xref: /petsc/src/snes/utils/dmplexsnes.c (revision 38cfc46e4752cf65941cec0be9bac4d1d6832cc8)
1 #include <petsc/private/dmpleximpl.h>   /*I "petscdmplex.h" I*/
2 #include <petsc/private/snesimpl.h>     /*I "petscsnes.h"   I*/
3 #include <petscds.h>
4 #include <petscblaslapack.h>
5 #include <petsc/private/petscimpl.h>
6 #include <petsc/private/petscfeimpl.h>
7 
8 /************************** Interpolation *******************************/
9 
10 static PetscErrorCode DMSNESConvertPlex(DM dm, DM *plex, PetscBool copy)
11 {
12   PetscBool      isPlex;
13   PetscErrorCode ierr;
14 
15   PetscFunctionBegin;
16   ierr = PetscObjectTypeCompare((PetscObject) dm, DMPLEX, &isPlex);CHKERRQ(ierr);
17   if (isPlex) {
18     *plex = dm;
19     ierr = PetscObjectReference((PetscObject) dm);CHKERRQ(ierr);
20   } else {
21     ierr = PetscObjectQuery((PetscObject) dm, "dm_plex", (PetscObject *) plex);CHKERRQ(ierr);
22     if (!*plex) {
23       ierr = DMConvert(dm,DMPLEX,plex);CHKERRQ(ierr);
24       ierr = PetscObjectCompose((PetscObject) dm, "dm_plex", (PetscObject) *plex);CHKERRQ(ierr);
25       if (copy) {
26         PetscInt    i;
27         PetscObject obj;
28         const char *comps[3] = {"A","dmAux","dmCh"};
29 
30         ierr = DMCopyDMSNES(dm, *plex);CHKERRQ(ierr);
31         for (i = 0; i < 3; i++) {
32           ierr = PetscObjectQuery((PetscObject) dm, comps[i], &obj);CHKERRQ(ierr);
33           ierr = PetscObjectCompose((PetscObject) *plex, comps[i], obj);CHKERRQ(ierr);
34         }
35       }
36     } else {
37       ierr = PetscObjectReference((PetscObject) *plex);CHKERRQ(ierr);
38     }
39   }
40   PetscFunctionReturn(0);
41 }
42 
43 /*@C
44   DMInterpolationCreate - Creates a DMInterpolationInfo context
45 
46   Collective
47 
48   Input Parameter:
49 . comm - the communicator
50 
51   Output Parameter:
52 . ctx - the context
53 
54   Level: beginner
55 
56 .seealso: DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationDestroy()
57 @*/
58 PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx)
59 {
60   PetscErrorCode ierr;
61 
62   PetscFunctionBegin;
63   PetscValidPointer(ctx, 2);
64   ierr = PetscNew(ctx);CHKERRQ(ierr);
65 
66   (*ctx)->comm   = comm;
67   (*ctx)->dim    = -1;
68   (*ctx)->nInput = 0;
69   (*ctx)->points = NULL;
70   (*ctx)->cells  = NULL;
71   (*ctx)->n      = -1;
72   (*ctx)->coords = NULL;
73   PetscFunctionReturn(0);
74 }
75 
76 /*@C
77   DMInterpolationSetDim - Sets the spatial dimension for the interpolation context
78 
79   Not collective
80 
81   Input Parameters:
82 + ctx - the context
83 - dim - the spatial dimension
84 
85   Level: intermediate
86 
87 .seealso: DMInterpolationGetDim(), DMInterpolationEvaluate(), DMInterpolationAddPoints()
88 @*/
89 PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim)
90 {
91   PetscFunctionBegin;
92   if ((dim < 1) || (dim > 3)) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %D", dim);
93   ctx->dim = dim;
94   PetscFunctionReturn(0);
95 }
96 
97 /*@C
98   DMInterpolationGetDim - Gets the spatial dimension for the interpolation context
99 
100   Not collective
101 
102   Input Parameter:
103 . ctx - the context
104 
105   Output Parameter:
106 . dim - the spatial dimension
107 
108   Level: intermediate
109 
110 .seealso: DMInterpolationSetDim(), DMInterpolationEvaluate(), DMInterpolationAddPoints()
111 @*/
112 PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim)
113 {
114   PetscFunctionBegin;
115   PetscValidIntPointer(dim, 2);
116   *dim = ctx->dim;
117   PetscFunctionReturn(0);
118 }
119 
120 /*@C
121   DMInterpolationSetDof - Sets the number of fields interpolated at a point for the interpolation context
122 
123   Not collective
124 
125   Input Parameters:
126 + ctx - the context
127 - dof - the number of fields
128 
129   Level: intermediate
130 
131 .seealso: DMInterpolationGetDof(), DMInterpolationEvaluate(), DMInterpolationAddPoints()
132 @*/
133 PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof)
134 {
135   PetscFunctionBegin;
136   if (dof < 1) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %D", dof);
137   ctx->dof = dof;
138   PetscFunctionReturn(0);
139 }
140 
141 /*@C
142   DMInterpolationGetDof - Gets the number of fields interpolated at a point for the interpolation context
143 
144   Not collective
145 
146   Input Parameter:
147 . ctx - the context
148 
149   Output Parameter:
150 . dof - the number of fields
151 
152   Level: intermediate
153 
154 .seealso: DMInterpolationSetDof(), DMInterpolationEvaluate(), DMInterpolationAddPoints()
155 @*/
156 PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof)
157 {
158   PetscFunctionBegin;
159   PetscValidIntPointer(dof, 2);
160   *dof = ctx->dof;
161   PetscFunctionReturn(0);
162 }
163 
164 /*@C
165   DMInterpolationAddPoints - Add points at which we will interpolate the fields
166 
167   Not collective
168 
169   Input Parameters:
170 + ctx    - the context
171 . n      - the number of points
172 - points - the coordinates for each point, an array of size n * dim
173 
174   Note: The coordinate information is copied.
175 
176   Level: intermediate
177 
178 .seealso: DMInterpolationSetDim(), DMInterpolationEvaluate(), DMInterpolationCreate()
179 @*/
180 PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[])
181 {
182   PetscErrorCode ierr;
183 
184   PetscFunctionBegin;
185   if (ctx->dim < 0) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
186   if (ctx->points)  SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "Cannot add points multiple times yet");
187   ctx->nInput = n;
188 
189   ierr = PetscMalloc1(n*ctx->dim, &ctx->points);CHKERRQ(ierr);
190   ierr = PetscArraycpy(ctx->points, points, n*ctx->dim);CHKERRQ(ierr);
191   PetscFunctionReturn(0);
192 }
193 
194 /*@C
195   DMInterpolationSetUp - Computea spatial indices that add in point location during interpolation
196 
197   Collective on ctx
198 
199   Input Parameters:
200 + ctx - the context
201 . dm  - the DM for the function space used for interpolation
202 - redundantPoints - If PETSC_TRUE, all processes are passing in the same array of points. Otherwise, points need to be communicated among processes.
203 
204   Level: intermediate
205 
206 .seealso: DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
207 @*/
208 PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints)
209 {
210   MPI_Comm          comm = ctx->comm;
211   PetscScalar       *a;
212   PetscInt          p, q, i;
213   PetscMPIInt       rank, size;
214   PetscErrorCode    ierr;
215   Vec               pointVec;
216   PetscSF           cellSF;
217   PetscLayout       layout;
218   PetscReal         *globalPoints;
219   PetscScalar       *globalPointsScalar;
220   const PetscInt    *ranges;
221   PetscMPIInt       *counts, *displs;
222   const PetscSFNode *foundCells;
223   const PetscInt    *foundPoints;
224   PetscMPIInt       *foundProcs, *globalProcs;
225   PetscInt          n, N, numFound;
226 
227   PetscFunctionBegin;
228   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
229   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
230   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
231   if (ctx->dim < 0) SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
232   /* Locate points */
233   n = ctx->nInput;
234   if (!redundantPoints) {
235     ierr = PetscLayoutCreate(comm, &layout);CHKERRQ(ierr);
236     ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
237     ierr = PetscLayoutSetLocalSize(layout, n);CHKERRQ(ierr);
238     ierr = PetscLayoutSetUp(layout);CHKERRQ(ierr);
239     ierr = PetscLayoutGetSize(layout, &N);CHKERRQ(ierr);
240     /* Communicate all points to all processes */
241     ierr = PetscMalloc3(N*ctx->dim,&globalPoints,size,&counts,size,&displs);CHKERRQ(ierr);
242     ierr = PetscLayoutGetRanges(layout, &ranges);CHKERRQ(ierr);
243     for (p = 0; p < size; ++p) {
244       counts[p] = (ranges[p+1] - ranges[p])*ctx->dim;
245       displs[p] = ranges[p]*ctx->dim;
246     }
247     ierr = MPI_Allgatherv(ctx->points, n*ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm);CHKERRQ(ierr);
248   } else {
249     N = n;
250     globalPoints = ctx->points;
251     counts = displs = NULL;
252     layout = NULL;
253   }
254 #if 0
255   ierr = PetscMalloc3(N,&foundCells,N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
256   /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */
257 #else
258 #if defined(PETSC_USE_COMPLEX)
259   ierr = PetscMalloc1(N*ctx->dim,&globalPointsScalar);CHKERRQ(ierr);
260   for (i=0; i<N*ctx->dim; i++) globalPointsScalar[i] = globalPoints[i];
261 #else
262   globalPointsScalar = globalPoints;
263 #endif
264   ierr = VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N*ctx->dim, globalPointsScalar, &pointVec);CHKERRQ(ierr);
265   ierr = PetscMalloc2(N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
266   for (p = 0; p < N; ++p) {foundProcs[p] = size;}
267   cellSF = NULL;
268   ierr = DMLocatePoints(dm, pointVec, DM_POINTLOCATION_REMOVE, &cellSF);CHKERRQ(ierr);
269   ierr = PetscSFGetGraph(cellSF,NULL,&numFound,&foundPoints,&foundCells);CHKERRQ(ierr);
270 #endif
271   for (p = 0; p < numFound; ++p) {
272     if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank;
273   }
274   /* Let the lowest rank process own each point */
275   ierr   = MPIU_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm);CHKERRQ(ierr);
276   ctx->n = 0;
277   for (p = 0; p < N; ++p) {
278     if (globalProcs[p] == size) 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));
279     else if (globalProcs[p] == rank) ctx->n++;
280   }
281   /* Create coordinates vector and array of owned cells */
282   ierr = PetscMalloc1(ctx->n, &ctx->cells);CHKERRQ(ierr);
283   ierr = VecCreate(comm, &ctx->coords);CHKERRQ(ierr);
284   ierr = VecSetSizes(ctx->coords, ctx->n*ctx->dim, PETSC_DECIDE);CHKERRQ(ierr);
285   ierr = VecSetBlockSize(ctx->coords, ctx->dim);CHKERRQ(ierr);
286   ierr = VecSetType(ctx->coords,VECSTANDARD);CHKERRQ(ierr);
287   ierr = VecGetArray(ctx->coords, &a);CHKERRQ(ierr);
288   for (p = 0, q = 0, i = 0; p < N; ++p) {
289     if (globalProcs[p] == rank) {
290       PetscInt d;
291 
292       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p*ctx->dim+d];
293       ctx->cells[q] = foundCells[q].index;
294       ++q;
295     }
296   }
297   ierr = VecRestoreArray(ctx->coords, &a);CHKERRQ(ierr);
298 #if 0
299   ierr = PetscFree3(foundCells,foundProcs,globalProcs);CHKERRQ(ierr);
300 #else
301   ierr = PetscFree2(foundProcs,globalProcs);CHKERRQ(ierr);
302   ierr = PetscSFDestroy(&cellSF);CHKERRQ(ierr);
303   ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
304 #endif
305   if ((void*)globalPointsScalar != (void*)globalPoints) {ierr = PetscFree(globalPointsScalar);CHKERRQ(ierr);}
306   if (!redundantPoints) {ierr = PetscFree3(globalPoints,counts,displs);CHKERRQ(ierr);}
307   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
308   PetscFunctionReturn(0);
309 }
310 
311 /*@C
312   DMInterpolationGetCoordinates - Gets a Vec with the coordinates of each interpolation point
313 
314   Collective on ctx
315 
316   Input Parameter:
317 . ctx - the context
318 
319   Output Parameter:
320 . coordinates  - the coordinates of interpolation points
321 
322   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.
323 
324   Level: intermediate
325 
326 .seealso: DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
327 @*/
328 PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates)
329 {
330   PetscFunctionBegin;
331   PetscValidPointer(coordinates, 2);
332   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
333   *coordinates = ctx->coords;
334   PetscFunctionReturn(0);
335 }
336 
337 /*@C
338   DMInterpolationGetVector - Gets a Vec which can hold all the interpolated field values
339 
340   Collective on ctx
341 
342   Input Parameter:
343 . ctx - the context
344 
345   Output Parameter:
346 . v  - a vector capable of holding the interpolated field values
347 
348   Note: This vector should be returned using DMInterpolationRestoreVector().
349 
350   Level: intermediate
351 
352 .seealso: DMInterpolationRestoreVector(), DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
353 @*/
354 PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v)
355 {
356   PetscErrorCode ierr;
357 
358   PetscFunctionBegin;
359   PetscValidPointer(v, 2);
360   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
361   ierr = VecCreate(ctx->comm, v);CHKERRQ(ierr);
362   ierr = VecSetSizes(*v, ctx->n*ctx->dof, PETSC_DECIDE);CHKERRQ(ierr);
363   ierr = VecSetBlockSize(*v, ctx->dof);CHKERRQ(ierr);
364   ierr = VecSetType(*v,VECSTANDARD);CHKERRQ(ierr);
365   PetscFunctionReturn(0);
366 }
367 
368 /*@C
369   DMInterpolationRestoreVector - Returns a Vec which can hold all the interpolated field values
370 
371   Collective on ctx
372 
373   Input Parameters:
374 + ctx - the context
375 - v  - a vector capable of holding the interpolated field values
376 
377   Level: intermediate
378 
379 .seealso: DMInterpolationGetVector(), DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
380 @*/
381 PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v)
382 {
383   PetscErrorCode ierr;
384 
385   PetscFunctionBegin;
386   PetscValidPointer(v, 2);
387   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
388   ierr = VecDestroy(v);CHKERRQ(ierr);
389   PetscFunctionReturn(0);
390 }
391 
392 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Triangle_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
393 {
394   PetscReal      *v0, *J, *invJ, detJ;
395   const PetscScalar *coords;
396   PetscScalar    *a;
397   PetscInt       p;
398   PetscErrorCode ierr;
399 
400   PetscFunctionBegin;
401   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
402   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
403   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
404   for (p = 0; p < ctx->n; ++p) {
405     PetscInt     c = ctx->cells[p];
406     PetscScalar *x = NULL;
407     PetscReal    xi[4];
408     PetscInt     d, f, comp;
409 
410     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
411     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D", (double)detJ, c);
412     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
413     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
414 
415     for (d = 0; d < ctx->dim; ++d) {
416       xi[d] = 0.0;
417       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
418       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];
419     }
420     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
421   }
422   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
423   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
424   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
425   PetscFunctionReturn(0);
426 }
427 
428 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Tetrahedron_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
429 {
430   PetscReal      *v0, *J, *invJ, detJ;
431   const PetscScalar *coords;
432   PetscScalar    *a;
433   PetscInt       p;
434   PetscErrorCode ierr;
435 
436   PetscFunctionBegin;
437   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
438   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
439   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
440   for (p = 0; p < ctx->n; ++p) {
441     PetscInt       c = ctx->cells[p];
442     const PetscInt order[3] = {2, 1, 3};
443     PetscScalar   *x = NULL;
444     PetscReal      xi[4];
445     PetscInt       d, f, comp;
446 
447     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
448     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D", (double)detJ, c);
449     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
450     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
451 
452     for (d = 0; d < ctx->dim; ++d) {
453       xi[d] = 0.0;
454       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
455       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];
456     }
457     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
458   }
459   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
460   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
461   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
462   PetscFunctionReturn(0);
463 }
464 
465 PETSC_STATIC_INLINE PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
466 {
467   const PetscScalar *vertices = (const PetscScalar*) ctx;
468   const PetscScalar x0        = vertices[0];
469   const PetscScalar y0        = vertices[1];
470   const PetscScalar x1        = vertices[2];
471   const PetscScalar y1        = vertices[3];
472   const PetscScalar x2        = vertices[4];
473   const PetscScalar y2        = vertices[5];
474   const PetscScalar x3        = vertices[6];
475   const PetscScalar y3        = vertices[7];
476   const PetscScalar f_1       = x1 - x0;
477   const PetscScalar g_1       = y1 - y0;
478   const PetscScalar f_3       = x3 - x0;
479   const PetscScalar g_3       = y3 - y0;
480   const PetscScalar f_01      = x2 - x1 - x3 + x0;
481   const PetscScalar g_01      = y2 - y1 - y3 + y0;
482   const PetscScalar *ref;
483   PetscScalar       *real;
484   PetscErrorCode    ierr;
485 
486   PetscFunctionBegin;
487   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
488   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
489   {
490     const PetscScalar p0 = ref[0];
491     const PetscScalar p1 = ref[1];
492 
493     real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1;
494     real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1;
495   }
496   ierr = PetscLogFlops(28);CHKERRQ(ierr);
497   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
498   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
499   PetscFunctionReturn(0);
500 }
501 
502 #include <petsc/private/dmimpl.h>
503 PETSC_STATIC_INLINE PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
504 {
505   const PetscScalar *vertices = (const PetscScalar*) ctx;
506   const PetscScalar x0        = vertices[0];
507   const PetscScalar y0        = vertices[1];
508   const PetscScalar x1        = vertices[2];
509   const PetscScalar y1        = vertices[3];
510   const PetscScalar x2        = vertices[4];
511   const PetscScalar y2        = vertices[5];
512   const PetscScalar x3        = vertices[6];
513   const PetscScalar y3        = vertices[7];
514   const PetscScalar f_01      = x2 - x1 - x3 + x0;
515   const PetscScalar g_01      = y2 - y1 - y3 + y0;
516   const PetscScalar *ref;
517   PetscErrorCode    ierr;
518 
519   PetscFunctionBegin;
520   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
521   {
522     const PetscScalar x       = ref[0];
523     const PetscScalar y       = ref[1];
524     const PetscInt    rows[2] = {0, 1};
525     PetscScalar       values[4];
526 
527     values[0] = (x1 - x0 + f_01*y) * 0.5; values[1] = (x3 - x0 + f_01*x) * 0.5;
528     values[2] = (y1 - y0 + g_01*y) * 0.5; values[3] = (y3 - y0 + g_01*x) * 0.5;
529     ierr      = MatSetValues(J, 2, rows, 2, rows, values, INSERT_VALUES);CHKERRQ(ierr);
530   }
531   ierr = PetscLogFlops(30);CHKERRQ(ierr);
532   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
533   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
534   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
535   PetscFunctionReturn(0);
536 }
537 
538 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
539 {
540   DM             dmCoord;
541   PetscFE        fem = NULL;
542   SNES           snes;
543   KSP            ksp;
544   PC             pc;
545   Vec            coordsLocal, r, ref, real;
546   Mat            J;
547   const PetscScalar *coords;
548   PetscScalar    *a;
549   PetscInt       Nf, p;
550   const PetscInt dof = ctx->dof;
551   PetscErrorCode ierr;
552 
553   PetscFunctionBegin;
554   ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
555   if (Nf) {ierr = DMGetField(dm, 0, NULL, (PetscObject *) &fem);CHKERRQ(ierr);}
556   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
557   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
558   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
559   ierr = SNESSetOptionsPrefix(snes, "quad_interp_");CHKERRQ(ierr);
560   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
561   ierr = VecSetSizes(r, 2, 2);CHKERRQ(ierr);
562   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
563   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
564   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
565   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
566   ierr = MatSetSizes(J, 2, 2, 2, 2);CHKERRQ(ierr);
567   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
568   ierr = MatSetUp(J);CHKERRQ(ierr);
569   ierr = SNESSetFunction(snes, r, QuadMap_Private, NULL);CHKERRQ(ierr);
570   ierr = SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);CHKERRQ(ierr);
571   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
572   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
573   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
574   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
575 
576   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
577   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
578   for (p = 0; p < ctx->n; ++p) {
579     PetscScalar *x = NULL, *vertices = NULL;
580     PetscScalar *xi;
581     PetscReal    xir[2];
582     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
583 
584     /* Can make this do all points at once */
585     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
586     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %D should be %d", coordSize, 4*2);
587     ierr   = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
588     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
589     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
590     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
591     xi[0]  = coords[p*ctx->dim+0];
592     xi[1]  = coords[p*ctx->dim+1];
593     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
594     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
595     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
596     xir[0] = PetscRealPart(xi[0]);
597     xir[1] = PetscRealPart(xi[1]);
598     if (4*dof != xSize) {
599       PetscReal *B;
600       PetscInt   d;
601 
602       xir[0] = 2.0*xir[0] - 1.0; xir[1] = 2.0*xir[1] - 1.0;
603       ierr = PetscFEGetTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
604       for (comp = 0; comp < dof; ++comp) {
605         a[p*dof+comp] = 0.0;
606         for (d = 0; d < xSize/dof; ++d) {
607           a[p*dof+comp] += x[d*dof+comp]*B[d*dof+comp];
608         }
609       }
610       ierr = PetscFERestoreTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
611     } else {
612       for (comp = 0; comp < dof; ++comp)
613         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];
614     }
615     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
616     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
617     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
618   }
619   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
620   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
621 
622   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
623   ierr = VecDestroy(&r);CHKERRQ(ierr);
624   ierr = VecDestroy(&ref);CHKERRQ(ierr);
625   ierr = VecDestroy(&real);CHKERRQ(ierr);
626   ierr = MatDestroy(&J);CHKERRQ(ierr);
627   PetscFunctionReturn(0);
628 }
629 
630 PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
631 {
632   const PetscScalar *vertices = (const PetscScalar*) ctx;
633   const PetscScalar x0        = vertices[0];
634   const PetscScalar y0        = vertices[1];
635   const PetscScalar z0        = vertices[2];
636   const PetscScalar x1        = vertices[9];
637   const PetscScalar y1        = vertices[10];
638   const PetscScalar z1        = vertices[11];
639   const PetscScalar x2        = vertices[6];
640   const PetscScalar y2        = vertices[7];
641   const PetscScalar z2        = vertices[8];
642   const PetscScalar x3        = vertices[3];
643   const PetscScalar y3        = vertices[4];
644   const PetscScalar z3        = vertices[5];
645   const PetscScalar x4        = vertices[12];
646   const PetscScalar y4        = vertices[13];
647   const PetscScalar z4        = vertices[14];
648   const PetscScalar x5        = vertices[15];
649   const PetscScalar y5        = vertices[16];
650   const PetscScalar z5        = vertices[17];
651   const PetscScalar x6        = vertices[18];
652   const PetscScalar y6        = vertices[19];
653   const PetscScalar z6        = vertices[20];
654   const PetscScalar x7        = vertices[21];
655   const PetscScalar y7        = vertices[22];
656   const PetscScalar z7        = vertices[23];
657   const PetscScalar f_1       = x1 - x0;
658   const PetscScalar g_1       = y1 - y0;
659   const PetscScalar h_1       = z1 - z0;
660   const PetscScalar f_3       = x3 - x0;
661   const PetscScalar g_3       = y3 - y0;
662   const PetscScalar h_3       = z3 - z0;
663   const PetscScalar f_4       = x4 - x0;
664   const PetscScalar g_4       = y4 - y0;
665   const PetscScalar h_4       = z4 - z0;
666   const PetscScalar f_01      = x2 - x1 - x3 + x0;
667   const PetscScalar g_01      = y2 - y1 - y3 + y0;
668   const PetscScalar h_01      = z2 - z1 - z3 + z0;
669   const PetscScalar f_12      = x7 - x3 - x4 + x0;
670   const PetscScalar g_12      = y7 - y3 - y4 + y0;
671   const PetscScalar h_12      = z7 - z3 - z4 + z0;
672   const PetscScalar f_02      = x5 - x1 - x4 + x0;
673   const PetscScalar g_02      = y5 - y1 - y4 + y0;
674   const PetscScalar h_02      = z5 - z1 - z4 + z0;
675   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
676   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
677   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
678   const PetscScalar *ref;
679   PetscScalar       *real;
680   PetscErrorCode    ierr;
681 
682   PetscFunctionBegin;
683   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
684   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
685   {
686     const PetscScalar p0 = ref[0];
687     const PetscScalar p1 = ref[1];
688     const PetscScalar p2 = ref[2];
689 
690     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;
691     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;
692     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;
693   }
694   ierr = PetscLogFlops(114);CHKERRQ(ierr);
695   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
696   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
697   PetscFunctionReturn(0);
698 }
699 
700 PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
701 {
702   const PetscScalar *vertices = (const PetscScalar*) ctx;
703   const PetscScalar x0        = vertices[0];
704   const PetscScalar y0        = vertices[1];
705   const PetscScalar z0        = vertices[2];
706   const PetscScalar x1        = vertices[9];
707   const PetscScalar y1        = vertices[10];
708   const PetscScalar z1        = vertices[11];
709   const PetscScalar x2        = vertices[6];
710   const PetscScalar y2        = vertices[7];
711   const PetscScalar z2        = vertices[8];
712   const PetscScalar x3        = vertices[3];
713   const PetscScalar y3        = vertices[4];
714   const PetscScalar z3        = vertices[5];
715   const PetscScalar x4        = vertices[12];
716   const PetscScalar y4        = vertices[13];
717   const PetscScalar z4        = vertices[14];
718   const PetscScalar x5        = vertices[15];
719   const PetscScalar y5        = vertices[16];
720   const PetscScalar z5        = vertices[17];
721   const PetscScalar x6        = vertices[18];
722   const PetscScalar y6        = vertices[19];
723   const PetscScalar z6        = vertices[20];
724   const PetscScalar x7        = vertices[21];
725   const PetscScalar y7        = vertices[22];
726   const PetscScalar z7        = vertices[23];
727   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
728   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
729   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
730   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
731   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
732   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
733   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
734   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
735   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
736   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
737   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
738   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
739   const PetscScalar *ref;
740   PetscErrorCode    ierr;
741 
742   PetscFunctionBegin;
743   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
744   {
745     const PetscScalar x       = ref[0];
746     const PetscScalar y       = ref[1];
747     const PetscScalar z       = ref[2];
748     const PetscInt    rows[3] = {0, 1, 2};
749     PetscScalar       values[9];
750 
751     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
752     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
753     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
754     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
755     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
756     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
757     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
758     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
759     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;
760 
761     ierr = MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);CHKERRQ(ierr);
762   }
763   ierr = PetscLogFlops(152);CHKERRQ(ierr);
764   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
765   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
766   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
767   PetscFunctionReturn(0);
768 }
769 
770 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
771 {
772   DM             dmCoord;
773   SNES           snes;
774   KSP            ksp;
775   PC             pc;
776   Vec            coordsLocal, r, ref, real;
777   Mat            J;
778   const PetscScalar *coords;
779   PetscScalar    *a;
780   PetscInt       p;
781   PetscErrorCode ierr;
782 
783   PetscFunctionBegin;
784   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
785   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
786   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
787   ierr = SNESSetOptionsPrefix(snes, "hex_interp_");CHKERRQ(ierr);
788   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
789   ierr = VecSetSizes(r, 3, 3);CHKERRQ(ierr);
790   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
791   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
792   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
793   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
794   ierr = MatSetSizes(J, 3, 3, 3, 3);CHKERRQ(ierr);
795   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
796   ierr = MatSetUp(J);CHKERRQ(ierr);
797   ierr = SNESSetFunction(snes, r, HexMap_Private, NULL);CHKERRQ(ierr);
798   ierr = SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);CHKERRQ(ierr);
799   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
800   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
801   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
802   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
803 
804   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
805   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
806   for (p = 0; p < ctx->n; ++p) {
807     PetscScalar *x = NULL, *vertices = NULL;
808     PetscScalar *xi;
809     PetscReal    xir[3];
810     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
811 
812     /* Can make this do all points at once */
813     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
814     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %D should be %d", coordSize, 8*3);
815     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
816     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %D should be %D", xSize, 8*ctx->dof);
817     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
818     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
819     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
820     xi[0]  = coords[p*ctx->dim+0];
821     xi[1]  = coords[p*ctx->dim+1];
822     xi[2]  = coords[p*ctx->dim+2];
823     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
824     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
825     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
826     xir[0] = PetscRealPart(xi[0]);
827     xir[1] = PetscRealPart(xi[1]);
828     xir[2] = PetscRealPart(xi[2]);
829     for (comp = 0; comp < ctx->dof; ++comp) {
830       a[p*ctx->dof+comp] =
831         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
832         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
833         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
834         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
835         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
836         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
837         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
838         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
839     }
840     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
841     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
842     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
843   }
844   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
845   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
846 
847   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
848   ierr = VecDestroy(&r);CHKERRQ(ierr);
849   ierr = VecDestroy(&ref);CHKERRQ(ierr);
850   ierr = VecDestroy(&real);CHKERRQ(ierr);
851   ierr = MatDestroy(&J);CHKERRQ(ierr);
852   PetscFunctionReturn(0);
853 }
854 
855 /*@C
856   DMInterpolationEvaluate - Using the input from dm and x, calculates interpolated field values at the interpolation points.
857 
858   Input Parameters:
859 + ctx - The DMInterpolationInfo context
860 . dm  - The DM
861 - x   - The local vector containing the field to be interpolated
862 
863   Output Parameters:
864 . v   - The vector containing the interpolated values
865 
866   Note: A suitable v can be obtained using DMInterpolationGetVector().
867 
868   Level: beginner
869 
870 .seealso: DMInterpolationGetVector(), DMInterpolationAddPoints(), DMInterpolationCreate()
871 @*/
872 PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
873 {
874   PetscInt       dim, coneSize, n;
875   PetscErrorCode ierr;
876 
877   PetscFunctionBegin;
878   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
879   PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
880   PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
881   ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
882   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);
883   if (n) {
884     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
885     ierr = DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);CHKERRQ(ierr);
886     if (dim == 2) {
887       if (coneSize == 3) {
888         ierr = DMInterpolate_Triangle_Private(ctx, dm, x, v);CHKERRQ(ierr);
889       } else if (coneSize == 4) {
890         ierr = DMInterpolate_Quad_Private(ctx, dm, x, v);CHKERRQ(ierr);
891       } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %D for point interpolation", dim);
892     } else if (dim == 3) {
893       if (coneSize == 4) {
894         ierr = DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);CHKERRQ(ierr);
895       } else {
896         ierr = DMInterpolate_Hex_Private(ctx, dm, x, v);CHKERRQ(ierr);
897       }
898     } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %D for point interpolation", dim);
899   }
900   PetscFunctionReturn(0);
901 }
902 
903 /*@C
904   DMInterpolationDestroy - Destroys a DMInterpolationInfo context
905 
906   Collective on ctx
907 
908   Input Parameter:
909 . ctx - the context
910 
911   Level: beginner
912 
913 .seealso: DMInterpolationEvaluate(), DMInterpolationAddPoints(), DMInterpolationCreate()
914 @*/
915 PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
916 {
917   PetscErrorCode ierr;
918 
919   PetscFunctionBegin;
920   PetscValidPointer(ctx, 2);
921   ierr = VecDestroy(&(*ctx)->coords);CHKERRQ(ierr);
922   ierr = PetscFree((*ctx)->points);CHKERRQ(ierr);
923   ierr = PetscFree((*ctx)->cells);CHKERRQ(ierr);
924   ierr = PetscFree(*ctx);CHKERRQ(ierr);
925   *ctx = NULL;
926   PetscFunctionReturn(0);
927 }
928 
929 /*@C
930   SNESMonitorFields - Monitors the residual for each field separately
931 
932   Collective on SNES
933 
934   Input Parameters:
935 + snes   - the SNES context
936 . its    - iteration number
937 . fgnorm - 2-norm of residual
938 - vf  - PetscViewerAndFormat of type ASCII
939 
940   Notes:
941   This routine prints the residual norm at each iteration.
942 
943   Level: intermediate
944 
945 .seealso: SNESMonitorSet(), SNESMonitorDefault()
946 @*/
947 PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
948 {
949   PetscViewer        viewer = vf->viewer;
950   Vec                res;
951   DM                 dm;
952   PetscSection       s;
953   const PetscScalar *r;
954   PetscReal         *lnorms, *norms;
955   PetscInt           numFields, f, pStart, pEnd, p;
956   PetscErrorCode     ierr;
957 
958   PetscFunctionBegin;
959   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
960   ierr = SNESGetFunction(snes, &res, 0, 0);CHKERRQ(ierr);
961   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
962   ierr = DMGetLocalSection(dm, &s);CHKERRQ(ierr);
963   ierr = PetscSectionGetNumFields(s, &numFields);CHKERRQ(ierr);
964   ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
965   ierr = PetscCalloc2(numFields, &lnorms, numFields, &norms);CHKERRQ(ierr);
966   ierr = VecGetArrayRead(res, &r);CHKERRQ(ierr);
967   for (p = pStart; p < pEnd; ++p) {
968     for (f = 0; f < numFields; ++f) {
969       PetscInt fdof, foff, d;
970 
971       ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
972       ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
973       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
974     }
975   }
976   ierr = VecRestoreArrayRead(res, &r);CHKERRQ(ierr);
977   ierr = MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
978   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
979   ierr = PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
980   ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
981   for (f = 0; f < numFields; ++f) {
982     if (f > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
983     ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));CHKERRQ(ierr);
984   }
985   ierr = PetscViewerASCIIPrintf(viewer, "]\n");CHKERRQ(ierr);
986   ierr = PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
987   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
988   ierr = PetscFree2(lnorms, norms);CHKERRQ(ierr);
989   PetscFunctionReturn(0);
990 }
991 
992 /********************* Residual Computation **************************/
993 
994 
995 /*@
996   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
997 
998   Input Parameter:
999 . dm - The DM
1000 
1001   Output Parameters:
1002 + facegeom - The values precomputed from face geometry
1003 . cellgeom - The values precomputed from cell geometry
1004 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
1005 
1006   Level: developer
1007 
1008 .seealso: DMPlexTSSetRHSFunctionLocal()
1009 @*/
1010 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
1011 {
1012   DM             plex;
1013   PetscErrorCode ierr;
1014 
1015   PetscFunctionBegin;
1016   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
1017   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
1018   ierr = DMPlexGetDataFVM(plex, NULL, cellgeom, facegeom, NULL);CHKERRQ(ierr);
1019   if (minRadius) {ierr = DMPlexGetMinRadius(plex, minRadius);CHKERRQ(ierr);}
1020   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1021   PetscFunctionReturn(0);
1022 }
1023 
1024 /*@
1025   DMPlexSNESGetGradientDM - Return gradient data layout
1026 
1027   Input Parameters:
1028 + dm - The DM
1029 - fv - The PetscFV
1030 
1031   Output Parameter:
1032 . dmGrad - The layout for gradient values
1033 
1034   Level: developer
1035 
1036 .seealso: DMPlexSNESGetGeometryFVM()
1037 @*/
1038 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
1039 {
1040   DM             plex;
1041   PetscBool      computeGradients;
1042   PetscErrorCode ierr;
1043 
1044   PetscFunctionBegin;
1045   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
1046   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
1047   PetscValidPointer(dmGrad,3);
1048   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
1049   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
1050   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
1051   ierr = DMPlexGetDataFVM(plex, fv, NULL, NULL, dmGrad);CHKERRQ(ierr);
1052   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1053   PetscFunctionReturn(0);
1054 }
1055 
1056 static PetscErrorCode DMPlexComputeBdResidual_Single_Internal(DM dm, PetscReal t, DMLabel label, PetscInt numValues, const PetscInt values[], PetscInt field, Vec locX, Vec locX_t, Vec locF, DMField coordField, IS facetIS)
1057 {
1058   DM_Plex         *mesh = (DM_Plex *) dm->data;
1059   DM               plex = NULL, plexA = NULL;
1060   PetscDS          prob, probAux = NULL;
1061   PetscSection     section, sectionAux = NULL;
1062   Vec              locA = NULL;
1063   PetscScalar     *u = NULL, *u_t = NULL, *a = NULL, *elemVec = NULL;
1064   PetscInt         v;
1065   PetscInt         totDim, totDimAux = 0;
1066   PetscErrorCode   ierr;
1067 
1068   PetscFunctionBegin;
1069   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
1070   ierr = DMGetLocalSection(dm, &section);CHKERRQ(ierr);
1071   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1072   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1073   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1074   if (locA) {
1075     DM dmAux;
1076 
1077     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1078     ierr = DMConvert(dmAux, DMPLEX, &plexA);CHKERRQ(ierr);
1079     ierr = DMGetDS(plexA, &probAux);CHKERRQ(ierr);
1080     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1081     ierr = DMGetLocalSection(plexA, &sectionAux);CHKERRQ(ierr);
1082   }
1083   for (v = 0; v < numValues; ++v) {
1084     PetscFEGeom    *fgeom;
1085     PetscInt        maxDegree;
1086     PetscQuadrature qGeom = NULL;
1087     IS              pointIS;
1088     const PetscInt *points;
1089     PetscInt        numFaces, face, Nq;
1090 
1091     ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1092     if (!pointIS) continue; /* No points with that id on this process */
1093     {
1094       IS isectIS;
1095 
1096       /* TODO: Special cases of ISIntersect where it is quick to check a priori if one is a superset of the other */
1097       ierr = ISIntersect_Caching_Internal(facetIS,pointIS,&isectIS);CHKERRQ(ierr);
1098       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1099       pointIS = isectIS;
1100     }
1101     ierr = ISGetLocalSize(pointIS,&numFaces);CHKERRQ(ierr);
1102     ierr = ISGetIndices(pointIS,&points);CHKERRQ(ierr);
1103     ierr = PetscMalloc4(numFaces*totDim, &u, locX_t ? numFaces*totDim : 0, &u_t, numFaces*totDim, &elemVec, locA ? numFaces*totDimAux : 0, &a);CHKERRQ(ierr);
1104     ierr = DMFieldGetDegree(coordField,pointIS,NULL,&maxDegree);CHKERRQ(ierr);
1105     if (maxDegree <= 1) {
1106       ierr = DMFieldCreateDefaultQuadrature(coordField,pointIS,&qGeom);CHKERRQ(ierr);
1107     }
1108     if (!qGeom) {
1109       PetscFE fe;
1110 
1111       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1112       ierr = PetscFEGetFaceQuadrature(fe, &qGeom);CHKERRQ(ierr);
1113       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
1114     }
1115     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1116     ierr = DMSNESGetFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
1117     for (face = 0; face < numFaces; ++face) {
1118       const PetscInt point = points[face], *support, *cone;
1119       PetscScalar   *x     = NULL;
1120       PetscInt       i, coneSize, faceLoc;
1121 
1122       ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
1123       ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
1124       ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
1125       for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
1126       if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %D in cone of support[0] %D", point, support[0]);
1127       fgeom->face[face][0] = faceLoc;
1128       ierr = DMPlexVecGetClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1129       for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
1130       ierr = DMPlexVecRestoreClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1131       if (locX_t) {
1132         ierr = DMPlexVecGetClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1133         for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
1134         ierr = DMPlexVecRestoreClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1135       }
1136       if (locA) {
1137         PetscInt subp;
1138 
1139         ierr = DMPlexGetAuxiliaryPoint(plex, plexA, support[0], &subp);CHKERRQ(ierr);
1140         ierr = DMPlexVecGetClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
1141         for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
1142         ierr = DMPlexVecRestoreClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
1143       }
1144     }
1145     ierr = PetscArrayzero(elemVec, numFaces*totDim);CHKERRQ(ierr);
1146     {
1147       PetscFE         fe;
1148       PetscInt        Nb;
1149       PetscFEGeom     *chunkGeom = NULL;
1150       /* Conforming batches */
1151       PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1152       /* Remainder */
1153       PetscInt        Nr, offset;
1154 
1155       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1156       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1157       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1158       /* TODO: documentation is unclear about what is going on with these numbers: how should Nb / Nq factor in ? */
1159       blockSize = Nb;
1160       batchSize = numBlocks * blockSize;
1161       ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1162       numChunks = numFaces / (numBatches*batchSize);
1163       Ne        = numChunks*numBatches*batchSize;
1164       Nr        = numFaces % (numBatches*batchSize);
1165       offset    = numFaces - Nr;
1166       ierr = PetscFEGeomGetChunk(fgeom,0,offset,&chunkGeom);CHKERRQ(ierr);
1167       ierr = PetscFEIntegrateBdResidual(prob, field, Ne, chunkGeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1168       ierr = PetscFEGeomRestoreChunk(fgeom, 0, offset, &chunkGeom);CHKERRQ(ierr);
1169       ierr = PetscFEGeomGetChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
1170       ierr = PetscFEIntegrateBdResidual(prob, field, Nr, chunkGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, a ? &a[offset*totDimAux] : NULL, t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1171       ierr = PetscFEGeomRestoreChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
1172     }
1173     for (face = 0; face < numFaces; ++face) {
1174       const PetscInt point = points[face], *support;
1175 
1176       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDim, &elemVec[face*totDim]);CHKERRQ(ierr);}
1177       ierr = DMPlexGetSupport(plex, point, &support);CHKERRQ(ierr);
1178       ierr = DMPlexVecSetClosure(plex, NULL, locF, support[0], &elemVec[face*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1179     }
1180     ierr = DMSNESRestoreFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
1181     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
1182     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1183     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1184     ierr = PetscFree4(u, u_t, elemVec, a);CHKERRQ(ierr);
1185   }
1186   if (plex)  {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
1187   if (plexA) {ierr = DMDestroy(&plexA);CHKERRQ(ierr);}
1188   PetscFunctionReturn(0);
1189 }
1190 
1191 PetscErrorCode DMPlexComputeBdResidualSingle(DM dm, PetscReal t, DMLabel label, PetscInt numValues, const PetscInt values[], PetscInt field, Vec locX, Vec locX_t, Vec locF)
1192 {
1193   DMField        coordField;
1194   DMLabel        depthLabel;
1195   IS             facetIS;
1196   PetscInt       dim;
1197   PetscErrorCode ierr;
1198 
1199   PetscFunctionBegin;
1200   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1201   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1202   ierr = DMLabelGetStratumIS(depthLabel, dim-1, &facetIS);CHKERRQ(ierr);
1203   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1204   ierr = DMPlexComputeBdResidual_Single_Internal(dm, t, label, numValues, values, field, locX, locX_t, locF, coordField, facetIS);CHKERRQ(ierr);
1205   ierr = ISDestroy(&facetIS);CHKERRQ(ierr);
1206   PetscFunctionReturn(0);
1207 }
1208 
1209 PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1210 {
1211   PetscDS        prob;
1212   PetscInt       numBd, bd;
1213   DMField        coordField = NULL;
1214   IS             facetIS    = NULL;
1215   DMLabel        depthLabel;
1216   PetscInt       dim;
1217   PetscErrorCode ierr;
1218 
1219   PetscFunctionBegin;
1220   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1221   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1222   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1223   ierr = DMLabelGetStratumIS(depthLabel,dim - 1,&facetIS);CHKERRQ(ierr);
1224   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
1225   for (bd = 0; bd < numBd; ++bd) {
1226     DMBoundaryConditionType type;
1227     const char             *bdLabel;
1228     DMLabel                 label;
1229     const PetscInt         *values;
1230     PetscInt                field, numValues;
1231     PetscObject             obj;
1232     PetscClassId            id;
1233 
1234     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1235     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
1236     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1237     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
1238     if (!facetIS) {
1239       DMLabel  depthLabel;
1240       PetscInt dim;
1241 
1242       ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1243       ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1244       ierr = DMLabelGetStratumIS(depthLabel, dim - 1, &facetIS);CHKERRQ(ierr);
1245     }
1246     ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1247     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1248     ierr = DMPlexComputeBdResidual_Single_Internal(dm, t, label, numValues, values, field, locX, locX_t, locF, coordField, facetIS);CHKERRQ(ierr);
1249   }
1250   ierr = ISDestroy(&facetIS);CHKERRQ(ierr);
1251   PetscFunctionReturn(0);
1252 }
1253 
1254 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, IS cellIS, PetscReal time, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1255 {
1256   DM_Plex         *mesh       = (DM_Plex *) dm->data;
1257   const char      *name       = "Residual";
1258   DM               dmAux      = NULL;
1259   DM               dmGrad     = NULL;
1260   DMLabel          ghostLabel = NULL;
1261   PetscDS          prob       = NULL;
1262   PetscDS          probAux    = NULL;
1263   PetscSection     section    = NULL;
1264   PetscBool        useFEM     = PETSC_FALSE;
1265   PetscBool        useFVM     = PETSC_FALSE;
1266   PetscBool        isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
1267   PetscFV          fvm        = NULL;
1268   PetscFVCellGeom *cgeomFVM   = NULL;
1269   PetscFVFaceGeom *fgeomFVM   = NULL;
1270   DMField          coordField = NULL;
1271   Vec              locA, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1272   PetscScalar     *u = NULL, *u_t, *a, *uL, *uR;
1273   IS               chunkIS;
1274   const PetscInt  *cells;
1275   PetscInt         cStart, cEnd, numCells;
1276   PetscInt         Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
1277   PetscInt         maxDegree = PETSC_MAX_INT;
1278   PetscQuadrature  affineQuad = NULL, *quads = NULL;
1279   PetscFEGeom     *affineGeom = NULL, **geoms = NULL;
1280   PetscErrorCode   ierr;
1281 
1282   PetscFunctionBegin;
1283   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1284   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1285   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
1286   /* FEM+FVM */
1287   ierr = ISGetPointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
1288   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1289   /* 1: Get sizes from dm and dmAux */
1290   ierr = DMGetLocalSection(dm, &section);CHKERRQ(ierr);
1291   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1292   ierr = DMGetCellDS(dm, cStart, &prob);CHKERRQ(ierr);
1293   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1294   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1295   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1296   if (locA) {
1297     PetscInt subcell;
1298     ierr = DMPlexGetAuxiliaryPoint(dm, dmAux, cStart, &subcell);CHKERRQ(ierr);
1299     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1300     ierr = DMGetCellDS(dmAux, subcell, &probAux);CHKERRQ(ierr);
1301     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1302   }
1303   /* 2: Get geometric data */
1304   for (f = 0; f < Nf; ++f) {
1305     PetscObject  obj;
1306     PetscClassId id;
1307     PetscBool    fimp;
1308 
1309     ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1310     if (isImplicit != fimp) continue;
1311     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1312     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1313     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1314     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1315   }
1316   if (useFEM) {
1317     ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1318     ierr = DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);CHKERRQ(ierr);
1319     if (maxDegree <= 1) {
1320       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&affineQuad);CHKERRQ(ierr);
1321       if (affineQuad) {
1322         ierr = DMSNESGetFEGeom(coordField,cellIS,affineQuad,PETSC_FALSE,&affineGeom);CHKERRQ(ierr);
1323       }
1324     } else {
1325       ierr = PetscCalloc2(Nf,&quads,Nf,&geoms);CHKERRQ(ierr);
1326       for (f = 0; f < Nf; ++f) {
1327         PetscObject  obj;
1328         PetscClassId id;
1329         PetscBool    fimp;
1330 
1331         ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1332         if (isImplicit != fimp) continue;
1333         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1334         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1335         if (id == PETSCFE_CLASSID) {
1336           PetscFE fe = (PetscFE) obj;
1337 
1338           ierr = PetscFEGetQuadrature(fe, &quads[f]);CHKERRQ(ierr);
1339           ierr = PetscObjectReference((PetscObject)quads[f]);CHKERRQ(ierr);
1340           ierr = DMSNESGetFEGeom(coordField,cellIS,quads[f],PETSC_FALSE,&geoms[f]);CHKERRQ(ierr);
1341         }
1342       }
1343     }
1344   }
1345   if (useFVM) {
1346     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1347     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1348     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1349     /* Reconstruct and limit cell gradients */
1350     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1351     if (dmGrad) {
1352       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1353       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1354       ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1355       /* Communicate gradient values */
1356       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1357       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1358       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1359       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1360     }
1361     /* Handle non-essential (e.g. outflow) boundary values */
1362     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1363   }
1364   /* Loop over chunks */
1365   if (useFEM) {ierr = ISCreate(PETSC_COMM_SELF, &chunkIS);CHKERRQ(ierr);}
1366   numCells      = cEnd - cStart;
1367   numChunks     = 1;
1368   cellChunkSize = numCells/numChunks;
1369   faceChunkSize = (fEnd - fStart)/numChunks;
1370   numChunks     = PetscMin(1,numCells);
1371   for (chunk = 0; chunk < numChunks; ++chunk) {
1372     PetscScalar     *elemVec, *fluxL, *fluxR;
1373     PetscReal       *vol;
1374     PetscFVFaceGeom *fgeom;
1375     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, c;
1376     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = 0, face;
1377 
1378     /* Extract field coefficients */
1379     if (useFEM) {
1380       ierr = ISGetPointSubrange(chunkIS, cS, cE, cells);CHKERRQ(ierr);
1381       ierr = DMPlexGetCellFields(dm, chunkIS, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1382       ierr = DMGetWorkArray(dm, numCells*totDim, MPIU_SCALAR, &elemVec);CHKERRQ(ierr);
1383       ierr = PetscArrayzero(elemVec, numCells*totDim);CHKERRQ(ierr);
1384     }
1385     if (useFVM) {
1386       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1387       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1388       ierr = DMGetWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxL);CHKERRQ(ierr);
1389       ierr = DMGetWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxR);CHKERRQ(ierr);
1390       ierr = PetscArrayzero(fluxL, numFaces*totDim);CHKERRQ(ierr);
1391       ierr = PetscArrayzero(fluxR, numFaces*totDim);CHKERRQ(ierr);
1392     }
1393     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1394     /* Loop over fields */
1395     for (f = 0; f < Nf; ++f) {
1396       PetscObject  obj;
1397       PetscClassId id;
1398       PetscBool    fimp;
1399       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1400 
1401       ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1402       if (isImplicit != fimp) continue;
1403       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1404       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1405       if (id == PETSCFE_CLASSID) {
1406         PetscFE         fe = (PetscFE) obj;
1407         PetscFEGeom    *geom = affineGeom ? affineGeom : geoms[f];
1408         PetscFEGeom    *chunkGeom = NULL;
1409         PetscQuadrature quad = affineQuad ? affineQuad : quads[f];
1410         PetscInt        Nq, Nb;
1411 
1412         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1413         ierr = PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1414         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1415         blockSize = Nb;
1416         batchSize = numBlocks * blockSize;
1417         ierr      = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1418         numChunks = numCells / (numBatches*batchSize);
1419         Ne        = numChunks*numBatches*batchSize;
1420         Nr        = numCells % (numBatches*batchSize);
1421         offset    = numCells - Nr;
1422         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1423         /*   For FV, I think we use a P0 basis and the cell coefficients (for subdivided cells, we can tweak the basis tabulation to be the indicator function) */
1424         ierr = PetscFEGeomGetChunk(geom,0,offset,&chunkGeom);CHKERRQ(ierr);
1425         ierr = PetscFEIntegrateResidual(prob, f, Ne, chunkGeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1426         ierr = PetscFEGeomGetChunk(geom,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1427         ierr = PetscFEIntegrateResidual(prob, f, Nr, chunkGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1428         ierr = PetscFEGeomRestoreChunk(geom,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1429       } else if (id == PETSCFV_CLASSID) {
1430         PetscFV fv = (PetscFV) obj;
1431 
1432         Ne = numFaces;
1433         /* Riemann solve over faces (need fields at face centroids) */
1434         /*   We need to evaluate FE fields at those coordinates */
1435         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1436       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %D", f);
1437     }
1438     /* Loop over domain */
1439     if (useFEM) {
1440       /* Add elemVec to locX */
1441       for (c = cS; c < cE; ++c) {
1442         const PetscInt cell = cells ? cells[c] : c;
1443         const PetscInt cind = c - cStart;
1444 
1445         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cind*totDim]);CHKERRQ(ierr);}
1446         if (ghostLabel) {
1447           PetscInt ghostVal;
1448 
1449           ierr = DMLabelGetValue(ghostLabel,cell,&ghostVal);CHKERRQ(ierr);
1450           if (ghostVal > 0) continue;
1451         }
1452         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cind*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1453       }
1454     }
1455     if (useFVM) {
1456       PetscScalar *fa;
1457       PetscInt     iface;
1458 
1459       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1460       for (f = 0; f < Nf; ++f) {
1461         PetscFV      fv;
1462         PetscObject  obj;
1463         PetscClassId id;
1464         PetscInt     foff, pdim;
1465 
1466         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1467         ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1468         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1469         if (id != PETSCFV_CLASSID) continue;
1470         fv   = (PetscFV) obj;
1471         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1472         /* Accumulate fluxes to cells */
1473         for (face = fS, iface = 0; face < fE; ++face) {
1474           const PetscInt *scells;
1475           PetscScalar    *fL = NULL, *fR = NULL;
1476           PetscInt        ghost, d, nsupp, nchild;
1477 
1478           ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1479           ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1480           ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1481           if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1482           ierr = DMPlexGetSupport(dm, face, &scells);CHKERRQ(ierr);
1483           ierr = DMLabelGetValue(ghostLabel,scells[0],&ghost);CHKERRQ(ierr);
1484           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, scells[0], f, fa, &fL);CHKERRQ(ierr);}
1485           ierr = DMLabelGetValue(ghostLabel,scells[1],&ghost);CHKERRQ(ierr);
1486           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, scells[1], f, fa, &fR);CHKERRQ(ierr);}
1487           for (d = 0; d < pdim; ++d) {
1488             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
1489             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
1490           }
1491           ++iface;
1492         }
1493       }
1494       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1495     }
1496     /* Handle time derivative */
1497     if (locX_t) {
1498       PetscScalar *x_t, *fa;
1499 
1500       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1501       ierr = VecGetArray(locX_t, &x_t);CHKERRQ(ierr);
1502       for (f = 0; f < Nf; ++f) {
1503         PetscFV      fv;
1504         PetscObject  obj;
1505         PetscClassId id;
1506         PetscInt     pdim, d;
1507 
1508         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1509         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1510         if (id != PETSCFV_CLASSID) continue;
1511         fv   = (PetscFV) obj;
1512         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1513         for (c = cS; c < cE; ++c) {
1514           const PetscInt cell = cells ? cells[c] : c;
1515           PetscScalar   *u_t, *r;
1516 
1517           if (ghostLabel) {
1518             PetscInt ghostVal;
1519 
1520             ierr = DMLabelGetValue(ghostLabel, cell, &ghostVal);CHKERRQ(ierr);
1521             if (ghostVal > 0) continue;
1522           }
1523           ierr = DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);CHKERRQ(ierr);
1524           ierr = DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);CHKERRQ(ierr);
1525           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
1526         }
1527       }
1528       ierr = VecRestoreArray(locX_t, &x_t);CHKERRQ(ierr);
1529       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1530     }
1531     if (useFEM) {
1532       ierr = DMPlexRestoreCellFields(dm, chunkIS, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1533       ierr = DMRestoreWorkArray(dm, numCells*totDim, MPIU_SCALAR, &elemVec);CHKERRQ(ierr);
1534     }
1535     if (useFVM) {
1536       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1537       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1538       ierr = DMRestoreWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxL);CHKERRQ(ierr);
1539       ierr = DMRestoreWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxR);CHKERRQ(ierr);
1540       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1541     }
1542   }
1543   if (useFEM) {ierr = ISDestroy(&chunkIS);CHKERRQ(ierr);}
1544   ierr = ISRestorePointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
1545 
1546   if (useFEM) {
1547     ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, t, locF, user);CHKERRQ(ierr);
1548 
1549     if (maxDegree <= 1) {
1550       ierr = DMSNESRestoreFEGeom(coordField,cellIS,affineQuad,PETSC_FALSE,&affineGeom);CHKERRQ(ierr);
1551       ierr = PetscQuadratureDestroy(&affineQuad);CHKERRQ(ierr);
1552     } else {
1553       for (f = 0; f < Nf; ++f) {
1554         ierr = DMSNESRestoreFEGeom(coordField,cellIS,quads[f],PETSC_FALSE,&geoms[f]);CHKERRQ(ierr);
1555         ierr = PetscQuadratureDestroy(&quads[f]);CHKERRQ(ierr);
1556       }
1557       ierr = PetscFree2(quads,geoms);CHKERRQ(ierr);
1558     }
1559   }
1560 
1561   /* FEM */
1562   /* 1: Get sizes from dm and dmAux */
1563   /* 2: Get geometric data */
1564   /* 3: Handle boundary values */
1565   /* 4: Loop over domain */
1566   /*   Extract coefficients */
1567   /* Loop over fields */
1568   /*   Set tiling for FE*/
1569   /*   Integrate FE residual to get elemVec */
1570   /*     Loop over subdomain */
1571   /*       Loop over quad points */
1572   /*         Transform coords to real space */
1573   /*         Evaluate field and aux fields at point */
1574   /*         Evaluate residual at point */
1575   /*         Transform residual to real space */
1576   /*       Add residual to elemVec */
1577   /* Loop over domain */
1578   /*   Add elemVec to locX */
1579 
1580   /* FVM */
1581   /* Get geometric data */
1582   /* If using gradients */
1583   /*   Compute gradient data */
1584   /*   Loop over domain faces */
1585   /*     Count computational faces */
1586   /*     Reconstruct cell gradient */
1587   /*   Loop over domain cells */
1588   /*     Limit cell gradients */
1589   /* Handle boundary values */
1590   /* Loop over domain faces */
1591   /*   Read out field, centroid, normal, volume for each side of face */
1592   /* Riemann solve over faces */
1593   /* Loop over domain faces */
1594   /*   Accumulate fluxes to cells */
1595   /* TODO Change printFEM to printDisc here */
1596   if (mesh->printFEM) {
1597     Vec         locFbc;
1598     PetscInt    pStart, pEnd, p, maxDof;
1599     PetscScalar *zeroes;
1600 
1601     ierr = VecDuplicate(locF,&locFbc);CHKERRQ(ierr);
1602     ierr = VecCopy(locF,locFbc);CHKERRQ(ierr);
1603     ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
1604     ierr = PetscSectionGetMaxDof(section,&maxDof);CHKERRQ(ierr);
1605     ierr = PetscCalloc1(maxDof,&zeroes);CHKERRQ(ierr);
1606     for (p = pStart; p < pEnd; p++) {
1607       ierr = VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);CHKERRQ(ierr);
1608     }
1609     ierr = PetscFree(zeroes);CHKERRQ(ierr);
1610     ierr = DMPrintLocalVec(dm, name, mesh->printTol, locFbc);CHKERRQ(ierr);
1611     ierr = VecDestroy(&locFbc);CHKERRQ(ierr);
1612   }
1613   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1614   PetscFunctionReturn(0);
1615 }
1616 
1617 /*@
1618   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1619 
1620   Input Parameters:
1621 + dm - The mesh
1622 . X  - Local solution
1623 - user - The user context
1624 
1625   Output Parameter:
1626 . F  - Local output vector
1627 
1628   Level: developer
1629 
1630 .seealso: DMPlexComputeJacobianAction()
1631 @*/
1632 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
1633 {
1634   DM             plex;
1635   IS             cellIS;
1636   PetscInt       depth;
1637   PetscErrorCode ierr;
1638 
1639   PetscFunctionBegin;
1640   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
1641   ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
1642   ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
1643   if (!cellIS) {
1644     ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);
1645   }
1646   ierr = DMPlexComputeResidual_Internal(plex, cellIS, PETSC_MIN_REAL, X, NULL, 0.0, F, user);CHKERRQ(ierr);
1647   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
1648   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1649   PetscFunctionReturn(0);
1650 }
1651 
1652 /*@
1653   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X
1654 
1655   Input Parameters:
1656 + dm - The mesh
1657 - user - The user context
1658 
1659   Output Parameter:
1660 . X  - Local solution
1661 
1662   Level: developer
1663 
1664 .seealso: DMPlexComputeJacobianAction()
1665 @*/
1666 PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
1667 {
1668   DM             plex;
1669   PetscErrorCode ierr;
1670 
1671   PetscFunctionBegin;
1672   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
1673   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);CHKERRQ(ierr);
1674   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1675   PetscFunctionReturn(0);
1676 }
1677 
1678 PetscErrorCode DMPlexComputeBdJacobian_Single_Internal(DM dm, PetscReal t, DMLabel label, PetscInt numValues, const PetscInt values[], PetscInt fieldI, Vec locX, Vec locX_t, PetscReal X_tShift, Mat Jac, Mat JacP, DMField coordField, IS facetIS)
1679 {
1680   DM_Plex       *mesh = (DM_Plex *) dm->data;
1681   DM             plex = NULL, plexA = NULL, tdm;
1682   PetscDS        prob, probAux = NULL;
1683   PetscSection   section, sectionAux = NULL;
1684   PetscSection   globalSection, subSection = NULL;
1685   Vec            locA = NULL, tv;
1686   PetscScalar   *u = NULL, *u_t = NULL, *a = NULL, *elemMat = NULL;
1687   PetscInt       v;
1688   PetscInt       Nf, totDim, totDimAux = 0;
1689   PetscBool      isMatISP, transform;
1690   PetscErrorCode ierr;
1691 
1692   PetscFunctionBegin;
1693   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
1694   ierr = DMHasBasisTransform(dm, &transform);CHKERRQ(ierr);
1695   ierr = DMGetBasisTransformDM_Internal(dm, &tdm);CHKERRQ(ierr);
1696   ierr = DMGetBasisTransformVec_Internal(dm, &tv);CHKERRQ(ierr);
1697   ierr = DMGetLocalSection(dm, &section);CHKERRQ(ierr);
1698   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1699   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1700   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1701   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1702   if (locA) {
1703     DM dmAux;
1704 
1705     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1706     ierr = DMConvert(dmAux, DMPLEX, &plexA);CHKERRQ(ierr);
1707     ierr = DMGetDS(plexA, &probAux);CHKERRQ(ierr);
1708     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1709     ierr = DMGetLocalSection(plexA, &sectionAux);CHKERRQ(ierr);
1710   }
1711 
1712   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
1713   ierr = DMGetGlobalSection(dm, &globalSection);CHKERRQ(ierr);
1714   if (isMatISP) {ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);}
1715   for (v = 0; v < numValues; ++v) {
1716     PetscFEGeom    *fgeom;
1717     PetscInt        maxDegree;
1718     PetscQuadrature qGeom = NULL;
1719     IS              pointIS;
1720     const PetscInt *points;
1721     PetscInt        numFaces, face, Nq;
1722 
1723     ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1724     if (!pointIS) continue; /* No points with that id on this process */
1725     {
1726       IS isectIS;
1727 
1728       /* TODO: Special cases of ISIntersect where it is quick to check a prior if one is a superset of the other */
1729       ierr = ISIntersect_Caching_Internal(facetIS,pointIS,&isectIS);CHKERRQ(ierr);
1730       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1731       pointIS = isectIS;
1732     }
1733     ierr = ISGetLocalSize(pointIS, &numFaces);CHKERRQ(ierr);
1734     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1735     ierr = PetscMalloc4(numFaces*totDim, &u, locX_t ? numFaces*totDim : 0, &u_t, numFaces*totDim*totDim, &elemMat, locA ? numFaces*totDimAux : 0, &a);CHKERRQ(ierr);
1736     ierr = DMFieldGetDegree(coordField,pointIS,NULL,&maxDegree);CHKERRQ(ierr);
1737     if (maxDegree <= 1) {
1738       ierr = DMFieldCreateDefaultQuadrature(coordField,pointIS,&qGeom);CHKERRQ(ierr);
1739     }
1740     if (!qGeom) {
1741       PetscFE fe;
1742 
1743       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
1744       ierr = PetscFEGetFaceQuadrature(fe, &qGeom);CHKERRQ(ierr);
1745       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
1746     }
1747     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1748     ierr = DMSNESGetFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
1749     for (face = 0; face < numFaces; ++face) {
1750       const PetscInt point = points[face], *support, *cone;
1751       PetscScalar   *x     = NULL;
1752       PetscInt       i, coneSize, faceLoc;
1753 
1754       ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
1755       ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
1756       ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
1757       for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
1758       if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %D in cone of support[0] %D", point, support[0]);
1759       fgeom->face[face][0] = faceLoc;
1760       ierr = DMPlexVecGetClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1761       for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
1762       ierr = DMPlexVecRestoreClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1763       if (locX_t) {
1764         ierr = DMPlexVecGetClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1765         for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
1766         ierr = DMPlexVecRestoreClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1767       }
1768       if (locA) {
1769         PetscInt subp;
1770         ierr = DMPlexGetSubpoint(plexA, support[0], &subp);CHKERRQ(ierr);
1771         ierr = DMPlexVecGetClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
1772         for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
1773         ierr = DMPlexVecRestoreClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
1774       }
1775     }
1776     ierr = PetscArrayzero(elemMat, numFaces*totDim*totDim);CHKERRQ(ierr);
1777     {
1778       PetscFE         fe;
1779       PetscInt        Nb;
1780       /* Conforming batches */
1781       PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1782       /* Remainder */
1783       PetscFEGeom    *chunkGeom = NULL;
1784       PetscInt        fieldJ, Nr, offset;
1785 
1786       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
1787       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1788       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1789       blockSize = Nb;
1790       batchSize = numBlocks * blockSize;
1791       ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1792       numChunks = numFaces / (numBatches*batchSize);
1793       Ne        = numChunks*numBatches*batchSize;
1794       Nr        = numFaces % (numBatches*batchSize);
1795       offset    = numFaces - Nr;
1796       ierr = PetscFEGeomGetChunk(fgeom,0,offset,&chunkGeom);CHKERRQ(ierr);
1797       for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1798         ierr = PetscFEIntegrateBdJacobian(prob, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
1799       }
1800       ierr = PetscFEGeomGetChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
1801       for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1802         ierr = PetscFEIntegrateBdJacobian(prob, fieldI, fieldJ, Nr, chunkGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, a ? &a[offset*totDimAux] : NULL, t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
1803       }
1804       ierr = PetscFEGeomRestoreChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
1805     }
1806     for (face = 0; face < numFaces; ++face) {
1807       const PetscInt point = points[face], *support;
1808 
1809       /* Transform to global basis before insertion in Jacobian */
1810       ierr = DMPlexGetSupport(plex, point, &support);CHKERRQ(ierr);
1811       if (transform) {ierr = DMPlexBasisTransformPointTensor_Internal(dm, tdm, tv, support[0], PETSC_TRUE, totDim, &elemMat[face*totDim*totDim]);CHKERRQ(ierr);}
1812       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDim, totDim, &elemMat[face*totDim*totDim]);CHKERRQ(ierr);}
1813       if (!isMatISP) {
1814         ierr = DMPlexMatSetClosure(plex, section, globalSection, JacP, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
1815       } else {
1816         Mat lJ;
1817 
1818         ierr = MatISGetLocalMat(JacP, &lJ);CHKERRQ(ierr);
1819         ierr = DMPlexMatSetClosure(plex, section, subSection, lJ, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
1820       }
1821     }
1822     ierr = DMSNESRestoreFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
1823     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
1824     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1825     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1826     ierr = PetscFree4(u, u_t, elemMat, a);CHKERRQ(ierr);
1827   }
1828   if (plex)  {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
1829   if (plexA) {ierr = DMDestroy(&plexA);CHKERRQ(ierr);}
1830   PetscFunctionReturn(0);
1831 }
1832 
1833 PetscErrorCode DMPlexComputeBdJacobianSingle(DM dm, PetscReal t, DMLabel label, PetscInt numValues, const PetscInt values[], PetscInt field, Vec locX, Vec locX_t, PetscReal X_tShift, Mat Jac, Mat JacP)
1834 {
1835   DMField        coordField;
1836   DMLabel        depthLabel;
1837   IS             facetIS;
1838   PetscInt       dim;
1839   PetscErrorCode ierr;
1840 
1841   PetscFunctionBegin;
1842   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1843   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1844   ierr = DMLabelGetStratumIS(depthLabel, dim-1, &facetIS);CHKERRQ(ierr);
1845   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1846   ierr = DMPlexComputeBdJacobian_Single_Internal(dm, t, label, numValues, values, field, locX, locX_t, X_tShift, Jac, JacP, coordField, facetIS);CHKERRQ(ierr);
1847   ierr = ISDestroy(&facetIS);CHKERRQ(ierr);
1848   PetscFunctionReturn(0);
1849 }
1850 
1851 PetscErrorCode DMPlexComputeBdJacobian_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, PetscReal X_tShift, Mat Jac, Mat JacP, void *user)
1852 {
1853   PetscDS          prob;
1854   PetscInt         dim, numBd, bd;
1855   DMLabel          depthLabel;
1856   DMField          coordField = NULL;
1857   IS               facetIS;
1858   PetscErrorCode   ierr;
1859 
1860   PetscFunctionBegin;
1861   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1862   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1863   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1864   ierr = DMLabelGetStratumIS(depthLabel, dim-1, &facetIS);CHKERRQ(ierr);
1865   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
1866   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1867   for (bd = 0; bd < numBd; ++bd) {
1868     DMBoundaryConditionType type;
1869     const char             *bdLabel;
1870     DMLabel                 label;
1871     const PetscInt         *values;
1872     PetscInt                fieldI, numValues;
1873     PetscObject             obj;
1874     PetscClassId            id;
1875 
1876     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &fieldI, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1877     ierr = PetscDSGetDiscretization(prob, fieldI, &obj);CHKERRQ(ierr);
1878     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1879     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
1880     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1881     ierr = DMPlexComputeBdJacobian_Single_Internal(dm, t, label, numValues, values, fieldI, locX, locX_t, X_tShift, Jac, JacP, coordField, facetIS);CHKERRQ(ierr);
1882   }
1883   ierr = ISDestroy(&facetIS);CHKERRQ(ierr);
1884   PetscFunctionReturn(0);
1885 }
1886 
1887 PetscErrorCode DMPlexComputeJacobian_Internal(DM dm, IS cellIS, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Mat Jac, Mat JacP,void *user)
1888 {
1889   DM_Plex        *mesh  = (DM_Plex *) dm->data;
1890   const char     *name  = "Jacobian";
1891   DM              dmAux, plex, tdm;
1892   Vec             A, tv;
1893   DMField         coordField;
1894   PetscDS         prob, probAux = NULL;
1895   PetscSection    section, globalSection, subSection, sectionAux;
1896   PetscScalar    *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
1897   const PetscInt *cells;
1898   PetscInt        Nf, fieldI, fieldJ;
1899   PetscInt        totDim, totDimAux, cStart, cEnd, numCells, c;
1900   PetscBool       isMatIS, isMatISP, hasJac, hasPrec, hasDyn, hasFV = PETSC_FALSE, transform;
1901   PetscErrorCode  ierr;
1902 
1903   PetscFunctionBegin;
1904   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1905   ierr = DMHasBasisTransform(dm, &transform);CHKERRQ(ierr);
1906   ierr = DMGetBasisTransformDM_Internal(dm, &tdm);CHKERRQ(ierr);
1907   ierr = DMGetBasisTransformVec_Internal(dm, &tv);CHKERRQ(ierr);
1908   ierr = DMGetLocalSection(dm, &section);CHKERRQ(ierr);
1909   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
1910   ierr = DMGetGlobalSection(dm, &globalSection);CHKERRQ(ierr);
1911   if (isMatISP) {ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);}
1912   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1913   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1914   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
1915   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
1916   /* user passed in the same matrix, avoid double contributions and
1917      only assemble the Jacobian */
1918   if (hasJac && Jac == JacP) hasPrec = PETSC_FALSE;
1919   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
1920   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
1921   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1922   ierr = ISGetLocalSize(cellIS, &numCells);CHKERRQ(ierr);
1923   ierr = ISGetPointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
1924   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1925   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1926   if (dmAux) {
1927     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
1928     ierr = DMGetLocalSection(plex, &sectionAux);CHKERRQ(ierr);
1929     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1930     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1931   }
1932   ierr = PetscMalloc5(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,hasJac ? numCells*totDim*totDim : 0,&elemMat,hasPrec ? numCells*totDim*totDim : 0, &elemMatP,hasDyn ? numCells*totDim*totDim : 0, &elemMatD);CHKERRQ(ierr);
1933   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1934   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1935   for (c = cStart; c < cEnd; ++c) {
1936     const PetscInt cell = cells ? cells[c] : c;
1937     const PetscInt cind = c - cStart;
1938     PetscScalar   *x = NULL,  *x_t = NULL;
1939     PetscInt       i;
1940 
1941     ierr = DMPlexVecGetClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
1942     for (i = 0; i < totDim; ++i) u[cind*totDim+i] = x[i];
1943     ierr = DMPlexVecRestoreClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
1944     if (X_t) {
1945       ierr = DMPlexVecGetClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
1946       for (i = 0; i < totDim; ++i) u_t[cind*totDim+i] = x_t[i];
1947       ierr = DMPlexVecRestoreClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
1948     }
1949     if (dmAux) {
1950       PetscInt subcell;
1951       ierr = DMPlexGetAuxiliaryPoint(dm, dmAux, cell, &subcell);CHKERRQ(ierr);
1952       ierr = DMPlexVecGetClosure(plex, sectionAux, A, subcell, NULL, &x);CHKERRQ(ierr);
1953       for (i = 0; i < totDimAux; ++i) a[cind*totDimAux+i] = x[i];
1954       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, subcell, NULL, &x);CHKERRQ(ierr);
1955     }
1956   }
1957   if (hasJac)  {ierr = PetscArrayzero(elemMat,  numCells*totDim*totDim);CHKERRQ(ierr);}
1958   if (hasPrec) {ierr = PetscArrayzero(elemMatP, numCells*totDim*totDim);CHKERRQ(ierr);}
1959   if (hasDyn)  {ierr = PetscArrayzero(elemMatD, numCells*totDim*totDim);CHKERRQ(ierr);}
1960   for (fieldI = 0; fieldI < Nf; ++fieldI) {
1961     PetscClassId    id;
1962     PetscFE         fe;
1963     PetscQuadrature qGeom = NULL;
1964     PetscInt        Nb;
1965     /* Conforming batches */
1966     PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1967     /* Remainder */
1968     PetscInt        Nr, offset, Nq;
1969     PetscInt        maxDegree;
1970     PetscFEGeom     *cgeomFEM, *chunkGeom = NULL, *remGeom = NULL;
1971 
1972     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
1973     ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
1974     if (id == PETSCFV_CLASSID) {hasFV = PETSC_TRUE; continue;}
1975     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1976     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1977     ierr = DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);CHKERRQ(ierr);
1978     if (maxDegree <= 1) {
1979       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);CHKERRQ(ierr);
1980     }
1981     if (!qGeom) {
1982       ierr = PetscFEGetQuadrature(fe,&qGeom);CHKERRQ(ierr);
1983       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
1984     }
1985     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1986     ierr = DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
1987     blockSize = Nb;
1988     batchSize = numBlocks * blockSize;
1989     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1990     numChunks = numCells / (numBatches*batchSize);
1991     Ne        = numChunks*numBatches*batchSize;
1992     Nr        = numCells % (numBatches*batchSize);
1993     offset    = numCells - Nr;
1994     ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
1995     ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
1996     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1997       if (hasJac) {
1998         ierr = PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
1999         ierr = PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2000       }
2001       if (hasPrec) {
2002         ierr = PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatP);CHKERRQ(ierr);
2003         ierr = PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMatP[offset*totDim*totDim]);CHKERRQ(ierr);
2004       }
2005       if (hasDyn) {
2006         ierr = PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2007         ierr = PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMatD[offset*totDim*totDim]);CHKERRQ(ierr);
2008       }
2009     }
2010     ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2011     ierr = PetscFEGeomRestoreChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2012     ierr = DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2013     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2014   }
2015   /*   Add contribution from X_t */
2016   if (hasDyn) {for (c = 0; c < numCells*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];}
2017   if (hasFV) {
2018     PetscClassId id;
2019     PetscFV      fv;
2020     PetscInt     offsetI, NcI, NbI = 1, fc, f;
2021 
2022     for (fieldI = 0; fieldI < Nf; ++fieldI) {
2023       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fv);CHKERRQ(ierr);
2024       ierr = PetscDSGetFieldOffset(prob, fieldI, &offsetI);CHKERRQ(ierr);
2025       ierr = PetscObjectGetClassId((PetscObject) fv, &id);CHKERRQ(ierr);
2026       if (id != PETSCFV_CLASSID) continue;
2027       /* Put in the identity */
2028       ierr = PetscFVGetNumComponents(fv, &NcI);CHKERRQ(ierr);
2029       for (c = cStart; c < cEnd; ++c) {
2030         const PetscInt cind    = c - cStart;
2031         const PetscInt eOffset = cind*totDim*totDim;
2032         for (fc = 0; fc < NcI; ++fc) {
2033           for (f = 0; f < NbI; ++f) {
2034             const PetscInt i = offsetI + f*NcI+fc;
2035             if (hasPrec) {
2036               if (hasJac) {elemMat[eOffset+i*totDim+i] = 1.0;}
2037               elemMatP[eOffset+i*totDim+i] = 1.0;
2038             } else {elemMat[eOffset+i*totDim+i] = 1.0;}
2039           }
2040         }
2041       }
2042     }
2043     /* No allocated space for FV stuff, so ignore the zero entries */
2044     ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2045   }
2046   /* Insert values into matrix */
2047   isMatIS = PETSC_FALSE;
2048   if (hasPrec && hasJac) {
2049     ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatIS);CHKERRQ(ierr);
2050   }
2051   if (isMatIS && !subSection) {
2052     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2053   }
2054   for (c = cStart; c < cEnd; ++c) {
2055     const PetscInt cell = cells ? cells[c] : c;
2056     const PetscInt cind = c - cStart;
2057 
2058     /* Transform to global basis before insertion in Jacobian */
2059     if (transform) {ierr = DMPlexBasisTransformPointTensor_Internal(dm, tdm, tv, cell, PETSC_TRUE, totDim, &elemMat[cind*totDim*totDim]);CHKERRQ(ierr);}
2060     if (hasPrec) {
2061       if (hasJac) {
2062         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, totDim, totDim, &elemMat[cind*totDim*totDim]);CHKERRQ(ierr);}
2063         if (!isMatIS) {
2064           ierr = DMPlexMatSetClosure(dm, section, globalSection, Jac, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2065         } else {
2066           Mat lJ;
2067 
2068           ierr = MatISGetLocalMat(Jac,&lJ);CHKERRQ(ierr);
2069           ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2070         }
2071       }
2072       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, totDim, totDim, &elemMatP[cind*totDim*totDim]);CHKERRQ(ierr);}
2073       if (!isMatISP) {
2074         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, cell, &elemMatP[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2075       } else {
2076         Mat lJ;
2077 
2078         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2079         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, cell, &elemMatP[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2080       }
2081     } else {
2082       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, totDim, totDim, &elemMat[cind*totDim*totDim]);CHKERRQ(ierr);}
2083       if (!isMatISP) {
2084         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2085       } else {
2086         Mat lJ;
2087 
2088         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2089         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2090       }
2091     }
2092   }
2093   ierr = ISRestorePointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
2094   if (hasFV) {ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);CHKERRQ(ierr);}
2095   ierr = PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);CHKERRQ(ierr);
2096   if (dmAux) {
2097     ierr = PetscFree(a);CHKERRQ(ierr);
2098     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2099   }
2100   /* Compute boundary integrals */
2101   ierr = DMPlexComputeBdJacobian_Internal(dm, X, X_t, t, X_tShift, Jac, JacP, user);CHKERRQ(ierr);
2102   /* Assemble matrix */
2103   if (hasJac && hasPrec) {
2104     ierr = MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2105     ierr = MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2106   }
2107   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2108   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2109   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2110   PetscFunctionReturn(0);
2111 }
2112 
2113 /*@
2114   DMPlexComputeJacobianAction - Form the local portion of the Jacobian action Z = J(X) Y at the local solution X using pointwise functions specified by the user.
2115 
2116   Input Parameters:
2117 + dm - The mesh
2118 . cellIS -
2119 . t  - The time
2120 . X_tShift - The multiplier for the Jacobian with repsect to X_t
2121 . X  - Local solution vector
2122 . X_t  - Time-derivative of the local solution vector
2123 . Y  - Local input vector
2124 - user - The user context
2125 
2126   Output Parameter:
2127 . Z - Local output vector
2128 
2129   Note:
2130   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2131   like a GPU, or vectorize on a multicore machine.
2132 
2133   Level: developer
2134 
2135 .seealso: FormFunctionLocal()
2136 @*/
2137 PetscErrorCode DMPlexComputeJacobianAction(DM dm, IS cellIS, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Vec Y, Vec Z, void *user)
2138 {
2139   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2140   const char       *name  = "Jacobian";
2141   DM                dmAux, plex, plexAux = NULL;
2142   Vec               A;
2143   PetscDS           prob, probAux = NULL;
2144   PetscQuadrature   quad;
2145   PetscSection      section, globalSection, sectionAux;
2146   PetscScalar      *elemMat, *elemMatD, *u, *u_t, *a = NULL, *y, *z;
2147   PetscInt          Nf, fieldI, fieldJ;
2148   PetscInt          totDim, totDimAux = 0;
2149   const PetscInt   *cells;
2150   PetscInt          cStart, cEnd, numCells, c;
2151   PetscBool         hasDyn;
2152   DMField           coordField;
2153   PetscErrorCode    ierr;
2154 
2155   PetscFunctionBegin;
2156   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2157   ierr = DMSNESConvertPlex(dm, &plex, PETSC_TRUE);CHKERRQ(ierr);
2158   if (!cellIS) {
2159     PetscInt depth;
2160 
2161     ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
2162     ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
2163     if (!cellIS) {ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);}
2164   } else {
2165     ierr = PetscObjectReference((PetscObject) cellIS);CHKERRQ(ierr);
2166   }
2167   ierr = DMGetLocalSection(dm, &section);CHKERRQ(ierr);
2168   ierr = DMGetGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2169   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2170   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2171   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2172   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2173   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2174   ierr = ISGetLocalSize(cellIS, &numCells);CHKERRQ(ierr);
2175   ierr = ISGetPointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
2176   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2177   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2178   if (dmAux) {
2179     ierr = DMConvert(dmAux, DMPLEX, &plexAux);CHKERRQ(ierr);
2180     ierr = DMGetLocalSection(plexAux, &sectionAux);CHKERRQ(ierr);
2181     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2182     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2183   }
2184   ierr = VecSet(Z, 0.0);CHKERRQ(ierr);
2185   ierr = PetscMalloc6(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim*totDim,&elemMat,hasDyn ? numCells*totDim*totDim : 0, &elemMatD,numCells*totDim,&y,totDim,&z);CHKERRQ(ierr);
2186   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2187   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2188   for (c = cStart; c < cEnd; ++c) {
2189     const PetscInt cell = cells ? cells[c] : c;
2190     const PetscInt cind = c - cStart;
2191     PetscScalar   *x = NULL,  *x_t = NULL;
2192     PetscInt       i;
2193 
2194     ierr = DMPlexVecGetClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
2195     for (i = 0; i < totDim; ++i) u[cind*totDim+i] = x[i];
2196     ierr = DMPlexVecRestoreClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
2197     if (X_t) {
2198       ierr = DMPlexVecGetClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
2199       for (i = 0; i < totDim; ++i) u_t[cind*totDim+i] = x_t[i];
2200       ierr = DMPlexVecRestoreClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
2201     }
2202     if (dmAux) {
2203       PetscInt subcell;
2204       ierr = DMPlexGetAuxiliaryPoint(dm, dmAux, cell, &subcell);CHKERRQ(ierr);
2205       ierr = DMPlexVecGetClosure(plexAux, sectionAux, A, subcell, NULL, &x);CHKERRQ(ierr);
2206       for (i = 0; i < totDimAux; ++i) a[cind*totDimAux+i] = x[i];
2207       ierr = DMPlexVecRestoreClosure(plexAux, sectionAux, A, subcell, NULL, &x);CHKERRQ(ierr);
2208     }
2209     ierr = DMPlexVecGetClosure(dm, section, Y, cell, NULL, &x);CHKERRQ(ierr);
2210     for (i = 0; i < totDim; ++i) y[cind*totDim+i] = x[i];
2211     ierr = DMPlexVecRestoreClosure(dm, section, Y, cell, NULL, &x);CHKERRQ(ierr);
2212   }
2213   ierr = PetscArrayzero(elemMat, numCells*totDim*totDim);CHKERRQ(ierr);
2214   if (hasDyn)  {ierr = PetscArrayzero(elemMatD, numCells*totDim*totDim);CHKERRQ(ierr);}
2215   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2216     PetscFE  fe;
2217     PetscInt Nb;
2218     /* Conforming batches */
2219     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2220     /* Remainder */
2221     PetscInt Nr, offset, Nq;
2222     PetscQuadrature qGeom = NULL;
2223     PetscInt    maxDegree;
2224     PetscFEGeom *cgeomFEM, *chunkGeom = NULL, *remGeom = NULL;
2225 
2226     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2227     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2228     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2229     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2230     ierr = DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);CHKERRQ(ierr);
2231     if (maxDegree <= 1) {ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);CHKERRQ(ierr);}
2232     if (!qGeom) {
2233       ierr = PetscFEGetQuadrature(fe,&qGeom);CHKERRQ(ierr);
2234       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
2235     }
2236     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
2237     ierr = DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2238     blockSize = Nb;
2239     batchSize = numBlocks * blockSize;
2240     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2241     numChunks = numCells / (numBatches*batchSize);
2242     Ne        = numChunks*numBatches*batchSize;
2243     Nr        = numCells % (numBatches*batchSize);
2244     offset    = numCells - Nr;
2245     ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2246     ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2247     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2248       ierr = PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2249       ierr = PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2250       if (hasDyn) {
2251         ierr = PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2252         ierr = PetscFEIntegrateJacobian(prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMatD[offset*totDim*totDim]);CHKERRQ(ierr);
2253       }
2254     }
2255     ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2256     ierr = PetscFEGeomRestoreChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2257     ierr = DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2258     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2259   }
2260   if (hasDyn) {
2261     for (c = 0; c < numCells*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2262   }
2263   for (c = cStart; c < cEnd; ++c) {
2264     const PetscInt     cell = cells ? cells[c] : c;
2265     const PetscInt     cind = c - cStart;
2266     const PetscBLASInt M = totDim, one = 1;
2267     const PetscScalar  a = 1.0, b = 0.0;
2268 
2269     PetscStackCallBLAS("BLASgemv", BLASgemv_("N", &M, &M, &a, &elemMat[cind*totDim*totDim], &M, &y[cind*totDim], &one, &b, z, &one));
2270     if (mesh->printFEM > 1) {
2271       ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[cind*totDim*totDim]);CHKERRQ(ierr);
2272       ierr = DMPrintCellVector(c, "Y",  totDim, &y[cind*totDim]);CHKERRQ(ierr);
2273       ierr = DMPrintCellVector(c, "Z",  totDim, z);CHKERRQ(ierr);
2274     }
2275     ierr = DMPlexVecSetClosure(dm, section, Z, cell, z, ADD_VALUES);CHKERRQ(ierr);
2276   }
2277   ierr = PetscFree6(u,u_t,elemMat,elemMatD,y,z);CHKERRQ(ierr);
2278   if (mesh->printFEM) {
2279     ierr = PetscPrintf(PETSC_COMM_WORLD, "Z:\n");CHKERRQ(ierr);
2280     ierr = VecView(Z, NULL);CHKERRQ(ierr);
2281   }
2282   ierr = PetscFree(a);CHKERRQ(ierr);
2283   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
2284   ierr = DMDestroy(&plexAux);CHKERRQ(ierr);
2285   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2286   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2287   PetscFunctionReturn(0);
2288 }
2289 
2290 /*@
2291   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2292 
2293   Input Parameters:
2294 + dm - The mesh
2295 . X  - Local input vector
2296 - user - The user context
2297 
2298   Output Parameter:
2299 . Jac  - Jacobian matrix
2300 
2301   Note:
2302   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2303   like a GPU, or vectorize on a multicore machine.
2304 
2305   Level: developer
2306 
2307 .seealso: FormFunctionLocal()
2308 @*/
2309 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2310 {
2311   DM             plex;
2312   PetscDS        prob;
2313   IS             cellIS;
2314   PetscBool      hasJac, hasPrec;
2315   PetscInt       depth;
2316   PetscErrorCode ierr;
2317 
2318   PetscFunctionBegin;
2319   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2320   ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
2321   ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
2322   if (!cellIS) {ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);}
2323   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2324   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2325   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2326   if (hasJac && hasPrec) {ierr = MatZeroEntries(Jac);CHKERRQ(ierr);}
2327   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
2328   ierr = DMPlexComputeJacobian_Internal(plex, cellIS, 0.0, 0.0, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2329   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
2330   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2331   PetscFunctionReturn(0);
2332 }
2333 
2334 /*
2335      MatComputeNeumannOverlap - Computes an unassembled (Neumann) local overlapping Mat in nonlinear context.
2336 
2337    Input Parameters:
2338 +     X - SNES linearization point
2339 .     ovl - index set of overlapping subdomains
2340 
2341    Output Parameter:
2342 .     J - unassembled (Neumann) local matrix
2343 
2344    Level: intermediate
2345 
2346 .seealso: DMCreateNeumannOverlap(), MATIS, PCHPDDMSetAuxiliaryMat()
2347 */
2348 static PetscErrorCode MatComputeNeumannOverlap_Plex(Mat J, PetscReal t, Vec X, Vec X_t, PetscReal s, IS ovl, void *ctx)
2349 {
2350   SNES           snes;
2351   Mat            pJ;
2352   DM             ovldm,origdm;
2353   DMSNES         sdm;
2354   PetscErrorCode (*bfun)(DM,Vec,void*);
2355   PetscErrorCode (*jfun)(DM,Vec,Mat,Mat,void*);
2356   void           *bctx,*jctx;
2357   PetscErrorCode ierr;
2358 
2359   PetscFunctionBegin;
2360   ierr = PetscObjectQuery((PetscObject)ovl,"_DM_Overlap_HPDDM_MATIS",(PetscObject*)&pJ);CHKERRQ(ierr);
2361   if (!pJ) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing overlapping Mat");CHKERRQ(ierr);
2362   ierr = PetscObjectQuery((PetscObject)ovl,"_DM_Original_HPDDM",(PetscObject*)&origdm);CHKERRQ(ierr);
2363   if (!origdm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing original DM");CHKERRQ(ierr);
2364   ierr = MatGetDM(pJ,&ovldm);CHKERRQ(ierr);
2365   ierr = DMSNESGetBoundaryLocal(origdm,&bfun,&bctx);CHKERRQ(ierr);
2366   ierr = DMSNESSetBoundaryLocal(ovldm,bfun,bctx);CHKERRQ(ierr);
2367   ierr = DMSNESGetJacobianLocal(origdm,&jfun,&jctx);CHKERRQ(ierr);
2368   ierr = DMSNESSetJacobianLocal(ovldm,jfun,jctx);CHKERRQ(ierr);
2369   ierr = PetscObjectQuery((PetscObject)ovl,"_DM_Overlap_HPDDM_SNES",(PetscObject*)&snes);CHKERRQ(ierr);
2370   if (!snes) {
2371     ierr = SNESCreate(PetscObjectComm((PetscObject)ovl),&snes);CHKERRQ(ierr);
2372     ierr = SNESSetDM(snes,ovldm);CHKERRQ(ierr);
2373     ierr = PetscObjectCompose((PetscObject)ovl,"_DM_Overlap_HPDDM_SNES",(PetscObject)snes);CHKERRQ(ierr);
2374     ierr = PetscObjectDereference((PetscObject)snes);CHKERRQ(ierr);
2375   }
2376   ierr = DMGetDMSNES(ovldm,&sdm);CHKERRQ(ierr);
2377   ierr = VecLockReadPush(X);CHKERRQ(ierr);
2378   PetscStackPush("SNES user Jacobian function");
2379   ierr = (*sdm->ops->computejacobian)(snes,X,pJ,pJ,sdm->jacobianctx);CHKERRQ(ierr);
2380   PetscStackPop;
2381   ierr = VecLockReadPop(X);CHKERRQ(ierr);
2382   /* this is a no-hop, just in case we decide to change the placeholder for the local Neumann matrix */
2383   {
2384     Mat locpJ;
2385 
2386     ierr = MatISGetLocalMat(pJ,&locpJ);CHKERRQ(ierr);
2387     ierr = MatCopy(locpJ,J,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2388   }
2389   PetscFunctionReturn(0);
2390 }
2391 
2392 /*@
2393   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.
2394 
2395   Input Parameters:
2396 + dm - The DM object
2397 . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see PetscDSAddBoundary())
2398 . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
2399 - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())
2400 
2401   Level: developer
2402 @*/
2403 PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
2404 {
2405   PetscErrorCode ierr;
2406 
2407   PetscFunctionBegin;
2408   ierr = DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);CHKERRQ(ierr);
2409   ierr = DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);CHKERRQ(ierr);
2410   ierr = DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);CHKERRQ(ierr);
2411   ierr = PetscObjectComposeFunction((PetscObject)dm,"MatComputeNeumannOverlap_C",MatComputeNeumannOverlap_Plex);CHKERRQ(ierr);
2412   PetscFunctionReturn(0);
2413 }
2414 
2415 /*@C
2416   DMSNESCheckDiscretization - Check the discretization error of the exact solution
2417 
2418   Input Parameters:
2419 + snes - the SNES object
2420 . dm   - the DM
2421 . u    - a DM vector
2422 . exactFuncs - pointwise functions of the exact solution for each field
2423 . ctxs - contexts for the functions
2424 . tol  - A tolerance for the check, or -1 to print the results instead
2425 
2426   Output Parameters:
2427 . error - An array which holds the discretization error in each field, or NULL
2428 
2429   Level: developer
2430 
2431 .seealso: DNSNESCheckFromOptions(), DMSNESCheckResidual(), DMSNESCheckJacobian()
2432 @*/
2433 PetscErrorCode DMSNESCheckDiscretization(SNES snes, DM dm, Vec u, PetscErrorCode (**exactFuncs)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx), void **ctxs, PetscReal tol, PetscReal error[])
2434 {
2435   PetscErrorCode (**exacts)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx);
2436   void            **ectxs;
2437   MPI_Comm          comm;
2438   PetscDS           ds;
2439   PetscReal        *err;
2440   PetscInt          Nf, f;
2441   PetscErrorCode    ierr;
2442 
2443   PetscFunctionBegin;
2444   PetscValidHeaderSpecific(snes, SNES_CLASSID, 1);
2445   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
2446   PetscValidHeaderSpecific(u, VEC_CLASSID, 3);
2447   if (error) PetscValidRealPointer(error, 6);
2448   ierr = PetscObjectGetComm((PetscObject) snes, &comm);CHKERRQ(ierr);
2449   ierr = DMGetDS(dm, &ds);CHKERRQ(ierr);
2450   ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
2451   ierr = PetscMalloc3(Nf, &exacts, Nf, &ectxs, PetscMax(1, Nf), &err);CHKERRQ(ierr);
2452   for (f = 0; f < Nf; ++f) {ierr = PetscDSGetExactSolution(ds, f, &exacts[f], &ectxs[f]);CHKERRQ(ierr);}
2453   ierr = DMProjectFunction(dm, 0.0, exactFuncs ? exactFuncs : exacts, ctxs ? ctxs : ectxs, INSERT_ALL_VALUES, u);CHKERRQ(ierr);
2454   ierr = PetscObjectSetName((PetscObject) u, "Exact Solution");CHKERRQ(ierr);
2455   ierr = PetscObjectSetOptionsPrefix((PetscObject) u, "exact_");CHKERRQ(ierr);
2456   ierr = VecViewFromOptions(u, NULL, "-vec_view");CHKERRQ(ierr);
2457   if (Nf > 1) {
2458     ierr = DMComputeL2FieldDiff(dm, 0.0, exactFuncs ? exactFuncs : exacts, ctxs ? ctxs : ectxs, u, err);CHKERRQ(ierr);
2459     if (tol >= 0.0) {
2460       for (f = 0; f < Nf; ++f) {
2461         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);
2462       }
2463     } else if (error) {
2464       for (f = 0; f < Nf; ++f) error[f] = err[f];
2465     } else {
2466       ierr = PetscPrintf(comm, "L_2 Error: [");CHKERRQ(ierr);
2467       for (f = 0; f < Nf; ++f) {
2468         if (f) {ierr = PetscPrintf(comm, ", ");CHKERRQ(ierr);}
2469         ierr = PetscPrintf(comm, "%g", (double)err[f]);CHKERRQ(ierr);
2470       }
2471       ierr = PetscPrintf(comm, "]\n");CHKERRQ(ierr);
2472     }
2473   } else {
2474     ierr = DMComputeL2Diff(dm, 0.0, exactFuncs ? exactFuncs : exacts, ctxs ? ctxs : ectxs , u, &err[0]);CHKERRQ(ierr);
2475     if (tol >= 0.0) {
2476       if (err[0] > tol) SETERRQ2(comm, PETSC_ERR_ARG_WRONG, "L_2 Error %g exceeds tolerance %g", (double) err[0], (double) tol);
2477     } else if (error) {
2478       error[0] = err[0];
2479     } else {
2480       ierr = PetscPrintf(comm, "L_2 Error: %g\n", (double)err[0]);CHKERRQ(ierr);
2481     }
2482   }
2483   ierr = PetscFree3(exacts, ectxs, err);CHKERRQ(ierr);
2484   PetscFunctionReturn(0);
2485 }
2486 
2487 /*@C
2488   DMSNESCheckResidual - Check the residual of the exact solution
2489 
2490   Input Parameters:
2491 + snes - the SNES object
2492 . dm   - the DM
2493 . u    - a DM vector
2494 . tol  - A tolerance for the check, or -1 to print the results instead
2495 
2496   Output Parameters:
2497 . residual - The residual norm of the exact solution, or NULL
2498 
2499   Level: developer
2500 
2501 .seealso: DNSNESCheckFromOptions(), DMSNESCheckDiscretization(), DMSNESCheckJacobian()
2502 @*/
2503 PetscErrorCode DMSNESCheckResidual(SNES snes, DM dm, Vec u, PetscReal tol, PetscReal *residual)
2504 {
2505   PetscErrorCode (**exacts)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx);
2506   void            **ectxs;
2507   MPI_Comm          comm;
2508   PetscDS           ds;
2509   Vec               r;
2510   PetscReal         res;
2511   PetscInt          Nf, f;
2512   PetscBool         computeSol = PETSC_FALSE;
2513   PetscErrorCode    ierr;
2514 
2515   PetscFunctionBegin;
2516   PetscValidHeaderSpecific(snes, SNES_CLASSID, 1);
2517   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
2518   PetscValidHeaderSpecific(u, VEC_CLASSID, 3);
2519   if (residual) PetscValidRealPointer(residual, 5);
2520   ierr = PetscObjectGetComm((PetscObject) snes, &comm);CHKERRQ(ierr);
2521   ierr = DMGetDS(dm, &ds);CHKERRQ(ierr);
2522   ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
2523   ierr = PetscMalloc2(Nf, &exacts, Nf, &ectxs);CHKERRQ(ierr);
2524   for (f = 0; f < Nf; ++f) {
2525     ierr = PetscDSGetExactSolution(ds, f, &exacts[f], &ectxs[f]);CHKERRQ(ierr);
2526     if (exacts[f]) computeSol = PETSC_TRUE;
2527   }
2528   if (computeSol) {ierr = DMProjectFunction(dm, 0.0, exacts, ectxs, INSERT_ALL_VALUES, u);CHKERRQ(ierr);}
2529   ierr = PetscFree2(exacts, ectxs);CHKERRQ(ierr);
2530 
2531   ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2532   ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2533   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2534   if (tol >= 0.0) {
2535     if (res > tol) SETERRQ2(comm, PETSC_ERR_ARG_WRONG, "L_2 Residual %g exceeds tolerance %g", (double) res, (double) tol);
2536   } else if (residual) {
2537     *residual = res;
2538   } else {
2539     ierr = PetscPrintf(comm, "L_2 Residual: %g\n", (double)res);CHKERRQ(ierr);
2540     ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2541     ierr = PetscObjectSetName((PetscObject) r, "Initial Residual");CHKERRQ(ierr);
2542     ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"res_");CHKERRQ(ierr);
2543     ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2544   }
2545   ierr = VecDestroy(&r);CHKERRQ(ierr);
2546   PetscFunctionReturn(0);
2547 }
2548 
2549 /*@C
2550   DMSNESCheckJacobian - Check the Jacobian of the exact solution against the residual using the Taylor Test
2551 
2552   Input Parameters:
2553 + snes - the SNES object
2554 . dm   - the DM
2555 . u    - a DM vector
2556 . tol  - A tolerance for the check, or -1 to print the results instead
2557 
2558   Output Parameters:
2559 + isLinear - Flag indicaing that the function looks linear, or NULL
2560 - convRate - The rate of convergence of the linear model, or NULL
2561 
2562   Level: developer
2563 
2564 .seealso: DNSNESCheckFromOptions(), DMSNESCheckDiscretization(), DMSNESCheckResidual()
2565 @*/
2566 PetscErrorCode DMSNESCheckJacobian(SNES snes, DM dm, Vec u, PetscReal tol, PetscBool *isLinear, PetscReal *convRate)
2567 {
2568   PetscErrorCode (**exacts)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx);
2569   void            **ectxs;
2570   MPI_Comm          comm;
2571   PetscDS           ds;
2572   Mat               J, M;
2573   MatNullSpace      nullspace;
2574   PetscReal         slope, intercept;
2575   PetscInt          Nf, f;
2576   PetscBool         hasJac, hasPrec, isLin = PETSC_FALSE, computeSol = PETSC_FALSE;
2577   PetscErrorCode    ierr;
2578 
2579   PetscFunctionBegin;
2580   PetscValidHeaderSpecific(snes, SNES_CLASSID, 1);
2581   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
2582   PetscValidHeaderSpecific(u, VEC_CLASSID, 3);
2583   if (isLinear) PetscValidBoolPointer(isLinear, 5);
2584   if (convRate) PetscValidRealPointer(convRate, 5);
2585   ierr = PetscObjectGetComm((PetscObject) snes, &comm);CHKERRQ(ierr);
2586   ierr = DMGetDS(dm, &ds);CHKERRQ(ierr);
2587   ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
2588   ierr = PetscMalloc2(Nf, &exacts, Nf, &ectxs);CHKERRQ(ierr);
2589   for (f = 0; f < Nf; ++f) {
2590     ierr = PetscDSGetExactSolution(ds, f, &exacts[f], &ectxs[f]);CHKERRQ(ierr);
2591     if (exacts[f]) computeSol = PETSC_TRUE;
2592   }
2593   if (computeSol) {ierr = DMProjectFunction(dm, 0.0, exacts, ectxs, INSERT_ALL_VALUES, u);CHKERRQ(ierr);}
2594   ierr = PetscFree2(exacts, ectxs);CHKERRQ(ierr);
2595 
2596   /* Create and view matrices */
2597   ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
2598   ierr = PetscDSHasJacobian(ds, &hasJac);CHKERRQ(ierr);
2599   ierr = PetscDSHasJacobianPreconditioner(ds, &hasPrec);CHKERRQ(ierr);
2600   if (hasJac && hasPrec) {
2601     ierr = DMCreateMatrix(dm, &M);CHKERRQ(ierr);
2602     ierr = SNESComputeJacobian(snes, u, J, M);CHKERRQ(ierr);
2603     ierr = PetscObjectSetName((PetscObject) M, "Preconditioning Matrix");CHKERRQ(ierr);
2604     ierr = PetscObjectSetOptionsPrefix((PetscObject) M, "jacpre_");CHKERRQ(ierr);
2605     ierr = MatViewFromOptions(M, NULL, "-mat_view");CHKERRQ(ierr);
2606     ierr = MatDestroy(&M);CHKERRQ(ierr);
2607   } else {
2608     ierr = SNESComputeJacobian(snes, u, J, J);CHKERRQ(ierr);
2609   }
2610   ierr = PetscObjectSetName((PetscObject) J, "Jacobian");CHKERRQ(ierr);
2611   ierr = PetscObjectSetOptionsPrefix((PetscObject) J, "jac_");CHKERRQ(ierr);
2612   ierr = MatViewFromOptions(J, NULL, "-mat_view");CHKERRQ(ierr);
2613   /* Check nullspace */
2614   ierr = MatGetNullSpace(J, &nullspace);CHKERRQ(ierr);
2615   if (nullspace) {
2616     PetscBool isNull;
2617     ierr = MatNullSpaceTest(nullspace, J, &isNull);CHKERRQ(ierr);
2618     if (!isNull) SETERRQ(comm, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
2619   }
2620   ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr);
2621   /* Taylor test */
2622   {
2623     PetscRandom rand;
2624     Vec         du, uhat, r, rhat, df;
2625     PetscReal   h;
2626     PetscReal  *es, *hs, *errors;
2627     PetscReal   hMax = 1.0, hMin = 1e-6, hMult = 0.1;
2628     PetscInt    Nv, v;
2629 
2630     /* Choose a perturbation direction */
2631     ierr = PetscRandomCreate(comm, &rand);CHKERRQ(ierr);
2632     ierr = VecDuplicate(u, &du);CHKERRQ(ierr);
2633     ierr = VecSetRandom(du, rand); CHKERRQ(ierr);
2634     ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
2635     ierr = VecDuplicate(u, &df);CHKERRQ(ierr);
2636     ierr = MatMult(J, du, df);CHKERRQ(ierr);
2637     /* Evaluate residual at u, F(u), save in vector r */
2638     ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2639     ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2640     /* Look at the convergence of our Taylor approximation as we approach u */
2641     for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv);
2642     ierr = PetscCalloc3(Nv, &es, Nv, &hs, Nv, &errors);CHKERRQ(ierr);
2643     ierr = VecDuplicate(u, &uhat);CHKERRQ(ierr);
2644     ierr = VecDuplicate(u, &rhat);CHKERRQ(ierr);
2645     for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv) {
2646       ierr = VecWAXPY(uhat, h, du, u);CHKERRQ(ierr);
2647       /* F(\hat u) \approx F(u) + J(u) (uhat - u) = F(u) + h * J(u) du */
2648       ierr = SNESComputeFunction(snes, uhat, rhat);CHKERRQ(ierr);
2649       ierr = VecAXPBYPCZ(rhat, -1.0, -h, 1.0, r, df);CHKERRQ(ierr);
2650       ierr = VecNorm(rhat, NORM_2, &errors[Nv]);CHKERRQ(ierr);
2651 
2652       es[Nv] = PetscLog10Real(errors[Nv]);
2653       hs[Nv] = PetscLog10Real(h);
2654     }
2655     ierr = VecDestroy(&uhat);CHKERRQ(ierr);
2656     ierr = VecDestroy(&rhat);CHKERRQ(ierr);
2657     ierr = VecDestroy(&df);CHKERRQ(ierr);
2658     ierr = VecDestroy(&r);CHKERRQ(ierr);
2659     ierr = VecDestroy(&du);CHKERRQ(ierr);
2660     for (v = 0; v < Nv; ++v) {
2661       if ((tol >= 0) && (errors[v] > tol)) break;
2662       else if (errors[v] > PETSC_SMALL)    break;
2663     }
2664     if (v == Nv) isLin = PETSC_TRUE;
2665     ierr = PetscLinearRegression(Nv, hs, es, &slope, &intercept);CHKERRQ(ierr);
2666     ierr = PetscFree3(es, hs, errors);CHKERRQ(ierr);
2667     /* Slope should be about 2 */
2668     if (tol >= 0) {
2669       if (!isLin && PetscAbsReal(2 - slope) > tol) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Taylor approximation convergence rate should be 2, not %0.2f", (double) slope);
2670     } else if (isLinear || convRate) {
2671       if (isLinear) *isLinear = isLin;
2672       if (convRate) *convRate = slope;
2673     } else {
2674       if (!isLin) {ierr = PetscPrintf(comm, "Taylor approximation converging at order %3.2f\n", (double) slope);CHKERRQ(ierr);}
2675       else        {ierr = PetscPrintf(comm, "Function appears to be linear\n");CHKERRQ(ierr);}
2676     }
2677   }
2678   ierr = MatDestroy(&J);CHKERRQ(ierr);
2679   PetscFunctionReturn(0);
2680 }
2681 
2682 PetscErrorCode DMSNESCheck_Internal(SNES snes, DM dm, Vec u, PetscErrorCode (**exactFuncs)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx), void **ctxs)
2683 {
2684   PetscErrorCode ierr;
2685 
2686   PetscFunctionBegin;
2687   ierr = DMSNESCheckDiscretization(snes, dm, u, exactFuncs, ctxs, -1.0, NULL);CHKERRQ(ierr);
2688   ierr = DMSNESCheckResidual(snes, dm, u, -1.0, NULL);CHKERRQ(ierr);
2689   ierr = DMSNESCheckJacobian(snes, dm, u, -1.0, NULL, NULL);CHKERRQ(ierr);
2690   PetscFunctionReturn(0);
2691 }
2692 
2693 /*@C
2694   DMSNESCheckFromOptions - Check the residual and Jacobian functions using the exact solution by outputting some diagnostic information
2695 
2696   Input Parameters:
2697 + snes - the SNES object
2698 . u    - representative SNES vector
2699 . exactFuncs - pointwise functions of the exact solution for each field
2700 - ctxs - contexts for the functions
2701 
2702   Level: developer
2703 @*/
2704 PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
2705 {
2706   DM             dm;
2707   Vec            sol;
2708   PetscBool      check;
2709   PetscErrorCode ierr;
2710 
2711   PetscFunctionBegin;
2712   ierr = PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);CHKERRQ(ierr);
2713   if (!check) PetscFunctionReturn(0);
2714   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
2715   ierr = VecDuplicate(u, &sol);CHKERRQ(ierr);
2716   ierr = SNESSetSolution(snes, sol);CHKERRQ(ierr);
2717   ierr = DMSNESCheck_Internal(snes, dm, sol, exactFuncs, ctxs);CHKERRQ(ierr);
2718   ierr = VecDestroy(&sol);CHKERRQ(ierr);
2719   PetscFunctionReturn(0);
2720 }
2721