xref: /petsc/src/snes/utils/dmplexsnes.c (revision 4d1a973fe17c9234e2cf908ebb478400f033ef22)
1 #include <petsc/private/dmpleximpl.h>   /*I "petscdmplex.h" I*/
2 #include <petsc/private/snesimpl.h>     /*I "petscsnes.h"   I*/
3 #include <petscds.h>
4 #include <petscblaslapack.h>
5 #include <petsc/private/petscimpl.h>
6 #include <petsc/private/petscfeimpl.h>
7 
8 /************************** Interpolation *******************************/
9 
10 static PetscErrorCode DMSNESConvertPlex(DM dm, DM *plex, PetscBool copy)
11 {
12   PetscBool      isPlex;
13   PetscErrorCode ierr;
14 
15   PetscFunctionBegin;
16   ierr = PetscObjectTypeCompare((PetscObject) dm, DMPLEX, &isPlex);CHKERRQ(ierr);
17   if (isPlex) {
18     *plex = dm;
19     ierr = PetscObjectReference((PetscObject) dm);CHKERRQ(ierr);
20   } else {
21     ierr = PetscObjectQuery((PetscObject) dm, "dm_plex", (PetscObject *) plex);CHKERRQ(ierr);
22     if (!*plex) {
23       ierr = DMConvert(dm,DMPLEX,plex);CHKERRQ(ierr);
24       ierr = PetscObjectCompose((PetscObject) dm, "dm_plex", (PetscObject) *plex);CHKERRQ(ierr);
25       if (copy) {
26         PetscInt    i;
27         PetscObject obj;
28         const char *comps[3] = {"A","dmAux","dmCh"};
29 
30         ierr = DMCopyDMSNES(dm, *plex);CHKERRQ(ierr);
31         for (i = 0; i < 3; i++) {
32           ierr = PetscObjectQuery((PetscObject) dm, comps[i], &obj);CHKERRQ(ierr);
33           ierr = PetscObjectCompose((PetscObject) *plex, comps[i], obj);CHKERRQ(ierr);
34         }
35       }
36     } else {
37       ierr = PetscObjectReference((PetscObject) *plex);CHKERRQ(ierr);
38     }
39   }
40   PetscFunctionReturn(0);
41 }
42 
43 PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx)
44 {
45   PetscErrorCode ierr;
46 
47   PetscFunctionBegin;
48   PetscValidPointer(ctx, 2);
49   ierr = PetscNew(ctx);CHKERRQ(ierr);
50 
51   (*ctx)->comm   = comm;
52   (*ctx)->dim    = -1;
53   (*ctx)->nInput = 0;
54   (*ctx)->points = NULL;
55   (*ctx)->cells  = NULL;
56   (*ctx)->n      = -1;
57   (*ctx)->coords = NULL;
58   PetscFunctionReturn(0);
59 }
60 
61 PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim)
62 {
63   PetscFunctionBegin;
64   if ((dim < 1) || (dim > 3)) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %d", dim);
65   ctx->dim = dim;
66   PetscFunctionReturn(0);
67 }
68 
69 PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim)
70 {
71   PetscFunctionBegin;
72   PetscValidIntPointer(dim, 2);
73   *dim = ctx->dim;
74   PetscFunctionReturn(0);
75 }
76 
77 PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof)
78 {
79   PetscFunctionBegin;
80   if (dof < 1) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %d", dof);
81   ctx->dof = dof;
82   PetscFunctionReturn(0);
83 }
84 
85 PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof)
86 {
87   PetscFunctionBegin;
88   PetscValidIntPointer(dof, 2);
89   *dof = ctx->dof;
90   PetscFunctionReturn(0);
91 }
92 
93 PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[])
94 {
95   PetscErrorCode ierr;
96 
97   PetscFunctionBegin;
98   if (ctx->dim < 0) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
99   if (ctx->points)  SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "Cannot add points multiple times yet");
100   ctx->nInput = n;
101 
102   ierr = PetscMalloc1(n*ctx->dim, &ctx->points);CHKERRQ(ierr);
103   ierr = PetscMemcpy(ctx->points, points, n*ctx->dim * sizeof(PetscReal));CHKERRQ(ierr);
104   PetscFunctionReturn(0);
105 }
106 
107 PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints)
108 {
109   MPI_Comm          comm = ctx->comm;
110   PetscScalar       *a;
111   PetscInt          p, q, i;
112   PetscMPIInt       rank, size;
113   PetscErrorCode    ierr;
114   Vec               pointVec;
115   PetscSF           cellSF;
116   PetscLayout       layout;
117   PetscReal         *globalPoints;
118   PetscScalar       *globalPointsScalar;
119   const PetscInt    *ranges;
120   PetscMPIInt       *counts, *displs;
121   const PetscSFNode *foundCells;
122   const PetscInt    *foundPoints;
123   PetscMPIInt       *foundProcs, *globalProcs;
124   PetscInt          n, N, numFound;
125 
126   PetscFunctionBegin;
127   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
128   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
129   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
130   if (ctx->dim < 0) SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
131   /* Locate points */
132   n = ctx->nInput;
133   if (!redundantPoints) {
134     ierr = PetscLayoutCreate(comm, &layout);CHKERRQ(ierr);
135     ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
136     ierr = PetscLayoutSetLocalSize(layout, n);CHKERRQ(ierr);
137     ierr = PetscLayoutSetUp(layout);CHKERRQ(ierr);
138     ierr = PetscLayoutGetSize(layout, &N);CHKERRQ(ierr);
139     /* Communicate all points to all processes */
140     ierr = PetscMalloc3(N*ctx->dim,&globalPoints,size,&counts,size,&displs);CHKERRQ(ierr);
141     ierr = PetscLayoutGetRanges(layout, &ranges);CHKERRQ(ierr);
142     for (p = 0; p < size; ++p) {
143       counts[p] = (ranges[p+1] - ranges[p])*ctx->dim;
144       displs[p] = ranges[p]*ctx->dim;
145     }
146     ierr = MPI_Allgatherv(ctx->points, n*ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm);CHKERRQ(ierr);
147   } else {
148     N = n;
149     globalPoints = ctx->points;
150     counts = displs = NULL;
151     layout = NULL;
152   }
153 #if 0
154   ierr = PetscMalloc3(N,&foundCells,N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
155   /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */
156 #else
157 #if defined(PETSC_USE_COMPLEX)
158   ierr = PetscMalloc1(N*ctx->dim,&globalPointsScalar);CHKERRQ(ierr);
159   for (i=0; i<N*ctx->dim; i++) globalPointsScalar[i] = globalPoints[i];
160 #else
161   globalPointsScalar = globalPoints;
162 #endif
163   ierr = VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N*ctx->dim, globalPointsScalar, &pointVec);CHKERRQ(ierr);
164   ierr = PetscMalloc2(N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
165   for (p = 0; p < N; ++p) {foundProcs[p] = size;}
166   cellSF = NULL;
167   ierr = DMLocatePoints(dm, pointVec, DM_POINTLOCATION_REMOVE, &cellSF);CHKERRQ(ierr);
168   ierr = PetscSFGetGraph(cellSF,NULL,&numFound,&foundPoints,&foundCells);CHKERRQ(ierr);
169 #endif
170   for (p = 0; p < numFound; ++p) {
171     if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank;
172   }
173   /* Let the lowest rank process own each point */
174   ierr   = MPIU_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm);CHKERRQ(ierr);
175   ctx->n = 0;
176   for (p = 0; p < N; ++p) {
177     if (globalProcs[p] == size) SETERRQ4(comm, PETSC_ERR_PLIB, "Point %d: %g %g %g not located in mesh", p, (double)globalPoints[p*ctx->dim+0], (double)(ctx->dim > 1 ? globalPoints[p*ctx->dim+1] : 0.0), (double)(ctx->dim > 2 ? globalPoints[p*ctx->dim+2] : 0.0));
178     else if (globalProcs[p] == rank) ctx->n++;
179   }
180   /* Create coordinates vector and array of owned cells */
181   ierr = PetscMalloc1(ctx->n, &ctx->cells);CHKERRQ(ierr);
182   ierr = VecCreate(comm, &ctx->coords);CHKERRQ(ierr);
183   ierr = VecSetSizes(ctx->coords, ctx->n*ctx->dim, PETSC_DECIDE);CHKERRQ(ierr);
184   ierr = VecSetBlockSize(ctx->coords, ctx->dim);CHKERRQ(ierr);
185   ierr = VecSetType(ctx->coords,VECSTANDARD);CHKERRQ(ierr);
186   ierr = VecGetArray(ctx->coords, &a);CHKERRQ(ierr);
187   for (p = 0, q = 0, i = 0; p < N; ++p) {
188     if (globalProcs[p] == rank) {
189       PetscInt d;
190 
191       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p*ctx->dim+d];
192       ctx->cells[q] = foundCells[q].index;
193       ++q;
194     }
195   }
196   ierr = VecRestoreArray(ctx->coords, &a);CHKERRQ(ierr);
197 #if 0
198   ierr = PetscFree3(foundCells,foundProcs,globalProcs);CHKERRQ(ierr);
199 #else
200   ierr = PetscFree2(foundProcs,globalProcs);CHKERRQ(ierr);
201   ierr = PetscSFDestroy(&cellSF);CHKERRQ(ierr);
202   ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
203 #endif
204   if ((void*)globalPointsScalar != (void*)globalPoints) {ierr = PetscFree(globalPointsScalar);CHKERRQ(ierr);}
205   if (!redundantPoints) {ierr = PetscFree3(globalPoints,counts,displs);CHKERRQ(ierr);}
206   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
207   PetscFunctionReturn(0);
208 }
209 
210 PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates)
211 {
212   PetscFunctionBegin;
213   PetscValidPointer(coordinates, 2);
214   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
215   *coordinates = ctx->coords;
216   PetscFunctionReturn(0);
217 }
218 
219 PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v)
220 {
221   PetscErrorCode ierr;
222 
223   PetscFunctionBegin;
224   PetscValidPointer(v, 2);
225   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
226   ierr = VecCreate(ctx->comm, v);CHKERRQ(ierr);
227   ierr = VecSetSizes(*v, ctx->n*ctx->dof, PETSC_DECIDE);CHKERRQ(ierr);
228   ierr = VecSetBlockSize(*v, ctx->dof);CHKERRQ(ierr);
229   ierr = VecSetType(*v,VECSTANDARD);CHKERRQ(ierr);
230   PetscFunctionReturn(0);
231 }
232 
233 PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v)
234 {
235   PetscErrorCode ierr;
236 
237   PetscFunctionBegin;
238   PetscValidPointer(v, 2);
239   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
240   ierr = VecDestroy(v);CHKERRQ(ierr);
241   PetscFunctionReturn(0);
242 }
243 
244 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Triangle_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
245 {
246   PetscReal      *v0, *J, *invJ, detJ;
247   const PetscScalar *coords;
248   PetscScalar    *a;
249   PetscInt       p;
250   PetscErrorCode ierr;
251 
252   PetscFunctionBegin;
253   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
254   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
255   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
256   for (p = 0; p < ctx->n; ++p) {
257     PetscInt     c = ctx->cells[p];
258     PetscScalar *x = NULL;
259     PetscReal    xi[4];
260     PetscInt     d, f, comp;
261 
262     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
263     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", (double)detJ, c);
264     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
265     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
266 
267     for (d = 0; d < ctx->dim; ++d) {
268       xi[d] = 0.0;
269       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
270       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];
271     }
272     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
273   }
274   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
275   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
276   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
277   PetscFunctionReturn(0);
278 }
279 
280 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Tetrahedron_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
281 {
282   PetscReal      *v0, *J, *invJ, detJ;
283   const PetscScalar *coords;
284   PetscScalar    *a;
285   PetscInt       p;
286   PetscErrorCode ierr;
287 
288   PetscFunctionBegin;
289   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
290   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
291   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
292   for (p = 0; p < ctx->n; ++p) {
293     PetscInt       c = ctx->cells[p];
294     const PetscInt order[3] = {2, 1, 3};
295     PetscScalar   *x = NULL;
296     PetscReal      xi[4];
297     PetscInt       d, f, comp;
298 
299     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
300     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", (double)detJ, c);
301     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
302     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
303 
304     for (d = 0; d < ctx->dim; ++d) {
305       xi[d] = 0.0;
306       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
307       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];
308     }
309     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
310   }
311   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
312   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
313   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
314   PetscFunctionReturn(0);
315 }
316 
317 PETSC_STATIC_INLINE PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
318 {
319   const PetscScalar *vertices = (const PetscScalar*) ctx;
320   const PetscScalar x0        = vertices[0];
321   const PetscScalar y0        = vertices[1];
322   const PetscScalar x1        = vertices[2];
323   const PetscScalar y1        = vertices[3];
324   const PetscScalar x2        = vertices[4];
325   const PetscScalar y2        = vertices[5];
326   const PetscScalar x3        = vertices[6];
327   const PetscScalar y3        = vertices[7];
328   const PetscScalar f_1       = x1 - x0;
329   const PetscScalar g_1       = y1 - y0;
330   const PetscScalar f_3       = x3 - x0;
331   const PetscScalar g_3       = y3 - y0;
332   const PetscScalar f_01      = x2 - x1 - x3 + x0;
333   const PetscScalar g_01      = y2 - y1 - y3 + y0;
334   const PetscScalar *ref;
335   PetscScalar       *real;
336   PetscErrorCode    ierr;
337 
338   PetscFunctionBegin;
339   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
340   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
341   {
342     const PetscScalar p0 = ref[0];
343     const PetscScalar p1 = ref[1];
344 
345     real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1;
346     real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1;
347   }
348   ierr = PetscLogFlops(28);CHKERRQ(ierr);
349   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
350   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
351   PetscFunctionReturn(0);
352 }
353 
354 #include <petsc/private/dmimpl.h>
355 PETSC_STATIC_INLINE PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
356 {
357   const PetscScalar *vertices = (const PetscScalar*) ctx;
358   const PetscScalar x0        = vertices[0];
359   const PetscScalar y0        = vertices[1];
360   const PetscScalar x1        = vertices[2];
361   const PetscScalar y1        = vertices[3];
362   const PetscScalar x2        = vertices[4];
363   const PetscScalar y2        = vertices[5];
364   const PetscScalar x3        = vertices[6];
365   const PetscScalar y3        = vertices[7];
366   const PetscScalar f_01      = x2 - x1 - x3 + x0;
367   const PetscScalar g_01      = y2 - y1 - y3 + y0;
368   const PetscScalar *ref;
369   PetscErrorCode    ierr;
370 
371   PetscFunctionBegin;
372   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
373   {
374     const PetscScalar x       = ref[0];
375     const PetscScalar y       = ref[1];
376     const PetscInt    rows[2] = {0, 1};
377     PetscScalar       values[4];
378 
379     values[0] = (x1 - x0 + f_01*y) * 0.5; values[1] = (x3 - x0 + f_01*x) * 0.5;
380     values[2] = (y1 - y0 + g_01*y) * 0.5; values[3] = (y3 - y0 + g_01*x) * 0.5;
381     ierr      = MatSetValues(J, 2, rows, 2, rows, values, INSERT_VALUES);CHKERRQ(ierr);
382   }
383   ierr = PetscLogFlops(30);CHKERRQ(ierr);
384   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
385   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
386   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
387   PetscFunctionReturn(0);
388 }
389 
390 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
391 {
392   DM             dmCoord;
393   PetscFE        fem = NULL;
394   SNES           snes;
395   KSP            ksp;
396   PC             pc;
397   Vec            coordsLocal, r, ref, real;
398   Mat            J;
399   const PetscScalar *coords;
400   PetscScalar    *a;
401   PetscInt       Nf, p;
402   const PetscInt dof = ctx->dof;
403   PetscErrorCode ierr;
404 
405   PetscFunctionBegin;
406   ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
407   if (Nf) {ierr = DMGetField(dm, 0, (PetscObject *) &fem);CHKERRQ(ierr);}
408   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
409   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
410   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
411   ierr = SNESSetOptionsPrefix(snes, "quad_interp_");CHKERRQ(ierr);
412   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
413   ierr = VecSetSizes(r, 2, 2);CHKERRQ(ierr);
414   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
415   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
416   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
417   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
418   ierr = MatSetSizes(J, 2, 2, 2, 2);CHKERRQ(ierr);
419   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
420   ierr = MatSetUp(J);CHKERRQ(ierr);
421   ierr = SNESSetFunction(snes, r, QuadMap_Private, NULL);CHKERRQ(ierr);
422   ierr = SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);CHKERRQ(ierr);
423   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
424   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
425   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
426   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
427 
428   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
429   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
430   for (p = 0; p < ctx->n; ++p) {
431     PetscScalar *x = NULL, *vertices = NULL;
432     PetscScalar *xi;
433     PetscReal    xir[2];
434     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
435 
436     /* Can make this do all points at once */
437     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
438     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 4*2);
439     ierr   = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
440     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
441     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
442     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
443     xi[0]  = coords[p*ctx->dim+0];
444     xi[1]  = coords[p*ctx->dim+1];
445     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
446     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
447     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
448     xir[0] = PetscRealPart(xi[0]);
449     xir[1] = PetscRealPart(xi[1]);
450     if (4*dof != xSize) {
451       PetscReal *B;
452       PetscInt   d;
453 
454       xir[0] = 2.0*xir[0] - 1.0; xir[1] = 2.0*xir[1] - 1.0;
455       ierr = PetscFEGetTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
456       for (comp = 0; comp < dof; ++comp) {
457         a[p*dof+comp] = 0.0;
458         for (d = 0; d < xSize/dof; ++d) {
459           a[p*dof+comp] += x[d*dof+comp]*B[d*dof+comp];
460         }
461       }
462       ierr = PetscFERestoreTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
463     } else {
464       for (comp = 0; comp < dof; ++comp)
465         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];
466     }
467     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
468     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
469     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
470   }
471   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
472   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
473 
474   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
475   ierr = VecDestroy(&r);CHKERRQ(ierr);
476   ierr = VecDestroy(&ref);CHKERRQ(ierr);
477   ierr = VecDestroy(&real);CHKERRQ(ierr);
478   ierr = MatDestroy(&J);CHKERRQ(ierr);
479   PetscFunctionReturn(0);
480 }
481 
482 PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
483 {
484   const PetscScalar *vertices = (const PetscScalar*) ctx;
485   const PetscScalar x0        = vertices[0];
486   const PetscScalar y0        = vertices[1];
487   const PetscScalar z0        = vertices[2];
488   const PetscScalar x1        = vertices[9];
489   const PetscScalar y1        = vertices[10];
490   const PetscScalar z1        = vertices[11];
491   const PetscScalar x2        = vertices[6];
492   const PetscScalar y2        = vertices[7];
493   const PetscScalar z2        = vertices[8];
494   const PetscScalar x3        = vertices[3];
495   const PetscScalar y3        = vertices[4];
496   const PetscScalar z3        = vertices[5];
497   const PetscScalar x4        = vertices[12];
498   const PetscScalar y4        = vertices[13];
499   const PetscScalar z4        = vertices[14];
500   const PetscScalar x5        = vertices[15];
501   const PetscScalar y5        = vertices[16];
502   const PetscScalar z5        = vertices[17];
503   const PetscScalar x6        = vertices[18];
504   const PetscScalar y6        = vertices[19];
505   const PetscScalar z6        = vertices[20];
506   const PetscScalar x7        = vertices[21];
507   const PetscScalar y7        = vertices[22];
508   const PetscScalar z7        = vertices[23];
509   const PetscScalar f_1       = x1 - x0;
510   const PetscScalar g_1       = y1 - y0;
511   const PetscScalar h_1       = z1 - z0;
512   const PetscScalar f_3       = x3 - x0;
513   const PetscScalar g_3       = y3 - y0;
514   const PetscScalar h_3       = z3 - z0;
515   const PetscScalar f_4       = x4 - x0;
516   const PetscScalar g_4       = y4 - y0;
517   const PetscScalar h_4       = z4 - z0;
518   const PetscScalar f_01      = x2 - x1 - x3 + x0;
519   const PetscScalar g_01      = y2 - y1 - y3 + y0;
520   const PetscScalar h_01      = z2 - z1 - z3 + z0;
521   const PetscScalar f_12      = x7 - x3 - x4 + x0;
522   const PetscScalar g_12      = y7 - y3 - y4 + y0;
523   const PetscScalar h_12      = z7 - z3 - z4 + z0;
524   const PetscScalar f_02      = x5 - x1 - x4 + x0;
525   const PetscScalar g_02      = y5 - y1 - y4 + y0;
526   const PetscScalar h_02      = z5 - z1 - z4 + z0;
527   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
528   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
529   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
530   const PetscScalar *ref;
531   PetscScalar       *real;
532   PetscErrorCode    ierr;
533 
534   PetscFunctionBegin;
535   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
536   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
537   {
538     const PetscScalar p0 = ref[0];
539     const PetscScalar p1 = ref[1];
540     const PetscScalar p2 = ref[2];
541 
542     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;
543     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;
544     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;
545   }
546   ierr = PetscLogFlops(114);CHKERRQ(ierr);
547   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
548   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
549   PetscFunctionReturn(0);
550 }
551 
552 PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
553 {
554   const PetscScalar *vertices = (const PetscScalar*) ctx;
555   const PetscScalar x0        = vertices[0];
556   const PetscScalar y0        = vertices[1];
557   const PetscScalar z0        = vertices[2];
558   const PetscScalar x1        = vertices[9];
559   const PetscScalar y1        = vertices[10];
560   const PetscScalar z1        = vertices[11];
561   const PetscScalar x2        = vertices[6];
562   const PetscScalar y2        = vertices[7];
563   const PetscScalar z2        = vertices[8];
564   const PetscScalar x3        = vertices[3];
565   const PetscScalar y3        = vertices[4];
566   const PetscScalar z3        = vertices[5];
567   const PetscScalar x4        = vertices[12];
568   const PetscScalar y4        = vertices[13];
569   const PetscScalar z4        = vertices[14];
570   const PetscScalar x5        = vertices[15];
571   const PetscScalar y5        = vertices[16];
572   const PetscScalar z5        = vertices[17];
573   const PetscScalar x6        = vertices[18];
574   const PetscScalar y6        = vertices[19];
575   const PetscScalar z6        = vertices[20];
576   const PetscScalar x7        = vertices[21];
577   const PetscScalar y7        = vertices[22];
578   const PetscScalar z7        = vertices[23];
579   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
580   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
581   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
582   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
583   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
584   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
585   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
586   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
587   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
588   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
589   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
590   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
591   const PetscScalar *ref;
592   PetscErrorCode    ierr;
593 
594   PetscFunctionBegin;
595   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
596   {
597     const PetscScalar x       = ref[0];
598     const PetscScalar y       = ref[1];
599     const PetscScalar z       = ref[2];
600     const PetscInt    rows[3] = {0, 1, 2};
601     PetscScalar       values[9];
602 
603     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
604     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
605     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
606     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
607     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
608     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
609     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
610     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
611     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;
612 
613     ierr = MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);CHKERRQ(ierr);
614   }
615   ierr = PetscLogFlops(152);CHKERRQ(ierr);
616   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
617   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
618   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
619   PetscFunctionReturn(0);
620 }
621 
622 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
623 {
624   DM             dmCoord;
625   SNES           snes;
626   KSP            ksp;
627   PC             pc;
628   Vec            coordsLocal, r, ref, real;
629   Mat            J;
630   const PetscScalar *coords;
631   PetscScalar    *a;
632   PetscInt       p;
633   PetscErrorCode ierr;
634 
635   PetscFunctionBegin;
636   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
637   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
638   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
639   ierr = SNESSetOptionsPrefix(snes, "hex_interp_");CHKERRQ(ierr);
640   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
641   ierr = VecSetSizes(r, 3, 3);CHKERRQ(ierr);
642   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
643   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
644   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
645   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
646   ierr = MatSetSizes(J, 3, 3, 3, 3);CHKERRQ(ierr);
647   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
648   ierr = MatSetUp(J);CHKERRQ(ierr);
649   ierr = SNESSetFunction(snes, r, HexMap_Private, NULL);CHKERRQ(ierr);
650   ierr = SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);CHKERRQ(ierr);
651   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
652   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
653   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
654   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
655 
656   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
657   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
658   for (p = 0; p < ctx->n; ++p) {
659     PetscScalar *x = NULL, *vertices = NULL;
660     PetscScalar *xi;
661     PetscReal    xir[3];
662     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
663 
664     /* Can make this do all points at once */
665     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
666     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 8*3);
667     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
668     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 8*ctx->dof);
669     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
670     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
671     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
672     xi[0]  = coords[p*ctx->dim+0];
673     xi[1]  = coords[p*ctx->dim+1];
674     xi[2]  = coords[p*ctx->dim+2];
675     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
676     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
677     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
678     xir[0] = PetscRealPart(xi[0]);
679     xir[1] = PetscRealPart(xi[1]);
680     xir[2] = PetscRealPart(xi[2]);
681     for (comp = 0; comp < ctx->dof; ++comp) {
682       a[p*ctx->dof+comp] =
683         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
684         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
685         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
686         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
687         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
688         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
689         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
690         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
691     }
692     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
693     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
694     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
695   }
696   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
697   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
698 
699   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
700   ierr = VecDestroy(&r);CHKERRQ(ierr);
701   ierr = VecDestroy(&ref);CHKERRQ(ierr);
702   ierr = VecDestroy(&real);CHKERRQ(ierr);
703   ierr = MatDestroy(&J);CHKERRQ(ierr);
704   PetscFunctionReturn(0);
705 }
706 
707 /*
708   Input Parameters:
709 + ctx - The DMInterpolationInfo context
710 . dm  - The DM
711 - x   - The local vector containing the field to be interpolated
712 
713   Output Parameters:
714 . v   - The vector containing the interpolated values
715 */
716 PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
717 {
718   PetscInt       dim, coneSize, n;
719   PetscErrorCode ierr;
720 
721   PetscFunctionBegin;
722   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
723   PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
724   PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
725   ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
726   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);
727   if (n) {
728     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
729     ierr = DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);CHKERRQ(ierr);
730     if (dim == 2) {
731       if (coneSize == 3) {
732         ierr = DMInterpolate_Triangle_Private(ctx, dm, x, v);CHKERRQ(ierr);
733       } else if (coneSize == 4) {
734         ierr = DMInterpolate_Quad_Private(ctx, dm, x, v);CHKERRQ(ierr);
735       } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
736     } else if (dim == 3) {
737       if (coneSize == 4) {
738         ierr = DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);CHKERRQ(ierr);
739       } else {
740         ierr = DMInterpolate_Hex_Private(ctx, dm, x, v);CHKERRQ(ierr);
741       }
742     } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
743   }
744   PetscFunctionReturn(0);
745 }
746 
747 PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
748 {
749   PetscErrorCode ierr;
750 
751   PetscFunctionBegin;
752   PetscValidPointer(ctx, 2);
753   ierr = VecDestroy(&(*ctx)->coords);CHKERRQ(ierr);
754   ierr = PetscFree((*ctx)->points);CHKERRQ(ierr);
755   ierr = PetscFree((*ctx)->cells);CHKERRQ(ierr);
756   ierr = PetscFree(*ctx);CHKERRQ(ierr);
757   *ctx = NULL;
758   PetscFunctionReturn(0);
759 }
760 
761 /*@C
762   SNESMonitorFields - Monitors the residual for each field separately
763 
764   Collective on SNES
765 
766   Input Parameters:
767 + snes   - the SNES context
768 . its    - iteration number
769 . fgnorm - 2-norm of residual
770 - vf  - PetscViewerAndFormat of type ASCII
771 
772   Notes:
773   This routine prints the residual norm at each iteration.
774 
775   Level: intermediate
776 
777 .keywords: SNES, nonlinear, default, monitor, norm
778 .seealso: SNESMonitorSet(), SNESMonitorDefault()
779 @*/
780 PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
781 {
782   PetscViewer        viewer = vf->viewer;
783   Vec                res;
784   DM                 dm;
785   PetscSection       s;
786   const PetscScalar *r;
787   PetscReal         *lnorms, *norms;
788   PetscInt           numFields, f, pStart, pEnd, p;
789   PetscErrorCode     ierr;
790 
791   PetscFunctionBegin;
792   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
793   ierr = SNESGetFunction(snes, &res, 0, 0);CHKERRQ(ierr);
794   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
795   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
796   ierr = PetscSectionGetNumFields(s, &numFields);CHKERRQ(ierr);
797   ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
798   ierr = PetscCalloc2(numFields, &lnorms, numFields, &norms);CHKERRQ(ierr);
799   ierr = VecGetArrayRead(res, &r);CHKERRQ(ierr);
800   for (p = pStart; p < pEnd; ++p) {
801     for (f = 0; f < numFields; ++f) {
802       PetscInt fdof, foff, d;
803 
804       ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
805       ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
806       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
807     }
808   }
809   ierr = VecRestoreArrayRead(res, &r);CHKERRQ(ierr);
810   ierr = MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
811   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
812   ierr = PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
813   ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
814   for (f = 0; f < numFields; ++f) {
815     if (f > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
816     ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));CHKERRQ(ierr);
817   }
818   ierr = PetscViewerASCIIPrintf(viewer, "]\n");CHKERRQ(ierr);
819   ierr = PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
820   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
821   ierr = PetscFree2(lnorms, norms);CHKERRQ(ierr);
822   PetscFunctionReturn(0);
823 }
824 
825 /********************* Residual Computation **************************/
826 
827 static PetscErrorCode PetscContainerUserDestroy_PetscFEGeom (void *ctx)
828 {
829   PetscFEGeom *geom = (PetscFEGeom *) ctx;
830   PetscErrorCode ierr;
831 
832   PetscFunctionBegin;
833   ierr = PetscFEGeomDestroy(&geom);CHKERRQ(ierr);
834   PetscFunctionReturn(0);
835 }
836 
837 static PetscErrorCode DMSNESGetFEGeom(DMField coordField, IS pointIS, PetscQuadrature quad, PetscBool faceData, PetscFEGeom **geom)
838 {
839   char            composeStr[33] = {0};
840   PetscObjectId   id;
841   PetscContainer  container;
842   PetscErrorCode  ierr;
843 
844   PetscFunctionBegin;
845   ierr = PetscObjectGetId((PetscObject)quad,&id);CHKERRQ(ierr);
846   ierr = PetscSNPrintf(composeStr, 32, "DMSNESGetFEGeom_%x\n", id);CHKERRQ(ierr);
847   ierr = PetscObjectQuery((PetscObject) pointIS, composeStr, (PetscObject *) &container);CHKERRQ(ierr);
848   if (container) {
849     ierr = PetscContainerGetPointer(container, (void **) geom);CHKERRQ(ierr);
850   } else {
851     ierr = DMFieldCreateFEGeom(coordField, pointIS, quad, faceData, geom);CHKERRQ(ierr);
852     ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
853     ierr = PetscContainerSetPointer(container, (void *) *geom);CHKERRQ(ierr);
854     ierr = PetscContainerSetUserDestroy(container, PetscContainerUserDestroy_PetscFEGeom);CHKERRQ(ierr);
855     ierr = PetscObjectCompose((PetscObject) pointIS, composeStr, (PetscObject) container);CHKERRQ(ierr);
856     ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
857   }
858   PetscFunctionReturn(0);
859 }
860 
861 static PetscErrorCode DMSNESRestoreFEGeom(DMField coordField, IS pointIS, PetscQuadrature quad, PetscBool faceData, PetscFEGeom **geom)
862 {
863   PetscFunctionBegin;
864   *geom = NULL;
865   PetscFunctionReturn(0);
866 }
867 
868 /*@
869   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
870 
871   Input Parameter:
872 . dm - The DM
873 
874   Output Parameters:
875 + facegeom - The values precomputed from face geometry
876 . cellgeom - The values precomputed from cell geometry
877 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
878 
879   Level: developer
880 
881 .seealso: DMPlexTSSetRHSFunctionLocal()
882 @*/
883 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
884 {
885   DM             plex;
886   PetscErrorCode ierr;
887 
888   PetscFunctionBegin;
889   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
890   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
891   ierr = DMPlexGetDataFVM(plex, NULL, cellgeom, facegeom, NULL);CHKERRQ(ierr);
892   if (minRadius) {ierr = DMPlexGetMinRadius(plex, minRadius);CHKERRQ(ierr);}
893   ierr = DMDestroy(&plex);CHKERRQ(ierr);
894   PetscFunctionReturn(0);
895 }
896 
897 /*@
898   DMPlexSNESGetGradientDM - Return gradient data layout
899 
900   Input Parameters:
901 + dm - The DM
902 - fv - The PetscFV
903 
904   Output Parameter:
905 . dmGrad - The layout for gradient values
906 
907   Level: developer
908 
909 .seealso: DMPlexSNESGetGeometryFVM()
910 @*/
911 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
912 {
913   DM             plex;
914   PetscBool      computeGradients;
915   PetscErrorCode ierr;
916 
917   PetscFunctionBegin;
918   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
919   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
920   PetscValidPointer(dmGrad,3);
921   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
922   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
923   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
924   ierr = DMPlexGetDataFVM(plex, fv, NULL, NULL, dmGrad);CHKERRQ(ierr);
925   ierr = DMDestroy(&plex);CHKERRQ(ierr);
926   PetscFunctionReturn(0);
927 }
928 
929 /*@C
930   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells
931 
932   Input Parameters:
933 + dm     - The DM
934 . cStart - The first cell to include
935 . cEnd   - The first cell to exclude
936 . locX   - A local vector with the solution fields
937 . locX_t - A local vector with solution field time derivatives, or NULL
938 - locA   - A local vector with auxiliary fields, or NULL
939 
940   Output Parameters:
941 + u   - The field coefficients
942 . u_t - The fields derivative coefficients
943 - a   - The auxiliary field coefficients
944 
945   Level: developer
946 
947 .seealso: DMPlexGetFaceFields()
948 @*/
949 PetscErrorCode DMPlexGetCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
950 {
951   DM             dmAux;
952   PetscSection   section, sectionAux;
953   PetscDS        prob;
954   PetscInt       numCells = cEnd - cStart, totDim, totDimAux, c;
955   PetscErrorCode ierr;
956 
957   PetscFunctionBegin;
958   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
959   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
960   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
961   if (locA)   {PetscValidHeaderSpecific(locA, VEC_CLASSID, 6);}
962   PetscValidPointer(u, 7);
963   PetscValidPointer(u_t, 8);
964   PetscValidPointer(a, 9);
965   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
966   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
967   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
968   if (locA) {
969     PetscDS probAux;
970 
971     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
972     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
973     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
974     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
975   }
976   ierr = DMGetWorkArray(dm, numCells*totDim, MPIU_SCALAR, u);CHKERRQ(ierr);
977   if (locX_t) {ierr = DMGetWorkArray(dm, numCells*totDim, MPIU_SCALAR, u_t);CHKERRQ(ierr);} else {*u_t = NULL;}
978   if (locA)   {ierr = DMGetWorkArray(dm, numCells*totDimAux, MPIU_SCALAR, a);CHKERRQ(ierr);} else {*a = NULL;}
979   for (c = cStart; c < cEnd; ++c) {
980     PetscScalar *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
981     PetscInt     i;
982 
983     ierr = DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
984     for (i = 0; i < totDim; ++i) ul[(c-cStart)*totDim+i] = x[i];
985     ierr = DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
986     if (locX_t) {
987       ierr = DMPlexVecGetClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
988       for (i = 0; i < totDim; ++i) ul_t[(c-cStart)*totDim+i] = x_t[i];
989       ierr = DMPlexVecRestoreClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
990     }
991     if (locA) {
992       DM dmAuxPlex;
993 
994       ierr = DMSNESConvertPlex(dmAux, &dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
995       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
996       for (i = 0; i < totDimAux; ++i) al[(c-cStart)*totDimAux+i] = x[i];
997       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
998       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
999     }
1000   }
1001   PetscFunctionReturn(0);
1002 }
1003 
1004 /*@C
1005   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells
1006 
1007   Input Parameters:
1008 + dm     - The DM
1009 . cStart - The first cell to include
1010 . cEnd   - The first cell to exclude
1011 . locX   - A local vector with the solution fields
1012 . locX_t - A local vector with solution field time derivatives, or NULL
1013 - locA   - A local vector with auxiliary fields, or NULL
1014 
1015   Output Parameters:
1016 + u   - The field coefficients
1017 . u_t - The fields derivative coefficients
1018 - a   - The auxiliary field coefficients
1019 
1020   Level: developer
1021 
1022 .seealso: DMPlexGetFaceFields()
1023 @*/
1024 PetscErrorCode DMPlexRestoreCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1025 {
1026   PetscErrorCode ierr;
1027 
1028   PetscFunctionBegin;
1029   ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, u);CHKERRQ(ierr);
1030   if (locX_t) {ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, u_t);CHKERRQ(ierr);}
1031   if (locA)   {ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, a);CHKERRQ(ierr);}
1032   PetscFunctionReturn(0);
1033 }
1034 
1035 /*@C
1036   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces
1037 
1038   Input Parameters:
1039 + dm     - The DM
1040 . fStart - The first face to include
1041 . fEnd   - The first face to exclude
1042 . locX   - A local vector with the solution fields
1043 . locX_t - A local vector with solution field time derivatives, or NULL
1044 . faceGeometry - A local vector with face geometry
1045 . cellGeometry - A local vector with cell geometry
1046 - locaGrad - A local vector with field gradients, or NULL
1047 
1048   Output Parameters:
1049 + Nface - The number of faces with field values
1050 . uL - The field values at the left side of the face
1051 - uR - The field values at the right side of the face
1052 
1053   Level: developer
1054 
1055 .seealso: DMPlexGetCellFields()
1056 @*/
1057 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)
1058 {
1059   DM                 dmFace, dmCell, dmGrad = NULL;
1060   PetscSection       section;
1061   PetscDS            prob;
1062   DMLabel            ghostLabel;
1063   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
1064   PetscBool         *isFE;
1065   PetscInt           dim, Nf, f, Nc, numFaces = fEnd - fStart, iface, face;
1066   PetscErrorCode     ierr;
1067 
1068   PetscFunctionBegin;
1069   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1070   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1071   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1072   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 6);
1073   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 7);
1074   if (locGrad) {PetscValidHeaderSpecific(locGrad, VEC_CLASSID, 8);}
1075   PetscValidPointer(uL, 9);
1076   PetscValidPointer(uR, 10);
1077   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1078   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1079   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1080   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1081   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1082   ierr = PetscMalloc1(Nf, &isFE);CHKERRQ(ierr);
1083   for (f = 0; f < Nf; ++f) {
1084     PetscObject  obj;
1085     PetscClassId id;
1086 
1087     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1088     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1089     if (id == PETSCFE_CLASSID)      {isFE[f] = PETSC_TRUE;}
1090     else if (id == PETSCFV_CLASSID) {isFE[f] = PETSC_FALSE;}
1091     else                            {isFE[f] = PETSC_FALSE;}
1092   }
1093   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1094   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1095   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1096   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1097   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1098   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1099   if (locGrad) {
1100     ierr = VecGetDM(locGrad, &dmGrad);CHKERRQ(ierr);
1101     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1102   }
1103   ierr = DMGetWorkArray(dm, numFaces*Nc, MPIU_SCALAR, uL);CHKERRQ(ierr);
1104   ierr = DMGetWorkArray(dm, numFaces*Nc, MPIU_SCALAR, uR);CHKERRQ(ierr);
1105   /* Right now just eat the extra work for FE (could make a cell loop) */
1106   for (face = fStart, iface = 0; face < fEnd; ++face) {
1107     const PetscInt        *cells;
1108     PetscFVFaceGeom       *fg;
1109     PetscFVCellGeom       *cgL, *cgR;
1110     PetscScalar           *xL, *xR, *gL, *gR;
1111     PetscScalar           *uLl = *uL, *uRl = *uR;
1112     PetscInt               ghost, nsupp, nchild;
1113 
1114     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1115     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1116     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1117     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1118     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1119     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1120     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1121     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1122     for (f = 0; f < Nf; ++f) {
1123       PetscInt off;
1124 
1125       ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1126       if (isFE[f]) {
1127         const PetscInt *cone;
1128         PetscInt        comp, coneSizeL, coneSizeR, faceLocL, faceLocR, ldof, rdof, d;
1129 
1130         xL = xR = NULL;
1131         ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1132         ierr = DMPlexVecGetClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1133         ierr = DMPlexVecGetClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1134         ierr = DMPlexGetCone(dm, cells[0], &cone);CHKERRQ(ierr);
1135         ierr = DMPlexGetConeSize(dm, cells[0], &coneSizeL);CHKERRQ(ierr);
1136         for (faceLocL = 0; faceLocL < coneSizeL; ++faceLocL) if (cone[faceLocL] == face) break;
1137         ierr = DMPlexGetCone(dm, cells[1], &cone);CHKERRQ(ierr);
1138         ierr = DMPlexGetConeSize(dm, cells[1], &coneSizeR);CHKERRQ(ierr);
1139         for (faceLocR = 0; faceLocR < coneSizeR; ++faceLocR) if (cone[faceLocR] == face) break;
1140         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]);
1141         /* Check that FEM field has values in the right cell (sometimes its an FV ghost cell) */
1142         /* TODO: this is a hack that might not be right for nonconforming */
1143         if (faceLocL < coneSizeL) {
1144           ierr = EvaluateFaceFields(prob, f, faceLocL, xL, &uLl[iface*Nc+off]);CHKERRQ(ierr);
1145           if (rdof == ldof && faceLocR < coneSizeR) {ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);}
1146           else              {for(d = 0; d < comp; ++d) uRl[iface*Nc+off+d] = uLl[iface*Nc+off+d];}
1147         }
1148         else {
1149           ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);
1150           ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1151           for(d = 0; d < comp; ++d) uLl[iface*Nc+off+d] = uRl[iface*Nc+off+d];
1152         }
1153         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1154         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1155       } else {
1156         PetscFV  fv;
1157         PetscInt numComp, c;
1158 
1159         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fv);CHKERRQ(ierr);
1160         ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1161         ierr = DMPlexPointLocalFieldRead(dm, cells[0], f, x, &xL);CHKERRQ(ierr);
1162         ierr = DMPlexPointLocalFieldRead(dm, cells[1], f, x, &xR);CHKERRQ(ierr);
1163         if (dmGrad) {
1164           PetscReal dxL[3], dxR[3];
1165 
1166           ierr = DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);CHKERRQ(ierr);
1167           ierr = DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);CHKERRQ(ierr);
1168           DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
1169           DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
1170           for (c = 0; c < numComp; ++c) {
1171             uLl[iface*Nc+off+c] = xL[c] + DMPlex_DotD_Internal(dim, &gL[c*dim], dxL);
1172             uRl[iface*Nc+off+c] = xR[c] + DMPlex_DotD_Internal(dim, &gR[c*dim], dxR);
1173           }
1174         } else {
1175           for (c = 0; c < numComp; ++c) {
1176             uLl[iface*Nc+off+c] = xL[c];
1177             uRl[iface*Nc+off+c] = xR[c];
1178           }
1179         }
1180       }
1181     }
1182     ++iface;
1183   }
1184   *Nface = iface;
1185   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1186   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1187   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1188   if (locGrad) {
1189     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1190   }
1191   ierr = PetscFree(isFE);CHKERRQ(ierr);
1192   PetscFunctionReturn(0);
1193 }
1194 
1195 /*@C
1196   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces
1197 
1198   Input Parameters:
1199 + dm     - The DM
1200 . fStart - The first face to include
1201 . fEnd   - The first face to exclude
1202 . locX   - A local vector with the solution fields
1203 . locX_t - A local vector with solution field time derivatives, or NULL
1204 . faceGeometry - A local vector with face geometry
1205 . cellGeometry - A local vector with cell geometry
1206 - locaGrad - A local vector with field gradients, or NULL
1207 
1208   Output Parameters:
1209 + Nface - The number of faces with field values
1210 . uL - The field values at the left side of the face
1211 - uR - The field values at the right side of the face
1212 
1213   Level: developer
1214 
1215 .seealso: DMPlexGetFaceFields()
1216 @*/
1217 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)
1218 {
1219   PetscErrorCode ierr;
1220 
1221   PetscFunctionBegin;
1222   ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, uL);CHKERRQ(ierr);
1223   ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, uR);CHKERRQ(ierr);
1224   PetscFunctionReturn(0);
1225 }
1226 
1227 /*@C
1228   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces
1229 
1230   Input Parameters:
1231 + dm     - The DM
1232 . fStart - The first face to include
1233 . fEnd   - The first face to exclude
1234 . faceGeometry - A local vector with face geometry
1235 - cellGeometry - A local vector with cell geometry
1236 
1237   Output Parameters:
1238 + Nface - The number of faces with field values
1239 . fgeom - The extract the face centroid and normal
1240 - vol   - The cell volume
1241 
1242   Level: developer
1243 
1244 .seealso: DMPlexGetCellFields()
1245 @*/
1246 PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1247 {
1248   DM                 dmFace, dmCell;
1249   DMLabel            ghostLabel;
1250   const PetscScalar *facegeom, *cellgeom;
1251   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
1252   PetscErrorCode     ierr;
1253 
1254   PetscFunctionBegin;
1255   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1256   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 4);
1257   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 5);
1258   PetscValidPointer(fgeom, 6);
1259   PetscValidPointer(vol, 7);
1260   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1261   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1262   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1263   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1264   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1265   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1266   ierr = PetscMalloc1(numFaces, fgeom);CHKERRQ(ierr);
1267   ierr = DMGetWorkArray(dm, numFaces*2, MPIU_SCALAR, vol);CHKERRQ(ierr);
1268   for (face = fStart, iface = 0; face < fEnd; ++face) {
1269     const PetscInt        *cells;
1270     PetscFVFaceGeom       *fg;
1271     PetscFVCellGeom       *cgL, *cgR;
1272     PetscFVFaceGeom       *fgeoml = *fgeom;
1273     PetscReal             *voll   = *vol;
1274     PetscInt               ghost, d, nchild, nsupp;
1275 
1276     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1277     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1278     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1279     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1280     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1281     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1282     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1283     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1284     for (d = 0; d < dim; ++d) {
1285       fgeoml[iface].centroid[d] = fg->centroid[d];
1286       fgeoml[iface].normal[d]   = fg->normal[d];
1287     }
1288     voll[iface*2+0] = cgL->volume;
1289     voll[iface*2+1] = cgR->volume;
1290     ++iface;
1291   }
1292   *Nface = iface;
1293   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1294   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1295   PetscFunctionReturn(0);
1296 }
1297 
1298 /*@C
1299   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces
1300 
1301   Input Parameters:
1302 + dm     - The DM
1303 . fStart - The first face to include
1304 . fEnd   - The first face to exclude
1305 . faceGeometry - A local vector with face geometry
1306 - cellGeometry - A local vector with cell geometry
1307 
1308   Output Parameters:
1309 + Nface - The number of faces with field values
1310 . fgeom - The extract the face centroid and normal
1311 - vol   - The cell volume
1312 
1313   Level: developer
1314 
1315 .seealso: DMPlexGetFaceFields()
1316 @*/
1317 PetscErrorCode DMPlexRestoreFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1318 {
1319   PetscErrorCode ierr;
1320 
1321   PetscFunctionBegin;
1322   ierr = PetscFree(*fgeom);CHKERRQ(ierr);
1323   ierr = DMRestoreWorkArray(dm, 0, MPIU_REAL, vol);CHKERRQ(ierr);
1324   PetscFunctionReturn(0);
1325 }
1326 
1327 static PetscErrorCode ISIntersect_Caching(IS is1, IS is2, IS *isect)
1328 {
1329   PetscErrorCode ierr;
1330 
1331   PetscFunctionBegin;
1332   *isect = NULL;
1333   if (is2 && is1) {
1334     char           composeStr[33] = {0};
1335     PetscObjectId  is2id;
1336 
1337     ierr = PetscObjectGetId((PetscObject)is2,&is2id);CHKERRQ(ierr);
1338     ierr = PetscSNPrintf(composeStr,32,"ISIntersect_Caching_%x",is2id);CHKERRQ(ierr);
1339     ierr = PetscObjectQuery((PetscObject) is1, composeStr, (PetscObject *) isect);CHKERRQ(ierr);
1340     if (*isect == NULL) {
1341       ierr = ISIntersect(is1, is2, isect);CHKERRQ(ierr);
1342       ierr = PetscObjectCompose((PetscObject) is1, composeStr, (PetscObject) *isect);CHKERRQ(ierr);
1343     } else {
1344       ierr = PetscObjectReference((PetscObject) *isect);CHKERRQ(ierr);
1345     }
1346   }
1347   PetscFunctionReturn(0);
1348 }
1349 
1350 static PetscErrorCode DMPlexComputeBdResidual_Single_Internal(DM dm, PetscReal t, DMLabel label, PetscInt numValues, const PetscInt values[], PetscInt field, Vec locX, Vec locX_t, Vec locF, DMField coordField, IS facetIS)
1351 {
1352   DM_Plex         *mesh = (DM_Plex *) dm->data;
1353   DM               plex = NULL;
1354   PetscDS          prob, probAux = NULL;
1355   PetscSection     section, sectionAux = NULL;
1356   Vec              locA = NULL;
1357   PetscFEGeom     *fgeom;
1358   PetscScalar     *u = NULL, *u_t = NULL, *a = NULL, *elemVec = NULL;
1359   PetscInt         v;
1360   PetscInt         totDim, totDimAux = 0;
1361   PetscErrorCode   ierr;
1362 
1363   PetscFunctionBegin;
1364   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1365   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1366   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1367   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1368   if (locA) {
1369     DM dmAux;
1370 
1371     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1372     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1373     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1374     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
1375     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
1376   }
1377   for (v = 0; v < numValues; ++v) {
1378     PetscBool        isAffine;
1379     PetscQuadrature  qGeom = NULL;
1380     IS               pointIS;
1381     const PetscInt  *points;
1382     PetscInt         numFaces, face, Nq;
1383 
1384     ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1385     if (!pointIS) continue; /* No points with that id on this process */
1386     {
1387       IS isectIS;
1388 
1389       /* TODO: Special cases of ISIntersect where it is quick to check a priori if one is a superset of the other */
1390       ierr = ISIntersect_Caching(facetIS,pointIS,&isectIS);CHKERRQ(ierr);
1391       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1392       pointIS = isectIS;
1393     }
1394     ierr = ISGetLocalSize(pointIS,&numFaces);CHKERRQ(ierr);
1395     ierr = ISGetIndices(pointIS,&points);CHKERRQ(ierr);
1396     ierr = PetscMalloc4(numFaces*totDim, &u, locX_t ? numFaces*totDim : 0, &u_t, numFaces*totDim, &elemVec, locA ? numFaces*totDimAux : 0, &a);CHKERRQ(ierr);
1397     ierr = DMFieldGetFEInvariance(coordField,pointIS,NULL,&isAffine,NULL);CHKERRQ(ierr);
1398     if (isAffine) {
1399       ierr = DMFieldCreateDefaultQuadrature(coordField,pointIS,&qGeom);CHKERRQ(ierr);
1400     }
1401     if (!qGeom) {
1402       PetscFE fe;
1403 
1404       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1405       ierr = PetscFEGetFaceQuadrature(fe, &qGeom);CHKERRQ(ierr);
1406       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
1407     }
1408     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1409     ierr = DMSNESGetFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
1410     for (face = 0; face < numFaces; ++face) {
1411       const PetscInt point = points[face], *support, *cone;
1412       PetscScalar   *x     = NULL;
1413       PetscInt       i, coneSize, faceLoc;
1414 
1415       ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
1416       ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
1417       ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
1418       for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
1419       if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %D in cone of support[0] %D", point, support[0]);
1420       fgeom->face[face][0] = faceLoc;
1421       ierr = DMPlexVecGetClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1422       for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
1423       ierr = DMPlexVecRestoreClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1424       if (locX_t) {
1425         ierr = DMPlexVecGetClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1426         for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
1427         ierr = DMPlexVecRestoreClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1428       }
1429       if (locA) {
1430         ierr = DMPlexVecGetClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
1431         for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
1432         ierr = DMPlexVecRestoreClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
1433       }
1434     }
1435     ierr = PetscMemzero(elemVec, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1436     {
1437       PetscFE         fe;
1438       PetscInt        Nb;
1439       PetscFEGeom     *chunkGeom = NULL;
1440       /* Conforming batches */
1441       PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1442       /* Remainder */
1443       PetscInt        Nr, offset;
1444 
1445       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1446       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1447       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1448       /* TODO: documentation is unclear about what is going on with these numbers: how should Nb / Nq factor in ? */
1449       blockSize = Nb;
1450       batchSize = numBlocks * blockSize;
1451       ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1452       numChunks = numFaces / (numBatches*batchSize);
1453       Ne        = numChunks*numBatches*batchSize;
1454       Nr        = numFaces % (numBatches*batchSize);
1455       offset    = numFaces - Nr;
1456       ierr = PetscFEGeomGetChunk(fgeom,0,offset,&chunkGeom);CHKERRQ(ierr);
1457       ierr = PetscFEIntegrateBdResidual(fe, prob, field, Ne, chunkGeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1458       ierr = PetscFEGeomGetChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
1459       ierr = PetscFEIntegrateBdResidual(fe, prob, field, Nr, chunkGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, a ? &a[offset*totDimAux] : NULL, t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1460       ierr = PetscFEGeomRestoreChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
1461     }
1462     for (face = 0; face < numFaces; ++face) {
1463       const PetscInt point = points[face], *support;
1464 
1465       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDim, &elemVec[face*totDim]);CHKERRQ(ierr);}
1466       ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
1467       ierr = DMPlexVecSetClosure(dm, NULL, locF, support[0], &elemVec[face*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1468     }
1469     ierr = DMSNESRestoreFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
1470     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
1471     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1472     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1473     ierr = PetscFree4(u, u_t, elemVec, a);CHKERRQ(ierr);
1474   }
1475   if (plex) {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
1476   PetscFunctionReturn(0);
1477 }
1478 
1479 PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1480 {
1481   PetscDS        prob;
1482   PetscInt       dim, numBd, bd;
1483   DMLabel        depthLabel;
1484   DMField        coordField = NULL;
1485   IS             facetIS;
1486   PetscErrorCode ierr;
1487 
1488   PetscFunctionBegin;
1489   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1490   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1491   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1492   ierr = DMLabelGetStratumIS(depthLabel,dim - 1,&facetIS);CHKERRQ(ierr);
1493   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
1494   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1495   for (bd = 0; bd < numBd; ++bd) {
1496     DMBoundaryConditionType type;
1497     const char             *bdLabel;
1498     DMLabel                 label;
1499     const PetscInt         *values;
1500     PetscInt                field, numValues;
1501     PetscObject             obj;
1502     PetscClassId            id;
1503 
1504     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1505     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
1506     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1507     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
1508     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1509     ierr = DMPlexComputeBdResidual_Single_Internal(dm, t, label, numValues, values, field, locX, locX_t, locF, coordField, facetIS);CHKERRQ(ierr);
1510   }
1511   ierr = ISDestroy(&facetIS);CHKERRQ(ierr);
1512   PetscFunctionReturn(0);
1513 }
1514 
1515 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, IS cellIS, PetscReal time, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1516 {
1517   DM_Plex          *mesh       = (DM_Plex *) dm->data;
1518   const char       *name       = "Residual";
1519   DM                dmAux      = NULL;
1520   DM                dmGrad     = NULL;
1521   DMLabel           ghostLabel = NULL;
1522   PetscDS           prob       = NULL;
1523   PetscDS           probAux    = NULL;
1524   PetscSection      section    = NULL;
1525   PetscBool         useFEM     = PETSC_FALSE;
1526   PetscBool         useFVM     = PETSC_FALSE;
1527   PetscBool         isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
1528   PetscFV           fvm        = NULL;
1529   PetscFVCellGeom  *cgeomFVM   = NULL;
1530   PetscFVFaceGeom  *fgeomFVM   = NULL;
1531   DMField           coordField = NULL;
1532   Vec               locA, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1533   PetscScalar      *u = NULL, *u_t, *a, *uL, *uR;
1534   PetscInt          Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
1535   PetscBool         isStride;
1536   PetscInt          cStart = -1, cEnd = -1, numCells;
1537   PetscBool         isAffine = PETSC_FALSE;
1538   PetscQuadrature   affineQuad = NULL, *quads = NULL;
1539   PetscFEGeom      *affineGeom = NULL, **geoms = NULL;
1540   PetscErrorCode    ierr;
1541 
1542   PetscFunctionBegin;
1543   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1544   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1545   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
1546   /* FEM+FVM */
1547   /* 1: Get sizes from dm and dmAux */
1548   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1549   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1550   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1551   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1552   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1553   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1554   if (locA) {
1555     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1556     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1557     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1558   }
1559   /* 2: Get geometric data */
1560   for (f = 0; f < Nf; ++f) {
1561     PetscObject  obj;
1562     PetscClassId id;
1563     PetscBool    fimp;
1564 
1565     ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1566     if (isImplicit != fimp) continue;
1567     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1568     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1569     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1570     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1571   }
1572   if (useFEM) {
1573     ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1574     ierr = DMFieldGetFEInvariance(coordField,cellIS,NULL,&isAffine,NULL);CHKERRQ(ierr);
1575     if (isAffine) {
1576       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&affineQuad);CHKERRQ(ierr);
1577       if (affineQuad) {
1578         ierr = DMSNESGetFEGeom(coordField,cellIS,affineQuad,PETSC_FALSE,&affineGeom);CHKERRQ(ierr);
1579       }
1580     } else {
1581       ierr = PetscCalloc2(Nf,&quads,Nf,&geoms);CHKERRQ(ierr);
1582       for (f = 0; f < Nf; ++f) {
1583         PetscObject  obj;
1584         PetscClassId id;
1585         PetscBool    fimp;
1586 
1587         ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1588         if (isImplicit != fimp) continue;
1589         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1590         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1591         if (id == PETSCFE_CLASSID) {
1592           PetscFE fe = (PetscFE) obj;
1593 
1594           ierr = PetscFEGetQuadrature(fe, &quads[f]);CHKERRQ(ierr);
1595           ierr = PetscObjectReference((PetscObject)quads[f]);CHKERRQ(ierr);
1596           ierr = DMSNESGetFEGeom(coordField,cellIS,quads[f],PETSC_FALSE,&geoms[f]);CHKERRQ(ierr);
1597         }
1598       }
1599     }
1600   }
1601   if (useFVM) {
1602     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1603     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1604     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1605     /* Reconstruct and limit cell gradients */
1606     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1607     if (dmGrad) {
1608       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1609       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1610       ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1611       /* Communicate gradient values */
1612       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1613       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1614       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1615       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1616     }
1617     /* Handle non-essential (e.g. outflow) boundary values */
1618     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1619   }
1620   /* Loop over chunks */
1621   ierr = ISGetLocalSize(cellIS, &numCells);CHKERRQ(ierr);
1622   ierr = PetscObjectTypeCompare((PetscObject) cellIS, ISSTRIDE, &isStride);CHKERRQ(ierr);
1623   if (isStride) {
1624     PetscInt step;
1625 
1626     ierr = ISStrideGetInfo(cellIS, &cStart, &step);CHKERRQ(ierr);
1627     cEnd = cStart + numCells;
1628     if (step != 1) {
1629       isStride = PETSC_FALSE;
1630     }
1631   }
1632   if (!isStride) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Not implemented yet");
1633   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1634   numChunks     = 1;
1635   cellChunkSize = numCells/numChunks;
1636   faceChunkSize = (fEnd - fStart)/numChunks;
1637   numChunks     = PetscMin(1,numCells);
1638   for (chunk = 0; chunk < numChunks; ++chunk) {
1639     PetscScalar     *elemVec, *fluxL, *fluxR;
1640     PetscReal       *vol;
1641     PetscFVFaceGeom *fgeom;
1642     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, cell;
1643     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = 0, face;
1644 
1645     /* Extract field coefficients */
1646     if (useFEM) {
1647       ierr = DMPlexGetCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1648       ierr = DMGetWorkArray(dm, numCells*totDim, MPIU_SCALAR, &elemVec);CHKERRQ(ierr);
1649       ierr = PetscMemzero(elemVec, numCells*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1650     }
1651     if (useFVM) {
1652       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1653       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1654       ierr = DMGetWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxL);CHKERRQ(ierr);
1655       ierr = DMGetWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxR);CHKERRQ(ierr);
1656       ierr = PetscMemzero(fluxL, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1657       ierr = PetscMemzero(fluxR, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1658     }
1659     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1660     /* Loop over fields */
1661     for (f = 0; f < Nf; ++f) {
1662       PetscObject  obj;
1663       PetscClassId id;
1664       PetscBool    fimp;
1665       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1666 
1667       ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1668       if (isImplicit != fimp) continue;
1669       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1670       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1671       if (id == PETSCFE_CLASSID) {
1672         PetscFE         fe = (PetscFE) obj;
1673         PetscFEGeom    *geom = affineGeom ? affineGeom : geoms[f];
1674         PetscFEGeom    *chunkGeom = NULL;
1675         PetscQuadrature quad = affineQuad ? affineQuad : quads[f];
1676         PetscInt        Nq, Nb;
1677 
1678         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1679         ierr = PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1680         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1681         blockSize = Nb;
1682         batchSize = numBlocks * blockSize;
1683         ierr      = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1684         numChunks = numCells / (numBatches*batchSize);
1685         Ne        = numChunks*numBatches*batchSize;
1686         Nr        = numCells % (numBatches*batchSize);
1687         offset    = numCells - Nr;
1688         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1689         /*   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) */
1690         ierr = PetscFEGeomGetChunk(geom,0,offset,&chunkGeom);CHKERRQ(ierr);
1691         ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, chunkGeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1692         ierr = PetscFEGeomGetChunk(geom,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1693         ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, chunkGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1694         ierr = PetscFEGeomRestoreChunk(geom,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1695       } else if (id == PETSCFV_CLASSID) {
1696         PetscFV fv = (PetscFV) obj;
1697 
1698         Ne = numFaces;
1699         /* Riemann solve over faces (need fields at face centroids) */
1700         /*   We need to evaluate FE fields at those coordinates */
1701         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1702       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1703     }
1704     /* Loop over domain */
1705     if (useFEM) {
1706       /* Add elemVec to locX */
1707       for (cell = cS; cell < cE; ++cell) {
1708         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cell*totDim]);CHKERRQ(ierr);}
1709         if (ghostLabel) {
1710           PetscInt ghostVal;
1711 
1712           ierr = DMLabelGetValue(ghostLabel,cell,&ghostVal);CHKERRQ(ierr);
1713           if (ghostVal > 0) continue;
1714         }
1715         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cell*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1716       }
1717     }
1718     if (useFVM) {
1719       PetscScalar *fa;
1720       PetscInt     iface;
1721 
1722       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1723       for (f = 0; f < Nf; ++f) {
1724         PetscFV      fv;
1725         PetscObject  obj;
1726         PetscClassId id;
1727         PetscInt     foff, pdim;
1728 
1729         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1730         ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1731         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1732         if (id != PETSCFV_CLASSID) continue;
1733         fv   = (PetscFV) obj;
1734         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1735         /* Accumulate fluxes to cells */
1736         for (face = fS, iface = 0; face < fE; ++face) {
1737           const PetscInt *cells;
1738           PetscScalar    *fL = NULL, *fR = NULL;
1739           PetscInt        ghost, d, nsupp, nchild;
1740 
1741           ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1742           ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1743           ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1744           if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1745           ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1746           ierr = DMLabelGetValue(ghostLabel,cells[0],&ghost);CHKERRQ(ierr);
1747           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, cells[0], f, fa, &fL);CHKERRQ(ierr);}
1748           ierr = DMLabelGetValue(ghostLabel,cells[1],&ghost);CHKERRQ(ierr);
1749           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, cells[1], f, fa, &fR);CHKERRQ(ierr);}
1750           for (d = 0; d < pdim; ++d) {
1751             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
1752             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
1753           }
1754           ++iface;
1755         }
1756       }
1757       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1758     }
1759     /* Handle time derivative */
1760     if (locX_t) {
1761       PetscScalar *x_t, *fa;
1762 
1763       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1764       ierr = VecGetArray(locX_t, &x_t);CHKERRQ(ierr);
1765       for (f = 0; f < Nf; ++f) {
1766         PetscFV      fv;
1767         PetscObject  obj;
1768         PetscClassId id;
1769         PetscInt     pdim, d;
1770 
1771         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1772         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1773         if (id != PETSCFV_CLASSID) continue;
1774         fv   = (PetscFV) obj;
1775         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1776         for (cell = cS; cell < cE; ++cell) {
1777           PetscScalar *u_t, *r;
1778 
1779           if (ghostLabel) {
1780             PetscInt ghostVal;
1781 
1782             ierr = DMLabelGetValue(ghostLabel,cell,&ghostVal);CHKERRQ(ierr);
1783             if (ghostVal > 0) continue;
1784           }
1785           ierr = DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);CHKERRQ(ierr);
1786           ierr = DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);CHKERRQ(ierr);
1787           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
1788         }
1789       }
1790       ierr = VecRestoreArray(locX_t, &x_t);CHKERRQ(ierr);
1791       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1792     }
1793     if (useFEM) {
1794       ierr = DMPlexRestoreCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1795       ierr = DMRestoreWorkArray(dm, numCells*totDim, MPIU_SCALAR, &elemVec);CHKERRQ(ierr);
1796     }
1797     if (useFVM) {
1798       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1799       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1800       ierr = DMRestoreWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxL);CHKERRQ(ierr);
1801       ierr = DMRestoreWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxR);CHKERRQ(ierr);
1802       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1803     }
1804   }
1805 
1806   if (useFEM) {
1807     ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, t, locF, user);CHKERRQ(ierr);
1808 
1809     if (isAffine) {
1810       ierr = DMSNESRestoreFEGeom(coordField,cellIS,affineQuad,PETSC_FALSE,&affineGeom);CHKERRQ(ierr);
1811       ierr = PetscQuadratureDestroy(&affineQuad);CHKERRQ(ierr);
1812     } else {
1813       for (f = 0; f < Nf; ++f) {
1814         ierr = DMSNESRestoreFEGeom(coordField,cellIS,quads[f],PETSC_FALSE,&geoms[f]);CHKERRQ(ierr);
1815         ierr = PetscQuadratureDestroy(&quads[f]);CHKERRQ(ierr);
1816       }
1817       ierr = PetscFree2(quads,geoms);CHKERRQ(ierr);
1818     }
1819   }
1820 
1821   /* FEM */
1822   /* 1: Get sizes from dm and dmAux */
1823   /* 2: Get geometric data */
1824   /* 3: Handle boundary values */
1825   /* 4: Loop over domain */
1826   /*   Extract coefficients */
1827   /* Loop over fields */
1828   /*   Set tiling for FE*/
1829   /*   Integrate FE residual to get elemVec */
1830   /*     Loop over subdomain */
1831   /*       Loop over quad points */
1832   /*         Transform coords to real space */
1833   /*         Evaluate field and aux fields at point */
1834   /*         Evaluate residual at point */
1835   /*         Transform residual to real space */
1836   /*       Add residual to elemVec */
1837   /* Loop over domain */
1838   /*   Add elemVec to locX */
1839 
1840   /* FVM */
1841   /* Get geometric data */
1842   /* If using gradients */
1843   /*   Compute gradient data */
1844   /*   Loop over domain faces */
1845   /*     Count computational faces */
1846   /*     Reconstruct cell gradient */
1847   /*   Loop over domain cells */
1848   /*     Limit cell gradients */
1849   /* Handle boundary values */
1850   /* Loop over domain faces */
1851   /*   Read out field, centroid, normal, volume for each side of face */
1852   /* Riemann solve over faces */
1853   /* Loop over domain faces */
1854   /*   Accumulate fluxes to cells */
1855   /* TODO Change printFEM to printDisc here */
1856   if (mesh->printFEM) {
1857     Vec         locFbc;
1858     PetscInt    pStart, pEnd, p, maxDof;
1859     PetscScalar *zeroes;
1860 
1861     ierr = VecDuplicate(locF,&locFbc);CHKERRQ(ierr);
1862     ierr = VecCopy(locF,locFbc);CHKERRQ(ierr);
1863     ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
1864     ierr = PetscSectionGetMaxDof(section,&maxDof);CHKERRQ(ierr);
1865     ierr = PetscCalloc1(maxDof,&zeroes);CHKERRQ(ierr);
1866     for (p = pStart; p < pEnd; p++) {
1867       ierr = VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);CHKERRQ(ierr);
1868     }
1869     ierr = PetscFree(zeroes);CHKERRQ(ierr);
1870     ierr = DMPrintLocalVec(dm, name, mesh->printTol, locFbc);CHKERRQ(ierr);
1871     ierr = VecDestroy(&locFbc);CHKERRQ(ierr);
1872   }
1873   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1874   PetscFunctionReturn(0);
1875 }
1876 
1877 static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, PetscReal t, Vec F, void *user)
1878 {
1879   DM                dmCh, dmAux;
1880   Vec               A;
1881   DMField           coordField = NULL;
1882   PetscDS           prob, probCh, probAux = NULL;
1883   PetscSection      section, sectionAux;
1884   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
1885   PetscInt          Nf, f, numCells, cStart, cEnd, c;
1886   PetscInt          totDim, totDimAux = 0, diffCell = 0;
1887   PetscInt          depth;
1888   PetscBool         isAffine;
1889   IS                cellIS;
1890   DMLabel           depthLabel;
1891   PetscErrorCode    ierr;
1892 
1893   PetscFunctionBegin;
1894   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1895   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1896   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1897   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1898   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1899   numCells = cEnd - cStart;
1900   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
1901   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
1902   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1903   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1904   if (dmAux) {
1905     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1906     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1907     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1908   }
1909   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1910   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);CHKERRQ(ierr);
1911   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
1912   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1913   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1914   ierr = DMPlexGetDepth(dm,&depth);CHKERRQ(ierr);
1915   ierr = DMLabelGetStratumIS(depthLabel,depth,&cellIS);CHKERRQ(ierr);
1916   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1917   for (c = cStart; c < cEnd; ++c) {
1918     PetscScalar *x = NULL, *x_t = NULL;
1919     PetscInt     i;
1920 
1921     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1922     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1923     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1924     if (X_t) {
1925       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1926       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1927       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1928     }
1929     if (dmAux) {
1930       DM dmAuxPlex;
1931 
1932       ierr = DMSNESConvertPlex(dmAux,&dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1933       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1934       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1935       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1936       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1937     }
1938   }
1939   for (f = 0; f < Nf; ++f) {
1940     PetscFE  fe, feCh;
1941     PetscInt Nq, Nb;
1942     /* Conforming batches */
1943     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1944     /* Remainder */
1945     PetscInt Nr, offset;
1946     PetscQuadrature qGeom = NULL;
1947     PetscFEGeom *cgeomFEM, *chunkGeom = NULL;
1948 
1949     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1950     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
1951     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1952     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1953     ierr = DMFieldGetFEInvariance(coordField,cellIS,NULL,&isAffine,NULL);CHKERRQ(ierr);
1954     if (isAffine) {
1955       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);CHKERRQ(ierr);
1956     }
1957     if (!qGeom) {
1958       ierr = PetscFEGetQuadrature(fe, &qGeom);CHKERRQ(ierr);
1959       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
1960     }
1961     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1962     ierr = DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
1963     blockSize = Nb;
1964     batchSize = numBlocks * blockSize;
1965     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1966     numChunks = numCells / (numBatches*batchSize);
1967     Ne        = numChunks*numBatches*batchSize;
1968     Nr        = numCells % (numBatches*batchSize);
1969     offset    = numCells - Nr;
1970     ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
1971     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, chunkGeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1972     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, chunkGeom, u, u_t, probAux, a, t, elemVecCh);CHKERRQ(ierr);
1973     ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1974     ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, chunkGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1975     ierr = PetscFEIntegrateResidual(feCh, prob, f, Nr, chunkGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVecCh[offset*totDim]);CHKERRQ(ierr);
1976     ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1977     ierr = DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
1978     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
1979   }
1980   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
1981   for (c = cStart; c < cEnd; ++c) {
1982     PetscBool diff = PETSC_FALSE;
1983     PetscInt  d;
1984 
1985     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
1986     if (diff) {
1987       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
1988       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
1989       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
1990       ++diffCell;
1991     }
1992     if (diffCell > 9) break;
1993     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1994   }
1995   ierr = PetscFree3(u,u_t,elemVec);CHKERRQ(ierr);
1996   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
1997   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1998   PetscFunctionReturn(0);
1999 }
2000 
2001 /*@
2002   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
2003 
2004   Input Parameters:
2005 + dm - The mesh
2006 . X  - Local solution
2007 - user - The user context
2008 
2009   Output Parameter:
2010 . F  - Local output vector
2011 
2012   Level: developer
2013 
2014 .seealso: DMPlexComputeJacobianActionFEM()
2015 @*/
2016 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
2017 {
2018   PetscObject    check;
2019   DM             plex;
2020   IS             cellIS;
2021   PetscInt       depth;
2022   PetscErrorCode ierr;
2023 
2024   PetscFunctionBegin;
2025   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2026   ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
2027   ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
2028   if (!cellIS) {
2029     ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);
2030   }
2031   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
2032   ierr = PetscObjectQuery((PetscObject) plex, "dmCh", &check);CHKERRQ(ierr);
2033   if (check) {ierr = DMPlexComputeResidualFEM_Check_Internal(plex, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2034   else       {ierr = DMPlexComputeResidual_Internal(plex, cellIS, PETSC_MIN_REAL, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2035   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
2036   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2037   PetscFunctionReturn(0);
2038 }
2039 
2040 /*@
2041   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X
2042 
2043   Input Parameters:
2044 + dm - The mesh
2045 - user - The user context
2046 
2047   Output Parameter:
2048 . X  - Local solution
2049 
2050   Level: developer
2051 
2052 .seealso: DMPlexComputeJacobianActionFEM()
2053 @*/
2054 PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
2055 {
2056   DM             plex;
2057   PetscErrorCode ierr;
2058 
2059   PetscFunctionBegin;
2060   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2061   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);CHKERRQ(ierr);
2062   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2063   PetscFunctionReturn(0);
2064 }
2065 
2066 PetscErrorCode DMPlexComputeBdJacobian_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, PetscReal X_tShift, Mat Jac, Mat JacP, void *user)
2067 {
2068   DM_Plex         *mesh = (DM_Plex *) dm->data;
2069   DM               dmAux = NULL, plex = NULL;
2070   DMField          coordField = NULL;
2071   PetscSection     section, globalSection, subSection, sectionAux = NULL;
2072   PetscDS          prob, probAux = NULL;
2073   DMLabel          depth;
2074   Vec              locA = NULL;
2075   PetscScalar     *u = NULL, *u_t = NULL, *a = NULL, *elemMat = NULL;
2076   PetscInt         dim, totDim, totDimAux, numBd, bd, Nf;
2077   PetscBool        isMatISP;
2078   IS               facetIS;
2079   PetscErrorCode   ierr;
2080 
2081   PetscFunctionBegin;
2082   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2083   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2084   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2085   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2086   if (isMatISP) {
2087     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2088   }
2089   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2090   ierr = DMLabelGetStratumIS(depth,dim-1,&facetIS);CHKERRQ(ierr);
2091   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2092   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
2093   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2094   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
2095   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
2096   if (locA) {
2097     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
2098     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2099     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2100     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2101     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2102   }
2103   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2104   for (bd = 0; bd < numBd; ++bd) {
2105     DMBoundaryConditionType type;
2106     const char             *bdLabel;
2107     DMLabel                 label;
2108     IS                      pointIS;
2109     const PetscInt         *points;
2110     const PetscInt         *values;
2111     PetscInt                fieldI, fieldJ, numValues, v, numFaces, face, Nq;
2112     PetscObject             obj;
2113     PetscBool               isAffine;
2114     PetscFE                 fe;
2115     PetscClassId            id;
2116 
2117     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &fieldI, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
2118     ierr = PetscDSGetDiscretization(prob, fieldI, &obj);CHKERRQ(ierr);
2119     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2120     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
2121     fe   = (PetscFE) obj;
2122     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
2123     for (v = 0; v < numValues; ++v) {
2124       PetscQuadrature qGeom = NULL;
2125       PetscFEGeom     *fgeom;
2126 
2127       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
2128       if (!pointIS) continue; /* No points with that id on this process */
2129       {
2130         IS isectIS;
2131 
2132         /* TODO: Special cases of ISIntersect where it is quick to check a prior if one is a superset of the other */
2133         ierr = ISIntersect_Caching(facetIS,pointIS,&isectIS);CHKERRQ(ierr);
2134         ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2135         pointIS = isectIS;
2136       }
2137       ierr = ISGetLocalSize(pointIS, &numFaces);CHKERRQ(ierr);
2138       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2139       ierr = PetscMalloc3(numFaces*totDim,&u,locX_t ? numFaces*totDim : 0,&u_t,numFaces*totDim*totDim,&elemMat);CHKERRQ(ierr);
2140       if (locA) {ierr = PetscMalloc1(numFaces*totDimAux,&a);CHKERRQ(ierr);}
2141       ierr = DMFieldGetFEInvariance(coordField,pointIS,NULL,&isAffine,NULL);CHKERRQ(ierr);
2142       if (isAffine) {
2143         ierr = DMFieldCreateDefaultQuadrature(coordField,pointIS,&qGeom);CHKERRQ(ierr);
2144       }
2145       if (!qGeom) {
2146         ierr = PetscFEGetFaceQuadrature(fe, &qGeom);CHKERRQ(ierr);
2147         ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
2148       }
2149       ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
2150       ierr = DMSNESGetFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
2151       for (face = 0; face < numFaces; ++face) {
2152         const PetscInt point = points[face], *support, *cone;
2153         PetscScalar   *x     = NULL;
2154         PetscInt       i, coneSize, faceLoc;
2155 
2156         ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
2157         ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
2158         ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
2159         for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
2160         if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of support[0] %d", point, support[0]);
2161         fgeom->face[face][0] = faceLoc;
2162         ierr = DMPlexVecGetClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
2163         for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
2164         ierr = DMPlexVecRestoreClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
2165         if (locX_t) {
2166           ierr = DMPlexVecGetClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
2167           for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
2168           ierr = DMPlexVecRestoreClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
2169         }
2170         if (locA) {
2171           ierr = DMPlexVecGetClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
2172           for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
2173           ierr = DMPlexVecRestoreClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
2174         }
2175       }
2176       ierr = PetscMemzero(elemMat, numFaces*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2177       {
2178         PetscFE         fe;
2179         PetscInt        Nb;
2180         /* Conforming batches */
2181         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2182         /* Remainder */
2183         PetscFEGeom    *chunkGeom = NULL;
2184         PetscInt        Nr, offset;
2185 
2186         ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2187         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2188         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2189         blockSize = Nb;
2190         batchSize = numBlocks * blockSize;
2191         ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2192         numChunks = numFaces / (numBatches*batchSize);
2193         Ne        = numChunks*numBatches*batchSize;
2194         Nr        = numFaces % (numBatches*batchSize);
2195         offset    = numFaces - Nr;
2196         ierr = PetscFEGeomGetChunk(fgeom,0,offset,&chunkGeom);CHKERRQ(ierr);
2197         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2198           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2199         }
2200         ierr = PetscFEGeomGetChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
2201         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2202           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Nr, chunkGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, a ? &a[offset*totDimAux] : NULL, t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2203         }
2204         ierr = PetscFEGeomRestoreChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
2205       }
2206       for (face = 0; face < numFaces; ++face) {
2207         const PetscInt point = points[face], *support;
2208 
2209         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDim, totDim, &elemMat[face*totDim*totDim]);CHKERRQ(ierr);}
2210         ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
2211         if (!isMatISP) {
2212           ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2213         } else {
2214           Mat lJ;
2215 
2216           ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2217           ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2218         }
2219       }
2220       ierr = DMSNESRestoreFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
2221       ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2222       ierr = PetscFree3(u,u_t,elemMat);CHKERRQ(ierr);
2223       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2224       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2225       if (locA) {ierr = PetscFree(a);CHKERRQ(ierr);}
2226     }
2227   }
2228   ierr = ISDestroy(&facetIS);CHKERRQ(ierr);
2229   if (plex) {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
2230   PetscFunctionReturn(0);
2231 }
2232 
2233 PetscErrorCode DMPlexComputeJacobian_Internal(DM dm, IS cellIS, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Mat Jac, Mat JacP,void *user)
2234 {
2235   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2236   const char       *name  = "Jacobian";
2237   DM                dmAux, plex;
2238   Vec               A;
2239   DMField           coordField;
2240   PetscDS           prob, probAux = NULL;
2241   PetscSection      section, globalSection, subSection, sectionAux;
2242   PetscScalar      *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
2243   PetscInt          Nf, fieldI, fieldJ, numCells, c;
2244   PetscInt          totDim, totDimAux, cStart = -1, cEnd = -1;
2245   PetscBool         isMatIS, isMatISP, isShell, hasJac, hasPrec, hasDyn, hasFV = PETSC_FALSE;
2246   PetscBool         isStride;
2247   PetscErrorCode    ierr;
2248 
2249   PetscFunctionBegin;
2250   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2251   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2252   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2253   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2254   if (isMatISP) {
2255     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2256   }
2257   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2258   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2259   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2260   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2261   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2262   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2263   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2264   ierr = ISGetLocalSize(cellIS, &numCells);CHKERRQ(ierr);
2265   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2266   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2267   if (dmAux) {
2268     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2269     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2270     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2271     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2272   }
2273   if (hasJac && hasPrec) {ierr = MatZeroEntries(Jac);CHKERRQ(ierr);}
2274   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
2275   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);
2276   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2277   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2278   ierr = PetscObjectTypeCompare((PetscObject) cellIS, ISSTRIDE, &isStride);CHKERRQ(ierr);
2279   if (isStride) {
2280     PetscInt step;
2281 
2282     ierr = ISStrideGetInfo(cellIS, &cStart, &step);CHKERRQ(ierr);
2283     cEnd = cStart + numCells;
2284     if (step != 1) {
2285       isStride = PETSC_FALSE;
2286     }
2287   }
2288   if (!isStride) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Not implemented yet");
2289   for (c = cStart; c < cEnd; ++c) {
2290     PetscScalar *x = NULL,  *x_t = NULL;
2291     PetscInt     i;
2292 
2293     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2294     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2295     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2296     if (X_t) {
2297       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2298       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2299       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2300     }
2301     if (dmAux) {
2302       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2303       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2304       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2305     }
2306   }
2307   if (hasJac)  {ierr = PetscMemzero(elemMat,  numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2308   if (hasPrec) {ierr = PetscMemzero(elemMatP, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2309   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2310   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2311     PetscClassId    id;
2312     PetscFE         fe;
2313     PetscQuadrature qGeom = NULL;
2314     PetscInt        Nb;
2315     /* Conforming batches */
2316     PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2317     /* Remainder */
2318     PetscInt        Nr, offset, Nq;
2319     PetscBool       isAffine;
2320     PetscFEGeom     *cgeomFEM, *chunkGeom = NULL, *remGeom = NULL;
2321 
2322     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2323     ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
2324     if (id == PETSCFV_CLASSID) {hasFV = PETSC_TRUE; continue;}
2325     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2326     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2327     ierr = DMFieldGetFEInvariance(coordField,cellIS,NULL,&isAffine,NULL);CHKERRQ(ierr);
2328     if (isAffine) {
2329       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);CHKERRQ(ierr);
2330     }
2331     if (!qGeom) {
2332       ierr = PetscFEGetQuadrature(fe,&qGeom);CHKERRQ(ierr);
2333       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
2334     }
2335     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
2336     ierr = DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2337     blockSize = Nb;
2338     batchSize = numBlocks * blockSize;
2339     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2340     numChunks = numCells / (numBatches*batchSize);
2341     Ne        = numChunks*numBatches*batchSize;
2342     Nr        = numCells % (numBatches*batchSize);
2343     offset    = numCells - Nr;
2344     ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2345     ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2346     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2347       if (hasJac) {
2348         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2349         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2350       }
2351       if (hasPrec) {
2352         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatP);CHKERRQ(ierr);
2353         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMatP[offset*totDim*totDim]);CHKERRQ(ierr);
2354       }
2355       if (hasDyn) {
2356         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2357         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMatD[offset*totDim*totDim]);CHKERRQ(ierr);
2358       }
2359     }
2360     ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2361     ierr = PetscFEGeomRestoreChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2362     ierr = DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2363     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2364   }
2365   if (hasDyn) {
2366     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2367   }
2368   if (hasFV) {
2369     PetscClassId id;
2370     PetscFV      fv;
2371     PetscInt     offsetI, NcI, NbI = 1, fc, f;
2372 
2373     for (fieldI = 0; fieldI < Nf; ++fieldI) {
2374       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fv);CHKERRQ(ierr);
2375       ierr = PetscDSGetFieldOffset(prob, fieldI, &offsetI);CHKERRQ(ierr);
2376       ierr = PetscObjectGetClassId((PetscObject) fv, &id);CHKERRQ(ierr);
2377       if (id != PETSCFV_CLASSID) continue;
2378       /* Put in the identity */
2379       ierr = PetscFVGetNumComponents(fv, &NcI);CHKERRQ(ierr);
2380       for (c = cStart; c < cEnd; ++c) {
2381         const PetscInt eOffset = (c-cStart)*totDim*totDim;
2382         for (fc = 0; fc < NcI; ++fc) {
2383           for (f = 0; f < NbI; ++f) {
2384             const PetscInt i = offsetI + f*NcI+fc;
2385             if (hasPrec) {
2386               if (hasJac) {elemMat[eOffset+i*totDim+i] = 1.0;}
2387               elemMatP[eOffset+i*totDim+i] = 1.0;
2388             } else {elemMat[eOffset+i*totDim+i] = 1.0;}
2389           }
2390         }
2391       }
2392     }
2393     /* No allocated space for FV stuff, so ignore the zero entries */
2394     ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2395   }
2396   isMatIS = PETSC_FALSE;
2397   if (hasPrec && hasJac) {
2398     ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatIS);CHKERRQ(ierr);
2399   }
2400   if (isMatIS && !subSection) {
2401     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2402   }
2403   for (c = cStart; c < cEnd; ++c) {
2404     if (hasPrec) {
2405       if (hasJac) {
2406         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2407         if (!isMatIS) {
2408           ierr = DMPlexMatSetClosure(dm, section, globalSection, Jac, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2409         } else {
2410           Mat lJ;
2411 
2412           ierr = MatISGetLocalMat(Jac,&lJ);CHKERRQ(ierr);
2413           ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2414         }
2415       }
2416       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMatP[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2417       if (!isMatISP) {
2418         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2419       } else {
2420         Mat lJ;
2421 
2422         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2423         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2424       }
2425     } else {
2426       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2427       if (!isMatISP) {
2428         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2429       } else {
2430         Mat lJ;
2431 
2432         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2433         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2434       }
2435     }
2436   }
2437   if (hasFV) {ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);CHKERRQ(ierr);}
2438   ierr = PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);CHKERRQ(ierr);
2439   if (dmAux) {
2440     ierr = PetscFree(a);CHKERRQ(ierr);
2441     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2442   }
2443   ierr = DMPlexComputeBdJacobian_Internal(dm, X, X_t, t, X_tShift, Jac, JacP, user);CHKERRQ(ierr);
2444   if (hasJac && hasPrec) {
2445     ierr = MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2446     ierr = MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2447   }
2448   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2449   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2450   if (mesh->printFEM) {
2451     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
2452     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
2453     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2454   }
2455   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2456   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
2457   if (isShell) {
2458     JacActionCtx *jctx;
2459 
2460     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
2461     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
2462   }
2463   PetscFunctionReturn(0);
2464 }
2465 
2466 PetscErrorCode DMPlexComputeJacobianAction_Internal(DM dm, IS cellIS, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Vec Y, Vec Z, void *user)
2467 {
2468   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2469   const char       *name  = "Jacobian";
2470   DM                dmAux, plex;
2471   Vec               A;
2472   PetscDS           prob, probAux = NULL;
2473   PetscQuadrature   quad;
2474   PetscSection      section, globalSection, sectionAux;
2475   PetscScalar      *elemMat, *elemMatD, *u, *u_t, *a = NULL, *y, *z;
2476   PetscInt          Nf, fieldI, fieldJ, numCells, c;
2477   PetscInt          totDim, totDimAux = 0;
2478   PetscBool         isStride;
2479   PetscInt          cStart = -1, cEnd = -1;
2480   PetscBool         hasDyn;
2481   DMField           coordField;
2482   PetscErrorCode    ierr;
2483 
2484   PetscFunctionBegin;
2485   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2486   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2487   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2488   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2489   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2490   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2491   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2492   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2493   ierr = ISGetLocalSize(cellIS, &numCells);CHKERRQ(ierr);
2494   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2495   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2496   if (dmAux) {
2497     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2498     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2499     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2500     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2501   }
2502   ierr = VecSet(Z, 0.0);CHKERRQ(ierr);
2503   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);
2504   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2505   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2506   ierr = PetscObjectTypeCompare((PetscObject) cellIS, ISSTRIDE, &isStride);CHKERRQ(ierr);
2507   if (isStride) {
2508     PetscInt step;
2509 
2510     ierr = ISStrideGetInfo(cellIS, &cStart, &step);CHKERRQ(ierr);
2511     cEnd = cStart + numCells;
2512     if (step != 1) {
2513       isStride = PETSC_FALSE;
2514     }
2515   }
2516   if (!isStride) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Not implemented yet");
2517   for (c = cStart; c < cEnd; ++c) {
2518     PetscScalar *x = NULL,  *x_t = NULL;
2519     PetscInt     i;
2520 
2521     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2522     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2523     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2524     if (X_t) {
2525       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2526       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2527       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2528     }
2529     if (dmAux) {
2530       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2531       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2532       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2533     }
2534     ierr = DMPlexVecGetClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2535     for (i = 0; i < totDim; ++i) y[(c-cStart)*totDim+i] = x[i];
2536     ierr = DMPlexVecRestoreClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2537   }
2538   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2539   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2540   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2541     PetscFE  fe;
2542     PetscInt Nb;
2543     /* Conforming batches */
2544     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2545     /* Remainder */
2546     PetscInt Nr, offset, Nq;
2547     PetscQuadrature qGeom = NULL;
2548     PetscBool   isAffine;
2549     PetscFEGeom *cgeomFEM, *chunkGeom = NULL, *remGeom = NULL;
2550 
2551     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2552     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2553     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2554     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2555     ierr = DMFieldGetFEInvariance(coordField,cellIS,NULL,&isAffine,NULL);CHKERRQ(ierr);
2556     if (isAffine) {
2557       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);CHKERRQ(ierr);
2558     }
2559     if (!qGeom) {
2560       ierr = PetscFEGetQuadrature(fe,&qGeom);CHKERRQ(ierr);
2561       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
2562     }
2563     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
2564     ierr = DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2565     blockSize = Nb;
2566     batchSize = numBlocks * blockSize;
2567     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2568     numChunks = numCells / (numBatches*batchSize);
2569     Ne        = numChunks*numBatches*batchSize;
2570     Nr        = numCells % (numBatches*batchSize);
2571     offset    = numCells - Nr;
2572     ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2573     ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2574     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2575       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2576       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2577       if (hasDyn) {
2578         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2579         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Nr, remGeom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, X_tShift, &elemMatD[offset*totDim*totDim]);CHKERRQ(ierr);
2580       }
2581     }
2582     ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2583     ierr = PetscFEGeomRestoreChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2584     ierr = DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2585     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2586   }
2587   if (hasDyn) {
2588     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2589   }
2590   for (c = cStart; c < cEnd; ++c) {
2591     const PetscBLASInt M = totDim, one = 1;
2592     const PetscScalar  a = 1.0, b = 0.0;
2593 
2594     PetscStackCallBLAS("BLASgemv", BLASgemv_("N", &M, &M, &a, &elemMat[(c-cStart)*totDim*totDim], &M, &y[(c-cStart)*totDim], &one, &b, z, &one));
2595     if (mesh->printFEM > 1) {
2596       ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);
2597       ierr = DMPrintCellVector(c, "Y",  totDim, &y[(c-cStart)*totDim]);CHKERRQ(ierr);
2598       ierr = DMPrintCellVector(c, "Z",  totDim, z);CHKERRQ(ierr);
2599     }
2600     ierr = DMPlexVecSetClosure(dm, section, Z, c, z, ADD_VALUES);CHKERRQ(ierr);
2601   }
2602   ierr = PetscFree6(u,u_t,elemMat,elemMatD,y,z);CHKERRQ(ierr);
2603   if (dmAux) {
2604     ierr = PetscFree(a);CHKERRQ(ierr);
2605     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2606   }
2607   if (mesh->printFEM) {
2608     ierr = PetscPrintf(PETSC_COMM_WORLD, "Z:\n");CHKERRQ(ierr);
2609     ierr = VecView(Z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2610   }
2611   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2612   PetscFunctionReturn(0);
2613 }
2614 
2615 /*@
2616   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2617 
2618   Input Parameters:
2619 + dm - The mesh
2620 . X  - Local input vector
2621 - user - The user context
2622 
2623   Output Parameter:
2624 . Jac  - Jacobian matrix
2625 
2626   Note:
2627   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2628   like a GPU, or vectorize on a multicore machine.
2629 
2630   Level: developer
2631 
2632 .seealso: FormFunctionLocal()
2633 @*/
2634 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2635 {
2636   DM             plex;
2637   IS             cellIS;
2638   PetscInt       depth;
2639   PetscErrorCode ierr;
2640 
2641   PetscFunctionBegin;
2642   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2643   ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
2644   ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
2645   if (!cellIS) {
2646     ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);
2647   }
2648   ierr = DMPlexComputeJacobian_Internal(plex, cellIS, 0.0, 0.0, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2649   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
2650   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2651   PetscFunctionReturn(0);
2652 }
2653 
2654 /*@
2655   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.
2656 
2657   Input Parameters:
2658 + dm - The mesh
2659 . X  - Local solution vector
2660 . Y  - Local input vector
2661 - user - The user context
2662 
2663   Output Parameter:
2664 . Z - Local output vector
2665 
2666   Note:
2667   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2668   like a GPU, or vectorize on a multicore machine.
2669 
2670   Level: developer
2671 
2672 .seealso: FormFunctionLocal()
2673 @*/
2674 PetscErrorCode DMPlexSNESComputeJacobianActionFEM(DM dm, Vec X, Vec Y, Vec Z, void *user)
2675 {
2676   DM             plex;
2677   IS             cellIS;
2678   PetscInt       depth;
2679   PetscErrorCode ierr;
2680 
2681   PetscFunctionBegin;
2682   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2683   ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
2684   ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
2685   if (!cellIS) {
2686     ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);
2687   }
2688   ierr = DMPlexComputeJacobianAction_Internal(plex, cellIS, 0.0, 0.0, X, NULL, Y, Z, user);CHKERRQ(ierr);
2689   ierr = ISDestroy(&cellIS);
2690   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2691   PetscFunctionReturn(0);
2692 }
2693 
2694 /*@
2695   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.
2696 
2697   Input Parameters:
2698 + dm - The DM object
2699 . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see PetscDSAddBoundary())
2700 . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
2701 - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())
2702 
2703   Level: developer
2704 @*/
2705 PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
2706 {
2707   PetscErrorCode ierr;
2708 
2709   PetscFunctionBegin;
2710   ierr = DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);CHKERRQ(ierr);
2711   ierr = DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);CHKERRQ(ierr);
2712   ierr = DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);CHKERRQ(ierr);
2713   PetscFunctionReturn(0);
2714 }
2715 
2716 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)
2717 {
2718   PetscDS        prob;
2719   Mat            J, M;
2720   Vec            r, b;
2721   MatNullSpace   nullSpace;
2722   PetscReal     *error, res = 0.0;
2723   PetscInt       numFields;
2724   PetscBool      hasJac, hasPrec;
2725   PetscErrorCode ierr;
2726 
2727   PetscFunctionBegin;
2728   ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2729   ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
2730   /* TODO Null space for J */
2731   /* Check discretization error */
2732   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
2733   ierr = PetscMalloc1(PetscMax(1, numFields), &error);CHKERRQ(ierr);
2734   if (numFields > 1) {
2735     PetscInt f;
2736 
2737     ierr = DMComputeL2FieldDiff(dm, 0.0, exactFuncs, ctxs, u, error);CHKERRQ(ierr);
2738     ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: [");CHKERRQ(ierr);
2739     for (f = 0; f < numFields; ++f) {
2740       if (f) {ierr = PetscPrintf(PETSC_COMM_WORLD, ", ");CHKERRQ(ierr);}
2741       if (error[f] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "%g", (double)error[f]);CHKERRQ(ierr);}
2742       else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "< 1.0e-11");CHKERRQ(ierr);}
2743     }
2744     ierr = PetscPrintf(PETSC_COMM_WORLD, "]\n");CHKERRQ(ierr);
2745   } else {
2746     ierr = DMComputeL2Diff(dm, 0.0, exactFuncs, ctxs, u, &error[0]);CHKERRQ(ierr);
2747     if (error[0] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", (double)error[0]);CHKERRQ(ierr);}
2748     else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
2749   }
2750   ierr = PetscFree(error);CHKERRQ(ierr);
2751   /* Check residual */
2752   ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2753   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2754   ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", (double)res);CHKERRQ(ierr);
2755   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2756   ierr = PetscObjectSetName((PetscObject) r, "Initial Residual");CHKERRQ(ierr);
2757   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"res_");CHKERRQ(ierr);
2758   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2759   /* Check Jacobian */
2760   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2761   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2762   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2763   if (hasJac && hasPrec) {
2764     ierr = DMCreateMatrix(dm, &M);CHKERRQ(ierr);
2765     ierr = SNESComputeJacobian(snes, u, J, M);CHKERRQ(ierr);
2766     ierr = PetscObjectSetOptionsPrefix((PetscObject) M, "jacpre_");CHKERRQ(ierr);
2767     ierr = MatViewFromOptions(M, NULL, "-mat_view");CHKERRQ(ierr);
2768     ierr = MatDestroy(&M);CHKERRQ(ierr);
2769   } else {
2770     ierr = SNESComputeJacobian(snes, u, J, J);CHKERRQ(ierr);
2771   }
2772   ierr = PetscObjectSetOptionsPrefix((PetscObject) J, "jac_");CHKERRQ(ierr);
2773   ierr = MatViewFromOptions(J, NULL, "-mat_view");CHKERRQ(ierr);
2774   ierr = MatGetNullSpace(J, &nullSpace);CHKERRQ(ierr);
2775   if (nullSpace) {
2776     PetscBool isNull;
2777     ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
2778     if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
2779   }
2780   ierr = VecDuplicate(u, &b);CHKERRQ(ierr);
2781   ierr = VecSet(r, 0.0);CHKERRQ(ierr);
2782   ierr = SNESComputeFunction(snes, r, b);CHKERRQ(ierr);
2783   ierr = MatMult(J, u, r);CHKERRQ(ierr);
2784   ierr = VecAXPY(r, 1.0, b);CHKERRQ(ierr);
2785   ierr = VecDestroy(&b);CHKERRQ(ierr);
2786   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2787   ierr = PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", (double)res);CHKERRQ(ierr);
2788   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2789   ierr = PetscObjectSetName((PetscObject) r, "Au - b = Au + F(0)");CHKERRQ(ierr);
2790   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"linear_res_");CHKERRQ(ierr);
2791   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2792   ierr = VecDestroy(&r);CHKERRQ(ierr);
2793   ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
2794   ierr = MatDestroy(&J);CHKERRQ(ierr);
2795   PetscFunctionReturn(0);
2796 }
2797 
2798 PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
2799 {
2800   DM             dm;
2801   Vec            sol;
2802   PetscBool      check;
2803   PetscErrorCode ierr;
2804 
2805   PetscFunctionBegin;
2806   ierr = PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);CHKERRQ(ierr);
2807   if (!check) PetscFunctionReturn(0);
2808   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
2809   ierr = VecDuplicate(u, &sol);CHKERRQ(ierr);
2810   ierr = SNESSetSolution(snes, sol);CHKERRQ(ierr);
2811   ierr = DMSNESCheckFromOptions_Internal(snes, dm, u, sol, exactFuncs, ctxs);CHKERRQ(ierr);
2812   ierr = VecDestroy(&sol);CHKERRQ(ierr);
2813   PetscFunctionReturn(0);
2814 }
2815