xref: /petsc/src/snes/utils/dmplexsnes.c (revision e0fc9d1bab9b7ad694b9fca9aec3126ff1e1f117)
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   PetscFE        fem;
425   SNES           snes;
426   KSP            ksp;
427   PC             pc;
428   Vec            coordsLocal, r, ref, real;
429   Mat            J;
430   const PetscScalar *coords;
431   PetscScalar    *a;
432   PetscInt       p;
433   const PetscInt dof = ctx->dof;
434   PetscErrorCode ierr;
435 
436   PetscFunctionBegin;
437   ierr = DMGetField(dm, 0, (PetscObject *) &fem);CHKERRQ(ierr);
438   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
439   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
440   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
441   ierr = SNESSetOptionsPrefix(snes, "quad_interp_");CHKERRQ(ierr);
442   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
443   ierr = VecSetSizes(r, 2, 2);CHKERRQ(ierr);
444   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
445   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
446   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
447   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
448   ierr = MatSetSizes(J, 2, 2, 2, 2);CHKERRQ(ierr);
449   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
450   ierr = MatSetUp(J);CHKERRQ(ierr);
451   ierr = SNESSetFunction(snes, r, QuadMap_Private, NULL);CHKERRQ(ierr);
452   ierr = SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);CHKERRQ(ierr);
453   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
454   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
455   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
456   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
457 
458   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
459   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
460   for (p = 0; p < ctx->n; ++p) {
461     PetscScalar *x = NULL, *vertices = NULL;
462     PetscScalar *xi;
463     PetscReal    xir[2];
464     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
465 
466     /* Can make this do all points at once */
467     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
468     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 4*2);
469     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
470     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
471     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
472     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
473     xi[0]  = coords[p*ctx->dim+0];
474     xi[1]  = coords[p*ctx->dim+1];
475     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
476     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
477     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
478     xir[0] = PetscRealPart(xi[0]);
479     xir[1] = PetscRealPart(xi[1]);
480     if (4*dof != xSize) {
481       PetscReal *B;
482       PetscInt   d;
483 
484       xir[0] = 2.0*xir[0] - 1.0; xir[1] = 2.0*xir[1] - 1.0;
485       ierr = PetscFEGetTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
486       for (comp = 0; comp < dof; ++comp) {
487         a[p*dof+comp] = 0.0;
488         for (d = 0; d < xSize/dof; ++d) {
489           a[p*dof+comp] += x[d*dof+comp]*B[d*dof+comp];
490         }
491       }
492       ierr = PetscFERestoreTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
493     } else {
494       for (comp = 0; comp < dof; ++comp)
495         a[p*dof+comp] = x[0*dof+comp]*(1 - xir[0])*(1 - xir[1]) + x[1*dof+comp]*xir[0]*(1 - xir[1]) + x[2*dof+comp]*xir[0]*xir[1] + x[3*dof+comp]*(1 - xir[0])*xir[1];
496     }
497     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
498     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
499     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
500   }
501   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
502   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
503 
504   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
505   ierr = VecDestroy(&r);CHKERRQ(ierr);
506   ierr = VecDestroy(&ref);CHKERRQ(ierr);
507   ierr = VecDestroy(&real);CHKERRQ(ierr);
508   ierr = MatDestroy(&J);CHKERRQ(ierr);
509   PetscFunctionReturn(0);
510 }
511 
512 #undef __FUNCT__
513 #define __FUNCT__ "HexMap_Private"
514 PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
515 {
516   const PetscScalar *vertices = (const PetscScalar*) ctx;
517   const PetscScalar x0        = vertices[0];
518   const PetscScalar y0        = vertices[1];
519   const PetscScalar z0        = vertices[2];
520   const PetscScalar x1        = vertices[9];
521   const PetscScalar y1        = vertices[10];
522   const PetscScalar z1        = vertices[11];
523   const PetscScalar x2        = vertices[6];
524   const PetscScalar y2        = vertices[7];
525   const PetscScalar z2        = vertices[8];
526   const PetscScalar x3        = vertices[3];
527   const PetscScalar y3        = vertices[4];
528   const PetscScalar z3        = vertices[5];
529   const PetscScalar x4        = vertices[12];
530   const PetscScalar y4        = vertices[13];
531   const PetscScalar z4        = vertices[14];
532   const PetscScalar x5        = vertices[15];
533   const PetscScalar y5        = vertices[16];
534   const PetscScalar z5        = vertices[17];
535   const PetscScalar x6        = vertices[18];
536   const PetscScalar y6        = vertices[19];
537   const PetscScalar z6        = vertices[20];
538   const PetscScalar x7        = vertices[21];
539   const PetscScalar y7        = vertices[22];
540   const PetscScalar z7        = vertices[23];
541   const PetscScalar f_1       = x1 - x0;
542   const PetscScalar g_1       = y1 - y0;
543   const PetscScalar h_1       = z1 - z0;
544   const PetscScalar f_3       = x3 - x0;
545   const PetscScalar g_3       = y3 - y0;
546   const PetscScalar h_3       = z3 - z0;
547   const PetscScalar f_4       = x4 - x0;
548   const PetscScalar g_4       = y4 - y0;
549   const PetscScalar h_4       = z4 - z0;
550   const PetscScalar f_01      = x2 - x1 - x3 + x0;
551   const PetscScalar g_01      = y2 - y1 - y3 + y0;
552   const PetscScalar h_01      = z2 - z1 - z3 + z0;
553   const PetscScalar f_12      = x7 - x3 - x4 + x0;
554   const PetscScalar g_12      = y7 - y3 - y4 + y0;
555   const PetscScalar h_12      = z7 - z3 - z4 + z0;
556   const PetscScalar f_02      = x5 - x1 - x4 + x0;
557   const PetscScalar g_02      = y5 - y1 - y4 + y0;
558   const PetscScalar h_02      = z5 - z1 - z4 + z0;
559   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
560   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
561   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
562   const PetscScalar *ref;
563   PetscScalar       *real;
564   PetscErrorCode    ierr;
565 
566   PetscFunctionBegin;
567   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
568   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
569   {
570     const PetscScalar p0 = ref[0];
571     const PetscScalar p1 = ref[1];
572     const PetscScalar p2 = ref[2];
573 
574     real[0] = x0 + f_1*p0 + f_3*p1 + f_4*p2 + f_01*p0*p1 + f_12*p1*p2 + f_02*p0*p2 + f_012*p0*p1*p2;
575     real[1] = y0 + g_1*p0 + g_3*p1 + g_4*p2 + g_01*p0*p1 + g_01*p0*p1 + g_12*p1*p2 + g_02*p0*p2 + g_012*p0*p1*p2;
576     real[2] = z0 + h_1*p0 + h_3*p1 + h_4*p2 + h_01*p0*p1 + h_01*p0*p1 + h_12*p1*p2 + h_02*p0*p2 + h_012*p0*p1*p2;
577   }
578   ierr = PetscLogFlops(114);CHKERRQ(ierr);
579   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
580   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
581   PetscFunctionReturn(0);
582 }
583 
584 #undef __FUNCT__
585 #define __FUNCT__ "HexJacobian_Private"
586 PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
587 {
588   const PetscScalar *vertices = (const PetscScalar*) ctx;
589   const PetscScalar x0        = vertices[0];
590   const PetscScalar y0        = vertices[1];
591   const PetscScalar z0        = vertices[2];
592   const PetscScalar x1        = vertices[9];
593   const PetscScalar y1        = vertices[10];
594   const PetscScalar z1        = vertices[11];
595   const PetscScalar x2        = vertices[6];
596   const PetscScalar y2        = vertices[7];
597   const PetscScalar z2        = vertices[8];
598   const PetscScalar x3        = vertices[3];
599   const PetscScalar y3        = vertices[4];
600   const PetscScalar z3        = vertices[5];
601   const PetscScalar x4        = vertices[12];
602   const PetscScalar y4        = vertices[13];
603   const PetscScalar z4        = vertices[14];
604   const PetscScalar x5        = vertices[15];
605   const PetscScalar y5        = vertices[16];
606   const PetscScalar z5        = vertices[17];
607   const PetscScalar x6        = vertices[18];
608   const PetscScalar y6        = vertices[19];
609   const PetscScalar z6        = vertices[20];
610   const PetscScalar x7        = vertices[21];
611   const PetscScalar y7        = vertices[22];
612   const PetscScalar z7        = vertices[23];
613   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
614   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
615   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
616   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
617   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
618   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
619   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
620   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
621   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
622   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
623   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
624   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
625   const PetscScalar *ref;
626   PetscErrorCode    ierr;
627 
628   PetscFunctionBegin;
629   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
630   {
631     const PetscScalar x       = ref[0];
632     const PetscScalar y       = ref[1];
633     const PetscScalar z       = ref[2];
634     const PetscInt    rows[3] = {0, 1, 2};
635     PetscScalar       values[9];
636 
637     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
638     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
639     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
640     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
641     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
642     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
643     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
644     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
645     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;
646 
647     ierr = MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);CHKERRQ(ierr);
648   }
649   ierr = PetscLogFlops(152);CHKERRQ(ierr);
650   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
651   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
652   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
653   PetscFunctionReturn(0);
654 }
655 
656 #undef __FUNCT__
657 #define __FUNCT__ "DMInterpolate_Hex_Private"
658 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
659 {
660   DM             dmCoord;
661   SNES           snes;
662   KSP            ksp;
663   PC             pc;
664   Vec            coordsLocal, r, ref, real;
665   Mat            J;
666   const PetscScalar *coords;
667   PetscScalar    *a;
668   PetscInt       p;
669   PetscErrorCode ierr;
670 
671   PetscFunctionBegin;
672   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
673   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
674   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
675   ierr = SNESSetOptionsPrefix(snes, "hex_interp_");CHKERRQ(ierr);
676   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
677   ierr = VecSetSizes(r, 3, 3);CHKERRQ(ierr);
678   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
679   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
680   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
681   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
682   ierr = MatSetSizes(J, 3, 3, 3, 3);CHKERRQ(ierr);
683   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
684   ierr = MatSetUp(J);CHKERRQ(ierr);
685   ierr = SNESSetFunction(snes, r, HexMap_Private, NULL);CHKERRQ(ierr);
686   ierr = SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);CHKERRQ(ierr);
687   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
688   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
689   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
690   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
691 
692   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
693   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
694   for (p = 0; p < ctx->n; ++p) {
695     PetscScalar *x = NULL, *vertices = NULL;
696     PetscScalar *xi;
697     PetscReal    xir[3];
698     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
699 
700     /* Can make this do all points at once */
701     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
702     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 8*3);
703     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
704     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 8*ctx->dof);
705     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
706     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
707     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
708     xi[0]  = coords[p*ctx->dim+0];
709     xi[1]  = coords[p*ctx->dim+1];
710     xi[2]  = coords[p*ctx->dim+2];
711     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
712     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
713     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
714     xir[0] = PetscRealPart(xi[0]);
715     xir[1] = PetscRealPart(xi[1]);
716     xir[2] = PetscRealPart(xi[2]);
717     for (comp = 0; comp < ctx->dof; ++comp) {
718       a[p*ctx->dof+comp] =
719         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
720         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
721         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
722         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
723         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
724         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
725         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
726         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
727     }
728     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
729     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
730     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
731   }
732   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
733   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
734 
735   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
736   ierr = VecDestroy(&r);CHKERRQ(ierr);
737   ierr = VecDestroy(&ref);CHKERRQ(ierr);
738   ierr = VecDestroy(&real);CHKERRQ(ierr);
739   ierr = MatDestroy(&J);CHKERRQ(ierr);
740   PetscFunctionReturn(0);
741 }
742 
743 #undef __FUNCT__
744 #define __FUNCT__ "DMInterpolationEvaluate"
745 /*
746   Input Parameters:
747 + ctx - The DMInterpolationInfo context
748 . dm  - The DM
749 - x   - The local vector containing the field to be interpolated
750 
751   Output Parameters:
752 . v   - The vector containing the interpolated values
753 */
754 PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
755 {
756   PetscInt       dim, coneSize, n;
757   PetscErrorCode ierr;
758 
759   PetscFunctionBegin;
760   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
761   PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
762   PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
763   ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
764   if (n != ctx->n*ctx->dof) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid input vector size %d should be %d", n, ctx->n*ctx->dof);
765   if (n) {
766     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
767     ierr = DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);CHKERRQ(ierr);
768     if (dim == 2) {
769       if (coneSize == 3) {
770         ierr = DMInterpolate_Triangle_Private(ctx, dm, x, v);CHKERRQ(ierr);
771       } else if (coneSize == 4) {
772         ierr = DMInterpolate_Quad_Private(ctx, dm, x, v);CHKERRQ(ierr);
773       } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
774     } else if (dim == 3) {
775       if (coneSize == 4) {
776         ierr = DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);CHKERRQ(ierr);
777       } else {
778         ierr = DMInterpolate_Hex_Private(ctx, dm, x, v);CHKERRQ(ierr);
779       }
780     } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
781   }
782   PetscFunctionReturn(0);
783 }
784 
785 #undef __FUNCT__
786 #define __FUNCT__ "DMInterpolationDestroy"
787 PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
788 {
789   PetscErrorCode ierr;
790 
791   PetscFunctionBegin;
792   PetscValidPointer(ctx, 2);
793   ierr = VecDestroy(&(*ctx)->coords);CHKERRQ(ierr);
794   ierr = PetscFree((*ctx)->points);CHKERRQ(ierr);
795   ierr = PetscFree((*ctx)->cells);CHKERRQ(ierr);
796   ierr = PetscFree(*ctx);CHKERRQ(ierr);
797   *ctx = NULL;
798   PetscFunctionReturn(0);
799 }
800 
801 #undef __FUNCT__
802 #define __FUNCT__ "SNESMonitorFields"
803 /*@C
804   SNESMonitorFields - Monitors the residual for each field separately
805 
806   Collective on SNES
807 
808   Input Parameters:
809 + snes   - the SNES context
810 . its    - iteration number
811 . fgnorm - 2-norm of residual
812 - vf  - PetscViewerAndFormat of type ASCII
813 
814   Notes:
815   This routine prints the residual norm at each iteration.
816 
817   Level: intermediate
818 
819 .keywords: SNES, nonlinear, default, monitor, norm
820 .seealso: SNESMonitorSet(), SNESMonitorDefault()
821 @*/
822 PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
823 {
824   PetscViewer        viewer = vf->viewer;
825   Vec                res;
826   DM                 dm;
827   PetscSection       s;
828   const PetscScalar *r;
829   PetscReal         *lnorms, *norms;
830   PetscInt           numFields, f, pStart, pEnd, p;
831   PetscErrorCode     ierr;
832 
833   PetscFunctionBegin;
834   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
835   ierr = SNESGetFunction(snes, &res, 0, 0);CHKERRQ(ierr);
836   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
837   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
838   ierr = PetscSectionGetNumFields(s, &numFields);CHKERRQ(ierr);
839   ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
840   ierr = PetscCalloc2(numFields, &lnorms, numFields, &norms);CHKERRQ(ierr);
841   ierr = VecGetArrayRead(res, &r);CHKERRQ(ierr);
842   for (p = pStart; p < pEnd; ++p) {
843     for (f = 0; f < numFields; ++f) {
844       PetscInt fdof, foff, d;
845 
846       ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
847       ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
848       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
849     }
850   }
851   ierr = VecRestoreArrayRead(res, &r);CHKERRQ(ierr);
852   ierr = MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
853   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
854   ierr = PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
855   ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
856   for (f = 0; f < numFields; ++f) {
857     if (f > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
858     ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));CHKERRQ(ierr);
859   }
860   ierr = PetscViewerASCIIPrintf(viewer, "]\n");CHKERRQ(ierr);
861   ierr = PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
862   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
863   ierr = PetscFree2(lnorms, norms);CHKERRQ(ierr);
864   PetscFunctionReturn(0);
865 }
866 
867 /********************* Residual Computation **************************/
868 
869 #undef __FUNCT__
870 #define __FUNCT__ "DMPlexSNESGetGeometryFEM"
871 /*@
872   DMPlexSNESGetGeometryFEM - Return precomputed geometric data
873 
874   Input Parameter:
875 . dm - The DM
876 
877   Output Parameters:
878 . cellgeom - The values precomputed from cell geometry
879 
880   Level: developer
881 
882 .seealso: DMPlexSNESSetFunctionLocal()
883 @*/
884 PetscErrorCode DMPlexSNESGetGeometryFEM(DM dm, Vec *cellgeom)
885 {
886   DMSNES         dmsnes;
887   PetscObject    obj;
888   PetscErrorCode ierr;
889 
890   PetscFunctionBegin;
891   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
892   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
893   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", &obj);CHKERRQ(ierr);
894   if (!obj) {
895     Vec cellgeom;
896 
897     ierr = DMPlexComputeGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
898     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject) cellgeom);CHKERRQ(ierr);
899     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
900   }
901   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject *) cellgeom);CHKERRQ(ierr);}
902   PetscFunctionReturn(0);
903 }
904 
905 #undef __FUNCT__
906 #define __FUNCT__ "DMPlexSNESGetGeometryFVM"
907 /*@
908   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
909 
910   Input Parameter:
911 . dm - The DM
912 
913   Output Parameters:
914 + facegeom - The values precomputed from face geometry
915 . cellgeom - The values precomputed from cell geometry
916 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
917 
918   Level: developer
919 
920 .seealso: DMPlexTSSetRHSFunctionLocal()
921 @*/
922 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
923 {
924   DMSNES         dmsnes;
925   PetscObject    obj;
926   PetscErrorCode ierr;
927 
928   PetscFunctionBegin;
929   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
930   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
931   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", &obj);CHKERRQ(ierr);
932   if (!obj) {
933     Vec cellgeom, facegeom;
934 
935     ierr = DMPlexComputeGeometryFVM(dm, &cellgeom, &facegeom);CHKERRQ(ierr);
936     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", (PetscObject) facegeom);CHKERRQ(ierr);
937     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fvm", (PetscObject) cellgeom);CHKERRQ(ierr);
938     ierr = VecDestroy(&facegeom);CHKERRQ(ierr);
939     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
940   }
941   if (facegeom) {PetscValidPointer(facegeom, 2); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", (PetscObject *) facegeom);CHKERRQ(ierr);}
942   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fvm", (PetscObject *) cellgeom);CHKERRQ(ierr);}
943   if (minRadius) {ierr = DMPlexGetMinRadius(dm, minRadius);CHKERRQ(ierr);}
944   PetscFunctionReturn(0);
945 }
946 
947 #undef __FUNCT__
948 #define __FUNCT__ "DMPlexSNESGetGradientDM"
949 /*@
950   DMPlexSNESGetGradientDM - Return gradient data layout
951 
952   Input Parameters:
953 + dm - The DM
954 - fv - The PetscFV
955 
956   Output Parameter:
957 . dmGrad - The layout for gradient values
958 
959   Level: developer
960 
961 .seealso: DMPlexSNESGetGeometryFVM()
962 @*/
963 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
964 {
965   DMSNES         dmsnes;
966   PetscObject    obj;
967   PetscBool      computeGradients;
968   PetscErrorCode ierr;
969 
970   PetscFunctionBegin;
971   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
972   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
973   PetscValidPointer(dmGrad,3);
974   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
975   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
976   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
977   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", &obj);CHKERRQ(ierr);
978   if (!obj) {
979     DM  dmGrad;
980     Vec faceGeometry, cellGeometry;
981 
982     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometry, &cellGeometry, NULL);CHKERRQ(ierr);
983     ierr = DMPlexComputeGradientFVM(dm, fv, faceGeometry, cellGeometry, &dmGrad);CHKERRQ(ierr);
984     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", (PetscObject) dmGrad);CHKERRQ(ierr);
985     ierr = DMDestroy(&dmGrad);CHKERRQ(ierr);
986   }
987   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", (PetscObject *) dmGrad);CHKERRQ(ierr);
988   PetscFunctionReturn(0);
989 }
990 
991 #undef __FUNCT__
992 #define __FUNCT__ "DMPlexGetCellFields"
993 /*@C
994   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells
995 
996   Input Parameters:
997 + dm     - The DM
998 . cStart - The first cell to include
999 . cEnd   - The first cell to exclude
1000 . locX   - A local vector with the solution fields
1001 . locX_t - A local vector with solution field time derivatives, or NULL
1002 - locA   - A local vector with auxiliary fields, or NULL
1003 
1004   Output Parameters:
1005 + u   - The field coefficients
1006 . u_t - The fields derivative coefficients
1007 - a   - The auxiliary field coefficients
1008 
1009   Level: developer
1010 
1011 .seealso: DMPlexGetFaceFields()
1012 @*/
1013 PetscErrorCode DMPlexGetCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1014 {
1015   DM             dmAux;
1016   PetscSection   section, sectionAux;
1017   PetscDS        prob;
1018   PetscInt       numCells = cEnd - cStart, totDim, totDimAux, c;
1019   PetscErrorCode ierr;
1020 
1021   PetscFunctionBegin;
1022   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1023   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1024   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1025   if (locA)   {PetscValidHeaderSpecific(locA, VEC_CLASSID, 6);}
1026   PetscValidPointer(u, 7);
1027   PetscValidPointer(u_t, 8);
1028   PetscValidPointer(a, 9);
1029   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1030   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1031   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1032   if (locA) {
1033     PetscDS probAux;
1034 
1035     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1036     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1037     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1038     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1039   }
1040   ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u);CHKERRQ(ierr);
1041   if (locX_t) {ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u_t);CHKERRQ(ierr);} else {*u_t = NULL;}
1042   if (locA)   {ierr = DMGetWorkArray(dm, numCells*totDimAux, PETSC_SCALAR, a);CHKERRQ(ierr);} else {*a = NULL;}
1043   for (c = cStart; c < cEnd; ++c) {
1044     PetscScalar *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
1045     PetscInt     i;
1046 
1047     ierr = DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1048     for (i = 0; i < totDim; ++i) ul[(c-cStart)*totDim+i] = x[i];
1049     ierr = DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1050     if (locX_t) {
1051       ierr = DMPlexVecGetClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1052       for (i = 0; i < totDim; ++i) ul_t[(c-cStart)*totDim+i] = x_t[i];
1053       ierr = DMPlexVecRestoreClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1054     }
1055     if (locA) {
1056       DM dmAuxPlex;
1057 
1058       ierr = DMSNESConvertPlex(dmAux, &dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1059       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1060       for (i = 0; i < totDimAux; ++i) al[(c-cStart)*totDimAux+i] = x[i];
1061       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1062       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1063     }
1064   }
1065   PetscFunctionReturn(0);
1066 }
1067 
1068 #undef __FUNCT__
1069 #define __FUNCT__ "DMPlexRestoreCellFields"
1070 /*@C
1071   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells
1072 
1073   Input Parameters:
1074 + dm     - The DM
1075 . cStart - The first cell to include
1076 . cEnd   - The first cell to exclude
1077 . locX   - A local vector with the solution fields
1078 . locX_t - A local vector with solution field time derivatives, or NULL
1079 - locA   - A local vector with auxiliary fields, or NULL
1080 
1081   Output Parameters:
1082 + u   - The field coefficients
1083 . u_t - The fields derivative coefficients
1084 - a   - The auxiliary field coefficients
1085 
1086   Level: developer
1087 
1088 .seealso: DMPlexGetFaceFields()
1089 @*/
1090 PetscErrorCode DMPlexRestoreCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1091 {
1092   PetscErrorCode ierr;
1093 
1094   PetscFunctionBegin;
1095   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u);CHKERRQ(ierr);
1096   if (*u_t) {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u_t);CHKERRQ(ierr);}
1097   if (*a)   {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, a);CHKERRQ(ierr);}
1098   PetscFunctionReturn(0);
1099 }
1100 
1101 #undef __FUNCT__
1102 #define __FUNCT__ "DMPlexGetFaceFields"
1103 /*@C
1104   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces
1105 
1106   Input Parameters:
1107 + dm     - The DM
1108 . fStart - The first face to include
1109 . fEnd   - The first face to exclude
1110 . locX   - A local vector with the solution fields
1111 . locX_t - A local vector with solution field time derivatives, or NULL
1112 . faceGeometry - A local vector with face geometry
1113 . cellGeometry - A local vector with cell geometry
1114 - locaGrad - A local vector with field gradients, or NULL
1115 
1116   Output Parameters:
1117 + uL - The field values at the left side of the face
1118 - uR - The field values at the right side of the face
1119 
1120   Level: developer
1121 
1122 .seealso: DMPlexGetCellFields()
1123 @*/
1124 PetscErrorCode DMPlexGetFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscScalar **uL, PetscScalar **uR)
1125 {
1126   DM                 dmFace, dmCell, dmGrad = NULL;
1127   PetscSection       section;
1128   PetscDS            prob;
1129   DMLabel            ghostLabel;
1130   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
1131   PetscBool         *isFE;
1132   PetscInt           dim, Nf, f, Nc, numFaces = fEnd - fStart, iface, face;
1133   PetscErrorCode     ierr;
1134 
1135   PetscFunctionBegin;
1136   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1137   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1138   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1139   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 6);
1140   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 7);
1141   if (locGrad) {PetscValidHeaderSpecific(locGrad, VEC_CLASSID, 8);}
1142   PetscValidPointer(uL, 9);
1143   PetscValidPointer(uR, 10);
1144   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1145   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1146   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1147   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1148   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1149   ierr = PetscMalloc1(Nf, &isFE);CHKERRQ(ierr);
1150   for (f = 0; f < Nf; ++f) {
1151     PetscObject  obj;
1152     PetscClassId id;
1153 
1154     ierr = DMGetField(dm, f, &obj);CHKERRQ(ierr);
1155     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1156     if (id == PETSCFE_CLASSID)      {isFE[f] = PETSC_TRUE;}
1157     else if (id == PETSCFV_CLASSID) {isFE[f] = PETSC_FALSE;}
1158     else                            {isFE[f] = PETSC_FALSE;}
1159   }
1160   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1161   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1162   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1163   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1164   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1165   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1166   if (locGrad) {
1167     ierr = VecGetDM(locGrad, &dmGrad);CHKERRQ(ierr);
1168     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1169   }
1170   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uL);CHKERRQ(ierr);
1171   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uR);CHKERRQ(ierr);
1172   /* Right now just eat the extra work for FE (could make a cell loop) */
1173   for (face = fStart, iface = 0; face < fEnd; ++face) {
1174     const PetscInt        *cells;
1175     PetscFVFaceGeom       *fg;
1176     PetscFVCellGeom       *cgL, *cgR;
1177     PetscScalar           *xL, *xR, *gL, *gR;
1178     PetscScalar           *uLl = *uL, *uRl = *uR;
1179     PetscInt               ghost, nsupp;
1180 
1181     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1182     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1183     if (ghost >= 0) continue;
1184     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1185     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1186     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1187     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1188     for (f = 0; f < Nf; ++f) {
1189       PetscInt off;
1190 
1191       ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1192       if (isFE[f]) {
1193         const PetscInt *cone;
1194         PetscInt        comp, coneSize, faceLocL, faceLocR, ldof, rdof, d;
1195 
1196         xL = xR = NULL;
1197         ierr = DMPlexVecGetClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1198         ierr = DMPlexVecGetClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1199         ierr = DMPlexGetCone(dm, cells[0], &cone);CHKERRQ(ierr);
1200         ierr = DMPlexGetConeSize(dm, cells[0], &coneSize);CHKERRQ(ierr);
1201         for (faceLocL = 0; faceLocL < coneSize; ++faceLocL) if (cone[faceLocL] == face) break;
1202         if (faceLocL == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of cell %d", face, cells[0]);
1203         ierr = DMPlexGetCone(dm, cells[1], &cone);CHKERRQ(ierr);
1204         ierr = DMPlexGetConeSize(dm, cells[1], &coneSize);CHKERRQ(ierr);
1205         for (faceLocR = 0; faceLocR < coneSize; ++faceLocR) if (cone[faceLocR] == face) break;
1206         if (faceLocR == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of cell %d", face, cells[1]);
1207         /* Check that FEM field has values in the right cell (sometimes its an FV ghost cell) */
1208         ierr = EvaluateFaceFields(prob, f, faceLocL, xL, &uLl[iface*Nc+off]);CHKERRQ(ierr);
1209         if (rdof == ldof) {ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);}
1210         else              {ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr); for(d = 0; d < comp; ++d) uRl[iface*Nc+off+d] = uLl[iface*Nc+off+d];}
1211         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1212         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1213       } else {
1214         PetscFV  fv;
1215         PetscInt numComp, c;
1216 
1217         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fv);CHKERRQ(ierr);
1218         ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1219         if (nsupp > 2) {
1220           for (f = 0; f < Nf; ++f) {
1221             PetscInt off;
1222 
1223             ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1224             ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1225             for (c = 0; c < numComp; ++c) {
1226               uLl[iface*Nc+off+c] = 0.;
1227               uRl[iface*Nc+off+c] = 0.;
1228             }
1229           }
1230           continue;
1231         }
1232         ierr = DMPlexPointLocalFieldRead(dm, cells[0], f, x, &xL);CHKERRQ(ierr);
1233         ierr = DMPlexPointLocalFieldRead(dm, cells[1], f, x, &xR);CHKERRQ(ierr);
1234         if (dmGrad) {
1235           PetscReal dxL[3], dxR[3];
1236 
1237           ierr = DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);CHKERRQ(ierr);
1238           ierr = DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);CHKERRQ(ierr);
1239           DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
1240           DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
1241           for (c = 0; c < numComp; ++c) {
1242             uLl[iface*Nc+off+c] = xL[c] + DMPlex_DotD_Internal(dim, &gL[c*dim], dxL);
1243             uRl[iface*Nc+off+c] = xR[c] + DMPlex_DotD_Internal(dim, &gR[c*dim], dxR);
1244           }
1245         } else {
1246           for (c = 0; c < numComp; ++c) {
1247             uLl[iface*Nc+off+c] = xL[c];
1248             uRl[iface*Nc+off+c] = xR[c];
1249           }
1250         }
1251       }
1252     }
1253     ++iface;
1254   }
1255   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1256   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1257   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1258   if (locGrad) {
1259     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1260   }
1261   ierr = PetscFree(isFE);CHKERRQ(ierr);
1262   PetscFunctionReturn(0);
1263 }
1264 
1265 #undef __FUNCT__
1266 #define __FUNCT__ "DMPlexRestoreFaceFields"
1267 /*@C
1268   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces
1269 
1270   Input Parameters:
1271 + dm     - The DM
1272 . fStart - The first face to include
1273 . fEnd   - The first face to exclude
1274 . locX   - A local vector with the solution fields
1275 . locX_t - A local vector with solution field time derivatives, or NULL
1276 . faceGeometry - A local vector with face geometry
1277 . cellGeometry - A local vector with cell geometry
1278 - locaGrad - A local vector with field gradients, or NULL
1279 
1280   Output Parameters:
1281 + uL - The field values at the left side of the face
1282 - uR - The field values at the right side of the face
1283 
1284   Level: developer
1285 
1286 .seealso: DMPlexGetFaceFields()
1287 @*/
1288 PetscErrorCode DMPlexRestoreFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscScalar **uL, PetscScalar **uR)
1289 {
1290   PetscErrorCode ierr;
1291 
1292   PetscFunctionBegin;
1293   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uL);CHKERRQ(ierr);
1294   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uR);CHKERRQ(ierr);
1295   PetscFunctionReturn(0);
1296 }
1297 
1298 #undef __FUNCT__
1299 #define __FUNCT__ "DMPlexGetFaceGeometry"
1300 /*@C
1301   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces
1302 
1303   Input Parameters:
1304 + dm     - The DM
1305 . fStart - The first face to include
1306 . fEnd   - The first face to exclude
1307 . faceGeometry - A local vector with face geometry
1308 - cellGeometry - A local vector with cell geometry
1309 
1310   Output Parameters:
1311 + fgeom - The extract the face centroid and normal
1312 - vol   - The cell volume
1313 
1314   Level: developer
1315 
1316 .seealso: DMPlexGetCellFields()
1317 @*/
1318 PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscFVFaceGeom **fgeom, PetscReal **vol)
1319 {
1320   DM                 dmFace, dmCell;
1321   DMLabel            ghostLabel;
1322   const PetscScalar *facegeom, *cellgeom;
1323   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
1324   PetscErrorCode     ierr;
1325 
1326   PetscFunctionBegin;
1327   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1328   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 4);
1329   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 5);
1330   PetscValidPointer(fgeom, 6);
1331   PetscValidPointer(vol, 7);
1332   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1333   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1334   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1335   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1336   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1337   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1338   ierr = PetscMalloc1(numFaces, fgeom);CHKERRQ(ierr);
1339   ierr = DMGetWorkArray(dm, numFaces*2, PETSC_SCALAR, vol);CHKERRQ(ierr);
1340   for (face = fStart, iface = 0; face < fEnd; ++face) {
1341     const PetscInt        *cells;
1342     PetscFVFaceGeom       *fg;
1343     PetscFVCellGeom       *cgL, *cgR;
1344     PetscFVFaceGeom       *fgeoml = *fgeom;
1345     PetscReal             *voll   = *vol;
1346     PetscInt               ghost, d;
1347 
1348     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1349     if (ghost >= 0) continue;
1350     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1351     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1352     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1353     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1354     for (d = 0; d < dim; ++d) {
1355       fgeoml[iface].centroid[d] = fg->centroid[d];
1356       fgeoml[iface].normal[d]   = fg->normal[d];
1357     }
1358     voll[iface*2+0] = cgL->volume;
1359     voll[iface*2+1] = cgR->volume;
1360     ++iface;
1361   }
1362   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1363   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1364   PetscFunctionReturn(0);
1365 }
1366 
1367 #undef __FUNCT__
1368 #define __FUNCT__ "DMPlexRestoreFaceGeometry"
1369 /*@C
1370   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces
1371 
1372   Input Parameters:
1373 + dm     - The DM
1374 . fStart - The first face to include
1375 . fEnd   - The first face to exclude
1376 . faceGeometry - A local vector with face geometry
1377 - cellGeometry - A local vector with cell geometry
1378 
1379   Output Parameters:
1380 + fgeom - The extract the face centroid and normal
1381 - vol   - The cell volume
1382 
1383   Level: developer
1384 
1385 .seealso: DMPlexGetFaceFields()
1386 @*/
1387 PetscErrorCode DMPlexRestoreFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscFVFaceGeom **fgeom, PetscReal **vol)
1388 {
1389   PetscErrorCode ierr;
1390 
1391   PetscFunctionBegin;
1392   ierr = PetscFree(*fgeom);CHKERRQ(ierr);
1393   ierr = DMRestoreWorkArray(dm, 0, PETSC_REAL, vol);CHKERRQ(ierr);
1394   PetscFunctionReturn(0);
1395 }
1396 
1397 #undef __FUNCT__
1398 #define __FUNCT__ "DMPlexComputeBdResidual_Internal"
1399 PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1400 {
1401   DM_Plex         *mesh = (DM_Plex *) dm->data;
1402   PetscSection     section;
1403   PetscDS          prob;
1404   DMLabel          depth;
1405   PetscFECellGeom *cgeom;
1406   PetscScalar     *u = NULL, *u_t = NULL, *elemVec = NULL;
1407   PetscInt         dim, Nf, f, totDimBd, numBd, bd;
1408   PetscErrorCode   ierr;
1409 
1410   PetscFunctionBegin;
1411   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1412   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1413   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1414   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1415   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
1416   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1417   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1418   for (bd = 0; bd < numBd; ++bd) {
1419     const char     *bdLabel;
1420     DMLabel         label;
1421     IS              pointIS;
1422     const PetscInt *points;
1423     const PetscInt *values;
1424     PetscInt        field, numValues, v, numPoints, p, dep, numFaces;
1425     PetscBool       isEssential;
1426     PetscObject     obj;
1427     PetscClassId    id;
1428 
1429     ierr = DMGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1430     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
1431     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1432     if ((id != PETSCFE_CLASSID) || isEssential) continue;
1433     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1434     for (v = 0; v < numValues; ++v) {
1435       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
1436       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1437       if (!pointIS) continue; /* No points with that id on this process */
1438       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1439       for (p = 0, numFaces = 0; p < numPoints; ++p) {
1440         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1441         if (dep == dim-1) ++numFaces;
1442       }
1443       ierr = PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd,&elemVec);CHKERRQ(ierr);
1444       if (locX_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
1445       for (p = 0, f = 0; p < numPoints; ++p) {
1446         const PetscInt point = points[p];
1447         PetscScalar   *x     = NULL;
1448         PetscInt       i;
1449 
1450         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1451         if (dep != dim-1) continue;
1452         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
1453         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);CHKERRQ(ierr);
1454         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
1455         /* TODO: Matt, this is wrong if feBd does not match fe: i.e., if the order differs. */
1456         ierr = DMPlexVecGetClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1457         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
1458         ierr = DMPlexVecRestoreClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1459         if (locX_t) {
1460           ierr = DMPlexVecGetClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1461           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
1462           ierr = DMPlexVecRestoreClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1463         }
1464         ++f;
1465       }
1466       for (f = 0; f < Nf; ++f) {
1467         PetscFE         fe;
1468         PetscQuadrature q;
1469         PetscInt        numQuadPoints, Nb;
1470         /* Conforming batches */
1471         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1472         /* Remainder */
1473         PetscInt        Nr, offset;
1474 
1475         ierr = PetscDSGetBdDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1476         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1477         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1478         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1479         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1480         blockSize = Nb*numQuadPoints;
1481         batchSize = numBlocks * blockSize;
1482         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1483         numChunks = numFaces / (numBatches*batchSize);
1484         Ne        = numChunks*numBatches*batchSize;
1485         Nr        = numFaces % (numBatches*batchSize);
1486         offset    = numFaces - Nr;
1487         ierr = PetscFEIntegrateBdResidual(fe, prob, f, Ne, cgeom, u, u_t, NULL, NULL, t, elemVec);CHKERRQ(ierr);
1488         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);
1489       }
1490       for (p = 0, f = 0; p < numPoints; ++p) {
1491         const PetscInt point = points[p];
1492 
1493         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1494         if (dep != dim-1) continue;
1495         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDimBd, &elemVec[f*totDimBd]);CHKERRQ(ierr);}
1496         ierr = DMPlexVecSetClosure(dm, NULL, locF, point, &elemVec[f*totDimBd], ADD_ALL_VALUES);CHKERRQ(ierr);
1497         ++f;
1498       }
1499       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1500       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1501       ierr = PetscFree3(u,cgeom,elemVec);CHKERRQ(ierr);
1502       if (locX_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
1503     }
1504   }
1505   PetscFunctionReturn(0);
1506 }
1507 
1508 #undef __FUNCT__
1509 #define __FUNCT__ "DMPlexReconstructGradientsFVM"
1510 /*@
1511   DMPlexReconstructGradientsFVM - reconstruct the gradient of a vector using a finite volume method.
1512 
1513   Input Parameters:
1514 + dm - the mesh
1515 - locX - the local representation of the vector
1516 
1517   Output Parameter:
1518 . grad - the global representation of the gradient
1519 
1520   Level: developer
1521 
1522 .seealso: DMPlexSNESGetGradientDM()
1523 @*/
1524 PetscErrorCode DMPlexReconstructGradientsFVM(DM dm, Vec locX, Vec grad)
1525 {
1526   PetscDS          prob;
1527   PetscInt         Nf, f, fStart, fEnd;
1528   PetscBool        useFVM = PETSC_FALSE;
1529   PetscFV          fvm = NULL;
1530   Vec              faceGeometryFVM, cellGeometryFVM;
1531   PetscFVCellGeom  *cgeomFVM   = NULL;
1532   PetscFVFaceGeom  *fgeomFVM   = NULL;
1533   DM               dmGrad = NULL;
1534   PetscErrorCode   ierr;
1535 
1536   PetscFunctionBegin;
1537   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1538   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1539   for (f = 0; f < Nf; ++f) {
1540     PetscObject  obj;
1541     PetscClassId id;
1542 
1543     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1544     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1545     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1546   }
1547   if (!useFVM) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"This dm does not have a finite volume discretization");
1548   ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1549   if (!dmGrad) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"This dm's finite volume discretization does not reconstruct gradients");
1550   ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1551   ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1552   ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1553   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1554   ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1555   PetscFunctionReturn(0);
1556 }
1557 
1558 #undef __FUNCT__
1559 #define __FUNCT__ "DMPlexComputeResidual_Internal"
1560 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal time, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1561 {
1562   DM_Plex          *mesh       = (DM_Plex *) dm->data;
1563   const char       *name       = "Residual";
1564   DM                dmAux      = NULL;
1565   DM                dmGrad     = NULL;
1566   DMLabel           ghostLabel = NULL;
1567   PetscDS           prob       = NULL;
1568   PetscDS           probAux    = NULL;
1569   PetscSection      section    = NULL;
1570   PetscBool         useFEM     = PETSC_FALSE;
1571   PetscBool         useFVM     = PETSC_FALSE;
1572   PetscBool         isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
1573   PetscFV           fvm        = NULL;
1574   PetscFECellGeom  *cgeomFEM   = NULL;
1575   PetscScalar      *cgeomScal;
1576   PetscFVCellGeom  *cgeomFVM   = NULL;
1577   PetscFVFaceGeom  *fgeomFVM   = NULL;
1578   Vec               locA, cellGeometryFEM = NULL, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1579   PetscScalar      *u, *u_t, *a, *uL, *uR;
1580   PetscInt          Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
1581   PetscErrorCode    ierr;
1582 
1583   PetscFunctionBegin;
1584   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1585   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1586   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
1587   /* FEM+FVM */
1588   /* 1: Get sizes from dm and dmAux */
1589   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1590   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1591   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1592   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1593   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1594   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1595   if (locA) {
1596     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1597     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1598     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1599   }
1600   /* 2: Get geometric data */
1601   for (f = 0; f < Nf; ++f) {
1602     PetscObject  obj;
1603     PetscClassId id;
1604     PetscBool    fimp;
1605 
1606     ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1607     if (isImplicit != fimp) continue;
1608     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1609     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1610     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1611     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1612   }
1613   if (useFEM) {
1614     ierr = DMPlexSNESGetGeometryFEM(dm, &cellGeometryFEM);CHKERRQ(ierr);
1615     ierr = VecGetArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);
1616     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1617       DM dmCell;
1618       PetscInt c;
1619 
1620       ierr = VecGetDM(cellGeometryFEM,&dmCell);CHKERRQ(ierr);
1621       ierr = PetscMalloc1(cEnd-cStart,&cgeomFEM);CHKERRQ(ierr);
1622       for (c = 0; c < cEnd - cStart; c++) {
1623         PetscScalar *thisgeom;
1624 
1625         ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1626         cgeomFEM[c] = *((PetscFECellGeom *) thisgeom);
1627       }
1628     }
1629     else {
1630       cgeomFEM = (PetscFECellGeom *) cgeomScal;
1631     }
1632   }
1633   if (useFVM) {
1634     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1635     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1636     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1637     /* Reconstruct and limit cell gradients */
1638     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1639     if (dmGrad) {
1640       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1641       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1642       ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1643       /* Communicate gradient values */
1644       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1645       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1646       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1647       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1648     }
1649     /* Handle non-essential (e.g. outflow) boundary values */
1650     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1651   }
1652   /* Loop over chunks */
1653   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1654   numChunks     = 1;
1655   cellChunkSize = (cEnd - cStart)/numChunks;
1656   faceChunkSize = (fEnd - fStart)/numChunks;
1657   for (chunk = 0; chunk < numChunks; ++chunk) {
1658     PetscScalar     *elemVec, *fluxL, *fluxR;
1659     PetscReal       *vol;
1660     PetscFVFaceGeom *fgeom;
1661     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, cell;
1662     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = fE - fS, face;
1663 
1664     /* Extract field coefficients */
1665     if (useFEM) {
1666       ierr = DMPlexGetCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1667       ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1668       ierr = PetscMemzero(elemVec, numCells*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1669     }
1670     if (useFVM) {
1671       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &uL, &uR);CHKERRQ(ierr);
1672       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &fgeom, &vol);CHKERRQ(ierr);
1673       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1674       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1675       ierr = PetscMemzero(fluxL, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1676       ierr = PetscMemzero(fluxR, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1677     }
1678     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1679     /* Loop over fields */
1680     for (f = 0; f < Nf; ++f) {
1681       PetscObject  obj;
1682       PetscClassId id;
1683       PetscBool    fimp;
1684       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1685 
1686       ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1687       if (isImplicit != fimp) continue;
1688       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1689       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1690       if (id == PETSCFE_CLASSID) {
1691         PetscFE         fe = (PetscFE) obj;
1692         PetscQuadrature q;
1693         PetscInt        Nq, Nb;
1694 
1695         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1696 
1697         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1698         ierr = PetscQuadratureGetData(q, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1699         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1700         blockSize = Nb*Nq;
1701         batchSize = numBlocks * blockSize;
1702         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1703         numChunks = numCells / (numBatches*batchSize);
1704         Ne        = numChunks*numBatches*batchSize;
1705         Nr        = numCells % (numBatches*batchSize);
1706         offset    = numCells - Nr;
1707         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1708         /*   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) */
1709         ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeomFEM, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1710         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);
1711       } else if (id == PETSCFV_CLASSID) {
1712         PetscFV fv = (PetscFV) obj;
1713 
1714         Ne = numFaces;
1715         /* Riemann solve over faces (need fields at face centroids) */
1716         /*   We need to evaluate FE fields at those coordinates */
1717         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1718       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1719     }
1720     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1721       ierr = PetscFree(cgeomFEM);CHKERRQ(ierr);
1722     }
1723     else {
1724       cgeomFEM = NULL;
1725     }
1726     if (cellGeometryFEM) {ierr = VecRestoreArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);}
1727     /* Loop over domain */
1728     if (useFEM) {
1729       /* Add elemVec to locX */
1730       for (cell = cS; cell < cE; ++cell) {
1731         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cell*totDim]);CHKERRQ(ierr);}
1732         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cell*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1733       }
1734     }
1735     if (useFVM) {
1736       PetscScalar *fa;
1737       PetscInt     iface;
1738 
1739       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1740       for (f = 0; f < Nf; ++f) {
1741         PetscFV      fv;
1742         PetscObject  obj;
1743         PetscClassId id;
1744         PetscInt     foff, pdim;
1745 
1746         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1747         ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1748         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1749         if (id != PETSCFV_CLASSID) continue;
1750         fv   = (PetscFV) obj;
1751         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1752         /* Accumulate fluxes to cells */
1753         for (face = fS, iface = 0; face < fE; ++face) {
1754           const PetscInt *cells;
1755           PetscScalar    *fL, *fR;
1756           PetscInt        ghost, d, nsupp;
1757 
1758           ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1759           ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1760           if (ghost >= 0) continue;
1761           if (nsupp > 2) { /* noop */
1762             ++iface;
1763             continue;
1764           }
1765           ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1766           ierr = DMPlexPointGlobalFieldRef(dm, cells[0], f, fa, &fL);CHKERRQ(ierr);
1767           ierr = DMPlexPointGlobalFieldRef(dm, cells[1], f, fa, &fR);CHKERRQ(ierr);
1768           for (d = 0; d < pdim; ++d) {
1769             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
1770             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
1771           }
1772           ++iface;
1773         }
1774       }
1775       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1776     }
1777     /* Handle time derivative */
1778     if (locX_t) {
1779       PetscScalar *x_t, *fa;
1780 
1781       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1782       ierr = VecGetArray(locX_t, &x_t);CHKERRQ(ierr);
1783       for (f = 0; f < Nf; ++f) {
1784         PetscFV      fv;
1785         PetscObject  obj;
1786         PetscClassId id;
1787         PetscInt     pdim, d;
1788 
1789         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1790         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1791         if (id != PETSCFV_CLASSID) continue;
1792         fv   = (PetscFV) obj;
1793         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1794         for (cell = cS; cell < cE; ++cell) {
1795           PetscScalar *u_t, *r;
1796 
1797           ierr = DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);CHKERRQ(ierr);
1798           ierr = DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);CHKERRQ(ierr);
1799           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
1800         }
1801       }
1802       ierr = VecRestoreArray(locX_t, &x_t);CHKERRQ(ierr);
1803       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1804     }
1805     if (useFEM) {
1806       ierr = DMPlexRestoreCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1807       ierr = DMRestoreWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1808     }
1809     if (useFVM) {
1810       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &uL, &uR);CHKERRQ(ierr);
1811       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &fgeom, &vol);CHKERRQ(ierr);
1812       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1813       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1814       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1815     }
1816   }
1817 
1818   if (useFEM) {ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, t, locF, user);CHKERRQ(ierr);}
1819 
1820   /* FEM */
1821   /* 1: Get sizes from dm and dmAux */
1822   /* 2: Get geometric data */
1823   /* 3: Handle boundary values */
1824   /* 4: Loop over domain */
1825   /*   Extract coefficients */
1826   /* Loop over fields */
1827   /*   Set tiling for FE*/
1828   /*   Integrate FE residual to get elemVec */
1829   /*     Loop over subdomain */
1830   /*       Loop over quad points */
1831   /*         Transform coords to real space */
1832   /*         Evaluate field and aux fields at point */
1833   /*         Evaluate residual at point */
1834   /*         Transform residual to real space */
1835   /*       Add residual to elemVec */
1836   /* Loop over domain */
1837   /*   Add elemVec to locX */
1838 
1839   /* FVM */
1840   /* Get geometric data */
1841   /* If using gradients */
1842   /*   Compute gradient data */
1843   /*   Loop over domain faces */
1844   /*     Count computational faces */
1845   /*     Reconstruct cell gradient */
1846   /*   Loop over domain cells */
1847   /*     Limit cell gradients */
1848   /* Handle boundary values */
1849   /* Loop over domain faces */
1850   /*   Read out field, centroid, normal, volume for each side of face */
1851   /* Riemann solve over faces */
1852   /* Loop over domain faces */
1853   /*   Accumulate fluxes to cells */
1854   /* TODO Change printFEM to printDisc here */
1855   if (mesh->printFEM) {
1856     Vec         locFbc;
1857     PetscInt    pStart, pEnd, p, maxDof;
1858     PetscScalar *zeroes;
1859 
1860     ierr = VecDuplicate(locF,&locFbc);CHKERRQ(ierr);
1861     ierr = VecCopy(locF,locFbc);CHKERRQ(ierr);
1862     ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
1863     ierr = PetscSectionGetMaxDof(section,&maxDof);CHKERRQ(ierr);
1864     ierr = PetscCalloc1(maxDof,&zeroes);CHKERRQ(ierr);
1865     for (p = pStart; p < pEnd; p++) {
1866       ierr = VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);CHKERRQ(ierr);
1867     }
1868     ierr = PetscFree(zeroes);CHKERRQ(ierr);
1869     ierr = DMPrintLocalVec(dm, name, mesh->printTol, locFbc);CHKERRQ(ierr);
1870     ierr = VecDestroy(&locFbc);CHKERRQ(ierr);
1871   }
1872   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1873   PetscFunctionReturn(0);
1874 }
1875 
1876 #undef __FUNCT__
1877 #define __FUNCT__ "DMPlexComputeResidualFEM_Check_Internal"
1878 static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, PetscReal t, Vec F, void *user)
1879 {
1880   DM                dmCh, dmAux;
1881   Vec               A, cellgeom;
1882   PetscDS           prob, probCh, probAux = NULL;
1883   PetscQuadrature   q;
1884   PetscSection      section, sectionAux;
1885   PetscFECellGeom  *cgeom = NULL;
1886   PetscScalar      *cgeomScal;
1887   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
1888   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
1889   PetscInt          totDim, totDimAux, diffCell = 0;
1890   PetscErrorCode    ierr;
1891 
1892   PetscFunctionBegin;
1893   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1894   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1895   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1896   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1897   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1898   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1899   numCells = cEnd - cStart;
1900   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
1901   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
1902   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1903   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1904   if (dmAux) {
1905     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1906     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1907     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1908   }
1909   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1910   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);CHKERRQ(ierr);
1911   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
1912   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1913   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
1914   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1915   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1916     DM dmCell;
1917 
1918     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
1919     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
1920     for (c = 0; c < cEnd - cStart; c++) {
1921       PetscScalar *thisgeom;
1922 
1923       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1924       cgeom[c] = *((PetscFECellGeom *) thisgeom);
1925     }
1926   }
1927   else {
1928     cgeom = (PetscFECellGeom *) cgeomScal;
1929   }
1930   for (c = cStart; c < cEnd; ++c) {
1931     PetscScalar *x = NULL, *x_t = NULL;
1932     PetscInt     i;
1933 
1934     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1935     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1936     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1937     if (X_t) {
1938       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1939       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1940       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1941     }
1942     if (dmAux) {
1943       DM dmAuxPlex;
1944 
1945       ierr = DMSNESConvertPlex(dmAux,&dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1946       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1947       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1948       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1949       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1950     }
1951   }
1952   for (f = 0; f < Nf; ++f) {
1953     PetscFE  fe, feCh;
1954     PetscInt numQuadPoints, Nb;
1955     /* Conforming batches */
1956     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1957     /* Remainder */
1958     PetscInt Nr, offset;
1959 
1960     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1961     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
1962     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1963     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1964     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1965     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1966     blockSize = Nb*numQuadPoints;
1967     batchSize = numBlocks * blockSize;
1968     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1969     numChunks = numCells / (numBatches*batchSize);
1970     Ne        = numChunks*numBatches*batchSize;
1971     Nr        = numCells % (numBatches*batchSize);
1972     offset    = numCells - Nr;
1973     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1974     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVecCh);CHKERRQ(ierr);
1975     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);
1976     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);
1977   }
1978   for (c = cStart; c < cEnd; ++c) {
1979     PetscBool diff = PETSC_FALSE;
1980     PetscInt  d;
1981 
1982     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
1983     if (diff) {
1984       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
1985       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
1986       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
1987       ++diffCell;
1988     }
1989     if (diffCell > 9) break;
1990     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1991   }
1992   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1993     ierr = PetscFree(cgeom);CHKERRQ(ierr);
1994   }
1995   else {
1996     cgeom = NULL;
1997   }
1998   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1999   ierr = PetscFree3(u,u_t,elemVec);CHKERRQ(ierr);
2000   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
2001   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
2002   PetscFunctionReturn(0);
2003 }
2004 
2005 #undef __FUNCT__
2006 #define __FUNCT__ "DMPlexSNESComputeResidualFEM"
2007 /*@
2008   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
2009 
2010   Input Parameters:
2011 + dm - The mesh
2012 . X  - Local solution
2013 - user - The user context
2014 
2015   Output Parameter:
2016 . F  - Local output vector
2017 
2018   Level: developer
2019 
2020 .seealso: DMPlexComputeJacobianActionFEM()
2021 @*/
2022 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
2023 {
2024   PetscObject    check;
2025   PetscInt       cStart, cEnd, cEndInterior;
2026   DM             plex;
2027   PetscErrorCode ierr;
2028 
2029   PetscFunctionBegin;
2030   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2031   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2032   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2033   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2034   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
2035   ierr = PetscObjectQuery((PetscObject) plex, "dmCh", &check);CHKERRQ(ierr);
2036   if (check) {ierr = DMPlexComputeResidualFEM_Check_Internal(plex, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2037   else       {ierr = DMPlexComputeResidual_Internal(plex, cStart, cEnd, PETSC_MIN_REAL, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2038   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2039   PetscFunctionReturn(0);
2040 }
2041 
2042 #undef __FUNCT__
2043 #define __FUNCT__ "DMPlexSNESComputeBoundaryFEM"
2044 /*@
2045   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X
2046 
2047   Input Parameters:
2048 + dm - The mesh
2049 - user - The user context
2050 
2051   Output Parameter:
2052 . X  - Local solution
2053 
2054   Level: developer
2055 
2056 .seealso: DMPlexComputeJacobianActionFEM()
2057 @*/
2058 PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
2059 {
2060   DM             plex;
2061   PetscErrorCode ierr;
2062 
2063   PetscFunctionBegin;
2064   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2065   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);CHKERRQ(ierr);
2066   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2067   PetscFunctionReturn(0);
2068 }
2069 
2070 #undef __FUNCT__
2071 #define __FUNCT__ "DMPlexComputeJacobian_Internal"
2072 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)
2073 {
2074   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2075   const char       *name  = "Jacobian";
2076   DM                dmAux, plex;
2077   DMLabel           depth;
2078   Vec               A, cellgeom;
2079   PetscDS           prob, probAux = NULL;
2080   PetscQuadrature   quad;
2081   PetscSection      section, globalSection, sectionAux;
2082   PetscFECellGeom  *cgeom = NULL;
2083   PetscScalar      *cgeomScal;
2084   PetscScalar      *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
2085   PetscInt          dim, Nf, f, fieldI, fieldJ, numCells, c;
2086   PetscInt          totDim, totDimBd, totDimAux, numBd, bd;
2087   PetscBool         isShell, hasJac, hasPrec, hasDyn, hasFV = PETSC_FALSE;
2088   PetscErrorCode    ierr;
2089 
2090   PetscFunctionBegin;
2091   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2092   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2093   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2094   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2095   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2096   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2097   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
2098   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2099   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2100   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2101   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2102   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2103   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2104   numCells = cEnd - cStart;
2105   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2106   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2107   if (dmAux) {
2108     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2109     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2110     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2111     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2112   }
2113   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
2114   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);
2115   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2116   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2117   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2118   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2119     DM dmCell;
2120 
2121     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2122     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2123     for (c = 0; c < cEnd - cStart; c++) {
2124       PetscScalar *thisgeom;
2125 
2126       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2127       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2128     }
2129   } else {
2130     cgeom = (PetscFECellGeom *) cgeomScal;
2131   }
2132   for (c = cStart; c < cEnd; ++c) {
2133     PetscScalar *x = NULL,  *x_t = NULL;
2134     PetscInt     i;
2135 
2136     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2137     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2138     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2139     if (X_t) {
2140       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2141       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2142       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2143     }
2144     if (dmAux) {
2145       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2146       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2147       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2148     }
2149   }
2150   if (hasJac)  {ierr = PetscMemzero(elemMat,  numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2151   if (hasPrec) {ierr = PetscMemzero(elemMatP, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2152   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2153   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2154     PetscClassId id;
2155     PetscFE  fe;
2156     PetscInt numQuadPoints, Nb;
2157     /* Conforming batches */
2158     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2159     /* Remainder */
2160     PetscInt Nr, offset;
2161 
2162     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2163     ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
2164     if (id == PETSCFV_CLASSID) {hasFV = PETSC_TRUE; continue;}
2165     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2166     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2167     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2168     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2169     blockSize = Nb*numQuadPoints;
2170     batchSize = numBlocks * blockSize;
2171     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2172     numChunks = numCells / (numBatches*batchSize);
2173     Ne        = numChunks*numBatches*batchSize;
2174     Nr        = numCells % (numBatches*batchSize);
2175     offset    = numCells - Nr;
2176     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2177       if (hasJac) {
2178         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2179         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);
2180       }
2181       if (hasPrec) {
2182         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatP);CHKERRQ(ierr);
2183         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);
2184       }
2185       if (hasDyn) {
2186         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2187         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);
2188       }
2189     }
2190   }
2191   if (hasDyn) {
2192     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2193   }
2194   if (hasFV) {
2195     PetscClassId id;
2196     PetscFV      fv;
2197     PetscInt     offsetI, NcI, NbI = 1, fc, f;
2198 
2199     for (fieldI = 0; fieldI < Nf; ++fieldI) {
2200       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fv);CHKERRQ(ierr);
2201       ierr = PetscDSGetFieldOffset(prob, fieldI, &offsetI);CHKERRQ(ierr);
2202       ierr = PetscObjectGetClassId((PetscObject) fv, &id);CHKERRQ(ierr);
2203       if (id != PETSCFV_CLASSID) continue;
2204       /* Put in the identity */
2205       ierr = PetscFVGetNumComponents(fv, &NcI);CHKERRQ(ierr);
2206       for (c = cStart; c < cEnd; ++c) {
2207         const PetscInt eOffset = (c-cStart)*totDim*totDim;
2208         for (fc = 0; fc < NcI; ++fc) {
2209           for (f = 0; f < NbI; ++f) {
2210             const PetscInt i = offsetI + f*NcI+fc;
2211             if (hasPrec) {
2212               if (hasJac) {elemMat[eOffset+i*totDim+i] = 1.0;}
2213               elemMatP[eOffset+i*totDim+i] = 1.0;
2214             } else {elemMat[eOffset+i*totDim+i] = 1.0;}
2215           }
2216         }
2217       }
2218     }
2219     /* No allocated space for FV stuff, so ignore the zero entries */
2220     ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2221   }
2222   for (c = cStart; c < cEnd; ++c) {
2223     if (hasPrec) {
2224       if (hasJac) {
2225         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2226         ierr = DMPlexMatSetClosure(dm, section, globalSection, Jac, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2227       }
2228       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMatP[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2229       ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2230     } else {
2231       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2232       ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2233     }
2234   }
2235   if (hasFV) {ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);CHKERRQ(ierr);}
2236   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2237     ierr = PetscFree(cgeom);CHKERRQ(ierr);
2238   } else {
2239     cgeom = NULL;
2240   }
2241   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2242   ierr = PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);CHKERRQ(ierr);
2243   if (dmAux) {
2244     ierr = PetscFree(a);CHKERRQ(ierr);
2245     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2246   }
2247   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2248   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
2249   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2250   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
2251   for (bd = 0; bd < numBd; ++bd) {
2252     const char     *bdLabel;
2253     DMLabel         label;
2254     IS              pointIS;
2255     const PetscInt *points;
2256     const PetscInt *values;
2257     PetscInt        field, numValues, v, numPoints, p, dep, numFaces;
2258     PetscBool       isEssential;
2259     PetscObject     obj;
2260     PetscClassId    id;
2261 
2262     ierr = DMGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
2263     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
2264     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2265     if ((id != PETSCFE_CLASSID) || isEssential) continue;
2266     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
2267     for (v = 0; v < numValues; ++v) {
2268       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
2269       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
2270       if (!pointIS) continue; /* No points with that id on this process */
2271       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2272       for (p = 0, numFaces = 0; p < numPoints; ++p) {
2273         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2274         if (dep == dim-1) ++numFaces;
2275       }
2276       ierr = PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd*totDimBd,&elemMat);CHKERRQ(ierr);
2277       if (X_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
2278       for (p = 0, f = 0; p < numPoints; ++p) {
2279         const PetscInt point = points[p];
2280         PetscScalar   *x     = NULL;
2281         PetscInt       i;
2282 
2283         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2284         if (dep != dim-1) continue;
2285         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
2286         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);CHKERRQ(ierr);
2287         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
2288         ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
2289         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
2290         ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
2291         if (X_t) {
2292           ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
2293           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
2294           ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
2295         }
2296         ++f;
2297       }
2298       ierr = PetscMemzero(elemMat, numFaces*totDimBd*totDimBd * sizeof(PetscScalar));CHKERRQ(ierr);
2299       for (fieldI = 0; fieldI < Nf; ++fieldI) {
2300         PetscFE  fe;
2301         PetscInt numQuadPoints, Nb;
2302         /* Conforming batches */
2303         PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2304         /* Remainder */
2305         PetscInt Nr, offset;
2306 
2307         ierr = PetscDSGetBdDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2308         ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2309         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2310         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2311         ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2312         blockSize = Nb*numQuadPoints;
2313         batchSize = numBlocks * blockSize;
2314         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2315         numChunks = numFaces / (numBatches*batchSize);
2316         Ne        = numChunks*numBatches*batchSize;
2317         Nr        = numFaces % (numBatches*batchSize);
2318         offset    = numFaces - Nr;
2319         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2320           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, cgeom, u, u_t, NULL, NULL, t, X_tShift, elemMat);CHKERRQ(ierr);
2321           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);
2322         }
2323       }
2324       for (p = 0, f = 0; p < numPoints; ++p) {
2325         const PetscInt point = points[p];
2326 
2327         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
2328         if (dep != dim-1) continue;
2329         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDimBd, totDimBd, &elemMat[f*totDimBd*totDimBd]);CHKERRQ(ierr);}
2330         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*totDimBd*totDimBd], ADD_VALUES);CHKERRQ(ierr);
2331         ++f;
2332       }
2333       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2334       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2335       ierr = PetscFree3(u,cgeom,elemMat);CHKERRQ(ierr);
2336       if (X_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
2337     }
2338   }
2339   if (hasJac && hasPrec) {
2340     ierr = MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2341     ierr = MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2342   }
2343   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2344   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2345   if (mesh->printFEM) {
2346     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
2347     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
2348     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2349   }
2350   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2351   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
2352   if (isShell) {
2353     JacActionCtx *jctx;
2354 
2355     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
2356     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
2357   }
2358   PetscFunctionReturn(0);
2359 }
2360 
2361 
2362 #undef __FUNCT__
2363 #define __FUNCT__ "DMPlexComputeJacobianAction_Internal"
2364 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)
2365 {
2366   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2367   const char       *name  = "Jacobian";
2368   DM                dmAux, plex;
2369   Vec               A, cellgeom;
2370   PetscDS           prob, probAux = NULL;
2371   PetscQuadrature   quad;
2372   PetscSection      section, globalSection, sectionAux;
2373   PetscFECellGeom  *cgeom = NULL;
2374   PetscScalar      *cgeomScal;
2375   PetscScalar      *elemMat, *elemMatD, *u, *u_t, *a = NULL, *y, *z;
2376   PetscInt          dim, Nf, fieldI, fieldJ, numCells, c;
2377   PetscInt          totDim, totDimBd, totDimAux;
2378   PetscBool         hasDyn;
2379   PetscErrorCode    ierr;
2380 
2381   PetscFunctionBegin;
2382   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2383   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2384   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2385   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2386   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2387   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2388   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
2389   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2390   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2391   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2392   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2393   numCells = cEnd - cStart;
2394   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2395   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2396   if (dmAux) {
2397     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2398     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2399     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2400     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2401   }
2402   ierr = VecSet(Z, 0.0);CHKERRQ(ierr);
2403   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);
2404   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2405   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2406   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2407   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2408     DM dmCell;
2409 
2410     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2411     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2412     for (c = 0; c < cEnd - cStart; c++) {
2413       PetscScalar *thisgeom;
2414 
2415       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2416       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2417     }
2418   } else {
2419     cgeom = (PetscFECellGeom *) cgeomScal;
2420   }
2421   for (c = cStart; c < cEnd; ++c) {
2422     PetscScalar *x = NULL,  *x_t = NULL;
2423     PetscInt     i;
2424 
2425     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2426     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2427     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2428     if (X_t) {
2429       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2430       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2431       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2432     }
2433     if (dmAux) {
2434       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2435       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2436       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2437     }
2438     ierr = DMPlexVecGetClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2439     for (i = 0; i < totDim; ++i) y[(c-cStart)*totDim+i] = x[i];
2440     ierr = DMPlexVecRestoreClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2441   }
2442   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2443   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2444   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2445     PetscFE  fe;
2446     PetscInt numQuadPoints, Nb;
2447     /* Conforming batches */
2448     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2449     /* Remainder */
2450     PetscInt Nr, offset;
2451 
2452     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2453     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2454     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2455     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2456     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2457     blockSize = Nb*numQuadPoints;
2458     batchSize = numBlocks * blockSize;
2459     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2460     numChunks = numCells / (numBatches*batchSize);
2461     Ne        = numChunks*numBatches*batchSize;
2462     Nr        = numCells % (numBatches*batchSize);
2463     offset    = numCells - Nr;
2464     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2465       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2466       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);
2467       if (hasDyn) {
2468         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2469         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);
2470       }
2471     }
2472   }
2473   if (hasDyn) {
2474     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2475   }
2476   for (c = cStart; c < cEnd; ++c) {
2477     const PetscBLASInt M = totDim, one = 1;
2478     const PetscScalar  a = 1.0, b = 0.0;
2479 
2480     PetscStackCallBLAS("BLASgemv", BLASgemv_("N", &M, &M, &a, &elemMat[(c-cStart)*totDim*totDim], &M, &y[(c-cStart)*totDim], &one, &b, z, &one));
2481     if (mesh->printFEM > 1) {
2482       ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);
2483       ierr = DMPrintCellVector(c, "Y",  totDim, &y[(c-cStart)*totDim]);CHKERRQ(ierr);
2484       ierr = DMPrintCellVector(c, "Z",  totDim, z);CHKERRQ(ierr);
2485     }
2486     ierr = DMPlexVecSetClosure(dm, section, Z, c, z, ADD_VALUES);CHKERRQ(ierr);
2487   }
2488   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {ierr = PetscFree(cgeom);CHKERRQ(ierr);}
2489   else                                               {cgeom = NULL;}
2490   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2491   ierr = PetscFree6(u,u_t,elemMat,elemMatD,y,z);CHKERRQ(ierr);
2492   if (dmAux) {
2493     ierr = PetscFree(a);CHKERRQ(ierr);
2494     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2495   }
2496   if (mesh->printFEM) {
2497     ierr = PetscPrintf(PETSC_COMM_WORLD, "Z:\n");CHKERRQ(ierr);
2498     ierr = VecView(Z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2499   }
2500   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2501   PetscFunctionReturn(0);
2502 }
2503 
2504 #undef __FUNCT__
2505 #define __FUNCT__ "DMPlexSNESComputeJacobianFEM"
2506 /*@
2507   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2508 
2509   Input Parameters:
2510 + dm - The mesh
2511 . X  - Local input vector
2512 - user - The user context
2513 
2514   Output Parameter:
2515 . Jac  - Jacobian matrix
2516 
2517   Note:
2518   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2519   like a GPU, or vectorize on a multicore machine.
2520 
2521   Level: developer
2522 
2523 .seealso: FormFunctionLocal()
2524 @*/
2525 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2526 {
2527   PetscInt       cStart, cEnd, cEndInterior;
2528   DM             plex;
2529   PetscErrorCode ierr;
2530 
2531   PetscFunctionBegin;
2532   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2533   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2534   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2535   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2536   ierr = DMPlexComputeJacobian_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2537   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2538   PetscFunctionReturn(0);
2539 }
2540 
2541 #undef __FUNCT__
2542 #define __FUNCT__ "DMPlexSNESComputeJacobianActionFEM"
2543 /*@
2544   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.
2545 
2546   Input Parameters:
2547 + dm - The mesh
2548 . X  - Local solution vector
2549 . Y  - Local input vector
2550 - user - The user context
2551 
2552   Output Parameter:
2553 . Z - Local output vector
2554 
2555   Note:
2556   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2557   like a GPU, or vectorize on a multicore machine.
2558 
2559   Level: developer
2560 
2561 .seealso: FormFunctionLocal()
2562 @*/
2563 PetscErrorCode DMPlexSNESComputeJacobianActionFEM(DM dm, Vec X, Vec Y, Vec Z, void *user)
2564 {
2565   PetscInt       cStart, cEnd, cEndInterior;
2566   DM             plex;
2567   PetscErrorCode ierr;
2568 
2569   PetscFunctionBegin;
2570   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2571   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2572   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2573   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2574   ierr = DMPlexComputeJacobianAction_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Y, Z, user);CHKERRQ(ierr);
2575   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2576   PetscFunctionReturn(0);
2577 }
2578 
2579 #undef __FUNCT__
2580 #define __FUNCT__ "DMPlexSetSNESLocalFEM"
2581 /*@
2582   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.
2583 
2584   Input Parameters:
2585 + dm - The DM object
2586 . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see DMAddBoundary())
2587 . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
2588 - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())
2589 
2590   Level: developer
2591 @*/
2592 PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
2593 {
2594   PetscErrorCode ierr;
2595 
2596   PetscFunctionBegin;
2597   ierr = DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);CHKERRQ(ierr);
2598   ierr = DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);CHKERRQ(ierr);
2599   ierr = DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);CHKERRQ(ierr);
2600   PetscFunctionReturn(0);
2601 }
2602 
2603 #undef __FUNCT__
2604 #define __FUNCT__ "DMSNESCheckFromOptions_Internal"
2605 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)
2606 {
2607   Mat            J, M;
2608   Vec            r, b;
2609   MatNullSpace   nullSpace;
2610   PetscReal     *error, res = 0.0;
2611   PetscInt       numFields;
2612   PetscErrorCode ierr;
2613 
2614   PetscFunctionBegin;
2615   ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2616   ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
2617   M    = J;
2618   /* TODO Null space for J */
2619   /* Check discretization error */
2620   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
2621   ierr = PetscMalloc1(PetscMax(1, numFields), &error);CHKERRQ(ierr);
2622   if (numFields > 1) {
2623     PetscInt f;
2624 
2625     ierr = DMComputeL2FieldDiff(dm, 0.0, exactFuncs, ctxs, u, error);CHKERRQ(ierr);
2626     ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: [");CHKERRQ(ierr);
2627     for (f = 0; f < numFields; ++f) {
2628       if (f) {ierr = PetscPrintf(PETSC_COMM_WORLD, ", ");CHKERRQ(ierr);}
2629       if (error[f] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "%g", error[f]);CHKERRQ(ierr);}
2630       else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "< 1.0e-11");CHKERRQ(ierr);}
2631     }
2632     ierr = PetscPrintf(PETSC_COMM_WORLD, "]\n");CHKERRQ(ierr);
2633   } else {
2634     ierr = DMComputeL2Diff(dm, 0.0, exactFuncs, ctxs, u, &error[0]);CHKERRQ(ierr);
2635     if (error[0] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error[0]);CHKERRQ(ierr);}
2636     else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
2637   }
2638   ierr = PetscFree(error);CHKERRQ(ierr);
2639   /* Check residual */
2640   ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2641   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2642   ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", res);CHKERRQ(ierr);
2643   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2644   ierr = PetscObjectSetName((PetscObject) r, "Initial Residual");CHKERRQ(ierr);
2645   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"res_");CHKERRQ(ierr);
2646   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2647   /* Check Jacobian */
2648   ierr = SNESComputeJacobian(snes, u, M, M);CHKERRQ(ierr);
2649   ierr = MatGetNullSpace(J, &nullSpace);CHKERRQ(ierr);
2650   if (nullSpace) {
2651     PetscBool isNull;
2652     ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
2653     if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
2654   }
2655   ierr = VecDuplicate(u, &b);CHKERRQ(ierr);
2656   ierr = VecSet(r, 0.0);CHKERRQ(ierr);
2657   ierr = SNESComputeFunction(snes, r, b);CHKERRQ(ierr);
2658   ierr = MatMult(M, u, r);CHKERRQ(ierr);
2659   ierr = VecAXPY(r, 1.0, b);CHKERRQ(ierr);
2660   ierr = VecDestroy(&b);CHKERRQ(ierr);
2661   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2662   ierr = PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", res);CHKERRQ(ierr);
2663   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2664   ierr = PetscObjectSetName((PetscObject) r, "Au - b = Au + F(0)");CHKERRQ(ierr);
2665   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"linear_res_");CHKERRQ(ierr);
2666   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2667   ierr = VecDestroy(&r);CHKERRQ(ierr);
2668   ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
2669   ierr = MatDestroy(&J);CHKERRQ(ierr);
2670   PetscFunctionReturn(0);
2671 }
2672 
2673 #undef __FUNCT__
2674 #define __FUNCT__ "DMSNESCheckFromOptions"
2675 PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
2676 {
2677   DM             dm;
2678   Vec            sol;
2679   PetscBool      check;
2680   PetscErrorCode ierr;
2681 
2682   PetscFunctionBegin;
2683   ierr = PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);CHKERRQ(ierr);
2684   if (!check) PetscFunctionReturn(0);
2685   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
2686   ierr = VecDuplicate(u, &sol);CHKERRQ(ierr);
2687   ierr = SNESSetSolution(snes, sol);CHKERRQ(ierr);
2688   ierr = DMSNESCheckFromOptions_Internal(snes, dm, u, sol, exactFuncs, ctxs);CHKERRQ(ierr);
2689   ierr = VecDestroy(&sol);CHKERRQ(ierr);
2690   PetscFunctionReturn(0);
2691 }
2692