xref: /petsc/src/snes/utils/dmplexsnes.c (revision a685ae26bbf9fb229cf02e15e73d16b8a9cd69e6)
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 on comm
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 = PetscMemcpy(ctx->points, points, n*ctx->dim * sizeof(PetscReal));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 .keywords: SNES, nonlinear, default, monitor, norm
946 .seealso: SNESMonitorSet(), SNESMonitorDefault()
947 @*/
948 PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
949 {
950   PetscViewer        viewer = vf->viewer;
951   Vec                res;
952   DM                 dm;
953   PetscSection       s;
954   const PetscScalar *r;
955   PetscReal         *lnorms, *norms;
956   PetscInt           numFields, f, pStart, pEnd, p;
957   PetscErrorCode     ierr;
958 
959   PetscFunctionBegin;
960   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
961   ierr = SNESGetFunction(snes, &res, 0, 0);CHKERRQ(ierr);
962   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
963   ierr = DMGetSection(dm, &s);CHKERRQ(ierr);
964   ierr = PetscSectionGetNumFields(s, &numFields);CHKERRQ(ierr);
965   ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
966   ierr = PetscCalloc2(numFields, &lnorms, numFields, &norms);CHKERRQ(ierr);
967   ierr = VecGetArrayRead(res, &r);CHKERRQ(ierr);
968   for (p = pStart; p < pEnd; ++p) {
969     for (f = 0; f < numFields; ++f) {
970       PetscInt fdof, foff, d;
971 
972       ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
973       ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
974       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
975     }
976   }
977   ierr = VecRestoreArrayRead(res, &r);CHKERRQ(ierr);
978   ierr = MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
979   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
980   ierr = PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
981   ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
982   for (f = 0; f < numFields; ++f) {
983     if (f > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
984     ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));CHKERRQ(ierr);
985   }
986   ierr = PetscViewerASCIIPrintf(viewer, "]\n");CHKERRQ(ierr);
987   ierr = PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
988   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
989   ierr = PetscFree2(lnorms, norms);CHKERRQ(ierr);
990   PetscFunctionReturn(0);
991 }
992 
993 /********************* Residual Computation **************************/
994 
995 
996 /*@
997   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
998 
999   Input Parameter:
1000 . dm - The DM
1001 
1002   Output Parameters:
1003 + facegeom - The values precomputed from face geometry
1004 . cellgeom - The values precomputed from cell geometry
1005 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
1006 
1007   Level: developer
1008 
1009 .seealso: DMPlexTSSetRHSFunctionLocal()
1010 @*/
1011 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
1012 {
1013   DM             plex;
1014   PetscErrorCode ierr;
1015 
1016   PetscFunctionBegin;
1017   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
1018   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
1019   ierr = DMPlexGetDataFVM(plex, NULL, cellgeom, facegeom, NULL);CHKERRQ(ierr);
1020   if (minRadius) {ierr = DMPlexGetMinRadius(plex, minRadius);CHKERRQ(ierr);}
1021   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1022   PetscFunctionReturn(0);
1023 }
1024 
1025 /*@
1026   DMPlexSNESGetGradientDM - Return gradient data layout
1027 
1028   Input Parameters:
1029 + dm - The DM
1030 - fv - The PetscFV
1031 
1032   Output Parameter:
1033 . dmGrad - The layout for gradient values
1034 
1035   Level: developer
1036 
1037 .seealso: DMPlexSNESGetGeometryFVM()
1038 @*/
1039 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
1040 {
1041   DM             plex;
1042   PetscBool      computeGradients;
1043   PetscErrorCode ierr;
1044 
1045   PetscFunctionBegin;
1046   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
1047   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
1048   PetscValidPointer(dmGrad,3);
1049   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
1050   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
1051   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
1052   ierr = DMPlexGetDataFVM(plex, fv, NULL, NULL, dmGrad);CHKERRQ(ierr);
1053   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1054   PetscFunctionReturn(0);
1055 }
1056 
1057 /*@C
1058   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells
1059 
1060   Input Parameters:
1061 + dm     - The DM
1062 . cellIS - The cells to include
1063 . locX   - A local vector with the solution fields
1064 . locX_t - A local vector with solution field time derivatives, or NULL
1065 - locA   - A local vector with auxiliary fields, or NULL
1066 
1067   Output Parameters:
1068 + u   - The field coefficients
1069 . u_t - The fields derivative coefficients
1070 - a   - The auxiliary field coefficients
1071 
1072   Level: developer
1073 
1074 .seealso: DMPlexGetFaceFields()
1075 @*/
1076 PetscErrorCode DMPlexGetCellFields(DM dm, IS cellIS, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1077 {
1078   DM              plex, plexA = NULL;
1079   PetscSection    section, sectionAux;
1080   PetscDS         prob;
1081   const PetscInt *cells;
1082   PetscInt        cStart, cEnd, numCells, totDim, totDimAux, c;
1083   PetscErrorCode  ierr;
1084 
1085   PetscFunctionBegin;
1086   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1087   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1088   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1089   if (locA)   {PetscValidHeaderSpecific(locA, VEC_CLASSID, 6);}
1090   PetscValidPointer(u, 7);
1091   PetscValidPointer(u_t, 8);
1092   PetscValidPointer(a, 9);
1093   ierr = DMSNESConvertPlex(dm, &plex, PETSC_FALSE);CHKERRQ(ierr);
1094   ierr = ISGetPointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
1095   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1096   ierr = DMGetCellDS(dm, cStart, &prob);CHKERRQ(ierr);
1097   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1098   if (locA) {
1099     DM      dmAux;
1100     PetscDS probAux;
1101 
1102     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1103     ierr = DMSNESConvertPlex(dmAux, &plexA, PETSC_FALSE);CHKERRQ(ierr);
1104     ierr = DMGetSection(dmAux, &sectionAux);CHKERRQ(ierr);
1105     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1106     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1107   }
1108   numCells = cEnd - cStart;
1109   ierr = DMGetWorkArray(dm, numCells*totDim, MPIU_SCALAR, u);CHKERRQ(ierr);
1110   if (locX_t) {ierr = DMGetWorkArray(dm, numCells*totDim, MPIU_SCALAR, u_t);CHKERRQ(ierr);} else {*u_t = NULL;}
1111   if (locA)   {ierr = DMGetWorkArray(dm, numCells*totDimAux, MPIU_SCALAR, a);CHKERRQ(ierr);} else {*a = NULL;}
1112   for (c = cStart; c < cEnd; ++c) {
1113     const PetscInt cell = cells ? cells[c] : c;
1114     const PetscInt cind = c - cStart;
1115     PetscScalar   *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
1116     PetscInt       i;
1117 
1118     ierr = DMPlexVecGetClosure(plex, section, locX, cell, NULL, &x);CHKERRQ(ierr);
1119     for (i = 0; i < totDim; ++i) ul[cind*totDim+i] = x[i];
1120     ierr = DMPlexVecRestoreClosure(plex, section, locX, cell, NULL, &x);CHKERRQ(ierr);
1121     if (locX_t) {
1122       ierr = DMPlexVecGetClosure(plex, section, locX_t, cell, NULL, &x_t);CHKERRQ(ierr);
1123       for (i = 0; i < totDim; ++i) ul_t[cind*totDim+i] = x_t[i];
1124       ierr = DMPlexVecRestoreClosure(plex, section, locX_t, cell, NULL, &x_t);CHKERRQ(ierr);
1125     }
1126     if (locA) {
1127       PetscInt subcell;
1128       ierr = DMPlexGetAuxiliaryPoint(plex, plexA, cell, &subcell);CHKERRQ(ierr);
1129       ierr = DMPlexVecGetClosure(plexA, sectionAux, locA, subcell, NULL, &x);CHKERRQ(ierr);
1130       for (i = 0; i < totDimAux; ++i) al[cind*totDimAux+i] = x[i];
1131       ierr = DMPlexVecRestoreClosure(plexA, sectionAux, locA, subcell, NULL, &x);CHKERRQ(ierr);
1132     }
1133   }
1134   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1135   if (locA) {ierr = DMDestroy(&plexA);CHKERRQ(ierr);}
1136   ierr = ISRestorePointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
1137   PetscFunctionReturn(0);
1138 }
1139 
1140 /*@C
1141   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells
1142 
1143   Input Parameters:
1144 + dm     - The DM
1145 . cellIS - The cells to include
1146 . locX   - A local vector with the solution fields
1147 . locX_t - A local vector with solution field time derivatives, or NULL
1148 - locA   - A local vector with auxiliary fields, or NULL
1149 
1150   Output Parameters:
1151 + u   - The field coefficients
1152 . u_t - The fields derivative coefficients
1153 - a   - The auxiliary field coefficients
1154 
1155   Level: developer
1156 
1157 .seealso: DMPlexGetFaceFields()
1158 @*/
1159 PetscErrorCode DMPlexRestoreCellFields(DM dm, IS cellIS, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1160 {
1161   PetscErrorCode ierr;
1162 
1163   PetscFunctionBegin;
1164   ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, u);CHKERRQ(ierr);
1165   if (locX_t) {ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, u_t);CHKERRQ(ierr);}
1166   if (locA)   {ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, a);CHKERRQ(ierr);}
1167   PetscFunctionReturn(0);
1168 }
1169 
1170 /*@C
1171   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces
1172 
1173   Input Parameters:
1174 + dm     - The DM
1175 . fStart - The first face to include
1176 . fEnd   - The first face to exclude
1177 . locX   - A local vector with the solution fields
1178 . locX_t - A local vector with solution field time derivatives, or NULL
1179 . faceGeometry - A local vector with face geometry
1180 . cellGeometry - A local vector with cell geometry
1181 - locaGrad - A local vector with field gradients, or NULL
1182 
1183   Output Parameters:
1184 + Nface - The number of faces with field values
1185 . uL - The field values at the left side of the face
1186 - uR - The field values at the right side of the face
1187 
1188   Level: developer
1189 
1190 .seealso: DMPlexGetCellFields()
1191 @*/
1192 PetscErrorCode DMPlexGetFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscInt *Nface, PetscScalar **uL, PetscScalar **uR)
1193 {
1194   DM                 dmFace, dmCell, dmGrad = NULL;
1195   PetscSection       section;
1196   PetscDS            prob;
1197   DMLabel            ghostLabel;
1198   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
1199   PetscBool         *isFE;
1200   PetscInt           dim, Nf, f, Nc, numFaces = fEnd - fStart, iface, face;
1201   PetscErrorCode     ierr;
1202 
1203   PetscFunctionBegin;
1204   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1205   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1206   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1207   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 6);
1208   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 7);
1209   if (locGrad) {PetscValidHeaderSpecific(locGrad, VEC_CLASSID, 8);}
1210   PetscValidPointer(uL, 9);
1211   PetscValidPointer(uR, 10);
1212   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1213   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1214   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1215   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1216   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1217   ierr = PetscMalloc1(Nf, &isFE);CHKERRQ(ierr);
1218   for (f = 0; f < Nf; ++f) {
1219     PetscObject  obj;
1220     PetscClassId id;
1221 
1222     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1223     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1224     if (id == PETSCFE_CLASSID)      {isFE[f] = PETSC_TRUE;}
1225     else if (id == PETSCFV_CLASSID) {isFE[f] = PETSC_FALSE;}
1226     else                            {isFE[f] = PETSC_FALSE;}
1227   }
1228   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1229   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1230   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1231   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1232   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1233   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1234   if (locGrad) {
1235     ierr = VecGetDM(locGrad, &dmGrad);CHKERRQ(ierr);
1236     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1237   }
1238   ierr = DMGetWorkArray(dm, numFaces*Nc, MPIU_SCALAR, uL);CHKERRQ(ierr);
1239   ierr = DMGetWorkArray(dm, numFaces*Nc, MPIU_SCALAR, uR);CHKERRQ(ierr);
1240   /* Right now just eat the extra work for FE (could make a cell loop) */
1241   for (face = fStart, iface = 0; face < fEnd; ++face) {
1242     const PetscInt        *cells;
1243     PetscFVFaceGeom       *fg;
1244     PetscFVCellGeom       *cgL, *cgR;
1245     PetscScalar           *xL, *xR, *gL, *gR;
1246     PetscScalar           *uLl = *uL, *uRl = *uR;
1247     PetscInt               ghost, nsupp, nchild;
1248 
1249     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1250     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1251     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1252     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1253     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1254     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1255     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1256     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1257     for (f = 0; f < Nf; ++f) {
1258       PetscInt off;
1259 
1260       ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1261       if (isFE[f]) {
1262         const PetscInt *cone;
1263         PetscInt        comp, coneSizeL, coneSizeR, faceLocL, faceLocR, ldof, rdof, d;
1264 
1265         xL = xR = NULL;
1266         ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1267         ierr = DMPlexVecGetClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1268         ierr = DMPlexVecGetClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1269         ierr = DMPlexGetCone(dm, cells[0], &cone);CHKERRQ(ierr);
1270         ierr = DMPlexGetConeSize(dm, cells[0], &coneSizeL);CHKERRQ(ierr);
1271         for (faceLocL = 0; faceLocL < coneSizeL; ++faceLocL) if (cone[faceLocL] == face) break;
1272         ierr = DMPlexGetCone(dm, cells[1], &cone);CHKERRQ(ierr);
1273         ierr = DMPlexGetConeSize(dm, cells[1], &coneSizeR);CHKERRQ(ierr);
1274         for (faceLocR = 0; faceLocR < coneSizeR; ++faceLocR) if (cone[faceLocR] == face) break;
1275         if (faceLocL == coneSizeL && faceLocR == coneSizeR) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of cell %d or cell %d", face, cells[0], cells[1]);
1276         /* Check that FEM field has values in the right cell (sometimes its an FV ghost cell) */
1277         /* TODO: this is a hack that might not be right for nonconforming */
1278         if (faceLocL < coneSizeL) {
1279           ierr = EvaluateFaceFields(prob, f, faceLocL, xL, &uLl[iface*Nc+off]);CHKERRQ(ierr);
1280           if (rdof == ldof && faceLocR < coneSizeR) {ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);}
1281           else              {for(d = 0; d < comp; ++d) uRl[iface*Nc+off+d] = uLl[iface*Nc+off+d];}
1282         }
1283         else {
1284           ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);
1285           ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1286           for(d = 0; d < comp; ++d) uLl[iface*Nc+off+d] = uRl[iface*Nc+off+d];
1287         }
1288         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1289         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1290       } else {
1291         PetscFV  fv;
1292         PetscInt numComp, c;
1293 
1294         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fv);CHKERRQ(ierr);
1295         ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1296         ierr = DMPlexPointLocalFieldRead(dm, cells[0], f, x, &xL);CHKERRQ(ierr);
1297         ierr = DMPlexPointLocalFieldRead(dm, cells[1], f, x, &xR);CHKERRQ(ierr);
1298         if (dmGrad) {
1299           PetscReal dxL[3], dxR[3];
1300 
1301           ierr = DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);CHKERRQ(ierr);
1302           ierr = DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);CHKERRQ(ierr);
1303           DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
1304           DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
1305           for (c = 0; c < numComp; ++c) {
1306             uLl[iface*Nc+off+c] = xL[c] + DMPlex_DotD_Internal(dim, &gL[c*dim], dxL);
1307             uRl[iface*Nc+off+c] = xR[c] + DMPlex_DotD_Internal(dim, &gR[c*dim], dxR);
1308           }
1309         } else {
1310           for (c = 0; c < numComp; ++c) {
1311             uLl[iface*Nc+off+c] = xL[c];
1312             uRl[iface*Nc+off+c] = xR[c];
1313           }
1314         }
1315       }
1316     }
1317     ++iface;
1318   }
1319   *Nface = iface;
1320   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1321   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1322   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1323   if (locGrad) {
1324     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1325   }
1326   ierr = PetscFree(isFE);CHKERRQ(ierr);
1327   PetscFunctionReturn(0);
1328 }
1329 
1330 /*@C
1331   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces
1332 
1333   Input Parameters:
1334 + dm     - The DM
1335 . fStart - The first face to include
1336 . fEnd   - The first face to exclude
1337 . locX   - A local vector with the solution fields
1338 . locX_t - A local vector with solution field time derivatives, or NULL
1339 . faceGeometry - A local vector with face geometry
1340 . cellGeometry - A local vector with cell geometry
1341 - locaGrad - A local vector with field gradients, or NULL
1342 
1343   Output Parameters:
1344 + Nface - The number of faces with field values
1345 . uL - The field values at the left side of the face
1346 - uR - The field values at the right side of the face
1347 
1348   Level: developer
1349 
1350 .seealso: DMPlexGetFaceFields()
1351 @*/
1352 PetscErrorCode DMPlexRestoreFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscInt *Nface, PetscScalar **uL, PetscScalar **uR)
1353 {
1354   PetscErrorCode ierr;
1355 
1356   PetscFunctionBegin;
1357   ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, uL);CHKERRQ(ierr);
1358   ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, uR);CHKERRQ(ierr);
1359   PetscFunctionReturn(0);
1360 }
1361 
1362 /*@C
1363   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces
1364 
1365   Input Parameters:
1366 + dm     - The DM
1367 . fStart - The first face to include
1368 . fEnd   - The first face to exclude
1369 . faceGeometry - A local vector with face geometry
1370 - cellGeometry - A local vector with cell geometry
1371 
1372   Output Parameters:
1373 + Nface - The number of faces with field values
1374 . fgeom - The extract the face centroid and normal
1375 - vol   - The cell volume
1376 
1377   Level: developer
1378 
1379 .seealso: DMPlexGetCellFields()
1380 @*/
1381 PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1382 {
1383   DM                 dmFace, dmCell;
1384   DMLabel            ghostLabel;
1385   const PetscScalar *facegeom, *cellgeom;
1386   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
1387   PetscErrorCode     ierr;
1388 
1389   PetscFunctionBegin;
1390   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1391   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 4);
1392   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 5);
1393   PetscValidPointer(fgeom, 6);
1394   PetscValidPointer(vol, 7);
1395   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1396   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1397   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1398   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1399   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1400   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1401   ierr = PetscMalloc1(numFaces, fgeom);CHKERRQ(ierr);
1402   ierr = DMGetWorkArray(dm, numFaces*2, MPIU_SCALAR, vol);CHKERRQ(ierr);
1403   for (face = fStart, iface = 0; face < fEnd; ++face) {
1404     const PetscInt        *cells;
1405     PetscFVFaceGeom       *fg;
1406     PetscFVCellGeom       *cgL, *cgR;
1407     PetscFVFaceGeom       *fgeoml = *fgeom;
1408     PetscReal             *voll   = *vol;
1409     PetscInt               ghost, d, nchild, nsupp;
1410 
1411     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1412     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1413     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1414     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1415     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1416     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1417     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1418     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1419     for (d = 0; d < dim; ++d) {
1420       fgeoml[iface].centroid[d] = fg->centroid[d];
1421       fgeoml[iface].normal[d]   = fg->normal[d];
1422     }
1423     voll[iface*2+0] = cgL->volume;
1424     voll[iface*2+1] = cgR->volume;
1425     ++iface;
1426   }
1427   *Nface = iface;
1428   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1429   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1430   PetscFunctionReturn(0);
1431 }
1432 
1433 /*@C
1434   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces
1435 
1436   Input Parameters:
1437 + dm     - The DM
1438 . fStart - The first face to include
1439 . fEnd   - The first face to exclude
1440 . faceGeometry - A local vector with face geometry
1441 - cellGeometry - A local vector with cell geometry
1442 
1443   Output Parameters:
1444 + Nface - The number of faces with field values
1445 . fgeom - The extract the face centroid and normal
1446 - vol   - The cell volume
1447 
1448   Level: developer
1449 
1450 .seealso: DMPlexGetFaceFields()
1451 @*/
1452 PetscErrorCode DMPlexRestoreFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1453 {
1454   PetscErrorCode ierr;
1455 
1456   PetscFunctionBegin;
1457   ierr = PetscFree(*fgeom);CHKERRQ(ierr);
1458   ierr = DMRestoreWorkArray(dm, 0, MPIU_REAL, vol);CHKERRQ(ierr);
1459   PetscFunctionReturn(0);
1460 }
1461 
1462 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)
1463 {
1464   DM_Plex         *mesh = (DM_Plex *) dm->data;
1465   DM               plex = NULL, plexA = NULL;
1466   PetscDS          prob, probAux = NULL;
1467   PetscSection     section, sectionAux = NULL;
1468   Vec              locA = NULL;
1469   PetscScalar     *u = NULL, *u_t = NULL, *a = NULL, *elemVec = NULL;
1470   PetscInt         v;
1471   PetscInt         totDim, totDimAux = 0;
1472   PetscErrorCode   ierr;
1473 
1474   PetscFunctionBegin;
1475   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
1476   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1477   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1478   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1479   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1480   if (locA) {
1481     DM dmAux;
1482 
1483     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1484     ierr = DMConvert(dmAux, DMPLEX, &plexA);CHKERRQ(ierr);
1485     ierr = DMGetDS(plexA, &probAux);CHKERRQ(ierr);
1486     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1487     ierr = DMGetSection(plexA, &sectionAux);CHKERRQ(ierr);
1488   }
1489   for (v = 0; v < numValues; ++v) {
1490     PetscFEGeom    *fgeom;
1491     PetscInt        maxDegree;
1492     PetscQuadrature qGeom = NULL;
1493     IS              pointIS;
1494     const PetscInt *points;
1495     PetscInt        numFaces, face, Nq;
1496 
1497     ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1498     if (!pointIS) continue; /* No points with that id on this process */
1499     {
1500       IS isectIS;
1501 
1502       /* TODO: Special cases of ISIntersect where it is quick to check a priori if one is a superset of the other */
1503       ierr = ISIntersect_Caching_Internal(facetIS,pointIS,&isectIS);CHKERRQ(ierr);
1504       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1505       pointIS = isectIS;
1506     }
1507     ierr = ISGetLocalSize(pointIS,&numFaces);CHKERRQ(ierr);
1508     ierr = ISGetIndices(pointIS,&points);CHKERRQ(ierr);
1509     ierr = PetscMalloc4(numFaces*totDim, &u, locX_t ? numFaces*totDim : 0, &u_t, numFaces*totDim, &elemVec, locA ? numFaces*totDimAux : 0, &a);CHKERRQ(ierr);
1510     ierr = DMFieldGetDegree(coordField,pointIS,NULL,&maxDegree);CHKERRQ(ierr);
1511     if (maxDegree <= 1) {
1512       ierr = DMFieldCreateDefaultQuadrature(coordField,pointIS,&qGeom);CHKERRQ(ierr);
1513     }
1514     if (!qGeom) {
1515       PetscFE fe;
1516 
1517       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1518       ierr = PetscFEGetFaceQuadrature(fe, &qGeom);CHKERRQ(ierr);
1519       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
1520     }
1521     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1522     ierr = DMSNESGetFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
1523     for (face = 0; face < numFaces; ++face) {
1524       const PetscInt point = points[face], *support, *cone;
1525       PetscScalar   *x     = NULL;
1526       PetscInt       i, coneSize, faceLoc;
1527 
1528       ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
1529       ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
1530       ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
1531       for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
1532       if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %D in cone of support[0] %D", point, support[0]);
1533       fgeom->face[face][0] = faceLoc;
1534       ierr = DMPlexVecGetClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1535       for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
1536       ierr = DMPlexVecRestoreClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1537       if (locX_t) {
1538         ierr = DMPlexVecGetClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1539         for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
1540         ierr = DMPlexVecRestoreClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1541       }
1542       if (locA) {
1543         PetscInt subp;
1544 
1545         ierr = DMPlexGetAuxiliaryPoint(plex, plexA, support[0], &subp);CHKERRQ(ierr);
1546         ierr = DMPlexVecGetClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
1547         for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
1548         ierr = DMPlexVecRestoreClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
1549       }
1550     }
1551     ierr = PetscMemzero(elemVec, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1552     {
1553       PetscFE         fe;
1554       PetscInt        Nb;
1555       PetscFEGeom     *chunkGeom = NULL;
1556       /* Conforming batches */
1557       PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1558       /* Remainder */
1559       PetscInt        Nr, offset;
1560 
1561       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1562       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1563       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1564       /* TODO: documentation is unclear about what is going on with these numbers: how should Nb / Nq factor in ? */
1565       blockSize = Nb;
1566       batchSize = numBlocks * blockSize;
1567       ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1568       numChunks = numFaces / (numBatches*batchSize);
1569       Ne        = numChunks*numBatches*batchSize;
1570       Nr        = numFaces % (numBatches*batchSize);
1571       offset    = numFaces - Nr;
1572       ierr = PetscFEGeomGetChunk(fgeom,0,offset,&chunkGeom);CHKERRQ(ierr);
1573       ierr = PetscFEIntegrateBdResidual(fe, prob, field, Ne, chunkGeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1574       ierr = PetscFEGeomRestoreChunk(fgeom, 0, offset, &chunkGeom);CHKERRQ(ierr);
1575       ierr = PetscFEGeomGetChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
1576       ierr = PetscFEIntegrateBdResidual(fe, 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);
1577       ierr = PetscFEGeomRestoreChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
1578     }
1579     for (face = 0; face < numFaces; ++face) {
1580       const PetscInt point = points[face], *support;
1581 
1582       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDim, &elemVec[face*totDim]);CHKERRQ(ierr);}
1583       ierr = DMPlexGetSupport(plex, point, &support);CHKERRQ(ierr);
1584       ierr = DMPlexVecSetClosure(plex, NULL, locF, support[0], &elemVec[face*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1585     }
1586     ierr = DMSNESRestoreFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
1587     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
1588     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1589     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1590     ierr = PetscFree4(u, u_t, elemVec, a);CHKERRQ(ierr);
1591   }
1592   if (plex)  {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
1593   if (plexA) {ierr = DMDestroy(&plexA);CHKERRQ(ierr);}
1594   PetscFunctionReturn(0);
1595 }
1596 
1597 PetscErrorCode DMPlexComputeBdResidualSingle(DM dm, PetscReal t, DMLabel label, PetscInt numValues, const PetscInt values[], PetscInt field, Vec locX, Vec locX_t, Vec locF)
1598 {
1599   DMField        coordField;
1600   DMLabel        depthLabel;
1601   IS             facetIS;
1602   PetscInt       dim;
1603   PetscErrorCode ierr;
1604 
1605   PetscFunctionBegin;
1606   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1607   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1608   ierr = DMLabelGetStratumIS(depthLabel, dim-1, &facetIS);CHKERRQ(ierr);
1609   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1610   ierr = DMPlexComputeBdResidual_Single_Internal(dm, t, label, numValues, values, field, locX, locX_t, locF, coordField, facetIS);CHKERRQ(ierr);
1611   PetscFunctionReturn(0);
1612 }
1613 
1614 PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1615 {
1616   PetscDS        prob;
1617   PetscInt       numBd, bd;
1618   DMField        coordField = NULL;
1619   IS             facetIS    = NULL;
1620   DMLabel        depthLabel;
1621   PetscInt       dim;
1622   PetscErrorCode ierr;
1623 
1624   PetscFunctionBegin;
1625   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1626   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1627   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1628   ierr = DMLabelGetStratumIS(depthLabel,dim - 1,&facetIS);CHKERRQ(ierr);
1629   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
1630   for (bd = 0; bd < numBd; ++bd) {
1631     DMBoundaryConditionType type;
1632     const char             *bdLabel;
1633     DMLabel                 label;
1634     const PetscInt         *values;
1635     PetscInt                field, numValues;
1636     PetscObject             obj;
1637     PetscClassId            id;
1638 
1639     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1640     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
1641     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1642     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
1643     if (!facetIS) {
1644       DMLabel  depthLabel;
1645       PetscInt dim;
1646 
1647       ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1648       ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1649       ierr = DMLabelGetStratumIS(depthLabel, dim - 1, &facetIS);CHKERRQ(ierr);
1650     }
1651     ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1652     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1653     ierr = DMPlexComputeBdResidual_Single_Internal(dm, t, label, numValues, values, field, locX, locX_t, locF, coordField, facetIS);CHKERRQ(ierr);
1654   }
1655   ierr = ISDestroy(&facetIS);CHKERRQ(ierr);
1656   PetscFunctionReturn(0);
1657 }
1658 
1659 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, IS cellIS, PetscReal time, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1660 {
1661   DM_Plex         *mesh       = (DM_Plex *) dm->data;
1662   const char      *name       = "Residual";
1663   DM               dmAux      = NULL;
1664   DM               dmGrad     = NULL;
1665   DMLabel          ghostLabel = NULL;
1666   PetscDS          prob       = NULL;
1667   PetscDS          probAux    = NULL;
1668   PetscSection     section    = NULL;
1669   PetscBool        useFEM     = PETSC_FALSE;
1670   PetscBool        useFVM     = PETSC_FALSE;
1671   PetscBool        isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
1672   PetscFV          fvm        = NULL;
1673   PetscFVCellGeom *cgeomFVM   = NULL;
1674   PetscFVFaceGeom *fgeomFVM   = NULL;
1675   DMField          coordField = NULL;
1676   Vec              locA, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1677   PetscScalar     *u = NULL, *u_t, *a, *uL, *uR;
1678   IS               chunkIS;
1679   const PetscInt  *cells;
1680   PetscInt         cStart, cEnd, numCells;
1681   PetscInt         Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
1682   PetscInt         maxDegree = PETSC_MAX_INT;
1683   PetscQuadrature  affineQuad = NULL, *quads = NULL;
1684   PetscFEGeom     *affineGeom = NULL, **geoms = NULL;
1685   PetscErrorCode   ierr;
1686 
1687   PetscFunctionBegin;
1688   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1689   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1690   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
1691   /* FEM+FVM */
1692   ierr = ISGetPointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
1693   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1694   /* 1: Get sizes from dm and dmAux */
1695   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1696   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1697   ierr = DMGetCellDS(dm, cStart, &prob);CHKERRQ(ierr);
1698   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1699   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1700   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1701   if (locA) {
1702     PetscInt subcell;
1703     ierr = DMPlexGetAuxiliaryPoint(dm, dmAux, cStart, &subcell);CHKERRQ(ierr);
1704     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1705     ierr = DMGetCellDS(dmAux, subcell, &probAux);CHKERRQ(ierr);
1706     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1707   }
1708   /* 2: Get geometric data */
1709   for (f = 0; f < Nf; ++f) {
1710     PetscObject  obj;
1711     PetscClassId id;
1712     PetscBool    fimp;
1713 
1714     ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1715     if (isImplicit != fimp) continue;
1716     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1717     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1718     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1719     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1720   }
1721   if (useFEM) {
1722     ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1723     ierr = DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);CHKERRQ(ierr);
1724     if (maxDegree <= 1) {
1725       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&affineQuad);CHKERRQ(ierr);
1726       if (affineQuad) {
1727         ierr = DMSNESGetFEGeom(coordField,cellIS,affineQuad,PETSC_FALSE,&affineGeom);CHKERRQ(ierr);
1728       }
1729     } else {
1730       ierr = PetscCalloc2(Nf,&quads,Nf,&geoms);CHKERRQ(ierr);
1731       for (f = 0; f < Nf; ++f) {
1732         PetscObject  obj;
1733         PetscClassId id;
1734         PetscBool    fimp;
1735 
1736         ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1737         if (isImplicit != fimp) continue;
1738         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1739         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1740         if (id == PETSCFE_CLASSID) {
1741           PetscFE fe = (PetscFE) obj;
1742 
1743           ierr = PetscFEGetQuadrature(fe, &quads[f]);CHKERRQ(ierr);
1744           ierr = PetscObjectReference((PetscObject)quads[f]);CHKERRQ(ierr);
1745           ierr = DMSNESGetFEGeom(coordField,cellIS,quads[f],PETSC_FALSE,&geoms[f]);CHKERRQ(ierr);
1746         }
1747       }
1748     }
1749   }
1750   if (useFVM) {
1751     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1752     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1753     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1754     /* Reconstruct and limit cell gradients */
1755     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1756     if (dmGrad) {
1757       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1758       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1759       ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1760       /* Communicate gradient values */
1761       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1762       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1763       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1764       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1765     }
1766     /* Handle non-essential (e.g. outflow) boundary values */
1767     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1768   }
1769   /* Loop over chunks */
1770   if (useFEM) {ierr = ISCreate(PETSC_COMM_SELF, &chunkIS);CHKERRQ(ierr);}
1771   numCells      = cEnd - cStart;
1772   numChunks     = 1;
1773   cellChunkSize = numCells/numChunks;
1774   faceChunkSize = (fEnd - fStart)/numChunks;
1775   numChunks     = PetscMin(1,numCells);
1776   for (chunk = 0; chunk < numChunks; ++chunk) {
1777     PetscScalar     *elemVec, *fluxL, *fluxR;
1778     PetscReal       *vol;
1779     PetscFVFaceGeom *fgeom;
1780     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, c;
1781     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = 0, face;
1782 
1783     /* Extract field coefficients */
1784     if (useFEM) {
1785       ierr = ISGetPointSubrange(chunkIS, cS, cE, cells);CHKERRQ(ierr);
1786       ierr = DMPlexGetCellFields(dm, chunkIS, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1787       ierr = DMGetWorkArray(dm, numCells*totDim, MPIU_SCALAR, &elemVec);CHKERRQ(ierr);
1788       ierr = PetscMemzero(elemVec, numCells*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1789     }
1790     if (useFVM) {
1791       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1792       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1793       ierr = DMGetWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxL);CHKERRQ(ierr);
1794       ierr = DMGetWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxR);CHKERRQ(ierr);
1795       ierr = PetscMemzero(fluxL, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1796       ierr = PetscMemzero(fluxR, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1797     }
1798     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1799     /* Loop over fields */
1800     for (f = 0; f < Nf; ++f) {
1801       PetscObject  obj;
1802       PetscClassId id;
1803       PetscBool    fimp;
1804       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1805 
1806       ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1807       if (isImplicit != fimp) continue;
1808       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1809       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1810       if (id == PETSCFE_CLASSID) {
1811         PetscFE         fe = (PetscFE) obj;
1812         PetscFEGeom    *geom = affineGeom ? affineGeom : geoms[f];
1813         PetscFEGeom    *chunkGeom = NULL;
1814         PetscQuadrature quad = affineQuad ? affineQuad : quads[f];
1815         PetscInt        Nq, Nb;
1816 
1817         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1818         ierr = PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1819         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1820         blockSize = Nb;
1821         batchSize = numBlocks * blockSize;
1822         ierr      = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1823         numChunks = numCells / (numBatches*batchSize);
1824         Ne        = numChunks*numBatches*batchSize;
1825         Nr        = numCells % (numBatches*batchSize);
1826         offset    = numCells - Nr;
1827         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1828         /*   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) */
1829         ierr = PetscFEGeomGetChunk(geom,0,offset,&chunkGeom);CHKERRQ(ierr);
1830         ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, chunkGeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1831         ierr = PetscFEGeomGetChunk(geom,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1832         ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, chunkGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1833         ierr = PetscFEGeomRestoreChunk(geom,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1834       } else if (id == PETSCFV_CLASSID) {
1835         PetscFV fv = (PetscFV) obj;
1836 
1837         Ne = numFaces;
1838         /* Riemann solve over faces (need fields at face centroids) */
1839         /*   We need to evaluate FE fields at those coordinates */
1840         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1841       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1842     }
1843     /* Loop over domain */
1844     if (useFEM) {
1845       /* Add elemVec to locX */
1846       for (c = cS; c < cE; ++c) {
1847         const PetscInt cell = cells ? cells[c] : c;
1848         const PetscInt cind = c - cStart;
1849 
1850         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cind*totDim]);CHKERRQ(ierr);}
1851         if (ghostLabel) {
1852           PetscInt ghostVal;
1853 
1854           ierr = DMLabelGetValue(ghostLabel,cell,&ghostVal);CHKERRQ(ierr);
1855           if (ghostVal > 0) continue;
1856         }
1857         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cind*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1858       }
1859     }
1860     if (useFVM) {
1861       PetscScalar *fa;
1862       PetscInt     iface;
1863 
1864       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1865       for (f = 0; f < Nf; ++f) {
1866         PetscFV      fv;
1867         PetscObject  obj;
1868         PetscClassId id;
1869         PetscInt     foff, pdim;
1870 
1871         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1872         ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1873         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1874         if (id != PETSCFV_CLASSID) continue;
1875         fv   = (PetscFV) obj;
1876         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1877         /* Accumulate fluxes to cells */
1878         for (face = fS, iface = 0; face < fE; ++face) {
1879           const PetscInt *scells;
1880           PetscScalar    *fL = NULL, *fR = NULL;
1881           PetscInt        ghost, d, nsupp, nchild;
1882 
1883           ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1884           ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1885           ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1886           if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1887           ierr = DMPlexGetSupport(dm, face, &scells);CHKERRQ(ierr);
1888           ierr = DMLabelGetValue(ghostLabel,scells[0],&ghost);CHKERRQ(ierr);
1889           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, scells[0], f, fa, &fL);CHKERRQ(ierr);}
1890           ierr = DMLabelGetValue(ghostLabel,scells[1],&ghost);CHKERRQ(ierr);
1891           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, scells[1], f, fa, &fR);CHKERRQ(ierr);}
1892           for (d = 0; d < pdim; ++d) {
1893             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
1894             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
1895           }
1896           ++iface;
1897         }
1898       }
1899       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1900     }
1901     /* Handle time derivative */
1902     if (locX_t) {
1903       PetscScalar *x_t, *fa;
1904 
1905       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1906       ierr = VecGetArray(locX_t, &x_t);CHKERRQ(ierr);
1907       for (f = 0; f < Nf; ++f) {
1908         PetscFV      fv;
1909         PetscObject  obj;
1910         PetscClassId id;
1911         PetscInt     pdim, d;
1912 
1913         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1914         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1915         if (id != PETSCFV_CLASSID) continue;
1916         fv   = (PetscFV) obj;
1917         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1918         for (c = cS; c < cE; ++c) {
1919           const PetscInt cell = cells ? cells[c] : c;
1920           PetscScalar   *u_t, *r;
1921 
1922           if (ghostLabel) {
1923             PetscInt ghostVal;
1924 
1925             ierr = DMLabelGetValue(ghostLabel, cell, &ghostVal);CHKERRQ(ierr);
1926             if (ghostVal > 0) continue;
1927           }
1928           ierr = DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);CHKERRQ(ierr);
1929           ierr = DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);CHKERRQ(ierr);
1930           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
1931         }
1932       }
1933       ierr = VecRestoreArray(locX_t, &x_t);CHKERRQ(ierr);
1934       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1935     }
1936     if (useFEM) {
1937       ierr = DMPlexRestoreCellFields(dm, chunkIS, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1938       ierr = DMRestoreWorkArray(dm, numCells*totDim, MPIU_SCALAR, &elemVec);CHKERRQ(ierr);
1939     }
1940     if (useFVM) {
1941       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1942       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1943       ierr = DMRestoreWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxL);CHKERRQ(ierr);
1944       ierr = DMRestoreWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxR);CHKERRQ(ierr);
1945       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1946     }
1947   }
1948   if (useFEM) {ierr = ISDestroy(&chunkIS);CHKERRQ(ierr);}
1949   ierr = ISRestorePointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
1950 
1951   if (useFEM) {
1952     ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, t, locF, user);CHKERRQ(ierr);
1953 
1954     if (maxDegree <= 1) {
1955       ierr = DMSNESRestoreFEGeom(coordField,cellIS,affineQuad,PETSC_FALSE,&affineGeom);CHKERRQ(ierr);
1956       ierr = PetscQuadratureDestroy(&affineQuad);CHKERRQ(ierr);
1957     } else {
1958       for (f = 0; f < Nf; ++f) {
1959         ierr = DMSNESRestoreFEGeom(coordField,cellIS,quads[f],PETSC_FALSE,&geoms[f]);CHKERRQ(ierr);
1960         ierr = PetscQuadratureDestroy(&quads[f]);CHKERRQ(ierr);
1961       }
1962       ierr = PetscFree2(quads,geoms);CHKERRQ(ierr);
1963     }
1964   }
1965 
1966   /* FEM */
1967   /* 1: Get sizes from dm and dmAux */
1968   /* 2: Get geometric data */
1969   /* 3: Handle boundary values */
1970   /* 4: Loop over domain */
1971   /*   Extract coefficients */
1972   /* Loop over fields */
1973   /*   Set tiling for FE*/
1974   /*   Integrate FE residual to get elemVec */
1975   /*     Loop over subdomain */
1976   /*       Loop over quad points */
1977   /*         Transform coords to real space */
1978   /*         Evaluate field and aux fields at point */
1979   /*         Evaluate residual at point */
1980   /*         Transform residual to real space */
1981   /*       Add residual to elemVec */
1982   /* Loop over domain */
1983   /*   Add elemVec to locX */
1984 
1985   /* FVM */
1986   /* Get geometric data */
1987   /* If using gradients */
1988   /*   Compute gradient data */
1989   /*   Loop over domain faces */
1990   /*     Count computational faces */
1991   /*     Reconstruct cell gradient */
1992   /*   Loop over domain cells */
1993   /*     Limit cell gradients */
1994   /* Handle boundary values */
1995   /* Loop over domain faces */
1996   /*   Read out field, centroid, normal, volume for each side of face */
1997   /* Riemann solve over faces */
1998   /* Loop over domain faces */
1999   /*   Accumulate fluxes to cells */
2000   /* TODO Change printFEM to printDisc here */
2001   if (mesh->printFEM) {
2002     Vec         locFbc;
2003     PetscInt    pStart, pEnd, p, maxDof;
2004     PetscScalar *zeroes;
2005 
2006     ierr = VecDuplicate(locF,&locFbc);CHKERRQ(ierr);
2007     ierr = VecCopy(locF,locFbc);CHKERRQ(ierr);
2008     ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
2009     ierr = PetscSectionGetMaxDof(section,&maxDof);CHKERRQ(ierr);
2010     ierr = PetscCalloc1(maxDof,&zeroes);CHKERRQ(ierr);
2011     for (p = pStart; p < pEnd; p++) {
2012       ierr = VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);CHKERRQ(ierr);
2013     }
2014     ierr = PetscFree(zeroes);CHKERRQ(ierr);
2015     ierr = DMPrintLocalVec(dm, name, mesh->printTol, locFbc);CHKERRQ(ierr);
2016     ierr = VecDestroy(&locFbc);CHKERRQ(ierr);
2017   }
2018   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
2019   PetscFunctionReturn(0);
2020 }
2021 
2022 static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, PetscReal t, Vec F, void *user)
2023 {
2024   DM                dmCh, dmAux;
2025   Vec               A;
2026   DMField           coordField = NULL;
2027   PetscDS           prob, probCh, probAux = NULL;
2028   PetscSection      section, sectionAux;
2029   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
2030   PetscInt          Nf, f, numCells, cStart, cEnd, c;
2031   PetscInt          totDim, totDimAux = 0, diffCell = 0;
2032   PetscInt          depth;
2033   PetscInt          maxDegree;
2034   IS                cellIS;
2035   DMLabel           depthLabel;
2036   PetscErrorCode    ierr;
2037 
2038   PetscFunctionBegin;
2039   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
2040   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2041   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2042   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2043   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2044   numCells = cEnd - cStart;
2045   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
2046   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
2047   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2048   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2049   if (dmAux) {
2050     ierr = DMGetSection(dmAux, &sectionAux);CHKERRQ(ierr);
2051     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2052     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2053   }
2054   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
2055   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);CHKERRQ(ierr);
2056   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
2057   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2058   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
2059   ierr = DMPlexGetDepth(dm,&depth);CHKERRQ(ierr);
2060   ierr = DMLabelGetStratumIS(depthLabel,depth,&cellIS);CHKERRQ(ierr);
2061   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2062   for (c = cStart; c < cEnd; ++c) {
2063     PetscScalar *x = NULL, *x_t = NULL;
2064     PetscInt     i;
2065 
2066     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2067     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
2068     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2069     if (X_t) {
2070       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2071       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
2072       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2073     }
2074     if (dmAux) {
2075       DM dmAuxPlex;
2076 
2077       ierr = DMSNESConvertPlex(dmAux,&dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
2078       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2079       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
2080       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2081       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
2082     }
2083   }
2084   for (f = 0; f < Nf; ++f) {
2085     PetscFE  fe, feCh;
2086     PetscInt Nq, Nb;
2087     /* Conforming batches */
2088     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2089     /* Remainder */
2090     PetscInt Nr, offset;
2091     PetscQuadrature qGeom = NULL;
2092     PetscFEGeom *cgeomFEM, *chunkGeom = NULL;
2093 
2094     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
2095     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
2096     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2097     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2098     ierr = DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);CHKERRQ(ierr);
2099     if (maxDegree <= 1) {
2100       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);CHKERRQ(ierr);
2101     }
2102     if (!qGeom) {
2103       ierr = PetscFEGetQuadrature(fe, &qGeom);CHKERRQ(ierr);
2104       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
2105     }
2106     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
2107     ierr = DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2108     blockSize = Nb;
2109     batchSize = numBlocks * blockSize;
2110     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2111     numChunks = numCells / (numBatches*batchSize);
2112     Ne        = numChunks*numBatches*batchSize;
2113     Nr        = numCells % (numBatches*batchSize);
2114     offset    = numCells - Nr;
2115     ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2116     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, chunkGeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
2117     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, chunkGeom, u, u_t, probAux, a, t, elemVecCh);CHKERRQ(ierr);
2118     ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&chunkGeom);CHKERRQ(ierr);
2119     ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, chunkGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVec[offset*totDim]);CHKERRQ(ierr);
2120     ierr = PetscFEIntegrateResidual(feCh, prob, f, Nr, chunkGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVecCh[offset*totDim]);CHKERRQ(ierr);
2121     ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&chunkGeom);CHKERRQ(ierr);
2122     ierr = DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2123     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2124   }
2125   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
2126   for (c = cStart; c < cEnd; ++c) {
2127     PetscBool diff = PETSC_FALSE;
2128     PetscInt  d;
2129 
2130     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
2131     if (diff) {
2132       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
2133       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
2134       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
2135       ++diffCell;
2136     }
2137     if (diffCell > 9) break;
2138     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
2139   }
2140   ierr = PetscFree3(u,u_t,elemVec);CHKERRQ(ierr);
2141   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
2142   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
2143   PetscFunctionReturn(0);
2144 }
2145 
2146 /*@
2147   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
2148 
2149   Input Parameters:
2150 + dm - The mesh
2151 . X  - Local solution
2152 - user - The user context
2153 
2154   Output Parameter:
2155 . F  - Local output vector
2156 
2157   Level: developer
2158 
2159 .seealso: DMPlexComputeJacobianAction()
2160 @*/
2161 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
2162 {
2163   PetscObject    check;
2164   DM             plex;
2165   IS             cellIS;
2166   PetscInt       depth;
2167   PetscErrorCode ierr;
2168 
2169   PetscFunctionBegin;
2170   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2171   ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
2172   ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
2173   if (!cellIS) {
2174     ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);
2175   }
2176   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
2177   ierr = PetscObjectQuery((PetscObject) plex, "dmCh", &check);CHKERRQ(ierr);
2178   if (check) {ierr = DMPlexComputeResidualFEM_Check_Internal(plex, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2179   else       {ierr = DMPlexComputeResidual_Internal(plex, cellIS, PETSC_MIN_REAL, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2180   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
2181   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2182   PetscFunctionReturn(0);
2183 }
2184 
2185 /*@
2186   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X
2187 
2188   Input Parameters:
2189 + dm - The mesh
2190 - user - The user context
2191 
2192   Output Parameter:
2193 . X  - Local solution
2194 
2195   Level: developer
2196 
2197 .seealso: DMPlexComputeJacobianAction()
2198 @*/
2199 PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
2200 {
2201   DM             plex;
2202   PetscErrorCode ierr;
2203 
2204   PetscFunctionBegin;
2205   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2206   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);CHKERRQ(ierr);
2207   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2208   PetscFunctionReturn(0);
2209 }
2210 
2211 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)
2212 {
2213   DM_Plex       *mesh = (DM_Plex *) dm->data;
2214   DM             plex = NULL, plexA = NULL;
2215   PetscDS        prob, probAux = NULL;
2216   PetscSection   section, sectionAux = NULL;
2217   PetscSection   globalSection, subSection = NULL;
2218   Vec            locA = NULL;
2219   PetscScalar   *u = NULL, *u_t = NULL, *a = NULL, *elemMat = NULL;
2220   PetscInt       v;
2221   PetscInt       Nf, totDim, totDimAux = 0;
2222   PetscBool      isMatISP;
2223   PetscErrorCode ierr;
2224 
2225   PetscFunctionBegin;
2226   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
2227   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
2228   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2229   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
2230   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2231   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
2232   if (locA) {
2233     DM dmAux;
2234 
2235     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
2236     ierr = DMConvert(dmAux, DMPLEX, &plexA);CHKERRQ(ierr);
2237     ierr = DMGetDS(plexA, &probAux);CHKERRQ(ierr);
2238     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2239     ierr = DMGetSection(plexA, &sectionAux);CHKERRQ(ierr);
2240   }
2241 
2242   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2243   ierr = DMGetGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2244   if (isMatISP) {ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);}
2245   for (v = 0; v < numValues; ++v) {
2246     PetscFEGeom    *fgeom;
2247     PetscInt        maxDegree;
2248     PetscQuadrature qGeom = NULL;
2249     IS              pointIS;
2250     const PetscInt *points;
2251     PetscInt        numFaces, face, Nq;
2252 
2253     ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
2254     if (!pointIS) continue; /* No points with that id on this process */
2255     {
2256       IS isectIS;
2257 
2258       /* TODO: Special cases of ISIntersect where it is quick to check a prior if one is a superset of the other */
2259       ierr = ISIntersect_Caching_Internal(facetIS,pointIS,&isectIS);CHKERRQ(ierr);
2260       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2261       pointIS = isectIS;
2262     }
2263     ierr = ISGetLocalSize(pointIS, &numFaces);CHKERRQ(ierr);
2264     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2265     ierr = PetscMalloc4(numFaces*totDim, &u, locX_t ? numFaces*totDim : 0, &u_t, numFaces*totDim*totDim, &elemMat, locA ? numFaces*totDimAux : 0, &a);CHKERRQ(ierr);
2266     ierr = DMFieldGetDegree(coordField,pointIS,NULL,&maxDegree);CHKERRQ(ierr);
2267     if (maxDegree <= 1) {
2268       ierr = DMFieldCreateDefaultQuadrature(coordField,pointIS,&qGeom);CHKERRQ(ierr);
2269     }
2270     if (!qGeom) {
2271       PetscFE fe;
2272 
2273       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2274       ierr = PetscFEGetFaceQuadrature(fe, &qGeom);CHKERRQ(ierr);
2275       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
2276     }
2277     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
2278     ierr = DMSNESGetFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
2279     for (face = 0; face < numFaces; ++face) {
2280       const PetscInt point = points[face], *support, *cone;
2281       PetscScalar   *x     = NULL;
2282       PetscInt       i, coneSize, faceLoc;
2283 
2284       ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
2285       ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
2286       ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
2287       for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
2288       if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of support[0] %d", point, support[0]);
2289       fgeom->face[face][0] = faceLoc;
2290       ierr = DMPlexVecGetClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
2291       for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
2292       ierr = DMPlexVecRestoreClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
2293       if (locX_t) {
2294         ierr = DMPlexVecGetClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
2295         for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
2296         ierr = DMPlexVecRestoreClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
2297       }
2298       if (locA) {
2299         PetscInt subp;
2300         ierr = DMPlexGetSubpoint(plexA, support[0], &subp);CHKERRQ(ierr);
2301         ierr = DMPlexVecGetClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
2302         for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
2303         ierr = DMPlexVecRestoreClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
2304       }
2305     }
2306     ierr = PetscMemzero(elemMat, numFaces*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2307     {
2308       PetscFE         fe;
2309       PetscInt        Nb;
2310       /* Conforming batches */
2311       PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2312       /* Remainder */
2313       PetscFEGeom    *chunkGeom = NULL;
2314       PetscInt        fieldJ, Nr, offset;
2315 
2316       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2317       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2318       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2319       blockSize = Nb;
2320       batchSize = numBlocks * blockSize;
2321       ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2322       numChunks = numFaces / (numBatches*batchSize);
2323       Ne        = numChunks*numBatches*batchSize;
2324       Nr        = numFaces % (numBatches*batchSize);
2325       offset    = numFaces - Nr;
2326       ierr = PetscFEGeomGetChunk(fgeom,0,offset,&chunkGeom);CHKERRQ(ierr);
2327       for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2328         ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2329       }
2330       ierr = PetscFEGeomGetChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
2331       for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2332         ierr = PetscFEIntegrateBdJacobian(fe, 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);
2333       }
2334       ierr = PetscFEGeomRestoreChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
2335     }
2336     for (face = 0; face < numFaces; ++face) {
2337       const PetscInt point = points[face], *support;
2338 
2339       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDim, totDim, &elemMat[face*totDim*totDim]);CHKERRQ(ierr);}
2340       ierr = DMPlexGetSupport(plex, point, &support);CHKERRQ(ierr);
2341       if (!isMatISP) {
2342         ierr = DMPlexMatSetClosure(plex, section, globalSection, JacP, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2343       } else {
2344         Mat lJ;
2345 
2346         ierr = MatISGetLocalMat(JacP, &lJ);CHKERRQ(ierr);
2347         ierr = DMPlexMatSetClosure(plex, section, subSection, lJ, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2348       }
2349     }
2350     ierr = DMSNESRestoreFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
2351     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2352     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2353     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2354     ierr = PetscFree4(u, u_t, elemMat, a);CHKERRQ(ierr);
2355   }
2356   if (plex)  {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
2357   if (plexA) {ierr = DMDestroy(&plexA);CHKERRQ(ierr);}
2358   PetscFunctionReturn(0);
2359 }
2360 
2361 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)
2362 {
2363   DMField        coordField;
2364   DMLabel        depthLabel;
2365   IS             facetIS;
2366   PetscInt       dim;
2367   PetscErrorCode ierr;
2368 
2369   PetscFunctionBegin;
2370   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2371   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
2372   ierr = DMLabelGetStratumIS(depthLabel, dim-1, &facetIS);CHKERRQ(ierr);
2373   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2374   ierr = DMPlexComputeBdJacobian_Single_Internal(dm, t, label, numValues, values, field, locX, locX_t, X_tShift, Jac, JacP, coordField, facetIS);CHKERRQ(ierr);
2375   PetscFunctionReturn(0);
2376 }
2377 
2378 PetscErrorCode DMPlexComputeBdJacobian_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, PetscReal X_tShift, Mat Jac, Mat JacP, void *user)
2379 {
2380   PetscDS          prob;
2381   PetscInt         dim, numBd, bd;
2382   DMLabel          depthLabel;
2383   DMField          coordField = NULL;
2384   IS               facetIS;
2385   PetscErrorCode   ierr;
2386 
2387   PetscFunctionBegin;
2388   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2389   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
2390   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2391   ierr = DMLabelGetStratumIS(depthLabel, dim-1, &facetIS);CHKERRQ(ierr);
2392   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
2393   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2394   for (bd = 0; bd < numBd; ++bd) {
2395     DMBoundaryConditionType type;
2396     const char             *bdLabel;
2397     DMLabel                 label;
2398     const PetscInt         *values;
2399     PetscInt                fieldI, numValues;
2400     PetscObject             obj;
2401     PetscClassId            id;
2402 
2403     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &fieldI, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
2404     ierr = PetscDSGetDiscretization(prob, fieldI, &obj);CHKERRQ(ierr);
2405     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2406     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
2407     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
2408     ierr = DMPlexComputeBdJacobian_Single_Internal(dm, t, label, numValues, values, fieldI, locX, locX_t, X_tShift, Jac, JacP, coordField, facetIS);CHKERRQ(ierr);
2409   }
2410   ierr = ISDestroy(&facetIS);CHKERRQ(ierr);
2411   PetscFunctionReturn(0);
2412 }
2413 
2414 PetscErrorCode DMPlexComputeJacobian_Internal(DM dm, IS cellIS, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Mat Jac, Mat JacP,void *user)
2415 {
2416   DM_Plex        *mesh  = (DM_Plex *) dm->data;
2417   const char     *name  = "Jacobian";
2418   DM              dmAux, plex;
2419   Vec             A;
2420   DMField         coordField;
2421   PetscDS         prob, probAux = NULL;
2422   PetscSection    section, globalSection, subSection, sectionAux;
2423   PetscScalar    *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
2424   const PetscInt *cells;
2425   PetscInt        Nf, fieldI, fieldJ;
2426   PetscInt        totDim, totDimAux, cStart, cEnd, numCells, c;
2427   PetscBool       isMatIS, isMatISP, hasJac, hasPrec, hasDyn, hasFV = PETSC_FALSE;
2428   PetscErrorCode  ierr;
2429 
2430   PetscFunctionBegin;
2431   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2432   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
2433   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2434   ierr = DMGetGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2435   if (isMatISP) {ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);}
2436   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2437   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2438   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2439   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2440   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2441   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2442   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2443   ierr = ISGetLocalSize(cellIS, &numCells);CHKERRQ(ierr);
2444   ierr = ISGetPointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
2445   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2446   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2447   if (dmAux) {
2448     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2449     ierr = DMGetSection(plex, &sectionAux);CHKERRQ(ierr);
2450     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2451     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2452   }
2453   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);
2454   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2455   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2456   for (c = cStart; c < cEnd; ++c) {
2457     const PetscInt cell = cells ? cells[c] : c;
2458     const PetscInt cind = c - cStart;
2459     PetscScalar   *x = NULL,  *x_t = NULL;
2460     PetscInt       i;
2461 
2462     ierr = DMPlexVecGetClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
2463     for (i = 0; i < totDim; ++i) u[cind*totDim+i] = x[i];
2464     ierr = DMPlexVecRestoreClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
2465     if (X_t) {
2466       ierr = DMPlexVecGetClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
2467       for (i = 0; i < totDim; ++i) u_t[cind*totDim+i] = x_t[i];
2468       ierr = DMPlexVecRestoreClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
2469     }
2470     if (dmAux) {
2471       PetscInt subcell;
2472       ierr = DMPlexGetAuxiliaryPoint(dm, dmAux, cell, &subcell);CHKERRQ(ierr);
2473       ierr = DMPlexVecGetClosure(plex, sectionAux, A, subcell, NULL, &x);CHKERRQ(ierr);
2474       for (i = 0; i < totDimAux; ++i) a[cind*totDimAux+i] = x[i];
2475       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, subcell, NULL, &x);CHKERRQ(ierr);
2476     }
2477   }
2478   if (hasJac)  {ierr = PetscMemzero(elemMat,  numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2479   if (hasPrec) {ierr = PetscMemzero(elemMatP, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2480   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2481   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2482     PetscClassId    id;
2483     PetscFE         fe;
2484     PetscQuadrature qGeom = NULL;
2485     PetscInt        Nb;
2486     /* Conforming batches */
2487     PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2488     /* Remainder */
2489     PetscInt        Nr, offset, Nq;
2490     PetscInt        maxDegree;
2491     PetscFEGeom     *cgeomFEM, *chunkGeom = NULL, *remGeom = NULL;
2492 
2493     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2494     ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
2495     if (id == PETSCFV_CLASSID) {hasFV = PETSC_TRUE; continue;}
2496     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2497     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2498     ierr = DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);CHKERRQ(ierr);
2499     if (maxDegree <= 1) {
2500       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);CHKERRQ(ierr);
2501     }
2502     if (!qGeom) {
2503       ierr = PetscFEGetQuadrature(fe,&qGeom);CHKERRQ(ierr);
2504       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
2505     }
2506     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
2507     ierr = DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2508     blockSize = Nb;
2509     batchSize = numBlocks * blockSize;
2510     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2511     numChunks = numCells / (numBatches*batchSize);
2512     Ne        = numChunks*numBatches*batchSize;
2513     Nr        = numCells % (numBatches*batchSize);
2514     offset    = numCells - Nr;
2515     ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2516     ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2517     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2518       if (hasJac) {
2519         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2520         ierr = PetscFEIntegrateJacobian(fe, 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);
2521       }
2522       if (hasPrec) {
2523         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatP);CHKERRQ(ierr);
2524         ierr = PetscFEIntegrateJacobian(fe, 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);
2525       }
2526       if (hasDyn) {
2527         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2528         ierr = PetscFEIntegrateJacobian(fe, 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);
2529       }
2530     }
2531     ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2532     ierr = PetscFEGeomRestoreChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2533     ierr = DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2534     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2535   }
2536   /*   Add contribution from X_t */
2537   if (hasDyn) {for (c = 0; c < numCells*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];}
2538   if (hasFV) {
2539     PetscClassId id;
2540     PetscFV      fv;
2541     PetscInt     offsetI, NcI, NbI = 1, fc, f;
2542 
2543     for (fieldI = 0; fieldI < Nf; ++fieldI) {
2544       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fv);CHKERRQ(ierr);
2545       ierr = PetscDSGetFieldOffset(prob, fieldI, &offsetI);CHKERRQ(ierr);
2546       ierr = PetscObjectGetClassId((PetscObject) fv, &id);CHKERRQ(ierr);
2547       if (id != PETSCFV_CLASSID) continue;
2548       /* Put in the identity */
2549       ierr = PetscFVGetNumComponents(fv, &NcI);CHKERRQ(ierr);
2550       for (c = cStart; c < cEnd; ++c) {
2551         const PetscInt cind    = c - cStart;
2552         const PetscInt eOffset = cind*totDim*totDim;
2553         for (fc = 0; fc < NcI; ++fc) {
2554           for (f = 0; f < NbI; ++f) {
2555             const PetscInt i = offsetI + f*NcI+fc;
2556             if (hasPrec) {
2557               if (hasJac) {elemMat[eOffset+i*totDim+i] = 1.0;}
2558               elemMatP[eOffset+i*totDim+i] = 1.0;
2559             } else {elemMat[eOffset+i*totDim+i] = 1.0;}
2560           }
2561         }
2562       }
2563     }
2564     /* No allocated space for FV stuff, so ignore the zero entries */
2565     ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2566   }
2567   /* Insert values into matrix */
2568   isMatIS = PETSC_FALSE;
2569   if (hasPrec && hasJac) {
2570     ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatIS);CHKERRQ(ierr);
2571   }
2572   if (isMatIS && !subSection) {
2573     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2574   }
2575   for (c = cStart; c < cEnd; ++c) {
2576     const PetscInt cell = cells ? cells[c] : c;
2577     const PetscInt cind = c - cStart;
2578 
2579     if (hasPrec) {
2580       if (hasJac) {
2581         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, totDim, totDim, &elemMat[cind*totDim*totDim]);CHKERRQ(ierr);}
2582         if (!isMatIS) {
2583           ierr = DMPlexMatSetClosure(dm, section, globalSection, Jac, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2584         } else {
2585           Mat lJ;
2586 
2587           ierr = MatISGetLocalMat(Jac,&lJ);CHKERRQ(ierr);
2588           ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2589         }
2590       }
2591       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, totDim, totDim, &elemMatP[cind*totDim*totDim]);CHKERRQ(ierr);}
2592       if (!isMatISP) {
2593         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, cell, &elemMatP[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2594       } else {
2595         Mat lJ;
2596 
2597         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2598         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, cell, &elemMatP[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2599       }
2600     } else {
2601       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, totDim, totDim, &elemMat[cind*totDim*totDim]);CHKERRQ(ierr);}
2602       if (!isMatISP) {
2603         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2604       } else {
2605         Mat lJ;
2606 
2607         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2608         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2609       }
2610     }
2611   }
2612   ierr = ISRestorePointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
2613   if (hasFV) {ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);CHKERRQ(ierr);}
2614   ierr = PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);CHKERRQ(ierr);
2615   if (dmAux) {
2616     ierr = PetscFree(a);CHKERRQ(ierr);
2617     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2618   }
2619   /* Compute boundary integrals */
2620   ierr = DMPlexComputeBdJacobian_Internal(dm, X, X_t, t, X_tShift, Jac, JacP, user);CHKERRQ(ierr);
2621   /* Assemble matrix */
2622   if (hasJac && hasPrec) {
2623     ierr = MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2624     ierr = MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2625   }
2626   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2627   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2628   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2629   PetscFunctionReturn(0);
2630 }
2631 
2632 /*@
2633   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.
2634 
2635   Input Parameters:
2636 + dm - The mesh
2637 . cellIS -
2638 . t  - The time
2639 . X_tShift - The multiplier for the Jacobian with repsect to X_t
2640 . X  - Local solution vector
2641 . X_t  - Time-derivative of the local solution vector
2642 . Y  - Local input vector
2643 - user - The user context
2644 
2645   Output Parameter:
2646 . Z - Local output vector
2647 
2648   Note:
2649   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2650   like a GPU, or vectorize on a multicore machine.
2651 
2652   Level: developer
2653 
2654 .seealso: FormFunctionLocal()
2655 @*/
2656 PetscErrorCode DMPlexComputeJacobianAction(DM dm, IS cellIS, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Vec Y, Vec Z, void *user)
2657 {
2658   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2659   const char       *name  = "Jacobian";
2660   DM                dmAux, plex, plexAux = NULL;
2661   Vec               A;
2662   PetscDS           prob, probAux = NULL;
2663   PetscQuadrature   quad;
2664   PetscSection      section, globalSection, sectionAux;
2665   PetscScalar      *elemMat, *elemMatD, *u, *u_t, *a = NULL, *y, *z;
2666   PetscInt          Nf, fieldI, fieldJ;
2667   PetscInt          totDim, totDimAux = 0;
2668   const PetscInt   *cells;
2669   PetscInt          cStart, cEnd, numCells, c;
2670   PetscBool         hasDyn;
2671   DMField           coordField;
2672   PetscErrorCode    ierr;
2673 
2674   PetscFunctionBegin;
2675   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2676   ierr = DMSNESConvertPlex(dm, &plex, PETSC_TRUE);CHKERRQ(ierr);
2677   if (!cellIS) {
2678     PetscInt depth;
2679 
2680     ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
2681     ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
2682     if (!cellIS) {ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);}
2683   } else {
2684     ierr = PetscObjectReference((PetscObject) cellIS);CHKERRQ(ierr);
2685   }
2686   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
2687   ierr = DMGetGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2688   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2689   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2690   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2691   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2692   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2693   ierr = ISGetLocalSize(cellIS, &numCells);CHKERRQ(ierr);
2694   ierr = ISGetPointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
2695   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2696   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2697   if (dmAux) {
2698     ierr = DMConvert(dmAux, DMPLEX, &plexAux);CHKERRQ(ierr);
2699     ierr = DMGetSection(plexAux, &sectionAux);CHKERRQ(ierr);
2700     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2701     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2702   }
2703   ierr = VecSet(Z, 0.0);CHKERRQ(ierr);
2704   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);
2705   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2706   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2707   for (c = cStart; c < cEnd; ++c) {
2708     const PetscInt cell = cells ? cells[c] : c;
2709     const PetscInt cind = c - cStart;
2710     PetscScalar   *x = NULL,  *x_t = NULL;
2711     PetscInt       i;
2712 
2713     ierr = DMPlexVecGetClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
2714     for (i = 0; i < totDim; ++i) u[cind*totDim+i] = x[i];
2715     ierr = DMPlexVecRestoreClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
2716     if (X_t) {
2717       ierr = DMPlexVecGetClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
2718       for (i = 0; i < totDim; ++i) u_t[cind*totDim+i] = x_t[i];
2719       ierr = DMPlexVecRestoreClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
2720     }
2721     if (dmAux) {
2722       PetscInt subcell;
2723       ierr = DMPlexGetAuxiliaryPoint(dm, dmAux, cell, &subcell);CHKERRQ(ierr);
2724       ierr = DMPlexVecGetClosure(plexAux, sectionAux, A, subcell, NULL, &x);CHKERRQ(ierr);
2725       for (i = 0; i < totDimAux; ++i) a[cind*totDimAux+i] = x[i];
2726       ierr = DMPlexVecRestoreClosure(plexAux, sectionAux, A, subcell, NULL, &x);CHKERRQ(ierr);
2727     }
2728     ierr = DMPlexVecGetClosure(dm, section, Y, cell, NULL, &x);CHKERRQ(ierr);
2729     for (i = 0; i < totDim; ++i) y[cind*totDim+i] = x[i];
2730     ierr = DMPlexVecRestoreClosure(dm, section, Y, cell, NULL, &x);CHKERRQ(ierr);
2731   }
2732   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2733   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2734   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2735     PetscFE  fe;
2736     PetscInt Nb;
2737     /* Conforming batches */
2738     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2739     /* Remainder */
2740     PetscInt Nr, offset, Nq;
2741     PetscQuadrature qGeom = NULL;
2742     PetscInt    maxDegree;
2743     PetscFEGeom *cgeomFEM, *chunkGeom = NULL, *remGeom = NULL;
2744 
2745     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2746     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2747     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2748     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2749     ierr = DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);CHKERRQ(ierr);
2750     if (maxDegree <= 1) {ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);CHKERRQ(ierr);}
2751     if (!qGeom) {
2752       ierr = PetscFEGetQuadrature(fe,&qGeom);CHKERRQ(ierr);
2753       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
2754     }
2755     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
2756     ierr = DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2757     blockSize = Nb;
2758     batchSize = numBlocks * blockSize;
2759     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2760     numChunks = numCells / (numBatches*batchSize);
2761     Ne        = numChunks*numBatches*batchSize;
2762     Nr        = numCells % (numBatches*batchSize);
2763     offset    = numCells - Nr;
2764     ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2765     ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2766     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2767       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2768       ierr = PetscFEIntegrateJacobian(fe, 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);
2769       if (hasDyn) {
2770         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2771         ierr = PetscFEIntegrateJacobian(fe, 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);
2772       }
2773     }
2774     ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2775     ierr = PetscFEGeomRestoreChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2776     ierr = DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2777     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2778   }
2779   if (hasDyn) {
2780     for (c = 0; c < numCells*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2781   }
2782   for (c = cStart; c < cEnd; ++c) {
2783     const PetscInt     cell = cells ? cells[c] : c;
2784     const PetscInt     cind = c - cStart;
2785     const PetscBLASInt M = totDim, one = 1;
2786     const PetscScalar  a = 1.0, b = 0.0;
2787 
2788     PetscStackCallBLAS("BLASgemv", BLASgemv_("N", &M, &M, &a, &elemMat[cind*totDim*totDim], &M, &y[cind*totDim], &one, &b, z, &one));
2789     if (mesh->printFEM > 1) {
2790       ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[cind*totDim*totDim]);CHKERRQ(ierr);
2791       ierr = DMPrintCellVector(c, "Y",  totDim, &y[cind*totDim]);CHKERRQ(ierr);
2792       ierr = DMPrintCellVector(c, "Z",  totDim, z);CHKERRQ(ierr);
2793     }
2794     ierr = DMPlexVecSetClosure(dm, section, Z, cell, z, ADD_VALUES);CHKERRQ(ierr);
2795   }
2796   ierr = PetscFree6(u,u_t,elemMat,elemMatD,y,z);CHKERRQ(ierr);
2797   if (mesh->printFEM) {
2798     ierr = PetscPrintf(PETSC_COMM_WORLD, "Z:\n");CHKERRQ(ierr);
2799     ierr = VecView(Z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2800   }
2801   ierr = PetscFree(a);CHKERRQ(ierr);
2802   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
2803   ierr = DMDestroy(&plexAux);CHKERRQ(ierr);
2804   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2805   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2806   PetscFunctionReturn(0);
2807 }
2808 
2809 /*@
2810   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2811 
2812   Input Parameters:
2813 + dm - The mesh
2814 . X  - Local input vector
2815 - user - The user context
2816 
2817   Output Parameter:
2818 . Jac  - Jacobian matrix
2819 
2820   Note:
2821   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2822   like a GPU, or vectorize on a multicore machine.
2823 
2824   Level: developer
2825 
2826 .seealso: FormFunctionLocal()
2827 @*/
2828 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2829 {
2830   DM             plex;
2831   PetscDS        prob;
2832   IS             cellIS;
2833   PetscBool      hasJac, hasPrec;
2834   PetscInt       depth;
2835   PetscErrorCode ierr;
2836 
2837   PetscFunctionBegin;
2838   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2839   ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
2840   ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
2841   if (!cellIS) {ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);}
2842   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2843   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2844   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2845   if (hasJac && hasPrec) {ierr = MatZeroEntries(Jac);CHKERRQ(ierr);}
2846   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
2847   ierr = DMPlexComputeJacobian_Internal(plex, cellIS, 0.0, 0.0, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2848   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
2849   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2850   PetscFunctionReturn(0);
2851 }
2852 
2853 /*@
2854   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.
2855 
2856   Input Parameters:
2857 + dm - The DM object
2858 . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see PetscDSAddBoundary())
2859 . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
2860 - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())
2861 
2862   Level: developer
2863 @*/
2864 PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
2865 {
2866   PetscErrorCode ierr;
2867 
2868   PetscFunctionBegin;
2869   ierr = DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);CHKERRQ(ierr);
2870   ierr = DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);CHKERRQ(ierr);
2871   ierr = DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);CHKERRQ(ierr);
2872   PetscFunctionReturn(0);
2873 }
2874 
2875 PetscErrorCode DMSNESCheckFromOptions_Internal(SNES snes, DM dm, Vec u, PetscErrorCode (**exactFuncs)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx), void **ctxs)
2876 {
2877   PetscErrorCode (**exacts)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx);
2878   PetscDS        prob;
2879   Mat            J, M;
2880   Vec            r, b;
2881   MatNullSpace   nullSpace;
2882   PetscReal     *error, res = 0.0;
2883   PetscInt       numFields;
2884   PetscBool      hasJac, hasPrec;
2885   PetscInt       Nf, f;
2886   PetscErrorCode ierr;
2887 
2888   PetscFunctionBegin;
2889   ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
2890   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2891   ierr = PetscMalloc1(Nf, &exacts);CHKERRQ(ierr);
2892   for (f = 0; f < Nf; ++f) {ierr = PetscDSGetExactSolution(prob, f, &exacts[f]);CHKERRQ(ierr);}
2893   ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2894   ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
2895   /* TODO Null space for J */
2896   /* Check discretization error */
2897   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
2898   ierr = PetscMalloc1(PetscMax(1, numFields), &error);CHKERRQ(ierr);
2899   ierr = DMProjectFunction(dm, 0.0, exactFuncs ? exactFuncs : exacts, ctxs, INSERT_ALL_VALUES, u);CHKERRQ(ierr);
2900   if (numFields > 1) {
2901     PetscInt f;
2902 
2903     ierr = DMComputeL2FieldDiff(dm, 0.0, exactFuncs ? exactFuncs : exacts, ctxs, u, error);CHKERRQ(ierr);
2904     ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: [");CHKERRQ(ierr);
2905     for (f = 0; f < numFields; ++f) {
2906       if (f) {ierr = PetscPrintf(PETSC_COMM_WORLD, ", ");CHKERRQ(ierr);}
2907       if (error[f] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "%g", (double)error[f]);CHKERRQ(ierr);}
2908       else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "< 1.0e-11");CHKERRQ(ierr);}
2909     }
2910     ierr = PetscPrintf(PETSC_COMM_WORLD, "]\n");CHKERRQ(ierr);
2911   } else {
2912     ierr = DMComputeL2Diff(dm, 0.0, exactFuncs ? exactFuncs : exacts, ctxs, u, &error[0]);CHKERRQ(ierr);
2913     if (error[0] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", (double)error[0]);CHKERRQ(ierr);}
2914     else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
2915   }
2916   ierr = PetscFree(error);CHKERRQ(ierr);
2917   /* Check residual */
2918   ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2919   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2920   ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", (double)res);CHKERRQ(ierr);
2921   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2922   ierr = PetscObjectSetName((PetscObject) r, "Initial Residual");CHKERRQ(ierr);
2923   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"res_");CHKERRQ(ierr);
2924   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2925   /* Check Jacobian */
2926   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2927   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2928   if (hasJac && hasPrec) {
2929     ierr = DMCreateMatrix(dm, &M);CHKERRQ(ierr);
2930     ierr = SNESComputeJacobian(snes, u, J, M);CHKERRQ(ierr);
2931     ierr = PetscObjectSetOptionsPrefix((PetscObject) M, "jacpre_");CHKERRQ(ierr);
2932     ierr = MatViewFromOptions(M, NULL, "-mat_view");CHKERRQ(ierr);
2933     ierr = MatDestroy(&M);CHKERRQ(ierr);
2934   } else {
2935     ierr = SNESComputeJacobian(snes, u, J, J);CHKERRQ(ierr);
2936   }
2937   ierr = PetscObjectSetOptionsPrefix((PetscObject) J, "jac_");CHKERRQ(ierr);
2938   ierr = MatViewFromOptions(J, NULL, "-mat_view");CHKERRQ(ierr);
2939   ierr = MatGetNullSpace(J, &nullSpace);CHKERRQ(ierr);
2940   if (nullSpace) {
2941     PetscBool isNull;
2942     ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
2943     if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
2944   }
2945   ierr = VecDuplicate(u, &b);CHKERRQ(ierr);
2946   ierr = VecSet(r, 0.0);CHKERRQ(ierr);
2947   ierr = SNESComputeFunction(snes, r, b);CHKERRQ(ierr);
2948   ierr = MatMult(J, u, r);CHKERRQ(ierr);
2949   ierr = VecAXPY(r, 1.0, b);CHKERRQ(ierr);
2950   ierr = VecDestroy(&b);CHKERRQ(ierr);
2951   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2952   ierr = PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", (double)res);CHKERRQ(ierr);
2953   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2954   ierr = PetscObjectSetName((PetscObject) r, "Au - b = Au + F(0)");CHKERRQ(ierr);
2955   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"linear_res_");CHKERRQ(ierr);
2956   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2957   ierr = VecDestroy(&r);CHKERRQ(ierr);
2958   ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
2959   ierr = MatDestroy(&J);CHKERRQ(ierr);
2960   ierr = PetscFree(exacts);CHKERRQ(ierr);
2961   PetscFunctionReturn(0);
2962 }
2963 
2964 /*@C
2965   DMSNESCheckFromOptions - Check the residual and Jacobian functions using the exact solution by outputting some diagnostic information
2966 
2967   Input Parameters:
2968 + snes - the SNES object
2969 . u    - representative SNES vector
2970 . exactFuncs - pointwise functions of the exact solution for each field
2971 - ctxs - contexts for the functions
2972 
2973   Level: developer
2974 @*/
2975 PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
2976 {
2977   PetscErrorCode (**exact)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *) = NULL;
2978   DM             dm;
2979   PetscDS        prob;
2980   Vec            sol;
2981   PetscBool      check;
2982   PetscInt       Nf, f;
2983   PetscErrorCode ierr;
2984 
2985   PetscFunctionBegin;
2986   ierr = PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);CHKERRQ(ierr);
2987   if (!check) PetscFunctionReturn(0);
2988   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
2989   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2990   if (!exactFuncs) {
2991     ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
2992     ierr = PetscMalloc1(Nf, &exact);CHKERRQ(ierr);
2993     for (f = 0; f < Nf; ++f) {ierr = PetscDSGetExactSolution(prob, f, &exact[f]);CHKERRQ(ierr);}
2994   }
2995   ierr = VecDuplicate(u, &sol);CHKERRQ(ierr);
2996   ierr = SNESSetSolution(snes, sol);CHKERRQ(ierr);
2997   ierr = DMSNESCheckFromOptions_Internal(snes, dm, sol, exactFuncs ? exactFuncs : exact, ctxs);CHKERRQ(ierr);
2998   ierr = VecDestroy(&sol);CHKERRQ(ierr);
2999   ierr = PetscFree(exact);CHKERRQ(ierr);
3000   PetscFunctionReturn(0);
3001 }
3002