Actual source code: dmplexsnes.c

  1: #include <petsc/private/dmpleximpl.h>
2: #include <petsc/private/snesimpl.h>
3: #include <petscds.h>
4: #include <petsc/private/petscimpl.h>
5: #include <petsc/private/petscfeimpl.h>

7: static void pressure_Private(PetscInt dim, PetscInt Nf, PetscInt NfAux,
8:                              const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
9:                              const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
10:                              PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar p[])
11: {
12:   p[0] = u[uOff[1]];
13: }

15: /*
16:   SNESCorrectDiscretePressure_Private - Add a vector in the nullspace to make the continuum integral of the pressure field equal to zero. This is normally used only to evaluate convergence rates for the pressure accurately.

18:   Collective on SNES

20:   Input Parameters:
21: + snes      - The SNES
22: . pfield    - The field number for pressure
23: . nullspace - The pressure nullspace
24: . u         - The solution vector
25: - ctx       - An optional user context

27:   Output Parameter:
28: . u         - The solution with a continuum pressure integral of zero

30:   Notes:
31:   If int(u) = a and int(n) = b, then int(u - a/b n) = a - a/b b = 0. We assume that the nullspace is a single vector given explicitly.

33:   Level: developer

35: .seealso: SNESConvergedCorrectPressure()
36: */
37: static PetscErrorCode SNESCorrectDiscretePressure_Private(SNES snes, PetscInt pfield, MatNullSpace nullspace, Vec u, void *ctx)
38: {
39:   DM             dm;
40:   PetscDS        ds;
41:   const Vec     *nullvecs;
42:   PetscScalar    pintd, *intc, *intn;
43:   MPI_Comm       comm;
44:   PetscInt       Nf, Nv;

48:   PetscObjectGetComm((PetscObject) snes, &comm);
49:   SNESGetDM(snes, &dm);
50:   if (!dm) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Cannot compute test without a SNES DM");
51:   if (!nullspace) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Cannot compute test without a Jacobian nullspace");
52:   DMGetDS(dm, &ds);
53:   PetscDSSetObjective(ds, pfield, pressure_Private);
54:   MatNullSpaceGetVecs(nullspace, NULL, &Nv, &nullvecs);
55:   if (Nv != 1) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Can only handle a single null vector for pressure, not %D", Nv);
56:   VecDot(nullvecs[0], u, &pintd);
57:   if (PetscAbsScalar(pintd) > PETSC_SMALL) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Discrete integral of pressure: %g\n", (double) PetscRealPart(pintd));
58:   PetscDSGetNumFields(ds, &Nf);
59:   PetscMalloc2(Nf, &intc, Nf, &intn);
60:   DMPlexComputeIntegralFEM(dm, nullvecs[0], intn, ctx);
61:   DMPlexComputeIntegralFEM(dm, u, intc, ctx);
62:   VecAXPY(u, -intc[pfield]/intn[pfield], nullvecs[0]);
63: #if defined (PETSC_USE_DEBUG)
64:   DMPlexComputeIntegralFEM(dm, u, intc, ctx);
65:   if (PetscAbsScalar(intc[pfield]) > PETSC_SMALL) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Continuum integral of pressure after correction: %g\n", (double) PetscRealPart(intc[pfield]));
66: #endif
67:   PetscFree2(intc, intn);
68:   return(0);
69: }

71: /*@C
72:    SNESConvergedCorrectPressure - Convergence test that adds a vector in the nullspace to make the continuum integral of the pressure field equal to zero. This is normally used only to evaluate convergence rates for the pressure accurately. The convergence test itself just mimics SNESConvergedDefault().

74:    Logically Collective on SNES

76:    Input Parameters:
77: +  snes - the SNES context
78: .  it - the iteration (0 indicates before any Newton steps)
79: .  xnorm - 2-norm of current iterate
80: .  snorm - 2-norm of current step
81: .  fnorm - 2-norm of function at current iterate
82: -  ctx   - Optional user context

84:    Output Parameter:
85: .  reason  - SNES_CONVERGED_ITERATING, SNES_CONVERGED_ITS, or SNES_DIVERGED_FNORM_NAN

87:    Notes:
88:    In order to use this monitor, you must setup several PETSc structures. First fields must be added to the DM, and a PetscDS must be created with discretizations of those fields. We currently assume that the pressure field has index 1. The pressure field must have a nullspace, likely created using the DMSetNullSpaceConstructor() interface. Last we must be able to integrate the pressure over the domain, so the DM attached to the SNES must be a Plex at this time.

92: .seealso: SNESConvergedDefault(), SNESSetConvergenceTest(), DMSetNullSpaceConstructor()
93: @*/
94: PetscErrorCode SNESConvergedCorrectPressure(SNES snes, PetscInt it, PetscReal xnorm, PetscReal gnorm, PetscReal f, SNESConvergedReason *reason, void *ctx)
95: {
96:   PetscBool      monitorIntegral = PETSC_FALSE;

100:   SNESConvergedDefault(snes, it, xnorm, gnorm, f, reason, ctx);
101:   if (monitorIntegral) {
102:     Mat          J;
103:     Vec          u;
104:     MatNullSpace nullspace;
105:     const Vec   *nullvecs;
106:     PetscScalar  pintd;

108:     SNESGetSolution(snes, &u);
109:     SNESGetJacobian(snes, &J, NULL, NULL, NULL);
110:     MatGetNullSpace(J, &nullspace);
111:     MatNullSpaceGetVecs(nullspace, NULL, NULL, &nullvecs);
112:     VecDot(nullvecs[0], u, &pintd);
113:     PetscInfo1(snes, "SNES: Discrete integral of pressure: %g\n", (double) PetscRealPart(pintd));
114:   }
115:   if (*reason > 0) {
116:     Mat          J;
117:     Vec          u;
118:     MatNullSpace nullspace;
119:     PetscInt     pfield = 1;

121:     SNESGetSolution(snes, &u);
122:     SNESGetJacobian(snes, &J, NULL, NULL, NULL);
123:     MatGetNullSpace(J, &nullspace);
124:     SNESCorrectDiscretePressure_Private(snes, pfield, nullspace, u, ctx);
125:   }
126:   return(0);
127: }

129: /************************** Interpolation *******************************/

131: static PetscErrorCode DMSNESConvertPlex(DM dm, DM *plex, PetscBool copy)
132: {
133:   PetscBool      isPlex;

137:   PetscObjectTypeCompare((PetscObject) dm, DMPLEX, &isPlex);
138:   if (isPlex) {
139:     *plex = dm;
140:     PetscObjectReference((PetscObject) dm);
141:   } else {
142:     PetscObjectQuery((PetscObject) dm, "dm_plex", (PetscObject *) plex);
143:     if (!*plex) {
144:       DMConvert(dm,DMPLEX,plex);
145:       PetscObjectCompose((PetscObject) dm, "dm_plex", (PetscObject) *plex);
146:       if (copy) {
147:         DMCopyDMSNES(dm, *plex);
148:         DMCopyAuxiliaryVec(dm, *plex);
149:       }
150:     } else {
151:       PetscObjectReference((PetscObject) *plex);
152:     }
153:   }
154:   return(0);
155: }

157: /*@C
158:   DMInterpolationCreate - Creates a DMInterpolationInfo context

160:   Collective

162:   Input Parameter:
163: . comm - the communicator

165:   Output Parameter:
166: . ctx - the context

168:   Level: beginner

171: @*/
172: PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx)
173: {

178:   PetscNew(ctx);

180:   (*ctx)->comm   = comm;
181:   (*ctx)->dim    = -1;
182:   (*ctx)->nInput = 0;
183:   (*ctx)->points = NULL;
184:   (*ctx)->cells  = NULL;
185:   (*ctx)->n      = -1;
186:   (*ctx)->coords = NULL;
187:   return(0);
188: }

190: /*@C
191:   DMInterpolationSetDim - Sets the spatial dimension for the interpolation context

193:   Not collective

195:   Input Parameters:
196: + ctx - the context
197: - dim - the spatial dimension

199:   Level: intermediate

202: @*/
203: PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim)
204: {
206:   if ((dim < 1) || (dim > 3)) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %D", dim);
207:   ctx->dim = dim;
208:   return(0);
209: }

211: /*@C
212:   DMInterpolationGetDim - Gets the spatial dimension for the interpolation context

214:   Not collective

216:   Input Parameter:
217: . ctx - the context

219:   Output Parameter:
220: . dim - the spatial dimension

222:   Level: intermediate

225: @*/
226: PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim)
227: {
230:   *dim = ctx->dim;
231:   return(0);
232: }

234: /*@C
235:   DMInterpolationSetDof - Sets the number of fields interpolated at a point for the interpolation context

237:   Not collective

239:   Input Parameters:
240: + ctx - the context
241: - dof - the number of fields

243:   Level: intermediate

246: @*/
247: PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof)
248: {
250:   if (dof < 1) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %D", dof);
251:   ctx->dof = dof;
252:   return(0);
253: }

255: /*@C
256:   DMInterpolationGetDof - Gets the number of fields interpolated at a point for the interpolation context

258:   Not collective

260:   Input Parameter:
261: . ctx - the context

263:   Output Parameter:
264: . dof - the number of fields

266:   Level: intermediate

269: @*/
270: PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof)
271: {
274:   *dof = ctx->dof;
275:   return(0);
276: }

278: /*@C
279:   DMInterpolationAddPoints - Add points at which we will interpolate the fields

281:   Not collective

283:   Input Parameters:
284: + ctx    - the context
285: . n      - the number of points
286: - points - the coordinates for each point, an array of size n * dim

288:   Note: The coordinate information is copied.

290:   Level: intermediate

292: .seealso: DMInterpolationSetDim(), DMInterpolationEvaluate(), DMInterpolationCreate()
293: @*/
294: PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[])
295: {

299:   if (ctx->dim < 0) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
300:   if (ctx->points)  SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "Cannot add points multiple times yet");
301:   ctx->nInput = n;

303:   PetscMalloc1(n*ctx->dim, &ctx->points);
304:   PetscArraycpy(ctx->points, points, n*ctx->dim);
305:   return(0);
306: }

308: /*@C
309:   DMInterpolationSetUp - Compute spatial indices for point location during interpolation

311:   Collective on ctx

313:   Input Parameters:
314: + ctx - the context
315: . dm  - the DM for the function space used for interpolation
316: . redundantPoints - If PETSC_TRUE, all processes are passing in the same array of points. Otherwise, points need to be communicated among processes.
317: - ignoreOutsideDomain - If PETSC_TRUE, ignore points outside the domain, otherwise return an error

319:   Level: intermediate

322: @*/
323: PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints, PetscBool ignoreOutsideDomain)
324: {
325:   MPI_Comm          comm = ctx->comm;
326:   PetscScalar       *a;
327:   PetscInt          p, q, i;
328:   PetscMPIInt       rank, size;
329:   PetscErrorCode    ierr;
330:   Vec               pointVec;
331:   PetscSF           cellSF;
332:   PetscLayout       layout;
333:   PetscReal         *globalPoints;
334:   PetscScalar       *globalPointsScalar;
335:   const PetscInt    *ranges;
336:   PetscMPIInt       *counts, *displs;
337:   const PetscSFNode *foundCells;
338:   const PetscInt    *foundPoints;
339:   PetscMPIInt       *foundProcs, *globalProcs;
340:   PetscInt          n, N, numFound;

344:   MPI_Comm_size(comm, &size);
345:   MPI_Comm_rank(comm, &rank);
346:   if (ctx->dim < 0) SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
347:   /* Locate points */
348:   n = ctx->nInput;
349:   if (!redundantPoints) {
350:     PetscLayoutCreate(comm, &layout);
351:     PetscLayoutSetBlockSize(layout, 1);
352:     PetscLayoutSetLocalSize(layout, n);
353:     PetscLayoutSetUp(layout);
354:     PetscLayoutGetSize(layout, &N);
355:     /* Communicate all points to all processes */
356:     PetscMalloc3(N*ctx->dim,&globalPoints,size,&counts,size,&displs);
357:     PetscLayoutGetRanges(layout, &ranges);
358:     for (p = 0; p < size; ++p) {
359:       counts[p] = (ranges[p+1] - ranges[p])*ctx->dim;
360:       displs[p] = ranges[p]*ctx->dim;
361:     }
362:     MPI_Allgatherv(ctx->points, n*ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm);
363:   } else {
364:     N = n;
365:     globalPoints = ctx->points;
366:     counts = displs = NULL;
367:     layout = NULL;
368:   }
369: #if 0
370:   PetscMalloc3(N,&foundCells,N,&foundProcs,N,&globalProcs);
371:   /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */
372: #else
373: #if defined(PETSC_USE_COMPLEX)
374:   PetscMalloc1(N*ctx->dim,&globalPointsScalar);
375:   for (i=0; i<N*ctx->dim; i++) globalPointsScalar[i] = globalPoints[i];
376: #else
377:   globalPointsScalar = globalPoints;
378: #endif
379:   VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N*ctx->dim, globalPointsScalar, &pointVec);
380:   PetscMalloc2(N,&foundProcs,N,&globalProcs);
381:   for (p = 0; p < N; ++p) {foundProcs[p] = size;}
382:   cellSF = NULL;
383:   DMLocatePoints(dm, pointVec, DM_POINTLOCATION_REMOVE, &cellSF);
384:   PetscSFGetGraph(cellSF,NULL,&numFound,&foundPoints,&foundCells);
385: #endif
386:   for (p = 0; p < numFound; ++p) {
387:     if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank;
388:   }
389:   /* Let the lowest rank process own each point */
390:   MPIU_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm);
391:   ctx->n = 0;
392:   for (p = 0; p < N; ++p) {
393:     if (globalProcs[p] == size) {
394:       if (!ignoreOutsideDomain) SETERRQ4(comm, PETSC_ERR_PLIB, "Point %d: %g %g %g not located in mesh", p, (double)globalPoints[p*ctx->dim+0], (double)(ctx->dim > 1 ? globalPoints[p*ctx->dim+1] : 0.0), (double)(ctx->dim > 2 ? globalPoints[p*ctx->dim+2] : 0.0));
395:       else if (!rank) ++ctx->n;
396:     } else if (globalProcs[p] == rank) ++ctx->n;
397:   }
398:   /* Create coordinates vector and array of owned cells */
399:   PetscMalloc1(ctx->n, &ctx->cells);
400:   VecCreate(comm, &ctx->coords);
401:   VecSetSizes(ctx->coords, ctx->n*ctx->dim, PETSC_DECIDE);
402:   VecSetBlockSize(ctx->coords, ctx->dim);
403:   VecSetType(ctx->coords,VECSTANDARD);
404:   VecGetArray(ctx->coords, &a);
405:   for (p = 0, q = 0, i = 0; p < N; ++p) {
406:     if (globalProcs[p] == rank) {
407:       PetscInt d;

409:       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p*ctx->dim+d];
410:       ctx->cells[q] = foundCells[q].index;
411:       ++q;
412:     }
413:     if (globalProcs[p] == size && !rank) {
414:       PetscInt d;

416:       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = 0.;
417:       ctx->cells[q] = -1;
418:       ++q;
419:     }
420:   }
421:   VecRestoreArray(ctx->coords, &a);
422: #if 0
423:   PetscFree3(foundCells,foundProcs,globalProcs);
424: #else
425:   PetscFree2(foundProcs,globalProcs);
426:   PetscSFDestroy(&cellSF);
427:   VecDestroy(&pointVec);
428: #endif
429:   if ((void*)globalPointsScalar != (void*)globalPoints) {PetscFree(globalPointsScalar);}
430:   if (!redundantPoints) {PetscFree3(globalPoints,counts,displs);}
431:   PetscLayoutDestroy(&layout);
432:   return(0);
433: }

435: /*@C
436:   DMInterpolationGetCoordinates - Gets a Vec with the coordinates of each interpolation point

438:   Collective on ctx

440:   Input Parameter:
441: . ctx - the context

443:   Output Parameter:
444: . coordinates  - the coordinates of interpolation points

446:   Note: The local vector entries correspond to interpolation points lying on this process, according to the associated DM. This is a borrowed vector that the user should not destroy.

448:   Level: intermediate

451: @*/
452: PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates)
453: {
456:   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
457:   *coordinates = ctx->coords;
458:   return(0);
459: }

461: /*@C
462:   DMInterpolationGetVector - Gets a Vec which can hold all the interpolated field values

464:   Collective on ctx

466:   Input Parameter:
467: . ctx - the context

469:   Output Parameter:
470: . v  - a vector capable of holding the interpolated field values

472:   Note: This vector should be returned using DMInterpolationRestoreVector().

474:   Level: intermediate

476: .seealso: DMInterpolationRestoreVector(), DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
477: @*/
478: PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v)
479: {

484:   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
485:   VecCreate(ctx->comm, v);
486:   VecSetSizes(*v, ctx->n*ctx->dof, PETSC_DECIDE);
487:   VecSetBlockSize(*v, ctx->dof);
488:   VecSetType(*v,VECSTANDARD);
489:   return(0);
490: }

492: /*@C
493:   DMInterpolationRestoreVector - Returns a Vec which can hold all the interpolated field values

495:   Collective on ctx

497:   Input Parameters:
498: + ctx - the context
499: - v  - a vector capable of holding the interpolated field values

501:   Level: intermediate

503: .seealso: DMInterpolationGetVector(), DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
504: @*/
505: PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v)
506: {

511:   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
512:   VecDestroy(v);
513:   return(0);
514: }

516: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Triangle_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
517: {
518:   PetscReal      *v0, *J, *invJ, detJ;
519:   const PetscScalar *coords;
520:   PetscScalar    *a;
521:   PetscInt       p;

525:   PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);
527:   VecGetArray(v, &a);
528:   for (p = 0; p < ctx->n; ++p) {
529:     PetscInt     c = ctx->cells[p];
530:     PetscScalar *x = NULL;
531:     PetscReal    xi[4];
532:     PetscInt     d, f, comp;

534:     DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
535:     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D", (double)detJ, c);
536:     DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);
537:     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];

539:     for (d = 0; d < ctx->dim; ++d) {
540:       xi[d] = 0.0;
541:       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
542:       for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] += PetscRealPart(x[(d+1)*ctx->dof+comp] - x[0*ctx->dof+comp])*xi[d];
543:     }
544:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);
545:   }
546:   VecRestoreArray(v, &a);
548:   PetscFree3(v0, J, invJ);
549:   return(0);
550: }

552: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Tetrahedron_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
553: {
554:   PetscReal      *v0, *J, *invJ, detJ;
555:   const PetscScalar *coords;
556:   PetscScalar    *a;
557:   PetscInt       p;

561:   PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);
563:   VecGetArray(v, &a);
564:   for (p = 0; p < ctx->n; ++p) {
565:     PetscInt       c = ctx->cells[p];
566:     const PetscInt order[3] = {2, 1, 3};
567:     PetscScalar   *x = NULL;
568:     PetscReal      xi[4];
569:     PetscInt       d, f, comp;

571:     DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
572:     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D", (double)detJ, c);
573:     DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);
574:     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];

576:     for (d = 0; d < ctx->dim; ++d) {
577:       xi[d] = 0.0;
578:       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
579:       for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] += PetscRealPart(x[order[d]*ctx->dof+comp] - x[0*ctx->dof+comp])*xi[d];
580:     }
581:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);
582:   }
583:   VecRestoreArray(v, &a);
585:   PetscFree3(v0, J, invJ);
586:   return(0);
587: }

589: PETSC_STATIC_INLINE PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
590: {
591:   const PetscScalar *vertices = (const PetscScalar*) ctx;
592:   const PetscScalar x0        = vertices[0];
593:   const PetscScalar y0        = vertices[1];
594:   const PetscScalar x1        = vertices[2];
595:   const PetscScalar y1        = vertices[3];
596:   const PetscScalar x2        = vertices[4];
597:   const PetscScalar y2        = vertices[5];
598:   const PetscScalar x3        = vertices[6];
599:   const PetscScalar y3        = vertices[7];
600:   const PetscScalar f_1       = x1 - x0;
601:   const PetscScalar g_1       = y1 - y0;
602:   const PetscScalar f_3       = x3 - x0;
603:   const PetscScalar g_3       = y3 - y0;
604:   const PetscScalar f_01      = x2 - x1 - x3 + x0;
605:   const PetscScalar g_01      = y2 - y1 - y3 + y0;
606:   const PetscScalar *ref;
607:   PetscScalar       *real;
608:   PetscErrorCode    ierr;

612:   VecGetArray(Xreal, &real);
613:   {
614:     const PetscScalar p0 = ref[0];
615:     const PetscScalar p1 = ref[1];

617:     real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1;
618:     real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1;
619:   }
620:   PetscLogFlops(28);
622:   VecRestoreArray(Xreal, &real);
623:   return(0);
624: }

626: #include <petsc/private/dmimpl.h>
627: PETSC_STATIC_INLINE PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
628: {
629:   const PetscScalar *vertices = (const PetscScalar*) ctx;
630:   const PetscScalar x0        = vertices[0];
631:   const PetscScalar y0        = vertices[1];
632:   const PetscScalar x1        = vertices[2];
633:   const PetscScalar y1        = vertices[3];
634:   const PetscScalar x2        = vertices[4];
635:   const PetscScalar y2        = vertices[5];
636:   const PetscScalar x3        = vertices[6];
637:   const PetscScalar y3        = vertices[7];
638:   const PetscScalar f_01      = x2 - x1 - x3 + x0;
639:   const PetscScalar g_01      = y2 - y1 - y3 + y0;
640:   const PetscScalar *ref;
641:   PetscErrorCode    ierr;

645:   {
646:     const PetscScalar x       = ref[0];
647:     const PetscScalar y       = ref[1];
648:     const PetscInt    rows[2] = {0, 1};
649:     PetscScalar       values[4];

651:     values[0] = (x1 - x0 + f_01*y) * 0.5; values[1] = (x3 - x0 + f_01*x) * 0.5;
652:     values[2] = (y1 - y0 + g_01*y) * 0.5; values[3] = (y3 - y0 + g_01*x) * 0.5;
653:     MatSetValues(J, 2, rows, 2, rows, values, INSERT_VALUES);
654:   }
655:   PetscLogFlops(30);
657:   MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);
658:   MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);
659:   return(0);
660: }

662: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
663: {
664:   DM             dmCoord;
665:   PetscFE        fem = NULL;
666:   SNES           snes;
667:   KSP            ksp;
668:   PC             pc;
669:   Vec            coordsLocal, r, ref, real;
670:   Mat            J;
671:   PetscTabulation    T;
672:   const PetscScalar *coords;
673:   PetscScalar    *a;
674:   PetscReal      xir[2];
675:   PetscInt       Nf, p;
676:   const PetscInt dof = ctx->dof;

680:   DMGetNumFields(dm, &Nf);
681:   if (Nf) {DMGetField(dm, 0, NULL, (PetscObject *) &fem);}
682:   DMGetCoordinatesLocal(dm, &coordsLocal);
683:   DMGetCoordinateDM(dm, &dmCoord);
684:   SNESCreate(PETSC_COMM_SELF, &snes);
686:   VecCreate(PETSC_COMM_SELF, &r);
687:   VecSetSizes(r, 2, 2);
688:   VecSetType(r,dm->vectype);
689:   VecDuplicate(r, &ref);
690:   VecDuplicate(r, &real);
691:   MatCreate(PETSC_COMM_SELF, &J);
692:   MatSetSizes(J, 2, 2, 2, 2);
693:   MatSetType(J, MATSEQDENSE);
694:   MatSetUp(J);
696:   SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);
697:   SNESGetKSP(snes, &ksp);
698:   KSPGetPC(ksp, &pc);
699:   PCSetType(pc, PCLU);
700:   SNESSetFromOptions(snes);

703:   VecGetArray(v, &a);
704:   PetscFECreateTabulation(fem, 1, 1, xir, 0, &T);
705:   for (p = 0; p < ctx->n; ++p) {
706:     PetscScalar *x = NULL, *vertices = NULL;
707:     PetscScalar *xi;
708:     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;

710:     /* Can make this do all points at once */
711:     DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
712:     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %D should be %d", coordSize, 4*2);
713:     DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);
714:     SNESSetFunction(snes, NULL, NULL, (void*) vertices);
715:     SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);
716:     VecGetArray(real, &xi);
717:     xi[0]  = coords[p*ctx->dim+0];
718:     xi[1]  = coords[p*ctx->dim+1];
719:     VecRestoreArray(real, &xi);
720:     SNESSolve(snes, real, ref);
721:     VecGetArray(ref, &xi);
722:     xir[0] = PetscRealPart(xi[0]);
723:     xir[1] = PetscRealPart(xi[1]);
724:     if (4*dof != xSize) {
725:       PetscInt d;

727:       xir[0] = 2.0*xir[0] - 1.0; xir[1] = 2.0*xir[1] - 1.0;
728:       PetscFEComputeTabulation(fem, 1, xir, 0, T);
729:       for (comp = 0; comp < dof; ++comp) {
730:         a[p*dof+comp] = 0.0;
731:         for (d = 0; d < xSize/dof; ++d) {
732:           a[p*dof+comp] += x[d*dof+comp]*T->T[0][d*dof+comp];
733:         }
734:       }
735:     } else {
736:       for (comp = 0; comp < dof; ++comp)
737:         a[p*dof+comp] = x[0*dof+comp]*(1 - xir[0])*(1 - xir[1]) + x[1*dof+comp]*xir[0]*(1 - xir[1]) + x[2*dof+comp]*xir[0]*xir[1] + x[3*dof+comp]*(1 - xir[0])*xir[1];
738:     }
739:     VecRestoreArray(ref, &xi);
740:     DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
741:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);
742:   }
743:   PetscTabulationDestroy(&T);
744:   VecRestoreArray(v, &a);

747:   SNESDestroy(&snes);
748:   VecDestroy(&r);
749:   VecDestroy(&ref);
750:   VecDestroy(&real);
751:   MatDestroy(&J);
752:   return(0);
753: }

755: PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
756: {
757:   const PetscScalar *vertices = (const PetscScalar*) ctx;
758:   const PetscScalar x0        = vertices[0];
759:   const PetscScalar y0        = vertices[1];
760:   const PetscScalar z0        = vertices[2];
761:   const PetscScalar x1        = vertices[9];
762:   const PetscScalar y1        = vertices[10];
763:   const PetscScalar z1        = vertices[11];
764:   const PetscScalar x2        = vertices[6];
765:   const PetscScalar y2        = vertices[7];
766:   const PetscScalar z2        = vertices[8];
767:   const PetscScalar x3        = vertices[3];
768:   const PetscScalar y3        = vertices[4];
769:   const PetscScalar z3        = vertices[5];
770:   const PetscScalar x4        = vertices[12];
771:   const PetscScalar y4        = vertices[13];
772:   const PetscScalar z4        = vertices[14];
773:   const PetscScalar x5        = vertices[15];
774:   const PetscScalar y5        = vertices[16];
775:   const PetscScalar z5        = vertices[17];
776:   const PetscScalar x6        = vertices[18];
777:   const PetscScalar y6        = vertices[19];
778:   const PetscScalar z6        = vertices[20];
779:   const PetscScalar x7        = vertices[21];
780:   const PetscScalar y7        = vertices[22];
781:   const PetscScalar z7        = vertices[23];
782:   const PetscScalar f_1       = x1 - x0;
783:   const PetscScalar g_1       = y1 - y0;
784:   const PetscScalar h_1       = z1 - z0;
785:   const PetscScalar f_3       = x3 - x0;
786:   const PetscScalar g_3       = y3 - y0;
787:   const PetscScalar h_3       = z3 - z0;
788:   const PetscScalar f_4       = x4 - x0;
789:   const PetscScalar g_4       = y4 - y0;
790:   const PetscScalar h_4       = z4 - z0;
791:   const PetscScalar f_01      = x2 - x1 - x3 + x0;
792:   const PetscScalar g_01      = y2 - y1 - y3 + y0;
793:   const PetscScalar h_01      = z2 - z1 - z3 + z0;
794:   const PetscScalar f_12      = x7 - x3 - x4 + x0;
795:   const PetscScalar g_12      = y7 - y3 - y4 + y0;
796:   const PetscScalar h_12      = z7 - z3 - z4 + z0;
797:   const PetscScalar f_02      = x5 - x1 - x4 + x0;
798:   const PetscScalar g_02      = y5 - y1 - y4 + y0;
799:   const PetscScalar h_02      = z5 - z1 - z4 + z0;
800:   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
801:   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
802:   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
803:   const PetscScalar *ref;
804:   PetscScalar       *real;
805:   PetscErrorCode    ierr;

809:   VecGetArray(Xreal, &real);
810:   {
811:     const PetscScalar p0 = ref[0];
812:     const PetscScalar p1 = ref[1];
813:     const PetscScalar p2 = ref[2];

815:     real[0] = x0 + f_1*p0 + f_3*p1 + f_4*p2 + f_01*p0*p1 + f_12*p1*p2 + f_02*p0*p2 + f_012*p0*p1*p2;
816:     real[1] = y0 + g_1*p0 + g_3*p1 + g_4*p2 + g_01*p0*p1 + g_01*p0*p1 + g_12*p1*p2 + g_02*p0*p2 + g_012*p0*p1*p2;
817:     real[2] = z0 + h_1*p0 + h_3*p1 + h_4*p2 + h_01*p0*p1 + h_01*p0*p1 + h_12*p1*p2 + h_02*p0*p2 + h_012*p0*p1*p2;
818:   }
819:   PetscLogFlops(114);
821:   VecRestoreArray(Xreal, &real);
822:   return(0);
823: }

825: PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
826: {
827:   const PetscScalar *vertices = (const PetscScalar*) ctx;
828:   const PetscScalar x0        = vertices[0];
829:   const PetscScalar y0        = vertices[1];
830:   const PetscScalar z0        = vertices[2];
831:   const PetscScalar x1        = vertices[9];
832:   const PetscScalar y1        = vertices[10];
833:   const PetscScalar z1        = vertices[11];
834:   const PetscScalar x2        = vertices[6];
835:   const PetscScalar y2        = vertices[7];
836:   const PetscScalar z2        = vertices[8];
837:   const PetscScalar x3        = vertices[3];
838:   const PetscScalar y3        = vertices[4];
839:   const PetscScalar z3        = vertices[5];
840:   const PetscScalar x4        = vertices[12];
841:   const PetscScalar y4        = vertices[13];
842:   const PetscScalar z4        = vertices[14];
843:   const PetscScalar x5        = vertices[15];
844:   const PetscScalar y5        = vertices[16];
845:   const PetscScalar z5        = vertices[17];
846:   const PetscScalar x6        = vertices[18];
847:   const PetscScalar y6        = vertices[19];
848:   const PetscScalar z6        = vertices[20];
849:   const PetscScalar x7        = vertices[21];
850:   const PetscScalar y7        = vertices[22];
851:   const PetscScalar z7        = vertices[23];
852:   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
853:   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
854:   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
855:   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
856:   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
857:   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
858:   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
859:   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
860:   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
861:   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
862:   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
863:   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
864:   const PetscScalar *ref;
865:   PetscErrorCode    ierr;

869:   {
870:     const PetscScalar x       = ref[0];
871:     const PetscScalar y       = ref[1];
872:     const PetscScalar z       = ref[2];
873:     const PetscInt    rows[3] = {0, 1, 2};
874:     PetscScalar       values[9];

876:     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
877:     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
878:     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
879:     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
880:     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
881:     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
882:     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
883:     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
884:     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;

886:     MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);
887:   }
888:   PetscLogFlops(152);
890:   MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);
891:   MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);
892:   return(0);
893: }

895: PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
896: {
897:   DM             dmCoord;
898:   SNES           snes;
899:   KSP            ksp;
900:   PC             pc;
901:   Vec            coordsLocal, r, ref, real;
902:   Mat            J;
903:   const PetscScalar *coords;
904:   PetscScalar    *a;
905:   PetscInt       p;

909:   DMGetCoordinatesLocal(dm, &coordsLocal);
910:   DMGetCoordinateDM(dm, &dmCoord);
911:   SNESCreate(PETSC_COMM_SELF, &snes);
912:   SNESSetOptionsPrefix(snes, "hex_interp_");
913:   VecCreate(PETSC_COMM_SELF, &r);
914:   VecSetSizes(r, 3, 3);
915:   VecSetType(r,dm->vectype);
916:   VecDuplicate(r, &ref);
917:   VecDuplicate(r, &real);
918:   MatCreate(PETSC_COMM_SELF, &J);
919:   MatSetSizes(J, 3, 3, 3, 3);
920:   MatSetType(J, MATSEQDENSE);
921:   MatSetUp(J);
922:   SNESSetFunction(snes, r, HexMap_Private, NULL);
923:   SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);
924:   SNESGetKSP(snes, &ksp);
925:   KSPGetPC(ksp, &pc);
926:   PCSetType(pc, PCLU);
927:   SNESSetFromOptions(snes);

930:   VecGetArray(v, &a);
931:   for (p = 0; p < ctx->n; ++p) {
932:     PetscScalar *x = NULL, *vertices = NULL;
933:     PetscScalar *xi;
934:     PetscReal    xir[3];
935:     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;

937:     /* Can make this do all points at once */
938:     DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
939:     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %D should be %d", coordSize, 8*3);
940:     DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);
941:     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %D should be %D", xSize, 8*ctx->dof);
942:     SNESSetFunction(snes, NULL, NULL, (void*) vertices);
943:     SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);
944:     VecGetArray(real, &xi);
945:     xi[0]  = coords[p*ctx->dim+0];
946:     xi[1]  = coords[p*ctx->dim+1];
947:     xi[2]  = coords[p*ctx->dim+2];
948:     VecRestoreArray(real, &xi);
949:     SNESSolve(snes, real, ref);
950:     VecGetArray(ref, &xi);
951:     xir[0] = PetscRealPart(xi[0]);
952:     xir[1] = PetscRealPart(xi[1]);
953:     xir[2] = PetscRealPart(xi[2]);
954:     for (comp = 0; comp < ctx->dof; ++comp) {
955:       a[p*ctx->dof+comp] =
956:         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
957:         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
958:         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
959:         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
960:         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
961:         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
962:         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
963:         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
964:     }
965:     VecRestoreArray(ref, &xi);
966:     DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);
967:     DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);
968:   }
969:   VecRestoreArray(v, &a);

972:   SNESDestroy(&snes);
973:   VecDestroy(&r);
974:   VecDestroy(&ref);
975:   VecDestroy(&real);
976:   MatDestroy(&J);
977:   return(0);
978: }

980: /*@C
981:   DMInterpolationEvaluate - Using the input from dm and x, calculates interpolated field values at the interpolation points.

983:   Input Parameters:
984: + ctx - The DMInterpolationInfo context
985: . dm  - The DM
986: - x   - The local vector containing the field to be interpolated

988:   Output Parameters:
989: . v   - The vector containing the interpolated values

991:   Note: A suitable v can be obtained using DMInterpolationGetVector().

993:   Level: beginner

996: @*/
997: PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
998: {
999:   PetscDS        ds;
1000:   PetscInt       n, p, Nf, field;
1001:   PetscBool      useDS = PETSC_FALSE;

1008:   VecGetLocalSize(v, &n);
1009:   if (n != ctx->n*ctx->dof) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid input vector size %D should be %D", n, ctx->n*ctx->dof);
1010:   if (!n) return(0);
1011:   DMGetDS(dm, &ds);
1012:   if (ds) {
1013:     useDS = PETSC_TRUE;
1014:     PetscDSGetNumFields(ds, &Nf);
1015:     for (field = 0; field < Nf; ++field) {
1016:       PetscObject  obj;
1017:       PetscClassId id;

1019:       PetscDSGetDiscretization(ds, field, &obj);
1020:       PetscObjectGetClassId(obj, &id);
1021:       if (id != PETSCFE_CLASSID) {useDS = PETSC_FALSE; break;}
1022:     }
1023:   }
1024:   if (useDS) {
1025:     const PetscScalar *coords;
1026:     PetscScalar       *interpolant;
1027:     PetscInt           cdim, d;

1029:     DMGetCoordinateDim(dm, &cdim);
1031:     VecGetArrayWrite(v, &interpolant);
1032:     for (p = 0; p < ctx->n; ++p) {
1033:       PetscReal    pcoords[3], xi[3];
1034:       PetscScalar *xa   = NULL;
1035:       PetscInt     coff = 0, foff = 0, clSize;

1037:       if (ctx->cells[p] < 0) continue;
1038:       for (d = 0; d < cdim; ++d) pcoords[d] = PetscRealPart(coords[p*cdim+d]);
1039:       DMPlexCoordinatesToReference(dm, ctx->cells[p], 1, pcoords, xi);
1040:       DMPlexVecGetClosure(dm, NULL, x, ctx->cells[p], &clSize, &xa);
1041:       for (field = 0; field < Nf; ++field) {
1042:         PetscTabulation T;
1043:         PetscFE         fe;

1045:         PetscDSGetDiscretization(ds, field, (PetscObject *) &fe);
1046:         PetscFECreateTabulation(fe, 1, 1, xi, 0, &T);
1047:         {
1048:           const PetscReal *basis = T->T[0];
1049:           const PetscInt   Nb    = T->Nb;
1050:           const PetscInt   Nc    = T->Nc;
1051:           PetscInt         f, fc;

1053:           for (fc = 0; fc < Nc; ++fc) {
1054:             interpolant[p*ctx->dof+coff+fc] = 0.0;
1055:             for (f = 0; f < Nb; ++f) {
1056:               interpolant[p*ctx->dof+coff+fc] += xa[foff+f]*basis[(0*Nb + f)*Nc + fc];
1057:             }
1058:           }
1059:           coff += Nc;
1060:           foff += Nb;
1061:         }
1062:         PetscTabulationDestroy(&T);
1063:       }
1064:       DMPlexVecRestoreClosure(dm, NULL, x, ctx->cells[p], &clSize, &xa);
1065:       if (coff != ctx->dof) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Total components %D != %D dof specified for interpolation", coff, ctx->dof);
1066:       if (foff != clSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Total FE space size %D != %D closure size", foff, clSize);
1067:     }
1069:     VecRestoreArrayWrite(v, &interpolant);
1070:   } else {
1071:     DMPolytopeType ct;

1073:     /* TODO Check each cell individually */
1074:     DMPlexGetCellType(dm, ctx->cells[0], &ct);
1075:     switch (ct) {
1076:       case DM_POLYTOPE_TRIANGLE:      DMInterpolate_Triangle_Private(ctx, dm, x, v);break;
1078:       case DM_POLYTOPE_TETRAHEDRON:   DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);break;
1079:       case DM_POLYTOPE_HEXAHEDRON:    DMInterpolate_Hex_Private(ctx, dm, x, v);break;
1080:       default: SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for cell type %s", DMPolytopeTypes[ct]);
1081:     }
1082:   }
1083:   return(0);
1084: }

1086: /*@C
1087:   DMInterpolationDestroy - Destroys a DMInterpolationInfo context

1089:   Collective on ctx

1091:   Input Parameter:
1092: . ctx - the context

1094:   Level: beginner

1097: @*/
1098: PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
1099: {

1104:   VecDestroy(&(*ctx)->coords);
1105:   PetscFree((*ctx)->points);
1106:   PetscFree((*ctx)->cells);
1107:   PetscFree(*ctx);
1108:   *ctx = NULL;
1109:   return(0);
1110: }

1112: /*@C
1113:   SNESMonitorFields - Monitors the residual for each field separately

1115:   Collective on SNES

1117:   Input Parameters:
1118: + snes   - the SNES context
1119: . its    - iteration number
1120: . fgnorm - 2-norm of residual
1121: - vf  - PetscViewerAndFormat of type ASCII

1123:   Notes:
1124:   This routine prints the residual norm at each iteration.

1126:   Level: intermediate

1128: .seealso: SNESMonitorSet(), SNESMonitorDefault()
1129: @*/
1130: PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
1131: {
1132:   PetscViewer        viewer = vf->viewer;
1133:   Vec                res;
1134:   DM                 dm;
1135:   PetscSection       s;
1136:   const PetscScalar *r;
1137:   PetscReal         *lnorms, *norms;
1138:   PetscInt           numFields, f, pStart, pEnd, p;
1139:   PetscErrorCode     ierr;

1143:   SNESGetFunction(snes, &res, NULL, NULL);
1144:   SNESGetDM(snes, &dm);
1145:   DMGetLocalSection(dm, &s);
1146:   PetscSectionGetNumFields(s, &numFields);
1147:   PetscSectionGetChart(s, &pStart, &pEnd);
1148:   PetscCalloc2(numFields, &lnorms, numFields, &norms);
1150:   for (p = pStart; p < pEnd; ++p) {
1151:     for (f = 0; f < numFields; ++f) {
1152:       PetscInt fdof, foff, d;

1154:       PetscSectionGetFieldDof(s, p, f, &fdof);
1155:       PetscSectionGetFieldOffset(s, p, f, &foff);
1156:       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
1157:     }
1158:   }
1160:   MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));
1161:   PetscViewerPushFormat(viewer,vf->format);
1163:   PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);
1164:   for (f = 0; f < numFields; ++f) {
1165:     if (f > 0) {PetscViewerASCIIPrintf(viewer, ", ");}
1166:     PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));
1167:   }
1168:   PetscViewerASCIIPrintf(viewer, "]\n");
1169:   PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);
1170:   PetscViewerPopFormat(viewer);
1171:   PetscFree2(lnorms, norms);
1172:   return(0);
1173: }

1175: /********************* Residual Computation **************************/

1177: PetscErrorCode DMPlexGetAllCells_Internal(DM plex, IS *cellIS)
1178: {
1179:   PetscInt       depth;

1183:   DMPlexGetDepth(plex, &depth);
1184:   DMGetStratumIS(plex, "dim", depth, cellIS);
1185:   if (!*cellIS) {DMGetStratumIS(plex, "depth", depth, cellIS);}
1186:   return(0);
1187: }

1189: /*@
1190:   DMPlexSNESComputeResidualFEM - Sums the local residual into vector F from the local input X using pointwise functions specified by the user

1192:   Input Parameters:
1193: + dm - The mesh
1194: . X  - Local solution
1195: - user - The user context

1197:   Output Parameter:
1198: . F  - Local output vector

1200:   Notes:
1201:   The residual is summed into F; the caller is responsible for using VecZeroEntries() or otherwise ensuring that any data in F is intentional.

1203:   Level: developer

1205: .seealso: DMPlexComputeJacobianAction()
1206: @*/
1207: PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
1208: {
1209:   DM             plex;
1210:   IS             allcellIS;
1211:   PetscInt       Nds, s;

1215:   DMSNESConvertPlex(dm, &plex, PETSC_TRUE);
1216:   DMPlexGetAllCells_Internal(plex, &allcellIS);
1217:   DMGetNumDS(dm, &Nds);
1218:   for (s = 0; s < Nds; ++s) {
1219:     PetscDS          ds;
1220:     IS               cellIS;
1221:     PetscFormKey key;

1223:     DMGetRegionNumDS(dm, s, &key.label, NULL, &ds);
1224:     key.value = 0;
1225:     key.field = 0;
1226:     key.part  = 0;
1227:     if (!key.label) {
1228:       PetscObjectReference((PetscObject) allcellIS);
1229:       cellIS = allcellIS;
1230:     } else {
1231:       IS pointIS;

1233:       key.value = 1;
1234:       DMLabelGetStratumIS(key.label, key.value, &pointIS);
1235:       ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS);
1236:       ISDestroy(&pointIS);
1237:     }
1238:     DMPlexComputeResidual_Internal(plex, key, cellIS, PETSC_MIN_REAL, X, NULL, 0.0, F, user);
1239:     ISDestroy(&cellIS);
1240:   }
1241:   ISDestroy(&allcellIS);
1242:   DMDestroy(&plex);
1243:   return(0);
1244: }

1246: PetscErrorCode DMSNESComputeResidual(DM dm, Vec X, Vec F, void *user)
1247: {
1248:   DM             plex;
1249:   IS             allcellIS;
1250:   PetscInt       Nds, s;

1254:   DMSNESConvertPlex(dm, &plex, PETSC_TRUE);
1255:   DMPlexGetAllCells_Internal(plex, &allcellIS);
1256:   DMGetNumDS(dm, &Nds);
1257:   for (s = 0; s < Nds; ++s) {
1258:     PetscDS ds;
1259:     DMLabel label;
1260:     IS      cellIS;

1262:     DMGetRegionNumDS(dm, s, &label, NULL, &ds);
1263:     {
1264:       PetscWeakFormKind resmap[2] = {PETSC_WF_F0, PETSC_WF_F1};
1265:       PetscWeakForm     wf;
1266:       PetscInt          Nm = 2, m, Nk = 0, k, kp, off = 0;
1267:       PetscFormKey *reskeys;

1269:       /* Get unique residual keys */
1270:       for (m = 0; m < Nm; ++m) {
1271:         PetscInt Nkm;
1272:         PetscHMapFormGetSize(ds->wf->form[resmap[m]], &Nkm);
1273:         Nk  += Nkm;
1274:       }
1275:       PetscMalloc1(Nk, &reskeys);
1276:       for (m = 0; m < Nm; ++m) {
1277:         PetscHMapFormGetKeys(ds->wf->form[resmap[m]], &off, reskeys);
1278:       }
1279:       if (off != Nk) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of keys %D should be %D", off, Nk);
1280:       PetscFormKeySort(Nk, reskeys);
1281:       for (k = 0, kp = 1; kp < Nk; ++kp) {
1282:         if ((reskeys[k].label != reskeys[kp].label) || (reskeys[k].value != reskeys[kp].value)) {
1283:           ++k;
1284:           if (kp != k) reskeys[k] = reskeys[kp];
1285:         }
1286:       }
1287:       Nk = k;

1289:       PetscDSGetWeakForm(ds, &wf);
1290:       for (k = 0; k < Nk; ++k) {
1291:         DMLabel  label = reskeys[k].label;
1292:         PetscInt val   = reskeys[k].value;

1294:         if (!label) {
1295:           PetscObjectReference((PetscObject) allcellIS);
1296:           cellIS = allcellIS;
1297:         } else {
1298:           IS pointIS;

1300:           DMLabelGetStratumIS(label, val, &pointIS);
1301:           ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS);
1302:           ISDestroy(&pointIS);
1303:         }
1304:         DMPlexComputeResidual_Internal(plex, reskeys[k], cellIS, PETSC_MIN_REAL, X, NULL, 0.0, F, user);
1305:         ISDestroy(&cellIS);
1306:       }
1307:       PetscFree(reskeys);
1308:     }
1309:   }
1310:   ISDestroy(&allcellIS);
1311:   DMDestroy(&plex);
1312:   return(0);
1313: }

1315: /*@
1316:   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X

1318:   Input Parameters:
1319: + dm - The mesh
1320: - user - The user context

1322:   Output Parameter:
1323: . X  - Local solution

1325:   Level: developer

1327: .seealso: DMPlexComputeJacobianAction()
1328: @*/
1329: PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
1330: {
1331:   DM             plex;

1335:   DMSNESConvertPlex(dm,&plex,PETSC_TRUE);
1336:   DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);
1337:   DMDestroy(&plex);
1338:   return(0);
1339: }

1341: /*@
1342:   DMSNESComputeJacobianAction - Compute the action of the Jacobian J(X) on Y

1344:   Input Parameters:
1345: + dm   - The DM
1346: . X    - Local solution vector
1347: . Y    - Local input vector
1348: - user - The user context

1350:   Output Parameter:
1351: . F    - lcoal output vector

1353:   Level: developer

1355:   Notes:
1356:   Users will typically use DMSNESCreateJacobianMF() followed by MatMult() instead of calling this routine directly.

1358: .seealso: DMSNESCreateJacobianMF(), DMPlexSNESComputeResidualFEM()
1359: @*/
1360: PetscErrorCode DMSNESComputeJacobianAction(DM dm, Vec X, Vec Y, Vec F, void *user)
1361: {
1362:   DM             plex;
1363:   IS             allcellIS;
1364:   PetscInt       Nds, s;

1368:   DMSNESConvertPlex(dm, &plex, PETSC_TRUE);
1369:   DMPlexGetAllCells_Internal(plex, &allcellIS);
1370:   DMGetNumDS(dm, &Nds);
1371:   for (s = 0; s < Nds; ++s) {
1372:     PetscDS ds;
1373:     DMLabel label;
1374:     IS      cellIS;

1376:     DMGetRegionNumDS(dm, s, &label, NULL, &ds);
1377:     {
1378:       PetscWeakFormKind jacmap[4] = {PETSC_WF_G0, PETSC_WF_G1, PETSC_WF_G2, PETSC_WF_G3};
1379:       PetscWeakForm     wf;
1380:       PetscInt          Nm = 4, m, Nk = 0, k, kp, off = 0;
1381:       PetscFormKey *jackeys;

1383:       /* Get unique Jacobian keys */
1384:       for (m = 0; m < Nm; ++m) {
1385:         PetscInt Nkm;
1386:         PetscHMapFormGetSize(ds->wf->form[jacmap[m]], &Nkm);
1387:         Nk  += Nkm;
1388:       }
1389:       PetscMalloc1(Nk, &jackeys);
1390:       for (m = 0; m < Nm; ++m) {
1391:         PetscHMapFormGetKeys(ds->wf->form[jacmap[m]], &off, jackeys);
1392:       }
1393:       if (off != Nk) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of keys %D should be %D", off, Nk);
1394:       PetscFormKeySort(Nk, jackeys);
1395:       for (k = 0, kp = 1; kp < Nk; ++kp) {
1396:         if ((jackeys[k].label != jackeys[kp].label) || (jackeys[k].value != jackeys[kp].value)) {
1397:           ++k;
1398:           if (kp != k) jackeys[k] = jackeys[kp];
1399:         }
1400:       }
1401:       Nk = k;

1403:       PetscDSGetWeakForm(ds, &wf);
1404:       for (k = 0; k < Nk; ++k) {
1405:         DMLabel  label = jackeys[k].label;
1406:         PetscInt val   = jackeys[k].value;

1408:         if (!label) {
1409:           PetscObjectReference((PetscObject) allcellIS);
1410:           cellIS = allcellIS;
1411:         } else {
1412:           IS pointIS;

1414:           DMLabelGetStratumIS(label, val, &pointIS);
1415:           ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS);
1416:           ISDestroy(&pointIS);
1417:         }
1418:         DMPlexComputeJacobian_Action_Internal(plex, jackeys[k], cellIS, 0.0, 0.0, X, NULL, Y, F, user);
1419:         ISDestroy(&cellIS);
1420:       }
1421:       PetscFree(jackeys);
1422:     }
1423:   }
1424:   ISDestroy(&allcellIS);
1425:   DMDestroy(&plex);
1426:   return(0);
1427: }

1429: /*@
1430:   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.

1432:   Input Parameters:
1433: + dm - The mesh
1434: . X  - Local input vector
1435: - user - The user context

1437:   Output Parameter:
1438: . Jac  - Jacobian matrix

1440:   Note:
1441:   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1442:   like a GPU, or vectorize on a multicore machine.

1444:   Level: developer

1446: .seealso: FormFunctionLocal()
1447: @*/
1448: PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
1449: {
1450:   DM             plex;
1451:   IS             allcellIS;
1452:   PetscBool      hasJac, hasPrec;
1453:   PetscInt       Nds, s;

1457:   DMSNESConvertPlex(dm, &plex, PETSC_TRUE);
1458:   DMPlexGetAllCells_Internal(plex, &allcellIS);
1459:   DMGetNumDS(dm, &Nds);
1460:   for (s = 0; s < Nds; ++s) {
1461:     PetscDS          ds;
1462:     IS               cellIS;
1463:     PetscFormKey key;

1465:     DMGetRegionNumDS(dm, s, &key.label, NULL, &ds);
1466:     key.value = 0;
1467:     key.field = 0;
1468:     key.part  = 0;
1469:     if (!key.label) {
1470:       PetscObjectReference((PetscObject) allcellIS);
1471:       cellIS = allcellIS;
1472:     } else {
1473:       IS pointIS;

1475:       key.value = 1;
1476:       DMLabelGetStratumIS(key.label, key.value, &pointIS);
1477:       ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS);
1478:       ISDestroy(&pointIS);
1479:     }
1480:     if (!s) {
1481:       PetscDSHasJacobian(ds, &hasJac);
1482:       PetscDSHasJacobianPreconditioner(ds, &hasPrec);
1483:       if (hasJac && hasPrec) {MatZeroEntries(Jac);}
1484:       MatZeroEntries(JacP);
1485:     }
1486:     DMPlexComputeJacobian_Internal(plex, key, cellIS, 0.0, 0.0, X, NULL, Jac, JacP, user);
1487:     ISDestroy(&cellIS);
1488:   }
1489:   ISDestroy(&allcellIS);
1490:   DMDestroy(&plex);
1491:   return(0);
1492: }

1494: struct _DMSNESJacobianMFCtx
1495: {
1496:   DM    dm;
1497:   Vec   X;
1498:   void *ctx;
1499: };

1501: static PetscErrorCode DMSNESJacobianMF_Destroy_Private(Mat A)
1502: {
1503:   struct _DMSNESJacobianMFCtx *ctx;
1504:   PetscErrorCode               ierr;

1507:   MatShellGetContext(A, (void **) &ctx);
1508:   MatShellSetContext(A, NULL);
1509:   DMDestroy(&ctx->dm);
1510:   VecDestroy(&ctx->X);
1511:   PetscFree(ctx);
1512:   return(0);
1513: }

1515: static PetscErrorCode DMSNESJacobianMF_Mult_Private(Mat A, Vec Y, Vec Z)
1516: {
1517:   struct _DMSNESJacobianMFCtx *ctx;
1518:   PetscErrorCode               ierr;

1521:   MatShellGetContext(A, (void **) &ctx);
1522:   DMSNESComputeJacobianAction(ctx->dm, ctx->X, Y, Z, ctx->ctx);
1523:   return(0);
1524: }

1526: /*@
1527:   DMSNESCreateJacobianMF - Create a Mat which computes the action of the Jacobian matrix-free

1529:   Collective on dm

1531:   Input Parameters:
1532: + dm   - The DM
1533: . X    - The evaluation point for the Jacobian
1534: - user - A user context, or NULL

1536:   Output Parameter:
1537: . J    - The Mat

1541:   Notes:
1542:   Vec X is kept in Mat J, so updating X then updates the evaluation point.

1544: .seealso: DMSNESComputeJacobianAction()
1545: @*/
1546: PetscErrorCode DMSNESCreateJacobianMF(DM dm, Vec X, void *user, Mat *J)
1547: {
1548:   struct _DMSNESJacobianMFCtx *ctx;
1549:   PetscInt                     n, N;
1550:   PetscErrorCode               ierr;

1553:   MatCreate(PetscObjectComm((PetscObject) dm), J);
1554:   MatSetType(*J, MATSHELL);
1555:   VecGetLocalSize(X, &n);
1556:   VecGetSize(X, &N);
1557:   MatSetSizes(*J, n, n, N, N);
1558:   PetscObjectReference((PetscObject) dm);
1559:   PetscObjectReference((PetscObject) X);
1560:   PetscMalloc1(1, &ctx);
1561:   ctx->dm  = dm;
1562:   ctx->X   = X;
1563:   ctx->ctx = user;
1564:   MatShellSetContext(*J, ctx);
1565:   MatShellSetOperation(*J, MATOP_DESTROY, (void (*)(void)) DMSNESJacobianMF_Destroy_Private);
1566:   MatShellSetOperation(*J, MATOP_MULT,    (void (*)(void)) DMSNESJacobianMF_Mult_Private);
1567:   return(0);
1568: }

1570: /*
1571:      MatComputeNeumannOverlap - Computes an unassembled (Neumann) local overlapping Mat in nonlinear context.

1573:    Input Parameters:
1574: +     X - SNES linearization point
1575: .     ovl - index set of overlapping subdomains

1577:    Output Parameter:
1578: .     J - unassembled (Neumann) local matrix

1580:    Level: intermediate

1582: .seealso: DMCreateNeumannOverlap(), MATIS, PCHPDDMSetAuxiliaryMat()
1583: */
1584: static PetscErrorCode MatComputeNeumannOverlap_Plex(Mat J, PetscReal t, Vec X, Vec X_t, PetscReal s, IS ovl, void *ctx)
1585: {
1586:   SNES           snes;
1587:   Mat            pJ;
1588:   DM             ovldm,origdm;
1589:   DMSNES         sdm;
1590:   PetscErrorCode (*bfun)(DM,Vec,void*);
1591:   PetscErrorCode (*jfun)(DM,Vec,Mat,Mat,void*);
1592:   void           *bctx,*jctx;

1596:   PetscObjectQuery((PetscObject)ovl,"_DM_Overlap_HPDDM_MATIS",(PetscObject*)&pJ);
1597:   if (!pJ) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing overlapping Mat");
1598:   PetscObjectQuery((PetscObject)ovl,"_DM_Original_HPDDM",(PetscObject*)&origdm);
1599:   if (!origdm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing original DM");
1600:   MatGetDM(pJ,&ovldm);
1601:   DMSNESGetBoundaryLocal(origdm,&bfun,&bctx);
1602:   DMSNESSetBoundaryLocal(ovldm,bfun,bctx);
1603:   DMSNESGetJacobianLocal(origdm,&jfun,&jctx);
1604:   DMSNESSetJacobianLocal(ovldm,jfun,jctx);
1605:   PetscObjectQuery((PetscObject)ovl,"_DM_Overlap_HPDDM_SNES",(PetscObject*)&snes);
1606:   if (!snes) {
1607:     SNESCreate(PetscObjectComm((PetscObject)ovl),&snes);
1608:     SNESSetDM(snes,ovldm);
1609:     PetscObjectCompose((PetscObject)ovl,"_DM_Overlap_HPDDM_SNES",(PetscObject)snes);
1610:     PetscObjectDereference((PetscObject)snes);
1611:   }
1612:   DMGetDMSNES(ovldm,&sdm);
1614:   PetscStackPush("SNES user Jacobian function");
1615:   (*sdm->ops->computejacobian)(snes,X,pJ,pJ,sdm->jacobianctx);
1616:   PetscStackPop;
1618:   /* this is a no-hop, just in case we decide to change the placeholder for the local Neumann matrix */
1619:   {
1620:     Mat locpJ;

1622:     MatISGetLocalMat(pJ,&locpJ);
1623:     MatCopy(locpJ,J,SAME_NONZERO_PATTERN);
1624:   }
1625:   return(0);
1626: }

1628: /*@
1629:   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.

1631:   Input Parameters:
1632: + dm - The DM object
1633: . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see PetscDSAddBoundary())
1634: . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
1635: - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())

1637:   Level: developer
1638: @*/
1639: PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
1640: {

1644:   DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);
1645:   DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);
1646:   DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);
1647:   PetscObjectComposeFunction((PetscObject)dm,"MatComputeNeumannOverlap_C",MatComputeNeumannOverlap_Plex);
1648:   return(0);
1649: }

1651: /*@C
1652:   DMSNESCheckDiscretization - Check the discretization error of the exact solution

1654:   Input Parameters:
1655: + snes - the SNES object
1656: . dm   - the DM
1657: . t    - the time
1658: . u    - a DM vector
1659: - tol  - A tolerance for the check, or -1 to print the results instead

1661:   Output Parameters:
1662: . error - An array which holds the discretization error in each field, or NULL

1664:   Note: The user must call PetscDSSetExactSolution() beforehand

1666:   Level: developer

1668: .seealso: DNSNESCheckFromOptions(), DMSNESCheckResidual(), DMSNESCheckJacobian(), PetscDSSetExactSolution()
1669: @*/
1670: PetscErrorCode DMSNESCheckDiscretization(SNES snes, DM dm, PetscReal t, Vec u, PetscReal tol, PetscReal error[])
1671: {
1672:   PetscErrorCode (**exacts)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx);
1673:   void            **ectxs;
1674:   PetscReal        *err;
1675:   MPI_Comm          comm;
1676:   PetscInt          Nf, f;
1677:   PetscErrorCode    ierr;

1685:   DMComputeExactSolution(dm, t, u, NULL);
1686:   VecViewFromOptions(u, NULL, "-vec_view");

1688:   PetscObjectGetComm((PetscObject) snes, &comm);
1689:   DMGetNumFields(dm, &Nf);
1690:   PetscCalloc3(Nf, &exacts, Nf, &ectxs, PetscMax(1, Nf), &err);
1691:   {
1692:     PetscInt Nds, s;

1694:     DMGetNumDS(dm, &Nds);
1695:     for (s = 0; s < Nds; ++s) {
1696:       PetscDS         ds;
1697:       DMLabel         label;
1698:       IS              fieldIS;
1699:       const PetscInt *fields;
1700:       PetscInt        dsNf, f;

1702:       DMGetRegionNumDS(dm, s, &label, &fieldIS, &ds);
1703:       PetscDSGetNumFields(ds, &dsNf);
1704:       ISGetIndices(fieldIS, &fields);
1705:       for (f = 0; f < dsNf; ++f) {
1706:         const PetscInt field = fields[f];
1707:         PetscDSGetExactSolution(ds, field, &exacts[field], &ectxs[field]);
1708:       }
1709:       ISRestoreIndices(fieldIS, &fields);
1710:     }
1711:   }
1712:   if (Nf > 1) {
1713:     DMComputeL2FieldDiff(dm, t, exacts, ectxs, u, err);
1714:     if (tol >= 0.0) {
1715:       for (f = 0; f < Nf; ++f) {
1716:         if (err[f] > tol) SETERRQ3(comm, PETSC_ERR_ARG_WRONG, "L_2 Error %g for field %D exceeds tolerance %g", (double) err[f], f, (double) tol);
1717:       }
1718:     } else if (error) {
1719:       for (f = 0; f < Nf; ++f) error[f] = err[f];
1720:     } else {
1721:       PetscPrintf(comm, "L_2 Error: [");
1722:       for (f = 0; f < Nf; ++f) {
1723:         if (f) {PetscPrintf(comm, ", ");}
1724:         PetscPrintf(comm, "%g", (double)err[f]);
1725:       }
1726:       PetscPrintf(comm, "]\n");
1727:     }
1728:   } else {
1729:     DMComputeL2Diff(dm, t, exacts, ectxs, u, &err[0]);
1730:     if (tol >= 0.0) {
1731:       if (err[0] > tol) SETERRQ2(comm, PETSC_ERR_ARG_WRONG, "L_2 Error %g exceeds tolerance %g", (double) err[0], (double) tol);
1732:     } else if (error) {
1733:       error[0] = err[0];
1734:     } else {
1735:       PetscPrintf(comm, "L_2 Error: %g\n", (double) err[0]);
1736:     }
1737:   }
1738:   PetscFree3(exacts, ectxs, err);
1739:   return(0);
1740: }

1742: /*@C
1743:   DMSNESCheckResidual - Check the residual of the exact solution

1745:   Input Parameters:
1746: + snes - the SNES object
1747: . dm   - the DM
1748: . u    - a DM vector
1749: - tol  - A tolerance for the check, or -1 to print the results instead

1751:   Output Parameters:
1752: . residual - The residual norm of the exact solution, or NULL

1754:   Level: developer

1756: .seealso: DNSNESCheckFromOptions(), DMSNESCheckDiscretization(), DMSNESCheckJacobian()
1757: @*/
1758: PetscErrorCode DMSNESCheckResidual(SNES snes, DM dm, Vec u, PetscReal tol, PetscReal *residual)
1759: {
1760:   MPI_Comm       comm;
1761:   Vec            r;
1762:   PetscReal      res;

1770:   PetscObjectGetComm((PetscObject) snes, &comm);
1771:   DMComputeExactSolution(dm, 0.0, u, NULL);
1772:   VecDuplicate(u, &r);
1773:   SNESComputeFunction(snes, u, r);
1774:   VecNorm(r, NORM_2, &res);
1775:   if (tol >= 0.0) {
1776:     if (res > tol) SETERRQ2(comm, PETSC_ERR_ARG_WRONG, "L_2 Residual %g exceeds tolerance %g", (double) res, (double) tol);
1777:   } else if (residual) {
1778:     *residual = res;
1779:   } else {
1780:     PetscPrintf(comm, "L_2 Residual: %g\n", (double)res);
1781:     VecChop(r, 1.0e-10);
1782:     PetscObjectSetName((PetscObject) r, "Initial Residual");
1783:     PetscObjectSetOptionsPrefix((PetscObject)r,"res_");
1784:     VecViewFromOptions(r, NULL, "-vec_view");
1785:   }
1786:   VecDestroy(&r);
1787:   return(0);
1788: }

1790: /*@C
1791:   DMSNESCheckJacobian - Check the Jacobian of the exact solution against the residual using the Taylor Test

1793:   Input Parameters:
1794: + snes - the SNES object
1795: . dm   - the DM
1796: . u    - a DM vector
1797: - tol  - A tolerance for the check, or -1 to print the results instead

1799:   Output Parameters:
1800: + isLinear - Flag indicaing that the function looks linear, or NULL
1801: - convRate - The rate of convergence of the linear model, or NULL

1803:   Level: developer

1805: .seealso: DNSNESCheckFromOptions(), DMSNESCheckDiscretization(), DMSNESCheckResidual()
1806: @*/
1807: PetscErrorCode DMSNESCheckJacobian(SNES snes, DM dm, Vec u, PetscReal tol, PetscBool *isLinear, PetscReal *convRate)
1808: {
1809:   MPI_Comm       comm;
1810:   PetscDS        ds;
1811:   Mat            J, M;
1812:   MatNullSpace   nullspace;
1813:   PetscReal      slope, intercept;
1814:   PetscBool      hasJac, hasPrec, isLin = PETSC_FALSE;

1823:   PetscObjectGetComm((PetscObject) snes, &comm);
1824:   DMComputeExactSolution(dm, 0.0, u, NULL);
1825:   /* Create and view matrices */
1826:   DMCreateMatrix(dm, &J);
1827:   DMGetDS(dm, &ds);
1828:   PetscDSHasJacobian(ds, &hasJac);
1829:   PetscDSHasJacobianPreconditioner(ds, &hasPrec);
1830:   if (hasJac && hasPrec) {
1831:     DMCreateMatrix(dm, &M);
1832:     SNESComputeJacobian(snes, u, J, M);
1833:     PetscObjectSetName((PetscObject) M, "Preconditioning Matrix");
1834:     PetscObjectSetOptionsPrefix((PetscObject) M, "jacpre_");
1835:     MatViewFromOptions(M, NULL, "-mat_view");
1836:     MatDestroy(&M);
1837:   } else {
1838:     SNESComputeJacobian(snes, u, J, J);
1839:   }
1840:   PetscObjectSetName((PetscObject) J, "Jacobian");
1841:   PetscObjectSetOptionsPrefix((PetscObject) J, "jac_");
1842:   MatViewFromOptions(J, NULL, "-mat_view");
1843:   /* Check nullspace */
1844:   MatGetNullSpace(J, &nullspace);
1845:   if (nullspace) {
1846:     PetscBool isNull;
1847:     MatNullSpaceTest(nullspace, J, &isNull);
1848:     if (!isNull) SETERRQ(comm, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
1849:   }
1850:   /* Taylor test */
1851:   {
1852:     PetscRandom rand;
1853:     Vec         du, uhat, r, rhat, df;
1854:     PetscReal   h;
1855:     PetscReal  *es, *hs, *errors;
1856:     PetscReal   hMax = 1.0, hMin = 1e-6, hMult = 0.1;
1857:     PetscInt    Nv, v;

1859:     /* Choose a perturbation direction */
1860:     PetscRandomCreate(comm, &rand);
1861:     VecDuplicate(u, &du);
1862:     VecSetRandom(du, rand);
1863:     PetscRandomDestroy(&rand);
1864:     VecDuplicate(u, &df);
1865:     MatMult(J, du, df);
1866:     /* Evaluate residual at u, F(u), save in vector r */
1867:     VecDuplicate(u, &r);
1868:     SNESComputeFunction(snes, u, r);
1869:     /* Look at the convergence of our Taylor approximation as we approach u */
1870:     for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv);
1871:     PetscCalloc3(Nv, &es, Nv, &hs, Nv, &errors);
1872:     VecDuplicate(u, &uhat);
1873:     VecDuplicate(u, &rhat);
1874:     for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv) {
1875:       VecWAXPY(uhat, h, du, u);
1876:       /* F(\hat u) \approx F(u) + J(u) (uhat - u) = F(u) + h * J(u) du */
1877:       SNESComputeFunction(snes, uhat, rhat);
1878:       VecAXPBYPCZ(rhat, -1.0, -h, 1.0, r, df);
1879:       VecNorm(rhat, NORM_2, &errors[Nv]);

1881:       es[Nv] = PetscLog10Real(errors[Nv]);
1882:       hs[Nv] = PetscLog10Real(h);
1883:     }
1884:     VecDestroy(&uhat);
1885:     VecDestroy(&rhat);
1886:     VecDestroy(&df);
1887:     VecDestroy(&r);
1888:     VecDestroy(&du);
1889:     for (v = 0; v < Nv; ++v) {
1890:       if ((tol >= 0) && (errors[v] > tol)) break;
1891:       else if (errors[v] > PETSC_SMALL)    break;
1892:     }
1893:     if (v == Nv) isLin = PETSC_TRUE;
1894:     PetscLinearRegression(Nv, hs, es, &slope, &intercept);
1895:     PetscFree3(es, hs, errors);
1896:     /* Slope should be about 2 */
1897:     if (tol >= 0) {
1898:       if (!isLin && PetscAbsReal(2 - slope) > tol) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Taylor approximation convergence rate should be 2, not %0.2f", (double) slope);
1899:     } else if (isLinear || convRate) {
1900:       if (isLinear) *isLinear = isLin;
1901:       if (convRate) *convRate = slope;
1902:     } else {
1903:       if (!isLin) {PetscPrintf(comm, "Taylor approximation converging at order %3.2f\n", (double) slope);}
1904:       else        {PetscPrintf(comm, "Function appears to be linear\n");}
1905:     }
1906:   }
1907:   MatDestroy(&J);
1908:   return(0);
1909: }

1911: PetscErrorCode DMSNESCheck_Internal(SNES snes, DM dm, Vec u)
1912: {

1916:   DMSNESCheckDiscretization(snes, dm, 0.0, u, -1.0, NULL);
1917:   DMSNESCheckResidual(snes, dm, u, -1.0, NULL);
1918:   DMSNESCheckJacobian(snes, dm, u, -1.0, NULL, NULL);
1919:   return(0);
1920: }

1922: /*@C
1923:   DMSNESCheckFromOptions - Check the residual and Jacobian functions using the exact solution by outputting some diagnostic information

1925:   Input Parameters:
1926: + snes - the SNES object
1927: - u    - representative SNES vector

1929:   Note: The user must call PetscDSSetExactSolution() beforehand

1931:   Level: developer
1932: @*/
1933: PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u)
1934: {
1935:   DM             dm;
1936:   Vec            sol;
1937:   PetscBool      check;

1941:   PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);
1942:   if (!check) return(0);
1943:   SNESGetDM(snes, &dm);
1944:   VecDuplicate(u, &sol);
1945:   SNESSetSolution(snes, sol);
1946:   DMSNESCheck_Internal(snes, dm, sol);
1947:   VecDestroy(&sol);
1948:   return(0);
1949: }