xref: /petsc/src/snes/utils/dmplexsnes.c (revision 1117012dd1dcc1f2efd4464db5d414fe72bd18a1)
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 = PetscMalloc(sizeof(struct _DMInterpolationInfo), 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   cellSF = NULL;
182   ierr = DMLocatePoints(dm, pointVec, DM_POINTLOCATION_NONE, &cellSF);CHKERRQ(ierr);
183   ierr = PetscSFGetGraph(cellSF,NULL,&numFound,&foundPoints,&foundCells);CHKERRQ(ierr);
184 #endif
185   for (p = 0; p < numFound; ++p) {
186     if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank;
187     else foundProcs[foundPoints ? foundPoints[p] : p] = size;
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   SNES           snes;
425   KSP            ksp;
426   PC             pc;
427   Vec            coordsLocal, r, ref, real;
428   Mat            J;
429   const PetscScalar *coords;
430   PetscScalar    *a;
431   PetscInt       p;
432   PetscErrorCode ierr;
433 
434   PetscFunctionBegin;
435   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
436   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
437   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
438   ierr = SNESSetOptionsPrefix(snes, "quad_interp_");CHKERRQ(ierr);
439   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
440   ierr = VecSetSizes(r, 2, 2);CHKERRQ(ierr);
441   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
442   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
443   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
444   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
445   ierr = MatSetSizes(J, 2, 2, 2, 2);CHKERRQ(ierr);
446   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
447   ierr = MatSetUp(J);CHKERRQ(ierr);
448   ierr = SNESSetFunction(snes, r, QuadMap_Private, NULL);CHKERRQ(ierr);
449   ierr = SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);CHKERRQ(ierr);
450   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
451   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
452   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
453   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
454 
455   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
456   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
457   for (p = 0; p < ctx->n; ++p) {
458     PetscScalar *x = NULL, *vertices = NULL;
459     PetscScalar *xi;
460     PetscReal    xir[2];
461     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
462 
463     /* Can make this do all points at once */
464     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
465     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 4*2);
466     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
467     if (4*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 4*ctx->dof);
468     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
469     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
470     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
471     xi[0]  = coords[p*ctx->dim+0];
472     xi[1]  = coords[p*ctx->dim+1];
473     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
474     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
475     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
476     xir[0] = PetscRealPart(xi[0]);
477     xir[1] = PetscRealPart(xi[1]);
478     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp]*(1 - xir[0])*(1 - xir[1]) + x[1*ctx->dof+comp]*xir[0]*(1 - xir[1]) + x[2*ctx->dof+comp]*xir[0]*xir[1] + x[3*ctx->dof+comp]*(1 - xir[0])*xir[1];
479 
480     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
481     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
482     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
483   }
484   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
485   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
486 
487   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
488   ierr = VecDestroy(&r);CHKERRQ(ierr);
489   ierr = VecDestroy(&ref);CHKERRQ(ierr);
490   ierr = VecDestroy(&real);CHKERRQ(ierr);
491   ierr = MatDestroy(&J);CHKERRQ(ierr);
492   PetscFunctionReturn(0);
493 }
494 
495 #undef __FUNCT__
496 #define __FUNCT__ "HexMap_Private"
497 PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
498 {
499   const PetscScalar *vertices = (const PetscScalar*) ctx;
500   const PetscScalar x0        = vertices[0];
501   const PetscScalar y0        = vertices[1];
502   const PetscScalar z0        = vertices[2];
503   const PetscScalar x1        = vertices[9];
504   const PetscScalar y1        = vertices[10];
505   const PetscScalar z1        = vertices[11];
506   const PetscScalar x2        = vertices[6];
507   const PetscScalar y2        = vertices[7];
508   const PetscScalar z2        = vertices[8];
509   const PetscScalar x3        = vertices[3];
510   const PetscScalar y3        = vertices[4];
511   const PetscScalar z3        = vertices[5];
512   const PetscScalar x4        = vertices[12];
513   const PetscScalar y4        = vertices[13];
514   const PetscScalar z4        = vertices[14];
515   const PetscScalar x5        = vertices[15];
516   const PetscScalar y5        = vertices[16];
517   const PetscScalar z5        = vertices[17];
518   const PetscScalar x6        = vertices[18];
519   const PetscScalar y6        = vertices[19];
520   const PetscScalar z6        = vertices[20];
521   const PetscScalar x7        = vertices[21];
522   const PetscScalar y7        = vertices[22];
523   const PetscScalar z7        = vertices[23];
524   const PetscScalar f_1       = x1 - x0;
525   const PetscScalar g_1       = y1 - y0;
526   const PetscScalar h_1       = z1 - z0;
527   const PetscScalar f_3       = x3 - x0;
528   const PetscScalar g_3       = y3 - y0;
529   const PetscScalar h_3       = z3 - z0;
530   const PetscScalar f_4       = x4 - x0;
531   const PetscScalar g_4       = y4 - y0;
532   const PetscScalar h_4       = z4 - z0;
533   const PetscScalar f_01      = x2 - x1 - x3 + x0;
534   const PetscScalar g_01      = y2 - y1 - y3 + y0;
535   const PetscScalar h_01      = z2 - z1 - z3 + z0;
536   const PetscScalar f_12      = x7 - x3 - x4 + x0;
537   const PetscScalar g_12      = y7 - y3 - y4 + y0;
538   const PetscScalar h_12      = z7 - z3 - z4 + z0;
539   const PetscScalar f_02      = x5 - x1 - x4 + x0;
540   const PetscScalar g_02      = y5 - y1 - y4 + y0;
541   const PetscScalar h_02      = z5 - z1 - z4 + z0;
542   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
543   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
544   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
545   const PetscScalar *ref;
546   PetscScalar       *real;
547   PetscErrorCode    ierr;
548 
549   PetscFunctionBegin;
550   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
551   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
552   {
553     const PetscScalar p0 = ref[0];
554     const PetscScalar p1 = ref[1];
555     const PetscScalar p2 = ref[2];
556 
557     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;
558     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;
559     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;
560   }
561   ierr = PetscLogFlops(114);CHKERRQ(ierr);
562   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
563   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
564   PetscFunctionReturn(0);
565 }
566 
567 #undef __FUNCT__
568 #define __FUNCT__ "HexJacobian_Private"
569 PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
570 {
571   const PetscScalar *vertices = (const PetscScalar*) ctx;
572   const PetscScalar x0        = vertices[0];
573   const PetscScalar y0        = vertices[1];
574   const PetscScalar z0        = vertices[2];
575   const PetscScalar x1        = vertices[9];
576   const PetscScalar y1        = vertices[10];
577   const PetscScalar z1        = vertices[11];
578   const PetscScalar x2        = vertices[6];
579   const PetscScalar y2        = vertices[7];
580   const PetscScalar z2        = vertices[8];
581   const PetscScalar x3        = vertices[3];
582   const PetscScalar y3        = vertices[4];
583   const PetscScalar z3        = vertices[5];
584   const PetscScalar x4        = vertices[12];
585   const PetscScalar y4        = vertices[13];
586   const PetscScalar z4        = vertices[14];
587   const PetscScalar x5        = vertices[15];
588   const PetscScalar y5        = vertices[16];
589   const PetscScalar z5        = vertices[17];
590   const PetscScalar x6        = vertices[18];
591   const PetscScalar y6        = vertices[19];
592   const PetscScalar z6        = vertices[20];
593   const PetscScalar x7        = vertices[21];
594   const PetscScalar y7        = vertices[22];
595   const PetscScalar z7        = vertices[23];
596   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
597   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
598   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
599   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
600   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
601   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
602   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
603   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
604   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
605   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
606   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
607   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
608   const PetscScalar *ref;
609   PetscErrorCode    ierr;
610 
611   PetscFunctionBegin;
612   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
613   {
614     const PetscScalar x       = ref[0];
615     const PetscScalar y       = ref[1];
616     const PetscScalar z       = ref[2];
617     const PetscInt    rows[3] = {0, 1, 2};
618     PetscScalar       values[9];
619 
620     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
621     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
622     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
623     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
624     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
625     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
626     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
627     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
628     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;
629 
630     ierr = MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);CHKERRQ(ierr);
631   }
632   ierr = PetscLogFlops(152);CHKERRQ(ierr);
633   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
634   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
635   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
636   PetscFunctionReturn(0);
637 }
638 
639 #undef __FUNCT__
640 #define __FUNCT__ "DMInterpolate_Hex_Private"
641 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
642 {
643   DM             dmCoord;
644   SNES           snes;
645   KSP            ksp;
646   PC             pc;
647   Vec            coordsLocal, r, ref, real;
648   Mat            J;
649   const PetscScalar *coords;
650   PetscScalar    *a;
651   PetscInt       p;
652   PetscErrorCode ierr;
653 
654   PetscFunctionBegin;
655   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
656   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
657   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
658   ierr = SNESSetOptionsPrefix(snes, "hex_interp_");CHKERRQ(ierr);
659   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
660   ierr = VecSetSizes(r, 3, 3);CHKERRQ(ierr);
661   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
662   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
663   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
664   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
665   ierr = MatSetSizes(J, 3, 3, 3, 3);CHKERRQ(ierr);
666   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
667   ierr = MatSetUp(J);CHKERRQ(ierr);
668   ierr = SNESSetFunction(snes, r, HexMap_Private, NULL);CHKERRQ(ierr);
669   ierr = SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);CHKERRQ(ierr);
670   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
671   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
672   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
673   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
674 
675   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
676   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
677   for (p = 0; p < ctx->n; ++p) {
678     PetscScalar *x = NULL, *vertices = NULL;
679     PetscScalar *xi;
680     PetscReal    xir[3];
681     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
682 
683     /* Can make this do all points at once */
684     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
685     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 8*3);
686     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
687     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 8*ctx->dof);
688     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
689     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
690     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
691     xi[0]  = coords[p*ctx->dim+0];
692     xi[1]  = coords[p*ctx->dim+1];
693     xi[2]  = coords[p*ctx->dim+2];
694     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
695     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
696     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
697     xir[0] = PetscRealPart(xi[0]);
698     xir[1] = PetscRealPart(xi[1]);
699     xir[2] = PetscRealPart(xi[2]);
700     for (comp = 0; comp < ctx->dof; ++comp) {
701       a[p*ctx->dof+comp] =
702         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
703         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
704         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
705         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
706         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
707         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
708         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
709         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
710     }
711     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
712     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
713     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
714   }
715   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
716   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
717 
718   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
719   ierr = VecDestroy(&r);CHKERRQ(ierr);
720   ierr = VecDestroy(&ref);CHKERRQ(ierr);
721   ierr = VecDestroy(&real);CHKERRQ(ierr);
722   ierr = MatDestroy(&J);CHKERRQ(ierr);
723   PetscFunctionReturn(0);
724 }
725 
726 #undef __FUNCT__
727 #define __FUNCT__ "DMInterpolationEvaluate"
728 /*
729   Input Parameters:
730 + ctx - The DMInterpolationInfo context
731 . dm  - The DM
732 - x   - The local vector containing the field to be interpolated
733 
734   Output Parameters:
735 . v   - The vector containing the interpolated values
736 */
737 PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
738 {
739   PetscInt       dim, coneSize, n;
740   PetscErrorCode ierr;
741 
742   PetscFunctionBegin;
743   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
744   PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
745   PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
746   ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
747   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);
748   if (n) {
749     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
750     ierr = DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);CHKERRQ(ierr);
751     if (dim == 2) {
752       if (coneSize == 3) {
753         ierr = DMInterpolate_Triangle_Private(ctx, dm, x, v);CHKERRQ(ierr);
754       } else if (coneSize == 4) {
755         ierr = DMInterpolate_Quad_Private(ctx, dm, x, v);CHKERRQ(ierr);
756       } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
757     } else if (dim == 3) {
758       if (coneSize == 4) {
759         ierr = DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);CHKERRQ(ierr);
760       } else {
761         ierr = DMInterpolate_Hex_Private(ctx, dm, x, v);CHKERRQ(ierr);
762       }
763     } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
764   }
765   PetscFunctionReturn(0);
766 }
767 
768 #undef __FUNCT__
769 #define __FUNCT__ "DMInterpolationDestroy"
770 PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
771 {
772   PetscErrorCode ierr;
773 
774   PetscFunctionBegin;
775   PetscValidPointer(ctx, 2);
776   ierr = VecDestroy(&(*ctx)->coords);CHKERRQ(ierr);
777   ierr = PetscFree((*ctx)->points);CHKERRQ(ierr);
778   ierr = PetscFree((*ctx)->cells);CHKERRQ(ierr);
779   ierr = PetscFree(*ctx);CHKERRQ(ierr);
780   *ctx = NULL;
781   PetscFunctionReturn(0);
782 }
783 
784 #undef __FUNCT__
785 #define __FUNCT__ "SNESMonitorFields"
786 /*@C
787   SNESMonitorFields - Monitors the residual for each field separately
788 
789   Collective on SNES
790 
791   Input Parameters:
792 + snes   - the SNES context
793 . its    - iteration number
794 . fgnorm - 2-norm of residual
795 - vf  - PetscViewerAndFormat of type ASCII
796 
797   Notes:
798   This routine prints the residual norm at each iteration.
799 
800   Level: intermediate
801 
802 .keywords: SNES, nonlinear, default, monitor, norm
803 .seealso: SNESMonitorSet(), SNESMonitorDefault()
804 @*/
805 PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
806 {
807   PetscViewer        viewer = vf->viewer;
808   Vec                res;
809   DM                 dm;
810   PetscSection       s;
811   const PetscScalar *r;
812   PetscReal         *lnorms, *norms;
813   PetscInt           numFields, f, pStart, pEnd, p;
814   PetscErrorCode     ierr;
815 
816   PetscFunctionBegin;
817   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
818   ierr = SNESGetFunction(snes, &res, 0, 0);CHKERRQ(ierr);
819   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
820   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
821   ierr = PetscSectionGetNumFields(s, &numFields);CHKERRQ(ierr);
822   ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
823   ierr = PetscCalloc2(numFields, &lnorms, numFields, &norms);CHKERRQ(ierr);
824   ierr = VecGetArrayRead(res, &r);CHKERRQ(ierr);
825   for (p = pStart; p < pEnd; ++p) {
826     for (f = 0; f < numFields; ++f) {
827       PetscInt fdof, foff, d;
828 
829       ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
830       ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
831       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
832     }
833   }
834   ierr = VecRestoreArrayRead(res, &r);CHKERRQ(ierr);
835   ierr = MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
836   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
837   ierr = PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
838   ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
839   for (f = 0; f < numFields; ++f) {
840     if (f > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
841     ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));CHKERRQ(ierr);
842   }
843   ierr = PetscViewerASCIIPrintf(viewer, "]\n");CHKERRQ(ierr);
844   ierr = PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
845   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
846   ierr = PetscFree2(lnorms, norms);CHKERRQ(ierr);
847   PetscFunctionReturn(0);
848 }
849 
850 /********************* Residual Computation **************************/
851 
852 #undef __FUNCT__
853 #define __FUNCT__ "DMPlexSNESGetGeometryFEM"
854 /*@
855   DMPlexSNESGetGeometryFEM - Return precomputed geometric data
856 
857   Input Parameter:
858 . dm - The DM
859 
860   Output Parameters:
861 . cellgeom - The values precomputed from cell geometry
862 
863   Level: developer
864 
865 .seealso: DMPlexSNESSetFunctionLocal()
866 @*/
867 PetscErrorCode DMPlexSNESGetGeometryFEM(DM dm, Vec *cellgeom)
868 {
869   DMSNES         dmsnes;
870   PetscObject    obj;
871   PetscErrorCode ierr;
872 
873   PetscFunctionBegin;
874   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
875   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
876   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", &obj);CHKERRQ(ierr);
877   if (!obj) {
878     Vec cellgeom;
879 
880     ierr = DMPlexComputeGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
881     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject) cellgeom);CHKERRQ(ierr);
882     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
883   }
884   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject *) cellgeom);CHKERRQ(ierr);}
885   PetscFunctionReturn(0);
886 }
887 
888 #undef __FUNCT__
889 #define __FUNCT__ "DMPlexSNESGetGeometryFVM"
890 /*@
891   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
892 
893   Input Parameter:
894 . dm - The DM
895 
896   Output Parameters:
897 + facegeom - The values precomputed from face geometry
898 . cellgeom - The values precomputed from cell geometry
899 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
900 
901   Level: developer
902 
903 .seealso: DMPlexTSSetRHSFunctionLocal()
904 @*/
905 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
906 {
907   DMSNES         dmsnes;
908   PetscObject    obj;
909   PetscErrorCode ierr;
910 
911   PetscFunctionBegin;
912   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
913   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
914   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", &obj);CHKERRQ(ierr);
915   if (!obj) {
916     Vec cellgeom, facegeom;
917 
918     ierr = DMPlexComputeGeometryFVM(dm, &cellgeom, &facegeom);CHKERRQ(ierr);
919     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", (PetscObject) facegeom);CHKERRQ(ierr);
920     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fvm", (PetscObject) cellgeom);CHKERRQ(ierr);
921     ierr = VecDestroy(&facegeom);CHKERRQ(ierr);
922     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
923   }
924   if (facegeom) {PetscValidPointer(facegeom, 2); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", (PetscObject *) facegeom);CHKERRQ(ierr);}
925   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fvm", (PetscObject *) cellgeom);CHKERRQ(ierr);}
926   if (minRadius) {ierr = DMPlexGetMinRadius(dm, minRadius);CHKERRQ(ierr);}
927   PetscFunctionReturn(0);
928 }
929 
930 #undef __FUNCT__
931 #define __FUNCT__ "DMPlexSNESGetGradientDM"
932 /*@
933   DMPlexSNESGetGradientDM - Return gradient data layout
934 
935   Input Parameters:
936 + dm - The DM
937 - fv - The PetscFV
938 
939   Output Parameter:
940 . dmGrad - The layout for gradient values
941 
942   Level: developer
943 
944 .seealso: DMPlexSNESGetGeometryFVM()
945 @*/
946 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
947 {
948   DMSNES         dmsnes;
949   PetscObject    obj;
950   PetscBool      computeGradients;
951   PetscErrorCode ierr;
952 
953   PetscFunctionBegin;
954   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
955   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
956   PetscValidPointer(dmGrad,3);
957   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
958   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
959   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
960   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", &obj);CHKERRQ(ierr);
961   if (!obj) {
962     DM  dmGrad;
963     Vec faceGeometry, cellGeometry;
964 
965     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometry, &cellGeometry, NULL);CHKERRQ(ierr);
966     ierr = DMPlexComputeGradientFVM(dm, fv, faceGeometry, cellGeometry, &dmGrad);CHKERRQ(ierr);
967     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", (PetscObject) dmGrad);CHKERRQ(ierr);
968     ierr = DMDestroy(&dmGrad);CHKERRQ(ierr);
969   }
970   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", (PetscObject *) dmGrad);CHKERRQ(ierr);
971   PetscFunctionReturn(0);
972 }
973 
974 #undef __FUNCT__
975 #define __FUNCT__ "DMPlexGetCellFields"
976 /*@C
977   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells
978 
979   Input Parameters:
980 + dm     - The DM
981 . cStart - The first cell to include
982 . cEnd   - The first cell to exclude
983 . locX   - A local vector with the solution fields
984 . locX_t - A local vector with solution field time derivatives, or NULL
985 - locA   - A local vector with auxiliary fields, or NULL
986 
987   Output Parameters:
988 + u   - The field coefficients
989 . u_t - The fields derivative coefficients
990 - a   - The auxiliary field coefficients
991 
992   Level: developer
993 
994 .seealso: DMPlexGetFaceFields()
995 @*/
996 PetscErrorCode DMPlexGetCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
997 {
998   DM             dmAux;
999   PetscSection   section, sectionAux;
1000   PetscDS        prob;
1001   PetscInt       numCells = cEnd - cStart, totDim, totDimAux, c;
1002   PetscErrorCode ierr;
1003 
1004   PetscFunctionBegin;
1005   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1006   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1007   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1008   if (locA)   {PetscValidHeaderSpecific(locA, VEC_CLASSID, 6);}
1009   PetscValidPointer(u, 7);
1010   PetscValidPointer(u_t, 8);
1011   PetscValidPointer(a, 9);
1012   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1013   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1014   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1015   if (locA) {
1016     PetscDS probAux;
1017 
1018     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1019     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1020     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1021     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1022   }
1023   ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u);CHKERRQ(ierr);
1024   if (locX_t) {ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u_t);CHKERRQ(ierr);} else {*u_t = NULL;}
1025   if (locA)   {ierr = DMGetWorkArray(dm, numCells*totDimAux, PETSC_SCALAR, a);CHKERRQ(ierr);} else {*a = NULL;}
1026   for (c = cStart; c < cEnd; ++c) {
1027     PetscScalar *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
1028     PetscInt     i;
1029 
1030     ierr = DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1031     for (i = 0; i < totDim; ++i) ul[(c-cStart)*totDim+i] = x[i];
1032     ierr = DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1033     if (locX_t) {
1034       ierr = DMPlexVecGetClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1035       for (i = 0; i < totDim; ++i) ul_t[(c-cStart)*totDim+i] = x_t[i];
1036       ierr = DMPlexVecRestoreClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1037     }
1038     if (locA) {
1039       DM dmAuxPlex;
1040 
1041       ierr = DMSNESConvertPlex(dmAux, &dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1042       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1043       for (i = 0; i < totDimAux; ++i) al[(c-cStart)*totDimAux+i] = x[i];
1044       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1045       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1046     }
1047   }
1048   PetscFunctionReturn(0);
1049 }
1050 
1051 #undef __FUNCT__
1052 #define __FUNCT__ "DMPlexRestoreCellFields"
1053 /*@C
1054   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells
1055 
1056   Input Parameters:
1057 + dm     - The DM
1058 . cStart - The first cell to include
1059 . cEnd   - The first cell to exclude
1060 . locX   - A local vector with the solution fields
1061 . locX_t - A local vector with solution field time derivatives, or NULL
1062 - locA   - A local vector with auxiliary fields, or NULL
1063 
1064   Output Parameters:
1065 + u   - The field coefficients
1066 . u_t - The fields derivative coefficients
1067 - a   - The auxiliary field coefficients
1068 
1069   Level: developer
1070 
1071 .seealso: DMPlexGetFaceFields()
1072 @*/
1073 PetscErrorCode DMPlexRestoreCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1074 {
1075   PetscErrorCode ierr;
1076 
1077   PetscFunctionBegin;
1078   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u);CHKERRQ(ierr);
1079   if (*u_t) {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u_t);CHKERRQ(ierr);}
1080   if (*a)   {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, a);CHKERRQ(ierr);}
1081   PetscFunctionReturn(0);
1082 }
1083 
1084 #undef __FUNCT__
1085 #define __FUNCT__ "DMPlexGetFaceFields"
1086 /*@C
1087   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces
1088 
1089   Input Parameters:
1090 + dm     - The DM
1091 . fStart - The first face to include
1092 . fEnd   - The first face to exclude
1093 . locX   - A local vector with the solution fields
1094 . locX_t - A local vector with solution field time derivatives, or NULL
1095 . faceGeometry - A local vector with face geometry
1096 . cellGeometry - A local vector with cell geometry
1097 - locaGrad - A local vector with field gradients, or NULL
1098 
1099   Output Parameters:
1100 + uL - The field values at the left side of the face
1101 - uR - The field values at the right side of the face
1102 
1103   Level: developer
1104 
1105 .seealso: DMPlexGetCellFields()
1106 @*/
1107 PetscErrorCode DMPlexGetFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscScalar **uL, PetscScalar **uR)
1108 {
1109   DM                 dmFace, dmCell, dmGrad = NULL;
1110   PetscSection       section;
1111   PetscDS            prob;
1112   DMLabel            ghostLabel;
1113   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
1114   PetscBool         *isFE;
1115   PetscInt           dim, Nf, f, Nc, numFaces = fEnd - fStart, iface, face;
1116   PetscErrorCode     ierr;
1117 
1118   PetscFunctionBegin;
1119   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1120   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1121   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1122   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 6);
1123   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 7);
1124   if (locGrad) {PetscValidHeaderSpecific(locGrad, VEC_CLASSID, 8);}
1125   PetscValidPointer(uL, 9);
1126   PetscValidPointer(uR, 10);
1127   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1128   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1129   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1130   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1131   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1132   ierr = PetscMalloc1(Nf, &isFE);CHKERRQ(ierr);
1133   for (f = 0; f < Nf; ++f) {
1134     PetscObject  obj;
1135     PetscClassId id;
1136 
1137     ierr = DMGetField(dm, f, &obj);CHKERRQ(ierr);
1138     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1139     if (id == PETSCFE_CLASSID)      {isFE[f] = PETSC_TRUE;}
1140     else if (id == PETSCFV_CLASSID) {isFE[f] = PETSC_FALSE;}
1141     else                            {isFE[f] = PETSC_FALSE;}
1142   }
1143   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1144   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1145   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1146   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1147   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1148   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1149   if (locGrad) {
1150     ierr = VecGetDM(locGrad, &dmGrad);CHKERRQ(ierr);
1151     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1152   }
1153   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uL);CHKERRQ(ierr);
1154   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uR);CHKERRQ(ierr);
1155   /* Right now just eat the extra work for FE (could make a cell loop) */
1156   for (face = fStart, iface = 0; face < fEnd; ++face) {
1157     const PetscInt        *cells;
1158     PetscFVFaceGeom       *fg;
1159     PetscFVCellGeom       *cgL, *cgR;
1160     PetscScalar           *xL, *xR, *gL, *gR;
1161     PetscScalar           *uLl = *uL, *uRl = *uR;
1162     PetscInt               ghost, nsupp;
1163 
1164     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1165     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1166     if (ghost >= 0) continue;
1167     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1168     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1169     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1170     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1171     for (f = 0; f < Nf; ++f) {
1172       PetscInt off;
1173 
1174       ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1175       if (isFE[f]) {
1176         const PetscInt *cone;
1177         PetscInt        comp, coneSize, faceLocL, faceLocR, ldof, rdof, d;
1178 
1179         xL = xR = NULL;
1180         ierr = DMPlexVecGetClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1181         ierr = DMPlexVecGetClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1182         ierr = DMPlexGetCone(dm, cells[0], &cone);CHKERRQ(ierr);
1183         ierr = DMPlexGetConeSize(dm, cells[0], &coneSize);CHKERRQ(ierr);
1184         for (faceLocL = 0; faceLocL < coneSize; ++faceLocL) if (cone[faceLocL] == face) break;
1185         if (faceLocL == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of cell %d", face, cells[0]);
1186         ierr = DMPlexGetCone(dm, cells[1], &cone);CHKERRQ(ierr);
1187         ierr = DMPlexGetConeSize(dm, cells[1], &coneSize);CHKERRQ(ierr);
1188         for (faceLocR = 0; faceLocR < coneSize; ++faceLocR) if (cone[faceLocR] == face) break;
1189         if (faceLocR == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of cell %d", face, cells[1]);
1190         /* Check that FEM field has values in the right cell (sometimes its an FV ghost cell) */
1191         ierr = EvaluateFaceFields(prob, f, faceLocL, xL, &uLl[iface*Nc+off]);CHKERRQ(ierr);
1192         if (rdof == ldof) {ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);}
1193         else              {ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr); for(d = 0; d < comp; ++d) uRl[iface*Nc+off+d] = uLl[iface*Nc+off+d];}
1194         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1195         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1196       } else {
1197         PetscFV  fv;
1198         PetscInt numComp, c;
1199 
1200         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fv);CHKERRQ(ierr);
1201         ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1202         if (nsupp > 2) {
1203           for (f = 0; f < Nf; ++f) {
1204             PetscInt off;
1205 
1206             ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1207             ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1208             for (c = 0; c < numComp; ++c) {
1209               uLl[iface*Nc+off+c] = 0.;
1210               uRl[iface*Nc+off+c] = 0.;
1211             }
1212           }
1213           continue;
1214         }
1215         ierr = DMPlexPointLocalFieldRead(dm, cells[0], f, x, &xL);CHKERRQ(ierr);
1216         ierr = DMPlexPointLocalFieldRead(dm, cells[1], f, x, &xR);CHKERRQ(ierr);
1217         if (dmGrad) {
1218           PetscReal dxL[3], dxR[3];
1219 
1220           ierr = DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);CHKERRQ(ierr);
1221           ierr = DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);CHKERRQ(ierr);
1222           DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
1223           DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
1224           for (c = 0; c < numComp; ++c) {
1225             uLl[iface*Nc+off+c] = xL[c] + DMPlex_DotD_Internal(dim, &gL[c*dim], dxL);
1226             uRl[iface*Nc+off+c] = xR[c] + DMPlex_DotD_Internal(dim, &gR[c*dim], dxR);
1227           }
1228         } else {
1229           for (c = 0; c < numComp; ++c) {
1230             uLl[iface*Nc+off+c] = xL[c];
1231             uRl[iface*Nc+off+c] = xR[c];
1232           }
1233         }
1234       }
1235     }
1236     ++iface;
1237   }
1238   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1239   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1240   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1241   if (locGrad) {
1242     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1243   }
1244   ierr = PetscFree(isFE);CHKERRQ(ierr);
1245   PetscFunctionReturn(0);
1246 }
1247 
1248 #undef __FUNCT__
1249 #define __FUNCT__ "DMPlexRestoreFaceFields"
1250 /*@C
1251   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces
1252 
1253   Input Parameters:
1254 + dm     - The DM
1255 . fStart - The first face to include
1256 . fEnd   - The first face to exclude
1257 . locX   - A local vector with the solution fields
1258 . locX_t - A local vector with solution field time derivatives, or NULL
1259 . faceGeometry - A local vector with face geometry
1260 . cellGeometry - A local vector with cell geometry
1261 - locaGrad - A local vector with field gradients, or NULL
1262 
1263   Output Parameters:
1264 + uL - The field values at the left side of the face
1265 - uR - The field values at the right side of the face
1266 
1267   Level: developer
1268 
1269 .seealso: DMPlexGetFaceFields()
1270 @*/
1271 PetscErrorCode DMPlexRestoreFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscScalar **uL, PetscScalar **uR)
1272 {
1273   PetscErrorCode ierr;
1274 
1275   PetscFunctionBegin;
1276   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uL);CHKERRQ(ierr);
1277   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uR);CHKERRQ(ierr);
1278   PetscFunctionReturn(0);
1279 }
1280 
1281 #undef __FUNCT__
1282 #define __FUNCT__ "DMPlexGetFaceGeometry"
1283 /*@C
1284   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces
1285 
1286   Input Parameters:
1287 + dm     - The DM
1288 . fStart - The first face to include
1289 . fEnd   - The first face to exclude
1290 . faceGeometry - A local vector with face geometry
1291 - cellGeometry - A local vector with cell geometry
1292 
1293   Output Parameters:
1294 + fgeom - The extract the face centroid and normal
1295 - vol   - The cell volume
1296 
1297   Level: developer
1298 
1299 .seealso: DMPlexGetCellFields()
1300 @*/
1301 PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscFVFaceGeom **fgeom, PetscReal **vol)
1302 {
1303   DM                 dmFace, dmCell;
1304   DMLabel            ghostLabel;
1305   const PetscScalar *facegeom, *cellgeom;
1306   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
1307   PetscErrorCode     ierr;
1308 
1309   PetscFunctionBegin;
1310   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1311   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 4);
1312   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 5);
1313   PetscValidPointer(fgeom, 6);
1314   PetscValidPointer(vol, 7);
1315   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1316   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1317   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1318   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1319   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1320   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1321   ierr = PetscMalloc1(numFaces, fgeom);CHKERRQ(ierr);
1322   ierr = DMGetWorkArray(dm, numFaces*2, PETSC_SCALAR, vol);CHKERRQ(ierr);
1323   for (face = fStart, iface = 0; face < fEnd; ++face) {
1324     const PetscInt        *cells;
1325     PetscFVFaceGeom       *fg;
1326     PetscFVCellGeom       *cgL, *cgR;
1327     PetscFVFaceGeom       *fgeoml = *fgeom;
1328     PetscReal             *voll   = *vol;
1329     PetscInt               ghost, d;
1330 
1331     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1332     if (ghost >= 0) continue;
1333     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1334     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1335     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1336     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1337     for (d = 0; d < dim; ++d) {
1338       fgeoml[iface].centroid[d] = fg->centroid[d];
1339       fgeoml[iface].normal[d]   = fg->normal[d];
1340     }
1341     voll[iface*2+0] = cgL->volume;
1342     voll[iface*2+1] = cgR->volume;
1343     ++iface;
1344   }
1345   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1346   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1347   PetscFunctionReturn(0);
1348 }
1349 
1350 #undef __FUNCT__
1351 #define __FUNCT__ "DMPlexRestoreFaceGeometry"
1352 /*@C
1353   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces
1354 
1355   Input Parameters:
1356 + dm     - The DM
1357 . fStart - The first face to include
1358 . fEnd   - The first face to exclude
1359 . faceGeometry - A local vector with face geometry
1360 - cellGeometry - A local vector with cell geometry
1361 
1362   Output Parameters:
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, 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   PetscSection     section;
1386   PetscDS          prob;
1387   DMLabel          depth;
1388   PetscFECellGeom *cgeom;
1389   PetscScalar     *u = NULL, *u_t = NULL, *elemVec = NULL;
1390   PetscInt         dim, Nf, f, totDimBd, numBd, bd;
1391   PetscErrorCode   ierr;
1392 
1393   PetscFunctionBegin;
1394   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1395   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1396   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1397   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1398   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
1399   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1400   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1401   for (bd = 0; bd < numBd; ++bd) {
1402     const char     *bdLabel;
1403     DMLabel         label;
1404     IS              pointIS;
1405     const PetscInt *points;
1406     const PetscInt *values;
1407     PetscInt        field, numValues, v, numPoints, p, dep, numFaces;
1408     PetscBool       isEssential;
1409     PetscObject     obj;
1410     PetscClassId    id;
1411 
1412     ierr = DMGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1413     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
1414     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1415     if ((id != PETSCFE_CLASSID) || isEssential) continue;
1416     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1417     for (v = 0; v < numValues; ++v) {
1418       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
1419       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1420       if (!pointIS) continue; /* No points with that id on this process */
1421       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1422       for (p = 0, numFaces = 0; p < numPoints; ++p) {
1423         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1424         if (dep == dim-1) ++numFaces;
1425       }
1426       ierr = PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd,&elemVec);CHKERRQ(ierr);
1427       if (locX_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
1428       for (p = 0, f = 0; p < numPoints; ++p) {
1429         const PetscInt point = points[p];
1430         PetscScalar   *x     = NULL;
1431         PetscInt       i;
1432 
1433         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1434         if (dep != dim-1) continue;
1435         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
1436         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);CHKERRQ(ierr);
1437         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
1438         /* TODO: Matt, this is wrong if feBd does not match fe: i.e., if the order differs. */
1439         ierr = DMPlexVecGetClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1440         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
1441         ierr = DMPlexVecRestoreClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1442         if (locX_t) {
1443           ierr = DMPlexVecGetClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1444           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
1445           ierr = DMPlexVecRestoreClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1446         }
1447         ++f;
1448       }
1449       for (f = 0; f < Nf; ++f) {
1450         PetscFE         fe;
1451         PetscQuadrature q;
1452         PetscInt        numQuadPoints, Nb;
1453         /* Conforming batches */
1454         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1455         /* Remainder */
1456         PetscInt        Nr, offset;
1457 
1458         ierr = PetscDSGetBdDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1459         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1460         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1461         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1462         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1463         blockSize = Nb*numQuadPoints;
1464         batchSize = numBlocks * blockSize;
1465         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1466         numChunks = numFaces / (numBatches*batchSize);
1467         Ne        = numChunks*numBatches*batchSize;
1468         Nr        = numFaces % (numBatches*batchSize);
1469         offset    = numFaces - Nr;
1470         ierr = PetscFEIntegrateBdResidual(fe, prob, f, Ne, cgeom, u, u_t, NULL, NULL, t, elemVec);CHKERRQ(ierr);
1471         ierr = PetscFEIntegrateBdResidual(fe, prob, f, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, t, &elemVec[offset*totDimBd]);CHKERRQ(ierr);
1472       }
1473       for (p = 0, f = 0; p < numPoints; ++p) {
1474         const PetscInt point = points[p];
1475 
1476         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1477         if (dep != dim-1) continue;
1478         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDimBd, &elemVec[f*totDimBd]);CHKERRQ(ierr);}
1479         ierr = DMPlexVecSetClosure(dm, NULL, locF, point, &elemVec[f*totDimBd], ADD_ALL_VALUES);CHKERRQ(ierr);
1480         ++f;
1481       }
1482       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1483       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1484       ierr = PetscFree3(u,cgeom,elemVec);CHKERRQ(ierr);
1485       if (locX_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
1486     }
1487   }
1488   PetscFunctionReturn(0);
1489 }
1490 
1491 #undef __FUNCT__
1492 #define __FUNCT__ "DMPlexReconstructGradientsFVM"
1493 /*@
1494   DMPlexReconstructGradientsFVM - reconstruct the gradient of a vector using a finite volume method.
1495 
1496   Input Parameters:
1497 + dm - the mesh
1498 - locX - the local representation of the vector
1499 
1500   Output Parameter:
1501 . grad - the global representation of the gradient
1502 
1503   Level: developer
1504 
1505 .seealso: DMPlexSNESGetGradientDM()
1506 @*/
1507 PetscErrorCode DMPlexReconstructGradientsFVM(DM dm, Vec locX, Vec grad)
1508 {
1509   PetscDS          prob;
1510   PetscInt         Nf, f, fStart, fEnd;
1511   PetscBool        useFVM = PETSC_FALSE;
1512   PetscFV          fvm = NULL;
1513   Vec              faceGeometryFVM, cellGeometryFVM;
1514   PetscFVCellGeom  *cgeomFVM   = NULL;
1515   PetscFVFaceGeom  *fgeomFVM   = NULL;
1516   DM               dmGrad = NULL;
1517   PetscErrorCode   ierr;
1518 
1519   PetscFunctionBegin;
1520   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1521   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1522   for (f = 0; f < Nf; ++f) {
1523     PetscObject  obj;
1524     PetscClassId id;
1525 
1526     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1527     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1528     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1529   }
1530   if (!useFVM) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"This dm does not have a finite volume discretization");
1531   ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1532   if (!dmGrad) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"This dm's finite volume discretization does not reconstruct gradients");
1533   ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1534   ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1535   ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1536   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1537   ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1538   PetscFunctionReturn(0);
1539 }
1540 
1541 #undef __FUNCT__
1542 #define __FUNCT__ "DMPlexComputeResidual_Internal"
1543 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal time, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1544 {
1545   DM_Plex          *mesh       = (DM_Plex *) dm->data;
1546   const char       *name       = "Residual";
1547   DM                dmAux      = NULL;
1548   DM                dmGrad     = NULL;
1549   DMLabel           ghostLabel = NULL;
1550   PetscDS           prob       = NULL;
1551   PetscDS           probAux    = NULL;
1552   PetscSection      section    = NULL;
1553   PetscBool         useFEM     = PETSC_FALSE;
1554   PetscBool         useFVM     = PETSC_FALSE;
1555   PetscBool         isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
1556   PetscFV           fvm        = NULL;
1557   PetscFECellGeom  *cgeomFEM   = NULL;
1558   PetscScalar      *cgeomScal;
1559   PetscFVCellGeom  *cgeomFVM   = NULL;
1560   PetscFVFaceGeom  *fgeomFVM   = NULL;
1561   Vec               locA, cellGeometryFEM = NULL, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1562   PetscScalar      *u, *u_t, *a, *uL, *uR;
1563   PetscInt          Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
1564   PetscErrorCode    ierr;
1565 
1566   PetscFunctionBegin;
1567   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1568   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1569   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
1570   /* FEM+FVM */
1571   /* 1: Get sizes from dm and dmAux */
1572   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1573   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1574   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1575   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1576   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1577   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1578   if (locA) {
1579     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1580     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1581     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1582   }
1583   /* 2: Get geometric data */
1584   for (f = 0; f < Nf; ++f) {
1585     PetscObject  obj;
1586     PetscClassId id;
1587     PetscBool    fimp;
1588 
1589     ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1590     if (isImplicit != fimp) continue;
1591     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1592     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1593     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1594     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1595   }
1596   if (useFEM) {
1597     ierr = DMPlexSNESGetGeometryFEM(dm, &cellGeometryFEM);CHKERRQ(ierr);
1598     ierr = VecGetArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);
1599     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1600       DM dmCell;
1601       PetscInt c;
1602 
1603       ierr = VecGetDM(cellGeometryFEM,&dmCell);CHKERRQ(ierr);
1604       ierr = PetscMalloc1(cEnd-cStart,&cgeomFEM);CHKERRQ(ierr);
1605       for (c = 0; c < cEnd - cStart; c++) {
1606         PetscScalar *thisgeom;
1607 
1608         ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1609         cgeomFEM[c] = *((PetscFECellGeom *) thisgeom);
1610       }
1611     }
1612     else {
1613       cgeomFEM = (PetscFECellGeom *) cgeomScal;
1614     }
1615   }
1616   if (useFVM) {
1617     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1618     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1619     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1620     /* Reconstruct and limit cell gradients */
1621     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1622     if (dmGrad) {
1623       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1624       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1625       ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1626       /* Communicate gradient values */
1627       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1628       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1629       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1630       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1631     }
1632     /* Handle non-essential (e.g. outflow) boundary values */
1633     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1634   }
1635   /* Loop over chunks */
1636   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1637   numChunks     = 1;
1638   cellChunkSize = (cEnd - cStart)/numChunks;
1639   faceChunkSize = (fEnd - fStart)/numChunks;
1640   for (chunk = 0; chunk < numChunks; ++chunk) {
1641     PetscScalar     *elemVec, *fluxL, *fluxR;
1642     PetscReal       *vol;
1643     PetscFVFaceGeom *fgeom;
1644     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, cell;
1645     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = fE - fS, face;
1646 
1647     /* Extract field coefficients */
1648     if (useFEM) {
1649       ierr = DMPlexGetCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1650       ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1651       ierr = PetscMemzero(elemVec, numCells*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1652     }
1653     if (useFVM) {
1654       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &uL, &uR);CHKERRQ(ierr);
1655       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &fgeom, &vol);CHKERRQ(ierr);
1656       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1657       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1658       ierr = PetscMemzero(fluxL, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1659       ierr = PetscMemzero(fluxR, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1660     }
1661     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1662     /* Loop over fields */
1663     for (f = 0; f < Nf; ++f) {
1664       PetscObject  obj;
1665       PetscClassId id;
1666       PetscBool    fimp;
1667       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1668 
1669       ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1670       if (isImplicit != fimp) continue;
1671       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1672       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1673       if (id == PETSCFE_CLASSID) {
1674         PetscFE         fe = (PetscFE) obj;
1675         PetscQuadrature q;
1676         PetscInt        Nq, Nb;
1677 
1678         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1679 
1680         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1681         ierr = PetscQuadratureGetData(q, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1682         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1683         blockSize = Nb*Nq;
1684         batchSize = numBlocks * blockSize;
1685         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1686         numChunks = numCells / (numBatches*batchSize);
1687         Ne        = numChunks*numBatches*batchSize;
1688         Nr        = numCells % (numBatches*batchSize);
1689         offset    = numCells - Nr;
1690         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1691         /*   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) */
1692         ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeomFEM, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1693         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);
1694       } else if (id == PETSCFV_CLASSID) {
1695         PetscFV fv = (PetscFV) obj;
1696 
1697         Ne = numFaces;
1698         /* Riemann solve over faces (need fields at face centroids) */
1699         /*   We need to evaluate FE fields at those coordinates */
1700         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1701       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1702     }
1703     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1704       ierr = PetscFree(cgeomFEM);CHKERRQ(ierr);
1705     }
1706     else {
1707       cgeomFEM = NULL;
1708     }
1709     if (cellGeometryFEM) {ierr = VecRestoreArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);}
1710     /* Loop over domain */
1711     if (useFEM) {
1712       /* Add elemVec to locX */
1713       for (cell = cS; cell < cE; ++cell) {
1714         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cell*totDim]);CHKERRQ(ierr);}
1715         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cell*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1716       }
1717     }
1718     if (useFVM) {
1719       PetscScalar *fa;
1720       PetscInt     iface;
1721 
1722       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1723       for (f = 0; f < Nf; ++f) {
1724         PetscFV      fv;
1725         PetscObject  obj;
1726         PetscClassId id;
1727         PetscInt     foff, pdim;
1728 
1729         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1730         ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1731         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1732         if (id != PETSCFV_CLASSID) continue;
1733         fv   = (PetscFV) obj;
1734         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1735         /* Accumulate fluxes to cells */
1736         for (face = fS, iface = 0; face < fE; ++face) {
1737           const PetscInt *cells;
1738           PetscScalar    *fL, *fR;
1739           PetscInt        ghost, d, nsupp;
1740 
1741           ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1742           ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1743           if (ghost >= 0) continue;
1744           if (nsupp > 2) { /* noop */
1745             ++iface;
1746             continue;
1747           }
1748           ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1749           ierr = DMPlexPointGlobalFieldRef(dm, cells[0], f, fa, &fL);CHKERRQ(ierr);
1750           ierr = DMPlexPointGlobalFieldRef(dm, cells[1], f, fa, &fR);CHKERRQ(ierr);
1751           for (d = 0; d < pdim; ++d) {
1752             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
1753             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
1754           }
1755           ++iface;
1756         }
1757       }
1758       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1759     }
1760     /* Handle time derivative */
1761     if (locX_t) {
1762       PetscScalar *x_t, *fa;
1763 
1764       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1765       ierr = VecGetArray(locX_t, &x_t);CHKERRQ(ierr);
1766       for (f = 0; f < Nf; ++f) {
1767         PetscFV      fv;
1768         PetscObject  obj;
1769         PetscClassId id;
1770         PetscInt     pdim, d;
1771 
1772         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1773         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1774         if (id != PETSCFV_CLASSID) continue;
1775         fv   = (PetscFV) obj;
1776         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1777         for (cell = cS; cell < cE; ++cell) {
1778           PetscScalar *u_t, *r;
1779 
1780           ierr = DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);CHKERRQ(ierr);
1781           ierr = DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);CHKERRQ(ierr);
1782           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
1783         }
1784       }
1785       ierr = VecRestoreArray(locX_t, &x_t);CHKERRQ(ierr);
1786       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1787     }
1788     if (useFEM) {
1789       ierr = DMPlexRestoreCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1790       ierr = DMRestoreWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1791     }
1792     if (useFVM) {
1793       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &uL, &uR);CHKERRQ(ierr);
1794       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &fgeom, &vol);CHKERRQ(ierr);
1795       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1796       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1797       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1798     }
1799   }
1800 
1801   if (useFEM) {ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, t, locF, user);CHKERRQ(ierr);}
1802 
1803   /* FEM */
1804   /* 1: Get sizes from dm and dmAux */
1805   /* 2: Get geometric data */
1806   /* 3: Handle boundary values */
1807   /* 4: Loop over domain */
1808   /*   Extract coefficients */
1809   /* Loop over fields */
1810   /*   Set tiling for FE*/
1811   /*   Integrate FE residual to get elemVec */
1812   /*     Loop over subdomain */
1813   /*       Loop over quad points */
1814   /*         Transform coords to real space */
1815   /*         Evaluate field and aux fields at point */
1816   /*         Evaluate residual at point */
1817   /*         Transform residual to real space */
1818   /*       Add residual to elemVec */
1819   /* Loop over domain */
1820   /*   Add elemVec to locX */
1821 
1822   /* FVM */
1823   /* Get geometric data */
1824   /* If using gradients */
1825   /*   Compute gradient data */
1826   /*   Loop over domain faces */
1827   /*     Count computational faces */
1828   /*     Reconstruct cell gradient */
1829   /*   Loop over domain cells */
1830   /*     Limit cell gradients */
1831   /* Handle boundary values */
1832   /* Loop over domain faces */
1833   /*   Read out field, centroid, normal, volume for each side of face */
1834   /* Riemann solve over faces */
1835   /* Loop over domain faces */
1836   /*   Accumulate fluxes to cells */
1837   /* TODO Change printFEM to printDisc here */
1838   if (mesh->printFEM) {
1839     Vec         locFbc;
1840     PetscInt    pStart, pEnd, p, maxDof;
1841     PetscScalar *zeroes;
1842 
1843     ierr = VecDuplicate(locF,&locFbc);CHKERRQ(ierr);
1844     ierr = VecCopy(locF,locFbc);CHKERRQ(ierr);
1845     ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
1846     ierr = PetscSectionGetMaxDof(section,&maxDof);CHKERRQ(ierr);
1847     ierr = PetscCalloc1(maxDof,&zeroes);CHKERRQ(ierr);
1848     for (p = pStart; p < pEnd; p++) {
1849       ierr = VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);CHKERRQ(ierr);
1850     }
1851     ierr = PetscFree(zeroes);CHKERRQ(ierr);
1852     ierr = DMPrintLocalVec(dm, name, mesh->printTol, locFbc);CHKERRQ(ierr);
1853     ierr = VecDestroy(&locFbc);CHKERRQ(ierr);
1854   }
1855   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1856   PetscFunctionReturn(0);
1857 }
1858 
1859 #undef __FUNCT__
1860 #define __FUNCT__ "DMPlexComputeResidualFEM_Check_Internal"
1861 static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, PetscReal t, Vec F, void *user)
1862 {
1863   DM                dmCh, dmAux;
1864   Vec               A, cellgeom;
1865   PetscDS           prob, probCh, probAux = NULL;
1866   PetscQuadrature   q;
1867   PetscSection      section, sectionAux;
1868   PetscFECellGeom  *cgeom = NULL;
1869   PetscScalar      *cgeomScal;
1870   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
1871   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
1872   PetscInt          totDim, totDimAux, diffCell = 0;
1873   PetscErrorCode    ierr;
1874 
1875   PetscFunctionBegin;
1876   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1877   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1878   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1879   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1880   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1881   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1882   numCells = cEnd - cStart;
1883   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
1884   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
1885   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1886   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1887   if (dmAux) {
1888     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1889     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1890     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1891   }
1892   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1893   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);CHKERRQ(ierr);
1894   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
1895   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1896   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
1897   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1898   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1899     DM dmCell;
1900 
1901     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
1902     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
1903     for (c = 0; c < cEnd - cStart; c++) {
1904       PetscScalar *thisgeom;
1905 
1906       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1907       cgeom[c] = *((PetscFECellGeom *) thisgeom);
1908     }
1909   }
1910   else {
1911     cgeom = (PetscFECellGeom *) cgeomScal;
1912   }
1913   for (c = cStart; c < cEnd; ++c) {
1914     PetscScalar *x = NULL, *x_t = NULL;
1915     PetscInt     i;
1916 
1917     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1918     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1919     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1920     if (X_t) {
1921       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1922       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1923       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1924     }
1925     if (dmAux) {
1926       DM dmAuxPlex;
1927 
1928       ierr = DMSNESConvertPlex(dmAux,&dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1929       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1930       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1931       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1932       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1933     }
1934   }
1935   for (f = 0; f < Nf; ++f) {
1936     PetscFE  fe, feCh;
1937     PetscInt numQuadPoints, Nb;
1938     /* Conforming batches */
1939     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1940     /* Remainder */
1941     PetscInt Nr, offset;
1942 
1943     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1944     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
1945     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1946     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1947     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1948     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1949     blockSize = Nb*numQuadPoints;
1950     batchSize = numBlocks * blockSize;
1951     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1952     numChunks = numCells / (numBatches*batchSize);
1953     Ne        = numChunks*numBatches*batchSize;
1954     Nr        = numCells % (numBatches*batchSize);
1955     offset    = numCells - Nr;
1956     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1957     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVecCh);CHKERRQ(ierr);
1958     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);
1959     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);
1960   }
1961   for (c = cStart; c < cEnd; ++c) {
1962     PetscBool diff = PETSC_FALSE;
1963     PetscInt  d;
1964 
1965     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
1966     if (diff) {
1967       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
1968       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
1969       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
1970       ++diffCell;
1971     }
1972     if (diffCell > 9) break;
1973     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1974   }
1975   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1976     ierr = PetscFree(cgeom);CHKERRQ(ierr);
1977   }
1978   else {
1979     cgeom = NULL;
1980   }
1981   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1982   ierr = PetscFree3(u,u_t,elemVec);CHKERRQ(ierr);
1983   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
1984   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1985   PetscFunctionReturn(0);
1986 }
1987 
1988 #undef __FUNCT__
1989 #define __FUNCT__ "DMPlexSNESComputeResidualFEM"
1990 /*@
1991   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1992 
1993   Input Parameters:
1994 + dm - The mesh
1995 . X  - Local solution
1996 - user - The user context
1997 
1998   Output Parameter:
1999 . F  - Local output vector
2000 
2001   Level: developer
2002 
2003 .seealso: DMPlexComputeJacobianActionFEM()
2004 @*/
2005 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
2006 {
2007   PetscObject    check;
2008   PetscInt       cStart, cEnd, cEndInterior;
2009   DM             plex;
2010   PetscErrorCode ierr;
2011 
2012   PetscFunctionBegin;
2013   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2014   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2015   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2016   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2017   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
2018   ierr = PetscObjectQuery((PetscObject) plex, "dmCh", &check);CHKERRQ(ierr);
2019   if (check) {ierr = DMPlexComputeResidualFEM_Check_Internal(plex, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2020   else       {ierr = DMPlexComputeResidual_Internal(plex, cStart, cEnd, PETSC_MIN_REAL, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2021   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2022   PetscFunctionReturn(0);
2023 }
2024 
2025 #undef __FUNCT__
2026 #define __FUNCT__ "DMPlexSNESComputeBoundaryFEM"
2027 /*@
2028   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X
2029 
2030   Input Parameters:
2031 + dm - The mesh
2032 - user - The user context
2033 
2034   Output Parameter:
2035 . X  - Local solution
2036 
2037   Level: developer
2038 
2039 .seealso: DMPlexComputeJacobianActionFEM()
2040 @*/
2041 PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
2042 {
2043   DM             plex;
2044   PetscErrorCode ierr;
2045 
2046   PetscFunctionBegin;
2047   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2048   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);CHKERRQ(ierr);
2049   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2050   PetscFunctionReturn(0);
2051 }
2052 
2053 #undef __FUNCT__
2054 #define __FUNCT__ "DMPlexComputeJacobian_Internal"
2055 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)
2056 {
2057   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2058   const char       *name  = "Jacobian";
2059   DM                dmAux, plex;
2060   DMLabel           depth;
2061   Vec               A, cellgeom;
2062   PetscDS           prob, probAux = NULL;
2063   PetscQuadrature   quad;
2064   PetscSection      section, globalSection, sectionAux;
2065   PetscFECellGeom  *cgeom = NULL;
2066   PetscScalar      *cgeomScal;
2067   PetscScalar      *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
2068   PetscInt          dim, Nf, f, fieldI, fieldJ, numCells, c;
2069   PetscInt          totDim, totDimBd, totDimAux, numBd, bd;
2070   PetscBool         isShell, hasJac, hasPrec, hasDyn, hasFV = PETSC_FALSE;
2071   PetscErrorCode    ierr;
2072 
2073   PetscFunctionBegin;
2074   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2075   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2076   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2077   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2078   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2079   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2080   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
2081   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2082   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2083   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2084   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2085   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2086   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2087   numCells = cEnd - cStart;
2088   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2089   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2090   if (dmAux) {
2091     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2092     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2093     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2094     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2095   }
2096   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
2097   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);
2098   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2099   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2100   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2101   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2102     DM dmCell;
2103 
2104     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2105     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2106     for (c = 0; c < cEnd - cStart; c++) {
2107       PetscScalar *thisgeom;
2108 
2109       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2110       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2111     }
2112   } else {
2113     cgeom = (PetscFECellGeom *) cgeomScal;
2114   }
2115   for (c = cStart; c < cEnd; ++c) {
2116     PetscScalar *x = NULL,  *x_t = NULL;
2117     PetscInt     i;
2118 
2119     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2120     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2121     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2122     if (X_t) {
2123       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2124       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2125       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2126     }
2127     if (dmAux) {
2128       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2129       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2130       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2131     }
2132   }
2133   if (hasJac)  {ierr = PetscMemzero(elemMat,  numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2134   if (hasPrec) {ierr = PetscMemzero(elemMatP, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2135   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2136   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2137     PetscClassId id;
2138     PetscFE  fe;
2139     PetscInt numQuadPoints, Nb;
2140     /* Conforming batches */
2141     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2142     /* Remainder */
2143     PetscInt Nr, offset;
2144 
2145     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2146     ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
2147     if (id == PETSCFV_CLASSID) {hasFV = PETSC_TRUE; continue;}
2148     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2149     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2150     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2151     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2152     blockSize = Nb*numQuadPoints;
2153     batchSize = numBlocks * blockSize;
2154     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2155     numChunks = numCells / (numBatches*batchSize);
2156     Ne        = numChunks*numBatches*batchSize;
2157     Nr        = numCells % (numBatches*batchSize);
2158     offset    = numCells - Nr;
2159     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2160       if (hasJac) {
2161         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2162         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);
2163       }
2164       if (hasPrec) {
2165         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatP);CHKERRQ(ierr);
2166         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);
2167       }
2168       if (hasDyn) {
2169         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2170         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);
2171       }
2172     }
2173   }
2174   if (hasDyn) {
2175     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2176   }
2177   if (hasFV) {
2178     PetscClassId id;
2179     PetscFV      fv;
2180     PetscInt     offsetI, NcI, NbI = 1, fc, f;
2181 
2182     for (fieldI = 0; fieldI < Nf; ++fieldI) {
2183       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fv);CHKERRQ(ierr);
2184       ierr = PetscDSGetFieldOffset(prob, fieldI, &offsetI);CHKERRQ(ierr);
2185       ierr = PetscObjectGetClassId((PetscObject) fv, &id);CHKERRQ(ierr);
2186       if (id != PETSCFV_CLASSID) continue;
2187       /* Put in the identity */
2188       ierr = PetscFVGetNumComponents(fv, &NcI);CHKERRQ(ierr);
2189       for (c = cStart; c < cEnd; ++c) {
2190         const PetscInt eOffset = (c-cStart)*totDim*totDim;
2191         for (fc = 0; fc < NcI; ++fc) {
2192           for (f = 0; f < NbI; ++f) {
2193             const PetscInt i = offsetI + f*NcI+fc;
2194             if (hasPrec) {
2195               if (hasJac) {elemMat[eOffset+i*totDim+i] = 1.0;}
2196               elemMatP[eOffset+i*totDim+i] = 1.0;
2197             } else {elemMat[eOffset+i*totDim+i] = 1.0;}
2198           }
2199         }
2200       }
2201     }
2202     /* No allocated space for FV stuff, so ignore the zero entries */
2203     ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2204   }
2205   for (c = cStart; c < cEnd; ++c) {
2206     if (hasPrec) {
2207       if (hasJac) {
2208         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2209         ierr = DMPlexMatSetClosure(dm, section, globalSection, Jac, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2210       }
2211       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMatP[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2212       ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2213     } else {
2214       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2215       ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2216     }
2217   }
2218   if (hasFV) {ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);CHKERRQ(ierr);}
2219   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2220     ierr = PetscFree(cgeom);CHKERRQ(ierr);
2221   } else {
2222     cgeom = NULL;
2223   }
2224   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2225   ierr = PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);CHKERRQ(ierr);
2226   if (dmAux) {
2227     ierr = PetscFree(a);CHKERRQ(ierr);
2228     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2229   }
2230   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2231   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
2232   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2233   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
2234   for (bd = 0; bd < numBd; ++bd) {
2235     const char     *bdLabel;
2236     DMLabel         label;
2237     IS              pointIS;
2238     const PetscInt *points;
2239     const PetscInt *values;
2240     PetscInt        field, numValues, v, numPoints, p, dep, numFaces;
2241     PetscBool       isEssential;
2242     PetscObject     obj;
2243     PetscClassId    id;
2244 
2245     ierr = DMGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
2246     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
2247     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2248     if ((id != PETSCFE_CLASSID) || isEssential) continue;
2249     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
2250     for (v = 0; v < numValues; ++v) {
2251       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
2252       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
2253       if (!pointIS) continue; /* No points with that id on this process */
2254       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2255       for (p = 0, numFaces = 0; p < numPoints; ++p) {
2256         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2257         if (dep == dim-1) ++numFaces;
2258       }
2259       ierr = PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd*totDimBd,&elemMat);CHKERRQ(ierr);
2260       if (X_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
2261       for (p = 0, f = 0; p < numPoints; ++p) {
2262         const PetscInt point = points[p];
2263         PetscScalar   *x     = NULL;
2264         PetscInt       i;
2265 
2266         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2267         if (dep != dim-1) continue;
2268         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
2269         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);CHKERRQ(ierr);
2270         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
2271         ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
2272         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
2273         ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
2274         if (X_t) {
2275           ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
2276           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
2277           ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
2278         }
2279         ++f;
2280       }
2281       ierr = PetscMemzero(elemMat, numFaces*totDimBd*totDimBd * sizeof(PetscScalar));CHKERRQ(ierr);
2282       for (fieldI = 0; fieldI < Nf; ++fieldI) {
2283         PetscFE  fe;
2284         PetscInt numQuadPoints, Nb;
2285         /* Conforming batches */
2286         PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2287         /* Remainder */
2288         PetscInt Nr, offset;
2289 
2290         ierr = PetscDSGetBdDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2291         ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2292         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2293         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2294         ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2295         blockSize = Nb*numQuadPoints;
2296         batchSize = numBlocks * blockSize;
2297         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2298         numChunks = numFaces / (numBatches*batchSize);
2299         Ne        = numChunks*numBatches*batchSize;
2300         Nr        = numFaces % (numBatches*batchSize);
2301         offset    = numFaces - Nr;
2302         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2303           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, cgeom, u, u_t, NULL, NULL, t, X_tShift, elemMat);CHKERRQ(ierr);
2304           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, t, X_tShift, &elemMat[offset*totDimBd*totDimBd]);CHKERRQ(ierr);
2305         }
2306       }
2307       for (p = 0, f = 0; p < numPoints; ++p) {
2308         const PetscInt point = points[p];
2309 
2310         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
2311         if (dep != dim-1) continue;
2312         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDimBd, totDimBd, &elemMat[f*totDimBd*totDimBd]);CHKERRQ(ierr);}
2313         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*totDimBd*totDimBd], ADD_VALUES);CHKERRQ(ierr);
2314         ++f;
2315       }
2316       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2317       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2318       ierr = PetscFree3(u,cgeom,elemMat);CHKERRQ(ierr);
2319       if (X_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
2320     }
2321   }
2322   if (hasJac && hasPrec) {
2323     ierr = MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2324     ierr = MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2325   }
2326   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2327   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2328   if (mesh->printFEM) {
2329     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
2330     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
2331     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2332   }
2333   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2334   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
2335   if (isShell) {
2336     JacActionCtx *jctx;
2337 
2338     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
2339     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
2340   }
2341   PetscFunctionReturn(0);
2342 }
2343 
2344 
2345 #undef __FUNCT__
2346 #define __FUNCT__ "DMPlexComputeJacobianAction_Internal"
2347 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)
2348 {
2349   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2350   const char       *name  = "Jacobian";
2351   DM                dmAux, plex;
2352   Vec               A, cellgeom;
2353   PetscDS           prob, probAux = NULL;
2354   PetscQuadrature   quad;
2355   PetscSection      section, globalSection, sectionAux;
2356   PetscFECellGeom  *cgeom = NULL;
2357   PetscScalar      *cgeomScal;
2358   PetscScalar      *elemMat, *elemMatD, *u, *u_t, *a = NULL, *y, *z;
2359   PetscInt          dim, Nf, fieldI, fieldJ, numCells, c;
2360   PetscInt          totDim, totDimBd, totDimAux;
2361   PetscBool         hasDyn;
2362   PetscErrorCode    ierr;
2363 
2364   PetscFunctionBegin;
2365   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2366   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2367   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2368   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2369   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2370   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2371   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
2372   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2373   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2374   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2375   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2376   numCells = cEnd - cStart;
2377   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2378   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2379   if (dmAux) {
2380     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2381     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2382     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2383     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2384   }
2385   ierr = VecSet(Z, 0.0);CHKERRQ(ierr);
2386   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);
2387   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2388   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2389   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2390   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2391     DM dmCell;
2392 
2393     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2394     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2395     for (c = 0; c < cEnd - cStart; c++) {
2396       PetscScalar *thisgeom;
2397 
2398       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2399       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2400     }
2401   } else {
2402     cgeom = (PetscFECellGeom *) cgeomScal;
2403   }
2404   for (c = cStart; c < cEnd; ++c) {
2405     PetscScalar *x = NULL,  *x_t = NULL;
2406     PetscInt     i;
2407 
2408     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2409     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2410     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2411     if (X_t) {
2412       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2413       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2414       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2415     }
2416     if (dmAux) {
2417       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2418       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2419       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2420     }
2421     ierr = DMPlexVecGetClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2422     for (i = 0; i < totDim; ++i) y[(c-cStart)*totDim+i] = x[i];
2423     ierr = DMPlexVecRestoreClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2424   }
2425   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2426   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2427   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2428     PetscFE  fe;
2429     PetscInt numQuadPoints, Nb;
2430     /* Conforming batches */
2431     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2432     /* Remainder */
2433     PetscInt Nr, offset;
2434 
2435     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2436     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2437     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2438     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2439     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2440     blockSize = Nb*numQuadPoints;
2441     batchSize = numBlocks * blockSize;
2442     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2443     numChunks = numCells / (numBatches*batchSize);
2444     Ne        = numChunks*numBatches*batchSize;
2445     Nr        = numCells % (numBatches*batchSize);
2446     offset    = numCells - Nr;
2447     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2448       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2449       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);
2450       if (hasDyn) {
2451         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2452         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);
2453       }
2454     }
2455   }
2456   if (hasDyn) {
2457     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2458   }
2459   for (c = cStart; c < cEnd; ++c) {
2460     const PetscBLASInt M = totDim, one = 1;
2461     const PetscScalar  a = 1.0, b = 0.0;
2462 
2463     PetscStackCallBLAS("BLASgemv", BLASgemv_("N", &M, &M, &a, &elemMat[(c-cStart)*totDim*totDim], &M, &y[(c-cStart)*totDim], &one, &b, z, &one));
2464     if (mesh->printFEM > 1) {
2465       ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);
2466       ierr = DMPrintCellVector(c, "Y",  totDim, &y[(c-cStart)*totDim]);CHKERRQ(ierr);
2467       ierr = DMPrintCellVector(c, "Z",  totDim, z);CHKERRQ(ierr);
2468     }
2469     ierr = DMPlexVecSetClosure(dm, section, Z, c, z, ADD_VALUES);CHKERRQ(ierr);
2470   }
2471   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {ierr = PetscFree(cgeom);CHKERRQ(ierr);}
2472   else                                               {cgeom = NULL;}
2473   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2474   ierr = PetscFree6(u,u_t,elemMat,elemMatD,y,z);CHKERRQ(ierr);
2475   if (dmAux) {
2476     ierr = PetscFree(a);CHKERRQ(ierr);
2477     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2478   }
2479   if (mesh->printFEM) {
2480     ierr = PetscPrintf(PETSC_COMM_WORLD, "Z:\n");CHKERRQ(ierr);
2481     ierr = VecView(Z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2482   }
2483   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2484   PetscFunctionReturn(0);
2485 }
2486 
2487 #undef __FUNCT__
2488 #define __FUNCT__ "DMPlexSNESComputeJacobianFEM"
2489 /*@
2490   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2491 
2492   Input Parameters:
2493 + dm - The mesh
2494 . X  - Local input vector
2495 - user - The user context
2496 
2497   Output Parameter:
2498 . Jac  - Jacobian matrix
2499 
2500   Note:
2501   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2502   like a GPU, or vectorize on a multicore machine.
2503 
2504   Level: developer
2505 
2506 .seealso: FormFunctionLocal()
2507 @*/
2508 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2509 {
2510   PetscInt       cStart, cEnd, cEndInterior;
2511   DM             plex;
2512   PetscErrorCode ierr;
2513 
2514   PetscFunctionBegin;
2515   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2516   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2517   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2518   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2519   ierr = DMPlexComputeJacobian_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2520   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2521   PetscFunctionReturn(0);
2522 }
2523 
2524 #undef __FUNCT__
2525 #define __FUNCT__ "DMPlexSNESComputeJacobianActionFEM"
2526 /*@
2527   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.
2528 
2529   Input Parameters:
2530 + dm - The mesh
2531 . X  - Local solution vector
2532 . Y  - Local input vector
2533 - user - The user context
2534 
2535   Output Parameter:
2536 . Z - Local output vector
2537 
2538   Note:
2539   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2540   like a GPU, or vectorize on a multicore machine.
2541 
2542   Level: developer
2543 
2544 .seealso: FormFunctionLocal()
2545 @*/
2546 PetscErrorCode DMPlexSNESComputeJacobianActionFEM(DM dm, Vec X, Vec Y, Vec Z, void *user)
2547 {
2548   PetscInt       cStart, cEnd, cEndInterior;
2549   DM             plex;
2550   PetscErrorCode ierr;
2551 
2552   PetscFunctionBegin;
2553   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2554   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2555   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2556   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2557   ierr = DMPlexComputeJacobianAction_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Y, Z, user);CHKERRQ(ierr);
2558   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2559   PetscFunctionReturn(0);
2560 }
2561 
2562 #undef __FUNCT__
2563 #define __FUNCT__ "DMPlexSetSNESLocalFEM"
2564 /*@
2565   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.
2566 
2567   Input Parameters:
2568 + dm - The DM object
2569 . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see DMAddBoundary())
2570 . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
2571 - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())
2572 
2573   Level: developer
2574 @*/
2575 PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
2576 {
2577   PetscErrorCode ierr;
2578 
2579   PetscFunctionBegin;
2580   ierr = DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);CHKERRQ(ierr);
2581   ierr = DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);CHKERRQ(ierr);
2582   ierr = DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);CHKERRQ(ierr);
2583   PetscFunctionReturn(0);
2584 }
2585 
2586 #undef __FUNCT__
2587 #define __FUNCT__ "DMSNESCheckFromOptions_Internal"
2588 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)
2589 {
2590   Mat            J, M;
2591   Vec            r, b;
2592   MatNullSpace   nullSpace;
2593   PetscReal     *error, res = 0.0;
2594   PetscInt       numFields;
2595   PetscErrorCode ierr;
2596 
2597   PetscFunctionBegin;
2598   ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2599   ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
2600   M    = J;
2601   /* TODO Null space for J */
2602   /* Check discretization error */
2603   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
2604   ierr = PetscMalloc1(PetscMax(1, numFields), &error);CHKERRQ(ierr);
2605   if (numFields > 1) {
2606     PetscInt f;
2607 
2608     ierr = DMComputeL2FieldDiff(dm, 0.0, exactFuncs, ctxs, u, error);CHKERRQ(ierr);
2609     ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: [");CHKERRQ(ierr);
2610     for (f = 0; f < numFields; ++f) {
2611       if (f) {ierr = PetscPrintf(PETSC_COMM_WORLD, ", ");CHKERRQ(ierr);}
2612       if (error[f] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "%g", error[f]);CHKERRQ(ierr);}
2613       else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "< 1.0e-11");CHKERRQ(ierr);}
2614     }
2615     ierr = PetscPrintf(PETSC_COMM_WORLD, "]\n");CHKERRQ(ierr);
2616   } else {
2617     ierr = DMComputeL2Diff(dm, 0.0, exactFuncs, ctxs, u, &error[0]);CHKERRQ(ierr);
2618     if (error[0] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error[0]);CHKERRQ(ierr);}
2619     else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
2620   }
2621   ierr = PetscFree(error);CHKERRQ(ierr);
2622   /* Check residual */
2623   ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2624   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2625   ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", res);CHKERRQ(ierr);
2626   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2627   ierr = PetscObjectSetName((PetscObject) r, "Initial Residual");CHKERRQ(ierr);
2628   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"res_");CHKERRQ(ierr);
2629   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2630   /* Check Jacobian */
2631   ierr = SNESComputeJacobian(snes, u, M, M);CHKERRQ(ierr);
2632   ierr = MatGetNullSpace(J, &nullSpace);CHKERRQ(ierr);
2633   if (nullSpace) {
2634     PetscBool isNull;
2635     ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
2636     if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
2637   }
2638   ierr = VecDuplicate(u, &b);CHKERRQ(ierr);
2639   ierr = VecSet(r, 0.0);CHKERRQ(ierr);
2640   ierr = SNESComputeFunction(snes, r, b);CHKERRQ(ierr);
2641   ierr = MatMult(M, u, r);CHKERRQ(ierr);
2642   ierr = VecAXPY(r, 1.0, b);CHKERRQ(ierr);
2643   ierr = VecDestroy(&b);CHKERRQ(ierr);
2644   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2645   ierr = PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", res);CHKERRQ(ierr);
2646   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2647   ierr = PetscObjectSetName((PetscObject) r, "Au - b = Au + F(0)");CHKERRQ(ierr);
2648   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"linear_res_");CHKERRQ(ierr);
2649   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2650   ierr = VecDestroy(&r);CHKERRQ(ierr);
2651   ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
2652   ierr = MatDestroy(&J);CHKERRQ(ierr);
2653   PetscFunctionReturn(0);
2654 }
2655 
2656 #undef __FUNCT__
2657 #define __FUNCT__ "DMSNESCheckFromOptions"
2658 PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
2659 {
2660   DM             dm;
2661   Vec            sol;
2662   PetscBool      check;
2663   PetscErrorCode ierr;
2664 
2665   PetscFunctionBegin;
2666   ierr = PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);CHKERRQ(ierr);
2667   if (!check) PetscFunctionReturn(0);
2668   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
2669   ierr = VecDuplicate(u, &sol);CHKERRQ(ierr);
2670   ierr = SNESSetSolution(snes, sol);CHKERRQ(ierr);
2671   ierr = DMSNESCheckFromOptions_Internal(snes, dm, u, sol, exactFuncs, ctxs);CHKERRQ(ierr);
2672   ierr = VecDestroy(&sol);CHKERRQ(ierr);
2673   PetscFunctionReturn(0);
2674 }
2675