR(G123) + SQR(G212) +
SQR(G222) + SQR(G223) + SQR(G312) + SQR(G322) + SQR(G323);
CCTK_REAL R23 = khalf*(2*(G112*G113 + G212*G213 + G312*G313) +
gu11*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 -
PDstandardNth23g11) + gu21*(-PDstandardNth12g23 + PDstandardNth13g22 +
PDstandardNth22g13 - PDstandardNth23g12) - 2*(G111*G123 + G211*G223 +
G311*G323 + gu23*PDstandardNth23g23) + gu13*(PDstandardNth12g33 -
PDstandardNth13g23 - PDstandardNth23g13 + PDstandardNth33g12) +
gu23*(PDstandardNth22g33 + PDstandardNth33g22));
CCTK_REAL R33 = -(G133*(G111 + G122 + G133)) - G233*(G211 + G222 +
G233) - G333*(G311 + G322 + G333) + khalf*(-(gu11*(PDstandardNth11g33 -
2*PDstandardNth13g13 + PDstandardNth33g11)) + gu12*(-PDstandardNth12g33
+ PDstandardNth13g23 + PDstandardNth23g13 - PDstandardNth33g12) +
gu21*(-PDstandardNth12g33 + PDstandardNth13g23 + PDstandardNth23g13 -
PDstandardNth33g12) - gu22*(PDstandardNth22g33 - 2*PDstandardNth23g23 +
PDstandardNth33g22)) + SQR(G113) + SQR(G123) + SQR(G133) + SQR(G213) +
SQR(G223) + SQR(G233) + SQR(G313) + SQR(G323) + SQR(G333);
CCTK_REAL trR = gu11*R11 + (gu12 + gu21)*R12 + (gu13 + gu31)*R13 +
gu22*R22 + (gu23 + gu32)*R23 + gu33*R33;
CCTK_REAL Km11 = gu11*K11L + gu12*K12L + gu13*K13L;
CCTK_REAL Km21 = gu21*K11L + gu22*K12L + gu23*K13L;
CCTK_REAL Km31 = gu31*K11L + gu32*K12L + gu33*K13L;
CCTK_REAL Km12 = gu11*K12L + gu12*K22L + gu13*K23L;
CCTK_REAL Km22 = gu21*K12L + gu22*K22L + gu23*K23L;
CCTK_REAL Km32 = gu31*K12L + gu32*K22L + gu33*K23L;
CCTK_REAL Km13 = gu11*K13L + gu12*K23L + gu13*K33L;
CCTK_REAL Km23 = gu21*K13L + gu22*K23L + gu23*K33L;
CCTK_REAL Km33 = gu31*K13L + gu32*K23L + gu33*K33L;
CCTK_REAL trK = Km11 + Km22 + Km33;
CCTK_REAL HL = -2*(Km12*Km21 + Km13*Km31 + Km23*Km32) + trR -
SQR(Km11) - SQR(Km22) - SQR(Km33) + SQR(trK);
CCTK_REAL M1L = gu21*(-(G112*K11L) + G111*K12L - G212*K12L - G312*K13L
+ G211*K22L + G311*K23L - PDstandardNth1K12 + PDstandardNth2K11) +
gu22*(-(G122*K11L) + G112*K12L - G222*K12L - G322*K13L + G212*K22L +
G312*K23L - PDstandardNth1K22 + PDstandardNth2K12) + gu23*(-(G123*K11L)
+ G113*K12L - G223*K12L - G323*K13L + G213*K22L + G313*K23L -
PDstandardNth1K23 + PDstandardNth2K13) + gu31*(-(G113*K11L) - G213*K12L
+ G111*K13L - G313*K13L + G211*K23L + G311*K33L - PDstandardNth1K13 +
PDstandardNth3K11) + gu32*(-(G123*K11L) - G223*K12L + G112*K13L -
G323*K13L + G212*K23L + G312*K33L - PDstandardNth1K23 +
PDstandardNth3K12) + gu33*(-(G133*K11L) - G233*K12L + G113*K13L -
G333*K13L + G213*K23L + G313*K33L - PDstandardNth1K33 +
PDstandardNth3K13);
CCTK_REAL M2L = gu11*(G112*K11L + (-G111 + G212)*K12L + G312*K13L -
G211*K22L - G311*K23L + PDstandardNth1K12 - PDstandardNth2K11) +
gu12*(G122*K11L + (-G112 + G222)*K12L + G322*K13L - G212*K22L -
G312*K23L + PDstandardNth1K22 - PDstandardNth2K12) + gu13*(G123*K11L +
(-G113 + G223)*K12L + G323*K13L - G213*K22L - G313*K23L +
PDstandardNth1K23 - PDstandardNth2K13) + gu31*(-(G113*K12L) + G112*K13L
- G213*K22L + G212*K23L - G313*K23L + G312*K33L - PDstandardNth2K13 +
PDstandardNth3K12) + gu32*(-(G123*K12L) + G122*K13L - G223*K22L +
G222*K23L - G323*K23L + G322*K33L - PDstandardNth2K23 +
PDstandardNth3K22) + gu33*(-(G133*K12L) + G123*K13L - G233*K22L +
G223*K23L - G333*K23L + G323*K33L - PDstandardNth2K33 +
PDstandardNth3K23);
CCTK_REAL M3L = gu11*(G113*K11L + G213*K12L + (-G111 + G313)*K13L -
G211*K23L - G311*K33L + PDstandardNth1K13 - PDstandardNth3K11) +
gu12*(G123*K11L + G223*K12L + (-G112 + G323)*K13L - G212*K23L -
G312*K33L + PDstandardNth1K23 - PDstandardNth3K12) + gu21*(G113*K12L -
G112*K13L + G213*K22L - G212*K23L + G313*K23L - G312*K33L +
PDstandardNth2K13 - PDstandardNth3K12) + gu13*(G133*K11L + G233*K12L +
(-G113 + G333)*K13L - G213*K23L - G313*K33L + PDstandardNth1K33 -
PDstandardNth3K13) + gu22*(G123*K12L - G122*K13L + G223*K22L -
G222*K23L + G323*K23L - G322*K33L + PDstandardNth2K23 -
PDstandardNth3K22) + gu23*(G133*K12L - G123*K13L + G233*K22L -
G223*K23L + G333*K23L - G323*K33L + PDstandardNth2K33 -
PDstandardNth3K23);
/* Copy local copies back to grid functions */
H[index] = HL;
M1[index] = M1L;
M2[index] = M2L;
M3[index] = M3L;
}
LC_ENDLOOP3 (ML_ADM_constraints);
}
void ML_ADM_constraints(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
GenericFD_LoopOverInterior(cctkGH, &ML_ADM_constraints_Body);
}
|
