Actual source code: plexmetric.c
1: #include <petsc/private/dmpleximpl.h>
2: #include <petscblaslapack.h>
4: PetscLogEvent DMPLEX_MetricEnforceSPD, DMPLEX_MetricNormalize, DMPLEX_MetricAverage, DMPLEX_MetricIntersection;
6: PetscErrorCode DMPlexMetricSetFromOptions(DM dm)
7: {
8: DM_Plex *plex = (DM_Plex *)dm->data;
9: MPI_Comm comm;
10: PetscBool isotropic = PETSC_FALSE, uniform = PETSC_FALSE, restrictAnisotropyFirst = PETSC_FALSE;
11: PetscBool noInsert = PETSC_FALSE, noSwap = PETSC_FALSE, noMove = PETSC_FALSE, noSurf = PETSC_FALSE;
12: PetscInt verbosity = -1, numIter = 3;
13: PetscReal h_min = 1.0e-30, h_max = 1.0e+30, a_max = 1.0e+05, p = 1.0, target = 1000.0, beta = 1.3, hausd = 0.01;
15: PetscFunctionBegin;
16: if (!plex->metricCtx) PetscCall(PetscNew(&plex->metricCtx));
17: PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
18: PetscOptionsBegin(comm, "", "Riemannian metric options", "DMPlexMetric");
19: PetscCall(PetscOptionsBool("-dm_plex_metric_isotropic", "Is the metric isotropic?", "DMPlexMetricCreateIsotropic", isotropic, &isotropic, NULL));
20: PetscCall(DMPlexMetricSetIsotropic(dm, isotropic));
21: PetscCall(PetscOptionsBool("-dm_plex_metric_uniform", "Is the metric uniform?", "DMPlexMetricCreateUniform", uniform, &uniform, NULL));
22: PetscCall(DMPlexMetricSetUniform(dm, uniform));
23: PetscCall(PetscOptionsBool("-dm_plex_metric_restrict_anisotropy_first", "Should anisotropy be restricted before normalization?", "DMPlexNormalize", restrictAnisotropyFirst, &restrictAnisotropyFirst, NULL));
24: PetscCall(DMPlexMetricSetRestrictAnisotropyFirst(dm, restrictAnisotropyFirst));
25: PetscCall(PetscOptionsBool("-dm_plex_metric_no_insert", "Turn off node insertion and deletion", "DMAdaptMetric", noInsert, &noInsert, NULL));
26: PetscCall(DMPlexMetricSetNoInsertion(dm, noInsert));
27: PetscCall(PetscOptionsBool("-dm_plex_metric_no_swap", "Turn off facet swapping", "DMAdaptMetric", noSwap, &noSwap, NULL));
28: PetscCall(DMPlexMetricSetNoSwapping(dm, noSwap));
29: PetscCall(PetscOptionsBool("-dm_plex_metric_no_move", "Turn off facet node movement", "DMAdaptMetric", noMove, &noMove, NULL));
30: PetscCall(DMPlexMetricSetNoMovement(dm, noMove));
31: PetscCall(PetscOptionsBool("-dm_plex_metric_no_surf", "Turn off surface modification", "DMAdaptMetric", noSurf, &noSurf, NULL));
32: PetscCall(DMPlexMetricSetNoSurf(dm, noSurf));
33: PetscCall(PetscOptionsBoundedInt("-dm_plex_metric_num_iterations", "Number of ParMmg adaptation iterations", "DMAdaptMetric", numIter, &numIter, NULL, 0));
34: PetscCall(DMPlexMetricSetNumIterations(dm, numIter));
35: PetscCall(PetscOptionsRangeInt("-dm_plex_metric_verbosity", "Verbosity of metric-based mesh adaptation package (-1 = silent, 10 = maximum)", "DMAdaptMetric", verbosity, &verbosity, NULL, -1, 10));
36: PetscCall(DMPlexMetricSetVerbosity(dm, verbosity));
37: PetscCall(PetscOptionsReal("-dm_plex_metric_h_min", "Minimum tolerated metric magnitude", "DMPlexMetricEnforceSPD", h_min, &h_min, NULL));
38: PetscCall(DMPlexMetricSetMinimumMagnitude(dm, h_min));
39: PetscCall(PetscOptionsReal("-dm_plex_metric_h_max", "Maximum tolerated metric magnitude", "DMPlexMetricEnforceSPD", h_max, &h_max, NULL));
40: PetscCall(DMPlexMetricSetMaximumMagnitude(dm, h_max));
41: PetscCall(PetscOptionsReal("-dm_plex_metric_a_max", "Maximum tolerated anisotropy", "DMPlexMetricEnforceSPD", a_max, &a_max, NULL));
42: PetscCall(DMPlexMetricSetMaximumAnisotropy(dm, a_max));
43: PetscCall(PetscOptionsReal("-dm_plex_metric_p", "L-p normalization order", "DMPlexMetricNormalize", p, &p, NULL));
44: PetscCall(DMPlexMetricSetNormalizationOrder(dm, p));
45: PetscCall(PetscOptionsReal("-dm_plex_metric_target_complexity", "Target metric complexity", "DMPlexMetricNormalize", target, &target, NULL));
46: PetscCall(DMPlexMetricSetTargetComplexity(dm, target));
47: PetscCall(PetscOptionsReal("-dm_plex_metric_gradation_factor", "Metric gradation factor", "DMAdaptMetric", beta, &beta, NULL));
48: PetscCall(DMPlexMetricSetGradationFactor(dm, beta));
49: PetscCall(PetscOptionsReal("-dm_plex_metric_hausdorff_number", "Metric Hausdorff number", "DMAdaptMetric", hausd, &hausd, NULL));
50: PetscCall(DMPlexMetricSetHausdorffNumber(dm, hausd));
51: PetscOptionsEnd();
52: PetscFunctionReturn(PETSC_SUCCESS);
53: }
55: /*@
56: DMPlexMetricSetIsotropic - Record whether a metric is isotropic
58: Input Parameters:
59: + dm - The `DM`
60: - isotropic - Is the metric isotropic?
62: Level: beginner
64: .seealso: `DMPLEX`, `DMPlexMetricIsIsotropic()`, `DMPlexMetricSetUniform()`, `DMPlexMetricSetRestrictAnisotropyFirst()`
65: @*/
66: PetscErrorCode DMPlexMetricSetIsotropic(DM dm, PetscBool isotropic)
67: {
68: DM_Plex *plex = (DM_Plex *)dm->data;
70: PetscFunctionBegin;
71: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
72: plex->metricCtx->isotropic = isotropic;
73: PetscFunctionReturn(PETSC_SUCCESS);
74: }
76: /*@
77: DMPlexMetricIsIsotropic - Is a metric isotropic?
79: Input Parameters:
80: . dm - The `DM`
82: Output Parameters:
83: . isotropic - Is the metric isotropic?
85: Level: beginner
87: .seealso: `DMPLEX`, `DMPlexMetricSetIsotropic()`, `DMPlexMetricIsUniform()`, `DMPlexMetricRestrictAnisotropyFirst()`
88: @*/
89: PetscErrorCode DMPlexMetricIsIsotropic(DM dm, PetscBool *isotropic)
90: {
91: DM_Plex *plex = (DM_Plex *)dm->data;
93: PetscFunctionBegin;
94: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
95: *isotropic = plex->metricCtx->isotropic;
96: PetscFunctionReturn(PETSC_SUCCESS);
97: }
99: /*@
100: DMPlexMetricSetUniform - Record whether a metric is uniform
102: Input Parameters:
103: + dm - The `DM`
104: - uniform - Is the metric uniform?
106: Level: beginner
108: Note:
109: If the metric is specified as uniform then it is assumed to be isotropic, too.
111: .seealso: `DMPLEX`, `DMPlexMetricIsUniform()`, `DMPlexMetricSetIsotropic()`, `DMPlexMetricSetRestrictAnisotropyFirst()`
112: @*/
113: PetscErrorCode DMPlexMetricSetUniform(DM dm, PetscBool uniform)
114: {
115: DM_Plex *plex = (DM_Plex *)dm->data;
117: PetscFunctionBegin;
118: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
119: plex->metricCtx->uniform = uniform;
120: if (uniform) plex->metricCtx->isotropic = uniform;
121: PetscFunctionReturn(PETSC_SUCCESS);
122: }
124: /*@
125: DMPlexMetricIsUniform - Is a metric uniform?
127: Input Parameters:
128: . dm - The `DM`
130: Output Parameters:
131: . uniform - Is the metric uniform?
133: Level: beginner
135: .seealso: `DMPLEX`, `DMPlexMetricSetUniform()`, `DMPlexMetricIsIsotropic()`, `DMPlexMetricRestrictAnisotropyFirst()`
136: @*/
137: PetscErrorCode DMPlexMetricIsUniform(DM dm, PetscBool *uniform)
138: {
139: DM_Plex *plex = (DM_Plex *)dm->data;
141: PetscFunctionBegin;
142: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
143: *uniform = plex->metricCtx->uniform;
144: PetscFunctionReturn(PETSC_SUCCESS);
145: }
147: /*@
148: DMPlexMetricSetRestrictAnisotropyFirst - Record whether anisotropy should be restricted before normalization
150: Input Parameters:
151: + dm - The `DM`
152: - restrictAnisotropyFirst - Should anisotropy be normalized first?
154: Level: beginner
156: .seealso: `DMPLEX`, `DMPlexMetricSetIsotropic()`, `DMPlexMetricRestrictAnisotropyFirst()`
157: @*/
158: PetscErrorCode DMPlexMetricSetRestrictAnisotropyFirst(DM dm, PetscBool restrictAnisotropyFirst)
159: {
160: DM_Plex *plex = (DM_Plex *)dm->data;
162: PetscFunctionBegin;
163: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
164: plex->metricCtx->restrictAnisotropyFirst = restrictAnisotropyFirst;
165: PetscFunctionReturn(PETSC_SUCCESS);
166: }
168: /*@
169: DMPlexMetricRestrictAnisotropyFirst - Is anisotropy restricted before normalization or after?
171: Input Parameters:
172: . dm - The `DM`
174: Output Parameters:
175: . restrictAnisotropyFirst - Is anisotropy be normalized first?
177: Level: beginner
179: .seealso: `DMPLEX`, `DMPlexMetricIsIsotropic()`, `DMPlexMetricSetRestrictAnisotropyFirst()`
180: @*/
181: PetscErrorCode DMPlexMetricRestrictAnisotropyFirst(DM dm, PetscBool *restrictAnisotropyFirst)
182: {
183: DM_Plex *plex = (DM_Plex *)dm->data;
185: PetscFunctionBegin;
186: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
187: *restrictAnisotropyFirst = plex->metricCtx->restrictAnisotropyFirst;
188: PetscFunctionReturn(PETSC_SUCCESS);
189: }
191: /*@
192: DMPlexMetricSetNoInsertion - Should node insertion and deletion be turned off?
194: Input Parameters:
195: + dm - The `DM`
196: - noInsert - Should node insertion and deletion be turned off?
198: Level: beginner
200: Note:
201: This is only used by Mmg and ParMmg (not Pragmatic).
203: .seealso: `DMPLEX`, `DMPlexMetricNoInsertion()`, `DMPlexMetricSetNoSwapping()`, `DMPlexMetricSetNoMovement()`, `DMPlexMetricSetNoSurf()`
204: @*/
205: PetscErrorCode DMPlexMetricSetNoInsertion(DM dm, PetscBool noInsert)
206: {
207: DM_Plex *plex = (DM_Plex *)dm->data;
209: PetscFunctionBegin;
210: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
211: plex->metricCtx->noInsert = noInsert;
212: PetscFunctionReturn(PETSC_SUCCESS);
213: }
215: /*@
216: DMPlexMetricNoInsertion - Are node insertion and deletion turned off?
218: Input Parameters:
219: . dm - The `DM`
221: Output Parameters:
222: . noInsert - Are node insertion and deletion turned off?
224: Level: beginner
226: Note:
227: This is only used by Mmg and ParMmg (not Pragmatic).
229: .seealso: `DMPLEX`, `DMPlexMetricSetNoInsertion()`, `DMPlexMetricNoSwapping()`, `DMPlexMetricNoMovement()`, `DMPlexMetricNoSurf()`
230: @*/
231: PetscErrorCode DMPlexMetricNoInsertion(DM dm, PetscBool *noInsert)
232: {
233: DM_Plex *plex = (DM_Plex *)dm->data;
235: PetscFunctionBegin;
236: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
237: *noInsert = plex->metricCtx->noInsert;
238: PetscFunctionReturn(PETSC_SUCCESS);
239: }
241: /*@
242: DMPlexMetricSetNoSwapping - Should facet swapping be turned off?
244: Input Parameters:
245: + dm - The `DM`
246: - noSwap - Should facet swapping be turned off?
248: Level: beginner
250: Note:
251: This is only used by Mmg and ParMmg (not Pragmatic).
253: .seealso: `DMPLEX`, `DMPlexMetricNoSwapping()`, `DMPlexMetricSetNoInsertion()`, `DMPlexMetricSetNoMovement()`, `DMPlexMetricSetNoSurf()`
254: @*/
255: PetscErrorCode DMPlexMetricSetNoSwapping(DM dm, PetscBool noSwap)
256: {
257: DM_Plex *plex = (DM_Plex *)dm->data;
259: PetscFunctionBegin;
260: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
261: plex->metricCtx->noSwap = noSwap;
262: PetscFunctionReturn(PETSC_SUCCESS);
263: }
265: /*@
266: DMPlexMetricNoSwapping - Is facet swapping turned off?
268: Input Parameters:
269: . dm - The `DM`
271: Output Parameters:
272: . noSwap - Is facet swapping turned off?
274: Level: beginner
276: Note:
277: This is only used by Mmg and ParMmg (not Pragmatic).
279: .seealso: `DMPLEX`, `DMPlexMetricSetNoSwapping()`, `DMPlexMetricNoInsertion()`, `DMPlexMetricNoMovement()`, `DMPlexMetricNoSurf()`
280: @*/
281: PetscErrorCode DMPlexMetricNoSwapping(DM dm, PetscBool *noSwap)
282: {
283: DM_Plex *plex = (DM_Plex *)dm->data;
285: PetscFunctionBegin;
286: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
287: *noSwap = plex->metricCtx->noSwap;
288: PetscFunctionReturn(PETSC_SUCCESS);
289: }
291: /*@
292: DMPlexMetricSetNoMovement - Should node movement be turned off?
294: Input Parameters:
295: + dm - The `DM`
296: - noMove - Should node movement be turned off?
298: Level: beginner
300: Note:
301: This is only used by Mmg and ParMmg (not Pragmatic).
303: .seealso: `DMPLEX`, `DMPlexMetricNoMovement()`, `DMPlexMetricSetNoInsertion()`, `DMPlexMetricSetNoSwapping()`, `DMPlexMetricSetNoSurf()`
304: @*/
305: PetscErrorCode DMPlexMetricSetNoMovement(DM dm, PetscBool noMove)
306: {
307: DM_Plex *plex = (DM_Plex *)dm->data;
309: PetscFunctionBegin;
310: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
311: plex->metricCtx->noMove = noMove;
312: PetscFunctionReturn(PETSC_SUCCESS);
313: }
315: /*@
316: DMPlexMetricNoMovement - Is node movement turned off?
318: Input Parameters:
319: . dm - The `DM`
321: Output Parameters:
322: . noMove - Is node movement turned off?
324: Level: beginner
326: Note:
327: This is only used by Mmg and ParMmg (not Pragmatic).
329: .seealso: `DMPLEX`, `DMPlexMetricSetNoMovement()`, `DMPlexMetricNoInsertion()`, `DMPlexMetricNoSwapping()`, `DMPlexMetricNoSurf()`
330: @*/
331: PetscErrorCode DMPlexMetricNoMovement(DM dm, PetscBool *noMove)
332: {
333: DM_Plex *plex = (DM_Plex *)dm->data;
335: PetscFunctionBegin;
336: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
337: *noMove = plex->metricCtx->noMove;
338: PetscFunctionReturn(PETSC_SUCCESS);
339: }
341: /*@
342: DMPlexMetricSetNoSurf - Should surface modification be turned off?
344: Input Parameters:
345: + dm - The `DM`
346: - noSurf - Should surface modification be turned off?
348: Level: beginner
350: Note:
351: This is only used by Mmg and ParMmg (not Pragmatic).
353: .seealso: `DMPLEX`, `DMPlexMetricNoSurf()`, `DMPlexMetricSetNoMovement()`, `DMPlexMetricSetNoInsertion()`, `DMPlexMetricSetNoSwapping()`
354: @*/
355: PetscErrorCode DMPlexMetricSetNoSurf(DM dm, PetscBool noSurf)
356: {
357: DM_Plex *plex = (DM_Plex *)dm->data;
359: PetscFunctionBegin;
360: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
361: plex->metricCtx->noSurf = noSurf;
362: PetscFunctionReturn(PETSC_SUCCESS);
363: }
365: /*@
366: DMPlexMetricNoSurf - Is surface modification turned off?
368: Input Parameters:
369: . dm - The `DM`
371: Output Parameters:
372: . noSurf - Is surface modification turned off?
374: Level: beginner
376: Note:
377: This is only used by Mmg and ParMmg (not Pragmatic).
379: .seealso: `DMPLEX`, `DMPlexMetricSetNoSurf()`, `DMPlexMetricNoMovement()`, `DMPlexMetricNoInsertion()`, `DMPlexMetricNoSwapping()`
380: @*/
381: PetscErrorCode DMPlexMetricNoSurf(DM dm, PetscBool *noSurf)
382: {
383: DM_Plex *plex = (DM_Plex *)dm->data;
385: PetscFunctionBegin;
386: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
387: *noSurf = plex->metricCtx->noSurf;
388: PetscFunctionReturn(PETSC_SUCCESS);
389: }
391: /*@
392: DMPlexMetricSetMinimumMagnitude - Set the minimum tolerated metric magnitude
394: Input Parameters:
395: + dm - The `DM`
396: - h_min - The minimum tolerated metric magnitude
398: Level: beginner
400: .seealso: `DMPLEX`, `DMPlexMetricGetMinimumMagnitude()`, `DMPlexMetricSetMaximumMagnitude()`
401: @*/
402: PetscErrorCode DMPlexMetricSetMinimumMagnitude(DM dm, PetscReal h_min)
403: {
404: DM_Plex *plex = (DM_Plex *)dm->data;
406: PetscFunctionBegin;
407: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
408: PetscCheck(h_min > 0.0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Metric magnitudes must be in (0, inf)");
409: plex->metricCtx->h_min = h_min;
410: PetscFunctionReturn(PETSC_SUCCESS);
411: }
413: /*@
414: DMPlexMetricGetMinimumMagnitude - Get the minimum tolerated metric magnitude
416: Input Parameters:
417: . dm - The `DM`
419: Output Parameters:
420: . h_min - The minimum tolerated metric magnitude
422: Level: beginner
424: .seealso: `DMPLEX`, `DMPlexMetricSetMinimumMagnitude()`, `DMPlexMetricGetMaximumMagnitude()`
425: @*/
426: PetscErrorCode DMPlexMetricGetMinimumMagnitude(DM dm, PetscReal *h_min)
427: {
428: DM_Plex *plex = (DM_Plex *)dm->data;
430: PetscFunctionBegin;
431: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
432: *h_min = plex->metricCtx->h_min;
433: PetscFunctionReturn(PETSC_SUCCESS);
434: }
436: /*@
437: DMPlexMetricSetMaximumMagnitude - Set the maximum tolerated metric magnitude
439: Input Parameters:
440: + dm - The `DM`
441: - h_max - The maximum tolerated metric magnitude
443: Level: beginner
445: .seealso: `DMPLEX`, `DMPlexMetricGetMaximumMagnitude()`, `DMPlexMetricSetMinimumMagnitude()`
446: @*/
447: PetscErrorCode DMPlexMetricSetMaximumMagnitude(DM dm, PetscReal h_max)
448: {
449: DM_Plex *plex = (DM_Plex *)dm->data;
451: PetscFunctionBegin;
452: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
453: PetscCheck(h_max > 0.0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Metric magnitudes must be in (0, inf)");
454: plex->metricCtx->h_max = h_max;
455: PetscFunctionReturn(PETSC_SUCCESS);
456: }
458: /*@
459: DMPlexMetricGetMaximumMagnitude - Get the maximum tolerated metric magnitude
461: Input Parameters:
462: . dm - The `DM`
464: Output Parameters:
465: . h_max - The maximum tolerated metric magnitude
467: Level: beginner
469: .seealso: `DMPLEX`, `DMPlexMetricSetMaximumMagnitude()`, `DMPlexMetricGetMinimumMagnitude()`
470: @*/
471: PetscErrorCode DMPlexMetricGetMaximumMagnitude(DM dm, PetscReal *h_max)
472: {
473: DM_Plex *plex = (DM_Plex *)dm->data;
475: PetscFunctionBegin;
476: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
477: *h_max = plex->metricCtx->h_max;
478: PetscFunctionReturn(PETSC_SUCCESS);
479: }
481: /*@
482: DMPlexMetricSetMaximumAnisotropy - Set the maximum tolerated metric anisotropy
484: Input Parameters:
485: + dm - The `DM`
486: - a_max - The maximum tolerated metric anisotropy
488: Level: beginner
490: Note:
491: If the value zero is given then anisotropy will not be restricted. Otherwise, it should be at least one.
493: .seealso: `DMPLEX`, `DMPlexMetricGetMaximumAnisotropy()`, `DMPlexMetricSetMaximumMagnitude()`
494: @*/
495: PetscErrorCode DMPlexMetricSetMaximumAnisotropy(DM dm, PetscReal a_max)
496: {
497: DM_Plex *plex = (DM_Plex *)dm->data;
499: PetscFunctionBegin;
500: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
501: PetscCheck(a_max >= 1.0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Anisotropy must be in [1, inf)");
502: plex->metricCtx->a_max = a_max;
503: PetscFunctionReturn(PETSC_SUCCESS);
504: }
506: /*@
507: DMPlexMetricGetMaximumAnisotropy - Get the maximum tolerated metric anisotropy
509: Input Parameters:
510: . dm - The `DM`
512: Output Parameters:
513: . a_max - The maximum tolerated metric anisotropy
515: Level: beginner
517: .seealso: `DMPLEX`, `DMPlexMetricSetMaximumAnisotropy()`, `DMPlexMetricGetMaximumMagnitude()`
518: @*/
519: PetscErrorCode DMPlexMetricGetMaximumAnisotropy(DM dm, PetscReal *a_max)
520: {
521: DM_Plex *plex = (DM_Plex *)dm->data;
523: PetscFunctionBegin;
524: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
525: *a_max = plex->metricCtx->a_max;
526: PetscFunctionReturn(PETSC_SUCCESS);
527: }
529: /*@
530: DMPlexMetricSetTargetComplexity - Set the target metric complexity
532: Input Parameters:
533: + dm - The `DM`
534: - targetComplexity - The target metric complexity
536: Level: beginner
538: .seealso: `DMPLEX`, `DMPlexMetricGetTargetComplexity()`, `DMPlexMetricSetNormalizationOrder()`
539: @*/
540: PetscErrorCode DMPlexMetricSetTargetComplexity(DM dm, PetscReal targetComplexity)
541: {
542: DM_Plex *plex = (DM_Plex *)dm->data;
544: PetscFunctionBegin;
545: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
546: PetscCheck(targetComplexity > 0.0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Metric complexity must be in (0, inf)");
547: plex->metricCtx->targetComplexity = targetComplexity;
548: PetscFunctionReturn(PETSC_SUCCESS);
549: }
551: /*@
552: DMPlexMetricGetTargetComplexity - Get the target metric complexity
554: Input Parameters:
555: . dm - The `DM`
557: Output Parameters:
558: . targetComplexity - The target metric complexity
560: Level: beginner
562: .seealso: `DMPLEX`, `DMPlexMetricSetTargetComplexity()`, `DMPlexMetricGetNormalizationOrder()`
563: @*/
564: PetscErrorCode DMPlexMetricGetTargetComplexity(DM dm, PetscReal *targetComplexity)
565: {
566: DM_Plex *plex = (DM_Plex *)dm->data;
568: PetscFunctionBegin;
569: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
570: *targetComplexity = plex->metricCtx->targetComplexity;
571: PetscFunctionReturn(PETSC_SUCCESS);
572: }
574: /*@
575: DMPlexMetricSetNormalizationOrder - Set the order p for L-p normalization
577: Input Parameters:
578: + dm - The `DM`
579: - p - The normalization order
581: Level: beginner
583: .seealso: `DMPLEX`, `DMPlexMetricGetNormalizationOrder()`, `DMPlexMetricSetTargetComplexity()`
584: @*/
585: PetscErrorCode DMPlexMetricSetNormalizationOrder(DM dm, PetscReal p)
586: {
587: DM_Plex *plex = (DM_Plex *)dm->data;
589: PetscFunctionBegin;
590: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
591: PetscCheck(p >= 1.0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Normalization order must be in [1, inf)");
592: plex->metricCtx->p = p;
593: PetscFunctionReturn(PETSC_SUCCESS);
594: }
596: /*@
597: DMPlexMetricGetNormalizationOrder - Get the order p for L-p normalization
599: Input Parameters:
600: . dm - The `DM`
602: Output Parameters:
603: . p - The normalization order
605: Level: beginner
607: .seealso: `DMPLEX`, `DMPlexMetricSetNormalizationOrder()`, `DMPlexMetricGetTargetComplexity()`
608: @*/
609: PetscErrorCode DMPlexMetricGetNormalizationOrder(DM dm, PetscReal *p)
610: {
611: DM_Plex *plex = (DM_Plex *)dm->data;
613: PetscFunctionBegin;
614: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
615: *p = plex->metricCtx->p;
616: PetscFunctionReturn(PETSC_SUCCESS);
617: }
619: /*@
620: DMPlexMetricSetGradationFactor - Set the metric gradation factor
622: Input Parameters:
623: + dm - The `DM`
624: - beta - The metric gradation factor
626: Level: beginner
628: Notes:
629: The gradation factor is the maximum tolerated length ratio between adjacent edges.
631: Turn off gradation by passing the value -1. Otherwise, pass a positive value.
633: This is only used by Mmg and ParMmg (not Pragmatic).
635: .seealso: `DMPLEX`, `DMPlexMetricGetGradationFactor()`, `DMPlexMetricSetHausdorffNumber()`
636: @*/
637: PetscErrorCode DMPlexMetricSetGradationFactor(DM dm, PetscReal beta)
638: {
639: DM_Plex *plex = (DM_Plex *)dm->data;
641: PetscFunctionBegin;
642: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
643: PetscCheck(beta > 0.0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Metric gradation factor must be in (0, inf)");
644: plex->metricCtx->gradationFactor = beta;
645: PetscFunctionReturn(PETSC_SUCCESS);
646: }
648: /*@
649: DMPlexMetricGetGradationFactor - Get the metric gradation factor
651: Input Parameters:
652: . dm - The `DM`
654: Output Parameters:
655: . beta - The metric gradation factor
657: Level: beginner
659: Notes:
660: The gradation factor is the maximum tolerated length ratio between adjacent edges.
662: The value -1 implies that gradation is turned off.
664: This is only used by Mmg and ParMmg (not Pragmatic).
666: .seealso: `DMPLEX`, `DMPlexMetricSetGradationFactor()`, `DMPlexMetricGetHausdorffNumber()`
667: @*/
668: PetscErrorCode DMPlexMetricGetGradationFactor(DM dm, PetscReal *beta)
669: {
670: DM_Plex *plex = (DM_Plex *)dm->data;
672: PetscFunctionBegin;
673: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
674: *beta = plex->metricCtx->gradationFactor;
675: PetscFunctionReturn(PETSC_SUCCESS);
676: }
678: /*@
679: DMPlexMetricSetHausdorffNumber - Set the metric Hausdorff number
681: Input Parameters:
682: + dm - The `DM`
683: - hausd - The metric Hausdorff number
685: Level: beginner
687: Notes:
688: The Hausdorff number imposes the maximal distance between the piecewise linear approximation of the
689: boundary and the reconstructed ideal boundary. Thus, a low Hausdorff parameter leads to refine the
690: high curvature areas. By default, the Hausdorff value is set to 0.01, which is a suitable value for
691: an object of size 1 in each direction. For smaller (resp. larger) objects, you may need to decrease
692: (resp. increase) the Hausdorff parameter. (Taken from
693: https://www.mmgtools.org/mmg-remesher-try-mmg/mmg-remesher-options/mmg-remesher-option-hausd).
695: This is only used by Mmg and ParMmg (not Pragmatic).
697: .seealso: `DMPLEX`, `DMPlexMetricSetGradationFactor()`, `DMPlexMetricGetHausdorffNumber()`
698: @*/
699: PetscErrorCode DMPlexMetricSetHausdorffNumber(DM dm, PetscReal hausd)
700: {
701: DM_Plex *plex = (DM_Plex *)dm->data;
703: PetscFunctionBegin;
704: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
705: PetscCheck(hausd > 0.0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Metric Hausdorff number must be in (0, inf)");
706: plex->metricCtx->hausdorffNumber = hausd;
707: PetscFunctionReturn(PETSC_SUCCESS);
708: }
710: /*@
711: DMPlexMetricGetHausdorffNumber - Get the metric Hausdorff number
713: Input Parameters:
714: . dm - The `DM`
716: Output Parameters:
717: . hausd - The metric Hausdorff number
719: Level: beginner
721: Notes:
722: The Hausdorff number imposes the maximal distance between the piecewise linear approximation of the
723: boundary and the reconstructed ideal boundary. Thus, a low Hausdorff parameter leads to refine the
724: high curvature areas. By default, the Hausdorff value is set to 0.01, which is a suitable value for
725: an object of size 1 in each direction. For smaller (resp. larger) objects, you may need to decrease
726: (resp. increase) the Hausdorff parameter. (Taken from
727: https://www.mmgtools.org/mmg-remesher-try-mmg/mmg-remesher-options/mmg-remesher-option-hausd).
729: This is only used by Mmg and ParMmg (not Pragmatic).
731: .seealso: `DMPLEX`, `DMPlexMetricGetGradationFactor()`, `DMPlexMetricSetHausdorffNumber()`
732: @*/
733: PetscErrorCode DMPlexMetricGetHausdorffNumber(DM dm, PetscReal *hausd)
734: {
735: DM_Plex *plex = (DM_Plex *)dm->data;
737: PetscFunctionBegin;
738: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
739: *hausd = plex->metricCtx->hausdorffNumber;
740: PetscFunctionReturn(PETSC_SUCCESS);
741: }
743: /*@
744: DMPlexMetricSetVerbosity - Set the verbosity of the mesh adaptation package
746: Input Parameters:
747: + dm - The `DM`
748: - verbosity - The verbosity, where -1 is silent and 10 is maximum
750: Level: beginner
752: Note:
753: This is only used by Mmg and ParMmg (not Pragmatic).
755: .seealso: `DMPLEX`, `DMPlexMetricGetVerbosity()`, `DMPlexMetricSetNumIterations()`
756: @*/
757: PetscErrorCode DMPlexMetricSetVerbosity(DM dm, PetscInt verbosity)
758: {
759: DM_Plex *plex = (DM_Plex *)dm->data;
761: PetscFunctionBegin;
762: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
763: plex->metricCtx->verbosity = verbosity;
764: PetscFunctionReturn(PETSC_SUCCESS);
765: }
767: /*@
768: DMPlexMetricGetVerbosity - Get the verbosity of the mesh adaptation package
770: Input Parameters:
771: . dm - The `DM`
773: Output Parameters:
774: . verbosity - The verbosity, where -1 is silent and 10 is maximum
776: Level: beginner
778: Note:
779: This is only used by Mmg and ParMmg (not Pragmatic).
781: .seealso: `DMPLEX`, `DMPlexMetricSetVerbosity()`, `DMPlexMetricGetNumIterations()`
782: @*/
783: PetscErrorCode DMPlexMetricGetVerbosity(DM dm, PetscInt *verbosity)
784: {
785: DM_Plex *plex = (DM_Plex *)dm->data;
787: PetscFunctionBegin;
788: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
789: *verbosity = plex->metricCtx->verbosity;
790: PetscFunctionReturn(PETSC_SUCCESS);
791: }
793: /*@
794: DMPlexMetricSetNumIterations - Set the number of parallel adaptation iterations
796: Input Parameters:
797: + dm - The `DM`
798: - numIter - the number of parallel adaptation iterations
800: Level: beginner
802: Note:
803: This is only used by ParMmg (not Pragmatic or Mmg).
805: .seealso: `DMPLEX`, `DMPlexMetricSetVerbosity()`, `DMPlexMetricGetNumIterations()`
806: @*/
807: PetscErrorCode DMPlexMetricSetNumIterations(DM dm, PetscInt numIter)
808: {
809: DM_Plex *plex = (DM_Plex *)dm->data;
811: PetscFunctionBegin;
812: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
813: plex->metricCtx->numIter = numIter;
814: PetscFunctionReturn(PETSC_SUCCESS);
815: }
817: /*@
818: DMPlexMetricGetNumIterations - Get the number of parallel adaptation iterations
820: Input Parameters:
821: . dm - The `DM`
823: Output Parameters:
824: . numIter - the number of parallel adaptation iterations
826: Level: beginner
828: Note:
829: This is only used by Mmg and ParMmg (not Pragmatic or Mmg).
831: .seealso: `DMPLEX`, `DMPlexMetricSetNumIterations()`, `DMPlexMetricGetVerbosity()`
832: @*/
833: PetscErrorCode DMPlexMetricGetNumIterations(DM dm, PetscInt *numIter)
834: {
835: DM_Plex *plex = (DM_Plex *)dm->data;
837: PetscFunctionBegin;
838: if (!plex->metricCtx) PetscCall(DMPlexMetricSetFromOptions(dm));
839: *numIter = plex->metricCtx->numIter;
840: PetscFunctionReturn(PETSC_SUCCESS);
841: }
843: static PetscErrorCode DMPlexP1FieldCreate_Private(DM dm, PetscInt f, PetscInt size, Vec *metric)
844: {
845: MPI_Comm comm;
846: PetscFE fe;
847: PetscInt dim;
849: PetscFunctionBegin;
850: /* Extract metadata from dm */
851: PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
852: PetscCall(DMGetDimension(dm, &dim));
854: /* Create a P1 field of the requested size */
855: PetscCall(PetscFECreateLagrange(comm, dim, size, PETSC_TRUE, 1, PETSC_DETERMINE, &fe));
856: PetscCall(DMSetField(dm, f, NULL, (PetscObject)fe));
857: PetscCall(DMCreateDS(dm));
858: PetscCall(PetscFEDestroy(&fe));
859: PetscCall(DMCreateLocalVector(dm, metric));
860: PetscFunctionReturn(PETSC_SUCCESS);
861: }
863: /*@
864: DMPlexMetricCreate - Create a Riemannian metric field
866: Input Parameters:
867: + dm - The `DM`
868: - f - The field number to use
870: Output Parameter:
871: . metric - The metric
873: Options Database Key:
874: . -dm_adaptor <pragmatic/mmg/parmmg> - specify dm adaptor to use
876: Options Database Keys for Mmg and ParMmg:
877: + -dm_plex_metric_gradation_factor - Maximum ratio by which edge lengths may grow during gradation
878: . -dm_plex_metric_num_iterations - Number of parallel mesh adaptation iterations for ParMmg
879: . -dm_plex_metric_no_insert - Should node insertion/deletion be turned off?
880: . -dm_plex_metric_no_swap - Should facet swapping be turned off?
881: . -dm_plex_metric_no_move - Should node movement be turned off?
882: - -dm_plex_metric_verbosity - Choose a verbosity level from -1 (silent) to 10 (maximum).
884: Options Database Keys for Riemannian metrics:
885: + -dm_plex_metric_isotropic - Is the metric isotropic?
886: . -dm_plex_metric_uniform - Is the metric uniform?
887: . -dm_plex_metric_restrict_anisotropy_first - Should anisotropy be restricted before normalization?
888: . -dm_plex_metric_h_min - Minimum tolerated metric magnitude
889: . -dm_plex_metric_h_max - Maximum tolerated metric magnitude
890: . -dm_plex_metric_a_max - Maximum tolerated anisotropy
891: . -dm_plex_metric_p - L-p normalization order
892: - -dm_plex_metric_target_complexity - Target metric complexity
894: Level: beginner
896: Note:
897: It is assumed that the `DM` is comprised of simplices.
899: .seealso: `DMPLEX`, `DMPlexMetricCreateUniform()`, `DMPlexMetricCreateIsotropic()`
900: @*/
901: PetscErrorCode DMPlexMetricCreate(DM dm, PetscInt f, Vec *metric)
902: {
903: PetscBool isotropic, uniform;
904: PetscInt coordDim, Nd;
906: PetscFunctionBegin;
907: PetscCall(DMGetCoordinateDim(dm, &coordDim));
908: Nd = coordDim * coordDim;
909: PetscCall(DMPlexMetricIsUniform(dm, &uniform));
910: PetscCall(DMPlexMetricIsIsotropic(dm, &isotropic));
911: if (uniform) {
912: MPI_Comm comm;
914: PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
915: PetscCheck(isotropic, comm, PETSC_ERR_SUP, "Uniform anisotropic metrics not supported");
916: PetscCall(VecCreate(comm, metric));
917: PetscCall(VecSetSizes(*metric, 1, PETSC_DECIDE));
918: PetscCall(VecSetFromOptions(*metric));
919: } else if (isotropic) PetscCall(DMPlexP1FieldCreate_Private(dm, f, 1, metric));
920: else PetscCall(DMPlexP1FieldCreate_Private(dm, f, Nd, metric));
921: PetscFunctionReturn(PETSC_SUCCESS);
922: }
924: /*@
925: DMPlexMetricCreateUniform - Construct a uniform isotropic metric
927: Input Parameters:
928: + dm - The `DM`
929: . f - The field number to use
930: - alpha - Scaling parameter for the diagonal
932: Output Parameter:
933: . metric - The uniform metric
935: Level: beginner
937: Note:
938: In this case, the metric is constant in space and so is only specified for a single vertex.
940: .seealso: `DMPLEX`, `DMPlexMetricCreate()`, `DMPlexMetricCreateIsotropic()`
941: @*/
942: PetscErrorCode DMPlexMetricCreateUniform(DM dm, PetscInt f, PetscReal alpha, Vec *metric)
943: {
944: PetscFunctionBegin;
945: PetscCall(DMPlexMetricSetUniform(dm, PETSC_TRUE));
946: PetscCall(DMPlexMetricCreate(dm, f, metric));
947: PetscCheck(alpha, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Uniform metric scaling is undefined");
948: PetscCheck(alpha > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Uniform metric scaling should be in (0, inf)");
949: PetscCall(VecSet(*metric, alpha));
950: PetscCall(VecAssemblyBegin(*metric));
951: PetscCall(VecAssemblyEnd(*metric));
952: PetscFunctionReturn(PETSC_SUCCESS);
953: }
955: static void identity(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
956: {
957: f0[0] = u[0];
958: }
960: /*@
961: DMPlexMetricCreateIsotropic - Construct an isotropic metric from an error indicator
963: Input Parameters:
964: + dm - The `DM`
965: . f - The field number to use
966: - indicator - The error indicator
968: Output Parameter:
969: . metric - The isotropic metric
971: Level: beginner
973: Notes:
974: It is assumed that the `DM` is comprised of simplices.
976: The indicator needs to be a scalar field. If it is not defined vertex-wise, then it is projected appropriately.
978: .seealso: `DMPLEX`, `DMPlexMetricCreate()`, `DMPlexMetricCreateUniform()`
979: @*/
980: PetscErrorCode DMPlexMetricCreateIsotropic(DM dm, PetscInt f, Vec indicator, Vec *metric)
981: {
982: PetscInt m, n;
984: PetscFunctionBegin;
985: PetscCall(DMPlexMetricSetIsotropic(dm, PETSC_TRUE));
986: PetscCall(DMPlexMetricCreate(dm, f, metric));
987: PetscCall(VecGetSize(indicator, &m));
988: PetscCall(VecGetSize(*metric, &n));
989: if (m == n) PetscCall(VecCopy(indicator, *metric));
990: else {
991: DM dmIndi;
992: void (*funcs[1])(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]);
994: PetscCall(VecGetDM(indicator, &dmIndi));
995: funcs[0] = identity;
996: PetscCall(DMProjectFieldLocal(dmIndi, 0.0, indicator, funcs, INSERT_VALUES, *metric));
997: }
998: PetscFunctionReturn(PETSC_SUCCESS);
999: }
1001: /*@
1002: DMPlexMetricDeterminantCreate - Create the determinant field for a Riemannian metric
1004: Input Parameters:
1005: + dm - The `DM` of the metric field
1006: - f - The field number to use
1008: Output Parameters:
1009: + determinant - The determinant field
1010: - dmDet - The corresponding `DM`
1012: Level: beginner
1014: .seealso: `DMPLEX`, `DMPlexMetricCreateUniform()`, `DMPlexMetricCreateIsotropic()`, `DMPlexMetricCreate()`
1015: @*/
1016: PetscErrorCode DMPlexMetricDeterminantCreate(DM dm, PetscInt f, Vec *determinant, DM *dmDet)
1017: {
1018: PetscBool uniform;
1020: PetscFunctionBegin;
1021: PetscCall(DMPlexMetricIsUniform(dm, &uniform));
1022: PetscCall(DMClone(dm, dmDet));
1023: if (uniform) {
1024: MPI_Comm comm;
1026: PetscCall(PetscObjectGetComm((PetscObject)*dmDet, &comm));
1027: PetscCall(VecCreate(comm, determinant));
1028: PetscCall(VecSetSizes(*determinant, 1, PETSC_DECIDE));
1029: PetscCall(VecSetFromOptions(*determinant));
1030: } else PetscCall(DMPlexP1FieldCreate_Private(*dmDet, f, 1, determinant));
1031: PetscFunctionReturn(PETSC_SUCCESS);
1032: }
1034: static PetscErrorCode LAPACKsyevFail(PetscInt dim, PetscScalar Mpos[])
1035: {
1036: PetscInt i, j;
1038: PetscFunctionBegin;
1039: PetscCall(PetscPrintf(PETSC_COMM_SELF, "Failed to apply LAPACKsyev to the matrix\n"));
1040: for (i = 0; i < dim; ++i) {
1041: if (i == 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, " [["));
1042: else PetscCall(PetscPrintf(PETSC_COMM_SELF, " ["));
1043: for (j = 0; j < dim; ++j) {
1044: if (j < dim - 1) PetscCall(PetscPrintf(PETSC_COMM_SELF, "%15.8e, ", (double)PetscAbsScalar(Mpos[i * dim + j])));
1045: else PetscCall(PetscPrintf(PETSC_COMM_SELF, "%15.8e", (double)PetscAbsScalar(Mpos[i * dim + j])));
1046: }
1047: if (i < dim - 1) PetscCall(PetscPrintf(PETSC_COMM_SELF, "]\n"));
1048: else PetscCall(PetscPrintf(PETSC_COMM_SELF, "]]\n"));
1049: }
1050: PetscFunctionReturn(PETSC_SUCCESS);
1051: }
1053: static PetscErrorCode DMPlexMetricModify_Private(PetscInt dim, PetscReal h_min, PetscReal h_max, PetscReal a_max, PetscScalar Mp[], PetscScalar *detMp)
1054: {
1055: PetscInt i, j, k;
1056: PetscReal *eigs, max_eig, l_min = 1.0 / (h_max * h_max), l_max = 1.0 / (h_min * h_min), la_min = 1.0 / (a_max * a_max);
1057: PetscScalar *Mpos;
1059: PetscFunctionBegin;
1060: PetscCall(PetscMalloc2(dim * dim, &Mpos, dim, &eigs));
1062: /* Symmetrize */
1063: for (i = 0; i < dim; ++i) {
1064: Mpos[i * dim + i] = Mp[i * dim + i];
1065: for (j = i + 1; j < dim; ++j) {
1066: Mpos[i * dim + j] = 0.5 * (Mp[i * dim + j] + Mp[j * dim + i]);
1067: Mpos[j * dim + i] = Mpos[i * dim + j];
1068: }
1069: }
1071: /* Compute eigendecomposition */
1072: if (dim == 1) {
1073: /* Isotropic case */
1074: eigs[0] = PetscRealPart(Mpos[0]);
1075: Mpos[0] = 1.0;
1076: } else {
1077: /* Anisotropic case */
1078: PetscScalar *work;
1079: PetscBLASInt lwork = (PetscBLASInt)(5 * dim);
1081: PetscCall(PetscMalloc1(5 * dim, &work));
1082: {
1083: PetscBLASInt lierr;
1084: PetscBLASInt nb;
1086: PetscCall(PetscBLASIntCast(dim, &nb));
1087: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
1088: #if defined(PETSC_USE_COMPLEX)
1089: {
1090: PetscReal *rwork;
1091: PetscCall(PetscMalloc1(3 * dim, &rwork));
1092: PetscCallBLAS("LAPACKsyev", LAPACKsyev_("V", "U", &nb, Mpos, &nb, eigs, work, &lwork, rwork, &lierr));
1093: PetscCall(PetscFree(rwork));
1094: }
1095: #else
1096: PetscCallBLAS("LAPACKsyev", LAPACKsyev_("V", "U", &nb, Mpos, &nb, eigs, work, &lwork, &lierr));
1097: #endif
1098: if (lierr) {
1099: for (i = 0; i < dim; ++i) {
1100: Mpos[i * dim + i] = Mp[i * dim + i];
1101: for (j = i + 1; j < dim; ++j) {
1102: Mpos[i * dim + j] = 0.5 * (Mp[i * dim + j] + Mp[j * dim + i]);
1103: Mpos[j * dim + i] = Mpos[i * dim + j];
1104: }
1105: }
1106: PetscCall(LAPACKsyevFail(dim, Mpos));
1107: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in LAPACK routine %d", (int)lierr);
1108: }
1109: PetscCall(PetscFPTrapPop());
1110: }
1111: PetscCall(PetscFree(work));
1112: }
1114: /* Reflect to positive orthant and enforce maximum and minimum size */
1115: max_eig = 0.0;
1116: for (i = 0; i < dim; ++i) {
1117: eigs[i] = PetscMin(l_max, PetscMax(l_min, PetscAbsReal(eigs[i])));
1118: max_eig = PetscMax(eigs[i], max_eig);
1119: }
1121: /* Enforce maximum anisotropy and compute determinant */
1122: *detMp = 1.0;
1123: for (i = 0; i < dim; ++i) {
1124: if (a_max >= 1.0) eigs[i] = PetscMax(eigs[i], max_eig * la_min);
1125: *detMp *= eigs[i];
1126: }
1128: /* Reconstruct Hessian */
1129: for (i = 0; i < dim; ++i) {
1130: for (j = 0; j < dim; ++j) {
1131: Mp[i * dim + j] = 0.0;
1132: for (k = 0; k < dim; ++k) Mp[i * dim + j] += Mpos[k * dim + i] * eigs[k] * Mpos[k * dim + j];
1133: }
1134: }
1135: PetscCall(PetscFree2(Mpos, eigs));
1136: PetscFunctionReturn(PETSC_SUCCESS);
1137: }
1139: /*@
1140: DMPlexMetricEnforceSPD - Enforce symmetric positive-definiteness of a metric
1142: Input Parameters:
1143: + dm - The `DM`
1144: . metricIn - The metric
1145: . restrictSizes - Should maximum/minimum metric magnitudes be enforced?
1146: - restrictAnisotropy - Should maximum anisotropy be enforced?
1148: Output Parameters:
1149: + metricOut - The metric
1150: - determinant - Its determinant
1152: Options Database Keys:
1153: + -dm_plex_metric_isotropic - Is the metric isotropic?
1154: . -dm_plex_metric_uniform - Is the metric uniform?
1155: . -dm_plex_metric_h_min - Minimum tolerated metric magnitude
1156: . -dm_plex_metric_h_max - Maximum tolerated metric magnitude
1157: - -dm_plex_metric_a_max - Maximum tolerated anisotropy
1159: Level: beginner
1161: .seealso: `DMPLEX`, `DMPlexMetricNormalize()`, `DMPlexMetricIntersection()`
1162: @*/
1163: PetscErrorCode DMPlexMetricEnforceSPD(DM dm, Vec metricIn, PetscBool restrictSizes, PetscBool restrictAnisotropy, Vec metricOut, Vec determinant)
1164: {
1165: DM dmDet;
1166: PetscBool isotropic, uniform;
1167: PetscInt dim, vStart, vEnd, v;
1168: PetscScalar *met, *det;
1169: PetscReal h_min = 1.0e-30, h_max = 1.0e+30, a_max = 1.0e+15;
1171: PetscFunctionBegin;
1172: PetscCall(PetscLogEventBegin(DMPLEX_MetricEnforceSPD, 0, 0, 0, 0));
1174: /* Extract metadata from dm */
1175: PetscCall(DMGetDimension(dm, &dim));
1176: if (restrictSizes) {
1177: PetscCall(DMPlexMetricGetMinimumMagnitude(dm, &h_min));
1178: PetscCall(DMPlexMetricGetMaximumMagnitude(dm, &h_max));
1179: h_min = PetscMax(h_min, 1.0e-30);
1180: h_max = PetscMin(h_max, 1.0e+30);
1181: PetscCheck(h_min < h_max, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Minimum metric magnitude should be smaller than maximum metric magnitude");
1182: }
1183: if (restrictAnisotropy) {
1184: PetscCall(DMPlexMetricGetMaximumAnisotropy(dm, &a_max));
1185: a_max = PetscMin(a_max, 1.0e+30);
1186: }
1188: /* Setup output metric */
1189: PetscCall(VecCopy(metricIn, metricOut));
1191: /* Enforce SPD and extract determinant */
1192: PetscCall(VecGetArray(metricOut, &met));
1193: PetscCall(DMPlexMetricIsUniform(dm, &uniform));
1194: PetscCall(DMPlexMetricIsIsotropic(dm, &isotropic));
1195: if (uniform) {
1196: PetscCheck(isotropic, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Uniform anisotropic metrics cannot exist");
1198: /* Uniform case */
1199: PetscCall(VecGetArray(determinant, &det));
1200: PetscCall(DMPlexMetricModify_Private(1, h_min, h_max, a_max, met, det));
1201: PetscCall(VecRestoreArray(determinant, &det));
1202: } else {
1203: /* Spatially varying case */
1204: PetscInt nrow;
1206: if (isotropic) nrow = 1;
1207: else nrow = dim;
1208: PetscCall(VecGetDM(determinant, &dmDet));
1209: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
1210: PetscCall(VecGetArray(determinant, &det));
1211: for (v = vStart; v < vEnd; ++v) {
1212: PetscScalar *vmet, *vdet;
1213: PetscCall(DMPlexPointLocalRef(dm, v, met, &vmet));
1214: PetscCall(DMPlexPointLocalRef(dmDet, v, det, &vdet));
1215: PetscCall(DMPlexMetricModify_Private(nrow, h_min, h_max, a_max, vmet, vdet));
1216: }
1217: PetscCall(VecRestoreArray(determinant, &det));
1218: }
1219: PetscCall(VecRestoreArray(metricOut, &met));
1221: PetscCall(PetscLogEventEnd(DMPLEX_MetricEnforceSPD, 0, 0, 0, 0));
1222: PetscFunctionReturn(PETSC_SUCCESS);
1223: }
1225: static void detMFunc(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
1226: {
1227: const PetscScalar p = constants[0];
1229: f0[0] = PetscPowScalar(u[0], p / (2.0 * p + dim));
1230: }
1232: /*@
1233: DMPlexMetricNormalize - Apply L-p normalization to a metric
1235: Input Parameters:
1236: + dm - The `DM`
1237: . metricIn - The unnormalized metric
1238: . restrictSizes - Should maximum/minimum metric magnitudes be enforced?
1239: - restrictAnisotropy - Should maximum metric anisotropy be enforced?
1241: Output Parameters:
1242: + metricOut - The normalized metric
1243: - determinant - computed determinant
1245: Options Database Keys:
1246: + -dm_plex_metric_isotropic - Is the metric isotropic?
1247: . -dm_plex_metric_uniform - Is the metric uniform?
1248: . -dm_plex_metric_restrict_anisotropy_first - Should anisotropy be restricted before normalization?
1249: . -dm_plex_metric_h_min - Minimum tolerated metric magnitude
1250: . -dm_plex_metric_h_max - Maximum tolerated metric magnitude
1251: . -dm_plex_metric_a_max - Maximum tolerated anisotropy
1252: . -dm_plex_metric_p - L-p normalization order
1253: - -dm_plex_metric_target_complexity - Target metric complexity
1255: Level: beginner
1257: .seealso: `DMPLEX`, `DMPlexMetricEnforceSPD()`, `DMPlexMetricIntersection()`
1258: @*/
1259: PetscErrorCode DMPlexMetricNormalize(DM dm, Vec metricIn, PetscBool restrictSizes, PetscBool restrictAnisotropy, Vec metricOut, Vec determinant)
1260: {
1261: DM dmDet;
1262: MPI_Comm comm;
1263: PetscBool restrictAnisotropyFirst, isotropic, uniform;
1264: PetscDS ds;
1265: PetscInt dim, Nd, vStart, vEnd, v, i;
1266: PetscScalar *met, *det, integral, constants[1];
1267: PetscReal p, h_min = 1.0e-30, h_max = 1.0e+30, a_max = 0.0, factGlob, fact, target, realIntegral;
1269: PetscFunctionBegin;
1270: PetscCall(PetscLogEventBegin(DMPLEX_MetricNormalize, 0, 0, 0, 0));
1272: /* Extract metadata from dm */
1273: PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
1274: PetscCall(DMGetDimension(dm, &dim));
1275: PetscCall(DMPlexMetricIsUniform(dm, &uniform));
1276: PetscCall(DMPlexMetricIsIsotropic(dm, &isotropic));
1277: if (isotropic) Nd = 1;
1278: else Nd = dim * dim;
1280: /* Set up metric and ensure it is SPD */
1281: PetscCall(DMPlexMetricRestrictAnisotropyFirst(dm, &restrictAnisotropyFirst));
1282: PetscCall(DMPlexMetricEnforceSPD(dm, metricIn, PETSC_FALSE, (PetscBool)(restrictAnisotropy && restrictAnisotropyFirst), metricOut, determinant));
1284: /* Compute global normalization factor */
1285: PetscCall(DMPlexMetricGetTargetComplexity(dm, &target));
1286: PetscCall(DMPlexMetricGetNormalizationOrder(dm, &p));
1287: constants[0] = p;
1288: if (uniform) {
1289: PetscCheck(isotropic, comm, PETSC_ERR_SUP, "Uniform anisotropic metrics not supported");
1290: DM dmTmp;
1291: Vec tmp;
1293: PetscCall(DMClone(dm, &dmTmp));
1294: PetscCall(DMPlexP1FieldCreate_Private(dmTmp, 0, 1, &tmp));
1295: PetscCall(VecGetArray(determinant, &det));
1296: PetscCall(VecSet(tmp, det[0]));
1297: PetscCall(VecRestoreArray(determinant, &det));
1298: PetscCall(DMGetDS(dmTmp, &ds));
1299: PetscCall(PetscDSSetConstants(ds, 1, constants));
1300: PetscCall(PetscDSSetObjective(ds, 0, detMFunc));
1301: PetscCall(DMPlexComputeIntegralFEM(dmTmp, tmp, &integral, NULL));
1302: PetscCall(VecDestroy(&tmp));
1303: PetscCall(DMDestroy(&dmTmp));
1304: } else {
1305: PetscCall(VecGetDM(determinant, &dmDet));
1306: PetscCall(DMGetDS(dmDet, &ds));
1307: PetscCall(PetscDSSetConstants(ds, 1, constants));
1308: PetscCall(PetscDSSetObjective(ds, 0, detMFunc));
1309: PetscCall(DMPlexComputeIntegralFEM(dmDet, determinant, &integral, NULL));
1310: }
1311: realIntegral = PetscRealPart(integral);
1312: PetscCheck(realIntegral > 1.0e-30, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Global metric normalization factor must be in (0, inf). Is the input metric positive-definite?");
1313: factGlob = PetscPowReal(target / realIntegral, 2.0 / dim);
1315: /* Apply local scaling */
1316: if (restrictSizes) {
1317: PetscCall(DMPlexMetricGetMinimumMagnitude(dm, &h_min));
1318: PetscCall(DMPlexMetricGetMaximumMagnitude(dm, &h_max));
1319: h_min = PetscMax(h_min, 1.0e-30);
1320: h_max = PetscMin(h_max, 1.0e+30);
1321: PetscCheck(h_min < h_max, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Minimum metric magnitude should be smaller than maximum metric magnitude");
1322: }
1323: if (restrictAnisotropy && !restrictAnisotropyFirst) {
1324: PetscCall(DMPlexMetricGetMaximumAnisotropy(dm, &a_max));
1325: a_max = PetscMin(a_max, 1.0e+30);
1326: }
1327: PetscCall(VecGetArray(metricOut, &met));
1328: PetscCall(VecGetArray(determinant, &det));
1329: if (uniform) {
1330: /* Uniform case */
1331: met[0] *= factGlob * PetscPowReal(PetscAbsScalar(det[0]), -1.0 / (2 * p + dim));
1332: if (restrictSizes) PetscCall(DMPlexMetricModify_Private(1, h_min, h_max, a_max, met, det));
1333: } else {
1334: /* Spatially varying case */
1335: PetscInt nrow;
1337: if (isotropic) nrow = 1;
1338: else nrow = dim;
1339: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
1340: PetscCall(VecGetDM(determinant, &dmDet));
1341: for (v = vStart; v < vEnd; ++v) {
1342: PetscScalar *Mp, *detM;
1344: PetscCall(DMPlexPointLocalRef(dm, v, met, &Mp));
1345: PetscCall(DMPlexPointLocalRef(dmDet, v, det, &detM));
1346: fact = factGlob * PetscPowReal(PetscAbsScalar(detM[0]), -1.0 / (2 * p + dim));
1347: for (i = 0; i < Nd; ++i) Mp[i] *= fact;
1348: if (restrictSizes) PetscCall(DMPlexMetricModify_Private(nrow, h_min, h_max, a_max, Mp, detM));
1349: }
1350: }
1351: PetscCall(VecRestoreArray(determinant, &det));
1352: PetscCall(VecRestoreArray(metricOut, &met));
1354: PetscCall(PetscLogEventEnd(DMPLEX_MetricNormalize, 0, 0, 0, 0));
1355: PetscFunctionReturn(PETSC_SUCCESS);
1356: }
1358: /*@
1359: DMPlexMetricAverage - Compute the average of a list of metrics
1361: Input Parameters:
1362: + dm - The `DM`
1363: . numMetrics - The number of metrics to be averaged
1364: . weights - Weights for the average
1365: - metrics - The metrics to be averaged
1367: Output Parameter:
1368: . metricAvg - The averaged metric
1370: Level: beginner
1372: Notes:
1373: The weights should sum to unity.
1375: If weights are not provided then an unweighted average is used.
1377: .seealso: `DMPLEX`, `DMPlexMetricAverage2()`, `DMPlexMetricAverage3()`, `DMPlexMetricIntersection()`
1378: @*/
1379: PetscErrorCode DMPlexMetricAverage(DM dm, PetscInt numMetrics, PetscReal weights[], Vec metrics[], Vec metricAvg)
1380: {
1381: PetscBool haveWeights = PETSC_TRUE;
1382: PetscInt i, m, n;
1383: PetscReal sum = 0.0, tol = 1.0e-10;
1385: PetscFunctionBegin;
1386: PetscCall(PetscLogEventBegin(DMPLEX_MetricAverage, 0, 0, 0, 0));
1387: PetscCheck(numMetrics >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot average %" PetscInt_FMT " < 1 metrics", numMetrics);
1388: PetscCall(VecSet(metricAvg, 0.0));
1389: PetscCall(VecGetSize(metricAvg, &m));
1390: for (i = 0; i < numMetrics; ++i) {
1391: PetscCall(VecGetSize(metrics[i], &n));
1392: PetscCheck(m == n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Averaging different metric types not implemented");
1393: }
1395: /* Default to the unweighted case */
1396: if (!weights) {
1397: PetscCall(PetscMalloc1(numMetrics, &weights));
1398: haveWeights = PETSC_FALSE;
1399: for (i = 0; i < numMetrics; ++i) weights[i] = 1.0 / numMetrics;
1400: }
1402: /* Check weights sum to unity */
1403: for (i = 0; i < numMetrics; ++i) sum += weights[i];
1404: PetscCheck(PetscAbsReal(sum - 1) <= tol, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Weights do not sum to unity");
1406: /* Compute metric average */
1407: for (i = 0; i < numMetrics; ++i) PetscCall(VecAXPY(metricAvg, weights[i], metrics[i]));
1408: if (!haveWeights) PetscCall(PetscFree(weights));
1410: PetscCall(PetscLogEventEnd(DMPLEX_MetricAverage, 0, 0, 0, 0));
1411: PetscFunctionReturn(PETSC_SUCCESS);
1412: }
1414: /*@
1415: DMPlexMetricAverage2 - Compute the unweighted average of two metrics
1417: Input Parameters:
1418: + dm - The `DM`
1419: . metric1 - The first metric to be averaged
1420: - metric2 - The second metric to be averaged
1422: Output Parameter:
1423: . metricAvg - The averaged metric
1425: Level: beginner
1427: .seealso: `DMPLEX`, `DMPlexMetricAverage()`, `DMPlexMetricAverage3()`
1428: @*/
1429: PetscErrorCode DMPlexMetricAverage2(DM dm, Vec metric1, Vec metric2, Vec metricAvg)
1430: {
1431: PetscReal weights[2] = {0.5, 0.5};
1432: Vec metrics[2] = {metric1, metric2};
1434: PetscFunctionBegin;
1435: PetscCall(DMPlexMetricAverage(dm, 2, weights, metrics, metricAvg));
1436: PetscFunctionReturn(PETSC_SUCCESS);
1437: }
1439: /*@
1440: DMPlexMetricAverage3 - Compute the unweighted average of three metrics
1442: Input Parameters:
1443: + dm - The `DM`
1444: . metric1 - The first metric to be averaged
1445: . metric2 - The second metric to be averaged
1446: - metric3 - The third metric to be averaged
1448: Output Parameter:
1449: . metricAvg - The averaged metric
1451: Level: beginner
1453: .seealso: `DMPLEX`, `DMPlexMetricAverage()`, `DMPlexMetricAverage2()`
1454: @*/
1455: PetscErrorCode DMPlexMetricAverage3(DM dm, Vec metric1, Vec metric2, Vec metric3, Vec metricAvg)
1456: {
1457: PetscReal weights[3] = {1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0};
1458: Vec metrics[3] = {metric1, metric2, metric3};
1460: PetscFunctionBegin;
1461: PetscCall(DMPlexMetricAverage(dm, 3, weights, metrics, metricAvg));
1462: PetscFunctionReturn(PETSC_SUCCESS);
1463: }
1465: static PetscErrorCode DMPlexMetricIntersection_Private(PetscInt dim, PetscScalar M1[], PetscScalar M2[])
1466: {
1467: PetscInt i, j, k, l, m;
1468: PetscReal *evals;
1469: PetscScalar *evecs, *sqrtM1, *isqrtM1;
1471: PetscFunctionBegin;
1472: /* Isotropic case */
1473: if (dim == 1) {
1474: M2[0] = (PetscScalar)PetscMax(PetscRealPart(M1[0]), PetscRealPart(M2[0]));
1475: PetscFunctionReturn(PETSC_SUCCESS);
1476: }
1478: /* Anisotropic case */
1479: PetscCall(PetscMalloc4(dim * dim, &evecs, dim * dim, &sqrtM1, dim * dim, &isqrtM1, dim, &evals));
1480: for (i = 0; i < dim; ++i) {
1481: for (j = 0; j < dim; ++j) evecs[i * dim + j] = M1[i * dim + j];
1482: }
1483: {
1484: PetscScalar *work;
1485: PetscBLASInt lwork = (PetscBLASInt)(5 * dim);
1486: PetscCall(PetscMalloc1(5 * dim, &work));
1487: {
1488: PetscBLASInt lierr, nb;
1489: PetscReal sqrtj;
1491: /* Compute eigendecomposition of M1 */
1492: PetscCall(PetscBLASIntCast(dim, &nb));
1493: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
1494: #if defined(PETSC_USE_COMPLEX)
1495: {
1496: PetscReal *rwork;
1497: PetscCall(PetscMalloc1(3 * dim, &rwork));
1498: PetscCallBLAS("LAPACKsyev", LAPACKsyev_("V", "U", &nb, evecs, &nb, evals, work, &lwork, rwork, &lierr));
1499: PetscCall(PetscFree(rwork));
1500: }
1501: #else
1502: PetscCallBLAS("LAPACKsyev", LAPACKsyev_("V", "U", &nb, evecs, &nb, evals, work, &lwork, &lierr));
1503: #endif
1504: if (lierr) {
1505: PetscCall(LAPACKsyevFail(dim, M1));
1506: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in LAPACK routine %d", (int)lierr);
1507: }
1508: PetscCall(PetscFPTrapPop());
1510: /* Compute square root and the reciprocal thereof */
1511: for (i = 0; i < dim; ++i) {
1512: for (k = 0; k < dim; ++k) {
1513: sqrtM1[i * dim + k] = 0.0;
1514: isqrtM1[i * dim + k] = 0.0;
1515: for (j = 0; j < dim; ++j) {
1516: sqrtj = PetscSqrtReal(evals[j]);
1517: sqrtM1[i * dim + k] += evecs[j * dim + i] * sqrtj * evecs[j * dim + k];
1518: isqrtM1[i * dim + k] += evecs[j * dim + i] * (1.0 / sqrtj) * evecs[j * dim + k];
1519: }
1520: }
1521: }
1523: /* Map M2 into the space spanned by the eigenvectors of M1 */
1524: for (i = 0; i < dim; ++i) {
1525: for (l = 0; l < dim; ++l) {
1526: evecs[i * dim + l] = 0.0;
1527: for (j = 0; j < dim; ++j) {
1528: for (k = 0; k < dim; ++k) evecs[i * dim + l] += isqrtM1[j * dim + i] * M2[j * dim + k] * isqrtM1[k * dim + l];
1529: }
1530: }
1531: }
1533: /* Compute eigendecomposition */
1534: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
1535: #if defined(PETSC_USE_COMPLEX)
1536: {
1537: PetscReal *rwork;
1538: PetscCall(PetscMalloc1(3 * dim, &rwork));
1539: PetscCallBLAS("LAPACKsyev", LAPACKsyev_("V", "U", &nb, evecs, &nb, evals, work, &lwork, rwork, &lierr));
1540: PetscCall(PetscFree(rwork));
1541: }
1542: #else
1543: PetscCallBLAS("LAPACKsyev", LAPACKsyev_("V", "U", &nb, evecs, &nb, evals, work, &lwork, &lierr));
1544: #endif
1545: if (lierr) {
1546: for (i = 0; i < dim; ++i) {
1547: for (l = 0; l < dim; ++l) {
1548: evecs[i * dim + l] = 0.0;
1549: for (j = 0; j < dim; ++j) {
1550: for (k = 0; k < dim; ++k) evecs[i * dim + l] += isqrtM1[j * dim + i] * M2[j * dim + k] * isqrtM1[k * dim + l];
1551: }
1552: }
1553: }
1554: PetscCall(LAPACKsyevFail(dim, evecs));
1555: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in LAPACK routine %d", (int)lierr);
1556: }
1557: PetscCall(PetscFPTrapPop());
1559: /* Modify eigenvalues */
1560: for (i = 0; i < dim; ++i) evals[i] = PetscMax(evals[i], 1.0);
1562: /* Map back to get the intersection */
1563: for (i = 0; i < dim; ++i) {
1564: for (m = 0; m < dim; ++m) {
1565: M2[i * dim + m] = 0.0;
1566: for (j = 0; j < dim; ++j) {
1567: for (k = 0; k < dim; ++k) {
1568: for (l = 0; l < dim; ++l) M2[i * dim + m] += sqrtM1[j * dim + i] * evecs[j * dim + k] * evals[k] * evecs[l * dim + k] * sqrtM1[l * dim + m];
1569: }
1570: }
1571: }
1572: }
1573: }
1574: PetscCall(PetscFree(work));
1575: }
1576: PetscCall(PetscFree4(evecs, sqrtM1, isqrtM1, evals));
1577: PetscFunctionReturn(PETSC_SUCCESS);
1578: }
1580: /*@
1581: DMPlexMetricIntersection - Compute the intersection of a list of metrics
1583: Input Parameters:
1584: + dm - The `DM`
1585: . numMetrics - The number of metrics to be intersected
1586: - metrics - The metrics to be intersected
1588: Output Parameter:
1589: . metricInt - The intersected metric
1591: Level: beginner
1593: Notes:
1594: The intersection of a list of metrics has the minimal ellipsoid which fits within the ellipsoids of the component metrics.
1596: The implementation used here is only consistent with the minimal ellipsoid definition in the case numMetrics = 2.
1598: .seealso: `DMPLEX`, `DMPlexMetricIntersection2()`, `DMPlexMetricIntersection3()`, `DMPlexMetricAverage()`
1599: @*/
1600: PetscErrorCode DMPlexMetricIntersection(DM dm, PetscInt numMetrics, Vec metrics[], Vec metricInt)
1601: {
1602: PetscBool isotropic, uniform;
1603: PetscInt v, i, m, n;
1604: PetscScalar *met, *meti;
1606: PetscFunctionBegin;
1607: PetscCall(PetscLogEventBegin(DMPLEX_MetricIntersection, 0, 0, 0, 0));
1608: PetscCheck(numMetrics >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot intersect %" PetscInt_FMT " < 1 metrics", numMetrics);
1610: /* Copy over the first metric */
1611: PetscCall(VecCopy(metrics[0], metricInt));
1612: if (numMetrics == 1) PetscFunctionReturn(PETSC_SUCCESS);
1613: PetscCall(VecGetSize(metricInt, &m));
1614: for (i = 0; i < numMetrics; ++i) {
1615: PetscCall(VecGetSize(metrics[i], &n));
1616: PetscCheck(m == n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Intersecting different metric types not implemented");
1617: }
1619: /* Intersect subsequent metrics in turn */
1620: PetscCall(DMPlexMetricIsUniform(dm, &uniform));
1621: PetscCall(DMPlexMetricIsIsotropic(dm, &isotropic));
1622: if (uniform) {
1623: /* Uniform case */
1624: PetscCall(VecGetArray(metricInt, &met));
1625: for (i = 1; i < numMetrics; ++i) {
1626: PetscCall(VecGetArray(metrics[i], &meti));
1627: PetscCall(DMPlexMetricIntersection_Private(1, meti, met));
1628: PetscCall(VecRestoreArray(metrics[i], &meti));
1629: }
1630: PetscCall(VecRestoreArray(metricInt, &met));
1631: } else {
1632: /* Spatially varying case */
1633: PetscInt dim, vStart, vEnd, nrow;
1634: PetscScalar *M, *Mi;
1636: PetscCall(DMGetDimension(dm, &dim));
1637: if (isotropic) nrow = 1;
1638: else nrow = dim;
1639: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
1640: PetscCall(VecGetArray(metricInt, &met));
1641: for (i = 1; i < numMetrics; ++i) {
1642: PetscCall(VecGetArray(metrics[i], &meti));
1643: for (v = vStart; v < vEnd; ++v) {
1644: PetscCall(DMPlexPointLocalRef(dm, v, met, &M));
1645: PetscCall(DMPlexPointLocalRef(dm, v, meti, &Mi));
1646: PetscCall(DMPlexMetricIntersection_Private(nrow, Mi, M));
1647: }
1648: PetscCall(VecRestoreArray(metrics[i], &meti));
1649: }
1650: PetscCall(VecRestoreArray(metricInt, &met));
1651: }
1653: PetscCall(PetscLogEventEnd(DMPLEX_MetricIntersection, 0, 0, 0, 0));
1654: PetscFunctionReturn(PETSC_SUCCESS);
1655: }
1657: /*@
1658: DMPlexMetricIntersection2 - Compute the intersection of two metrics
1660: Input Parameters:
1661: + dm - The `DM`
1662: . metric1 - The first metric to be intersected
1663: - metric2 - The second metric to be intersected
1665: Output Parameter:
1666: . metricInt - The intersected metric
1668: Level: beginner
1670: .seealso: `DMPLEX`, `DMPlexMetricIntersection()`, `DMPlexMetricIntersection3()`
1671: @*/
1672: PetscErrorCode DMPlexMetricIntersection2(DM dm, Vec metric1, Vec metric2, Vec metricInt)
1673: {
1674: Vec metrics[2] = {metric1, metric2};
1676: PetscFunctionBegin;
1677: PetscCall(DMPlexMetricIntersection(dm, 2, metrics, metricInt));
1678: PetscFunctionReturn(PETSC_SUCCESS);
1679: }
1681: /*@
1682: DMPlexMetricIntersection3 - Compute the intersection of three metrics
1684: Input Parameters:
1685: + dm - The `DM`
1686: . metric1 - The first metric to be intersected
1687: . metric2 - The second metric to be intersected
1688: - metric3 - The third metric to be intersected
1690: Output Parameter:
1691: . metricInt - The intersected metric
1693: Level: beginner
1695: .seealso: `DMPLEX`, `DMPlexMetricIntersection()`, `DMPlexMetricIntersection2()`
1696: @*/
1697: PetscErrorCode DMPlexMetricIntersection3(DM dm, Vec metric1, Vec metric2, Vec metric3, Vec metricInt)
1698: {
1699: Vec metrics[3] = {metric1, metric2, metric3};
1701: PetscFunctionBegin;
1702: PetscCall(DMPlexMetricIntersection(dm, 3, metrics, metricInt));
1703: PetscFunctionReturn(PETSC_SUCCESS);
1704: }