xref: /petsc/src/snes/utils/dmplexsnes.c (revision 34136279daf4c5803e26cd9ecf5a2cf0d75aa7fe)
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 = DMGetSection(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 
828 /*@
829   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
830 
831   Input Parameter:
832 . dm - The DM
833 
834   Output Parameters:
835 + facegeom - The values precomputed from face geometry
836 . cellgeom - The values precomputed from cell geometry
837 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
838 
839   Level: developer
840 
841 .seealso: DMPlexTSSetRHSFunctionLocal()
842 @*/
843 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
844 {
845   DM             plex;
846   PetscErrorCode ierr;
847 
848   PetscFunctionBegin;
849   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
850   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
851   ierr = DMPlexGetDataFVM(plex, NULL, cellgeom, facegeom, NULL);CHKERRQ(ierr);
852   if (minRadius) {ierr = DMPlexGetMinRadius(plex, minRadius);CHKERRQ(ierr);}
853   ierr = DMDestroy(&plex);CHKERRQ(ierr);
854   PetscFunctionReturn(0);
855 }
856 
857 /*@
858   DMPlexSNESGetGradientDM - Return gradient data layout
859 
860   Input Parameters:
861 + dm - The DM
862 - fv - The PetscFV
863 
864   Output Parameter:
865 . dmGrad - The layout for gradient values
866 
867   Level: developer
868 
869 .seealso: DMPlexSNESGetGeometryFVM()
870 @*/
871 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
872 {
873   DM             plex;
874   PetscBool      computeGradients;
875   PetscErrorCode ierr;
876 
877   PetscFunctionBegin;
878   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
879   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
880   PetscValidPointer(dmGrad,3);
881   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
882   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
883   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
884   ierr = DMPlexGetDataFVM(plex, fv, NULL, NULL, dmGrad);CHKERRQ(ierr);
885   ierr = DMDestroy(&plex);CHKERRQ(ierr);
886   PetscFunctionReturn(0);
887 }
888 
889 /*@C
890   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells
891 
892   Input Parameters:
893 + dm     - The DM
894 . cellIS - The cells to include
895 . locX   - A local vector with the solution fields
896 . locX_t - A local vector with solution field time derivatives, or NULL
897 - locA   - A local vector with auxiliary fields, or NULL
898 
899   Output Parameters:
900 + u   - The field coefficients
901 . u_t - The fields derivative coefficients
902 - a   - The auxiliary field coefficients
903 
904   Level: developer
905 
906 .seealso: DMPlexGetFaceFields()
907 @*/
908 PetscErrorCode DMPlexGetCellFields(DM dm, IS cellIS, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
909 {
910   DM              plex, plexA = NULL;
911   PetscSection    section, sectionAux;
912   PetscDS         prob;
913   const PetscInt *cells;
914   PetscInt        cStart, cEnd, numCells, totDim, totDimAux, c;
915   PetscErrorCode  ierr;
916 
917   PetscFunctionBegin;
918   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
919   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
920   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
921   if (locA)   {PetscValidHeaderSpecific(locA, VEC_CLASSID, 6);}
922   PetscValidPointer(u, 7);
923   PetscValidPointer(u_t, 8);
924   PetscValidPointer(a, 9);
925   ierr = DMSNESConvertPlex(dm, &plex, PETSC_FALSE);CHKERRQ(ierr);
926   ierr = ISGetPointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
927   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
928   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
929   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
930   if (locA) {
931     DM      dmAux;
932     PetscDS probAux;
933 
934     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
935     ierr = DMSNESConvertPlex(dmAux, &plexA, PETSC_FALSE);CHKERRQ(ierr);
936     ierr = DMGetSection(dmAux, &sectionAux);CHKERRQ(ierr);
937     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
938     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
939   }
940   numCells = cEnd - cStart;
941   ierr = DMGetWorkArray(dm, numCells*totDim, MPIU_SCALAR, u);CHKERRQ(ierr);
942   if (locX_t) {ierr = DMGetWorkArray(dm, numCells*totDim, MPIU_SCALAR, u_t);CHKERRQ(ierr);} else {*u_t = NULL;}
943   if (locA)   {ierr = DMGetWorkArray(dm, numCells*totDimAux, MPIU_SCALAR, a);CHKERRQ(ierr);} else {*a = NULL;}
944   for (c = cStart; c < cEnd; ++c) {
945     const PetscInt cell = cells ? cells[c] : c;
946     const PetscInt cind = c - cStart;
947     PetscScalar   *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
948     PetscInt       i;
949 
950     ierr = DMPlexVecGetClosure(plex, section, locX, cell, NULL, &x);CHKERRQ(ierr);
951     for (i = 0; i < totDim; ++i) ul[cind*totDim+i] = x[i];
952     ierr = DMPlexVecRestoreClosure(plex, section, locX, cell, NULL, &x);CHKERRQ(ierr);
953     if (locX_t) {
954       ierr = DMPlexVecGetClosure(plex, section, locX_t, cell, NULL, &x_t);CHKERRQ(ierr);
955       for (i = 0; i < totDim; ++i) ul_t[cind*totDim+i] = x_t[i];
956       ierr = DMPlexVecRestoreClosure(plex, section, locX_t, cell, NULL, &x_t);CHKERRQ(ierr);
957     }
958     if (locA) {
959       ierr = DMPlexVecGetClosure(plexA, sectionAux, locA, cell, NULL, &x);CHKERRQ(ierr);
960       for (i = 0; i < totDimAux; ++i) al[cind*totDimAux+i] = x[i];
961       ierr = DMPlexVecRestoreClosure(plexA, sectionAux, locA, cell, NULL, &x);CHKERRQ(ierr);
962     }
963   }
964   ierr = DMDestroy(&plex);CHKERRQ(ierr);
965   if (locA) {ierr = DMDestroy(&plexA);CHKERRQ(ierr);}
966   ierr = ISRestorePointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
967   PetscFunctionReturn(0);
968 }
969 
970 /*@C
971   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells
972 
973   Input Parameters:
974 + dm     - The DM
975 . cellIS - The cells to include
976 . locX   - A local vector with the solution fields
977 . locX_t - A local vector with solution field time derivatives, or NULL
978 - locA   - A local vector with auxiliary fields, or NULL
979 
980   Output Parameters:
981 + u   - The field coefficients
982 . u_t - The fields derivative coefficients
983 - a   - The auxiliary field coefficients
984 
985   Level: developer
986 
987 .seealso: DMPlexGetFaceFields()
988 @*/
989 PetscErrorCode DMPlexRestoreCellFields(DM dm, IS cellIS, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
990 {
991   PetscErrorCode ierr;
992 
993   PetscFunctionBegin;
994   ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, u);CHKERRQ(ierr);
995   if (locX_t) {ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, u_t);CHKERRQ(ierr);}
996   if (locA)   {ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, a);CHKERRQ(ierr);}
997   PetscFunctionReturn(0);
998 }
999 
1000 /*@C
1001   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces
1002 
1003   Input Parameters:
1004 + dm     - The DM
1005 . fStart - The first face to include
1006 . fEnd   - The first face to exclude
1007 . locX   - A local vector with the solution fields
1008 . locX_t - A local vector with solution field time derivatives, or NULL
1009 . faceGeometry - A local vector with face geometry
1010 . cellGeometry - A local vector with cell geometry
1011 - locaGrad - A local vector with field gradients, or NULL
1012 
1013   Output Parameters:
1014 + Nface - The number of faces with field values
1015 . uL - The field values at the left side of the face
1016 - uR - The field values at the right side of the face
1017 
1018   Level: developer
1019 
1020 .seealso: DMPlexGetCellFields()
1021 @*/
1022 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)
1023 {
1024   DM                 dmFace, dmCell, dmGrad = NULL;
1025   PetscSection       section;
1026   PetscDS            prob;
1027   DMLabel            ghostLabel;
1028   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
1029   PetscBool         *isFE;
1030   PetscInt           dim, Nf, f, Nc, numFaces = fEnd - fStart, iface, face;
1031   PetscErrorCode     ierr;
1032 
1033   PetscFunctionBegin;
1034   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1035   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1036   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1037   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 6);
1038   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 7);
1039   if (locGrad) {PetscValidHeaderSpecific(locGrad, VEC_CLASSID, 8);}
1040   PetscValidPointer(uL, 9);
1041   PetscValidPointer(uR, 10);
1042   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1043   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1044   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1045   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1046   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1047   ierr = PetscMalloc1(Nf, &isFE);CHKERRQ(ierr);
1048   for (f = 0; f < Nf; ++f) {
1049     PetscObject  obj;
1050     PetscClassId id;
1051 
1052     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1053     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1054     if (id == PETSCFE_CLASSID)      {isFE[f] = PETSC_TRUE;}
1055     else if (id == PETSCFV_CLASSID) {isFE[f] = PETSC_FALSE;}
1056     else                            {isFE[f] = PETSC_FALSE;}
1057   }
1058   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1059   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1060   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1061   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1062   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1063   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1064   if (locGrad) {
1065     ierr = VecGetDM(locGrad, &dmGrad);CHKERRQ(ierr);
1066     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1067   }
1068   ierr = DMGetWorkArray(dm, numFaces*Nc, MPIU_SCALAR, uL);CHKERRQ(ierr);
1069   ierr = DMGetWorkArray(dm, numFaces*Nc, MPIU_SCALAR, uR);CHKERRQ(ierr);
1070   /* Right now just eat the extra work for FE (could make a cell loop) */
1071   for (face = fStart, iface = 0; face < fEnd; ++face) {
1072     const PetscInt        *cells;
1073     PetscFVFaceGeom       *fg;
1074     PetscFVCellGeom       *cgL, *cgR;
1075     PetscScalar           *xL, *xR, *gL, *gR;
1076     PetscScalar           *uLl = *uL, *uRl = *uR;
1077     PetscInt               ghost, nsupp, nchild;
1078 
1079     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1080     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1081     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1082     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1083     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1084     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1085     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1086     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1087     for (f = 0; f < Nf; ++f) {
1088       PetscInt off;
1089 
1090       ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1091       if (isFE[f]) {
1092         const PetscInt *cone;
1093         PetscInt        comp, coneSizeL, coneSizeR, faceLocL, faceLocR, ldof, rdof, d;
1094 
1095         xL = xR = NULL;
1096         ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1097         ierr = DMPlexVecGetClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1098         ierr = DMPlexVecGetClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1099         ierr = DMPlexGetCone(dm, cells[0], &cone);CHKERRQ(ierr);
1100         ierr = DMPlexGetConeSize(dm, cells[0], &coneSizeL);CHKERRQ(ierr);
1101         for (faceLocL = 0; faceLocL < coneSizeL; ++faceLocL) if (cone[faceLocL] == face) break;
1102         ierr = DMPlexGetCone(dm, cells[1], &cone);CHKERRQ(ierr);
1103         ierr = DMPlexGetConeSize(dm, cells[1], &coneSizeR);CHKERRQ(ierr);
1104         for (faceLocR = 0; faceLocR < coneSizeR; ++faceLocR) if (cone[faceLocR] == face) break;
1105         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]);
1106         /* Check that FEM field has values in the right cell (sometimes its an FV ghost cell) */
1107         /* TODO: this is a hack that might not be right for nonconforming */
1108         if (faceLocL < coneSizeL) {
1109           ierr = EvaluateFaceFields(prob, f, faceLocL, xL, &uLl[iface*Nc+off]);CHKERRQ(ierr);
1110           if (rdof == ldof && faceLocR < coneSizeR) {ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);}
1111           else              {for(d = 0; d < comp; ++d) uRl[iface*Nc+off+d] = uLl[iface*Nc+off+d];}
1112         }
1113         else {
1114           ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);
1115           ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1116           for(d = 0; d < comp; ++d) uLl[iface*Nc+off+d] = uRl[iface*Nc+off+d];
1117         }
1118         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1119         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1120       } else {
1121         PetscFV  fv;
1122         PetscInt numComp, c;
1123 
1124         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fv);CHKERRQ(ierr);
1125         ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1126         ierr = DMPlexPointLocalFieldRead(dm, cells[0], f, x, &xL);CHKERRQ(ierr);
1127         ierr = DMPlexPointLocalFieldRead(dm, cells[1], f, x, &xR);CHKERRQ(ierr);
1128         if (dmGrad) {
1129           PetscReal dxL[3], dxR[3];
1130 
1131           ierr = DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);CHKERRQ(ierr);
1132           ierr = DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);CHKERRQ(ierr);
1133           DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
1134           DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
1135           for (c = 0; c < numComp; ++c) {
1136             uLl[iface*Nc+off+c] = xL[c] + DMPlex_DotD_Internal(dim, &gL[c*dim], dxL);
1137             uRl[iface*Nc+off+c] = xR[c] + DMPlex_DotD_Internal(dim, &gR[c*dim], dxR);
1138           }
1139         } else {
1140           for (c = 0; c < numComp; ++c) {
1141             uLl[iface*Nc+off+c] = xL[c];
1142             uRl[iface*Nc+off+c] = xR[c];
1143           }
1144         }
1145       }
1146     }
1147     ++iface;
1148   }
1149   *Nface = iface;
1150   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1151   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1152   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1153   if (locGrad) {
1154     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1155   }
1156   ierr = PetscFree(isFE);CHKERRQ(ierr);
1157   PetscFunctionReturn(0);
1158 }
1159 
1160 /*@C
1161   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces
1162 
1163   Input Parameters:
1164 + dm     - The DM
1165 . fStart - The first face to include
1166 . fEnd   - The first face to exclude
1167 . locX   - A local vector with the solution fields
1168 . locX_t - A local vector with solution field time derivatives, or NULL
1169 . faceGeometry - A local vector with face geometry
1170 . cellGeometry - A local vector with cell geometry
1171 - locaGrad - A local vector with field gradients, or NULL
1172 
1173   Output Parameters:
1174 + Nface - The number of faces with field values
1175 . uL - The field values at the left side of the face
1176 - uR - The field values at the right side of the face
1177 
1178   Level: developer
1179 
1180 .seealso: DMPlexGetFaceFields()
1181 @*/
1182 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)
1183 {
1184   PetscErrorCode ierr;
1185 
1186   PetscFunctionBegin;
1187   ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, uL);CHKERRQ(ierr);
1188   ierr = DMRestoreWorkArray(dm, 0, MPIU_SCALAR, uR);CHKERRQ(ierr);
1189   PetscFunctionReturn(0);
1190 }
1191 
1192 /*@C
1193   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces
1194 
1195   Input Parameters:
1196 + dm     - The DM
1197 . fStart - The first face to include
1198 . fEnd   - The first face to exclude
1199 . faceGeometry - A local vector with face geometry
1200 - cellGeometry - A local vector with cell geometry
1201 
1202   Output Parameters:
1203 + Nface - The number of faces with field values
1204 . fgeom - The extract the face centroid and normal
1205 - vol   - The cell volume
1206 
1207   Level: developer
1208 
1209 .seealso: DMPlexGetCellFields()
1210 @*/
1211 PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1212 {
1213   DM                 dmFace, dmCell;
1214   DMLabel            ghostLabel;
1215   const PetscScalar *facegeom, *cellgeom;
1216   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
1217   PetscErrorCode     ierr;
1218 
1219   PetscFunctionBegin;
1220   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1221   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 4);
1222   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 5);
1223   PetscValidPointer(fgeom, 6);
1224   PetscValidPointer(vol, 7);
1225   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1226   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1227   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1228   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1229   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1230   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1231   ierr = PetscMalloc1(numFaces, fgeom);CHKERRQ(ierr);
1232   ierr = DMGetWorkArray(dm, numFaces*2, MPIU_SCALAR, vol);CHKERRQ(ierr);
1233   for (face = fStart, iface = 0; face < fEnd; ++face) {
1234     const PetscInt        *cells;
1235     PetscFVFaceGeom       *fg;
1236     PetscFVCellGeom       *cgL, *cgR;
1237     PetscFVFaceGeom       *fgeoml = *fgeom;
1238     PetscReal             *voll   = *vol;
1239     PetscInt               ghost, d, nchild, nsupp;
1240 
1241     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1242     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1243     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1244     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1245     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1246     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1247     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1248     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1249     for (d = 0; d < dim; ++d) {
1250       fgeoml[iface].centroid[d] = fg->centroid[d];
1251       fgeoml[iface].normal[d]   = fg->normal[d];
1252     }
1253     voll[iface*2+0] = cgL->volume;
1254     voll[iface*2+1] = cgR->volume;
1255     ++iface;
1256   }
1257   *Nface = iface;
1258   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1259   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1260   PetscFunctionReturn(0);
1261 }
1262 
1263 /*@C
1264   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces
1265 
1266   Input Parameters:
1267 + dm     - The DM
1268 . fStart - The first face to include
1269 . fEnd   - The first face to exclude
1270 . faceGeometry - A local vector with face geometry
1271 - cellGeometry - A local vector with cell geometry
1272 
1273   Output Parameters:
1274 + Nface - The number of faces with field values
1275 . fgeom - The extract the face centroid and normal
1276 - vol   - The cell volume
1277 
1278   Level: developer
1279 
1280 .seealso: DMPlexGetFaceFields()
1281 @*/
1282 PetscErrorCode DMPlexRestoreFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1283 {
1284   PetscErrorCode ierr;
1285 
1286   PetscFunctionBegin;
1287   ierr = PetscFree(*fgeom);CHKERRQ(ierr);
1288   ierr = DMRestoreWorkArray(dm, 0, MPIU_REAL, vol);CHKERRQ(ierr);
1289   PetscFunctionReturn(0);
1290 }
1291 
1292 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)
1293 {
1294   DM_Plex         *mesh = (DM_Plex *) dm->data;
1295   DM               plex = NULL, plexA = NULL;
1296   PetscDS          prob, probAux = NULL;
1297   PetscSection     section, sectionAux = NULL;
1298   Vec              locA = NULL;
1299   PetscScalar     *u = NULL, *u_t = NULL, *a = NULL, *elemVec = NULL;
1300   PetscInt         v;
1301   PetscInt         totDim, totDimAux = 0;
1302   PetscErrorCode   ierr;
1303 
1304   PetscFunctionBegin;
1305   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
1306   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1307   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1308   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1309   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1310   if (locA) {
1311     DM dmAux;
1312 
1313     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1314     ierr = DMConvert(dmAux, DMPLEX, &plexA);CHKERRQ(ierr);
1315     ierr = DMGetDS(plexA, &probAux);CHKERRQ(ierr);
1316     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1317     ierr = DMGetSection(plexA, &sectionAux);CHKERRQ(ierr);
1318   }
1319   for (v = 0; v < numValues; ++v) {
1320     PetscFEGeom    *fgeom;
1321     PetscInt        maxDegree;
1322     PetscQuadrature qGeom = NULL;
1323     IS              pointIS;
1324     const PetscInt *points;
1325     PetscInt        numFaces, face, Nq;
1326 
1327     ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1328     if (!pointIS) continue; /* No points with that id on this process */
1329     {
1330       IS isectIS;
1331 
1332       /* TODO: Special cases of ISIntersect where it is quick to check a priori if one is a superset of the other */
1333       ierr = ISIntersect_Caching_Internal(facetIS,pointIS,&isectIS);CHKERRQ(ierr);
1334       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1335       pointIS = isectIS;
1336     }
1337     ierr = ISGetLocalSize(pointIS,&numFaces);CHKERRQ(ierr);
1338     ierr = ISGetIndices(pointIS,&points);CHKERRQ(ierr);
1339     ierr = PetscMalloc4(numFaces*totDim, &u, locX_t ? numFaces*totDim : 0, &u_t, numFaces*totDim, &elemVec, locA ? numFaces*totDimAux : 0, &a);CHKERRQ(ierr);
1340     ierr = DMFieldGetDegree(coordField,pointIS,NULL,&maxDegree);CHKERRQ(ierr);
1341     if (maxDegree <= 1) {
1342       ierr = DMFieldCreateDefaultQuadrature(coordField,pointIS,&qGeom);CHKERRQ(ierr);
1343     }
1344     if (!qGeom) {
1345       PetscFE fe;
1346 
1347       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1348       ierr = PetscFEGetFaceQuadrature(fe, &qGeom);CHKERRQ(ierr);
1349       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
1350     }
1351     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1352     ierr = DMSNESGetFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
1353     for (face = 0; face < numFaces; ++face) {
1354       const PetscInt point = points[face], *support, *cone;
1355       PetscScalar   *x     = NULL;
1356       PetscInt       i, coneSize, faceLoc;
1357 
1358       ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
1359       ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
1360       ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
1361       for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
1362       if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %D in cone of support[0] %D", point, support[0]);
1363       fgeom->face[face][0] = faceLoc;
1364       ierr = DMPlexVecGetClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1365       for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
1366       ierr = DMPlexVecRestoreClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1367       if (locX_t) {
1368         ierr = DMPlexVecGetClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1369         for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
1370         ierr = DMPlexVecRestoreClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1371       }
1372       if (locA) {
1373         DMLabel  spmap;
1374         PetscInt subp = support[0];
1375 
1376         /* If dm is a submesh, do not get subpoint */
1377         ierr = DMPlexGetSubpointMap(dm, &spmap);CHKERRQ(ierr);
1378         if (!spmap) {ierr = DMPlexGetSubpoint(plexA, support[0], &subp);CHKERRQ(ierr);}
1379         ierr = DMPlexVecGetClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
1380         for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
1381         ierr = DMPlexVecRestoreClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
1382       }
1383     }
1384     ierr = PetscMemzero(elemVec, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1385     {
1386       PetscFE         fe;
1387       PetscInt        Nb;
1388       PetscFEGeom     *chunkGeom = NULL;
1389       /* Conforming batches */
1390       PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1391       /* Remainder */
1392       PetscInt        Nr, offset;
1393 
1394       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1395       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1396       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1397       /* TODO: documentation is unclear about what is going on with these numbers: how should Nb / Nq factor in ? */
1398       blockSize = Nb;
1399       batchSize = numBlocks * blockSize;
1400       ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1401       numChunks = numFaces / (numBatches*batchSize);
1402       Ne        = numChunks*numBatches*batchSize;
1403       Nr        = numFaces % (numBatches*batchSize);
1404       offset    = numFaces - Nr;
1405       ierr = PetscFEGeomGetChunk(fgeom,0,offset,&chunkGeom);CHKERRQ(ierr);
1406       ierr = PetscFEIntegrateBdResidual(fe, prob, field, Ne, chunkGeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1407       ierr = PetscFEGeomRestoreChunk(fgeom, 0, offset, &chunkGeom);CHKERRQ(ierr);
1408       ierr = PetscFEGeomGetChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
1409       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);
1410       ierr = PetscFEGeomRestoreChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
1411     }
1412     for (face = 0; face < numFaces; ++face) {
1413       const PetscInt point = points[face], *support;
1414 
1415       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDim, &elemVec[face*totDim]);CHKERRQ(ierr);}
1416       ierr = DMPlexGetSupport(plex, point, &support);CHKERRQ(ierr);
1417       ierr = DMPlexVecSetClosure(plex, NULL, locF, support[0], &elemVec[face*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1418     }
1419     ierr = DMSNESRestoreFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
1420     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
1421     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1422     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1423     ierr = PetscFree4(u, u_t, elemVec, a);CHKERRQ(ierr);
1424   }
1425   if (plex)  {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
1426   if (plexA) {ierr = DMDestroy(&plexA);CHKERRQ(ierr);}
1427   PetscFunctionReturn(0);
1428 }
1429 
1430 PetscErrorCode DMPlexComputeBdResidualSingle(DM dm, PetscReal t, DMLabel label, PetscInt numValues, const PetscInt values[], PetscInt field, Vec locX, Vec locX_t, Vec locF)
1431 {
1432   DMField        coordField;
1433   DMLabel        depthLabel;
1434   IS             facetIS;
1435   PetscInt       dim;
1436   PetscErrorCode ierr;
1437 
1438   PetscFunctionBegin;
1439   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1440   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1441   ierr = DMLabelGetStratumIS(depthLabel, dim-1, &facetIS);CHKERRQ(ierr);
1442   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1443   ierr = DMPlexComputeBdResidual_Single_Internal(dm, t, label, numValues, values, field, locX, locX_t, locF, coordField, facetIS);CHKERRQ(ierr);
1444   PetscFunctionReturn(0);
1445 }
1446 
1447 PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1448 {
1449   PetscDS        prob;
1450   PetscInt       dim, numBd, bd;
1451   DMLabel        depthLabel;
1452   DMField        coordField = NULL;
1453   IS             facetIS;
1454   PetscErrorCode ierr;
1455 
1456   PetscFunctionBegin;
1457   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1458   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1459   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1460   ierr = DMLabelGetStratumIS(depthLabel,dim - 1,&facetIS);CHKERRQ(ierr);
1461   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
1462   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1463   for (bd = 0; bd < numBd; ++bd) {
1464     DMBoundaryConditionType type;
1465     const char             *bdLabel;
1466     DMLabel                 label;
1467     const PetscInt         *values;
1468     PetscInt                field, numValues;
1469     PetscObject             obj;
1470     PetscClassId            id;
1471 
1472     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1473     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
1474     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1475     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
1476     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1477     ierr = DMPlexComputeBdResidual_Single_Internal(dm, t, label, numValues, values, field, locX, locX_t, locF, coordField, facetIS);CHKERRQ(ierr);
1478   }
1479   ierr = ISDestroy(&facetIS);CHKERRQ(ierr);
1480   PetscFunctionReturn(0);
1481 }
1482 
1483 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, IS cellIS, PetscReal time, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1484 {
1485   DM_Plex         *mesh       = (DM_Plex *) dm->data;
1486   const char      *name       = "Residual";
1487   DM               dmAux      = NULL;
1488   DM               dmGrad     = NULL;
1489   DMLabel          ghostLabel = NULL;
1490   PetscDS          prob       = NULL;
1491   PetscDS          probAux    = NULL;
1492   PetscSection     section    = NULL;
1493   PetscBool        useFEM     = PETSC_FALSE;
1494   PetscBool        useFVM     = PETSC_FALSE;
1495   PetscBool        isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
1496   PetscFV          fvm        = NULL;
1497   PetscFVCellGeom *cgeomFVM   = NULL;
1498   PetscFVFaceGeom *fgeomFVM   = NULL;
1499   DMField          coordField = NULL;
1500   Vec              locA, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1501   PetscScalar     *u = NULL, *u_t, *a, *uL, *uR;
1502   IS               chunkIS;
1503   const PetscInt  *cells;
1504   PetscInt         cStart, cEnd, numCells;
1505   PetscInt         Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
1506   PetscInt         maxDegree = PETSC_MAX_INT;
1507   PetscQuadrature  affineQuad = NULL, *quads = NULL;
1508   PetscFEGeom     *affineGeom = NULL, **geoms = NULL;
1509   PetscErrorCode   ierr;
1510 
1511   PetscFunctionBegin;
1512   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1513   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1514   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
1515   /* FEM+FVM */
1516   /* 1: Get sizes from dm and dmAux */
1517   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1518   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1519   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1520   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1521   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1522   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1523   if (locA) {
1524     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1525     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1526     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1527   }
1528   /* 2: Get geometric data */
1529   for (f = 0; f < Nf; ++f) {
1530     PetscObject  obj;
1531     PetscClassId id;
1532     PetscBool    fimp;
1533 
1534     ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1535     if (isImplicit != fimp) continue;
1536     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1537     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1538     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1539     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1540   }
1541   if (useFEM) {
1542     ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1543     ierr = DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);CHKERRQ(ierr);
1544     if (maxDegree <= 1) {
1545       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&affineQuad);CHKERRQ(ierr);
1546       if (affineQuad) {
1547         ierr = DMSNESGetFEGeom(coordField,cellIS,affineQuad,PETSC_FALSE,&affineGeom);CHKERRQ(ierr);
1548       }
1549     } else {
1550       ierr = PetscCalloc2(Nf,&quads,Nf,&geoms);CHKERRQ(ierr);
1551       for (f = 0; f < Nf; ++f) {
1552         PetscObject  obj;
1553         PetscClassId id;
1554         PetscBool    fimp;
1555 
1556         ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1557         if (isImplicit != fimp) continue;
1558         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1559         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1560         if (id == PETSCFE_CLASSID) {
1561           PetscFE fe = (PetscFE) obj;
1562 
1563           ierr = PetscFEGetQuadrature(fe, &quads[f]);CHKERRQ(ierr);
1564           ierr = PetscObjectReference((PetscObject)quads[f]);CHKERRQ(ierr);
1565           ierr = DMSNESGetFEGeom(coordField,cellIS,quads[f],PETSC_FALSE,&geoms[f]);CHKERRQ(ierr);
1566         }
1567       }
1568     }
1569   }
1570   if (useFVM) {
1571     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1572     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1573     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1574     /* Reconstruct and limit cell gradients */
1575     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1576     if (dmGrad) {
1577       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1578       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1579       ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1580       /* Communicate gradient values */
1581       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1582       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1583       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1584       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1585     }
1586     /* Handle non-essential (e.g. outflow) boundary values */
1587     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1588   }
1589   /* Loop over chunks */
1590   ierr = ISGetPointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
1591   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1592   if (useFEM) {ierr = ISCreate(PETSC_COMM_SELF, &chunkIS);CHKERRQ(ierr);}
1593   numCells      = cEnd - cStart;
1594   numChunks     = 1;
1595   cellChunkSize = numCells/numChunks;
1596   faceChunkSize = (fEnd - fStart)/numChunks;
1597   numChunks     = PetscMin(1,numCells);
1598   for (chunk = 0; chunk < numChunks; ++chunk) {
1599     PetscScalar     *elemVec, *fluxL, *fluxR;
1600     PetscReal       *vol;
1601     PetscFVFaceGeom *fgeom;
1602     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, c;
1603     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = 0, face;
1604 
1605     /* Extract field coefficients */
1606     if (useFEM) {
1607       ierr = ISGetPointSubrange(chunkIS, cS, cE, cells);CHKERRQ(ierr);
1608       ierr = DMPlexGetCellFields(dm, chunkIS, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1609       ierr = DMGetWorkArray(dm, numCells*totDim, MPIU_SCALAR, &elemVec);CHKERRQ(ierr);
1610       ierr = PetscMemzero(elemVec, numCells*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1611     }
1612     if (useFVM) {
1613       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1614       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1615       ierr = DMGetWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxL);CHKERRQ(ierr);
1616       ierr = DMGetWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxR);CHKERRQ(ierr);
1617       ierr = PetscMemzero(fluxL, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1618       ierr = PetscMemzero(fluxR, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1619     }
1620     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1621     /* Loop over fields */
1622     for (f = 0; f < Nf; ++f) {
1623       PetscObject  obj;
1624       PetscClassId id;
1625       PetscBool    fimp;
1626       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1627 
1628       ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1629       if (isImplicit != fimp) continue;
1630       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1631       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1632       if (id == PETSCFE_CLASSID) {
1633         PetscFE         fe = (PetscFE) obj;
1634         PetscFEGeom    *geom = affineGeom ? affineGeom : geoms[f];
1635         PetscFEGeom    *chunkGeom = NULL;
1636         PetscQuadrature quad = affineQuad ? affineQuad : quads[f];
1637         PetscInt        Nq, Nb;
1638 
1639         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1640         ierr = PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1641         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1642         blockSize = Nb;
1643         batchSize = numBlocks * blockSize;
1644         ierr      = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1645         numChunks = numCells / (numBatches*batchSize);
1646         Ne        = numChunks*numBatches*batchSize;
1647         Nr        = numCells % (numBatches*batchSize);
1648         offset    = numCells - Nr;
1649         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1650         /*   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) */
1651         ierr = PetscFEGeomGetChunk(geom,0,offset,&chunkGeom);CHKERRQ(ierr);
1652         ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, chunkGeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1653         ierr = PetscFEGeomGetChunk(geom,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1654         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);
1655         ierr = PetscFEGeomRestoreChunk(geom,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1656       } else if (id == PETSCFV_CLASSID) {
1657         PetscFV fv = (PetscFV) obj;
1658 
1659         Ne = numFaces;
1660         /* Riemann solve over faces (need fields at face centroids) */
1661         /*   We need to evaluate FE fields at those coordinates */
1662         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1663       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1664     }
1665     /* Loop over domain */
1666     if (useFEM) {
1667       /* Add elemVec to locX */
1668       for (c = cS; c < cE; ++c) {
1669         const PetscInt cell = cells ? cells[c] : c;
1670         const PetscInt cind = c - cStart;
1671 
1672         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cind*totDim]);CHKERRQ(ierr);}
1673         if (ghostLabel) {
1674           PetscInt ghostVal;
1675 
1676           ierr = DMLabelGetValue(ghostLabel,cell,&ghostVal);CHKERRQ(ierr);
1677           if (ghostVal > 0) continue;
1678         }
1679         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cind*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1680       }
1681     }
1682     if (useFVM) {
1683       PetscScalar *fa;
1684       PetscInt     iface;
1685 
1686       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1687       for (f = 0; f < Nf; ++f) {
1688         PetscFV      fv;
1689         PetscObject  obj;
1690         PetscClassId id;
1691         PetscInt     foff, pdim;
1692 
1693         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1694         ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1695         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1696         if (id != PETSCFV_CLASSID) continue;
1697         fv   = (PetscFV) obj;
1698         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1699         /* Accumulate fluxes to cells */
1700         for (face = fS, iface = 0; face < fE; ++face) {
1701           const PetscInt *scells;
1702           PetscScalar    *fL = NULL, *fR = NULL;
1703           PetscInt        ghost, d, nsupp, nchild;
1704 
1705           ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1706           ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1707           ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1708           if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1709           ierr = DMPlexGetSupport(dm, face, &scells);CHKERRQ(ierr);
1710           ierr = DMLabelGetValue(ghostLabel,scells[0],&ghost);CHKERRQ(ierr);
1711           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, scells[0], f, fa, &fL);CHKERRQ(ierr);}
1712           ierr = DMLabelGetValue(ghostLabel,scells[1],&ghost);CHKERRQ(ierr);
1713           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, scells[1], f, fa, &fR);CHKERRQ(ierr);}
1714           for (d = 0; d < pdim; ++d) {
1715             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
1716             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
1717           }
1718           ++iface;
1719         }
1720       }
1721       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1722     }
1723     /* Handle time derivative */
1724     if (locX_t) {
1725       PetscScalar *x_t, *fa;
1726 
1727       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1728       ierr = VecGetArray(locX_t, &x_t);CHKERRQ(ierr);
1729       for (f = 0; f < Nf; ++f) {
1730         PetscFV      fv;
1731         PetscObject  obj;
1732         PetscClassId id;
1733         PetscInt     pdim, d;
1734 
1735         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1736         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1737         if (id != PETSCFV_CLASSID) continue;
1738         fv   = (PetscFV) obj;
1739         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1740         for (c = cS; c < cE; ++c) {
1741           const PetscInt cell = cells ? cells[c] : c;
1742           PetscScalar   *u_t, *r;
1743 
1744           if (ghostLabel) {
1745             PetscInt ghostVal;
1746 
1747             ierr = DMLabelGetValue(ghostLabel, cell, &ghostVal);CHKERRQ(ierr);
1748             if (ghostVal > 0) continue;
1749           }
1750           ierr = DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);CHKERRQ(ierr);
1751           ierr = DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);CHKERRQ(ierr);
1752           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
1753         }
1754       }
1755       ierr = VecRestoreArray(locX_t, &x_t);CHKERRQ(ierr);
1756       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1757     }
1758     if (useFEM) {
1759       ierr = DMPlexRestoreCellFields(dm, chunkIS, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1760       ierr = DMRestoreWorkArray(dm, numCells*totDim, MPIU_SCALAR, &elemVec);CHKERRQ(ierr);
1761     }
1762     if (useFVM) {
1763       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1764       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1765       ierr = DMRestoreWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxL);CHKERRQ(ierr);
1766       ierr = DMRestoreWorkArray(dm, numFaces*totDim, MPIU_SCALAR, &fluxR);CHKERRQ(ierr);
1767       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1768     }
1769   }
1770   if (useFEM) {ierr = ISDestroy(&chunkIS);CHKERRQ(ierr);}
1771   ierr = ISRestorePointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
1772 
1773   if (useFEM) {
1774     ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, t, locF, user);CHKERRQ(ierr);
1775 
1776     if (maxDegree <= 1) {
1777       ierr = DMSNESRestoreFEGeom(coordField,cellIS,affineQuad,PETSC_FALSE,&affineGeom);CHKERRQ(ierr);
1778       ierr = PetscQuadratureDestroy(&affineQuad);CHKERRQ(ierr);
1779     } else {
1780       for (f = 0; f < Nf; ++f) {
1781         ierr = DMSNESRestoreFEGeom(coordField,cellIS,quads[f],PETSC_FALSE,&geoms[f]);CHKERRQ(ierr);
1782         ierr = PetscQuadratureDestroy(&quads[f]);CHKERRQ(ierr);
1783       }
1784       ierr = PetscFree2(quads,geoms);CHKERRQ(ierr);
1785     }
1786   }
1787 
1788   /* FEM */
1789   /* 1: Get sizes from dm and dmAux */
1790   /* 2: Get geometric data */
1791   /* 3: Handle boundary values */
1792   /* 4: Loop over domain */
1793   /*   Extract coefficients */
1794   /* Loop over fields */
1795   /*   Set tiling for FE*/
1796   /*   Integrate FE residual to get elemVec */
1797   /*     Loop over subdomain */
1798   /*       Loop over quad points */
1799   /*         Transform coords to real space */
1800   /*         Evaluate field and aux fields at point */
1801   /*         Evaluate residual at point */
1802   /*         Transform residual to real space */
1803   /*       Add residual to elemVec */
1804   /* Loop over domain */
1805   /*   Add elemVec to locX */
1806 
1807   /* FVM */
1808   /* Get geometric data */
1809   /* If using gradients */
1810   /*   Compute gradient data */
1811   /*   Loop over domain faces */
1812   /*     Count computational faces */
1813   /*     Reconstruct cell gradient */
1814   /*   Loop over domain cells */
1815   /*     Limit cell gradients */
1816   /* Handle boundary values */
1817   /* Loop over domain faces */
1818   /*   Read out field, centroid, normal, volume for each side of face */
1819   /* Riemann solve over faces */
1820   /* Loop over domain faces */
1821   /*   Accumulate fluxes to cells */
1822   /* TODO Change printFEM to printDisc here */
1823   if (mesh->printFEM) {
1824     Vec         locFbc;
1825     PetscInt    pStart, pEnd, p, maxDof;
1826     PetscScalar *zeroes;
1827 
1828     ierr = VecDuplicate(locF,&locFbc);CHKERRQ(ierr);
1829     ierr = VecCopy(locF,locFbc);CHKERRQ(ierr);
1830     ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
1831     ierr = PetscSectionGetMaxDof(section,&maxDof);CHKERRQ(ierr);
1832     ierr = PetscCalloc1(maxDof,&zeroes);CHKERRQ(ierr);
1833     for (p = pStart; p < pEnd; p++) {
1834       ierr = VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);CHKERRQ(ierr);
1835     }
1836     ierr = PetscFree(zeroes);CHKERRQ(ierr);
1837     ierr = DMPrintLocalVec(dm, name, mesh->printTol, locFbc);CHKERRQ(ierr);
1838     ierr = VecDestroy(&locFbc);CHKERRQ(ierr);
1839   }
1840   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1841   PetscFunctionReturn(0);
1842 }
1843 
1844 static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, PetscReal t, Vec F, void *user)
1845 {
1846   DM                dmCh, dmAux;
1847   Vec               A;
1848   DMField           coordField = NULL;
1849   PetscDS           prob, probCh, probAux = NULL;
1850   PetscSection      section, sectionAux;
1851   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
1852   PetscInt          Nf, f, numCells, cStart, cEnd, c;
1853   PetscInt          totDim, totDimAux = 0, diffCell = 0;
1854   PetscInt          depth;
1855   PetscInt          maxDegree;
1856   IS                cellIS;
1857   DMLabel           depthLabel;
1858   PetscErrorCode    ierr;
1859 
1860   PetscFunctionBegin;
1861   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1862   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1863   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1864   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1865   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1866   numCells = cEnd - cStart;
1867   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
1868   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
1869   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1870   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1871   if (dmAux) {
1872     ierr = DMGetSection(dmAux, &sectionAux);CHKERRQ(ierr);
1873     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1874     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1875   }
1876   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1877   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);CHKERRQ(ierr);
1878   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
1879   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1880   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
1881   ierr = DMPlexGetDepth(dm,&depth);CHKERRQ(ierr);
1882   ierr = DMLabelGetStratumIS(depthLabel,depth,&cellIS);CHKERRQ(ierr);
1883   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
1884   for (c = cStart; c < cEnd; ++c) {
1885     PetscScalar *x = NULL, *x_t = NULL;
1886     PetscInt     i;
1887 
1888     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1889     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1890     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1891     if (X_t) {
1892       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1893       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1894       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1895     }
1896     if (dmAux) {
1897       DM dmAuxPlex;
1898 
1899       ierr = DMSNESConvertPlex(dmAux,&dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1900       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1901       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1902       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1903       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1904     }
1905   }
1906   for (f = 0; f < Nf; ++f) {
1907     PetscFE  fe, feCh;
1908     PetscInt Nq, Nb;
1909     /* Conforming batches */
1910     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1911     /* Remainder */
1912     PetscInt Nr, offset;
1913     PetscQuadrature qGeom = NULL;
1914     PetscFEGeom *cgeomFEM, *chunkGeom = NULL;
1915 
1916     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1917     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
1918     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1919     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1920     ierr = DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);CHKERRQ(ierr);
1921     if (maxDegree <= 1) {
1922       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);CHKERRQ(ierr);
1923     }
1924     if (!qGeom) {
1925       ierr = PetscFEGetQuadrature(fe, &qGeom);CHKERRQ(ierr);
1926       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
1927     }
1928     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1929     ierr = DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
1930     blockSize = Nb;
1931     batchSize = numBlocks * blockSize;
1932     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1933     numChunks = numCells / (numBatches*batchSize);
1934     Ne        = numChunks*numBatches*batchSize;
1935     Nr        = numCells % (numBatches*batchSize);
1936     offset    = numCells - Nr;
1937     ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
1938     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, chunkGeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1939     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, chunkGeom, u, u_t, probAux, a, t, elemVecCh);CHKERRQ(ierr);
1940     ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1941     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);
1942     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);
1943     ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1944     ierr = DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
1945     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
1946   }
1947   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
1948   for (c = cStart; c < cEnd; ++c) {
1949     PetscBool diff = PETSC_FALSE;
1950     PetscInt  d;
1951 
1952     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
1953     if (diff) {
1954       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
1955       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
1956       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
1957       ++diffCell;
1958     }
1959     if (diffCell > 9) break;
1960     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1961   }
1962   ierr = PetscFree3(u,u_t,elemVec);CHKERRQ(ierr);
1963   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
1964   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1965   PetscFunctionReturn(0);
1966 }
1967 
1968 /*@
1969   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1970 
1971   Input Parameters:
1972 + dm - The mesh
1973 . X  - Local solution
1974 - user - The user context
1975 
1976   Output Parameter:
1977 . F  - Local output vector
1978 
1979   Level: developer
1980 
1981 .seealso: DMPlexComputeJacobianAction()
1982 @*/
1983 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
1984 {
1985   PetscObject    check;
1986   DM             plex;
1987   IS             cellIS;
1988   PetscInt       depth;
1989   PetscErrorCode ierr;
1990 
1991   PetscFunctionBegin;
1992   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
1993   ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
1994   ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
1995   if (!cellIS) {
1996     ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);
1997   }
1998   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
1999   ierr = PetscObjectQuery((PetscObject) plex, "dmCh", &check);CHKERRQ(ierr);
2000   if (check) {ierr = DMPlexComputeResidualFEM_Check_Internal(plex, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2001   else       {ierr = DMPlexComputeResidual_Internal(plex, cellIS, PETSC_MIN_REAL, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2002   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
2003   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2004   PetscFunctionReturn(0);
2005 }
2006 
2007 /*@
2008   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X
2009 
2010   Input Parameters:
2011 + dm - The mesh
2012 - user - The user context
2013 
2014   Output Parameter:
2015 . X  - Local solution
2016 
2017   Level: developer
2018 
2019 .seealso: DMPlexComputeJacobianAction()
2020 @*/
2021 PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
2022 {
2023   DM             plex;
2024   PetscErrorCode ierr;
2025 
2026   PetscFunctionBegin;
2027   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2028   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);CHKERRQ(ierr);
2029   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2030   PetscFunctionReturn(0);
2031 }
2032 
2033 PetscErrorCode DMPlexComputeBdJacobian_Single_Internal(DM dm, PetscReal t, DMLabel label, PetscInt numValues, const PetscInt values[], PetscInt fieldI, Vec locX, Vec locX_t, PetscReal X_tShift, Mat Jac, Mat JacP, DMField coordField, IS facetIS)
2034 {
2035   DM_Plex       *mesh = (DM_Plex *) dm->data;
2036   DM             plex = NULL, plexA = NULL;
2037   PetscDS        prob, probAux = NULL;
2038   PetscSection   section, sectionAux = NULL;
2039   PetscSection   globalSection, subSection = NULL;
2040   Vec            locA = NULL;
2041   PetscScalar   *u = NULL, *u_t = NULL, *a = NULL, *elemMat = NULL;
2042   PetscInt       v;
2043   PetscInt       Nf, totDim, totDimAux = 0;
2044   PetscBool      isMatISP;
2045   PetscErrorCode ierr;
2046 
2047   PetscFunctionBegin;
2048   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
2049   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
2050   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2051   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
2052   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2053   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
2054   if (locA) {
2055     DM dmAux;
2056 
2057     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
2058     ierr = DMConvert(dmAux, DMPLEX, &plexA);CHKERRQ(ierr);
2059     ierr = DMGetDS(plexA, &probAux);CHKERRQ(ierr);
2060     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2061     ierr = DMGetSection(plexA, &sectionAux);CHKERRQ(ierr);
2062   }
2063 
2064   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2065   ierr = DMGetGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2066   if (isMatISP) {ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);}
2067   for (v = 0; v < numValues; ++v) {
2068     PetscFEGeom    *fgeom;
2069     PetscInt        maxDegree;
2070     PetscQuadrature qGeom = NULL;
2071     IS              pointIS;
2072     const PetscInt *points;
2073     PetscInt        numFaces, face, Nq;
2074 
2075     ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
2076     if (!pointIS) continue; /* No points with that id on this process */
2077     {
2078       IS isectIS;
2079 
2080       /* TODO: Special cases of ISIntersect where it is quick to check a prior if one is a superset of the other */
2081       ierr = ISIntersect_Caching_Internal(facetIS,pointIS,&isectIS);CHKERRQ(ierr);
2082       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2083       pointIS = isectIS;
2084     }
2085     ierr = ISGetLocalSize(pointIS, &numFaces);CHKERRQ(ierr);
2086     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2087     ierr = PetscMalloc4(numFaces*totDim, &u, locX_t ? numFaces*totDim : 0, &u_t, numFaces*totDim*totDim, &elemMat, locA ? numFaces*totDimAux : 0, &a);CHKERRQ(ierr);
2088     ierr = DMFieldGetDegree(coordField,pointIS,NULL,&maxDegree);CHKERRQ(ierr);
2089     if (maxDegree <= 1) {
2090       ierr = DMFieldCreateDefaultQuadrature(coordField,pointIS,&qGeom);CHKERRQ(ierr);
2091     }
2092     if (!qGeom) {
2093       PetscFE fe;
2094 
2095       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2096       ierr = PetscFEGetFaceQuadrature(fe, &qGeom);CHKERRQ(ierr);
2097       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
2098     }
2099     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
2100     ierr = DMSNESGetFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
2101     for (face = 0; face < numFaces; ++face) {
2102       const PetscInt point = points[face], *support, *cone;
2103       PetscScalar   *x     = NULL;
2104       PetscInt       i, coneSize, faceLoc;
2105 
2106       ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
2107       ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
2108       ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
2109       for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
2110       if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of support[0] %d", point, support[0]);
2111       fgeom->face[face][0] = faceLoc;
2112       ierr = DMPlexVecGetClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
2113       for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
2114       ierr = DMPlexVecRestoreClosure(plex, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
2115       if (locX_t) {
2116         ierr = DMPlexVecGetClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
2117         for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
2118         ierr = DMPlexVecRestoreClosure(plex, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
2119       }
2120       if (locA) {
2121         PetscInt subp;
2122         ierr = DMPlexGetSubpoint(plexA, support[0], &subp);CHKERRQ(ierr);
2123         ierr = DMPlexVecGetClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
2124         for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
2125         ierr = DMPlexVecRestoreClosure(plexA, sectionAux, locA, subp, NULL, &x);CHKERRQ(ierr);
2126       }
2127     }
2128     ierr = PetscMemzero(elemMat, numFaces*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2129     {
2130       PetscFE         fe;
2131       PetscInt        Nb;
2132       /* Conforming batches */
2133       PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2134       /* Remainder */
2135       PetscFEGeom    *chunkGeom = NULL;
2136       PetscInt        fieldJ, Nr, offset;
2137 
2138       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2139       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2140       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2141       blockSize = Nb;
2142       batchSize = numBlocks * blockSize;
2143       ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2144       numChunks = numFaces / (numBatches*batchSize);
2145       Ne        = numChunks*numBatches*batchSize;
2146       Nr        = numFaces % (numBatches*batchSize);
2147       offset    = numFaces - Nr;
2148       ierr = PetscFEGeomGetChunk(fgeom,0,offset,&chunkGeom);CHKERRQ(ierr);
2149       for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2150         ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2151       }
2152       ierr = PetscFEGeomGetChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
2153       for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2154         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);
2155       }
2156       ierr = PetscFEGeomRestoreChunk(fgeom,offset,numFaces,&chunkGeom);CHKERRQ(ierr);
2157     }
2158     for (face = 0; face < numFaces; ++face) {
2159       const PetscInt point = points[face], *support;
2160 
2161       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDim, totDim, &elemMat[face*totDim*totDim]);CHKERRQ(ierr);}
2162       ierr = DMPlexGetSupport(plex, point, &support);CHKERRQ(ierr);
2163       if (!isMatISP) {
2164         ierr = DMPlexMatSetClosure(plex, section, globalSection, JacP, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2165       } else {
2166         Mat lJ;
2167 
2168         ierr = MatISGetLocalMat(JacP, &lJ);CHKERRQ(ierr);
2169         ierr = DMPlexMatSetClosure(plex, section, subSection, lJ, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2170       }
2171     }
2172     ierr = DMSNESRestoreFEGeom(coordField,pointIS,qGeom,PETSC_TRUE,&fgeom);CHKERRQ(ierr);
2173     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2174     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2175     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2176     ierr = PetscFree4(u, u_t, elemMat, a);CHKERRQ(ierr);
2177   }
2178   if (plex)  {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
2179   if (plexA) {ierr = DMDestroy(&plexA);CHKERRQ(ierr);}
2180   PetscFunctionReturn(0);
2181 }
2182 
2183 PetscErrorCode DMPlexComputeBdJacobianSingle(DM dm, PetscReal t, DMLabel label, PetscInt numValues, const PetscInt values[], PetscInt field, Vec locX, Vec locX_t, PetscReal X_tShift, Mat Jac, Mat JacP)
2184 {
2185   DMField        coordField;
2186   DMLabel        depthLabel;
2187   IS             facetIS;
2188   PetscInt       dim;
2189   PetscErrorCode ierr;
2190 
2191   PetscFunctionBegin;
2192   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2193   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
2194   ierr = DMLabelGetStratumIS(depthLabel, dim-1, &facetIS);CHKERRQ(ierr);
2195   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2196   ierr = DMPlexComputeBdJacobian_Single_Internal(dm, t, label, numValues, values, field, locX, locX_t, X_tShift, Jac, JacP, coordField, facetIS);CHKERRQ(ierr);
2197   PetscFunctionReturn(0);
2198 }
2199 
2200 PetscErrorCode DMPlexComputeBdJacobian_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, PetscReal X_tShift, Mat Jac, Mat JacP, void *user)
2201 {
2202   PetscDS          prob;
2203   PetscInt         dim, numBd, bd;
2204   DMLabel          depthLabel;
2205   DMField          coordField = NULL;
2206   IS               facetIS;
2207   PetscErrorCode   ierr;
2208 
2209   PetscFunctionBegin;
2210   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2211   ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
2212   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2213   ierr = DMLabelGetStratumIS(depthLabel, dim-1, &facetIS);CHKERRQ(ierr);
2214   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
2215   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2216   for (bd = 0; bd < numBd; ++bd) {
2217     DMBoundaryConditionType type;
2218     const char             *bdLabel;
2219     DMLabel                 label;
2220     const PetscInt         *values;
2221     PetscInt                fieldI, numValues;
2222     PetscObject             obj;
2223     PetscClassId            id;
2224 
2225     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &fieldI, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
2226     ierr = PetscDSGetDiscretization(prob, fieldI, &obj);CHKERRQ(ierr);
2227     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2228     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
2229     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
2230     ierr = DMPlexComputeBdJacobian_Single_Internal(dm, t, label, numValues, values, fieldI, locX, locX_t, X_tShift, Jac, JacP, coordField, facetIS);CHKERRQ(ierr);
2231   }
2232   ierr = ISDestroy(&facetIS);CHKERRQ(ierr);
2233   PetscFunctionReturn(0);
2234 }
2235 
2236 PetscErrorCode DMPlexComputeJacobian_Internal(DM dm, IS cellIS, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Mat Jac, Mat JacP,void *user)
2237 {
2238   DM_Plex        *mesh  = (DM_Plex *) dm->data;
2239   const char     *name  = "Jacobian";
2240   DM              dmAux, plex;
2241   Vec             A;
2242   DMField         coordField;
2243   PetscDS         prob, probAux = NULL;
2244   PetscSection    section, globalSection, subSection, sectionAux;
2245   PetscScalar    *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
2246   const PetscInt *cells;
2247   PetscInt        Nf, fieldI, fieldJ;
2248   PetscInt        totDim, totDimAux, cStart, cEnd, numCells, c;
2249   PetscBool       isMatIS, isMatISP, hasJac, hasPrec, hasDyn, hasFV = PETSC_FALSE;
2250   PetscErrorCode  ierr;
2251 
2252   PetscFunctionBegin;
2253   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2254   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
2255   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2256   ierr = DMGetGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2257   if (isMatISP) {ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);}
2258   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2259   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2260   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2261   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2262   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2263   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2264   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2265   ierr = ISGetLocalSize(cellIS, &numCells);CHKERRQ(ierr);
2266   ierr = ISGetPointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
2267   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2268   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2269   if (dmAux) {
2270     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2271     ierr = DMGetSection(plex, &sectionAux);CHKERRQ(ierr);
2272     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2273     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2274   }
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   for (c = cStart; c < cEnd; ++c) {
2279     const PetscInt cell = cells ? cells[c] : c;
2280     const PetscInt cind = c - cStart;
2281     PetscScalar   *x = NULL,  *x_t = NULL;
2282     PetscInt       i;
2283 
2284     ierr = DMPlexVecGetClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
2285     for (i = 0; i < totDim; ++i) u[cind*totDim+i] = x[i];
2286     ierr = DMPlexVecRestoreClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
2287     if (X_t) {
2288       ierr = DMPlexVecGetClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
2289       for (i = 0; i < totDim; ++i) u_t[cind*totDim+i] = x_t[i];
2290       ierr = DMPlexVecRestoreClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
2291     }
2292     if (dmAux) {
2293       ierr = DMPlexVecGetClosure(plex, sectionAux, A, cell, NULL, &x);CHKERRQ(ierr);
2294       for (i = 0; i < totDimAux; ++i) a[cind*totDimAux+i] = x[i];
2295       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, cell, NULL, &x);CHKERRQ(ierr);
2296     }
2297   }
2298   if (hasJac)  {ierr = PetscMemzero(elemMat,  numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2299   if (hasPrec) {ierr = PetscMemzero(elemMatP, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2300   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2301   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2302     PetscClassId    id;
2303     PetscFE         fe;
2304     PetscQuadrature qGeom = NULL;
2305     PetscInt        Nb;
2306     /* Conforming batches */
2307     PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2308     /* Remainder */
2309     PetscInt        Nr, offset, Nq;
2310     PetscInt        maxDegree;
2311     PetscFEGeom     *cgeomFEM, *chunkGeom = NULL, *remGeom = NULL;
2312 
2313     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2314     ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
2315     if (id == PETSCFV_CLASSID) {hasFV = PETSC_TRUE; continue;}
2316     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2317     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2318     ierr = DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);CHKERRQ(ierr);
2319     if (maxDegree <= 1) {
2320       ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);CHKERRQ(ierr);
2321     }
2322     if (!qGeom) {
2323       ierr = PetscFEGetQuadrature(fe,&qGeom);CHKERRQ(ierr);
2324       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
2325     }
2326     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
2327     ierr = DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2328     blockSize = Nb;
2329     batchSize = numBlocks * blockSize;
2330     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2331     numChunks = numCells / (numBatches*batchSize);
2332     Ne        = numChunks*numBatches*batchSize;
2333     Nr        = numCells % (numBatches*batchSize);
2334     offset    = numCells - Nr;
2335     ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2336     ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2337     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2338       if (hasJac) {
2339         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2340         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);
2341       }
2342       if (hasPrec) {
2343         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatP);CHKERRQ(ierr);
2344         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);
2345       }
2346       if (hasDyn) {
2347         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2348         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);
2349       }
2350     }
2351     ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2352     ierr = PetscFEGeomRestoreChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2353     ierr = DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2354     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2355   }
2356   /*   Add contribution from X_t */
2357   if (hasDyn) {for (c = 0; c < numCells*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];}
2358   if (hasFV) {
2359     PetscClassId id;
2360     PetscFV      fv;
2361     PetscInt     offsetI, NcI, NbI = 1, fc, f;
2362 
2363     for (fieldI = 0; fieldI < Nf; ++fieldI) {
2364       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fv);CHKERRQ(ierr);
2365       ierr = PetscDSGetFieldOffset(prob, fieldI, &offsetI);CHKERRQ(ierr);
2366       ierr = PetscObjectGetClassId((PetscObject) fv, &id);CHKERRQ(ierr);
2367       if (id != PETSCFV_CLASSID) continue;
2368       /* Put in the identity */
2369       ierr = PetscFVGetNumComponents(fv, &NcI);CHKERRQ(ierr);
2370       for (c = cStart; c < cEnd; ++c) {
2371         const PetscInt cind    = c - cStart;
2372         const PetscInt eOffset = cind*totDim*totDim;
2373         for (fc = 0; fc < NcI; ++fc) {
2374           for (f = 0; f < NbI; ++f) {
2375             const PetscInt i = offsetI + f*NcI+fc;
2376             if (hasPrec) {
2377               if (hasJac) {elemMat[eOffset+i*totDim+i] = 1.0;}
2378               elemMatP[eOffset+i*totDim+i] = 1.0;
2379             } else {elemMat[eOffset+i*totDim+i] = 1.0;}
2380           }
2381         }
2382       }
2383     }
2384     /* No allocated space for FV stuff, so ignore the zero entries */
2385     ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2386   }
2387   /* Insert values into matrix */
2388   isMatIS = PETSC_FALSE;
2389   if (hasPrec && hasJac) {
2390     ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatIS);CHKERRQ(ierr);
2391   }
2392   if (isMatIS && !subSection) {
2393     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2394   }
2395   for (c = cStart; c < cEnd; ++c) {
2396     const PetscInt cell = cells ? cells[c] : c;
2397     const PetscInt cind = c - cStart;
2398 
2399     if (hasPrec) {
2400       if (hasJac) {
2401         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, totDim, totDim, &elemMat[cind*totDim*totDim]);CHKERRQ(ierr);}
2402         if (!isMatIS) {
2403           ierr = DMPlexMatSetClosure(dm, section, globalSection, Jac, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2404         } else {
2405           Mat lJ;
2406 
2407           ierr = MatISGetLocalMat(Jac,&lJ);CHKERRQ(ierr);
2408           ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2409         }
2410       }
2411       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, totDim, totDim, &elemMatP[cind*totDim*totDim]);CHKERRQ(ierr);}
2412       if (!isMatISP) {
2413         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, cell, &elemMatP[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2414       } else {
2415         Mat lJ;
2416 
2417         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2418         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, cell, &elemMatP[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2419       }
2420     } else {
2421       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, totDim, totDim, &elemMat[cind*totDim*totDim]);CHKERRQ(ierr);}
2422       if (!isMatISP) {
2423         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2424       } else {
2425         Mat lJ;
2426 
2427         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2428         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, cell, &elemMat[cind*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2429       }
2430     }
2431   }
2432   ierr = ISRestorePointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
2433   if (hasFV) {ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);CHKERRQ(ierr);}
2434   ierr = PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);CHKERRQ(ierr);
2435   if (dmAux) {
2436     ierr = PetscFree(a);CHKERRQ(ierr);
2437     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2438   }
2439   /* Compute boundary integrals */
2440   ierr = DMPlexComputeBdJacobian_Internal(dm, X, X_t, t, X_tShift, Jac, JacP, user);CHKERRQ(ierr);
2441   /* Assemble matrix */
2442   if (hasJac && hasPrec) {
2443     ierr = MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2444     ierr = MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2445   }
2446   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2447   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2448   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2449   PetscFunctionReturn(0);
2450 }
2451 
2452 /*@
2453   DMPlexComputeJacobianAction - Form the local portion of the Jacobian action Z = J(X) Y at the local solution X using pointwise functions specified by the user.
2454 
2455   Input Parameters:
2456 + dm - The mesh
2457 . cellIS -
2458 . t  - The time
2459 . X_tShift - The multiplier for the Jacobian with repsect to X_t
2460 . X  - Local solution vector
2461 . X_t  - Time-derivative of the local solution vector
2462 . Y  - Local input vector
2463 - user - The user context
2464 
2465   Output Parameter:
2466 . Z - Local output vector
2467 
2468   Note:
2469   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2470   like a GPU, or vectorize on a multicore machine.
2471 
2472   Level: developer
2473 
2474 .seealso: FormFunctionLocal()
2475 @*/
2476 PetscErrorCode DMPlexComputeJacobianAction(DM dm, IS cellIS, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Vec Y, Vec Z, void *user)
2477 {
2478   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2479   const char       *name  = "Jacobian";
2480   DM                dmAux, plex, plexAux = NULL;
2481   Vec               A;
2482   PetscDS           prob, probAux = NULL;
2483   PetscQuadrature   quad;
2484   PetscSection      section, globalSection, sectionAux;
2485   PetscScalar      *elemMat, *elemMatD, *u, *u_t, *a = NULL, *y, *z;
2486   PetscInt          Nf, fieldI, fieldJ;
2487   PetscInt          totDim, totDimAux = 0;
2488   const PetscInt   *cells;
2489   PetscInt          cStart, cEnd, numCells, c;
2490   PetscBool         hasDyn;
2491   DMField           coordField;
2492   PetscErrorCode    ierr;
2493 
2494   PetscFunctionBegin;
2495   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2496   ierr = DMSNESConvertPlex(dm, &plex, PETSC_TRUE);CHKERRQ(ierr);
2497   if (!cellIS) {
2498     PetscInt depth;
2499 
2500     ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
2501     ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
2502     if (!cellIS) {ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);}
2503   } else {
2504     ierr = PetscObjectReference((PetscObject) cellIS);CHKERRQ(ierr);
2505   }
2506   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
2507   ierr = DMGetGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2508   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2509   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2510   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2511   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2512   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2513   ierr = ISGetLocalSize(cellIS, &numCells);CHKERRQ(ierr);
2514   ierr = ISGetPointRange(cellIS, &cStart, &cEnd, &cells);CHKERRQ(ierr);
2515   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2516   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2517   if (dmAux) {
2518     ierr = DMConvert(dmAux, DMPLEX, &plexAux);CHKERRQ(ierr);
2519     ierr = DMGetSection(plexAux, &sectionAux);CHKERRQ(ierr);
2520     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2521     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2522   }
2523   ierr = VecSet(Z, 0.0);CHKERRQ(ierr);
2524   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);
2525   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2526   ierr = DMGetCoordinateField(dm, &coordField);CHKERRQ(ierr);
2527   for (c = cStart; c < cEnd; ++c) {
2528     const PetscInt cell = cells ? cells[c] : c;
2529     const PetscInt cind = c - cStart;
2530     PetscScalar   *x = NULL,  *x_t = NULL;
2531     PetscInt       i;
2532 
2533     ierr = DMPlexVecGetClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
2534     for (i = 0; i < totDim; ++i) u[cind*totDim+i] = x[i];
2535     ierr = DMPlexVecRestoreClosure(dm, section, X, cell, NULL, &x);CHKERRQ(ierr);
2536     if (X_t) {
2537       ierr = DMPlexVecGetClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
2538       for (i = 0; i < totDim; ++i) u_t[cind*totDim+i] = x_t[i];
2539       ierr = DMPlexVecRestoreClosure(dm, section, X_t, cell, NULL, &x_t);CHKERRQ(ierr);
2540     }
2541     if (dmAux) {
2542       ierr = DMPlexVecGetClosure(plexAux, sectionAux, A, cell, NULL, &x);CHKERRQ(ierr);
2543       for (i = 0; i < totDimAux; ++i) a[cind*totDimAux+i] = x[i];
2544       ierr = DMPlexVecRestoreClosure(plexAux, sectionAux, A, cell, NULL, &x);CHKERRQ(ierr);
2545     }
2546     ierr = DMPlexVecGetClosure(dm, section, Y, cell, NULL, &x);CHKERRQ(ierr);
2547     for (i = 0; i < totDim; ++i) y[cind*totDim+i] = x[i];
2548     ierr = DMPlexVecRestoreClosure(dm, section, Y, cell, NULL, &x);CHKERRQ(ierr);
2549   }
2550   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2551   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2552   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2553     PetscFE  fe;
2554     PetscInt Nb;
2555     /* Conforming batches */
2556     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2557     /* Remainder */
2558     PetscInt Nr, offset, Nq;
2559     PetscQuadrature qGeom = NULL;
2560     PetscInt    maxDegree;
2561     PetscFEGeom *cgeomFEM, *chunkGeom = NULL, *remGeom = NULL;
2562 
2563     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2564     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2565     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2566     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2567     ierr = DMFieldGetDegree(coordField,cellIS,NULL,&maxDegree);CHKERRQ(ierr);
2568     if (maxDegree <= 1) {ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&qGeom);CHKERRQ(ierr);}
2569     if (!qGeom) {
2570       ierr = PetscFEGetQuadrature(fe,&qGeom);CHKERRQ(ierr);
2571       ierr = PetscObjectReference((PetscObject)qGeom);CHKERRQ(ierr);
2572     }
2573     ierr = PetscQuadratureGetData(qGeom, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
2574     ierr = DMSNESGetFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2575     blockSize = Nb;
2576     batchSize = numBlocks * blockSize;
2577     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2578     numChunks = numCells / (numBatches*batchSize);
2579     Ne        = numChunks*numBatches*batchSize;
2580     Nr        = numCells % (numBatches*batchSize);
2581     offset    = numCells - Nr;
2582     ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2583     ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2584     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2585       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2586       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);
2587       if (hasDyn) {
2588         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, chunkGeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2589         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);
2590       }
2591     }
2592     ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&remGeom);CHKERRQ(ierr);
2593     ierr = PetscFEGeomRestoreChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
2594     ierr = DMSNESRestoreFEGeom(coordField,cellIS,qGeom,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
2595     ierr = PetscQuadratureDestroy(&qGeom);CHKERRQ(ierr);
2596   }
2597   if (hasDyn) {
2598     for (c = 0; c < numCells*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2599   }
2600   for (c = cStart; c < cEnd; ++c) {
2601     const PetscInt     cell = cells ? cells[c] : c;
2602     const PetscInt     cind = c - cStart;
2603     const PetscBLASInt M = totDim, one = 1;
2604     const PetscScalar  a = 1.0, b = 0.0;
2605 
2606     PetscStackCallBLAS("BLASgemv", BLASgemv_("N", &M, &M, &a, &elemMat[cind*totDim*totDim], &M, &y[cind*totDim], &one, &b, z, &one));
2607     if (mesh->printFEM > 1) {
2608       ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[cind*totDim*totDim]);CHKERRQ(ierr);
2609       ierr = DMPrintCellVector(c, "Y",  totDim, &y[cind*totDim]);CHKERRQ(ierr);
2610       ierr = DMPrintCellVector(c, "Z",  totDim, z);CHKERRQ(ierr);
2611     }
2612     ierr = DMPlexVecSetClosure(dm, section, Z, cell, z, ADD_VALUES);CHKERRQ(ierr);
2613   }
2614   ierr = PetscFree6(u,u_t,elemMat,elemMatD,y,z);CHKERRQ(ierr);
2615   if (mesh->printFEM) {
2616     ierr = PetscPrintf(PETSC_COMM_WORLD, "Z:\n");CHKERRQ(ierr);
2617     ierr = VecView(Z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2618   }
2619   ierr = PetscFree(a);CHKERRQ(ierr);
2620   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
2621   ierr = DMDestroy(&plexAux);CHKERRQ(ierr);
2622   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2623   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2624   PetscFunctionReturn(0);
2625 }
2626 
2627 /*@
2628   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2629 
2630   Input Parameters:
2631 + dm - The mesh
2632 . X  - Local input vector
2633 - user - The user context
2634 
2635   Output Parameter:
2636 . Jac  - Jacobian matrix
2637 
2638   Note:
2639   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2640   like a GPU, or vectorize on a multicore machine.
2641 
2642   Level: developer
2643 
2644 .seealso: FormFunctionLocal()
2645 @*/
2646 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2647 {
2648   DM             plex;
2649   PetscDS        prob;
2650   IS             cellIS;
2651   PetscBool      hasJac, hasPrec;
2652   PetscInt       depth;
2653   PetscErrorCode ierr;
2654 
2655   PetscFunctionBegin;
2656   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2657   ierr = DMPlexGetDepth(plex, &depth);CHKERRQ(ierr);
2658   ierr = DMGetStratumIS(plex, "dim", depth, &cellIS);CHKERRQ(ierr);
2659   if (!cellIS) {ierr = DMGetStratumIS(plex, "depth", depth, &cellIS);CHKERRQ(ierr);}
2660   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2661   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2662   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2663   if (hasJac && hasPrec) {ierr = MatZeroEntries(Jac);CHKERRQ(ierr);}
2664   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
2665   ierr = DMPlexComputeJacobian_Internal(plex, cellIS, 0.0, 0.0, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2666   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
2667   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2668   PetscFunctionReturn(0);
2669 }
2670 
2671 /*@
2672   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.
2673 
2674   Input Parameters:
2675 + dm - The DM object
2676 . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see PetscDSAddBoundary())
2677 . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
2678 - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())
2679 
2680   Level: developer
2681 @*/
2682 PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
2683 {
2684   PetscErrorCode ierr;
2685 
2686   PetscFunctionBegin;
2687   ierr = DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);CHKERRQ(ierr);
2688   ierr = DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);CHKERRQ(ierr);
2689   ierr = DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);CHKERRQ(ierr);
2690   PetscFunctionReturn(0);
2691 }
2692 
2693 PetscErrorCode DMSNESCheckFromOptions_Internal(SNES snes, DM dm, Vec u, PetscErrorCode (**exactFuncs)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx), void **ctxs)
2694 {
2695   PetscErrorCode (**exacts)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx);
2696   PetscDS        prob;
2697   Mat            J, M;
2698   Vec            r, b;
2699   MatNullSpace   nullSpace;
2700   PetscReal     *error, res = 0.0;
2701   PetscInt       numFields;
2702   PetscBool      hasJac, hasPrec;
2703   PetscInt       Nf, f;
2704   PetscErrorCode ierr;
2705 
2706   PetscFunctionBegin;
2707   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2708   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
2709   ierr = PetscMalloc1(Nf, &exacts);CHKERRQ(ierr);
2710   for (f = 0; f < Nf; ++f) {ierr = PetscDSGetExactSolution(prob, f, &exacts[f]);CHKERRQ(ierr);}
2711   ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2712   ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
2713   /* TODO Null space for J */
2714   /* Check discretization error */
2715   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
2716   ierr = PetscMalloc1(PetscMax(1, numFields), &error);CHKERRQ(ierr);
2717   ierr = DMProjectFunction(dm, 0.0, exactFuncs ? exactFuncs : exacts, ctxs, INSERT_ALL_VALUES, u);CHKERRQ(ierr);
2718   if (numFields > 1) {
2719     PetscInt f;
2720 
2721     ierr = DMComputeL2FieldDiff(dm, 0.0, exactFuncs ? exactFuncs : exacts, ctxs, u, error);CHKERRQ(ierr);
2722     ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: [");CHKERRQ(ierr);
2723     for (f = 0; f < numFields; ++f) {
2724       if (f) {ierr = PetscPrintf(PETSC_COMM_WORLD, ", ");CHKERRQ(ierr);}
2725       if (error[f] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "%g", (double)error[f]);CHKERRQ(ierr);}
2726       else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "< 1.0e-11");CHKERRQ(ierr);}
2727     }
2728     ierr = PetscPrintf(PETSC_COMM_WORLD, "]\n");CHKERRQ(ierr);
2729   } else {
2730     ierr = DMComputeL2Diff(dm, 0.0, exactFuncs ? exactFuncs : exacts, ctxs, u, &error[0]);CHKERRQ(ierr);
2731     if (error[0] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", (double)error[0]);CHKERRQ(ierr);}
2732     else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
2733   }
2734   ierr = PetscFree(error);CHKERRQ(ierr);
2735   /* Check residual */
2736   ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2737   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2738   ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", (double)res);CHKERRQ(ierr);
2739   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2740   ierr = PetscObjectSetName((PetscObject) r, "Initial Residual");CHKERRQ(ierr);
2741   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"res_");CHKERRQ(ierr);
2742   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2743   /* Check Jacobian */
2744   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2745   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2746   if (hasJac && hasPrec) {
2747     ierr = DMCreateMatrix(dm, &M);CHKERRQ(ierr);
2748     ierr = SNESComputeJacobian(snes, u, J, M);CHKERRQ(ierr);
2749     ierr = PetscObjectSetOptionsPrefix((PetscObject) M, "jacpre_");CHKERRQ(ierr);
2750     ierr = MatViewFromOptions(M, NULL, "-mat_view");CHKERRQ(ierr);
2751     ierr = MatDestroy(&M);CHKERRQ(ierr);
2752   } else {
2753     ierr = SNESComputeJacobian(snes, u, J, J);CHKERRQ(ierr);
2754   }
2755   ierr = PetscObjectSetOptionsPrefix((PetscObject) J, "jac_");CHKERRQ(ierr);
2756   ierr = MatViewFromOptions(J, NULL, "-mat_view");CHKERRQ(ierr);
2757   ierr = MatGetNullSpace(J, &nullSpace);CHKERRQ(ierr);
2758   if (nullSpace) {
2759     PetscBool isNull;
2760     ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
2761     if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
2762   }
2763   ierr = VecDuplicate(u, &b);CHKERRQ(ierr);
2764   ierr = VecSet(r, 0.0);CHKERRQ(ierr);
2765   ierr = SNESComputeFunction(snes, r, b);CHKERRQ(ierr);
2766   ierr = MatMult(J, u, r);CHKERRQ(ierr);
2767   ierr = VecAXPY(r, 1.0, b);CHKERRQ(ierr);
2768   ierr = VecDestroy(&b);CHKERRQ(ierr);
2769   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2770   ierr = PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", (double)res);CHKERRQ(ierr);
2771   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2772   ierr = PetscObjectSetName((PetscObject) r, "Au - b = Au + F(0)");CHKERRQ(ierr);
2773   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"linear_res_");CHKERRQ(ierr);
2774   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2775   ierr = VecDestroy(&r);CHKERRQ(ierr);
2776   ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
2777   ierr = MatDestroy(&J);CHKERRQ(ierr);
2778   ierr = PetscFree(exacts);CHKERRQ(ierr);
2779   PetscFunctionReturn(0);
2780 }
2781 
2782 /*@C
2783   DMSNESCheckFromOptions - Check the residual and Jacobian functions using the exact solution by outputting some diagnostic information
2784 
2785   Input Parameters:
2786 + snes - the SNES object
2787 . u    - representative SNES vector
2788 . exactFuncs - pointwise functions of the exact solution for each field
2789 - ctxs - contexts for the functions
2790 
2791   Level: developer
2792 @*/
2793 PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
2794 {
2795   PetscErrorCode (**exact)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *) = NULL;
2796   DM             dm;
2797   PetscDS        prob;
2798   Vec            sol;
2799   PetscBool      check;
2800   PetscInt       Nf, f;
2801   PetscErrorCode ierr;
2802 
2803   PetscFunctionBegin;
2804   ierr = PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);CHKERRQ(ierr);
2805   if (!check) PetscFunctionReturn(0);
2806   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
2807   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2808   if (!exactFuncs) {
2809     ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
2810     ierr = PetscMalloc1(Nf, &exact);CHKERRQ(ierr);
2811     for (f = 0; f < Nf; ++f) {ierr = PetscDSGetExactSolution(prob, f, &exact[f]);CHKERRQ(ierr);}
2812   }
2813   ierr = VecDuplicate(u, &sol);CHKERRQ(ierr);
2814   ierr = SNESSetSolution(snes, sol);CHKERRQ(ierr);
2815   ierr = DMSNESCheckFromOptions_Internal(snes, dm, sol, exactFuncs ? exactFuncs : exact, ctxs);CHKERRQ(ierr);
2816   ierr = VecDestroy(&sol);CHKERRQ(ierr);
2817   ierr = PetscFree(exact);CHKERRQ(ierr);
2818   PetscFunctionReturn(0);
2819 }
2820