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
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
|
/*@@
@file GenericFD/src/GenericFD.h
@date June 16 2002
@author S. Husa
@desc
$Id$
@enddesc
@@*/
/* Copyright 2004 Sascha Husa, Ian Hinder, Christiane Lechner
This file is part of Kranc.
Kranc is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
Kranc is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Foobar; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#ifndef NOPRECOMPUTE
#define PRECOMPUTE
#endif
#if defined(FD_C0) || defined(FD_C2) || defined(FD_C4) || defined(FD_C2C4)
#define FD_SET_BY_USER
#endif
#ifndef FD_SET_BY_USER
#define FD_C2
#endif
#if defined(FD_C0)
#define FD_METHOD_DESC "FD method: replace derivatives by zero"
#endif
#if defined(FD_C2)
#define FD_METHOD_DESC "FD method: second order centered finite differences"
#endif
#if defined(FD_C4)
#define FD_METHOD_DESC "FD method: fourth order centered finite differences"
#endif
#if defined(FD_C2C4)
#define FD_METHOD_DESC "FD method: weighted 2nd/4th order centered finite differences"
#endif
/* utility functions */
#if defined(KRANC_C)
#define string(d,f) d ## f
#else
#define string(d,f) d/**/f
#endif
#if defined(KRANC_C)
#define IMAX(int1, int2) ((int1) > (int2) ? (int1) : (int2))
#endif
#include "MathematicaCompat.h"
/* finite differencing macros */
/* */
/* add method argument to shorthands */
/* */
/* third derivatives */
#define D111x(gf) string(D111,gf)
#define D211x(gf) string(D211,gf)
#define D311x(gf) string(D311,gf)
#define D221x(gf) string(D221,gf)
#define D321x(gf) string(D321,gf)
#define D331x(gf) string(D331,gf)
#define D222x(gf) string(D222,gf)
#define D322x(gf) string(D322,gf)
#define D332x(gf) string(D332,gf)
#define D333x(gf) string(D333,gf)
/* second derivatives */
#define D11x(gf) string(D11,gf)
#define D22x(gf) string(D22,gf)
#define D33x(gf) string(D33,gf)
#define D21x(gf) string(D21,gf)
#define D32x(gf) string(D32,gf)
#define D31x(gf) string(D31,gf)
/* first derivatives */
#define D1x(gf) string(D1,gf)
#define D2x(gf) string(D2,gf)
#define D3x(gf) string(D3,gf)
#ifdef PRECOMPUTE
/* third derivatives */
#define D111(gf) string(D111,gf)
#define D211(gf) string(D211,gf)
#define D311(gf) string(D311,gf)
#define D221(gf) string(D221,gf)
#define D321(gf) string(D321,gf)
#define D331(gf) string(D331,gf)
#define D222(gf) string(D222,gf)
#define D322(gf) string(D322,gf)
#define D332(gf) string(D332,gf)
#define D333(gf) string(D333,gf)
/* second derivatives */
#define D11(gf,i,j,k) string(D11,gf)
#define D22(gf,i,j,k) string(D22,gf)
#define D33(gf,i,j,k) string(D33,gf)
#define D21(gf,i,j,k) string(D21,gf)
#define D32(gf,i,j,k) string(D32,gf)
#define D31(gf,i,j,k) string(D31,gf)
/* first derivatives */
#define D1(gf,i,j,k) string(D1,gf)
#define D2(gf,i,j,k) string(D2,gf)
#define D3(gf,i,j,k) string(D3,gf)
#else
/* third derivatives */
#define D111(gf) D111gf(gf,i,j,k)
#define D211(gf) D211gf(gf,i,j,k)
#define D311(gf) D311gf(gf,i,j,k)
#define D221(gf) D221gf(gf,i,j,k)
#define D321(gf) D321gf(gf,i,j,k)
#define D331(gf) D331gf(gf,i,j,k)
#define D222(gf) D222gf(gf,i,j,k)
#define D322(gf) D322gf(gf,i,j,k)
#define D332(gf) D332gf(gf,i,j,k)
#define D333(gf) D333gf(gf,i,j,k)
/* second derivatives */
#define D11(gf,i,j,k) D11gf(gf,i,j,k)
#define D22(gf,i,j,k) D22gf(gf,i,j,k)
#define D33(gf,i,j,k) D33gf(gf,i,j,k)
#define D21(gf,i,j,k) D21gf(gf,i,j,k)
#define D32(gf,i,j,k) D32gf(gf,i,j,k)
#define D31(gf,i,j,k) D31gf(gf,i,j,k)
/* first derivatives */
#define D1(gf,i,j,k) D1gf(gf, i,j,k)
#define D2(gf,i,j,k) D2gf(gf, i,j,k)
#define D3(gf,i,j,k) D3gf(gf, i,j,k)
#endif
#ifdef FD_C0
/* third derivatives */
#define D111gf(gf,i,j,k) D111_c0(gf,i,j,k)
#define D211gf(gf,i,j,k) D211_c0(gf,i,j,k)
#define D311gf(gf,i,j,k) D311_c0(gf,i,j,k)
#define D221gf(gf,i,j,k) D221_c0(gf,i,j,k)
#define D321gf(gf,i,j,k) D321_c0(gf,i,j,k)
#define D331gf(gf,i,j,k) D331_c0(gf,i,j,k)
#define D222gf(gf,i,j,k) D222_c0(gf,i,j,k)
#define D322gf(gf,i,j,k) D322_c0(gf,i,j,k)
#define D332gf(gf,i,j,k) D332_c0(gf,i,j,k)
#define D333gf(gf,i,j,k) D333_c0(gf,i,j,k)
/* second derivatives */
#define D11gf(gf,i,j,k) D11_c0(gf,i,j,k)
#define D22gf(gf,i,j,k) D22_c0(gf,i,j,k)
#define D33gf(gf,i,j,k) D33_c0(gf,i,j,k)
#define D21gf(gf,i,j,k) D21_c0(gf,i,j,k)
#define D32gf(gf,i,j,k) D32_c0(gf,i,j,k)
#define D31gf(gf,i,j,k) D31_c0(gf,i,j,k)
/* first derivatives */
#define D1gf(gf,i,j,k) D1_c0(gf, i,j,k)
#define D2gf(gf,i,j,k) D2_c0(gf, i,j,k)
#define D3gf(gf,i,j,k) D3_c0(gf, i,j,k)
#endif
#ifdef FD_C2
/* third derivatives */
#define D111gf(gf,i,j,k) D111_c2(gf,i,j,k)
#define D211gf(gf,i,j,k) D211_c2(gf,i,j,k)
#define D311gf(gf,i,j,k) D311_c2(gf,i,j,k)
#define D221gf(gf,i,j,k) D221_c2(gf,i,j,k)
#define D321gf(gf,i,j,k) D321_c2(gf,i,j,k)
#define D331gf(gf,i,j,k) D331_c2(gf,i,j,k)
#define D222gf(gf,i,j,k) D222_c2(gf,i,j,k)
#define D322gf(gf,i,j,k) D322_c2(gf,i,j,k)
#define D332gf(gf,i,j,k) D332_c2(gf,i,j,k)
#define D333gf(gf,i,j,k) D333_c2(gf,i,j,k)
/* second derivatives */
#define D11gf(gf,i,j,k) D11_c2(gf,i,j,k)
#define D22gf(gf,i,j,k) D22_c2(gf,i,j,k)
#define D33gf(gf,i,j,k) D33_c2(gf,i,j,k)
#define D21gf(gf,i,j,k) D21_c2(gf,i,j,k)
#define D32gf(gf,i,j,k) D32_c2(gf,i,j,k)
#define D31gf(gf,i,j,k) D31_c2(gf,i,j,k)
/* first derivatives */
#define D1gf(gf,i,j,k) D1_c2(gf, i,j,k)
#define D2gf(gf,i,j,k) D2_c2(gf, i,j,k)
#define D3gf(gf,i,j,k) D3_c2(gf, i,j,k)
#endif
#ifdef FD_C4
/* third derivatives */
#define D111gf(gf,i,j,k) D111_c4(gf,i,j,k)
#define D211gf(gf,i,j,k) D211_c4(gf,i,j,k)
#define D311gf(gf,i,j,k) D311_c4(gf,i,j,k)
#define D221gf(gf,i,j,k) D221_c4(gf,i,j,k)
#define D321gf(gf,i,j,k) D321_c4(gf,i,j,k)
#define D331gf(gf,i,j,k) D331_c4(gf,i,j,k)
#define D222gf(gf,i,j,k) D222_c4(gf,i,j,k)
#define D322gf(gf,i,j,k) D322_c4(gf,i,j,k)
#define D332gf(gf,i,j,k) D332_c4(gf,i,j,k)
#define D333gf(gf,i,j,k) D333_c4(gf,i,j,k)
/* second derivatives */
#define D11gf(gf,i,j,k) D11_c4(gf,i,j,k)
#define D22gf(gf,i,j,k) D22_c4(gf,i,j,k)
#define D33gf(gf,i,j,k) D33_c4(gf,i,j,k)
#define D21gf(gf,i,j,k) D21_c4(gf,i,j,k)
#define D32gf(gf,i,j,k) D32_c4(gf,i,j,k)
#define D31gf(gf,i,j,k) D31_c4(gf,i,j,k)
/* first derivatives */
#define D1gf(gf,i,j,k) D1_c4(gf, i,j,k)
#define D2gf(gf,i,j,k) D2_c4(gf, i,j,k)
#define D3gf(gf,i,j,k) D3_c4(gf, i,j,k)
#endif
#ifdef FD_C2C4
/* third derivatives */
#define D111gf(gf,i,j,k) D111_c2c4(gf,i,j,k)
#define D211gf(gf,i,j,k) D211_c2c4(gf,i,j,k)
#define D311gf(gf,i,j,k) D311_c2c4(gf,i,j,k)
#define D221gf(gf,i,j,k) D221_c2c4(gf,i,j,k)
#define D321gf(gf,i,j,k) D321_c2c4(gf,i,j,k)
#define D331gf(gf,i,j,k) D331_c2c4(gf,i,j,k)
#define D222gf(gf,i,j,k) D222_c2c4(gf,i,j,k)
#define D322gf(gf,i,j,k) D322_c2c4(gf,i,j,k)
#define D332gf(gf,i,j,k) D332_c2c4(gf,i,j,k)
#define D333gf(gf,i,j,k) D333_c2c4(gf,i,j,k)
/* second derivatives */
#define D11gf(gf,i,j,k) D11_c2c4(gf,i,j,k)
#define D22gf(gf,i,j,k) D22_c2c4(gf,i,j,k)
#define D33gf(gf,i,j,k) D33_c2c4(gf,i,j,k)
#define D21gf(gf,i,j,k) D21_c2c4(gf,i,j,k)
#define D32gf(gf,i,j,k) D32_c2c4(gf,i,j,k)
#define D31gf(gf,i,j,k) D31_c2c4(gf,i,j,k)
/* first derivatives */
#define D1gf(gf,i,j,k) D1_c2c4(gf, i,j,k)
#define D2gf(gf,i,j,k) D2_c2c4(gf, i,j,k)
#define D3gf(gf,i,j,k) D3_c2c4(gf, i,j,k)
#endif
/*****************************************************/
/* */
/* METHODS */
/* */
/*****************************************************/
/* c0 */
/* set all derivatives = 0 */
/* for debugging and benchmarking */
/* third derivatives */
#define D111_c0(gf,i,j,k) 0.
#define D211_c0(gf,i,j,k) 0.
#define D311_c0(gf,i,j,k) 0.
#define D221_c0(gf,i,j,k) 0.
#define D321_c0(gf,i,j,k) 0.
#define D331_c0(gf,i,j,k) 0.
#define D222_c0(gf,i,j,k) 0.
#define D322_c0(gf,i,j,k) 0.
#define D332_c0(gf,i,j,k) 0.
#define D333_c0(gf,i,j,k) 0.
/* second derivatives */
#define D11_c0(gf,i,j,k) 0.
#define D22_c0(gf,i,j,k) 0.
#define D33_c0(gf,i,j,k) 0.
#define D21_c0(gf,i,j,k) 0.
#define D32_c0(gf,i,j,k) 0.
#define D31_c0(gf,i,j,k) 0.
/* first derivatives */
#define D1_c0(gf,i,j,k) 0.
#define D2_c0(gf,i,j,k) 0.
#define D3_c0(gf,i,j,k) 0.
#ifndef KRANC_C
/* c2 */
/* */
/* 2nd order centered */
/* */
/* third derivatives, centered, 2nd order */
#define D111_c2(gf,i,j,k) ((- gf(i+2,j,k) + 2*gf(i+1,j,k) - 2*gf(i-1,j,k) + gf(i-2,j,k)) * dxi*dxi*dxi * (1.0/2.0))
#define D211_c2(gf,i,j,k) ((gf(i+1,j+1,k) - 2*gf(i,j+1,k) + gf(i-1,j+1,k) - gf(i+1,j-1,k) + 2*gf(i,j-1,k) - gf(i-1,j-1,k)) * dxi*dxi*dyi * (1.0/2.0))
#define D311_c2(gf,i,j,k) ((gf(i+1,j,k+1) - 2*gf(i,j,k+1) + gf(i-1,j,k+1) - gf(i+1,j,k-1) + 2*gf(i,j,k-1) - gf(i-1,j,k-1)) * dxi*dxi*dzi * (1.0/2.0))
#define D221_c2(gf,i,j,k) ((gf(i+1,j+1,k) - 2*gf(i+1,j,k) + gf(i+1,j-1,k) - gf(i-1,j+1,k) + 2*gf(i-1,j,k) - gf(i-1,j-1,k)) * dxi*dyi*dyi * (1.0/2.0))
#define D321_c2(gf,i,j,k) ((gf(i+1,j+1,k+1) - gf(i-1,j+1,k+1) - gf(i+1,j-1,k+1) + gf(i-1,j-1,k+1) - gf(i+1,j+1,k-1) + gf(i-1,j+1,k-1) + gf(i+1,j-1,k-1) - gf(i-1,j-1,k-1)) * dxi*dyi*dzi * (1.0/8.0))
#define D331_c2(gf,i,j,k) ((gf(i+1,j,k+1) - 2*gf(i+1,j,k) + gf(i+1,j,k-1) - gf(i-1,j,k+1) + 2*gf(i-1,j,k) - gf(i-1,j,k-1)) * dxi*dzi*dzi * (1.0/2.0))
#define D222_c2(gf,i,j,k) ((- gf(i,j+2,k) + 2*gf(i,j+1,k) - 2*gf(i,j-1,k) + gf(i,j-2,k)) * dyi*dyi*dyi * (1.0/2.0))
#define D322_c2(gf,i,j,k) ((gf(i,j+1,k+1) - 2*gf(i,j,k+1) + gf(i,j-1,k+1) - gf(i,j+1,k-1) + 2*gf(i,j,k-1) - gf(i,j-1,k-1)) * dyi*dyi*dzi * (1.0/2.0))
#define D332_c2(gf,i,j,k) ((gf(i,j+1,k+1) - 2*gf(i,j+1,k) + gf(i,j+1,k-1) - gf(i,j-1,k+1) + 2*gf(i,j-1,k) - gf(i,j-1,k-1)) * dyi*dzi*dzi * (1.0/2.0))
#define D333_c2(gf,i,j,k) ((- gf(i,j,k+2) + 2*gf(i,j,k+1) - 2*gf(i,j,k-1) + gf(i,j,k-2)) * dzi*dzi*dzi * (1.0/2.0))
/* second derivatives, centered, 2nd order */
#define D11_c2(gf,i,j,k) \
(( gf(i+1,j,k) \
- 2.*gf(i, j,k) \
+ gf(i-1,j,k)) * dxi * dxi )
#define D22_c2(gf,i,j,k) \
(( gf(i,j+1,k) \
- 2.*gf(i,j, k) \
+ gf(i,j-1,k)) * dyi * dyi )
#define D33_c2(gf,i,j,k) \
(( gf(i,j,k+1) \
- 2.*gf(i,j,k ) \
+ gf(i,j,k-1)) * dzi * dzi )
#define D21_c2(gf,i,j,k) \
((gf(i+1,j+1,k) \
+ gf(i-1,j-1,k) \
- gf(i+1,j-1,k) \
- gf(i-1,j+1,k)) * hdxi * hdyi )
#define D32_c2(gf,i,j,k) \
((gf(i,j+1,k+1) \
+ gf(i,j-1,k-1) \
- gf(i,j+1,k-1) \
- gf(i,j-1,k+1)) * hdyi * hdzi )
#define D31_c2(gf,i,j,k) \
((gf(i+1,j,k+1) \
+ gf(i-1,j,k-1) \
- gf(i+1,j,k-1) \
- gf(i-1,j,k+1)) * hdxi * hdzi )
/* first derivatives, centered, 2nd order */
#define D1_c2(gf,i,j,k) \
((gf(i+1,j,k) \
- gf(i-1,j,k)) * hdxi)
#define D2_c2(gf,i,j,k) \
((gf(i,j+1,k) \
- gf(i,j-1,k)) * hdyi)
#define D3_c2(gf,i,j,k) \
((gf(i,j,k+1) \
- gf(i,j,k-1)) * hdzi)
#else
#define D11_c2(gf,i,j,k) \
(( gf[CCTK_GFINDEX3D(cctkGH,i+1,j,k)] \
- 2.*gf[CCTK_GFINDEX3D(cctkGH,i, j,k)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i-1,j,k)]) * dxi * dxi )
#define D22_c2(gf,i,j,k) \
(( gf[CCTK_GFINDEX3D(cctkGH,i,j+1,k)] \
- 2.*gf[CCTK_GFINDEX3D(cctkGH,i,j, k)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i,j-1,k)]) * dyi * dyi )
#define D33_c2(gf,i,j,k) \
(( gf[CCTK_GFINDEX3D(cctkGH,i,j,k+1)] \
- 2.*gf[CCTK_GFINDEX3D(cctkGH,i,j,k )] \
+ gf[CCTK_GFINDEX3D(cctkGH,i,j,k-1)]) * dzi * dzi )
#define D21_c2(gf,i,j,k) \
((gf[CCTK_GFINDEX3D(cctkGH,i+1,j+1,k)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i-1,j-1,k)] \
- gf[CCTK_GFINDEX3D(cctkGH,i+1,j-1,k)] \
- gf[CCTK_GFINDEX3D(cctkGH,i-1,j+1,k)]) * hdxi * hdyi )
#define D32_c2(gf,i,j,k) \
((gf[CCTK_GFINDEX3D(cctkGH,i,j+1,k+1)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i,j-1,k-1)] \
- gf[CCTK_GFINDEX3D(cctkGH,i,j+1,k-1)] \
- gf[CCTK_GFINDEX3D(cctkGH,i,j-1,k+1)]) * hdyi * hdzi )
#define D31_c2(gf,i,j,k) \
((gf[CCTK_GFINDEX3D(cctkGH,i+1,j,k+1)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i-1,j,k-1)] \
- gf[CCTK_GFINDEX3D(cctkGH,i+1,j,k-1)] \
- gf[CCTK_GFINDEX3D(cctkGH,i-1,j,k+1)]) * hdxi * hdzi )
/* first derivatives, centered, 2nd order */
#define D1_c2(gf,i,j,k) \
((gf[CCTK_GFINDEX3D(cctkGH,i+1,j,k)] \
- gf[CCTK_GFINDEX3D(cctkGH,i-1,j,k)]) * hdxi)
#define D2_c2(gf,i,j,k) \
((gf[CCTK_GFINDEX3D(cctkGH,i,j+1,k)] \
- gf[CCTK_GFINDEX3D(cctkGH,i,j-1,k)]) * hdyi)
#define D3_c2(gf,i,j,k) \
((gf[CCTK_GFINDEX3D(cctkGH,i,j,k+1)] \
- gf[CCTK_GFINDEX3D(cctkGH,i,j,k-1)]) * hdzi)
#endif
/* c4 */
/* */
/* 4th order centered */
/* */
/* second derivatives, centered, 4th order */
#ifndef KRANC_C
#define D11_c4(gf,i,j,k) \
((- gf(i+2,j,k) \
+ 16. * gf(i+1,j,k) \
- 30. * gf(i, j,k) \
+ 16. * gf(i-1,j,k) \
- gf(i-2,j,k)) * dxi * dxi / 12.)
#define D22_c4(gf,i,j,k) \
((- gf(i,j+2,k) \
+ 16. * gf(i,j+1,k) \
- 30. * gf(i,j, k) \
+ 16. * gf(i,j-1,k) \
- gf(i,j-2,k)) * dyi * dyi / 12.)
#define D33_c4(gf,i,j,k) \
((- gf(i,j,k+2) \
+ 16. * gf(i,j,k+1) \
- 30. * gf(i,j,k ) \
+ 16. * gf(i,j,k-1) \
- gf(i,j,k-2)) * dzi * dzi / 12.)
#define D21_c4(gf,i,j,k) \
((- gf(i+2,j+2,k) \
+ gf(i+2,j-2,k) \
+ gf(i-2,j+2,k) \
- gf(i-2,j-2,k) \
+ 16. * gf(i+1,j+1,k) \
- 16. * gf(i+1,j-1,k) \
- 16. * gf(i-1,j+1,k) \
+ 16. * gf(i-1,j-1,k)) * dxi * dyi / 48.)
#define D31_c4(gf,i,j,k) \
((- gf(i+2,j,k+2) \
+ gf(i+2,j,k-2) \
+ gf(i-2,j,k+2) \
- gf(i-2,j,k-2) \
+ 16. * gf(i+1,j,k+1) \
- 16. * gf(i+1,j,k-1) \
- 16. * gf(i-1,j,k+1) \
+ 16. * gf(i-1,j,k-1)) * dxi * dzi / 48.)
#define D32_c4(gf,i,j,k) \
((- gf(i,j+2,k+2) \
+ gf(i,j+2,k-2) \
+ gf(i,j-2,k+2) \
- gf(i,j-2,k-2) \
+ 16. * gf(i,j+1,k+1) \
- 16. * gf(i,j+1,k-1) \
- 16. * gf(i,j-1,k+1) \
+ 16. * gf(i,j-1,k-1)) * dzi * dyi / 48.)
/* first derivatives, centered, 4th order */
#define D1_c4(gf,i,j,k) \
((- gf(i+2,j,k) \
+ 8. * gf(i+1,j,k) \
- 8. * gf(i-1,j,k) \
+ gf(i-2,j,k)) * (dxi / 12.))
#define D2_c4(gf,i,j,k) \
((- gf(i,j+2,k) \
+ 8. * gf(i,j+1,k) \
- 8. * gf(i,j-1,k) \
+ gf(i,j-2,k)) * (dyi / 12.))
#define D3_c4(gf,i,j,k) \
((- gf(i,j,k+2) \
+ 8. * gf(i,j,k+1) \
- 8. * gf(i,j,k-1) \
+ gf(i,j,k-2)) * (dzi / 12.))
#else
#define D11_c4(gf,i,j,k) \
((- gf[CCTK_GFINDEX3D(cctkGH,i+2,j,k)] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i+1,j,k)] \
- 30. * gf[CCTK_GFINDEX3D(cctkGH,i, j,k)] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i-1,j,k)] \
- gf[CCTK_GFINDEX3D(cctkGH,i-2,j,k)]) * dxi * dxi / 12.)
#define D22_c4(gf,i,j,k) \
((- gf[CCTK_GFINDEX3D(cctkGH,i,j+2,k)] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i,j+1,k)] \
- 30. * gf[CCTK_GFINDEX3D(cctkGH,i,j, k)] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i,j-1,k)] \
- gf[CCTK_GFINDEX3D(cctkGH,i,j-2,k)]) * dyi * dyi / 12.)
#define D33_c4(gf,i,j,k) \
((- gf[CCTK_GFINDEX3D(cctkGH,i,j,k+2)] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i,j,k+1)] \
- 30. * gf[CCTK_GFINDEX3D(cctkGH,i,j,k )] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i,j,k-1)] \
- gf[CCTK_GFINDEX3D(cctkGH,i,j,k-2)]) * dzi * dzi / 12.)
#define D21_c4(gf,i,j,k) \
((- gf[CCTK_GFINDEX3D(cctkGH,i+2,j+2,k)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i+2,j-2,k)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i-2,j+2,k)] \
- gf[CCTK_GFINDEX3D(cctkGH,i-2,j-2,k)] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i+1,j+1,k)] \
- 16. * gf[CCTK_GFINDEX3D(cctkGH,i+1,j-1,k)] \
- 16. * gf[CCTK_GFINDEX3D(cctkGH,i-1,j+1,k)] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i-1,j-1,k)]) * dxi * dyi / 48.)
#define D31_c4(gf,i,j,k) \
((- gf[CCTK_GFINDEX3D(cctkGH,i+2,j,k+2)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i+2,j,k-2)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i-2,j,k+2)] \
- gf[CCTK_GFINDEX3D(cctkGH,i-2,j,k-2)] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i+1,j,k+1)] \
- 16. * gf[CCTK_GFINDEX3D(cctkGH,i+1,j,k-1)] \
- 16. * gf[CCTK_GFINDEX3D(cctkGH,i-1,j,k+1)] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i-1,j,k-1)]) * dxi * dzi / 48.)
#define D32_c4(gf,i,j,k) \
((- gf[CCTK_GFINDEX3D(cctkGH,i,j+2,k+2)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i,j+2,k-2)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i,j-2,k+2)] \
- gf[CCTK_GFINDEX3D(cctkGH,i,j-2,k-2)] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i,j+1,k+1)] \
- 16. * gf[CCTK_GFINDEX3D(cctkGH,i,j+1,k-1)] \
- 16. * gf[CCTK_GFINDEX3D(cctkGH,i,j-1,k+1)] \
+ 16. * gf[CCTK_GFINDEX3D(cctkGH,i,j-1,k-1)]) * dzi * dyi / 48.)
/* first derivatives, centered, 4th order */
#define D1_c4(gf,i,j,k) \
((- gf[CCTK_GFINDEX3D(cctkGH,i+2,j,k)] \
+ 8. * gf[CCTK_GFINDEX3D(cctkGH,i+1,j,k)] \
- 8. * gf[CCTK_GFINDEX3D(cctkGH,i-1,j,k)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i-2,j,k)]) * (dxi / 12.))
#define D2_c4(gf,i,j,k) \
((- gf[CCTK_GFINDEX3D(cctkGH,i,j+2,k)] \
+ 8. * gf[CCTK_GFINDEX3D(cctkGH,i,j+1,k)] \
- 8. * gf[CCTK_GFINDEX3D(cctkGH,i,j-1,k)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i,j-2,k)]) * (dyi / 12.))
#define D3_c4(gf,i,j,k) \
((- gf[CCTK_GFINDEX3D(cctkGH,i,j,k+2)] \
+ 8. * gf[CCTK_GFINDEX3D(cctkGH,i,j,k+1)] \
- 8. * gf[CCTK_GFINDEX3D(cctkGH,i,j,k-1)] \
+ gf[CCTK_GFINDEX3D(cctkGH,i,j,k-2)]) * (dzi / 12.))
#endif
/*****************************************************/
/* */
/* DERIVED METHODS */
/* */
/******************************************************/
/* blend c2 and c4 */
/* second derivatives */
#define D11_c2c4(gf,i,j,k) (fdweight_c2*D11_c2(gf,i,j,k) + fdweight_c4*D11_c4(gf,i,j,k))
#define D22_c2c4(gf,i,j,k) (fdweight_c2*D22_c2(gf,i,j,k) + fdweight_c4*D22_c4(gf,i,j,k))
#define D33_c2c4(gf,i,j,k) (fdweight_c2*D33_c2(gf,i,j,k) + fdweight_c4*D33_c4(gf,i,j,k))
#define D21_c2c4(gf,i,j,k) (fdweight_c2*D21_c2(gf,i,j,k) + fdweight_c4*D21_c4(gf,i,j,k))
#define D32_c2c4(gf,i,j,k) (fdweight_c2*D32_c2(gf,i,j,k) + fdweight_c4*D32_c4(gf,i,j,k))
#define D31_c2c4(gf,i,j,k) (fdweight_c2*D31_c2(gf,i,j,k) + fdweight_c4*D31_c4(gf,i,j,k))
/* first derivatives */
#define D1_c2c4(gf,i,j,k) (fdweight_c2*D1_c2(gf, i,j,k) + fdweight_c4*D1_c4(gf,i,j,k))
#define D2_c2c4(gf,i,j,k) (fdweight_c2*D2_c2(gf, i,j,k) + fdweight_c4*D2_c4(gf,i,j,k))
#define D3_c2c4(gf,i,j,k) (fdweight_c2*D3_c2(gf, i,j,k) + fdweight_c4*D3_c4(gf,i,j,k))
/*****************************************************/
/* */
/* Poor man's one-sided derivatives */
/* */
/******************************************************/
#define Dplus1(gf,i,j,k) string(Dplus1,gf)
#define Dplus2(gf,i,j,k) string(Dplus2,gf)
#define Dplus3(gf,i,j,k) string(Dplus3,gf)
#define Dplus1gf(gf,i,j,k) Dplus1x(gf, i,j,k)
#define Dplus2gf(gf,i,j,k) Dplus2x(gf, i,j,k)
#define Dplus3gf(gf,i,j,k) Dplus3x(gf, i,j,k)
#ifdef KRANC_C
#define Dplus1x(gf,i,j,k) \
((gf[CCTK_GFINDEX3D(cctkGH,i+1,j,k)] \
- gf[CCTK_GFINDEX3D(cctkGH,i,j,k)]) * dxi)
#define Dplus2x(gf,i,j,k) \
((gf[CCTK_GFINDEX3D(cctkGH,i,j+1,k)] \
- gf[CCTK_GFINDEX3D(cctkGH,i,j,k)]) * dyi)
#define Dplus3x(gf,i,j,k) \
((gf[CCTK_GFINDEX3D(cctkGH,i,j,k+1)] \
- gf[CCTK_GFINDEX3D(cctkGH,i,j,k)]) * dzi)
#else
#define Dplus1x(gf,i,j,k) ( ( gf(i+1, j, k) - gf(i,j,k) ) * dxi )
#define Dplus2x(gf,i,j,k) ( ( gf(i, j + 1, k) - gf(i,j,k) ) * dxi )
#define Dplus3x(gf,i,j,k) ( ( gf(i, j, k + 1) - gf(i,j,k) ) * dxi )
#endif
#ifdef KRANC_C
CCTK_INT sgn(CCTK_REAL x);
#define Dupwind1(gf,dir,i,j,k) ((dir * gf[CCTK_GFINDEX3D(cctkGH,i+dir,j,k)] \
- dir * gf[CCTK_GFINDEX3D(cctkGH,i,j,k)]) * dxi)
#define Dupwind2(gf,dir,i,j,k) ((dir * gf[CCTK_GFINDEX3D(cctkGH,i,j+dir,k)] \
- dir * gf[CCTK_GFINDEX3D(cctkGH,i,j,k)]) * dxi)
#define Dupwind3(gf,dir,i,j,k) ((dir * gf[CCTK_GFINDEX3D(cctkGH,i,j,k+dir)] \
- dir * gf[CCTK_GFINDEX3D(cctkGH,i,j,k)]) * dxi)
void GenericFD_GetBoundaryInfo(cGH const * restrict cctkGH,
CCTK_INT const * restrict cctk_lsh,
CCTK_INT const * restrict cctk_bbox,
CCTK_INT const * restrict cctk_nghostzones,
CCTK_INT * restrict imin,
CCTK_INT * restrict imax,
CCTK_INT * restrict is_symbnd,
CCTK_INT * restrict is_physbnd,
CCTK_INT * restrict is_ipbnd);
/* Summation by parts */
static inline CCTK_REAL sbp_deriv_x(int i, int j, int k,
CCTK_INT min[], CCTK_INT max[],
CCTK_REAL d,
CCTK_REAL *var, CCTK_REAL *q, cGH *cctkGH)
{
CCTK_REAL dvarl = 0;
int ni = cctkGH->cctk_lsh[0];
for (int ii=min[i]-1; ii<=max[i]-1; ++ii) {
dvarl += q[ii+ni*i]*var[CCTK_GFINDEX3D (cctkGH, ii, j, k)];
}
dvarl /= d;
return dvarl;
}
static inline CCTK_REAL sbp_deriv_y(int i, int j, int k,
CCTK_INT min[], CCTK_INT max[],
CCTK_REAL d,
CCTK_REAL *var, CCTK_REAL *q, cGH *cctkGH)
{
CCTK_REAL dvarl = 0;
int nj = cctkGH->cctk_lsh[1];
for (int jj=min[j]-1; jj<=max[j]-1; ++jj) {
dvarl += q[jj+nj*j]*var[CCTK_GFINDEX3D (cctkGH, i, jj, k)];
}
dvarl /= d;
return dvarl;
}
static inline CCTK_REAL sbp_deriv_z(int i, int j, int k,
CCTK_INT min[], CCTK_INT max[],
CCTK_REAL d,
CCTK_REAL *var, CCTK_REAL *q, cGH *cctkGH)
{
CCTK_REAL dvarl = 0;
int nk = cctkGH->cctk_lsh[2];
for (int kk=min[k]-1; kk<=max[k]-1; ++kk) {
dvarl += q[kk+nk*k]*var[CCTK_GFINDEX3D (cctkGH, i, j, kk)];
}
dvarl /= d;
return dvarl;
}
/* New calculation format */
typedef void(*Kranc_Calculation)(cGH const * cctkGH,
CCTK_INT dir,
CCTK_INT face,
CCTK_REAL const normal[3],
CCTK_REAL const tangentA[3],
CCTK_REAL const tangentB[3],
CCTK_INT const min[3],
CCTK_INT const max[3],
CCTK_INT n_subblock_gfs,
CCTK_REAL * const subblock_gfs[]);
void GenericFD_LoopOverEverything(cGH *cctkGH, Kranc_Calculation calc);
void GenericFD_LoopOverBoundary(cGH *cctkGH, Kranc_Calculation calc);
void GenericFD_LoopOverBoundaryWithGhosts(cGH *cctkGH, Kranc_Calculation calc);
void GenericFD_LoopOverInterior(cGH *cctkGH, Kranc_Calculation calc);
#endif
|
