xref: /petsc/src/snes/utils/dmplexsnes.c (revision 2d91c9818a784ae628fba61425cc587ede032d33)
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 #undef __FUNCT__
11 #define __FUNCT__ "DMSNESConvertPlex"
12 static PetscErrorCode DMSNESConvertPlex(DM dm, DM *plex, PetscBool copy)
13 {
14   PetscBool      isPlex;
15   PetscErrorCode ierr;
16 
17   PetscFunctionBegin;
18   ierr = PetscObjectTypeCompare((PetscObject) dm, DMPLEX, &isPlex);CHKERRQ(ierr);
19   if (isPlex) {
20     *plex = dm;
21     ierr = PetscObjectReference((PetscObject) dm);CHKERRQ(ierr);
22   } else {
23     ierr = PetscObjectQuery((PetscObject) dm, "dm_plex", (PetscObject *) plex);CHKERRQ(ierr);
24     if (!*plex) {
25       ierr = DMConvert(dm,DMPLEX,plex);CHKERRQ(ierr);
26       ierr = PetscObjectCompose((PetscObject) dm, "dm_plex", (PetscObject) *plex);CHKERRQ(ierr);
27       if (copy) {
28         PetscInt    i;
29         PetscObject obj;
30         const char *comps[3] = {"A","dmAux","dmCh"};
31 
32         ierr = DMCopyDMSNES(dm, *plex);CHKERRQ(ierr);
33         for (i = 0; i < 3; i++) {
34           ierr = PetscObjectQuery((PetscObject) dm, comps[i], &obj);CHKERRQ(ierr);
35           ierr = PetscObjectCompose((PetscObject) *plex, comps[i], obj);CHKERRQ(ierr);
36         }
37       }
38     } else {
39       ierr = PetscObjectReference((PetscObject) *plex);CHKERRQ(ierr);
40     }
41   }
42   PetscFunctionReturn(0);
43 }
44 
45 #undef __FUNCT__
46 #define __FUNCT__ "DMInterpolationCreate"
47 PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx)
48 {
49   PetscErrorCode ierr;
50 
51   PetscFunctionBegin;
52   PetscValidPointer(ctx, 2);
53   ierr = PetscNew(ctx);CHKERRQ(ierr);
54 
55   (*ctx)->comm   = comm;
56   (*ctx)->dim    = -1;
57   (*ctx)->nInput = 0;
58   (*ctx)->points = NULL;
59   (*ctx)->cells  = NULL;
60   (*ctx)->n      = -1;
61   (*ctx)->coords = NULL;
62   PetscFunctionReturn(0);
63 }
64 
65 #undef __FUNCT__
66 #define __FUNCT__ "DMInterpolationSetDim"
67 PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim)
68 {
69   PetscFunctionBegin;
70   if ((dim < 1) || (dim > 3)) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %d", dim);
71   ctx->dim = dim;
72   PetscFunctionReturn(0);
73 }
74 
75 #undef __FUNCT__
76 #define __FUNCT__ "DMInterpolationGetDim"
77 PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim)
78 {
79   PetscFunctionBegin;
80   PetscValidIntPointer(dim, 2);
81   *dim = ctx->dim;
82   PetscFunctionReturn(0);
83 }
84 
85 #undef __FUNCT__
86 #define __FUNCT__ "DMInterpolationSetDof"
87 PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof)
88 {
89   PetscFunctionBegin;
90   if (dof < 1) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %d", dof);
91   ctx->dof = dof;
92   PetscFunctionReturn(0);
93 }
94 
95 #undef __FUNCT__
96 #define __FUNCT__ "DMInterpolationGetDof"
97 PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof)
98 {
99   PetscFunctionBegin;
100   PetscValidIntPointer(dof, 2);
101   *dof = ctx->dof;
102   PetscFunctionReturn(0);
103 }
104 
105 #undef __FUNCT__
106 #define __FUNCT__ "DMInterpolationAddPoints"
107 PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[])
108 {
109   PetscErrorCode ierr;
110 
111   PetscFunctionBegin;
112   if (ctx->dim < 0) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
113   if (ctx->points)  SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "Cannot add points multiple times yet");
114   ctx->nInput = n;
115 
116   ierr = PetscMalloc1(n*ctx->dim, &ctx->points);CHKERRQ(ierr);
117   ierr = PetscMemcpy(ctx->points, points, n*ctx->dim * sizeof(PetscReal));CHKERRQ(ierr);
118   PetscFunctionReturn(0);
119 }
120 
121 #undef __FUNCT__
122 #define __FUNCT__ "DMInterpolationSetUp"
123 PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints)
124 {
125   MPI_Comm          comm = ctx->comm;
126   PetscScalar       *a;
127   PetscInt          p, q, i;
128   PetscMPIInt       rank, size;
129   PetscErrorCode    ierr;
130   Vec               pointVec;
131   PetscSF           cellSF;
132   PetscLayout       layout;
133   PetscReal         *globalPoints;
134   PetscScalar       *globalPointsScalar;
135   const PetscInt    *ranges;
136   PetscMPIInt       *counts, *displs;
137   const PetscSFNode *foundCells;
138   const PetscInt    *foundPoints;
139   PetscMPIInt       *foundProcs, *globalProcs;
140   PetscInt          n, N, numFound;
141 
142   PetscFunctionBegin;
143   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
144   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
145   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
146   if (ctx->dim < 0) SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
147   /* Locate points */
148   n = ctx->nInput;
149   if (!redundantPoints) {
150     ierr = PetscLayoutCreate(comm, &layout);CHKERRQ(ierr);
151     ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
152     ierr = PetscLayoutSetLocalSize(layout, n);CHKERRQ(ierr);
153     ierr = PetscLayoutSetUp(layout);CHKERRQ(ierr);
154     ierr = PetscLayoutGetSize(layout, &N);CHKERRQ(ierr);
155     /* Communicate all points to all processes */
156     ierr = PetscMalloc3(N*ctx->dim,&globalPoints,size,&counts,size,&displs);CHKERRQ(ierr);
157     ierr = PetscLayoutGetRanges(layout, &ranges);CHKERRQ(ierr);
158     for (p = 0; p < size; ++p) {
159       counts[p] = (ranges[p+1] - ranges[p])*ctx->dim;
160       displs[p] = ranges[p]*ctx->dim;
161     }
162     ierr = MPI_Allgatherv(ctx->points, n*ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm);CHKERRQ(ierr);
163   } else {
164     N = n;
165     globalPoints = ctx->points;
166     counts = displs = NULL;
167     layout = NULL;
168   }
169 #if 0
170   ierr = PetscMalloc3(N,&foundCells,N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
171   /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */
172 #else
173 #if defined(PETSC_USE_COMPLEX)
174   ierr = PetscMalloc1(N,&globalPointsScalar);CHKERRQ(ierr);
175   for (i=0; i<N; i++) globalPointsScalar[i] = globalPoints[i];
176 #else
177   globalPointsScalar = globalPoints;
178 #endif
179   ierr = VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N*ctx->dim, globalPointsScalar, &pointVec);CHKERRQ(ierr);
180   ierr = PetscMalloc2(N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
181   for (p = 0; p < N; ++p) {foundProcs[p] = size;}
182   cellSF = NULL;
183   ierr = DMLocatePoints(dm, pointVec, DM_POINTLOCATION_REMOVE, &cellSF);CHKERRQ(ierr);
184   ierr = PetscSFGetGraph(cellSF,NULL,&numFound,&foundPoints,&foundCells);CHKERRQ(ierr);
185 #endif
186   for (p = 0; p < numFound; ++p) {
187     if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank;
188   }
189   /* Let the lowest rank process own each point */
190   ierr   = MPIU_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm);CHKERRQ(ierr);
191   ctx->n = 0;
192   for (p = 0; p < N; ++p) {
193     if (globalProcs[p] == size) SETERRQ4(comm, PETSC_ERR_PLIB, "Point %d: %g %g %g not located in mesh", p, globalPoints[p*ctx->dim+0], ctx->dim > 1 ? globalPoints[p*ctx->dim+1] : 0.0, ctx->dim > 2 ? globalPoints[p*ctx->dim+2] : 0.0);
194     else if (globalProcs[p] == rank) ctx->n++;
195   }
196   /* Create coordinates vector and array of owned cells */
197   ierr = PetscMalloc1(ctx->n, &ctx->cells);CHKERRQ(ierr);
198   ierr = VecCreate(comm, &ctx->coords);CHKERRQ(ierr);
199   ierr = VecSetSizes(ctx->coords, ctx->n*ctx->dim, PETSC_DECIDE);CHKERRQ(ierr);
200   ierr = VecSetBlockSize(ctx->coords, ctx->dim);CHKERRQ(ierr);
201   ierr = VecSetType(ctx->coords,VECSTANDARD);CHKERRQ(ierr);
202   ierr = VecGetArray(ctx->coords, &a);CHKERRQ(ierr);
203   for (p = 0, q = 0, i = 0; p < N; ++p) {
204     if (globalProcs[p] == rank) {
205       PetscInt d;
206 
207       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p*ctx->dim+d];
208       ctx->cells[q++] = foundCells[p].index;
209     }
210   }
211   ierr = VecRestoreArray(ctx->coords, &a);CHKERRQ(ierr);
212 #if 0
213   ierr = PetscFree3(foundCells,foundProcs,globalProcs);CHKERRQ(ierr);
214 #else
215   ierr = PetscFree2(foundProcs,globalProcs);CHKERRQ(ierr);
216   ierr = PetscSFDestroy(&cellSF);CHKERRQ(ierr);
217   ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
218 #endif
219   if ((void*)globalPointsScalar != (void*)globalPoints) {ierr = PetscFree(globalPointsScalar);CHKERRQ(ierr);}
220   if (!redundantPoints) {ierr = PetscFree3(globalPoints,counts,displs);CHKERRQ(ierr);}
221   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
222   PetscFunctionReturn(0);
223 }
224 
225 #undef __FUNCT__
226 #define __FUNCT__ "DMInterpolationGetCoordinates"
227 PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates)
228 {
229   PetscFunctionBegin;
230   PetscValidPointer(coordinates, 2);
231   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
232   *coordinates = ctx->coords;
233   PetscFunctionReturn(0);
234 }
235 
236 #undef __FUNCT__
237 #define __FUNCT__ "DMInterpolationGetVector"
238 PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v)
239 {
240   PetscErrorCode ierr;
241 
242   PetscFunctionBegin;
243   PetscValidPointer(v, 2);
244   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
245   ierr = VecCreate(ctx->comm, v);CHKERRQ(ierr);
246   ierr = VecSetSizes(*v, ctx->n*ctx->dof, PETSC_DECIDE);CHKERRQ(ierr);
247   ierr = VecSetBlockSize(*v, ctx->dof);CHKERRQ(ierr);
248   ierr = VecSetType(*v,VECSTANDARD);CHKERRQ(ierr);
249   PetscFunctionReturn(0);
250 }
251 
252 #undef __FUNCT__
253 #define __FUNCT__ "DMInterpolationRestoreVector"
254 PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v)
255 {
256   PetscErrorCode ierr;
257 
258   PetscFunctionBegin;
259   PetscValidPointer(v, 2);
260   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
261   ierr = VecDestroy(v);CHKERRQ(ierr);
262   PetscFunctionReturn(0);
263 }
264 
265 #undef __FUNCT__
266 #define __FUNCT__ "DMInterpolate_Triangle_Private"
267 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Triangle_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
268 {
269   PetscReal      *v0, *J, *invJ, detJ;
270   const PetscScalar *coords;
271   PetscScalar    *a;
272   PetscInt       p;
273   PetscErrorCode ierr;
274 
275   PetscFunctionBegin;
276   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
277   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
278   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
279   for (p = 0; p < ctx->n; ++p) {
280     PetscInt     c = ctx->cells[p];
281     PetscScalar *x = NULL;
282     PetscReal    xi[4];
283     PetscInt     d, f, comp;
284 
285     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
286     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
287     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
288     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
289 
290     for (d = 0; d < ctx->dim; ++d) {
291       xi[d] = 0.0;
292       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
293       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];
294     }
295     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
296   }
297   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
298   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
299   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
300   PetscFunctionReturn(0);
301 }
302 
303 #undef __FUNCT__
304 #define __FUNCT__ "DMInterpolate_Tetrahedron_Private"
305 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Tetrahedron_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
306 {
307   PetscReal      *v0, *J, *invJ, detJ;
308   const PetscScalar *coords;
309   PetscScalar    *a;
310   PetscInt       p;
311   PetscErrorCode ierr;
312 
313   PetscFunctionBegin;
314   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
315   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
316   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
317   for (p = 0; p < ctx->n; ++p) {
318     PetscInt       c = ctx->cells[p];
319     const PetscInt order[3] = {2, 1, 3};
320     PetscScalar   *x = NULL;
321     PetscReal      xi[4];
322     PetscInt       d, f, comp;
323 
324     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
325     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
326     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
327     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
328 
329     for (d = 0; d < ctx->dim; ++d) {
330       xi[d] = 0.0;
331       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
332       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];
333     }
334     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
335   }
336   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
337   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
338   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
339   PetscFunctionReturn(0);
340 }
341 
342 #undef __FUNCT__
343 #define __FUNCT__ "QuadMap_Private"
344 PETSC_STATIC_INLINE PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
345 {
346   const PetscScalar *vertices = (const PetscScalar*) ctx;
347   const PetscScalar x0        = vertices[0];
348   const PetscScalar y0        = vertices[1];
349   const PetscScalar x1        = vertices[2];
350   const PetscScalar y1        = vertices[3];
351   const PetscScalar x2        = vertices[4];
352   const PetscScalar y2        = vertices[5];
353   const PetscScalar x3        = vertices[6];
354   const PetscScalar y3        = vertices[7];
355   const PetscScalar f_1       = x1 - x0;
356   const PetscScalar g_1       = y1 - y0;
357   const PetscScalar f_3       = x3 - x0;
358   const PetscScalar g_3       = y3 - y0;
359   const PetscScalar f_01      = x2 - x1 - x3 + x0;
360   const PetscScalar g_01      = y2 - y1 - y3 + y0;
361   const PetscScalar *ref;
362   PetscScalar       *real;
363   PetscErrorCode    ierr;
364 
365   PetscFunctionBegin;
366   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
367   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
368   {
369     const PetscScalar p0 = ref[0];
370     const PetscScalar p1 = ref[1];
371 
372     real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1;
373     real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1;
374   }
375   ierr = PetscLogFlops(28);CHKERRQ(ierr);
376   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
377   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
378   PetscFunctionReturn(0);
379 }
380 
381 #include <petsc/private/dmimpl.h>
382 #undef __FUNCT__
383 #define __FUNCT__ "QuadJacobian_Private"
384 PETSC_STATIC_INLINE PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
385 {
386   const PetscScalar *vertices = (const PetscScalar*) ctx;
387   const PetscScalar x0        = vertices[0];
388   const PetscScalar y0        = vertices[1];
389   const PetscScalar x1        = vertices[2];
390   const PetscScalar y1        = vertices[3];
391   const PetscScalar x2        = vertices[4];
392   const PetscScalar y2        = vertices[5];
393   const PetscScalar x3        = vertices[6];
394   const PetscScalar y3        = vertices[7];
395   const PetscScalar f_01      = x2 - x1 - x3 + x0;
396   const PetscScalar g_01      = y2 - y1 - y3 + y0;
397   const PetscScalar *ref;
398   PetscErrorCode    ierr;
399 
400   PetscFunctionBegin;
401   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
402   {
403     const PetscScalar x       = ref[0];
404     const PetscScalar y       = ref[1];
405     const PetscInt    rows[2] = {0, 1};
406     PetscScalar       values[4];
407 
408     values[0] = (x1 - x0 + f_01*y) * 0.5; values[1] = (x3 - x0 + f_01*x) * 0.5;
409     values[2] = (y1 - y0 + g_01*y) * 0.5; values[3] = (y3 - y0 + g_01*x) * 0.5;
410     ierr      = MatSetValues(J, 2, rows, 2, rows, values, INSERT_VALUES);CHKERRQ(ierr);
411   }
412   ierr = PetscLogFlops(30);CHKERRQ(ierr);
413   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
414   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
415   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
416   PetscFunctionReturn(0);
417 }
418 
419 #undef __FUNCT__
420 #define __FUNCT__ "DMInterpolate_Quad_Private"
421 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
422 {
423   DM             dmCoord;
424   PetscFE        fem;
425   SNES           snes;
426   KSP            ksp;
427   PC             pc;
428   Vec            coordsLocal, r, ref, real;
429   Mat            J;
430   const PetscScalar *coords;
431   PetscScalar    *a;
432   PetscInt       p;
433   const PetscInt dof = ctx->dof;
434   PetscErrorCode ierr;
435 
436   PetscFunctionBegin;
437   ierr = DMGetField(dm, 0, (PetscObject *) &fem);CHKERRQ(ierr);
438   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
439   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
440   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
441   ierr = SNESSetOptionsPrefix(snes, "quad_interp_");CHKERRQ(ierr);
442   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
443   ierr = VecSetSizes(r, 2, 2);CHKERRQ(ierr);
444   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
445   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
446   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
447   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
448   ierr = MatSetSizes(J, 2, 2, 2, 2);CHKERRQ(ierr);
449   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
450   ierr = MatSetUp(J);CHKERRQ(ierr);
451   ierr = SNESSetFunction(snes, r, QuadMap_Private, NULL);CHKERRQ(ierr);
452   ierr = SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);CHKERRQ(ierr);
453   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
454   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
455   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
456   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
457 
458   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
459   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
460   for (p = 0; p < ctx->n; ++p) {
461     PetscScalar *x = NULL, *vertices = NULL;
462     PetscScalar *xi;
463     PetscReal    xir[2];
464     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
465 
466     /* Can make this do all points at once */
467     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
468     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 4*2);
469     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
470     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
471     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
472     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
473     xi[0]  = coords[p*ctx->dim+0];
474     xi[1]  = coords[p*ctx->dim+1];
475     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
476     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
477     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
478     xir[0] = PetscRealPart(xi[0]);
479     xir[1] = PetscRealPart(xi[1]);
480     if (4*dof != xSize) {
481       PetscReal *B;
482       PetscInt   d;
483 
484       xir[0] = 2.0*xir[0] - 1.0; xir[1] = 2.0*xir[1] - 1.0;
485       ierr = PetscFEGetTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
486       for (comp = 0; comp < dof; ++comp) {
487         a[p*dof+comp] = 0.0;
488         for (d = 0; d < xSize/dof; ++d) {
489           a[p*dof+comp] += x[d*dof+comp]*B[d*dof+comp];
490         }
491       }
492       ierr = PetscFERestoreTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
493     } else {
494       for (comp = 0; comp < dof; ++comp)
495         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];
496     }
497     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
498     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
499     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
500   }
501   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
502   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
503 
504   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
505   ierr = VecDestroy(&r);CHKERRQ(ierr);
506   ierr = VecDestroy(&ref);CHKERRQ(ierr);
507   ierr = VecDestroy(&real);CHKERRQ(ierr);
508   ierr = MatDestroy(&J);CHKERRQ(ierr);
509   PetscFunctionReturn(0);
510 }
511 
512 #undef __FUNCT__
513 #define __FUNCT__ "HexMap_Private"
514 PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
515 {
516   const PetscScalar *vertices = (const PetscScalar*) ctx;
517   const PetscScalar x0        = vertices[0];
518   const PetscScalar y0        = vertices[1];
519   const PetscScalar z0        = vertices[2];
520   const PetscScalar x1        = vertices[9];
521   const PetscScalar y1        = vertices[10];
522   const PetscScalar z1        = vertices[11];
523   const PetscScalar x2        = vertices[6];
524   const PetscScalar y2        = vertices[7];
525   const PetscScalar z2        = vertices[8];
526   const PetscScalar x3        = vertices[3];
527   const PetscScalar y3        = vertices[4];
528   const PetscScalar z3        = vertices[5];
529   const PetscScalar x4        = vertices[12];
530   const PetscScalar y4        = vertices[13];
531   const PetscScalar z4        = vertices[14];
532   const PetscScalar x5        = vertices[15];
533   const PetscScalar y5        = vertices[16];
534   const PetscScalar z5        = vertices[17];
535   const PetscScalar x6        = vertices[18];
536   const PetscScalar y6        = vertices[19];
537   const PetscScalar z6        = vertices[20];
538   const PetscScalar x7        = vertices[21];
539   const PetscScalar y7        = vertices[22];
540   const PetscScalar z7        = vertices[23];
541   const PetscScalar f_1       = x1 - x0;
542   const PetscScalar g_1       = y1 - y0;
543   const PetscScalar h_1       = z1 - z0;
544   const PetscScalar f_3       = x3 - x0;
545   const PetscScalar g_3       = y3 - y0;
546   const PetscScalar h_3       = z3 - z0;
547   const PetscScalar f_4       = x4 - x0;
548   const PetscScalar g_4       = y4 - y0;
549   const PetscScalar h_4       = z4 - z0;
550   const PetscScalar f_01      = x2 - x1 - x3 + x0;
551   const PetscScalar g_01      = y2 - y1 - y3 + y0;
552   const PetscScalar h_01      = z2 - z1 - z3 + z0;
553   const PetscScalar f_12      = x7 - x3 - x4 + x0;
554   const PetscScalar g_12      = y7 - y3 - y4 + y0;
555   const PetscScalar h_12      = z7 - z3 - z4 + z0;
556   const PetscScalar f_02      = x5 - x1 - x4 + x0;
557   const PetscScalar g_02      = y5 - y1 - y4 + y0;
558   const PetscScalar h_02      = z5 - z1 - z4 + z0;
559   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
560   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
561   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
562   const PetscScalar *ref;
563   PetscScalar       *real;
564   PetscErrorCode    ierr;
565 
566   PetscFunctionBegin;
567   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
568   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
569   {
570     const PetscScalar p0 = ref[0];
571     const PetscScalar p1 = ref[1];
572     const PetscScalar p2 = ref[2];
573 
574     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;
575     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;
576     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;
577   }
578   ierr = PetscLogFlops(114);CHKERRQ(ierr);
579   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
580   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
581   PetscFunctionReturn(0);
582 }
583 
584 #undef __FUNCT__
585 #define __FUNCT__ "HexJacobian_Private"
586 PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
587 {
588   const PetscScalar *vertices = (const PetscScalar*) ctx;
589   const PetscScalar x0        = vertices[0];
590   const PetscScalar y0        = vertices[1];
591   const PetscScalar z0        = vertices[2];
592   const PetscScalar x1        = vertices[9];
593   const PetscScalar y1        = vertices[10];
594   const PetscScalar z1        = vertices[11];
595   const PetscScalar x2        = vertices[6];
596   const PetscScalar y2        = vertices[7];
597   const PetscScalar z2        = vertices[8];
598   const PetscScalar x3        = vertices[3];
599   const PetscScalar y3        = vertices[4];
600   const PetscScalar z3        = vertices[5];
601   const PetscScalar x4        = vertices[12];
602   const PetscScalar y4        = vertices[13];
603   const PetscScalar z4        = vertices[14];
604   const PetscScalar x5        = vertices[15];
605   const PetscScalar y5        = vertices[16];
606   const PetscScalar z5        = vertices[17];
607   const PetscScalar x6        = vertices[18];
608   const PetscScalar y6        = vertices[19];
609   const PetscScalar z6        = vertices[20];
610   const PetscScalar x7        = vertices[21];
611   const PetscScalar y7        = vertices[22];
612   const PetscScalar z7        = vertices[23];
613   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
614   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
615   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
616   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
617   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
618   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
619   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
620   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
621   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
622   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
623   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
624   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
625   const PetscScalar *ref;
626   PetscErrorCode    ierr;
627 
628   PetscFunctionBegin;
629   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
630   {
631     const PetscScalar x       = ref[0];
632     const PetscScalar y       = ref[1];
633     const PetscScalar z       = ref[2];
634     const PetscInt    rows[3] = {0, 1, 2};
635     PetscScalar       values[9];
636 
637     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
638     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
639     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
640     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
641     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
642     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
643     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
644     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
645     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;
646 
647     ierr = MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);CHKERRQ(ierr);
648   }
649   ierr = PetscLogFlops(152);CHKERRQ(ierr);
650   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
651   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
652   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
653   PetscFunctionReturn(0);
654 }
655 
656 #undef __FUNCT__
657 #define __FUNCT__ "DMInterpolate_Hex_Private"
658 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
659 {
660   DM             dmCoord;
661   SNES           snes;
662   KSP            ksp;
663   PC             pc;
664   Vec            coordsLocal, r, ref, real;
665   Mat            J;
666   const PetscScalar *coords;
667   PetscScalar    *a;
668   PetscInt       p;
669   PetscErrorCode ierr;
670 
671   PetscFunctionBegin;
672   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
673   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
674   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
675   ierr = SNESSetOptionsPrefix(snes, "hex_interp_");CHKERRQ(ierr);
676   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
677   ierr = VecSetSizes(r, 3, 3);CHKERRQ(ierr);
678   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
679   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
680   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
681   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
682   ierr = MatSetSizes(J, 3, 3, 3, 3);CHKERRQ(ierr);
683   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
684   ierr = MatSetUp(J);CHKERRQ(ierr);
685   ierr = SNESSetFunction(snes, r, HexMap_Private, NULL);CHKERRQ(ierr);
686   ierr = SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);CHKERRQ(ierr);
687   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
688   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
689   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
690   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
691 
692   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
693   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
694   for (p = 0; p < ctx->n; ++p) {
695     PetscScalar *x = NULL, *vertices = NULL;
696     PetscScalar *xi;
697     PetscReal    xir[3];
698     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
699 
700     /* Can make this do all points at once */
701     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
702     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 8*3);
703     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
704     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 8*ctx->dof);
705     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
706     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
707     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
708     xi[0]  = coords[p*ctx->dim+0];
709     xi[1]  = coords[p*ctx->dim+1];
710     xi[2]  = coords[p*ctx->dim+2];
711     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
712     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
713     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
714     xir[0] = PetscRealPart(xi[0]);
715     xir[1] = PetscRealPart(xi[1]);
716     xir[2] = PetscRealPart(xi[2]);
717     for (comp = 0; comp < ctx->dof; ++comp) {
718       a[p*ctx->dof+comp] =
719         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
720         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
721         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
722         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
723         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
724         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
725         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
726         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
727     }
728     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
729     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
730     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
731   }
732   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
733   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
734 
735   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
736   ierr = VecDestroy(&r);CHKERRQ(ierr);
737   ierr = VecDestroy(&ref);CHKERRQ(ierr);
738   ierr = VecDestroy(&real);CHKERRQ(ierr);
739   ierr = MatDestroy(&J);CHKERRQ(ierr);
740   PetscFunctionReturn(0);
741 }
742 
743 #undef __FUNCT__
744 #define __FUNCT__ "DMInterpolationEvaluate"
745 /*
746   Input Parameters:
747 + ctx - The DMInterpolationInfo context
748 . dm  - The DM
749 - x   - The local vector containing the field to be interpolated
750 
751   Output Parameters:
752 . v   - The vector containing the interpolated values
753 */
754 PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
755 {
756   PetscInt       dim, coneSize, n;
757   PetscErrorCode ierr;
758 
759   PetscFunctionBegin;
760   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
761   PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
762   PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
763   ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
764   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);
765   if (n) {
766     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
767     ierr = DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);CHKERRQ(ierr);
768     if (dim == 2) {
769       if (coneSize == 3) {
770         ierr = DMInterpolate_Triangle_Private(ctx, dm, x, v);CHKERRQ(ierr);
771       } else if (coneSize == 4) {
772         ierr = DMInterpolate_Quad_Private(ctx, dm, x, v);CHKERRQ(ierr);
773       } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
774     } else if (dim == 3) {
775       if (coneSize == 4) {
776         ierr = DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);CHKERRQ(ierr);
777       } else {
778         ierr = DMInterpolate_Hex_Private(ctx, dm, x, v);CHKERRQ(ierr);
779       }
780     } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
781   }
782   PetscFunctionReturn(0);
783 }
784 
785 #undef __FUNCT__
786 #define __FUNCT__ "DMInterpolationDestroy"
787 PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
788 {
789   PetscErrorCode ierr;
790 
791   PetscFunctionBegin;
792   PetscValidPointer(ctx, 2);
793   ierr = VecDestroy(&(*ctx)->coords);CHKERRQ(ierr);
794   ierr = PetscFree((*ctx)->points);CHKERRQ(ierr);
795   ierr = PetscFree((*ctx)->cells);CHKERRQ(ierr);
796   ierr = PetscFree(*ctx);CHKERRQ(ierr);
797   *ctx = NULL;
798   PetscFunctionReturn(0);
799 }
800 
801 #undef __FUNCT__
802 #define __FUNCT__ "SNESMonitorFields"
803 /*@C
804   SNESMonitorFields - Monitors the residual for each field separately
805 
806   Collective on SNES
807 
808   Input Parameters:
809 + snes   - the SNES context
810 . its    - iteration number
811 . fgnorm - 2-norm of residual
812 - vf  - PetscViewerAndFormat of type ASCII
813 
814   Notes:
815   This routine prints the residual norm at each iteration.
816 
817   Level: intermediate
818 
819 .keywords: SNES, nonlinear, default, monitor, norm
820 .seealso: SNESMonitorSet(), SNESMonitorDefault()
821 @*/
822 PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
823 {
824   PetscViewer        viewer = vf->viewer;
825   Vec                res;
826   DM                 dm;
827   PetscSection       s;
828   const PetscScalar *r;
829   PetscReal         *lnorms, *norms;
830   PetscInt           numFields, f, pStart, pEnd, p;
831   PetscErrorCode     ierr;
832 
833   PetscFunctionBegin;
834   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
835   ierr = SNESGetFunction(snes, &res, 0, 0);CHKERRQ(ierr);
836   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
837   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
838   ierr = PetscSectionGetNumFields(s, &numFields);CHKERRQ(ierr);
839   ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
840   ierr = PetscCalloc2(numFields, &lnorms, numFields, &norms);CHKERRQ(ierr);
841   ierr = VecGetArrayRead(res, &r);CHKERRQ(ierr);
842   for (p = pStart; p < pEnd; ++p) {
843     for (f = 0; f < numFields; ++f) {
844       PetscInt fdof, foff, d;
845 
846       ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
847       ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
848       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
849     }
850   }
851   ierr = VecRestoreArrayRead(res, &r);CHKERRQ(ierr);
852   ierr = MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
853   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
854   ierr = PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
855   ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
856   for (f = 0; f < numFields; ++f) {
857     if (f > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
858     ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));CHKERRQ(ierr);
859   }
860   ierr = PetscViewerASCIIPrintf(viewer, "]\n");CHKERRQ(ierr);
861   ierr = PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
862   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
863   ierr = PetscFree2(lnorms, norms);CHKERRQ(ierr);
864   PetscFunctionReturn(0);
865 }
866 
867 /********************* Residual Computation **************************/
868 
869 #undef __FUNCT__
870 #define __FUNCT__ "DMPlexSNESGetGeometryFEM"
871 /*@
872   DMPlexSNESGetGeometryFEM - Return precomputed geometric data
873 
874   Input Parameter:
875 . dm - The DM
876 
877   Output Parameters:
878 . cellgeom - The values precomputed from cell geometry
879 
880   Level: developer
881 
882 .seealso: DMPlexSNESSetFunctionLocal()
883 @*/
884 PetscErrorCode DMPlexSNESGetGeometryFEM(DM dm, Vec *cellgeom)
885 {
886   DMSNES         dmsnes;
887   PetscObject    obj;
888   PetscErrorCode ierr;
889 
890   PetscFunctionBegin;
891   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
892   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
893   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", &obj);CHKERRQ(ierr);
894   if (!obj) {
895     Vec cellgeom;
896 
897     ierr = DMPlexComputeGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
898     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject) cellgeom);CHKERRQ(ierr);
899     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
900   }
901   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject *) cellgeom);CHKERRQ(ierr);}
902   PetscFunctionReturn(0);
903 }
904 
905 #undef __FUNCT__
906 #define __FUNCT__ "DMPlexSNESGetGeometryFVM"
907 /*@
908   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
909 
910   Input Parameter:
911 . dm - The DM
912 
913   Output Parameters:
914 + facegeom - The values precomputed from face geometry
915 . cellgeom - The values precomputed from cell geometry
916 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
917 
918   Level: developer
919 
920 .seealso: DMPlexTSSetRHSFunctionLocal()
921 @*/
922 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
923 {
924   DM             plex;
925   PetscErrorCode ierr;
926 
927   PetscFunctionBegin;
928   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
929   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
930   ierr = DMPlexGetDataFVM(plex, NULL, cellgeom, facegeom, NULL);CHKERRQ(ierr);
931   if (minRadius) {ierr = DMPlexGetMinRadius(plex, minRadius);CHKERRQ(ierr);}
932   ierr = DMDestroy(&plex);CHKERRQ(ierr);
933   PetscFunctionReturn(0);
934 }
935 
936 #undef __FUNCT__
937 #define __FUNCT__ "DMPlexSNESGetGradientDM"
938 /*@
939   DMPlexSNESGetGradientDM - Return gradient data layout
940 
941   Input Parameters:
942 + dm - The DM
943 - fv - The PetscFV
944 
945   Output Parameter:
946 . dmGrad - The layout for gradient values
947 
948   Level: developer
949 
950 .seealso: DMPlexSNESGetGeometryFVM()
951 @*/
952 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
953 {
954   DM             plex;
955   PetscBool      computeGradients;
956   PetscErrorCode ierr;
957 
958   PetscFunctionBegin;
959   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
960   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
961   PetscValidPointer(dmGrad,3);
962   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
963   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
964   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
965   ierr = DMPlexGetDataFVM(plex, fv, NULL, NULL, dmGrad);CHKERRQ(ierr);
966   ierr = DMDestroy(&plex);CHKERRQ(ierr);
967   PetscFunctionReturn(0);
968 }
969 
970 #undef __FUNCT__
971 #define __FUNCT__ "DMPlexGetCellFields"
972 /*@C
973   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells
974 
975   Input Parameters:
976 + dm     - The DM
977 . cStart - The first cell to include
978 . cEnd   - The first cell to exclude
979 . locX   - A local vector with the solution fields
980 . locX_t - A local vector with solution field time derivatives, or NULL
981 - locA   - A local vector with auxiliary fields, or NULL
982 
983   Output Parameters:
984 + u   - The field coefficients
985 . u_t - The fields derivative coefficients
986 - a   - The auxiliary field coefficients
987 
988   Level: developer
989 
990 .seealso: DMPlexGetFaceFields()
991 @*/
992 PetscErrorCode DMPlexGetCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
993 {
994   DM             dmAux;
995   PetscSection   section, sectionAux;
996   PetscDS        prob;
997   PetscInt       numCells = cEnd - cStart, totDim, totDimAux, c;
998   PetscErrorCode ierr;
999 
1000   PetscFunctionBegin;
1001   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1002   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1003   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1004   if (locA)   {PetscValidHeaderSpecific(locA, VEC_CLASSID, 6);}
1005   PetscValidPointer(u, 7);
1006   PetscValidPointer(u_t, 8);
1007   PetscValidPointer(a, 9);
1008   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1009   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1010   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1011   if (locA) {
1012     PetscDS probAux;
1013 
1014     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1015     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1016     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1017     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1018   }
1019   ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u);CHKERRQ(ierr);
1020   if (locX_t) {ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u_t);CHKERRQ(ierr);} else {*u_t = NULL;}
1021   if (locA)   {ierr = DMGetWorkArray(dm, numCells*totDimAux, PETSC_SCALAR, a);CHKERRQ(ierr);} else {*a = NULL;}
1022   for (c = cStart; c < cEnd; ++c) {
1023     PetscScalar *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
1024     PetscInt     i;
1025 
1026     ierr = DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1027     for (i = 0; i < totDim; ++i) ul[(c-cStart)*totDim+i] = x[i];
1028     ierr = DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1029     if (locX_t) {
1030       ierr = DMPlexVecGetClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1031       for (i = 0; i < totDim; ++i) ul_t[(c-cStart)*totDim+i] = x_t[i];
1032       ierr = DMPlexVecRestoreClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1033     }
1034     if (locA) {
1035       DM dmAuxPlex;
1036 
1037       ierr = DMSNESConvertPlex(dmAux, &dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1038       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1039       for (i = 0; i < totDimAux; ++i) al[(c-cStart)*totDimAux+i] = x[i];
1040       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1041       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1042     }
1043   }
1044   PetscFunctionReturn(0);
1045 }
1046 
1047 #undef __FUNCT__
1048 #define __FUNCT__ "DMPlexRestoreCellFields"
1049 /*@C
1050   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells
1051 
1052   Input Parameters:
1053 + dm     - The DM
1054 . cStart - The first cell to include
1055 . cEnd   - The first cell to exclude
1056 . locX   - A local vector with the solution fields
1057 . locX_t - A local vector with solution field time derivatives, or NULL
1058 - locA   - A local vector with auxiliary fields, or NULL
1059 
1060   Output Parameters:
1061 + u   - The field coefficients
1062 . u_t - The fields derivative coefficients
1063 - a   - The auxiliary field coefficients
1064 
1065   Level: developer
1066 
1067 .seealso: DMPlexGetFaceFields()
1068 @*/
1069 PetscErrorCode DMPlexRestoreCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1070 {
1071   PetscErrorCode ierr;
1072 
1073   PetscFunctionBegin;
1074   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u);CHKERRQ(ierr);
1075   if (*u_t) {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u_t);CHKERRQ(ierr);}
1076   if (*a)   {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, a);CHKERRQ(ierr);}
1077   PetscFunctionReturn(0);
1078 }
1079 
1080 #undef __FUNCT__
1081 #define __FUNCT__ "DMPlexGetFaceFields"
1082 /*@C
1083   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces
1084 
1085   Input Parameters:
1086 + dm     - The DM
1087 . fStart - The first face to include
1088 . fEnd   - The first face to exclude
1089 . locX   - A local vector with the solution fields
1090 . locX_t - A local vector with solution field time derivatives, or NULL
1091 . faceGeometry - A local vector with face geometry
1092 . cellGeometry - A local vector with cell geometry
1093 - locaGrad - A local vector with field gradients, or NULL
1094 
1095   Output Parameters:
1096 + Nface - The number of faces with field values
1097 . uL - The field values at the left side of the face
1098 - uR - The field values at the right side of the face
1099 
1100   Level: developer
1101 
1102 .seealso: DMPlexGetCellFields()
1103 @*/
1104 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)
1105 {
1106   DM                 dmFace, dmCell, dmGrad = NULL;
1107   PetscSection       section;
1108   PetscDS            prob;
1109   DMLabel            ghostLabel;
1110   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
1111   PetscBool         *isFE;
1112   PetscInt           dim, Nf, f, Nc, numFaces = fEnd - fStart, iface, face;
1113   PetscErrorCode     ierr;
1114 
1115   PetscFunctionBegin;
1116   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1117   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1118   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1119   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 6);
1120   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 7);
1121   if (locGrad) {PetscValidHeaderSpecific(locGrad, VEC_CLASSID, 8);}
1122   PetscValidPointer(uL, 9);
1123   PetscValidPointer(uR, 10);
1124   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1125   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1126   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1127   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1128   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1129   ierr = PetscMalloc1(Nf, &isFE);CHKERRQ(ierr);
1130   for (f = 0; f < Nf; ++f) {
1131     PetscObject  obj;
1132     PetscClassId id;
1133 
1134     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1135     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1136     if (id == PETSCFE_CLASSID)      {isFE[f] = PETSC_TRUE;}
1137     else if (id == PETSCFV_CLASSID) {isFE[f] = PETSC_FALSE;}
1138     else                            {isFE[f] = PETSC_FALSE;}
1139   }
1140   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1141   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1142   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1143   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1144   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1145   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1146   if (locGrad) {
1147     ierr = VecGetDM(locGrad, &dmGrad);CHKERRQ(ierr);
1148     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1149   }
1150   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uL);CHKERRQ(ierr);
1151   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uR);CHKERRQ(ierr);
1152   /* Right now just eat the extra work for FE (could make a cell loop) */
1153   for (face = fStart, iface = 0; face < fEnd; ++face) {
1154     const PetscInt        *cells;
1155     PetscFVFaceGeom       *fg;
1156     PetscFVCellGeom       *cgL, *cgR;
1157     PetscScalar           *xL, *xR, *gL, *gR;
1158     PetscScalar           *uLl = *uL, *uRl = *uR;
1159     PetscInt               ghost, nsupp, nchild;
1160 
1161     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1162     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1163     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1164     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1165     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1166     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1167     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1168     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1169     for (f = 0; f < Nf; ++f) {
1170       PetscInt off;
1171 
1172       ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1173       if (isFE[f]) {
1174         const PetscInt *cone;
1175         PetscInt        comp, coneSizeL, coneSizeR, faceLocL, faceLocR, ldof, rdof, d;
1176 
1177         xL = xR = NULL;
1178         ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1179         ierr = DMPlexVecGetClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1180         ierr = DMPlexVecGetClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1181         ierr = DMPlexGetCone(dm, cells[0], &cone);CHKERRQ(ierr);
1182         ierr = DMPlexGetConeSize(dm, cells[0], &coneSizeL);CHKERRQ(ierr);
1183         for (faceLocL = 0; faceLocL < coneSizeL; ++faceLocL) if (cone[faceLocL] == face) break;
1184         ierr = DMPlexGetCone(dm, cells[1], &cone);CHKERRQ(ierr);
1185         ierr = DMPlexGetConeSize(dm, cells[1], &coneSizeR);CHKERRQ(ierr);
1186         for (faceLocR = 0; faceLocR < coneSizeR; ++faceLocR) if (cone[faceLocR] == face) break;
1187         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]);
1188         /* Check that FEM field has values in the right cell (sometimes its an FV ghost cell) */
1189         /* TODO: this is a hack that might not be right for nonconforming */
1190         if (faceLocL < coneSizeL) {
1191           ierr = EvaluateFaceFields(prob, f, faceLocL, xL, &uLl[iface*Nc+off]);CHKERRQ(ierr);
1192           if (rdof == ldof && faceLocR < coneSizeR) {ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);}
1193           else              {for(d = 0; d < comp; ++d) uRl[iface*Nc+off+d] = uLl[iface*Nc+off+d];}
1194         }
1195         else {
1196           ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);
1197           ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1198           for(d = 0; d < comp; ++d) uLl[iface*Nc+off+d] = uRl[iface*Nc+off+d];
1199         }
1200         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1201         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1202       } else {
1203         PetscFV  fv;
1204         PetscInt numComp, c;
1205 
1206         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fv);CHKERRQ(ierr);
1207         ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1208         ierr = DMPlexPointLocalFieldRead(dm, cells[0], f, x, &xL);CHKERRQ(ierr);
1209         ierr = DMPlexPointLocalFieldRead(dm, cells[1], f, x, &xR);CHKERRQ(ierr);
1210         if (dmGrad) {
1211           PetscReal dxL[3], dxR[3];
1212 
1213           ierr = DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);CHKERRQ(ierr);
1214           ierr = DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);CHKERRQ(ierr);
1215           DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
1216           DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
1217           for (c = 0; c < numComp; ++c) {
1218             uLl[iface*Nc+off+c] = xL[c] + DMPlex_DotD_Internal(dim, &gL[c*dim], dxL);
1219             uRl[iface*Nc+off+c] = xR[c] + DMPlex_DotD_Internal(dim, &gR[c*dim], dxR);
1220           }
1221         } else {
1222           for (c = 0; c < numComp; ++c) {
1223             uLl[iface*Nc+off+c] = xL[c];
1224             uRl[iface*Nc+off+c] = xR[c];
1225           }
1226         }
1227       }
1228     }
1229     ++iface;
1230   }
1231   *Nface = iface;
1232   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1233   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1234   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1235   if (locGrad) {
1236     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1237   }
1238   ierr = PetscFree(isFE);CHKERRQ(ierr);
1239   PetscFunctionReturn(0);
1240 }
1241 
1242 #undef __FUNCT__
1243 #define __FUNCT__ "DMPlexRestoreFaceFields"
1244 /*@C
1245   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces
1246 
1247   Input Parameters:
1248 + dm     - The DM
1249 . fStart - The first face to include
1250 . fEnd   - The first face to exclude
1251 . locX   - A local vector with the solution fields
1252 . locX_t - A local vector with solution field time derivatives, or NULL
1253 . faceGeometry - A local vector with face geometry
1254 . cellGeometry - A local vector with cell geometry
1255 - locaGrad - A local vector with field gradients, or NULL
1256 
1257   Output Parameters:
1258 + Nface - The number of faces with field values
1259 . uL - The field values at the left side of the face
1260 - uR - The field values at the right side of the face
1261 
1262   Level: developer
1263 
1264 .seealso: DMPlexGetFaceFields()
1265 @*/
1266 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)
1267 {
1268   PetscErrorCode ierr;
1269 
1270   PetscFunctionBegin;
1271   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uL);CHKERRQ(ierr);
1272   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uR);CHKERRQ(ierr);
1273   PetscFunctionReturn(0);
1274 }
1275 
1276 #undef __FUNCT__
1277 #define __FUNCT__ "DMPlexGetFaceGeometry"
1278 /*@C
1279   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces
1280 
1281   Input Parameters:
1282 + dm     - The DM
1283 . fStart - The first face to include
1284 . fEnd   - The first face to exclude
1285 . faceGeometry - A local vector with face geometry
1286 - cellGeometry - A local vector with cell geometry
1287 
1288   Output Parameters:
1289 + Nface - The number of faces with field values
1290 . fgeom - The extract the face centroid and normal
1291 - vol   - The cell volume
1292 
1293   Level: developer
1294 
1295 .seealso: DMPlexGetCellFields()
1296 @*/
1297 PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1298 {
1299   DM                 dmFace, dmCell;
1300   DMLabel            ghostLabel;
1301   const PetscScalar *facegeom, *cellgeom;
1302   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
1303   PetscErrorCode     ierr;
1304 
1305   PetscFunctionBegin;
1306   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1307   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 4);
1308   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 5);
1309   PetscValidPointer(fgeom, 6);
1310   PetscValidPointer(vol, 7);
1311   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1312   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1313   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1314   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1315   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1316   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1317   ierr = PetscMalloc1(numFaces, fgeom);CHKERRQ(ierr);
1318   ierr = DMGetWorkArray(dm, numFaces*2, PETSC_SCALAR, vol);CHKERRQ(ierr);
1319   for (face = fStart, iface = 0; face < fEnd; ++face) {
1320     const PetscInt        *cells;
1321     PetscFVFaceGeom       *fg;
1322     PetscFVCellGeom       *cgL, *cgR;
1323     PetscFVFaceGeom       *fgeoml = *fgeom;
1324     PetscReal             *voll   = *vol;
1325     PetscInt               ghost, d, nchild, nsupp;
1326 
1327     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1328     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1329     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1330     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1331     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1332     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1333     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1334     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1335     for (d = 0; d < dim; ++d) {
1336       fgeoml[iface].centroid[d] = fg->centroid[d];
1337       fgeoml[iface].normal[d]   = fg->normal[d];
1338     }
1339     voll[iface*2+0] = cgL->volume;
1340     voll[iface*2+1] = cgR->volume;
1341     ++iface;
1342   }
1343   *Nface = iface;
1344   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1345   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1346   PetscFunctionReturn(0);
1347 }
1348 
1349 #undef __FUNCT__
1350 #define __FUNCT__ "DMPlexRestoreFaceGeometry"
1351 /*@C
1352   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces
1353 
1354   Input Parameters:
1355 + dm     - The DM
1356 . fStart - The first face to include
1357 . fEnd   - The first face to exclude
1358 . faceGeometry - A local vector with face geometry
1359 - cellGeometry - A local vector with cell geometry
1360 
1361   Output Parameters:
1362 + Nface - The number of faces with field values
1363 . fgeom - The extract the face centroid and normal
1364 - vol   - The cell volume
1365 
1366   Level: developer
1367 
1368 .seealso: DMPlexGetFaceFields()
1369 @*/
1370 PetscErrorCode DMPlexRestoreFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1371 {
1372   PetscErrorCode ierr;
1373 
1374   PetscFunctionBegin;
1375   ierr = PetscFree(*fgeom);CHKERRQ(ierr);
1376   ierr = DMRestoreWorkArray(dm, 0, PETSC_REAL, vol);CHKERRQ(ierr);
1377   PetscFunctionReturn(0);
1378 }
1379 
1380 #undef __FUNCT__
1381 #define __FUNCT__ "DMPlexComputeBdResidual_Internal"
1382 PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1383 {
1384   DM_Plex         *mesh = (DM_Plex *) dm->data;
1385   DM               dmAux = NULL, plex = NULL;
1386   PetscSection     section, sectionAux = NULL;
1387   PetscDS          prob, probAux = NULL;
1388   DMLabel          depth;
1389   Vec              locA = NULL;
1390   PetscFECellGeom *cgeom;
1391   PetscScalar     *u = NULL, *u_t = NULL, *a = NULL, *elemVec = NULL;
1392   PetscInt         dim, Nf, f, totDimBd, totDimAuxBd, numBd, bd;
1393   PetscErrorCode   ierr;
1394 
1395   PetscFunctionBegin;
1396   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1397   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1398   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1399   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1400   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1401   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
1402   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
1403   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1404   if (locA) {
1405     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1406     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
1407     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
1408     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1409     ierr = PetscDSGetTotalBdDimension(probAux, &totDimAuxBd);CHKERRQ(ierr);
1410   }
1411   for (bd = 0; bd < numBd; ++bd) {
1412     const char     *bdLabel;
1413     DMLabel         label;
1414     IS              pointIS;
1415     const PetscInt *points;
1416     const PetscInt *values;
1417     PetscInt        field, numValues, v, numPoints, p, dep, numFaces;
1418     PetscBool       isEssential;
1419     PetscObject     obj;
1420     PetscClassId    id;
1421 
1422     ierr = PetscDSGetBoundary(prob, bd, &isEssential, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1423     ierr = PetscDSGetBdDiscretization(prob, field, &obj);CHKERRQ(ierr);
1424     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1425     if ((id != PETSCFE_CLASSID) || isEssential) continue;
1426     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1427     for (v = 0; v < numValues; ++v) {
1428       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
1429       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1430       if (!pointIS) continue; /* No points with that id on this process */
1431       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1432       for (p = 0, numFaces = 0; p < numPoints; ++p) {
1433         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1434         if (dep == dim-1) ++numFaces;
1435       }
1436       ierr = PetscMalloc4(numFaces*totDimBd,&u,locX_t ? numFaces*totDimBd : 0,&u_t,numFaces,&cgeom,numFaces*totDimBd,&elemVec);CHKERRQ(ierr);
1437       if (locA) {ierr = PetscMalloc1(numFaces*totDimAuxBd,&a);CHKERRQ(ierr);}
1438       for (p = 0, f = 0; p < numPoints; ++p) {
1439         const PetscInt point = points[p];
1440         PetscScalar   *x     = NULL;
1441         PetscInt       i;
1442 
1443         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1444         if (dep != dim-1) continue;
1445         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
1446         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);CHKERRQ(ierr);
1447         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
1448         /* TODO: Matt, this is wrong if feBd does not match fe: i.e., if the order differs. */
1449         ierr = DMPlexVecGetClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1450         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
1451         ierr = DMPlexVecRestoreClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1452         if (locX_t) {
1453           ierr = DMPlexVecGetClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1454           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
1455           ierr = DMPlexVecRestoreClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1456         }
1457         if (locA) {
1458           ierr = DMPlexVecGetClosure(plex, sectionAux, locA, point, NULL, &x);CHKERRQ(ierr);
1459           for (i = 0; i < totDimAuxBd; ++i) a[f*totDimAuxBd+i] = x[i];
1460           ierr = DMPlexVecRestoreClosure(plex, sectionAux, locA, point, NULL, &x);CHKERRQ(ierr);
1461         }
1462         ++f;
1463       }
1464       ierr = PetscMemzero(elemVec, numFaces*totDimBd * sizeof(PetscScalar));CHKERRQ(ierr);
1465       {
1466         PetscFE         fe;
1467         PetscQuadrature q;
1468         PetscInt        numQuadPoints, Nb;
1469         /* Conforming batches */
1470         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1471         /* Remainder */
1472         PetscInt        Nr, offset;
1473 
1474         ierr = PetscDSGetBdDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1475         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1476         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1477         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1478         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1479         blockSize = Nb*numQuadPoints;
1480         batchSize = numBlocks * blockSize;
1481         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1482         numChunks = numFaces / (numBatches*batchSize);
1483         Ne        = numChunks*numBatches*batchSize;
1484         Nr        = numFaces % (numBatches*batchSize);
1485         offset    = numFaces - Nr;
1486         ierr = PetscFEIntegrateBdResidual(fe, prob, field, Ne, cgeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1487         ierr = PetscFEIntegrateBdResidual(fe, prob, field, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, probAux, a ? &a[offset*totDimAuxBd] : NULL, t, &elemVec[offset*totDimBd]);CHKERRQ(ierr);
1488       }
1489       for (p = 0, f = 0; p < numPoints; ++p) {
1490         const PetscInt point = points[p];
1491 
1492         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1493         if (dep != dim-1) continue;
1494         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDimBd, &elemVec[f*totDimBd]);CHKERRQ(ierr);}
1495         ierr = DMPlexVecSetClosure(dm, NULL, locF, point, &elemVec[f*totDimBd], ADD_ALL_VALUES);CHKERRQ(ierr);
1496         ++f;
1497       }
1498       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1499       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1500       ierr = PetscFree4(u,u_t,cgeom,elemVec);CHKERRQ(ierr);
1501       if (locA) {
1502         ierr = PetscFree(a);CHKERRQ(ierr);
1503         ierr = DMDestroy(&plex);CHKERRQ(ierr);
1504       }
1505     }
1506   }
1507   PetscFunctionReturn(0);
1508 }
1509 
1510 #undef __FUNCT__
1511 #define __FUNCT__ "DMPlexComputeResidual_Internal"
1512 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal time, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1513 {
1514   DM_Plex          *mesh       = (DM_Plex *) dm->data;
1515   const char       *name       = "Residual";
1516   DM                dmAux      = NULL;
1517   DM                dmGrad     = NULL;
1518   DMLabel           ghostLabel = NULL;
1519   PetscDS           prob       = NULL;
1520   PetscDS           probAux    = NULL;
1521   PetscSection      section    = NULL;
1522   PetscBool         useFEM     = PETSC_FALSE;
1523   PetscBool         useFVM     = PETSC_FALSE;
1524   PetscBool         isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
1525   PetscFV           fvm        = NULL;
1526   PetscFECellGeom  *cgeomFEM   = NULL;
1527   PetscScalar      *cgeomScal;
1528   PetscFVCellGeom  *cgeomFVM   = NULL;
1529   PetscFVFaceGeom  *fgeomFVM   = NULL;
1530   Vec               locA, cellGeometryFEM = NULL, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1531   PetscScalar      *u = NULL, *u_t, *a, *uL, *uR;
1532   PetscInt          Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
1533   PetscErrorCode    ierr;
1534 
1535   PetscFunctionBegin;
1536   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1537   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1538   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
1539   /* FEM+FVM */
1540   /* 1: Get sizes from dm and dmAux */
1541   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1542   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1543   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1544   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1545   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1546   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1547   if (locA) {
1548     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1549     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1550     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1551   }
1552   /* 2: Get geometric data */
1553   for (f = 0; f < Nf; ++f) {
1554     PetscObject  obj;
1555     PetscClassId id;
1556     PetscBool    fimp;
1557 
1558     ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1559     if (isImplicit != fimp) continue;
1560     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1561     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1562     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1563     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1564   }
1565   if (useFEM) {
1566     ierr = DMPlexSNESGetGeometryFEM(dm, &cellGeometryFEM);CHKERRQ(ierr);
1567     ierr = VecGetArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);
1568     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1569       DM dmCell;
1570       PetscInt c;
1571 
1572       ierr = VecGetDM(cellGeometryFEM,&dmCell);CHKERRQ(ierr);
1573       ierr = PetscMalloc1(cEnd-cStart,&cgeomFEM);CHKERRQ(ierr);
1574       for (c = 0; c < cEnd - cStart; c++) {
1575         PetscScalar *thisgeom;
1576 
1577         ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1578         cgeomFEM[c] = *((PetscFECellGeom *) thisgeom);
1579       }
1580     }
1581     else {
1582       cgeomFEM = (PetscFECellGeom *) cgeomScal;
1583     }
1584   }
1585   if (useFVM) {
1586     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1587     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1588     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1589     /* Reconstruct and limit cell gradients */
1590     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1591     if (dmGrad) {
1592       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1593       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1594       ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1595       /* Communicate gradient values */
1596       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1597       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1598       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1599       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1600     }
1601     /* Handle non-essential (e.g. outflow) boundary values */
1602     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1603   }
1604   /* Loop over chunks */
1605   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1606   numChunks     = 1;
1607   cellChunkSize = (cEnd - cStart)/numChunks;
1608   faceChunkSize = (fEnd - fStart)/numChunks;
1609   for (chunk = 0; chunk < numChunks; ++chunk) {
1610     PetscScalar     *elemVec, *fluxL, *fluxR;
1611     PetscReal       *vol;
1612     PetscFVFaceGeom *fgeom;
1613     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, cell;
1614     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = 0, face;
1615 
1616     /* Extract field coefficients */
1617     if (useFEM) {
1618       ierr = DMPlexGetCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1619       ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1620       ierr = PetscMemzero(elemVec, numCells*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1621     }
1622     if (useFVM) {
1623       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1624       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1625       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1626       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1627       ierr = PetscMemzero(fluxL, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1628       ierr = PetscMemzero(fluxR, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1629     }
1630     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1631     /* Loop over fields */
1632     for (f = 0; f < Nf; ++f) {
1633       PetscObject  obj;
1634       PetscClassId id;
1635       PetscBool    fimp;
1636       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1637 
1638       ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1639       if (isImplicit != fimp) continue;
1640       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1641       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1642       if (id == PETSCFE_CLASSID) {
1643         PetscFE         fe = (PetscFE) obj;
1644         PetscQuadrature q;
1645         PetscInt        Nq, Nb;
1646 
1647         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1648 
1649         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1650         ierr = PetscQuadratureGetData(q, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1651         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1652         blockSize = Nb*Nq;
1653         batchSize = numBlocks * blockSize;
1654         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1655         numChunks = numCells / (numBatches*batchSize);
1656         Ne        = numChunks*numBatches*batchSize;
1657         Nr        = numCells % (numBatches*batchSize);
1658         offset    = numCells - Nr;
1659         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1660         /*   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) */
1661         ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeomFEM, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1662         ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, &cgeomFEM[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1663       } else if (id == PETSCFV_CLASSID) {
1664         PetscFV fv = (PetscFV) obj;
1665 
1666         Ne = numFaces;
1667         /* Riemann solve over faces (need fields at face centroids) */
1668         /*   We need to evaluate FE fields at those coordinates */
1669         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1670       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1671     }
1672     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1673       ierr = PetscFree(cgeomFEM);CHKERRQ(ierr);
1674     }
1675     else {
1676       cgeomFEM = NULL;
1677     }
1678     if (cellGeometryFEM) {ierr = VecRestoreArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);}
1679     /* Loop over domain */
1680     if (useFEM) {
1681       /* Add elemVec to locX */
1682       for (cell = cS; cell < cE; ++cell) {
1683         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cell*totDim]);CHKERRQ(ierr);}
1684         if (ghostLabel) {
1685           PetscInt ghostVal;
1686 
1687           ierr = DMLabelGetValue(ghostLabel,cell,&ghostVal);CHKERRQ(ierr);
1688           if (ghostVal > 0) continue;
1689         }
1690         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cell*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1691       }
1692     }
1693     if (useFVM) {
1694       PetscScalar *fa;
1695       PetscInt     iface;
1696 
1697       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1698       for (f = 0; f < Nf; ++f) {
1699         PetscFV      fv;
1700         PetscObject  obj;
1701         PetscClassId id;
1702         PetscInt     foff, pdim;
1703 
1704         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1705         ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1706         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1707         if (id != PETSCFV_CLASSID) continue;
1708         fv   = (PetscFV) obj;
1709         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1710         /* Accumulate fluxes to cells */
1711         for (face = fS, iface = 0; face < fE; ++face) {
1712           const PetscInt *cells;
1713           PetscScalar    *fL = NULL, *fR = NULL;
1714           PetscInt        ghost, d, nsupp, nchild;
1715 
1716           ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1717           ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1718           ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1719           if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1720           ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1721           ierr = DMLabelGetValue(ghostLabel,cells[0],&ghost);CHKERRQ(ierr);
1722           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, cells[0], f, fa, &fL);CHKERRQ(ierr);}
1723           ierr = DMLabelGetValue(ghostLabel,cells[1],&ghost);CHKERRQ(ierr);
1724           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, cells[1], f, fa, &fR);CHKERRQ(ierr);}
1725           for (d = 0; d < pdim; ++d) {
1726             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
1727             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
1728           }
1729           ++iface;
1730         }
1731       }
1732       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1733     }
1734     /* Handle time derivative */
1735     if (locX_t) {
1736       PetscScalar *x_t, *fa;
1737 
1738       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1739       ierr = VecGetArray(locX_t, &x_t);CHKERRQ(ierr);
1740       for (f = 0; f < Nf; ++f) {
1741         PetscFV      fv;
1742         PetscObject  obj;
1743         PetscClassId id;
1744         PetscInt     pdim, d;
1745 
1746         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1747         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1748         if (id != PETSCFV_CLASSID) continue;
1749         fv   = (PetscFV) obj;
1750         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1751         for (cell = cS; cell < cE; ++cell) {
1752           PetscScalar *u_t, *r;
1753 
1754           if (ghostLabel) {
1755             PetscInt ghostVal;
1756 
1757             ierr = DMLabelGetValue(ghostLabel,cell,&ghostVal);CHKERRQ(ierr);
1758             if (ghostVal > 0) continue;
1759           }
1760           ierr = DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);CHKERRQ(ierr);
1761           ierr = DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);CHKERRQ(ierr);
1762           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
1763         }
1764       }
1765       ierr = VecRestoreArray(locX_t, &x_t);CHKERRQ(ierr);
1766       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1767     }
1768     if (useFEM) {
1769       ierr = DMPlexRestoreCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1770       ierr = DMRestoreWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1771     }
1772     if (useFVM) {
1773       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1774       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1775       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1776       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1777       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1778     }
1779   }
1780 
1781   if (useFEM) {ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, t, locF, user);CHKERRQ(ierr);}
1782 
1783   /* FEM */
1784   /* 1: Get sizes from dm and dmAux */
1785   /* 2: Get geometric data */
1786   /* 3: Handle boundary values */
1787   /* 4: Loop over domain */
1788   /*   Extract coefficients */
1789   /* Loop over fields */
1790   /*   Set tiling for FE*/
1791   /*   Integrate FE residual to get elemVec */
1792   /*     Loop over subdomain */
1793   /*       Loop over quad points */
1794   /*         Transform coords to real space */
1795   /*         Evaluate field and aux fields at point */
1796   /*         Evaluate residual at point */
1797   /*         Transform residual to real space */
1798   /*       Add residual to elemVec */
1799   /* Loop over domain */
1800   /*   Add elemVec to locX */
1801 
1802   /* FVM */
1803   /* Get geometric data */
1804   /* If using gradients */
1805   /*   Compute gradient data */
1806   /*   Loop over domain faces */
1807   /*     Count computational faces */
1808   /*     Reconstruct cell gradient */
1809   /*   Loop over domain cells */
1810   /*     Limit cell gradients */
1811   /* Handle boundary values */
1812   /* Loop over domain faces */
1813   /*   Read out field, centroid, normal, volume for each side of face */
1814   /* Riemann solve over faces */
1815   /* Loop over domain faces */
1816   /*   Accumulate fluxes to cells */
1817   /* TODO Change printFEM to printDisc here */
1818   if (mesh->printFEM) {
1819     Vec         locFbc;
1820     PetscInt    pStart, pEnd, p, maxDof;
1821     PetscScalar *zeroes;
1822 
1823     ierr = VecDuplicate(locF,&locFbc);CHKERRQ(ierr);
1824     ierr = VecCopy(locF,locFbc);CHKERRQ(ierr);
1825     ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
1826     ierr = PetscSectionGetMaxDof(section,&maxDof);CHKERRQ(ierr);
1827     ierr = PetscCalloc1(maxDof,&zeroes);CHKERRQ(ierr);
1828     for (p = pStart; p < pEnd; p++) {
1829       ierr = VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);CHKERRQ(ierr);
1830     }
1831     ierr = PetscFree(zeroes);CHKERRQ(ierr);
1832     ierr = DMPrintLocalVec(dm, name, mesh->printTol, locFbc);CHKERRQ(ierr);
1833     ierr = VecDestroy(&locFbc);CHKERRQ(ierr);
1834   }
1835   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1836   PetscFunctionReturn(0);
1837 }
1838 
1839 #undef __FUNCT__
1840 #define __FUNCT__ "DMPlexComputeResidualFEM_Check_Internal"
1841 static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, PetscReal t, Vec F, void *user)
1842 {
1843   DM                dmCh, dmAux;
1844   Vec               A, cellgeom;
1845   PetscDS           prob, probCh, probAux = NULL;
1846   PetscQuadrature   q;
1847   PetscSection      section, sectionAux;
1848   PetscFECellGeom  *cgeom = NULL;
1849   PetscScalar      *cgeomScal;
1850   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
1851   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
1852   PetscInt          totDim, totDimAux = 0, diffCell = 0;
1853   PetscErrorCode    ierr;
1854 
1855   PetscFunctionBegin;
1856   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1857   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1858   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1859   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1860   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1861   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1862   numCells = cEnd - cStart;
1863   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
1864   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
1865   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1866   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1867   if (dmAux) {
1868     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1869     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1870     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1871   }
1872   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1873   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);CHKERRQ(ierr);
1874   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
1875   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1876   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
1877   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1878   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1879     DM dmCell;
1880 
1881     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
1882     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
1883     for (c = 0; c < cEnd - cStart; c++) {
1884       PetscScalar *thisgeom;
1885 
1886       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1887       cgeom[c] = *((PetscFECellGeom *) thisgeom);
1888     }
1889   }
1890   else {
1891     cgeom = (PetscFECellGeom *) cgeomScal;
1892   }
1893   for (c = cStart; c < cEnd; ++c) {
1894     PetscScalar *x = NULL, *x_t = NULL;
1895     PetscInt     i;
1896 
1897     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1898     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1899     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1900     if (X_t) {
1901       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1902       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1903       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1904     }
1905     if (dmAux) {
1906       DM dmAuxPlex;
1907 
1908       ierr = DMSNESConvertPlex(dmAux,&dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1909       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1910       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1911       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1912       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1913     }
1914   }
1915   for (f = 0; f < Nf; ++f) {
1916     PetscFE  fe, feCh;
1917     PetscInt numQuadPoints, Nb;
1918     /* Conforming batches */
1919     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1920     /* Remainder */
1921     PetscInt Nr, offset;
1922 
1923     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1924     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
1925     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1926     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1927     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1928     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1929     blockSize = Nb*numQuadPoints;
1930     batchSize = numBlocks * blockSize;
1931     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1932     numChunks = numCells / (numBatches*batchSize);
1933     Ne        = numChunks*numBatches*batchSize;
1934     Nr        = numCells % (numBatches*batchSize);
1935     offset    = numCells - Nr;
1936     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1937     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVecCh);CHKERRQ(ierr);
1938     ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1939     ierr = PetscFEIntegrateResidual(feCh, prob, f, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVecCh[offset*totDim]);CHKERRQ(ierr);
1940   }
1941   for (c = cStart; c < cEnd; ++c) {
1942     PetscBool diff = PETSC_FALSE;
1943     PetscInt  d;
1944 
1945     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
1946     if (diff) {
1947       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
1948       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
1949       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
1950       ++diffCell;
1951     }
1952     if (diffCell > 9) break;
1953     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1954   }
1955   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1956     ierr = PetscFree(cgeom);CHKERRQ(ierr);
1957   }
1958   else {
1959     cgeom = NULL;
1960   }
1961   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1962   ierr = PetscFree3(u,u_t,elemVec);CHKERRQ(ierr);
1963   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
1964   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1965   PetscFunctionReturn(0);
1966 }
1967 
1968 #undef __FUNCT__
1969 #define __FUNCT__ "DMPlexSNESComputeResidualFEM"
1970 /*@
1971   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1972 
1973   Input Parameters:
1974 + dm - The mesh
1975 . X  - Local solution
1976 - user - The user context
1977 
1978   Output Parameter:
1979 . F  - Local output vector
1980 
1981   Level: developer
1982 
1983 .seealso: DMPlexComputeJacobianActionFEM()
1984 @*/
1985 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
1986 {
1987   PetscObject    check;
1988   PetscInt       cStart, cEnd, cEndInterior;
1989   DM             plex;
1990   PetscErrorCode ierr;
1991 
1992   PetscFunctionBegin;
1993   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
1994   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
1995   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1996   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
1997   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
1998   ierr = PetscObjectQuery((PetscObject) plex, "dmCh", &check);CHKERRQ(ierr);
1999   if (check) {ierr = DMPlexComputeResidualFEM_Check_Internal(plex, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2000   else       {ierr = DMPlexComputeResidual_Internal(plex, cStart, cEnd, PETSC_MIN_REAL, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2001   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2002   PetscFunctionReturn(0);
2003 }
2004 
2005 #undef __FUNCT__
2006 #define __FUNCT__ "DMPlexSNESComputeBoundaryFEM"
2007 /*@
2008   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X
2009 
2010   Input Parameters:
2011 + dm - The mesh
2012 - user - The user context
2013 
2014   Output Parameter:
2015 . X  - Local solution
2016 
2017   Level: developer
2018 
2019 .seealso: DMPlexComputeJacobianActionFEM()
2020 @*/
2021 PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
2022 {
2023   DM             plex;
2024   PetscErrorCode ierr;
2025 
2026   PetscFunctionBegin;
2027   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2028   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);CHKERRQ(ierr);
2029   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2030   PetscFunctionReturn(0);
2031 }
2032 
2033 #undef __FUNCT__
2034 #define __FUNCT__ "DMPlexComputeBdJacobian_Internal"
2035 PetscErrorCode DMPlexComputeBdJacobian_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, PetscReal X_tShift, Mat Jac, Mat JacP, void *user)
2036 {
2037   DM_Plex         *mesh = (DM_Plex *) dm->data;
2038   DM               dmAux = NULL, plex = NULL;
2039   PetscSection     section, globalSection, subSection, sectionAux = NULL;
2040   PetscDS          prob, probAux = NULL;
2041   DMLabel          depth;
2042   Vec              locA = NULL;
2043   PetscFECellGeom *cgeom;
2044   PetscScalar     *u = NULL, *u_t = NULL, *a = NULL, *elemMat = NULL;
2045   PetscInt         dim, Nf, f, totDimBd, totDimAuxBd, numBd, bd;
2046   PetscBool        isMatISP;
2047   PetscErrorCode   ierr;
2048 
2049   PetscFunctionBegin;
2050   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2051   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2052   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2053   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2054   if (isMatISP) {
2055     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2056   }
2057   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2058   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2059   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
2060   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
2061   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
2062   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
2063   if (locA) {
2064     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
2065     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2066     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2067     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2068     ierr = PetscDSGetTotalBdDimension(probAux, &totDimAuxBd);CHKERRQ(ierr);
2069   }
2070   for (bd = 0; bd < numBd; ++bd) {
2071     const char     *bdLabel;
2072     DMLabel         label;
2073     IS              pointIS;
2074     const PetscInt *points;
2075     const PetscInt *values;
2076     PetscInt        fieldI, fieldJ, numValues, v, numPoints, p, dep, numFaces;
2077     PetscBool       isEssential;
2078     PetscObject     obj;
2079     PetscClassId    id;
2080 
2081     ierr = PetscDSGetBoundary(prob, bd, &isEssential, NULL, &bdLabel, &fieldI, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
2082     ierr = PetscDSGetBdDiscretization(prob, fieldI, &obj);CHKERRQ(ierr);
2083     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2084     if ((id != PETSCFE_CLASSID) || isEssential) continue;
2085     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
2086     for (v = 0; v < numValues; ++v) {
2087       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
2088       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
2089       if (!pointIS) continue; /* No points with that id on this process */
2090       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2091       for (p = 0, numFaces = 0; p < numPoints; ++p) {
2092         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2093         if (dep == dim-1) ++numFaces;
2094       }
2095       ierr = PetscMalloc4(numFaces*totDimBd,&u,locX_t ? numFaces*totDimBd : 0,&u_t,numFaces,&cgeom,numFaces*totDimBd*totDimBd,&elemMat);CHKERRQ(ierr);
2096       if (locA) {ierr = PetscMalloc1(numFaces*totDimAuxBd,&a);CHKERRQ(ierr);}
2097       for (p = 0, f = 0; p < numPoints; ++p) {
2098         const PetscInt point = points[p];
2099         PetscScalar   *x     = NULL;
2100         PetscInt       i;
2101 
2102         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
2103         if (dep != dim-1) continue;
2104         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
2105         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);CHKERRQ(ierr);
2106         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
2107         ierr = DMPlexVecGetClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
2108         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
2109         ierr = DMPlexVecRestoreClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
2110         if (locX_t) {
2111           ierr = DMPlexVecGetClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
2112           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
2113           ierr = DMPlexVecRestoreClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
2114         }
2115         if (locA) {
2116           ierr = DMPlexVecGetClosure(plex, sectionAux, locA, point, NULL, &x);CHKERRQ(ierr);
2117           for (i = 0; i < totDimAuxBd; ++i) a[f*totDimAuxBd+i] = x[i];
2118           ierr = DMPlexVecRestoreClosure(plex, sectionAux, locA, point, NULL, &x);CHKERRQ(ierr);
2119         }
2120         ++f;
2121       }
2122       ierr = PetscMemzero(elemMat, numFaces*totDimBd*totDimBd * sizeof(PetscScalar));CHKERRQ(ierr);
2123       {
2124         PetscFE         fe;
2125         PetscQuadrature q;
2126         PetscInt        numQuadPoints, Nb;
2127         /* Conforming batches */
2128         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2129         /* Remainder */
2130         PetscInt        Nr, offset;
2131 
2132         ierr = PetscDSGetBdDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2133         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
2134         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2135         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2136         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2137         blockSize = Nb*numQuadPoints;
2138         batchSize = numBlocks * blockSize;
2139         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2140         numChunks = numFaces / (numBatches*batchSize);
2141         Ne        = numChunks*numBatches*batchSize;
2142         Nr        = numFaces % (numBatches*batchSize);
2143         offset    = numFaces - Nr;
2144         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2145           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2146           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, probAux, a ? &a[offset*totDimAuxBd] : NULL, t, X_tShift, &elemMat[offset*totDimBd*totDimBd]);CHKERRQ(ierr);
2147         }
2148       }
2149       for (p = 0, f = 0; p < numPoints; ++p) {
2150         const PetscInt point = points[p];
2151 
2152         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
2153         if (dep != dim-1) continue;
2154         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDimBd, totDimBd, &elemMat[f*totDimBd*totDimBd]);CHKERRQ(ierr);}
2155         if (!isMatISP) {
2156           ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*totDimBd*totDimBd], ADD_VALUES);CHKERRQ(ierr);
2157         } else {
2158           Mat lJ;
2159 
2160           ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2161           ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, point, &elemMat[f*totDimBd*totDimBd], ADD_VALUES);CHKERRQ(ierr);
2162         }
2163         ++f;
2164       }
2165       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2166       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2167       ierr = PetscFree4(u,u_t,cgeom,elemMat);CHKERRQ(ierr);
2168       if (locA) {
2169         ierr = PetscFree(a);CHKERRQ(ierr);
2170         ierr = DMDestroy(&plex);CHKERRQ(ierr);
2171       }
2172     }
2173   }
2174   PetscFunctionReturn(0);
2175 }
2176 
2177 #undef __FUNCT__
2178 #define __FUNCT__ "DMPlexComputeJacobian_Internal"
2179 PetscErrorCode DMPlexComputeJacobian_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Mat Jac, Mat JacP,void *user)
2180 {
2181   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2182   const char       *name  = "Jacobian";
2183   DM                dmAux, plex;
2184   DMLabel           depth;
2185   Vec               A, cellgeom;
2186   PetscDS           prob, probAux = NULL;
2187   PetscSection      section, globalSection, subSection, sectionAux;
2188   PetscFECellGeom  *cgeom = NULL;
2189   PetscScalar      *cgeomScal;
2190   PetscScalar      *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
2191   PetscInt          dim, Nf, f, fieldI, fieldJ, numCells, c;
2192   PetscInt          totDim, totDimAux;
2193   PetscBool         isMatIS, isMatISP, isShell, hasJac, hasPrec, hasDyn, hasFV = PETSC_FALSE;
2194   PetscErrorCode    ierr;
2195 
2196   PetscFunctionBegin;
2197   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2198   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2199   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2200   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2201   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2202   if (isMatISP) {
2203     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2204   }
2205   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2206   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2207   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2208   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2209   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2210   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2211   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2212   numCells = cEnd - cStart;
2213   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2214   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2215   if (dmAux) {
2216     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2217     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2218     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2219     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2220   }
2221   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
2222   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);
2223   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2224   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2225   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2226   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2227     DM dmCell;
2228 
2229     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2230     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2231     for (c = 0; c < cEnd - cStart; c++) {
2232       PetscScalar *thisgeom;
2233 
2234       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2235       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2236     }
2237   } else {
2238     cgeom = (PetscFECellGeom *) cgeomScal;
2239   }
2240   for (c = cStart; c < cEnd; ++c) {
2241     PetscScalar *x = NULL,  *x_t = NULL;
2242     PetscInt     i;
2243 
2244     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2245     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2246     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2247     if (X_t) {
2248       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2249       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2250       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2251     }
2252     if (dmAux) {
2253       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2254       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2255       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2256     }
2257   }
2258   if (hasJac)  {ierr = PetscMemzero(elemMat,  numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2259   if (hasPrec) {ierr = PetscMemzero(elemMatP, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2260   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2261   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2262     PetscClassId    id;
2263     PetscFE         fe;
2264     PetscQuadrature q;
2265     PetscInt        numQuadPoints, Nb;
2266     /* Conforming batches */
2267     PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2268     /* Remainder */
2269     PetscInt        Nr, offset;
2270 
2271     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2272     ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
2273     if (id == PETSCFV_CLASSID) {hasFV = PETSC_TRUE; continue;}
2274     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
2275     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2276     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2277     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2278     blockSize = Nb*numQuadPoints;
2279     batchSize = numBlocks * blockSize;
2280     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2281     numChunks = numCells / (numBatches*batchSize);
2282     Ne        = numChunks*numBatches*batchSize;
2283     Nr        = numCells % (numBatches*batchSize);
2284     offset    = numCells - Nr;
2285     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2286       if (hasJac) {
2287         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2288         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2289       }
2290       if (hasPrec) {
2291         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatP);CHKERRQ(ierr);
2292         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMatP[offset*totDim*totDim]);CHKERRQ(ierr);
2293       }
2294       if (hasDyn) {
2295         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2296         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMatD[offset*totDim*totDim]);CHKERRQ(ierr);
2297       }
2298     }
2299   }
2300   if (hasDyn) {
2301     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2302   }
2303   if (hasFV) {
2304     PetscClassId id;
2305     PetscFV      fv;
2306     PetscInt     offsetI, NcI, NbI = 1, fc, f;
2307 
2308     for (fieldI = 0; fieldI < Nf; ++fieldI) {
2309       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fv);CHKERRQ(ierr);
2310       ierr = PetscDSGetFieldOffset(prob, fieldI, &offsetI);CHKERRQ(ierr);
2311       ierr = PetscObjectGetClassId((PetscObject) fv, &id);CHKERRQ(ierr);
2312       if (id != PETSCFV_CLASSID) continue;
2313       /* Put in the identity */
2314       ierr = PetscFVGetNumComponents(fv, &NcI);CHKERRQ(ierr);
2315       for (c = cStart; c < cEnd; ++c) {
2316         const PetscInt eOffset = (c-cStart)*totDim*totDim;
2317         for (fc = 0; fc < NcI; ++fc) {
2318           for (f = 0; f < NbI; ++f) {
2319             const PetscInt i = offsetI + f*NcI+fc;
2320             if (hasPrec) {
2321               if (hasJac) {elemMat[eOffset+i*totDim+i] = 1.0;}
2322               elemMatP[eOffset+i*totDim+i] = 1.0;
2323             } else {elemMat[eOffset+i*totDim+i] = 1.0;}
2324           }
2325         }
2326       }
2327     }
2328     /* No allocated space for FV stuff, so ignore the zero entries */
2329     ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2330   }
2331   isMatIS = PETSC_FALSE;
2332   if (hasPrec && hasJac) {
2333     ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatIS);CHKERRQ(ierr);
2334   }
2335   if (isMatIS && !subSection) {
2336     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2337   }
2338   for (c = cStart; c < cEnd; ++c) {
2339     if (hasPrec) {
2340       if (hasJac) {
2341         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2342         if (!isMatIS) {
2343           ierr = DMPlexMatSetClosure(dm, section, globalSection, Jac, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2344         } else {
2345           Mat lJ;
2346 
2347           ierr = MatISGetLocalMat(Jac,&lJ);CHKERRQ(ierr);
2348           ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2349         }
2350       }
2351       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMatP[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2352       if (!isMatISP) {
2353         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2354       } else {
2355         Mat lJ;
2356 
2357         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2358         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2359       }
2360     } else {
2361       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2362       if (!isMatISP) {
2363         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2364       } else {
2365         Mat lJ;
2366 
2367         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2368         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2369       }
2370     }
2371   }
2372   if (hasFV) {ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);CHKERRQ(ierr);}
2373   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2374     ierr = PetscFree(cgeom);CHKERRQ(ierr);
2375   } else {
2376     cgeom = NULL;
2377   }
2378   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2379   ierr = PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);CHKERRQ(ierr);
2380   if (dmAux) {
2381     ierr = PetscFree(a);CHKERRQ(ierr);
2382     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2383   }
2384   ierr = DMPlexComputeBdJacobian_Internal(dm, X, X_t, t, X_tShift, Jac, JacP, user);CHKERRQ(ierr);
2385   if (hasJac && hasPrec) {
2386     ierr = MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2387     ierr = MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2388   }
2389   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2390   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2391   if (mesh->printFEM) {
2392     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
2393     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
2394     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2395   }
2396   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2397   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
2398   if (isShell) {
2399     JacActionCtx *jctx;
2400 
2401     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
2402     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
2403   }
2404   PetscFunctionReturn(0);
2405 }
2406 
2407 
2408 #undef __FUNCT__
2409 #define __FUNCT__ "DMPlexComputeJacobianAction_Internal"
2410 PetscErrorCode DMPlexComputeJacobianAction_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Vec Y, Vec Z, void *user)
2411 {
2412   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2413   const char       *name  = "Jacobian";
2414   DM                dmAux, plex;
2415   Vec               A, cellgeom;
2416   PetscDS           prob, probAux = NULL;
2417   PetscQuadrature   quad;
2418   PetscSection      section, globalSection, sectionAux;
2419   PetscFECellGeom  *cgeom = NULL;
2420   PetscScalar      *cgeomScal;
2421   PetscScalar      *elemMat, *elemMatD, *u, *u_t, *a = NULL, *y, *z;
2422   PetscInt          dim, Nf, fieldI, fieldJ, numCells, c;
2423   PetscInt          totDim, totDimBd, totDimAux = 0;
2424   PetscBool         hasDyn;
2425   PetscErrorCode    ierr;
2426 
2427   PetscFunctionBegin;
2428   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2429   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2430   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2431   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2432   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2433   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2434   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
2435   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2436   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2437   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2438   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2439   numCells = cEnd - cStart;
2440   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2441   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2442   if (dmAux) {
2443     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2444     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2445     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2446     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2447   }
2448   ierr = VecSet(Z, 0.0);CHKERRQ(ierr);
2449   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);
2450   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2451   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2452   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2453   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2454     DM dmCell;
2455 
2456     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2457     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2458     for (c = 0; c < cEnd - cStart; c++) {
2459       PetscScalar *thisgeom;
2460 
2461       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2462       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2463     }
2464   } else {
2465     cgeom = (PetscFECellGeom *) cgeomScal;
2466   }
2467   for (c = cStart; c < cEnd; ++c) {
2468     PetscScalar *x = NULL,  *x_t = NULL;
2469     PetscInt     i;
2470 
2471     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2472     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2473     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2474     if (X_t) {
2475       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2476       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2477       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2478     }
2479     if (dmAux) {
2480       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2481       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2482       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2483     }
2484     ierr = DMPlexVecGetClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2485     for (i = 0; i < totDim; ++i) y[(c-cStart)*totDim+i] = x[i];
2486     ierr = DMPlexVecRestoreClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2487   }
2488   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2489   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2490   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2491     PetscFE  fe;
2492     PetscInt numQuadPoints, Nb;
2493     /* Conforming batches */
2494     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2495     /* Remainder */
2496     PetscInt Nr, offset;
2497 
2498     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2499     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2500     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2501     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2502     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2503     blockSize = Nb*numQuadPoints;
2504     batchSize = numBlocks * blockSize;
2505     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2506     numChunks = numCells / (numBatches*batchSize);
2507     Ne        = numChunks*numBatches*batchSize;
2508     Nr        = numCells % (numBatches*batchSize);
2509     offset    = numCells - Nr;
2510     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2511       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2512       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2513       if (hasDyn) {
2514         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2515         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMatD[offset*totDim*totDim]);CHKERRQ(ierr);
2516       }
2517     }
2518   }
2519   if (hasDyn) {
2520     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2521   }
2522   for (c = cStart; c < cEnd; ++c) {
2523     const PetscBLASInt M = totDim, one = 1;
2524     const PetscScalar  a = 1.0, b = 0.0;
2525 
2526     PetscStackCallBLAS("BLASgemv", BLASgemv_("N", &M, &M, &a, &elemMat[(c-cStart)*totDim*totDim], &M, &y[(c-cStart)*totDim], &one, &b, z, &one));
2527     if (mesh->printFEM > 1) {
2528       ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);
2529       ierr = DMPrintCellVector(c, "Y",  totDim, &y[(c-cStart)*totDim]);CHKERRQ(ierr);
2530       ierr = DMPrintCellVector(c, "Z",  totDim, z);CHKERRQ(ierr);
2531     }
2532     ierr = DMPlexVecSetClosure(dm, section, Z, c, z, ADD_VALUES);CHKERRQ(ierr);
2533   }
2534   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {ierr = PetscFree(cgeom);CHKERRQ(ierr);}
2535   else                                               {cgeom = NULL;}
2536   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2537   ierr = PetscFree6(u,u_t,elemMat,elemMatD,y,z);CHKERRQ(ierr);
2538   if (dmAux) {
2539     ierr = PetscFree(a);CHKERRQ(ierr);
2540     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2541   }
2542   if (mesh->printFEM) {
2543     ierr = PetscPrintf(PETSC_COMM_WORLD, "Z:\n");CHKERRQ(ierr);
2544     ierr = VecView(Z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2545   }
2546   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2547   PetscFunctionReturn(0);
2548 }
2549 
2550 #undef __FUNCT__
2551 #define __FUNCT__ "DMPlexSNESComputeJacobianFEM"
2552 /*@
2553   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2554 
2555   Input Parameters:
2556 + dm - The mesh
2557 . X  - Local input vector
2558 - user - The user context
2559 
2560   Output Parameter:
2561 . Jac  - Jacobian matrix
2562 
2563   Note:
2564   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2565   like a GPU, or vectorize on a multicore machine.
2566 
2567   Level: developer
2568 
2569 .seealso: FormFunctionLocal()
2570 @*/
2571 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2572 {
2573   PetscInt       cStart, cEnd, cEndInterior;
2574   DM             plex;
2575   PetscErrorCode ierr;
2576 
2577   PetscFunctionBegin;
2578   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2579   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2580   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2581   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2582   ierr = DMPlexComputeJacobian_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2583   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2584   PetscFunctionReturn(0);
2585 }
2586 
2587 #undef __FUNCT__
2588 #define __FUNCT__ "DMPlexSNESComputeJacobianActionFEM"
2589 /*@
2590   DMPlexSNESComputeJacobianActionFEM - Form the local portion of the Jacobian action Z = J(X) Y at the local solution X using pointwise functions specified by the user.
2591 
2592   Input Parameters:
2593 + dm - The mesh
2594 . X  - Local solution vector
2595 . Y  - Local input vector
2596 - user - The user context
2597 
2598   Output Parameter:
2599 . Z - Local output vector
2600 
2601   Note:
2602   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2603   like a GPU, or vectorize on a multicore machine.
2604 
2605   Level: developer
2606 
2607 .seealso: FormFunctionLocal()
2608 @*/
2609 PetscErrorCode DMPlexSNESComputeJacobianActionFEM(DM dm, Vec X, Vec Y, Vec Z, void *user)
2610 {
2611   PetscInt       cStart, cEnd, cEndInterior;
2612   DM             plex;
2613   PetscErrorCode ierr;
2614 
2615   PetscFunctionBegin;
2616   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2617   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2618   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2619   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2620   ierr = DMPlexComputeJacobianAction_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Y, Z, user);CHKERRQ(ierr);
2621   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2622   PetscFunctionReturn(0);
2623 }
2624 
2625 #undef __FUNCT__
2626 #define __FUNCT__ "DMPlexSetSNESLocalFEM"
2627 /*@
2628   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.
2629 
2630   Input Parameters:
2631 + dm - The DM object
2632 . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see PetscDSAddBoundary())
2633 . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
2634 - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())
2635 
2636   Level: developer
2637 @*/
2638 PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
2639 {
2640   PetscErrorCode ierr;
2641 
2642   PetscFunctionBegin;
2643   ierr = DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);CHKERRQ(ierr);
2644   ierr = DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);CHKERRQ(ierr);
2645   ierr = DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);CHKERRQ(ierr);
2646   PetscFunctionReturn(0);
2647 }
2648 
2649 #undef __FUNCT__
2650 #define __FUNCT__ "DMSNESCheckFromOptions_Internal"
2651 PetscErrorCode DMSNESCheckFromOptions_Internal(SNES snes, DM dm, Vec u, Vec sol, PetscErrorCode (**exactFuncs)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx), void **ctxs)
2652 {
2653   Mat            J, M;
2654   Vec            r, b;
2655   MatNullSpace   nullSpace;
2656   PetscReal     *error, res = 0.0;
2657   PetscInt       numFields;
2658   PetscErrorCode ierr;
2659 
2660   PetscFunctionBegin;
2661   ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2662   ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
2663   M    = J;
2664   /* TODO Null space for J */
2665   /* Check discretization error */
2666   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
2667   ierr = PetscMalloc1(PetscMax(1, numFields), &error);CHKERRQ(ierr);
2668   if (numFields > 1) {
2669     PetscInt f;
2670 
2671     ierr = DMComputeL2FieldDiff(dm, 0.0, exactFuncs, ctxs, u, error);CHKERRQ(ierr);
2672     ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: [");CHKERRQ(ierr);
2673     for (f = 0; f < numFields; ++f) {
2674       if (f) {ierr = PetscPrintf(PETSC_COMM_WORLD, ", ");CHKERRQ(ierr);}
2675       if (error[f] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "%g", error[f]);CHKERRQ(ierr);}
2676       else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "< 1.0e-11");CHKERRQ(ierr);}
2677     }
2678     ierr = PetscPrintf(PETSC_COMM_WORLD, "]\n");CHKERRQ(ierr);
2679   } else {
2680     ierr = DMComputeL2Diff(dm, 0.0, exactFuncs, ctxs, u, &error[0]);CHKERRQ(ierr);
2681     if (error[0] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error[0]);CHKERRQ(ierr);}
2682     else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
2683   }
2684   ierr = PetscFree(error);CHKERRQ(ierr);
2685   /* Check residual */
2686   ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2687   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2688   ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", res);CHKERRQ(ierr);
2689   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2690   ierr = PetscObjectSetName((PetscObject) r, "Initial Residual");CHKERRQ(ierr);
2691   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"res_");CHKERRQ(ierr);
2692   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2693   /* Check Jacobian */
2694   ierr = SNESComputeJacobian(snes, u, M, M);CHKERRQ(ierr);
2695   ierr = MatGetNullSpace(J, &nullSpace);CHKERRQ(ierr);
2696   if (nullSpace) {
2697     PetscBool isNull;
2698     ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
2699     if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
2700   }
2701   ierr = VecDuplicate(u, &b);CHKERRQ(ierr);
2702   ierr = VecSet(r, 0.0);CHKERRQ(ierr);
2703   ierr = SNESComputeFunction(snes, r, b);CHKERRQ(ierr);
2704   ierr = MatMult(M, u, r);CHKERRQ(ierr);
2705   ierr = VecAXPY(r, 1.0, b);CHKERRQ(ierr);
2706   ierr = VecDestroy(&b);CHKERRQ(ierr);
2707   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2708   ierr = PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", res);CHKERRQ(ierr);
2709   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2710   ierr = PetscObjectSetName((PetscObject) r, "Au - b = Au + F(0)");CHKERRQ(ierr);
2711   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"linear_res_");CHKERRQ(ierr);
2712   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2713   ierr = VecDestroy(&r);CHKERRQ(ierr);
2714   ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
2715   ierr = MatDestroy(&J);CHKERRQ(ierr);
2716   PetscFunctionReturn(0);
2717 }
2718 
2719 #undef __FUNCT__
2720 #define __FUNCT__ "DMSNESCheckFromOptions"
2721 PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
2722 {
2723   DM             dm;
2724   Vec            sol;
2725   PetscBool      check;
2726   PetscErrorCode ierr;
2727 
2728   PetscFunctionBegin;
2729   ierr = PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);CHKERRQ(ierr);
2730   if (!check) PetscFunctionReturn(0);
2731   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
2732   ierr = VecDuplicate(u, &sol);CHKERRQ(ierr);
2733   ierr = SNESSetSolution(snes, sol);CHKERRQ(ierr);
2734   ierr = DMSNESCheckFromOptions_Internal(snes, dm, u, sol, exactFuncs, ctxs);CHKERRQ(ierr);
2735   ierr = VecDestroy(&sol);CHKERRQ(ierr);
2736   PetscFunctionReturn(0);
2737 }
2738