xref: /petsc/src/snes/utils/dmplexsnes.c (revision 7ae38d14048e535a346ba522ffbdb8e04ba6fa16)
1 #include <petsc/private/dmpleximpl.h>   /*I "petscdmplex.h" I*/
2 #include <petsc/private/snesimpl.h>     /*I "petscsnes.h"   I*/
3 #include <petscds.h>
4 #include <petscblaslapack.h>
5 #include <petsc/private/petscimpl.h>
6 #include <petsc/private/petscfeimpl.h>
7 
8 /************************** Interpolation *******************************/
9 
10 #undef __FUNCT__
11 #define __FUNCT__ "DMSNESConvertPlex"
12 static PetscErrorCode DMSNESConvertPlex(DM dm, DM *plex, PetscBool copy)
13 {
14   PetscBool      isPlex;
15   PetscErrorCode ierr;
16 
17   PetscFunctionBegin;
18   ierr = PetscObjectTypeCompare((PetscObject) dm, DMPLEX, &isPlex);CHKERRQ(ierr);
19   if (isPlex) {
20     *plex = dm;
21     ierr = PetscObjectReference((PetscObject) dm);CHKERRQ(ierr);
22   } else {
23     ierr = PetscObjectQuery((PetscObject) dm, "dm_plex", (PetscObject *) plex);CHKERRQ(ierr);
24     if (!*plex) {
25       ierr = DMConvert(dm,DMPLEX,plex);CHKERRQ(ierr);
26       ierr = PetscObjectCompose((PetscObject) dm, "dm_plex", (PetscObject) *plex);CHKERRQ(ierr);
27       if (copy) {
28         PetscInt    i;
29         PetscObject obj;
30         const char *comps[3] = {"A","dmAux","dmCh"};
31 
32         ierr = DMCopyDMSNES(dm, *plex);CHKERRQ(ierr);
33         for (i = 0; i < 3; i++) {
34           ierr = PetscObjectQuery((PetscObject) dm, comps[i], &obj);CHKERRQ(ierr);
35           ierr = PetscObjectCompose((PetscObject) *plex, comps[i], obj);CHKERRQ(ierr);
36         }
37       }
38     } else {
39       ierr = PetscObjectReference((PetscObject) *plex);CHKERRQ(ierr);
40     }
41   }
42   PetscFunctionReturn(0);
43 }
44 
45 #undef __FUNCT__
46 #define __FUNCT__ "DMInterpolationCreate"
47 PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx)
48 {
49   PetscErrorCode ierr;
50 
51   PetscFunctionBegin;
52   PetscValidPointer(ctx, 2);
53   ierr = PetscNew(ctx);CHKERRQ(ierr);
54 
55   (*ctx)->comm   = comm;
56   (*ctx)->dim    = -1;
57   (*ctx)->nInput = 0;
58   (*ctx)->points = NULL;
59   (*ctx)->cells  = NULL;
60   (*ctx)->n      = -1;
61   (*ctx)->coords = NULL;
62   PetscFunctionReturn(0);
63 }
64 
65 #undef __FUNCT__
66 #define __FUNCT__ "DMInterpolationSetDim"
67 PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim)
68 {
69   PetscFunctionBegin;
70   if ((dim < 1) || (dim > 3)) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %d", dim);
71   ctx->dim = dim;
72   PetscFunctionReturn(0);
73 }
74 
75 #undef __FUNCT__
76 #define __FUNCT__ "DMInterpolationGetDim"
77 PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim)
78 {
79   PetscFunctionBegin;
80   PetscValidIntPointer(dim, 2);
81   *dim = ctx->dim;
82   PetscFunctionReturn(0);
83 }
84 
85 #undef __FUNCT__
86 #define __FUNCT__ "DMInterpolationSetDof"
87 PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof)
88 {
89   PetscFunctionBegin;
90   if (dof < 1) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %d", dof);
91   ctx->dof = dof;
92   PetscFunctionReturn(0);
93 }
94 
95 #undef __FUNCT__
96 #define __FUNCT__ "DMInterpolationGetDof"
97 PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof)
98 {
99   PetscFunctionBegin;
100   PetscValidIntPointer(dof, 2);
101   *dof = ctx->dof;
102   PetscFunctionReturn(0);
103 }
104 
105 #undef __FUNCT__
106 #define __FUNCT__ "DMInterpolationAddPoints"
107 PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[])
108 {
109   PetscErrorCode ierr;
110 
111   PetscFunctionBegin;
112   if (ctx->dim < 0) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
113   if (ctx->points)  SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "Cannot add points multiple times yet");
114   ctx->nInput = n;
115 
116   ierr = PetscMalloc1(n*ctx->dim, &ctx->points);CHKERRQ(ierr);
117   ierr = PetscMemcpy(ctx->points, points, n*ctx->dim * sizeof(PetscReal));CHKERRQ(ierr);
118   PetscFunctionReturn(0);
119 }
120 
121 #undef __FUNCT__
122 #define __FUNCT__ "DMInterpolationSetUp"
123 PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints)
124 {
125   MPI_Comm          comm = ctx->comm;
126   PetscScalar       *a;
127   PetscInt          p, q, i;
128   PetscMPIInt       rank, size;
129   PetscErrorCode    ierr;
130   Vec               pointVec;
131   PetscSF           cellSF;
132   PetscLayout       layout;
133   PetscReal         *globalPoints;
134   PetscScalar       *globalPointsScalar;
135   const PetscInt    *ranges;
136   PetscMPIInt       *counts, *displs;
137   const PetscSFNode *foundCells;
138   const PetscInt    *foundPoints;
139   PetscMPIInt       *foundProcs, *globalProcs;
140   PetscInt          n, N, numFound;
141 
142   PetscFunctionBegin;
143   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
144   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
145   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
146   if (ctx->dim < 0) SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
147   /* Locate points */
148   n = ctx->nInput;
149   if (!redundantPoints) {
150     ierr = PetscLayoutCreate(comm, &layout);CHKERRQ(ierr);
151     ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
152     ierr = PetscLayoutSetLocalSize(layout, n);CHKERRQ(ierr);
153     ierr = PetscLayoutSetUp(layout);CHKERRQ(ierr);
154     ierr = PetscLayoutGetSize(layout, &N);CHKERRQ(ierr);
155     /* Communicate all points to all processes */
156     ierr = PetscMalloc3(N*ctx->dim,&globalPoints,size,&counts,size,&displs);CHKERRQ(ierr);
157     ierr = PetscLayoutGetRanges(layout, &ranges);CHKERRQ(ierr);
158     for (p = 0; p < size; ++p) {
159       counts[p] = (ranges[p+1] - ranges[p])*ctx->dim;
160       displs[p] = ranges[p]*ctx->dim;
161     }
162     ierr = MPI_Allgatherv(ctx->points, n*ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm);CHKERRQ(ierr);
163   } else {
164     N = n;
165     globalPoints = ctx->points;
166     counts = displs = NULL;
167     layout = NULL;
168   }
169 #if 0
170   ierr = PetscMalloc3(N,&foundCells,N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
171   /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */
172 #else
173 #if defined(PETSC_USE_COMPLEX)
174   ierr = PetscMalloc1(N,&globalPointsScalar);CHKERRQ(ierr);
175   for (i=0; i<N; i++) globalPointsScalar[i] = globalPoints[i];
176 #else
177   globalPointsScalar = globalPoints;
178 #endif
179   ierr = VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N*ctx->dim, globalPointsScalar, &pointVec);CHKERRQ(ierr);
180   ierr = PetscMalloc2(N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
181   for (p = 0; p < N; ++p) {foundProcs[p] = size;}
182   cellSF = NULL;
183   ierr = DMLocatePoints(dm, pointVec, DM_POINTLOCATION_REMOVE, &cellSF);CHKERRQ(ierr);
184   ierr = PetscSFGetGraph(cellSF,NULL,&numFound,&foundPoints,&foundCells);CHKERRQ(ierr);
185 #endif
186   for (p = 0; p < numFound; ++p) {
187     if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank;
188   }
189   /* Let the lowest rank process own each point */
190   ierr   = MPIU_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm);CHKERRQ(ierr);
191   ctx->n = 0;
192   for (p = 0; p < N; ++p) {
193     if (globalProcs[p] == size) SETERRQ4(comm, PETSC_ERR_PLIB, "Point %d: %g %g %g not located in mesh", p, globalPoints[p*ctx->dim+0], ctx->dim > 1 ? globalPoints[p*ctx->dim+1] : 0.0, ctx->dim > 2 ? globalPoints[p*ctx->dim+2] : 0.0);
194     else if (globalProcs[p] == rank) ctx->n++;
195   }
196   /* Create coordinates vector and array of owned cells */
197   ierr = PetscMalloc1(ctx->n, &ctx->cells);CHKERRQ(ierr);
198   ierr = VecCreate(comm, &ctx->coords);CHKERRQ(ierr);
199   ierr = VecSetSizes(ctx->coords, ctx->n*ctx->dim, PETSC_DECIDE);CHKERRQ(ierr);
200   ierr = VecSetBlockSize(ctx->coords, ctx->dim);CHKERRQ(ierr);
201   ierr = VecSetType(ctx->coords,VECSTANDARD);CHKERRQ(ierr);
202   ierr = VecGetArray(ctx->coords, &a);CHKERRQ(ierr);
203   for (p = 0, q = 0, i = 0; p < N; ++p) {
204     if (globalProcs[p] == rank) {
205       PetscInt d;
206 
207       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p*ctx->dim+d];
208       ctx->cells[q++] = foundCells[p].index;
209     }
210   }
211   ierr = VecRestoreArray(ctx->coords, &a);CHKERRQ(ierr);
212 #if 0
213   ierr = PetscFree3(foundCells,foundProcs,globalProcs);CHKERRQ(ierr);
214 #else
215   ierr = PetscFree2(foundProcs,globalProcs);CHKERRQ(ierr);
216   ierr = PetscSFDestroy(&cellSF);CHKERRQ(ierr);
217   ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
218 #endif
219   if ((void*)globalPointsScalar != (void*)globalPoints) {ierr = PetscFree(globalPointsScalar);CHKERRQ(ierr);}
220   if (!redundantPoints) {ierr = PetscFree3(globalPoints,counts,displs);CHKERRQ(ierr);}
221   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
222   PetscFunctionReturn(0);
223 }
224 
225 #undef __FUNCT__
226 #define __FUNCT__ "DMInterpolationGetCoordinates"
227 PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates)
228 {
229   PetscFunctionBegin;
230   PetscValidPointer(coordinates, 2);
231   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
232   *coordinates = ctx->coords;
233   PetscFunctionReturn(0);
234 }
235 
236 #undef __FUNCT__
237 #define __FUNCT__ "DMInterpolationGetVector"
238 PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v)
239 {
240   PetscErrorCode ierr;
241 
242   PetscFunctionBegin;
243   PetscValidPointer(v, 2);
244   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
245   ierr = VecCreate(ctx->comm, v);CHKERRQ(ierr);
246   ierr = VecSetSizes(*v, ctx->n*ctx->dof, PETSC_DECIDE);CHKERRQ(ierr);
247   ierr = VecSetBlockSize(*v, ctx->dof);CHKERRQ(ierr);
248   ierr = VecSetType(*v,VECSTANDARD);CHKERRQ(ierr);
249   PetscFunctionReturn(0);
250 }
251 
252 #undef __FUNCT__
253 #define __FUNCT__ "DMInterpolationRestoreVector"
254 PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v)
255 {
256   PetscErrorCode ierr;
257 
258   PetscFunctionBegin;
259   PetscValidPointer(v, 2);
260   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
261   ierr = VecDestroy(v);CHKERRQ(ierr);
262   PetscFunctionReturn(0);
263 }
264 
265 #undef __FUNCT__
266 #define __FUNCT__ "DMInterpolate_Triangle_Private"
267 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Triangle_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
268 {
269   PetscReal      *v0, *J, *invJ, detJ;
270   const PetscScalar *coords;
271   PetscScalar    *a;
272   PetscInt       p;
273   PetscErrorCode ierr;
274 
275   PetscFunctionBegin;
276   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
277   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
278   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
279   for (p = 0; p < ctx->n; ++p) {
280     PetscInt     c = ctx->cells[p];
281     PetscScalar *x = NULL;
282     PetscReal    xi[4];
283     PetscInt     d, f, comp;
284 
285     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
286     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
287     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
288     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
289 
290     for (d = 0; d < ctx->dim; ++d) {
291       xi[d] = 0.0;
292       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
293       for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] += PetscRealPart(x[(d+1)*ctx->dof+comp] - x[0*ctx->dof+comp])*xi[d];
294     }
295     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
296   }
297   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
298   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
299   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
300   PetscFunctionReturn(0);
301 }
302 
303 #undef __FUNCT__
304 #define __FUNCT__ "DMInterpolate_Tetrahedron_Private"
305 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Tetrahedron_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
306 {
307   PetscReal      *v0, *J, *invJ, detJ;
308   const PetscScalar *coords;
309   PetscScalar    *a;
310   PetscInt       p;
311   PetscErrorCode ierr;
312 
313   PetscFunctionBegin;
314   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
315   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
316   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
317   for (p = 0; p < ctx->n; ++p) {
318     PetscInt       c = ctx->cells[p];
319     const PetscInt order[3] = {2, 1, 3};
320     PetscScalar   *x = NULL;
321     PetscReal      xi[4];
322     PetscInt       d, f, comp;
323 
324     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
325     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
326     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
327     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
328 
329     for (d = 0; d < ctx->dim; ++d) {
330       xi[d] = 0.0;
331       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
332       for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] += PetscRealPart(x[order[d]*ctx->dof+comp] - x[0*ctx->dof+comp])*xi[d];
333     }
334     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
335   }
336   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
337   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
338   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
339   PetscFunctionReturn(0);
340 }
341 
342 #undef __FUNCT__
343 #define __FUNCT__ "QuadMap_Private"
344 PETSC_STATIC_INLINE PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
345 {
346   const PetscScalar *vertices = (const PetscScalar*) ctx;
347   const PetscScalar x0        = vertices[0];
348   const PetscScalar y0        = vertices[1];
349   const PetscScalar x1        = vertices[2];
350   const PetscScalar y1        = vertices[3];
351   const PetscScalar x2        = vertices[4];
352   const PetscScalar y2        = vertices[5];
353   const PetscScalar x3        = vertices[6];
354   const PetscScalar y3        = vertices[7];
355   const PetscScalar f_1       = x1 - x0;
356   const PetscScalar g_1       = y1 - y0;
357   const PetscScalar f_3       = x3 - x0;
358   const PetscScalar g_3       = y3 - y0;
359   const PetscScalar f_01      = x2 - x1 - x3 + x0;
360   const PetscScalar g_01      = y2 - y1 - y3 + y0;
361   const PetscScalar *ref;
362   PetscScalar       *real;
363   PetscErrorCode    ierr;
364 
365   PetscFunctionBegin;
366   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
367   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
368   {
369     const PetscScalar p0 = ref[0];
370     const PetscScalar p1 = ref[1];
371 
372     real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1;
373     real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1;
374   }
375   ierr = PetscLogFlops(28);CHKERRQ(ierr);
376   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
377   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
378   PetscFunctionReturn(0);
379 }
380 
381 #include <petsc/private/dmimpl.h>
382 #undef __FUNCT__
383 #define __FUNCT__ "QuadJacobian_Private"
384 PETSC_STATIC_INLINE PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
385 {
386   const PetscScalar *vertices = (const PetscScalar*) ctx;
387   const PetscScalar x0        = vertices[0];
388   const PetscScalar y0        = vertices[1];
389   const PetscScalar x1        = vertices[2];
390   const PetscScalar y1        = vertices[3];
391   const PetscScalar x2        = vertices[4];
392   const PetscScalar y2        = vertices[5];
393   const PetscScalar x3        = vertices[6];
394   const PetscScalar y3        = vertices[7];
395   const PetscScalar f_01      = x2 - x1 - x3 + x0;
396   const PetscScalar g_01      = y2 - y1 - y3 + y0;
397   const PetscScalar *ref;
398   PetscErrorCode    ierr;
399 
400   PetscFunctionBegin;
401   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
402   {
403     const PetscScalar x       = ref[0];
404     const PetscScalar y       = ref[1];
405     const PetscInt    rows[2] = {0, 1};
406     PetscScalar       values[4];
407 
408     values[0] = (x1 - x0 + f_01*y) * 0.5; values[1] = (x3 - x0 + f_01*x) * 0.5;
409     values[2] = (y1 - y0 + g_01*y) * 0.5; values[3] = (y3 - y0 + g_01*x) * 0.5;
410     ierr      = MatSetValues(J, 2, rows, 2, rows, values, INSERT_VALUES);CHKERRQ(ierr);
411   }
412   ierr = PetscLogFlops(30);CHKERRQ(ierr);
413   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
414   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
415   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
416   PetscFunctionReturn(0);
417 }
418 
419 #undef __FUNCT__
420 #define __FUNCT__ "DMInterpolate_Quad_Private"
421 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
422 {
423   DM             dmCoord;
424   PetscFE        fem = NULL;
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       Nf, p;
433   const PetscInt dof = ctx->dof;
434   PetscErrorCode ierr;
435 
436   PetscFunctionBegin;
437   ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
438   if (Nf) {ierr = DMGetField(dm, 0, (PetscObject *) &fem);CHKERRQ(ierr);}
439   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
440   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
441   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
442   ierr = SNESSetOptionsPrefix(snes, "quad_interp_");CHKERRQ(ierr);
443   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
444   ierr = VecSetSizes(r, 2, 2);CHKERRQ(ierr);
445   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
446   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
447   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
448   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
449   ierr = MatSetSizes(J, 2, 2, 2, 2);CHKERRQ(ierr);
450   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
451   ierr = MatSetUp(J);CHKERRQ(ierr);
452   ierr = SNESSetFunction(snes, r, QuadMap_Private, NULL);CHKERRQ(ierr);
453   ierr = SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);CHKERRQ(ierr);
454   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
455   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
456   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
457   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
458 
459   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
460   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
461   for (p = 0; p < ctx->n; ++p) {
462     PetscScalar *x = NULL, *vertices = NULL;
463     PetscScalar *xi;
464     PetscReal    xir[2];
465     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
466 
467     /* Can make this do all points at once */
468     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
469     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 4*2);
470     ierr   = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
471     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
472     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
473     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
474     xi[0]  = coords[p*ctx->dim+0];
475     xi[1]  = coords[p*ctx->dim+1];
476     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
477     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
478     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
479     xir[0] = PetscRealPart(xi[0]);
480     xir[1] = PetscRealPart(xi[1]);
481     if (4*dof != xSize) {
482       PetscReal *B;
483       PetscInt   d;
484 
485       xir[0] = 2.0*xir[0] - 1.0; xir[1] = 2.0*xir[1] - 1.0;
486       ierr = PetscFEGetTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
487       for (comp = 0; comp < dof; ++comp) {
488         a[p*dof+comp] = 0.0;
489         for (d = 0; d < xSize/dof; ++d) {
490           a[p*dof+comp] += x[d*dof+comp]*B[d*dof+comp];
491         }
492       }
493       ierr = PetscFERestoreTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
494     } else {
495       for (comp = 0; comp < dof; ++comp)
496         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];
497     }
498     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
499     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
500     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
501   }
502   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
503   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
504 
505   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
506   ierr = VecDestroy(&r);CHKERRQ(ierr);
507   ierr = VecDestroy(&ref);CHKERRQ(ierr);
508   ierr = VecDestroy(&real);CHKERRQ(ierr);
509   ierr = MatDestroy(&J);CHKERRQ(ierr);
510   PetscFunctionReturn(0);
511 }
512 
513 #undef __FUNCT__
514 #define __FUNCT__ "HexMap_Private"
515 PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
516 {
517   const PetscScalar *vertices = (const PetscScalar*) ctx;
518   const PetscScalar x0        = vertices[0];
519   const PetscScalar y0        = vertices[1];
520   const PetscScalar z0        = vertices[2];
521   const PetscScalar x1        = vertices[9];
522   const PetscScalar y1        = vertices[10];
523   const PetscScalar z1        = vertices[11];
524   const PetscScalar x2        = vertices[6];
525   const PetscScalar y2        = vertices[7];
526   const PetscScalar z2        = vertices[8];
527   const PetscScalar x3        = vertices[3];
528   const PetscScalar y3        = vertices[4];
529   const PetscScalar z3        = vertices[5];
530   const PetscScalar x4        = vertices[12];
531   const PetscScalar y4        = vertices[13];
532   const PetscScalar z4        = vertices[14];
533   const PetscScalar x5        = vertices[15];
534   const PetscScalar y5        = vertices[16];
535   const PetscScalar z5        = vertices[17];
536   const PetscScalar x6        = vertices[18];
537   const PetscScalar y6        = vertices[19];
538   const PetscScalar z6        = vertices[20];
539   const PetscScalar x7        = vertices[21];
540   const PetscScalar y7        = vertices[22];
541   const PetscScalar z7        = vertices[23];
542   const PetscScalar f_1       = x1 - x0;
543   const PetscScalar g_1       = y1 - y0;
544   const PetscScalar h_1       = z1 - z0;
545   const PetscScalar f_3       = x3 - x0;
546   const PetscScalar g_3       = y3 - y0;
547   const PetscScalar h_3       = z3 - z0;
548   const PetscScalar f_4       = x4 - x0;
549   const PetscScalar g_4       = y4 - y0;
550   const PetscScalar h_4       = z4 - z0;
551   const PetscScalar f_01      = x2 - x1 - x3 + x0;
552   const PetscScalar g_01      = y2 - y1 - y3 + y0;
553   const PetscScalar h_01      = z2 - z1 - z3 + z0;
554   const PetscScalar f_12      = x7 - x3 - x4 + x0;
555   const PetscScalar g_12      = y7 - y3 - y4 + y0;
556   const PetscScalar h_12      = z7 - z3 - z4 + z0;
557   const PetscScalar f_02      = x5 - x1 - x4 + x0;
558   const PetscScalar g_02      = y5 - y1 - y4 + y0;
559   const PetscScalar h_02      = z5 - z1 - z4 + z0;
560   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
561   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
562   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
563   const PetscScalar *ref;
564   PetscScalar       *real;
565   PetscErrorCode    ierr;
566 
567   PetscFunctionBegin;
568   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
569   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
570   {
571     const PetscScalar p0 = ref[0];
572     const PetscScalar p1 = ref[1];
573     const PetscScalar p2 = ref[2];
574 
575     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;
576     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;
577     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;
578   }
579   ierr = PetscLogFlops(114);CHKERRQ(ierr);
580   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
581   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
582   PetscFunctionReturn(0);
583 }
584 
585 #undef __FUNCT__
586 #define __FUNCT__ "HexJacobian_Private"
587 PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
588 {
589   const PetscScalar *vertices = (const PetscScalar*) ctx;
590   const PetscScalar x0        = vertices[0];
591   const PetscScalar y0        = vertices[1];
592   const PetscScalar z0        = vertices[2];
593   const PetscScalar x1        = vertices[9];
594   const PetscScalar y1        = vertices[10];
595   const PetscScalar z1        = vertices[11];
596   const PetscScalar x2        = vertices[6];
597   const PetscScalar y2        = vertices[7];
598   const PetscScalar z2        = vertices[8];
599   const PetscScalar x3        = vertices[3];
600   const PetscScalar y3        = vertices[4];
601   const PetscScalar z3        = vertices[5];
602   const PetscScalar x4        = vertices[12];
603   const PetscScalar y4        = vertices[13];
604   const PetscScalar z4        = vertices[14];
605   const PetscScalar x5        = vertices[15];
606   const PetscScalar y5        = vertices[16];
607   const PetscScalar z5        = vertices[17];
608   const PetscScalar x6        = vertices[18];
609   const PetscScalar y6        = vertices[19];
610   const PetscScalar z6        = vertices[20];
611   const PetscScalar x7        = vertices[21];
612   const PetscScalar y7        = vertices[22];
613   const PetscScalar z7        = vertices[23];
614   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
615   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
616   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
617   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
618   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
619   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
620   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
621   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
622   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
623   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
624   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
625   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
626   const PetscScalar *ref;
627   PetscErrorCode    ierr;
628 
629   PetscFunctionBegin;
630   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
631   {
632     const PetscScalar x       = ref[0];
633     const PetscScalar y       = ref[1];
634     const PetscScalar z       = ref[2];
635     const PetscInt    rows[3] = {0, 1, 2};
636     PetscScalar       values[9];
637 
638     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
639     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
640     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
641     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
642     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
643     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
644     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
645     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
646     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;
647 
648     ierr = MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);CHKERRQ(ierr);
649   }
650   ierr = PetscLogFlops(152);CHKERRQ(ierr);
651   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
652   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
653   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
654   PetscFunctionReturn(0);
655 }
656 
657 #undef __FUNCT__
658 #define __FUNCT__ "DMInterpolate_Hex_Private"
659 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
660 {
661   DM             dmCoord;
662   SNES           snes;
663   KSP            ksp;
664   PC             pc;
665   Vec            coordsLocal, r, ref, real;
666   Mat            J;
667   const PetscScalar *coords;
668   PetscScalar    *a;
669   PetscInt       p;
670   PetscErrorCode ierr;
671 
672   PetscFunctionBegin;
673   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
674   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
675   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
676   ierr = SNESSetOptionsPrefix(snes, "hex_interp_");CHKERRQ(ierr);
677   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
678   ierr = VecSetSizes(r, 3, 3);CHKERRQ(ierr);
679   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
680   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
681   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
682   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
683   ierr = MatSetSizes(J, 3, 3, 3, 3);CHKERRQ(ierr);
684   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
685   ierr = MatSetUp(J);CHKERRQ(ierr);
686   ierr = SNESSetFunction(snes, r, HexMap_Private, NULL);CHKERRQ(ierr);
687   ierr = SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);CHKERRQ(ierr);
688   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
689   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
690   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
691   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
692 
693   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
694   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
695   for (p = 0; p < ctx->n; ++p) {
696     PetscScalar *x = NULL, *vertices = NULL;
697     PetscScalar *xi;
698     PetscReal    xir[3];
699     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
700 
701     /* Can make this do all points at once */
702     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
703     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 8*3);
704     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
705     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 8*ctx->dof);
706     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
707     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
708     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
709     xi[0]  = coords[p*ctx->dim+0];
710     xi[1]  = coords[p*ctx->dim+1];
711     xi[2]  = coords[p*ctx->dim+2];
712     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
713     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
714     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
715     xir[0] = PetscRealPart(xi[0]);
716     xir[1] = PetscRealPart(xi[1]);
717     xir[2] = PetscRealPart(xi[2]);
718     for (comp = 0; comp < ctx->dof; ++comp) {
719       a[p*ctx->dof+comp] =
720         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
721         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
722         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
723         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
724         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
725         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
726         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
727         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
728     }
729     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
730     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
731     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
732   }
733   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
734   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
735 
736   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
737   ierr = VecDestroy(&r);CHKERRQ(ierr);
738   ierr = VecDestroy(&ref);CHKERRQ(ierr);
739   ierr = VecDestroy(&real);CHKERRQ(ierr);
740   ierr = MatDestroy(&J);CHKERRQ(ierr);
741   PetscFunctionReturn(0);
742 }
743 
744 #undef __FUNCT__
745 #define __FUNCT__ "DMInterpolationEvaluate"
746 /*
747   Input Parameters:
748 + ctx - The DMInterpolationInfo context
749 . dm  - The DM
750 - x   - The local vector containing the field to be interpolated
751 
752   Output Parameters:
753 . v   - The vector containing the interpolated values
754 */
755 PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
756 {
757   PetscInt       dim, coneSize, n;
758   PetscErrorCode ierr;
759 
760   PetscFunctionBegin;
761   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
762   PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
763   PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
764   ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
765   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);
766   if (n) {
767     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
768     ierr = DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);CHKERRQ(ierr);
769     if (dim == 2) {
770       if (coneSize == 3) {
771         ierr = DMInterpolate_Triangle_Private(ctx, dm, x, v);CHKERRQ(ierr);
772       } else if (coneSize == 4) {
773         ierr = DMInterpolate_Quad_Private(ctx, dm, x, v);CHKERRQ(ierr);
774       } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
775     } else if (dim == 3) {
776       if (coneSize == 4) {
777         ierr = DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);CHKERRQ(ierr);
778       } else {
779         ierr = DMInterpolate_Hex_Private(ctx, dm, x, v);CHKERRQ(ierr);
780       }
781     } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
782   }
783   PetscFunctionReturn(0);
784 }
785 
786 #undef __FUNCT__
787 #define __FUNCT__ "DMInterpolationDestroy"
788 PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
789 {
790   PetscErrorCode ierr;
791 
792   PetscFunctionBegin;
793   PetscValidPointer(ctx, 2);
794   ierr = VecDestroy(&(*ctx)->coords);CHKERRQ(ierr);
795   ierr = PetscFree((*ctx)->points);CHKERRQ(ierr);
796   ierr = PetscFree((*ctx)->cells);CHKERRQ(ierr);
797   ierr = PetscFree(*ctx);CHKERRQ(ierr);
798   *ctx = NULL;
799   PetscFunctionReturn(0);
800 }
801 
802 #undef __FUNCT__
803 #define __FUNCT__ "SNESMonitorFields"
804 /*@C
805   SNESMonitorFields - Monitors the residual for each field separately
806 
807   Collective on SNES
808 
809   Input Parameters:
810 + snes   - the SNES context
811 . its    - iteration number
812 . fgnorm - 2-norm of residual
813 - vf  - PetscViewerAndFormat of type ASCII
814 
815   Notes:
816   This routine prints the residual norm at each iteration.
817 
818   Level: intermediate
819 
820 .keywords: SNES, nonlinear, default, monitor, norm
821 .seealso: SNESMonitorSet(), SNESMonitorDefault()
822 @*/
823 PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
824 {
825   PetscViewer        viewer = vf->viewer;
826   Vec                res;
827   DM                 dm;
828   PetscSection       s;
829   const PetscScalar *r;
830   PetscReal         *lnorms, *norms;
831   PetscInt           numFields, f, pStart, pEnd, p;
832   PetscErrorCode     ierr;
833 
834   PetscFunctionBegin;
835   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
836   ierr = SNESGetFunction(snes, &res, 0, 0);CHKERRQ(ierr);
837   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
838   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
839   ierr = PetscSectionGetNumFields(s, &numFields);CHKERRQ(ierr);
840   ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
841   ierr = PetscCalloc2(numFields, &lnorms, numFields, &norms);CHKERRQ(ierr);
842   ierr = VecGetArrayRead(res, &r);CHKERRQ(ierr);
843   for (p = pStart; p < pEnd; ++p) {
844     for (f = 0; f < numFields; ++f) {
845       PetscInt fdof, foff, d;
846 
847       ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
848       ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
849       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
850     }
851   }
852   ierr = VecRestoreArrayRead(res, &r);CHKERRQ(ierr);
853   ierr = MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
854   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
855   ierr = PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
856   ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
857   for (f = 0; f < numFields; ++f) {
858     if (f > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
859     ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));CHKERRQ(ierr);
860   }
861   ierr = PetscViewerASCIIPrintf(viewer, "]\n");CHKERRQ(ierr);
862   ierr = PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
863   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
864   ierr = PetscFree2(lnorms, norms);CHKERRQ(ierr);
865   PetscFunctionReturn(0);
866 }
867 
868 /********************* Residual Computation **************************/
869 
870 #undef __FUNCT__
871 #define __FUNCT__ "DMPlexSNESGetGeometryFEM"
872 /*@
873   DMPlexSNESGetGeometryFEM - Return precomputed geometric data
874 
875   Input Parameter:
876 . dm - The DM
877 
878   Output Parameters:
879 . cellgeom - The values precomputed from cell geometry
880 
881   Level: developer
882 
883 .seealso: DMPlexSNESSetFunctionLocal()
884 @*/
885 PetscErrorCode DMPlexSNESGetGeometryFEM(DM dm, Vec *cellgeom)
886 {
887   DMSNES         dmsnes;
888   PetscObject    obj;
889   PetscErrorCode ierr;
890 
891   PetscFunctionBegin;
892   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
893   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
894   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", &obj);CHKERRQ(ierr);
895   if (!obj) {
896     Vec cellgeom;
897 
898     ierr = DMPlexComputeGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
899     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject) cellgeom);CHKERRQ(ierr);
900     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
901   }
902   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject *) cellgeom);CHKERRQ(ierr);}
903   PetscFunctionReturn(0);
904 }
905 
906 #undef __FUNCT__
907 #define __FUNCT__ "DMPlexSNESGetGeometryFVM"
908 /*@
909   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
910 
911   Input Parameter:
912 . dm - The DM
913 
914   Output Parameters:
915 + facegeom - The values precomputed from face geometry
916 . cellgeom - The values precomputed from cell geometry
917 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
918 
919   Level: developer
920 
921 .seealso: DMPlexTSSetRHSFunctionLocal()
922 @*/
923 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
924 {
925   DM             plex;
926   PetscErrorCode ierr;
927 
928   PetscFunctionBegin;
929   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
930   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
931   ierr = DMPlexGetDataFVM(plex, NULL, cellgeom, facegeom, NULL);CHKERRQ(ierr);
932   if (minRadius) {ierr = DMPlexGetMinRadius(plex, minRadius);CHKERRQ(ierr);}
933   ierr = DMDestroy(&plex);CHKERRQ(ierr);
934   PetscFunctionReturn(0);
935 }
936 
937 #undef __FUNCT__
938 #define __FUNCT__ "DMPlexSNESGetGradientDM"
939 /*@
940   DMPlexSNESGetGradientDM - Return gradient data layout
941 
942   Input Parameters:
943 + dm - The DM
944 - fv - The PetscFV
945 
946   Output Parameter:
947 . dmGrad - The layout for gradient values
948 
949   Level: developer
950 
951 .seealso: DMPlexSNESGetGeometryFVM()
952 @*/
953 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
954 {
955   DM             plex;
956   PetscBool      computeGradients;
957   PetscErrorCode ierr;
958 
959   PetscFunctionBegin;
960   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
961   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
962   PetscValidPointer(dmGrad,3);
963   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
964   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
965   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
966   ierr = DMPlexGetDataFVM(plex, fv, NULL, NULL, dmGrad);CHKERRQ(ierr);
967   ierr = DMDestroy(&plex);CHKERRQ(ierr);
968   PetscFunctionReturn(0);
969 }
970 
971 #undef __FUNCT__
972 #define __FUNCT__ "DMPlexGetCellFields"
973 /*@C
974   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells
975 
976   Input Parameters:
977 + dm     - The DM
978 . cStart - The first cell to include
979 . cEnd   - The first cell to exclude
980 . locX   - A local vector with the solution fields
981 . locX_t - A local vector with solution field time derivatives, or NULL
982 - locA   - A local vector with auxiliary fields, or NULL
983 
984   Output Parameters:
985 + u   - The field coefficients
986 . u_t - The fields derivative coefficients
987 - a   - The auxiliary field coefficients
988 
989   Level: developer
990 
991 .seealso: DMPlexGetFaceFields()
992 @*/
993 PetscErrorCode DMPlexGetCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
994 {
995   DM             dmAux;
996   PetscSection   section, sectionAux;
997   PetscDS        prob;
998   PetscInt       numCells = cEnd - cStart, totDim, totDimAux, c;
999   PetscErrorCode ierr;
1000 
1001   PetscFunctionBegin;
1002   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1003   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1004   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1005   if (locA)   {PetscValidHeaderSpecific(locA, VEC_CLASSID, 6);}
1006   PetscValidPointer(u, 7);
1007   PetscValidPointer(u_t, 8);
1008   PetscValidPointer(a, 9);
1009   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1010   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1011   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1012   if (locA) {
1013     PetscDS probAux;
1014 
1015     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1016     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1017     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1018     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1019   }
1020   ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u);CHKERRQ(ierr);
1021   if (locX_t) {ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u_t);CHKERRQ(ierr);} else {*u_t = NULL;}
1022   if (locA)   {ierr = DMGetWorkArray(dm, numCells*totDimAux, PETSC_SCALAR, a);CHKERRQ(ierr);} else {*a = NULL;}
1023   for (c = cStart; c < cEnd; ++c) {
1024     PetscScalar *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
1025     PetscInt     i;
1026 
1027     ierr = DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1028     for (i = 0; i < totDim; ++i) ul[(c-cStart)*totDim+i] = x[i];
1029     ierr = DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1030     if (locX_t) {
1031       ierr = DMPlexVecGetClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1032       for (i = 0; i < totDim; ++i) ul_t[(c-cStart)*totDim+i] = x_t[i];
1033       ierr = DMPlexVecRestoreClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1034     }
1035     if (locA) {
1036       DM dmAuxPlex;
1037 
1038       ierr = DMSNESConvertPlex(dmAux, &dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1039       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1040       for (i = 0; i < totDimAux; ++i) al[(c-cStart)*totDimAux+i] = x[i];
1041       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1042       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1043     }
1044   }
1045   PetscFunctionReturn(0);
1046 }
1047 
1048 #undef __FUNCT__
1049 #define __FUNCT__ "DMPlexRestoreCellFields"
1050 /*@C
1051   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells
1052 
1053   Input Parameters:
1054 + dm     - The DM
1055 . cStart - The first cell to include
1056 . cEnd   - The first cell to exclude
1057 . locX   - A local vector with the solution fields
1058 . locX_t - A local vector with solution field time derivatives, or NULL
1059 - locA   - A local vector with auxiliary fields, or NULL
1060 
1061   Output Parameters:
1062 + u   - The field coefficients
1063 . u_t - The fields derivative coefficients
1064 - a   - The auxiliary field coefficients
1065 
1066   Level: developer
1067 
1068 .seealso: DMPlexGetFaceFields()
1069 @*/
1070 PetscErrorCode DMPlexRestoreCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1071 {
1072   PetscErrorCode ierr;
1073 
1074   PetscFunctionBegin;
1075   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u);CHKERRQ(ierr);
1076   if (*u_t) {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u_t);CHKERRQ(ierr);}
1077   if (*a)   {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, a);CHKERRQ(ierr);}
1078   PetscFunctionReturn(0);
1079 }
1080 
1081 #undef __FUNCT__
1082 #define __FUNCT__ "DMPlexGetFaceFields"
1083 /*@C
1084   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces
1085 
1086   Input Parameters:
1087 + dm     - The DM
1088 . fStart - The first face to include
1089 . fEnd   - The first face to exclude
1090 . locX   - A local vector with the solution fields
1091 . locX_t - A local vector with solution field time derivatives, or NULL
1092 . faceGeometry - A local vector with face geometry
1093 . cellGeometry - A local vector with cell geometry
1094 - locaGrad - A local vector with field gradients, or NULL
1095 
1096   Output Parameters:
1097 + Nface - The number of faces with field values
1098 . uL - The field values at the left side of the face
1099 - uR - The field values at the right side of the face
1100 
1101   Level: developer
1102 
1103 .seealso: DMPlexGetCellFields()
1104 @*/
1105 PetscErrorCode DMPlexGetFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscInt *Nface, PetscScalar **uL, PetscScalar **uR)
1106 {
1107   DM                 dmFace, dmCell, dmGrad = NULL;
1108   PetscSection       section;
1109   PetscDS            prob;
1110   DMLabel            ghostLabel;
1111   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
1112   PetscBool         *isFE;
1113   PetscInt           dim, Nf, f, Nc, numFaces = fEnd - fStart, iface, face;
1114   PetscErrorCode     ierr;
1115 
1116   PetscFunctionBegin;
1117   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1118   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1119   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1120   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 6);
1121   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 7);
1122   if (locGrad) {PetscValidHeaderSpecific(locGrad, VEC_CLASSID, 8);}
1123   PetscValidPointer(uL, 9);
1124   PetscValidPointer(uR, 10);
1125   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1126   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1127   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1128   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1129   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1130   ierr = PetscMalloc1(Nf, &isFE);CHKERRQ(ierr);
1131   for (f = 0; f < Nf; ++f) {
1132     PetscObject  obj;
1133     PetscClassId id;
1134 
1135     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1136     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1137     if (id == PETSCFE_CLASSID)      {isFE[f] = PETSC_TRUE;}
1138     else if (id == PETSCFV_CLASSID) {isFE[f] = PETSC_FALSE;}
1139     else                            {isFE[f] = PETSC_FALSE;}
1140   }
1141   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1142   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1143   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1144   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1145   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1146   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1147   if (locGrad) {
1148     ierr = VecGetDM(locGrad, &dmGrad);CHKERRQ(ierr);
1149     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1150   }
1151   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uL);CHKERRQ(ierr);
1152   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uR);CHKERRQ(ierr);
1153   /* Right now just eat the extra work for FE (could make a cell loop) */
1154   for (face = fStart, iface = 0; face < fEnd; ++face) {
1155     const PetscInt        *cells;
1156     PetscFVFaceGeom       *fg;
1157     PetscFVCellGeom       *cgL, *cgR;
1158     PetscScalar           *xL, *xR, *gL, *gR;
1159     PetscScalar           *uLl = *uL, *uRl = *uR;
1160     PetscInt               ghost, nsupp, nchild;
1161 
1162     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1163     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1164     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1165     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1166     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1167     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1168     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1169     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1170     for (f = 0; f < Nf; ++f) {
1171       PetscInt off;
1172 
1173       ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1174       if (isFE[f]) {
1175         const PetscInt *cone;
1176         PetscInt        comp, coneSizeL, coneSizeR, faceLocL, faceLocR, ldof, rdof, d;
1177 
1178         xL = xR = NULL;
1179         ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1180         ierr = DMPlexVecGetClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1181         ierr = DMPlexVecGetClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1182         ierr = DMPlexGetCone(dm, cells[0], &cone);CHKERRQ(ierr);
1183         ierr = DMPlexGetConeSize(dm, cells[0], &coneSizeL);CHKERRQ(ierr);
1184         for (faceLocL = 0; faceLocL < coneSizeL; ++faceLocL) if (cone[faceLocL] == face) break;
1185         ierr = DMPlexGetCone(dm, cells[1], &cone);CHKERRQ(ierr);
1186         ierr = DMPlexGetConeSize(dm, cells[1], &coneSizeR);CHKERRQ(ierr);
1187         for (faceLocR = 0; faceLocR < coneSizeR; ++faceLocR) if (cone[faceLocR] == face) break;
1188         if (faceLocL == coneSizeL && faceLocR == coneSizeR) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of cell %d or cell %d", face, cells[0], cells[1]);
1189         /* Check that FEM field has values in the right cell (sometimes its an FV ghost cell) */
1190         /* TODO: this is a hack that might not be right for nonconforming */
1191         if (faceLocL < coneSizeL) {
1192           ierr = EvaluateFaceFields(prob, f, faceLocL, xL, &uLl[iface*Nc+off]);CHKERRQ(ierr);
1193           if (rdof == ldof && faceLocR < coneSizeR) {ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);}
1194           else              {for(d = 0; d < comp; ++d) uRl[iface*Nc+off+d] = uLl[iface*Nc+off+d];}
1195         }
1196         else {
1197           ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);
1198           ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1199           for(d = 0; d < comp; ++d) uLl[iface*Nc+off+d] = uRl[iface*Nc+off+d];
1200         }
1201         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1202         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1203       } else {
1204         PetscFV  fv;
1205         PetscInt numComp, c;
1206 
1207         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fv);CHKERRQ(ierr);
1208         ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1209         ierr = DMPlexPointLocalFieldRead(dm, cells[0], f, x, &xL);CHKERRQ(ierr);
1210         ierr = DMPlexPointLocalFieldRead(dm, cells[1], f, x, &xR);CHKERRQ(ierr);
1211         if (dmGrad) {
1212           PetscReal dxL[3], dxR[3];
1213 
1214           ierr = DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);CHKERRQ(ierr);
1215           ierr = DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);CHKERRQ(ierr);
1216           DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
1217           DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
1218           for (c = 0; c < numComp; ++c) {
1219             uLl[iface*Nc+off+c] = xL[c] + DMPlex_DotD_Internal(dim, &gL[c*dim], dxL);
1220             uRl[iface*Nc+off+c] = xR[c] + DMPlex_DotD_Internal(dim, &gR[c*dim], dxR);
1221           }
1222         } else {
1223           for (c = 0; c < numComp; ++c) {
1224             uLl[iface*Nc+off+c] = xL[c];
1225             uRl[iface*Nc+off+c] = xR[c];
1226           }
1227         }
1228       }
1229     }
1230     ++iface;
1231   }
1232   *Nface = iface;
1233   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1234   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1235   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1236   if (locGrad) {
1237     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1238   }
1239   ierr = PetscFree(isFE);CHKERRQ(ierr);
1240   PetscFunctionReturn(0);
1241 }
1242 
1243 #undef __FUNCT__
1244 #define __FUNCT__ "DMPlexRestoreFaceFields"
1245 /*@C
1246   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces
1247 
1248   Input Parameters:
1249 + dm     - The DM
1250 . fStart - The first face to include
1251 . fEnd   - The first face to exclude
1252 . locX   - A local vector with the solution fields
1253 . locX_t - A local vector with solution field time derivatives, or NULL
1254 . faceGeometry - A local vector with face geometry
1255 . cellGeometry - A local vector with cell geometry
1256 - locaGrad - A local vector with field gradients, or NULL
1257 
1258   Output Parameters:
1259 + Nface - The number of faces with field values
1260 . uL - The field values at the left side of the face
1261 - uR - The field values at the right side of the face
1262 
1263   Level: developer
1264 
1265 .seealso: DMPlexGetFaceFields()
1266 @*/
1267 PetscErrorCode DMPlexRestoreFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscInt *Nface, PetscScalar **uL, PetscScalar **uR)
1268 {
1269   PetscErrorCode ierr;
1270 
1271   PetscFunctionBegin;
1272   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uL);CHKERRQ(ierr);
1273   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uR);CHKERRQ(ierr);
1274   PetscFunctionReturn(0);
1275 }
1276 
1277 #undef __FUNCT__
1278 #define __FUNCT__ "DMPlexGetFaceGeometry"
1279 /*@C
1280   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces
1281 
1282   Input Parameters:
1283 + dm     - The DM
1284 . fStart - The first face to include
1285 . fEnd   - The first face to exclude
1286 . faceGeometry - A local vector with face geometry
1287 - cellGeometry - A local vector with cell geometry
1288 
1289   Output Parameters:
1290 + Nface - The number of faces with field values
1291 . fgeom - The extract the face centroid and normal
1292 - vol   - The cell volume
1293 
1294   Level: developer
1295 
1296 .seealso: DMPlexGetCellFields()
1297 @*/
1298 PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1299 {
1300   DM                 dmFace, dmCell;
1301   DMLabel            ghostLabel;
1302   const PetscScalar *facegeom, *cellgeom;
1303   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
1304   PetscErrorCode     ierr;
1305 
1306   PetscFunctionBegin;
1307   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1308   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 4);
1309   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 5);
1310   PetscValidPointer(fgeom, 6);
1311   PetscValidPointer(vol, 7);
1312   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1313   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1314   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1315   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1316   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1317   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1318   ierr = PetscMalloc1(numFaces, fgeom);CHKERRQ(ierr);
1319   ierr = DMGetWorkArray(dm, numFaces*2, PETSC_SCALAR, vol);CHKERRQ(ierr);
1320   for (face = fStart, iface = 0; face < fEnd; ++face) {
1321     const PetscInt        *cells;
1322     PetscFVFaceGeom       *fg;
1323     PetscFVCellGeom       *cgL, *cgR;
1324     PetscFVFaceGeom       *fgeoml = *fgeom;
1325     PetscReal             *voll   = *vol;
1326     PetscInt               ghost, d, nchild, nsupp;
1327 
1328     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1329     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1330     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1331     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1332     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1333     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1334     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1335     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1336     for (d = 0; d < dim; ++d) {
1337       fgeoml[iface].centroid[d] = fg->centroid[d];
1338       fgeoml[iface].normal[d]   = fg->normal[d];
1339     }
1340     voll[iface*2+0] = cgL->volume;
1341     voll[iface*2+1] = cgR->volume;
1342     ++iface;
1343   }
1344   *Nface = iface;
1345   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1346   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1347   PetscFunctionReturn(0);
1348 }
1349 
1350 #undef __FUNCT__
1351 #define __FUNCT__ "DMPlexRestoreFaceGeometry"
1352 /*@C
1353   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces
1354 
1355   Input Parameters:
1356 + dm     - The DM
1357 . fStart - The first face to include
1358 . fEnd   - The first face to exclude
1359 . faceGeometry - A local vector with face geometry
1360 - cellGeometry - A local vector with cell geometry
1361 
1362   Output Parameters:
1363 + Nface - The number of faces with field values
1364 . fgeom - The extract the face centroid and normal
1365 - vol   - The cell volume
1366 
1367   Level: developer
1368 
1369 .seealso: DMPlexGetFaceFields()
1370 @*/
1371 PetscErrorCode DMPlexRestoreFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1372 {
1373   PetscErrorCode ierr;
1374 
1375   PetscFunctionBegin;
1376   ierr = PetscFree(*fgeom);CHKERRQ(ierr);
1377   ierr = DMRestoreWorkArray(dm, 0, PETSC_REAL, vol);CHKERRQ(ierr);
1378   PetscFunctionReturn(0);
1379 }
1380 
1381 #undef __FUNCT__
1382 #define __FUNCT__ "DMPlexComputeBdResidual_Internal"
1383 PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1384 {
1385   DM_Plex         *mesh = (DM_Plex *) dm->data;
1386   DM               dmAux = NULL, plex = NULL;
1387   PetscSection     section, sectionAux = NULL;
1388   PetscDS          prob, probAux = NULL;
1389   DMLabel          depth;
1390   Vec              locA = NULL;
1391   PetscFEFaceGeom *fgeom;
1392   PetscScalar     *u = NULL, *u_t = NULL, *a = NULL, *elemVec = NULL;
1393   PetscInt         dim, totDim, totDimAux, numBd, bd;
1394   PetscErrorCode   ierr;
1395 
1396   PetscFunctionBegin;
1397   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1398   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1399   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1400   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1401   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1402   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
1403   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1404   if (locA) {
1405     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1406     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
1407     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
1408     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1409     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1410   }
1411   for (bd = 0; bd < numBd; ++bd) {
1412     DMBoundaryConditionType type;
1413     const char             *bdLabel;
1414     DMLabel                 label;
1415     IS                      pointIS;
1416     const PetscInt         *points;
1417     const PetscInt         *values;
1418     PetscInt                field, numValues, v, numPoints, p, dep, numFaces, face;
1419     PetscObject             obj;
1420     PetscClassId            id;
1421 
1422     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1423     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
1424     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1425     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
1426     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1427     for (v = 0; v < numValues; ++v) {
1428       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
1429       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1430       if (!pointIS) continue; /* No points with that id on this process */
1431       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1432       for (p = 0, numFaces = 0; p < numPoints; ++p) {
1433         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1434         if (dep == dim-1) ++numFaces;
1435       }
1436       ierr = PetscMalloc4(numFaces*totDim,&u,locX_t ? numFaces*totDim : 0, &u_t, numFaces,&fgeom, numFaces*totDim,&elemVec);CHKERRQ(ierr);
1437       if (locA) {ierr = PetscMalloc1(numFaces*totDimAux,&a);CHKERRQ(ierr);}
1438       for (p = 0, face = 0; p < numPoints; ++p) {
1439         const PetscInt point = points[p], *support, *cone;
1440         PetscScalar   *x     = NULL;
1441         PetscReal      dummyJ[9], dummyDetJ;
1442         PetscInt       i, coneSize, faceLoc;
1443 
1444         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1445         if (dep != dim-1) continue;
1446         ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
1447         ierr = DMPlexComputeCellGeometryFEM(dm, support[0], NULL, NULL, dummyJ, fgeom[face].invJ[0], &dummyDetJ);CHKERRQ(ierr);
1448         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, fgeom[face].v0, fgeom[face].J, NULL, &fgeom[face].detJ);CHKERRQ(ierr);
1449         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, fgeom[face].n);CHKERRQ(ierr);
1450         if (fgeom[face].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", fgeom[face].detJ, point);
1451         ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
1452         ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
1453         for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
1454         if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of support[0] %d", point, support[0]);
1455         fgeom[face].face[0] = faceLoc;
1456         ierr = DMPlexVecGetClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1457         for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
1458         ierr = DMPlexVecRestoreClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1459         if (locX_t) {
1460           ierr = DMPlexVecGetClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1461           for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
1462           ierr = DMPlexVecRestoreClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1463         }
1464         if (locA) {
1465           ierr = DMPlexVecGetClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
1466           for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
1467           ierr = DMPlexVecRestoreClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
1468         }
1469         ++face;
1470       }
1471       ierr = PetscMemzero(elemVec, numFaces* totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1472       {
1473         PetscFE         fe;
1474         PetscQuadrature q;
1475         PetscInt        numQuadPoints, Nb;
1476         /* Conforming batches */
1477         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1478         /* Remainder */
1479         PetscInt        Nr, offset;
1480 
1481         ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1482         ierr = PetscFEGetFaceQuadrature(fe, &q);CHKERRQ(ierr);
1483         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1484         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1485         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1486         blockSize = Nb*numQuadPoints;
1487         batchSize = numBlocks * blockSize;
1488         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1489         numChunks = numFaces / (numBatches*batchSize);
1490         Ne        = numChunks*numBatches*batchSize;
1491         Nr        = numFaces % (numBatches*batchSize);
1492         offset    = numFaces - Nr;
1493         ierr = PetscFEIntegrateBdResidual(fe, prob, field, Ne, fgeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1494         ierr = PetscFEIntegrateBdResidual(fe, prob, field, Nr, &fgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, a ? &a[offset*totDimAux] : NULL, t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1495       }
1496       for (p = 0, face = 0; p < numPoints; ++p) {
1497         const PetscInt point = points[p], *support;
1498 
1499         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1500         if (dep != dim-1) continue;
1501         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDim, &elemVec[face*totDim]);CHKERRQ(ierr);}
1502         ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
1503         ierr = DMPlexVecSetClosure(dm, NULL, locF, support[0], &elemVec[face*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1504         ++face;
1505       }
1506       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1507       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1508       ierr = PetscFree4(u,u_t,fgeom,elemVec);CHKERRQ(ierr);
1509       if (locA) {ierr = PetscFree(a);CHKERRQ(ierr);}
1510     }
1511   }
1512   if (plex) {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
1513   PetscFunctionReturn(0);
1514 }
1515 
1516 #undef __FUNCT__
1517 #define __FUNCT__ "DMPlexComputeResidual_Internal"
1518 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal time, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1519 {
1520   DM_Plex          *mesh       = (DM_Plex *) dm->data;
1521   const char       *name       = "Residual";
1522   DM                dmAux      = NULL;
1523   DM                dmGrad     = NULL;
1524   DMLabel           ghostLabel = NULL;
1525   PetscDS           prob       = NULL;
1526   PetscDS           probAux    = NULL;
1527   PetscSection      section    = NULL;
1528   PetscBool         useFEM     = PETSC_FALSE;
1529   PetscBool         useFVM     = PETSC_FALSE;
1530   PetscBool         isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
1531   PetscFV           fvm        = NULL;
1532   PetscFECellGeom  *cgeomFEM   = NULL;
1533   PetscScalar      *cgeomScal;
1534   PetscFVCellGeom  *cgeomFVM   = NULL;
1535   PetscFVFaceGeom  *fgeomFVM   = NULL;
1536   Vec               locA, cellGeometryFEM = NULL, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1537   PetscScalar      *u = NULL, *u_t, *a, *uL, *uR;
1538   PetscInt          Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
1539   PetscErrorCode    ierr;
1540 
1541   PetscFunctionBegin;
1542   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1543   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1544   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
1545   /* FEM+FVM */
1546   /* 1: Get sizes from dm and dmAux */
1547   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1548   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1549   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1550   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1551   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1552   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1553   if (locA) {
1554     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1555     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1556     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1557   }
1558   /* 2: Get geometric data */
1559   for (f = 0; f < Nf; ++f) {
1560     PetscObject  obj;
1561     PetscClassId id;
1562     PetscBool    fimp;
1563 
1564     ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1565     if (isImplicit != fimp) continue;
1566     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1567     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1568     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1569     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1570   }
1571   if (useFEM) {
1572     ierr = DMPlexSNESGetGeometryFEM(dm, &cellGeometryFEM);CHKERRQ(ierr);
1573     ierr = VecGetArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);
1574     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1575       DM dmCell;
1576       PetscInt c;
1577 
1578       ierr = VecGetDM(cellGeometryFEM,&dmCell);CHKERRQ(ierr);
1579       ierr = PetscMalloc1(cEnd-cStart,&cgeomFEM);CHKERRQ(ierr);
1580       for (c = 0; c < cEnd - cStart; c++) {
1581         PetscScalar *thisgeom;
1582 
1583         ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1584         cgeomFEM[c] = *((PetscFECellGeom *) thisgeom);
1585       }
1586     }
1587     else {
1588       cgeomFEM = (PetscFECellGeom *) cgeomScal;
1589     }
1590   }
1591   if (useFVM) {
1592     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1593     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1594     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1595     /* Reconstruct and limit cell gradients */
1596     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1597     if (dmGrad) {
1598       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1599       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1600       ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1601       /* Communicate gradient values */
1602       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1603       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1604       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1605       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1606     }
1607     /* Handle non-essential (e.g. outflow) boundary values */
1608     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1609   }
1610   /* Loop over chunks */
1611   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1612   numChunks     = 1;
1613   cellChunkSize = (cEnd - cStart)/numChunks;
1614   faceChunkSize = (fEnd - fStart)/numChunks;
1615   for (chunk = 0; chunk < numChunks; ++chunk) {
1616     PetscScalar     *elemVec, *fluxL, *fluxR;
1617     PetscReal       *vol;
1618     PetscFVFaceGeom *fgeom;
1619     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, cell;
1620     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = 0, face;
1621 
1622     /* Extract field coefficients */
1623     if (useFEM) {
1624       ierr = DMPlexGetCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1625       ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1626       ierr = PetscMemzero(elemVec, numCells*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1627     }
1628     if (useFVM) {
1629       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1630       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1631       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1632       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1633       ierr = PetscMemzero(fluxL, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1634       ierr = PetscMemzero(fluxR, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1635     }
1636     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1637     /* Loop over fields */
1638     for (f = 0; f < Nf; ++f) {
1639       PetscObject  obj;
1640       PetscClassId id;
1641       PetscBool    fimp;
1642       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1643 
1644       ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1645       if (isImplicit != fimp) continue;
1646       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1647       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1648       if (id == PETSCFE_CLASSID) {
1649         PetscFE         fe = (PetscFE) obj;
1650         PetscQuadrature q;
1651         PetscInt        Nq, Nb;
1652 
1653         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1654 
1655         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1656         ierr = PetscQuadratureGetData(q, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1657         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1658         blockSize = Nb*Nq;
1659         batchSize = numBlocks * blockSize;
1660         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1661         numChunks = numCells / (numBatches*batchSize);
1662         Ne        = numChunks*numBatches*batchSize;
1663         Nr        = numCells % (numBatches*batchSize);
1664         offset    = numCells - Nr;
1665         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1666         /*   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) */
1667         ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeomFEM, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1668         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);
1669       } else if (id == PETSCFV_CLASSID) {
1670         PetscFV fv = (PetscFV) obj;
1671 
1672         Ne = numFaces;
1673         /* Riemann solve over faces (need fields at face centroids) */
1674         /*   We need to evaluate FE fields at those coordinates */
1675         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1676       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1677     }
1678     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1679       ierr = PetscFree(cgeomFEM);CHKERRQ(ierr);
1680     }
1681     else {
1682       cgeomFEM = NULL;
1683     }
1684     if (cellGeometryFEM) {ierr = VecRestoreArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);}
1685     /* Loop over domain */
1686     if (useFEM) {
1687       /* Add elemVec to locX */
1688       for (cell = cS; cell < cE; ++cell) {
1689         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cell*totDim]);CHKERRQ(ierr);}
1690         if (ghostLabel) {
1691           PetscInt ghostVal;
1692 
1693           ierr = DMLabelGetValue(ghostLabel,cell,&ghostVal);CHKERRQ(ierr);
1694           if (ghostVal > 0) continue;
1695         }
1696         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cell*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1697       }
1698     }
1699     if (useFVM) {
1700       PetscScalar *fa;
1701       PetscInt     iface;
1702 
1703       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1704       for (f = 0; f < Nf; ++f) {
1705         PetscFV      fv;
1706         PetscObject  obj;
1707         PetscClassId id;
1708         PetscInt     foff, pdim;
1709 
1710         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1711         ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1712         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1713         if (id != PETSCFV_CLASSID) continue;
1714         fv   = (PetscFV) obj;
1715         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1716         /* Accumulate fluxes to cells */
1717         for (face = fS, iface = 0; face < fE; ++face) {
1718           const PetscInt *cells;
1719           PetscScalar    *fL = NULL, *fR = NULL;
1720           PetscInt        ghost, d, nsupp, nchild;
1721 
1722           ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1723           ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1724           ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1725           if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1726           ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1727           ierr = DMLabelGetValue(ghostLabel,cells[0],&ghost);CHKERRQ(ierr);
1728           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, cells[0], f, fa, &fL);CHKERRQ(ierr);}
1729           ierr = DMLabelGetValue(ghostLabel,cells[1],&ghost);CHKERRQ(ierr);
1730           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, cells[1], f, fa, &fR);CHKERRQ(ierr);}
1731           for (d = 0; d < pdim; ++d) {
1732             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
1733             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
1734           }
1735           ++iface;
1736         }
1737       }
1738       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1739     }
1740     /* Handle time derivative */
1741     if (locX_t) {
1742       PetscScalar *x_t, *fa;
1743 
1744       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1745       ierr = VecGetArray(locX_t, &x_t);CHKERRQ(ierr);
1746       for (f = 0; f < Nf; ++f) {
1747         PetscFV      fv;
1748         PetscObject  obj;
1749         PetscClassId id;
1750         PetscInt     pdim, d;
1751 
1752         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1753         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1754         if (id != PETSCFV_CLASSID) continue;
1755         fv   = (PetscFV) obj;
1756         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1757         for (cell = cS; cell < cE; ++cell) {
1758           PetscScalar *u_t, *r;
1759 
1760           if (ghostLabel) {
1761             PetscInt ghostVal;
1762 
1763             ierr = DMLabelGetValue(ghostLabel,cell,&ghostVal);CHKERRQ(ierr);
1764             if (ghostVal > 0) continue;
1765           }
1766           ierr = DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);CHKERRQ(ierr);
1767           ierr = DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);CHKERRQ(ierr);
1768           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
1769         }
1770       }
1771       ierr = VecRestoreArray(locX_t, &x_t);CHKERRQ(ierr);
1772       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1773     }
1774     if (useFEM) {
1775       ierr = DMPlexRestoreCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1776       ierr = DMRestoreWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1777     }
1778     if (useFVM) {
1779       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1780       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1781       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1782       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1783       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1784     }
1785   }
1786 
1787   if (useFEM) {ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, t, locF, user);CHKERRQ(ierr);}
1788 
1789   /* FEM */
1790   /* 1: Get sizes from dm and dmAux */
1791   /* 2: Get geometric data */
1792   /* 3: Handle boundary values */
1793   /* 4: Loop over domain */
1794   /*   Extract coefficients */
1795   /* Loop over fields */
1796   /*   Set tiling for FE*/
1797   /*   Integrate FE residual to get elemVec */
1798   /*     Loop over subdomain */
1799   /*       Loop over quad points */
1800   /*         Transform coords to real space */
1801   /*         Evaluate field and aux fields at point */
1802   /*         Evaluate residual at point */
1803   /*         Transform residual to real space */
1804   /*       Add residual to elemVec */
1805   /* Loop over domain */
1806   /*   Add elemVec to locX */
1807 
1808   /* FVM */
1809   /* Get geometric data */
1810   /* If using gradients */
1811   /*   Compute gradient data */
1812   /*   Loop over domain faces */
1813   /*     Count computational faces */
1814   /*     Reconstruct cell gradient */
1815   /*   Loop over domain cells */
1816   /*     Limit cell gradients */
1817   /* Handle boundary values */
1818   /* Loop over domain faces */
1819   /*   Read out field, centroid, normal, volume for each side of face */
1820   /* Riemann solve over faces */
1821   /* Loop over domain faces */
1822   /*   Accumulate fluxes to cells */
1823   /* TODO Change printFEM to printDisc here */
1824   if (mesh->printFEM) {
1825     Vec         locFbc;
1826     PetscInt    pStart, pEnd, p, maxDof;
1827     PetscScalar *zeroes;
1828 
1829     ierr = VecDuplicate(locF,&locFbc);CHKERRQ(ierr);
1830     ierr = VecCopy(locF,locFbc);CHKERRQ(ierr);
1831     ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
1832     ierr = PetscSectionGetMaxDof(section,&maxDof);CHKERRQ(ierr);
1833     ierr = PetscCalloc1(maxDof,&zeroes);CHKERRQ(ierr);
1834     for (p = pStart; p < pEnd; p++) {
1835       ierr = VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);CHKERRQ(ierr);
1836     }
1837     ierr = PetscFree(zeroes);CHKERRQ(ierr);
1838     ierr = DMPrintLocalVec(dm, name, mesh->printTol, locFbc);CHKERRQ(ierr);
1839     ierr = VecDestroy(&locFbc);CHKERRQ(ierr);
1840   }
1841   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1842   PetscFunctionReturn(0);
1843 }
1844 
1845 #undef __FUNCT__
1846 #define __FUNCT__ "DMPlexComputeResidualFEM_Check_Internal"
1847 static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, PetscReal t, Vec F, void *user)
1848 {
1849   DM                dmCh, dmAux;
1850   Vec               A, cellgeom;
1851   PetscDS           prob, probCh, probAux = NULL;
1852   PetscQuadrature   q;
1853   PetscSection      section, sectionAux;
1854   PetscFECellGeom  *cgeom = NULL;
1855   PetscScalar      *cgeomScal;
1856   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
1857   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
1858   PetscInt          totDim, totDimAux = 0, diffCell = 0;
1859   PetscErrorCode    ierr;
1860 
1861   PetscFunctionBegin;
1862   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1863   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1864   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1865   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1866   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1867   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1868   numCells = cEnd - cStart;
1869   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
1870   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
1871   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1872   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1873   if (dmAux) {
1874     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1875     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1876     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1877   }
1878   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1879   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);CHKERRQ(ierr);
1880   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
1881   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1882   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
1883   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1884   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1885     DM dmCell;
1886 
1887     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
1888     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
1889     for (c = 0; c < cEnd - cStart; c++) {
1890       PetscScalar *thisgeom;
1891 
1892       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1893       cgeom[c] = *((PetscFECellGeom *) thisgeom);
1894     }
1895   }
1896   else {
1897     cgeom = (PetscFECellGeom *) cgeomScal;
1898   }
1899   for (c = cStart; c < cEnd; ++c) {
1900     PetscScalar *x = NULL, *x_t = NULL;
1901     PetscInt     i;
1902 
1903     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1904     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1905     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1906     if (X_t) {
1907       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1908       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1909       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1910     }
1911     if (dmAux) {
1912       DM dmAuxPlex;
1913 
1914       ierr = DMSNESConvertPlex(dmAux,&dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1915       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1916       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1917       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1918       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1919     }
1920   }
1921   for (f = 0; f < Nf; ++f) {
1922     PetscFE  fe, feCh;
1923     PetscInt numQuadPoints, Nb;
1924     /* Conforming batches */
1925     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1926     /* Remainder */
1927     PetscInt Nr, offset;
1928 
1929     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1930     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
1931     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1932     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1933     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1934     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1935     blockSize = Nb*numQuadPoints;
1936     batchSize = numBlocks * blockSize;
1937     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1938     numChunks = numCells / (numBatches*batchSize);
1939     Ne        = numChunks*numBatches*batchSize;
1940     Nr        = numCells % (numBatches*batchSize);
1941     offset    = numCells - Nr;
1942     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1943     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVecCh);CHKERRQ(ierr);
1944     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);
1945     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);
1946   }
1947   for (c = cStart; c < cEnd; ++c) {
1948     PetscBool diff = PETSC_FALSE;
1949     PetscInt  d;
1950 
1951     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
1952     if (diff) {
1953       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
1954       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
1955       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
1956       ++diffCell;
1957     }
1958     if (diffCell > 9) break;
1959     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1960   }
1961   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1962     ierr = PetscFree(cgeom);CHKERRQ(ierr);
1963   }
1964   else {
1965     cgeom = NULL;
1966   }
1967   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1968   ierr = PetscFree3(u,u_t,elemVec);CHKERRQ(ierr);
1969   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
1970   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1971   PetscFunctionReturn(0);
1972 }
1973 
1974 #undef __FUNCT__
1975 #define __FUNCT__ "DMPlexSNESComputeResidualFEM"
1976 /*@
1977   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1978 
1979   Input Parameters:
1980 + dm - The mesh
1981 . X  - Local solution
1982 - user - The user context
1983 
1984   Output Parameter:
1985 . F  - Local output vector
1986 
1987   Level: developer
1988 
1989 .seealso: DMPlexComputeJacobianActionFEM()
1990 @*/
1991 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
1992 {
1993   PetscObject    check;
1994   PetscInt       cStart, cEnd, cEndInterior;
1995   DM             plex;
1996   PetscErrorCode ierr;
1997 
1998   PetscFunctionBegin;
1999   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2000   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2001   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2002   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2003   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
2004   ierr = PetscObjectQuery((PetscObject) plex, "dmCh", &check);CHKERRQ(ierr);
2005   if (check) {ierr = DMPlexComputeResidualFEM_Check_Internal(plex, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2006   else       {ierr = DMPlexComputeResidual_Internal(plex, cStart, cEnd, PETSC_MIN_REAL, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2007   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2008   PetscFunctionReturn(0);
2009 }
2010 
2011 #undef __FUNCT__
2012 #define __FUNCT__ "DMPlexSNESComputeBoundaryFEM"
2013 /*@
2014   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X
2015 
2016   Input Parameters:
2017 + dm - The mesh
2018 - user - The user context
2019 
2020   Output Parameter:
2021 . X  - Local solution
2022 
2023   Level: developer
2024 
2025 .seealso: DMPlexComputeJacobianActionFEM()
2026 @*/
2027 PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
2028 {
2029   DM             plex;
2030   PetscErrorCode ierr;
2031 
2032   PetscFunctionBegin;
2033   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2034   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);CHKERRQ(ierr);
2035   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2036   PetscFunctionReturn(0);
2037 }
2038 
2039 #undef __FUNCT__
2040 #define __FUNCT__ "DMPlexComputeBdJacobian_Internal"
2041 PetscErrorCode DMPlexComputeBdJacobian_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, PetscReal X_tShift, Mat Jac, Mat JacP, void *user)
2042 {
2043   DM_Plex         *mesh = (DM_Plex *) dm->data;
2044   DM               dmAux = NULL, plex = NULL;
2045   PetscSection     section, globalSection, subSection, sectionAux = NULL;
2046   PetscDS          prob, probAux = NULL;
2047   DMLabel          depth;
2048   Vec              locA = NULL;
2049   PetscFEFaceGeom *fgeom;
2050   PetscScalar     *u = NULL, *u_t = NULL, *a = NULL, *elemMat = NULL;
2051   PetscInt         dim, totDim, totDimAux, numBd, bd, Nf;
2052   PetscBool        isMatISP;
2053   PetscErrorCode   ierr;
2054 
2055   PetscFunctionBegin;
2056   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2057   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2058   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2059   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2060   if (isMatISP) {
2061     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2062   }
2063   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2064   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2065   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
2066   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2067   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
2068   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
2069   if (locA) {
2070     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
2071     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2072     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2073     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2074     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2075   }
2076   for (bd = 0; bd < numBd; ++bd) {
2077     DMBoundaryConditionType type;
2078     const char             *bdLabel;
2079     DMLabel                 label;
2080     IS                      pointIS;
2081     const PetscInt         *points;
2082     const PetscInt         *values;
2083     PetscInt                fieldI, fieldJ, numValues, v, numPoints, p, dep, numFaces, face;
2084     PetscObject             obj;
2085     PetscClassId            id;
2086 
2087     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &fieldI, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
2088     ierr = PetscDSGetDiscretization(prob, fieldI, &obj);CHKERRQ(ierr);
2089     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2090     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
2091     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
2092     for (v = 0; v < numValues; ++v) {
2093       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
2094       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
2095       if (!pointIS) continue; /* No points with that id on this process */
2096       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2097       for (p = 0, numFaces = 0; p < numPoints; ++p) {
2098         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2099         if (dep == dim-1) ++numFaces;
2100       }
2101       ierr = PetscMalloc4(numFaces*totDim,&u,locX_t ? numFaces*totDim : 0,&u_t,numFaces,&fgeom,numFaces*totDim*totDim,&elemMat);CHKERRQ(ierr);
2102       if (locA) {ierr = PetscMalloc1(numFaces*totDimAux,&a);CHKERRQ(ierr);}
2103       for (p = 0, face = 0; p < numPoints; ++p) {
2104         const PetscInt point = points[p], *support, *cone;
2105         PetscScalar   *x     = NULL;
2106         PetscReal      dummyJ[9], dummyDetJ;
2107         PetscInt       i, coneSize, faceLoc;
2108 
2109         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2110         if (dep != dim-1) continue;
2111         ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
2112         ierr = DMPlexComputeCellGeometryFEM(dm, support[0], NULL, NULL, dummyJ, fgeom[face].invJ[0], &dummyDetJ);CHKERRQ(ierr);
2113         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, fgeom[face].v0, fgeom[face].J, NULL, &fgeom[face].detJ);CHKERRQ(ierr);
2114         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, fgeom[face].n);CHKERRQ(ierr);
2115         if (fgeom[face].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", fgeom[face].detJ, point);
2116         ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
2117         ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
2118         for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
2119         if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of support[0] %d", point, support[0]);
2120         fgeom[face].face[0] = faceLoc;
2121         ierr = DMPlexVecGetClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
2122         for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
2123         ierr = DMPlexVecRestoreClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
2124         if (locX_t) {
2125           ierr = DMPlexVecGetClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
2126           for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
2127           ierr = DMPlexVecRestoreClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
2128         }
2129         if (locA) {
2130           ierr = DMPlexVecGetClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
2131           for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
2132           ierr = DMPlexVecRestoreClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
2133         }
2134         ++face;
2135       }
2136       ierr = PetscMemzero(elemMat, numFaces*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2137       {
2138         PetscFE         fe;
2139         PetscQuadrature q;
2140         PetscInt        numQuadPoints, Nb;
2141         /* Conforming batches */
2142         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2143         /* Remainder */
2144         PetscInt        Nr, offset;
2145 
2146         ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2147         ierr = PetscFEGetFaceQuadrature(fe, &q);CHKERRQ(ierr);
2148         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2149         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2150         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2151         blockSize = Nb*numQuadPoints;
2152         batchSize = numBlocks * blockSize;
2153         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2154         numChunks = numFaces / (numBatches*batchSize);
2155         Ne        = numChunks*numBatches*batchSize;
2156         Nr        = numFaces % (numBatches*batchSize);
2157         offset    = numFaces - Nr;
2158         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2159           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, fgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2160           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Nr, &fgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, a ? &a[offset*totDimAux] : NULL, t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2161         }
2162       }
2163       for (p = 0, face = 0; p < numPoints; ++p) {
2164         const PetscInt point = points[p], *support;
2165 
2166         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
2167         if (dep != dim-1) continue;
2168         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDim, totDim, &elemMat[face*totDim*totDim]);CHKERRQ(ierr);}
2169         ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
2170         if (!isMatISP) {
2171           ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2172         } else {
2173           Mat lJ;
2174 
2175           ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2176           ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2177         }
2178         ++face;
2179       }
2180       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2181       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2182       ierr = PetscFree4(u,u_t,fgeom,elemMat);CHKERRQ(ierr);
2183       if (locA) {ierr = PetscFree(a);CHKERRQ(ierr);}
2184     }
2185   }
2186   if (plex) {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
2187   PetscFunctionReturn(0);
2188 }
2189 
2190 #undef __FUNCT__
2191 #define __FUNCT__ "DMPlexComputeJacobian_Internal"
2192 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)
2193 {
2194   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2195   const char       *name  = "Jacobian";
2196   DM                dmAux, plex;
2197   Vec               A, cellgeom;
2198   PetscDS           prob, probAux = NULL;
2199   PetscSection      section, globalSection, subSection, sectionAux;
2200   PetscFECellGeom  *cgeom = NULL;
2201   PetscScalar      *cgeomScal;
2202   PetscScalar      *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
2203   PetscInt          dim, Nf, fieldI, fieldJ, numCells, c;
2204   PetscInt          totDim, totDimAux;
2205   PetscBool         isMatIS, isMatISP, isShell, hasJac, hasPrec, hasDyn, hasFV = PETSC_FALSE;
2206   PetscErrorCode    ierr;
2207 
2208   PetscFunctionBegin;
2209   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2210   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2211   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2212   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2213   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2214   if (isMatISP) {
2215     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2216   }
2217   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2218   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2219   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2220   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2221   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2222   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2223   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2224   numCells = cEnd - cStart;
2225   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2226   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2227   if (dmAux) {
2228     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2229     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2230     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2231     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2232   }
2233   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
2234   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);
2235   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2236   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2237   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2238   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2239     DM dmCell;
2240 
2241     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2242     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2243     for (c = 0; c < cEnd - cStart; c++) {
2244       PetscScalar *thisgeom;
2245 
2246       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2247       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2248     }
2249   } else {
2250     cgeom = (PetscFECellGeom *) cgeomScal;
2251   }
2252   for (c = cStart; c < cEnd; ++c) {
2253     PetscScalar *x = NULL,  *x_t = NULL;
2254     PetscInt     i;
2255 
2256     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2257     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2258     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2259     if (X_t) {
2260       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2261       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2262       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2263     }
2264     if (dmAux) {
2265       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2266       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2267       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2268     }
2269   }
2270   if (hasJac)  {ierr = PetscMemzero(elemMat,  numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2271   if (hasPrec) {ierr = PetscMemzero(elemMatP, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2272   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2273   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2274     PetscClassId    id;
2275     PetscFE         fe;
2276     PetscQuadrature q;
2277     PetscInt        numQuadPoints, Nb;
2278     /* Conforming batches */
2279     PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2280     /* Remainder */
2281     PetscInt        Nr, offset;
2282 
2283     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2284     ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
2285     if (id == PETSCFV_CLASSID) {hasFV = PETSC_TRUE; continue;}
2286     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
2287     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2288     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2289     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2290     blockSize = Nb*numQuadPoints;
2291     batchSize = numBlocks * blockSize;
2292     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2293     numChunks = numCells / (numBatches*batchSize);
2294     Ne        = numChunks*numBatches*batchSize;
2295     Nr        = numCells % (numBatches*batchSize);
2296     offset    = numCells - Nr;
2297     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2298       if (hasJac) {
2299         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2300         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);
2301       }
2302       if (hasPrec) {
2303         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatP);CHKERRQ(ierr);
2304         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);
2305       }
2306       if (hasDyn) {
2307         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2308         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);
2309       }
2310     }
2311   }
2312   if (hasDyn) {
2313     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2314   }
2315   if (hasFV) {
2316     PetscClassId id;
2317     PetscFV      fv;
2318     PetscInt     offsetI, NcI, NbI = 1, fc, f;
2319 
2320     for (fieldI = 0; fieldI < Nf; ++fieldI) {
2321       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fv);CHKERRQ(ierr);
2322       ierr = PetscDSGetFieldOffset(prob, fieldI, &offsetI);CHKERRQ(ierr);
2323       ierr = PetscObjectGetClassId((PetscObject) fv, &id);CHKERRQ(ierr);
2324       if (id != PETSCFV_CLASSID) continue;
2325       /* Put in the identity */
2326       ierr = PetscFVGetNumComponents(fv, &NcI);CHKERRQ(ierr);
2327       for (c = cStart; c < cEnd; ++c) {
2328         const PetscInt eOffset = (c-cStart)*totDim*totDim;
2329         for (fc = 0; fc < NcI; ++fc) {
2330           for (f = 0; f < NbI; ++f) {
2331             const PetscInt i = offsetI + f*NcI+fc;
2332             if (hasPrec) {
2333               if (hasJac) {elemMat[eOffset+i*totDim+i] = 1.0;}
2334               elemMatP[eOffset+i*totDim+i] = 1.0;
2335             } else {elemMat[eOffset+i*totDim+i] = 1.0;}
2336           }
2337         }
2338       }
2339     }
2340     /* No allocated space for FV stuff, so ignore the zero entries */
2341     ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2342   }
2343   isMatIS = PETSC_FALSE;
2344   if (hasPrec && hasJac) {
2345     ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatIS);CHKERRQ(ierr);
2346   }
2347   if (isMatIS && !subSection) {
2348     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2349   }
2350   for (c = cStart; c < cEnd; ++c) {
2351     if (hasPrec) {
2352       if (hasJac) {
2353         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2354         if (!isMatIS) {
2355           ierr = DMPlexMatSetClosure(dm, section, globalSection, Jac, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2356         } else {
2357           Mat lJ;
2358 
2359           ierr = MatISGetLocalMat(Jac,&lJ);CHKERRQ(ierr);
2360           ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2361         }
2362       }
2363       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMatP[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2364       if (!isMatISP) {
2365         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2366       } else {
2367         Mat lJ;
2368 
2369         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2370         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2371       }
2372     } else {
2373       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2374       if (!isMatISP) {
2375         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2376       } else {
2377         Mat lJ;
2378 
2379         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2380         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2381       }
2382     }
2383   }
2384   if (hasFV) {ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);CHKERRQ(ierr);}
2385   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2386     ierr = PetscFree(cgeom);CHKERRQ(ierr);
2387   } else {
2388     cgeom = NULL;
2389   }
2390   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2391   ierr = PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);CHKERRQ(ierr);
2392   if (dmAux) {
2393     ierr = PetscFree(a);CHKERRQ(ierr);
2394     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2395   }
2396   ierr = DMPlexComputeBdJacobian_Internal(dm, X, X_t, t, X_tShift, Jac, JacP, user);CHKERRQ(ierr);
2397   if (hasJac && hasPrec) {
2398     ierr = MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2399     ierr = MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2400   }
2401   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2402   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2403   if (mesh->printFEM) {
2404     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
2405     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
2406     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2407   }
2408   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2409   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
2410   if (isShell) {
2411     JacActionCtx *jctx;
2412 
2413     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
2414     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
2415   }
2416   PetscFunctionReturn(0);
2417 }
2418 
2419 
2420 #undef __FUNCT__
2421 #define __FUNCT__ "DMPlexComputeJacobianAction_Internal"
2422 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)
2423 {
2424   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2425   const char       *name  = "Jacobian";
2426   DM                dmAux, plex;
2427   Vec               A, cellgeom;
2428   PetscDS           prob, probAux = NULL;
2429   PetscQuadrature   quad;
2430   PetscSection      section, globalSection, sectionAux;
2431   PetscFECellGeom  *cgeom = NULL;
2432   PetscScalar      *cgeomScal;
2433   PetscScalar      *elemMat, *elemMatD, *u, *u_t, *a = NULL, *y, *z;
2434   PetscInt          dim, Nf, fieldI, fieldJ, numCells, c;
2435   PetscInt          totDim, totDimAux = 0;
2436   PetscBool         hasDyn;
2437   PetscErrorCode    ierr;
2438 
2439   PetscFunctionBegin;
2440   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2441   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2442   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2443   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2444   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2445   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2446   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2447   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2448   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2449   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2450   numCells = cEnd - cStart;
2451   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2452   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2453   if (dmAux) {
2454     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2455     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2456     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2457     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2458   }
2459   ierr = VecSet(Z, 0.0);CHKERRQ(ierr);
2460   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);
2461   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2462   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2463   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2464   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2465     DM dmCell;
2466 
2467     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2468     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2469     for (c = 0; c < cEnd - cStart; c++) {
2470       PetscScalar *thisgeom;
2471 
2472       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2473       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2474     }
2475   } else {
2476     cgeom = (PetscFECellGeom *) cgeomScal;
2477   }
2478   for (c = cStart; c < cEnd; ++c) {
2479     PetscScalar *x = NULL,  *x_t = NULL;
2480     PetscInt     i;
2481 
2482     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2483     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2484     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2485     if (X_t) {
2486       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2487       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2488       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2489     }
2490     if (dmAux) {
2491       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2492       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2493       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2494     }
2495     ierr = DMPlexVecGetClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2496     for (i = 0; i < totDim; ++i) y[(c-cStart)*totDim+i] = x[i];
2497     ierr = DMPlexVecRestoreClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2498   }
2499   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2500   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2501   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2502     PetscFE  fe;
2503     PetscInt numQuadPoints, Nb;
2504     /* Conforming batches */
2505     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2506     /* Remainder */
2507     PetscInt Nr, offset;
2508 
2509     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2510     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2511     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2512     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2513     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2514     blockSize = Nb*numQuadPoints;
2515     batchSize = numBlocks * blockSize;
2516     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2517     numChunks = numCells / (numBatches*batchSize);
2518     Ne        = numChunks*numBatches*batchSize;
2519     Nr        = numCells % (numBatches*batchSize);
2520     offset    = numCells - Nr;
2521     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2522       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2523       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);
2524       if (hasDyn) {
2525         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2526         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);
2527       }
2528     }
2529   }
2530   if (hasDyn) {
2531     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2532   }
2533   for (c = cStart; c < cEnd; ++c) {
2534     const PetscBLASInt M = totDim, one = 1;
2535     const PetscScalar  a = 1.0, b = 0.0;
2536 
2537     PetscStackCallBLAS("BLASgemv", BLASgemv_("N", &M, &M, &a, &elemMat[(c-cStart)*totDim*totDim], &M, &y[(c-cStart)*totDim], &one, &b, z, &one));
2538     if (mesh->printFEM > 1) {
2539       ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);
2540       ierr = DMPrintCellVector(c, "Y",  totDim, &y[(c-cStart)*totDim]);CHKERRQ(ierr);
2541       ierr = DMPrintCellVector(c, "Z",  totDim, z);CHKERRQ(ierr);
2542     }
2543     ierr = DMPlexVecSetClosure(dm, section, Z, c, z, ADD_VALUES);CHKERRQ(ierr);
2544   }
2545   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {ierr = PetscFree(cgeom);CHKERRQ(ierr);}
2546   else                                               {cgeom = NULL;}
2547   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2548   ierr = PetscFree6(u,u_t,elemMat,elemMatD,y,z);CHKERRQ(ierr);
2549   if (dmAux) {
2550     ierr = PetscFree(a);CHKERRQ(ierr);
2551     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2552   }
2553   if (mesh->printFEM) {
2554     ierr = PetscPrintf(PETSC_COMM_WORLD, "Z:\n");CHKERRQ(ierr);
2555     ierr = VecView(Z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2556   }
2557   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2558   PetscFunctionReturn(0);
2559 }
2560 
2561 #undef __FUNCT__
2562 #define __FUNCT__ "DMPlexSNESComputeJacobianFEM"
2563 /*@
2564   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2565 
2566   Input Parameters:
2567 + dm - The mesh
2568 . X  - Local input vector
2569 - user - The user context
2570 
2571   Output Parameter:
2572 . Jac  - Jacobian matrix
2573 
2574   Note:
2575   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2576   like a GPU, or vectorize on a multicore machine.
2577 
2578   Level: developer
2579 
2580 .seealso: FormFunctionLocal()
2581 @*/
2582 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2583 {
2584   PetscInt       cStart, cEnd, cEndInterior;
2585   DM             plex;
2586   PetscErrorCode ierr;
2587 
2588   PetscFunctionBegin;
2589   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2590   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2591   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2592   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2593   ierr = DMPlexComputeJacobian_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2594   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2595   PetscFunctionReturn(0);
2596 }
2597 
2598 #undef __FUNCT__
2599 #define __FUNCT__ "DMPlexSNESComputeJacobianActionFEM"
2600 /*@
2601   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.
2602 
2603   Input Parameters:
2604 + dm - The mesh
2605 . X  - Local solution vector
2606 . Y  - Local input vector
2607 - user - The user context
2608 
2609   Output Parameter:
2610 . Z - Local output vector
2611 
2612   Note:
2613   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2614   like a GPU, or vectorize on a multicore machine.
2615 
2616   Level: developer
2617 
2618 .seealso: FormFunctionLocal()
2619 @*/
2620 PetscErrorCode DMPlexSNESComputeJacobianActionFEM(DM dm, Vec X, Vec Y, Vec Z, void *user)
2621 {
2622   PetscInt       cStart, cEnd, cEndInterior;
2623   DM             plex;
2624   PetscErrorCode ierr;
2625 
2626   PetscFunctionBegin;
2627   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2628   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2629   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2630   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2631   ierr = DMPlexComputeJacobianAction_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Y, Z, user);CHKERRQ(ierr);
2632   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2633   PetscFunctionReturn(0);
2634 }
2635 
2636 #undef __FUNCT__
2637 #define __FUNCT__ "DMPlexSetSNESLocalFEM"
2638 /*@
2639   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.
2640 
2641   Input Parameters:
2642 + dm - The DM object
2643 . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see PetscDSAddBoundary())
2644 . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
2645 - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())
2646 
2647   Level: developer
2648 @*/
2649 PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
2650 {
2651   PetscErrorCode ierr;
2652 
2653   PetscFunctionBegin;
2654   ierr = DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);CHKERRQ(ierr);
2655   ierr = DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);CHKERRQ(ierr);
2656   ierr = DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);CHKERRQ(ierr);
2657   PetscFunctionReturn(0);
2658 }
2659 
2660 #undef __FUNCT__
2661 #define __FUNCT__ "DMSNESCheckFromOptions_Internal"
2662 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)
2663 {
2664   Mat            J, M;
2665   Vec            r, b;
2666   MatNullSpace   nullSpace;
2667   PetscReal     *error, res = 0.0;
2668   PetscInt       numFields;
2669   PetscErrorCode ierr;
2670 
2671   PetscFunctionBegin;
2672   ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2673   ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
2674   M    = J;
2675   /* TODO Null space for J */
2676   /* Check discretization error */
2677   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
2678   ierr = PetscMalloc1(PetscMax(1, numFields), &error);CHKERRQ(ierr);
2679   if (numFields > 1) {
2680     PetscInt f;
2681 
2682     ierr = DMComputeL2FieldDiff(dm, 0.0, exactFuncs, ctxs, u, error);CHKERRQ(ierr);
2683     ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: [");CHKERRQ(ierr);
2684     for (f = 0; f < numFields; ++f) {
2685       if (f) {ierr = PetscPrintf(PETSC_COMM_WORLD, ", ");CHKERRQ(ierr);}
2686       if (error[f] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "%g", error[f]);CHKERRQ(ierr);}
2687       else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "< 1.0e-11");CHKERRQ(ierr);}
2688     }
2689     ierr = PetscPrintf(PETSC_COMM_WORLD, "]\n");CHKERRQ(ierr);
2690   } else {
2691     ierr = DMComputeL2Diff(dm, 0.0, exactFuncs, ctxs, u, &error[0]);CHKERRQ(ierr);
2692     if (error[0] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error[0]);CHKERRQ(ierr);}
2693     else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
2694   }
2695   ierr = PetscFree(error);CHKERRQ(ierr);
2696   /* Check residual */
2697   ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2698   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2699   ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", res);CHKERRQ(ierr);
2700   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2701   ierr = PetscObjectSetName((PetscObject) r, "Initial Residual");CHKERRQ(ierr);
2702   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"res_");CHKERRQ(ierr);
2703   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2704   /* Check Jacobian */
2705   ierr = SNESComputeJacobian(snes, u, M, M);CHKERRQ(ierr);
2706   ierr = MatGetNullSpace(J, &nullSpace);CHKERRQ(ierr);
2707   if (nullSpace) {
2708     PetscBool isNull;
2709     ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
2710     if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
2711   }
2712   ierr = VecDuplicate(u, &b);CHKERRQ(ierr);
2713   ierr = VecSet(r, 0.0);CHKERRQ(ierr);
2714   ierr = SNESComputeFunction(snes, r, b);CHKERRQ(ierr);
2715   ierr = MatMult(M, u, r);CHKERRQ(ierr);
2716   ierr = VecAXPY(r, 1.0, b);CHKERRQ(ierr);
2717   ierr = VecDestroy(&b);CHKERRQ(ierr);
2718   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2719   ierr = PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", res);CHKERRQ(ierr);
2720   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2721   ierr = PetscObjectSetName((PetscObject) r, "Au - b = Au + F(0)");CHKERRQ(ierr);
2722   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"linear_res_");CHKERRQ(ierr);
2723   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2724   ierr = VecDestroy(&r);CHKERRQ(ierr);
2725   ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
2726   ierr = MatDestroy(&J);CHKERRQ(ierr);
2727   PetscFunctionReturn(0);
2728 }
2729 
2730 #undef __FUNCT__
2731 #define __FUNCT__ "DMSNESCheckFromOptions"
2732 PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
2733 {
2734   DM             dm;
2735   Vec            sol;
2736   PetscBool      check;
2737   PetscErrorCode ierr;
2738 
2739   PetscFunctionBegin;
2740   ierr = PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);CHKERRQ(ierr);
2741   if (!check) PetscFunctionReturn(0);
2742   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
2743   ierr = VecDuplicate(u, &sol);CHKERRQ(ierr);
2744   ierr = SNESSetSolution(snes, sol);CHKERRQ(ierr);
2745   ierr = DMSNESCheckFromOptions_Internal(snes, dm, u, sol, exactFuncs, ctxs);CHKERRQ(ierr);
2746   ierr = VecDestroy(&sol);CHKERRQ(ierr);
2747   PetscFunctionReturn(0);
2748 }
2749