xref: /petsc/src/snes/utils/dmplexsnes.c (revision 0f51fdf84cc2af9c6ef13eed784e698b930e50d2)
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 <petsc-private/petscimpl.h>
5 
6 /************************** Interpolation *******************************/
7 
8 #undef __FUNCT__
9 #define __FUNCT__ "DMInterpolationCreate"
10 PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx)
11 {
12   PetscErrorCode ierr;
13 
14   PetscFunctionBegin;
15   PetscValidPointer(ctx, 2);
16   ierr = PetscMalloc(sizeof(struct _DMInterpolationInfo), ctx);CHKERRQ(ierr);
17 
18   (*ctx)->comm   = comm;
19   (*ctx)->dim    = -1;
20   (*ctx)->nInput = 0;
21   (*ctx)->points = NULL;
22   (*ctx)->cells  = NULL;
23   (*ctx)->n      = -1;
24   (*ctx)->coords = NULL;
25   PetscFunctionReturn(0);
26 }
27 
28 #undef __FUNCT__
29 #define __FUNCT__ "DMInterpolationSetDim"
30 PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim)
31 {
32   PetscFunctionBegin;
33   if ((dim < 1) || (dim > 3)) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %d", dim);
34   ctx->dim = dim;
35   PetscFunctionReturn(0);
36 }
37 
38 #undef __FUNCT__
39 #define __FUNCT__ "DMInterpolationGetDim"
40 PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim)
41 {
42   PetscFunctionBegin;
43   PetscValidIntPointer(dim, 2);
44   *dim = ctx->dim;
45   PetscFunctionReturn(0);
46 }
47 
48 #undef __FUNCT__
49 #define __FUNCT__ "DMInterpolationSetDof"
50 PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof)
51 {
52   PetscFunctionBegin;
53   if (dof < 1) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %d", dof);
54   ctx->dof = dof;
55   PetscFunctionReturn(0);
56 }
57 
58 #undef __FUNCT__
59 #define __FUNCT__ "DMInterpolationGetDof"
60 PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof)
61 {
62   PetscFunctionBegin;
63   PetscValidIntPointer(dof, 2);
64   *dof = ctx->dof;
65   PetscFunctionReturn(0);
66 }
67 
68 #undef __FUNCT__
69 #define __FUNCT__ "DMInterpolationAddPoints"
70 PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[])
71 {
72   PetscErrorCode ierr;
73 
74   PetscFunctionBegin;
75   if (ctx->dim < 0) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
76   if (ctx->points)  SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "Cannot add points multiple times yet");
77   ctx->nInput = n;
78 
79   ierr = PetscMalloc1(n*ctx->dim, &ctx->points);CHKERRQ(ierr);
80   ierr = PetscMemcpy(ctx->points, points, n*ctx->dim * sizeof(PetscReal));CHKERRQ(ierr);
81   PetscFunctionReturn(0);
82 }
83 
84 #undef __FUNCT__
85 #define __FUNCT__ "DMInterpolationSetUp"
86 PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints)
87 {
88   MPI_Comm       comm = ctx->comm;
89   PetscScalar    *a;
90   PetscInt       p, q, i;
91   PetscMPIInt    rank, size;
92   PetscErrorCode ierr;
93   Vec            pointVec;
94   IS             cellIS;
95   PetscLayout    layout;
96   PetscReal      *globalPoints;
97   PetscScalar    *globalPointsScalar;
98   const PetscInt *ranges;
99   PetscMPIInt    *counts, *displs;
100   const PetscInt *foundCells;
101   PetscMPIInt    *foundProcs, *globalProcs;
102   PetscInt       n, N;
103 
104   PetscFunctionBegin;
105   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
106   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
107   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
108   if (ctx->dim < 0) SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
109   /* Locate points */
110   n = ctx->nInput;
111   if (!redundantPoints) {
112     ierr = PetscLayoutCreate(comm, &layout);CHKERRQ(ierr);
113     ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
114     ierr = PetscLayoutSetLocalSize(layout, n);CHKERRQ(ierr);
115     ierr = PetscLayoutSetUp(layout);CHKERRQ(ierr);
116     ierr = PetscLayoutGetSize(layout, &N);CHKERRQ(ierr);
117     /* Communicate all points to all processes */
118     ierr = PetscMalloc3(N*ctx->dim,&globalPoints,size,&counts,size,&displs);CHKERRQ(ierr);
119     ierr = PetscLayoutGetRanges(layout, &ranges);CHKERRQ(ierr);
120     for (p = 0; p < size; ++p) {
121       counts[p] = (ranges[p+1] - ranges[p])*ctx->dim;
122       displs[p] = ranges[p]*ctx->dim;
123     }
124     ierr = MPI_Allgatherv(ctx->points, n*ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm);CHKERRQ(ierr);
125   } else {
126     N = n;
127     globalPoints = ctx->points;
128     counts = displs = NULL;
129     layout = NULL;
130   }
131 #if 0
132   ierr = PetscMalloc3(N,&foundCells,N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
133   /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */
134 #else
135 #if defined(PETSC_USE_COMPLEX)
136   ierr = PetscMalloc1(N,&globalPointsScalar);CHKERRQ(ierr);
137   for (i=0; i<N; i++) globalPointsScalar[i] = globalPoints[i];
138 #else
139   globalPointsScalar = globalPoints;
140 #endif
141   ierr = VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N*ctx->dim, globalPointsScalar, &pointVec);CHKERRQ(ierr);
142   ierr = PetscMalloc2(N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
143   ierr = DMLocatePoints(dm, pointVec, &cellIS);CHKERRQ(ierr);
144   ierr = ISGetIndices(cellIS, &foundCells);CHKERRQ(ierr);
145 #endif
146   for (p = 0; p < N; ++p) {
147     if (foundCells[p] >= 0) foundProcs[p] = rank;
148     else foundProcs[p] = size;
149   }
150   /* Let the lowest rank process own each point */
151   ierr   = MPI_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm);CHKERRQ(ierr);
152   ctx->n = 0;
153   for (p = 0; p < N; ++p) {
154     if (globalProcs[p] == size) SETERRQ4(comm, PETSC_ERR_PLIB, "Point %d: %g %g %g not located in mesh", p, globalPoints[p*ctx->dim+0], ctx->dim > 1 ? globalPoints[p*ctx->dim+1] : 0.0, ctx->dim > 2 ? globalPoints[p*ctx->dim+2] : 0.0);
155     else if (globalProcs[p] == rank) ctx->n++;
156   }
157   /* Create coordinates vector and array of owned cells */
158   ierr = PetscMalloc1(ctx->n, &ctx->cells);CHKERRQ(ierr);
159   ierr = VecCreate(comm, &ctx->coords);CHKERRQ(ierr);
160   ierr = VecSetSizes(ctx->coords, ctx->n*ctx->dim, PETSC_DECIDE);CHKERRQ(ierr);
161   ierr = VecSetBlockSize(ctx->coords, ctx->dim);CHKERRQ(ierr);
162   ierr = VecSetType(ctx->coords,VECSTANDARD);CHKERRQ(ierr);
163   ierr = VecGetArray(ctx->coords, &a);CHKERRQ(ierr);
164   for (p = 0, q = 0, i = 0; p < N; ++p) {
165     if (globalProcs[p] == rank) {
166       PetscInt d;
167 
168       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p*ctx->dim+d];
169       ctx->cells[q++] = foundCells[p];
170     }
171   }
172   ierr = VecRestoreArray(ctx->coords, &a);CHKERRQ(ierr);
173 #if 0
174   ierr = PetscFree3(foundCells,foundProcs,globalProcs);CHKERRQ(ierr);
175 #else
176   ierr = PetscFree2(foundProcs,globalProcs);CHKERRQ(ierr);
177   ierr = ISRestoreIndices(cellIS, &foundCells);CHKERRQ(ierr);
178   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
179   ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
180 #endif
181   if ((void*)globalPointsScalar != (void*)globalPoints) {ierr = PetscFree(globalPointsScalar);CHKERRQ(ierr);}
182   if (!redundantPoints) {ierr = PetscFree3(globalPoints,counts,displs);CHKERRQ(ierr);}
183   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
184   PetscFunctionReturn(0);
185 }
186 
187 #undef __FUNCT__
188 #define __FUNCT__ "DMInterpolationGetCoordinates"
189 PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates)
190 {
191   PetscFunctionBegin;
192   PetscValidPointer(coordinates, 2);
193   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
194   *coordinates = ctx->coords;
195   PetscFunctionReturn(0);
196 }
197 
198 #undef __FUNCT__
199 #define __FUNCT__ "DMInterpolationGetVector"
200 PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v)
201 {
202   PetscErrorCode ierr;
203 
204   PetscFunctionBegin;
205   PetscValidPointer(v, 2);
206   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
207   ierr = VecCreate(ctx->comm, v);CHKERRQ(ierr);
208   ierr = VecSetSizes(*v, ctx->n*ctx->dof, PETSC_DECIDE);CHKERRQ(ierr);
209   ierr = VecSetBlockSize(*v, ctx->dof);CHKERRQ(ierr);
210   ierr = VecSetType(*v,VECSTANDARD);CHKERRQ(ierr);
211   PetscFunctionReturn(0);
212 }
213 
214 #undef __FUNCT__
215 #define __FUNCT__ "DMInterpolationRestoreVector"
216 PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v)
217 {
218   PetscErrorCode ierr;
219 
220   PetscFunctionBegin;
221   PetscValidPointer(v, 2);
222   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
223   ierr = VecDestroy(v);CHKERRQ(ierr);
224   PetscFunctionReturn(0);
225 }
226 
227 #undef __FUNCT__
228 #define __FUNCT__ "DMInterpolate_Triangle_Private"
229 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Triangle_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
230 {
231   PetscReal      *v0, *J, *invJ, detJ;
232   PetscScalar    *a, *coords;
233   PetscInt       p;
234   PetscErrorCode ierr;
235 
236   PetscFunctionBegin;
237   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
238   ierr = VecGetArray(ctx->coords, &coords);CHKERRQ(ierr);
239   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
240   for (p = 0; p < ctx->n; ++p) {
241     PetscInt     c = ctx->cells[p];
242     PetscScalar *x = NULL;
243     PetscReal    xi[4];
244     PetscInt     d, f, comp;
245 
246     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
247     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
248     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
249     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
250 
251     for (d = 0; d < ctx->dim; ++d) {
252       xi[d] = 0.0;
253       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
254       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];
255     }
256     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
257   }
258   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
259   ierr = VecRestoreArray(ctx->coords, &coords);CHKERRQ(ierr);
260   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
261   PetscFunctionReturn(0);
262 }
263 
264 #undef __FUNCT__
265 #define __FUNCT__ "DMInterpolate_Tetrahedron_Private"
266 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Tetrahedron_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
267 {
268   PetscReal      *v0, *J, *invJ, detJ;
269   PetscScalar    *a, *coords;
270   PetscInt       p;
271   PetscErrorCode ierr;
272 
273   PetscFunctionBegin;
274   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
275   ierr = VecGetArray(ctx->coords, &coords);CHKERRQ(ierr);
276   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
277   for (p = 0; p < ctx->n; ++p) {
278     PetscInt       c = ctx->cells[p];
279     const PetscInt order[3] = {2, 1, 3};
280     PetscScalar   *x = NULL;
281     PetscReal      xi[4];
282     PetscInt       d, f, comp;
283 
284     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
285     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
286     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
287     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
288 
289     for (d = 0; d < ctx->dim; ++d) {
290       xi[d] = 0.0;
291       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
292       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];
293     }
294     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
295   }
296   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
297   ierr = VecRestoreArray(ctx->coords, &coords);CHKERRQ(ierr);
298   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
299   PetscFunctionReturn(0);
300 }
301 
302 #undef __FUNCT__
303 #define __FUNCT__ "QuadMap_Private"
304 PETSC_STATIC_INLINE PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
305 {
306   const PetscScalar *vertices = (const PetscScalar*) ctx;
307   const PetscScalar x0        = vertices[0];
308   const PetscScalar y0        = vertices[1];
309   const PetscScalar x1        = vertices[2];
310   const PetscScalar y1        = vertices[3];
311   const PetscScalar x2        = vertices[4];
312   const PetscScalar y2        = vertices[5];
313   const PetscScalar x3        = vertices[6];
314   const PetscScalar y3        = vertices[7];
315   const PetscScalar f_1       = x1 - x0;
316   const PetscScalar g_1       = y1 - y0;
317   const PetscScalar f_3       = x3 - x0;
318   const PetscScalar g_3       = y3 - y0;
319   const PetscScalar f_01      = x2 - x1 - x3 + x0;
320   const PetscScalar g_01      = y2 - y1 - y3 + y0;
321   PetscScalar       *ref, *real;
322   PetscErrorCode    ierr;
323 
324   PetscFunctionBegin;
325   ierr = VecGetArray(Xref,  &ref);CHKERRQ(ierr);
326   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
327   {
328     const PetscScalar p0 = ref[0];
329     const PetscScalar p1 = ref[1];
330 
331     real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1;
332     real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1;
333   }
334   ierr = PetscLogFlops(28);CHKERRQ(ierr);
335   ierr = VecRestoreArray(Xref,  &ref);CHKERRQ(ierr);
336   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
337   PetscFunctionReturn(0);
338 }
339 
340 #include <petsc-private/dmimpl.h>
341 #undef __FUNCT__
342 #define __FUNCT__ "QuadJacobian_Private"
343 PETSC_STATIC_INLINE PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
344 {
345   const PetscScalar *vertices = (const PetscScalar*) ctx;
346   const PetscScalar x0        = vertices[0];
347   const PetscScalar y0        = vertices[1];
348   const PetscScalar x1        = vertices[2];
349   const PetscScalar y1        = vertices[3];
350   const PetscScalar x2        = vertices[4];
351   const PetscScalar y2        = vertices[5];
352   const PetscScalar x3        = vertices[6];
353   const PetscScalar y3        = vertices[7];
354   const PetscScalar f_01      = x2 - x1 - x3 + x0;
355   const PetscScalar g_01      = y2 - y1 - y3 + y0;
356   PetscScalar       *ref;
357   PetscErrorCode    ierr;
358 
359   PetscFunctionBegin;
360   ierr = VecGetArray(Xref,  &ref);CHKERRQ(ierr);
361   {
362     const PetscScalar x       = ref[0];
363     const PetscScalar y       = ref[1];
364     const PetscInt    rows[2] = {0, 1};
365     PetscScalar       values[4];
366 
367     values[0] = (x1 - x0 + f_01*y) * 0.5; values[1] = (x3 - x0 + f_01*x) * 0.5;
368     values[2] = (y1 - y0 + g_01*y) * 0.5; values[3] = (y3 - y0 + g_01*x) * 0.5;
369     ierr      = MatSetValues(J, 2, rows, 2, rows, values, INSERT_VALUES);CHKERRQ(ierr);
370   }
371   ierr = PetscLogFlops(30);CHKERRQ(ierr);
372   ierr = VecRestoreArray(Xref,  &ref);CHKERRQ(ierr);
373   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
374   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
375   PetscFunctionReturn(0);
376 }
377 
378 #undef __FUNCT__
379 #define __FUNCT__ "DMInterpolate_Quad_Private"
380 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
381 {
382   DM             dmCoord;
383   SNES           snes;
384   KSP            ksp;
385   PC             pc;
386   Vec            coordsLocal, r, ref, real;
387   Mat            J;
388   PetscScalar    *a, *coords;
389   PetscInt       p;
390   PetscErrorCode ierr;
391 
392   PetscFunctionBegin;
393   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
394   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
395   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
396   ierr = SNESSetOptionsPrefix(snes, "quad_interp_");CHKERRQ(ierr);
397   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
398   ierr = VecSetSizes(r, 2, 2);CHKERRQ(ierr);
399   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
400   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
401   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
402   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
403   ierr = MatSetSizes(J, 2, 2, 2, 2);CHKERRQ(ierr);
404   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
405   ierr = MatSetUp(J);CHKERRQ(ierr);
406   ierr = SNESSetFunction(snes, r, QuadMap_Private, NULL);CHKERRQ(ierr);
407   ierr = SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);CHKERRQ(ierr);
408   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
409   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
410   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
411   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
412 
413   ierr = VecGetArray(ctx->coords, &coords);CHKERRQ(ierr);
414   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
415   for (p = 0; p < ctx->n; ++p) {
416     PetscScalar *x = NULL, *vertices = NULL;
417     PetscScalar *xi;
418     PetscReal    xir[2];
419     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
420 
421     /* Can make this do all points at once */
422     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
423     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 4*2);
424     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
425     if (4*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 4*ctx->dof);
426     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
427     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
428     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
429     xi[0]  = coords[p*ctx->dim+0];
430     xi[1]  = coords[p*ctx->dim+1];
431     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
432     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
433     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
434     xir[0] = PetscRealPart(xi[0]);
435     xir[1] = PetscRealPart(xi[1]);
436     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp]*(1 - xir[0])*(1 - xir[1]) + x[1*ctx->dof+comp]*xir[0]*(1 - xir[1]) + x[2*ctx->dof+comp]*xir[0]*xir[1] + x[3*ctx->dof+comp]*(1 - xir[0])*xir[1];
437 
438     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
439     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
440     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
441   }
442   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
443   ierr = VecRestoreArray(ctx->coords, &coords);CHKERRQ(ierr);
444 
445   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
446   ierr = VecDestroy(&r);CHKERRQ(ierr);
447   ierr = VecDestroy(&ref);CHKERRQ(ierr);
448   ierr = VecDestroy(&real);CHKERRQ(ierr);
449   ierr = MatDestroy(&J);CHKERRQ(ierr);
450   PetscFunctionReturn(0);
451 }
452 
453 #undef __FUNCT__
454 #define __FUNCT__ "HexMap_Private"
455 PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
456 {
457   const PetscScalar *vertices = (const PetscScalar*) ctx;
458   const PetscScalar x0        = vertices[0];
459   const PetscScalar y0        = vertices[1];
460   const PetscScalar z0        = vertices[2];
461   const PetscScalar x1        = vertices[9];
462   const PetscScalar y1        = vertices[10];
463   const PetscScalar z1        = vertices[11];
464   const PetscScalar x2        = vertices[6];
465   const PetscScalar y2        = vertices[7];
466   const PetscScalar z2        = vertices[8];
467   const PetscScalar x3        = vertices[3];
468   const PetscScalar y3        = vertices[4];
469   const PetscScalar z3        = vertices[5];
470   const PetscScalar x4        = vertices[12];
471   const PetscScalar y4        = vertices[13];
472   const PetscScalar z4        = vertices[14];
473   const PetscScalar x5        = vertices[15];
474   const PetscScalar y5        = vertices[16];
475   const PetscScalar z5        = vertices[17];
476   const PetscScalar x6        = vertices[18];
477   const PetscScalar y6        = vertices[19];
478   const PetscScalar z6        = vertices[20];
479   const PetscScalar x7        = vertices[21];
480   const PetscScalar y7        = vertices[22];
481   const PetscScalar z7        = vertices[23];
482   const PetscScalar f_1       = x1 - x0;
483   const PetscScalar g_1       = y1 - y0;
484   const PetscScalar h_1       = z1 - z0;
485   const PetscScalar f_3       = x3 - x0;
486   const PetscScalar g_3       = y3 - y0;
487   const PetscScalar h_3       = z3 - z0;
488   const PetscScalar f_4       = x4 - x0;
489   const PetscScalar g_4       = y4 - y0;
490   const PetscScalar h_4       = z4 - z0;
491   const PetscScalar f_01      = x2 - x1 - x3 + x0;
492   const PetscScalar g_01      = y2 - y1 - y3 + y0;
493   const PetscScalar h_01      = z2 - z1 - z3 + z0;
494   const PetscScalar f_12      = x7 - x3 - x4 + x0;
495   const PetscScalar g_12      = y7 - y3 - y4 + y0;
496   const PetscScalar h_12      = z7 - z3 - z4 + z0;
497   const PetscScalar f_02      = x5 - x1 - x4 + x0;
498   const PetscScalar g_02      = y5 - y1 - y4 + y0;
499   const PetscScalar h_02      = z5 - z1 - z4 + z0;
500   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
501   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
502   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
503   PetscScalar       *ref, *real;
504   PetscErrorCode    ierr;
505 
506   PetscFunctionBegin;
507   ierr = VecGetArray(Xref,  &ref);CHKERRQ(ierr);
508   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
509   {
510     const PetscScalar p0 = ref[0];
511     const PetscScalar p1 = ref[1];
512     const PetscScalar p2 = ref[2];
513 
514     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;
515     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;
516     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;
517   }
518   ierr = PetscLogFlops(114);CHKERRQ(ierr);
519   ierr = VecRestoreArray(Xref,  &ref);CHKERRQ(ierr);
520   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
521   PetscFunctionReturn(0);
522 }
523 
524 #undef __FUNCT__
525 #define __FUNCT__ "HexJacobian_Private"
526 PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
527 {
528   const PetscScalar *vertices = (const PetscScalar*) ctx;
529   const PetscScalar x0        = vertices[0];
530   const PetscScalar y0        = vertices[1];
531   const PetscScalar z0        = vertices[2];
532   const PetscScalar x1        = vertices[9];
533   const PetscScalar y1        = vertices[10];
534   const PetscScalar z1        = vertices[11];
535   const PetscScalar x2        = vertices[6];
536   const PetscScalar y2        = vertices[7];
537   const PetscScalar z2        = vertices[8];
538   const PetscScalar x3        = vertices[3];
539   const PetscScalar y3        = vertices[4];
540   const PetscScalar z3        = vertices[5];
541   const PetscScalar x4        = vertices[12];
542   const PetscScalar y4        = vertices[13];
543   const PetscScalar z4        = vertices[14];
544   const PetscScalar x5        = vertices[15];
545   const PetscScalar y5        = vertices[16];
546   const PetscScalar z5        = vertices[17];
547   const PetscScalar x6        = vertices[18];
548   const PetscScalar y6        = vertices[19];
549   const PetscScalar z6        = vertices[20];
550   const PetscScalar x7        = vertices[21];
551   const PetscScalar y7        = vertices[22];
552   const PetscScalar z7        = vertices[23];
553   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
554   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
555   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
556   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
557   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
558   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
559   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
560   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
561   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
562   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
563   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
564   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
565   PetscScalar       *ref;
566   PetscErrorCode    ierr;
567 
568   PetscFunctionBegin;
569   ierr = VecGetArray(Xref,  &ref);CHKERRQ(ierr);
570   {
571     const PetscScalar x       = ref[0];
572     const PetscScalar y       = ref[1];
573     const PetscScalar z       = ref[2];
574     const PetscInt    rows[3] = {0, 1, 2};
575     PetscScalar       values[9];
576 
577     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
578     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
579     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
580     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
581     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
582     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
583     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
584     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
585     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;
586 
587     ierr = MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);CHKERRQ(ierr);
588   }
589   ierr = PetscLogFlops(152);CHKERRQ(ierr);
590   ierr = VecRestoreArray(Xref,  &ref);CHKERRQ(ierr);
591   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
592   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
593   PetscFunctionReturn(0);
594 }
595 
596 #undef __FUNCT__
597 #define __FUNCT__ "DMInterpolate_Hex_Private"
598 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
599 {
600   DM             dmCoord;
601   SNES           snes;
602   KSP            ksp;
603   PC             pc;
604   Vec            coordsLocal, r, ref, real;
605   Mat            J;
606   PetscScalar    *a, *coords;
607   PetscInt       p;
608   PetscErrorCode ierr;
609 
610   PetscFunctionBegin;
611   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
612   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
613   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
614   ierr = SNESSetOptionsPrefix(snes, "hex_interp_");CHKERRQ(ierr);
615   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
616   ierr = VecSetSizes(r, 3, 3);CHKERRQ(ierr);
617   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
618   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
619   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
620   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
621   ierr = MatSetSizes(J, 3, 3, 3, 3);CHKERRQ(ierr);
622   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
623   ierr = MatSetUp(J);CHKERRQ(ierr);
624   ierr = SNESSetFunction(snes, r, HexMap_Private, NULL);CHKERRQ(ierr);
625   ierr = SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);CHKERRQ(ierr);
626   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
627   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
628   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
629   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
630 
631   ierr = VecGetArray(ctx->coords, &coords);CHKERRQ(ierr);
632   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
633   for (p = 0; p < ctx->n; ++p) {
634     PetscScalar *x = NULL, *vertices = NULL;
635     PetscScalar *xi;
636     PetscReal    xir[3];
637     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
638 
639     /* Can make this do all points at once */
640     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
641     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 8*3);
642     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
643     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 8*ctx->dof);
644     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
645     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
646     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
647     xi[0]  = coords[p*ctx->dim+0];
648     xi[1]  = coords[p*ctx->dim+1];
649     xi[2]  = coords[p*ctx->dim+2];
650     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
651     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
652     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
653     xir[0] = PetscRealPart(xi[0]);
654     xir[1] = PetscRealPart(xi[1]);
655     xir[2] = PetscRealPart(xi[2]);
656     for (comp = 0; comp < ctx->dof; ++comp) {
657       a[p*ctx->dof+comp] =
658         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
659         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
660         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
661         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
662         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
663         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
664         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
665         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
666     }
667     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
668     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
669     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
670   }
671   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
672   ierr = VecRestoreArray(ctx->coords, &coords);CHKERRQ(ierr);
673 
674   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
675   ierr = VecDestroy(&r);CHKERRQ(ierr);
676   ierr = VecDestroy(&ref);CHKERRQ(ierr);
677   ierr = VecDestroy(&real);CHKERRQ(ierr);
678   ierr = MatDestroy(&J);CHKERRQ(ierr);
679   PetscFunctionReturn(0);
680 }
681 
682 #undef __FUNCT__
683 #define __FUNCT__ "DMInterpolationEvaluate"
684 /*
685   Input Parameters:
686 + ctx - The DMInterpolationInfo context
687 . dm  - The DM
688 - x   - The local vector containing the field to be interpolated
689 
690   Output Parameters:
691 . v   - The vector containing the interpolated values
692 */
693 PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
694 {
695   PetscInt       dim, coneSize, n;
696   PetscErrorCode ierr;
697 
698   PetscFunctionBegin;
699   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
700   PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
701   PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
702   ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
703   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);
704   if (n) {
705     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
706     ierr = DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);CHKERRQ(ierr);
707     if (dim == 2) {
708       if (coneSize == 3) {
709         ierr = DMInterpolate_Triangle_Private(ctx, dm, x, v);CHKERRQ(ierr);
710       } else if (coneSize == 4) {
711         ierr = DMInterpolate_Quad_Private(ctx, dm, x, v);CHKERRQ(ierr);
712       } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
713     } else if (dim == 3) {
714       if (coneSize == 4) {
715         ierr = DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);CHKERRQ(ierr);
716       } else {
717         ierr = DMInterpolate_Hex_Private(ctx, dm, x, v);CHKERRQ(ierr);
718       }
719     } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
720   }
721   PetscFunctionReturn(0);
722 }
723 
724 #undef __FUNCT__
725 #define __FUNCT__ "DMInterpolationDestroy"
726 PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
727 {
728   PetscErrorCode ierr;
729 
730   PetscFunctionBegin;
731   PetscValidPointer(ctx, 2);
732   ierr = VecDestroy(&(*ctx)->coords);CHKERRQ(ierr);
733   ierr = PetscFree((*ctx)->points);CHKERRQ(ierr);
734   ierr = PetscFree((*ctx)->cells);CHKERRQ(ierr);
735   ierr = PetscFree(*ctx);CHKERRQ(ierr);
736   *ctx = NULL;
737   PetscFunctionReturn(0);
738 }
739 
740 #undef __FUNCT__
741 #define __FUNCT__ "SNESMonitorFields"
742 /*@C
743   SNESMonitorFields - Monitors the residual for each field separately
744 
745   Collective on SNES
746 
747   Input Parameters:
748 + snes   - the SNES context
749 . its    - iteration number
750 . fgnorm - 2-norm of residual
751 - dummy  - unused context
752 
753   Notes:
754   This routine prints the residual norm at each iteration.
755 
756   Level: intermediate
757 
758 .keywords: SNES, nonlinear, default, monitor, norm
759 .seealso: SNESMonitorSet(), SNESMonitorDefault()
760 @*/
761 PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, void *dummy)
762 {
763   PetscViewer        viewer = dummy ? (PetscViewer) dummy : PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject) snes));
764   Vec                res;
765   DM                 dm;
766   PetscSection       s;
767   const PetscScalar *r;
768   PetscReal         *lnorms, *norms;
769   PetscInt           numFields, f, pStart, pEnd, p;
770   PetscErrorCode     ierr;
771 
772   PetscFunctionBegin;
773   ierr = SNESGetFunction(snes, &res, 0, 0);CHKERRQ(ierr);
774   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
775   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
776   ierr = PetscSectionGetNumFields(s, &numFields);CHKERRQ(ierr);
777   ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
778   ierr = PetscCalloc2(numFields, &lnorms, numFields, &norms);CHKERRQ(ierr);
779   ierr = VecGetArrayRead(res, &r);CHKERRQ(ierr);
780   for (p = pStart; p < pEnd; ++p) {
781     for (f = 0; f < numFields; ++f) {
782       PetscInt fdof, foff, d;
783 
784       ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
785       ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
786       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
787     }
788   }
789   ierr = VecRestoreArrayRead(res, &r);CHKERRQ(ierr);
790   ierr = MPI_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
791   ierr = PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
792   ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
793   for (f = 0; f < numFields; ++f) {
794     if (f > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
795     ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));CHKERRQ(ierr);
796   }
797   ierr = PetscViewerASCIIPrintf(viewer, "]\n");CHKERRQ(ierr);
798   ierr = PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
799   ierr = PetscFree2(lnorms, norms);CHKERRQ(ierr);
800   PetscFunctionReturn(0);
801 }
802 
803 /********************* Residual Computation **************************/
804 
805 #undef __FUNCT__
806 #define __FUNCT__ "DMPlexSNESGetGeometryFEM"
807 /*@
808   DMPlexSNESGetGeometryFEM - Return precomputed geometric data
809 
810   Input Parameter:
811 . dm - The DM
812 
813   Output Parameters:
814 . cellgeom - The values precomputed from cell geometry
815 
816   Level: developer
817 
818 .seealso: DMPlexSNESSetFunctionLocal()
819 @*/
820 PetscErrorCode DMPlexSNESGetGeometryFEM(DM dm, Vec *cellgeom)
821 {
822   DMSNES         dmsnes;
823   PetscObject    obj;
824   PetscErrorCode ierr;
825 
826   PetscFunctionBegin;
827   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
828   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
829   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", &obj);CHKERRQ(ierr);
830   if (!obj) {
831     Vec cellgeom;
832 
833     ierr = DMPlexComputeGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
834     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject) cellgeom);CHKERRQ(ierr);
835     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
836   }
837   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject *) cellgeom);CHKERRQ(ierr);}
838   PetscFunctionReturn(0);
839 }
840 
841 #undef __FUNCT__
842 #define __FUNCT__ "DMPlexSNESGetGeometryFVM"
843 /*@
844   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
845 
846   Input Parameter:
847 . dm - The DM
848 
849   Output Parameters:
850 + facegeom - The values precomputed from face geometry
851 . cellgeom - The values precomputed from cell geometry
852 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
853 
854   Level: developer
855 
856 .seealso: DMPlexTSSetRHSFunctionLocal()
857 @*/
858 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
859 {
860   DMSNES         dmsnes;
861   PetscObject    obj;
862   PetscErrorCode ierr;
863 
864   PetscFunctionBegin;
865   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
866   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
867   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", &obj);CHKERRQ(ierr);
868   if (!obj) {
869     Vec cellgeom, facegeom;
870 
871     ierr = DMPlexComputeGeometryFVM(dm, &cellgeom, &facegeom);CHKERRQ(ierr);
872     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", (PetscObject) facegeom);CHKERRQ(ierr);
873     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fvm", (PetscObject) cellgeom);CHKERRQ(ierr);
874     ierr = VecDestroy(&facegeom);CHKERRQ(ierr);
875     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
876   }
877   if (facegeom) {PetscValidPointer(facegeom, 2); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", (PetscObject *) facegeom);CHKERRQ(ierr);}
878   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fvm", (PetscObject *) cellgeom);CHKERRQ(ierr);}
879   if (minRadius) {ierr = DMPlexGetMinRadius(dm, minRadius);CHKERRQ(ierr);}
880   PetscFunctionReturn(0);
881 }
882 
883 #undef __FUNCT__
884 #define __FUNCT__ "DMPlexSNESGetGradientDM"
885 /*@C
886   DMPlexSNESGetGradientDM - Return gradient data layout
887 
888   Input Parameters:
889 + dm - The DM
890 - fv - The PetscFV
891 
892   Output Parameter:
893 . dmGrad - The layout for gradient values
894 
895   Level: developer
896 
897 .seealso: DMPlexSNESGetGeometryFVM()
898 @*/
899 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
900 {
901   DMSNES         dmsnes;
902   PetscObject    obj;
903   PetscBool      computeGradients;
904   PetscErrorCode ierr;
905 
906   PetscFunctionBegin;
907   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
908   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
909   PetscValidPointer(dmGrad,3);
910   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
911   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
912   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
913   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", &obj);CHKERRQ(ierr);
914   if (!obj) {
915     DM  dmGrad;
916     Vec faceGeometry, cellGeometry;
917 
918     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometry, &cellGeometry, NULL);CHKERRQ(ierr);
919     ierr = DMPlexComputeGradientFVM(dm, fv, faceGeometry, cellGeometry, &dmGrad);CHKERRQ(ierr);
920     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", (PetscObject) dmGrad);CHKERRQ(ierr);
921     ierr = DMDestroy(&dmGrad);CHKERRQ(ierr);
922   }
923   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", (PetscObject *) dmGrad);CHKERRQ(ierr);
924   PetscFunctionReturn(0);
925 }
926 
927 #undef __FUNCT__
928 #define __FUNCT__ "DMPlexGetCellFields"
929 /*@C
930   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells
931 
932   Input Parameters:
933 + dm     - The DM
934 . cStart - The first cell to include
935 . cEnd   - The first cell to exclude
936 . locX   - A local vector with the solution fields
937 . locX_t - A local vector with solution field time derivatives, or NULL
938 - locA   - A local vector with auxiliary fields, or NULL
939 
940   Output Parameters:
941 + u   - The field coefficients
942 . u_t - The fields derivative coefficients
943 - a   - The auxiliary field coefficients
944 
945   Level: developer
946 
947 .seealso: DMPlexGetFaceFields()
948 @*/
949 PetscErrorCode DMPlexGetCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
950 {
951   DM             dmAux;
952   PetscSection   section, sectionAux;
953   PetscDS        prob;
954   PetscInt       numCells = cEnd - cStart, totDim, totDimAux, c;
955   PetscErrorCode ierr;
956 
957   PetscFunctionBegin;
958   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
959   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
960   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
961   if (locA)   {PetscValidHeaderSpecific(locA, VEC_CLASSID, 6);}
962   PetscValidPointer(u, 7);
963   PetscValidPointer(u_t, 8);
964   PetscValidPointer(a, 9);
965   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
966   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
967   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
968   if (locA) {
969     PetscDS probAux;
970 
971     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
972     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
973     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
974     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
975   }
976   ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u);CHKERRQ(ierr);
977   ierr = DMGetWorkArray(dm, locX_t ? numCells*totDim : 0, PETSC_SCALAR, u_t);CHKERRQ(ierr);
978   ierr = DMGetWorkArray(dm, locA ? numCells*totDimAux : 0, PETSC_SCALAR, a);CHKERRQ(ierr);
979   for (c = cStart; c < cEnd; ++c) {
980     PetscScalar *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
981     PetscInt     i;
982 
983     ierr = DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
984     for (i = 0; i < totDim; ++i) ul[c*totDim+i] = x[i];
985     ierr = DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
986     if (locX_t) {
987       ierr = DMPlexVecGetClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
988       for (i = 0; i < totDim; ++i) ul_t[c*totDim+i] = x_t[i];
989       ierr = DMPlexVecRestoreClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
990     }
991     if (locA) {
992       ierr = DMPlexVecGetClosure(dmAux, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
993       for (i = 0; i < totDimAux; ++i) al[c*totDimAux+i] = x[i];
994       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
995     }
996   }
997   PetscFunctionReturn(0);
998 }
999 
1000 #undef __FUNCT__
1001 #define __FUNCT__ "DMPlexRestoreCellFields"
1002 /*@C
1003   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells
1004 
1005   Input Parameters:
1006 + dm     - The DM
1007 . cStart - The first cell to include
1008 . cEnd   - The first cell to exclude
1009 . locX   - A local vector with the solution fields
1010 . locX_t - A local vector with solution field time derivatives, or NULL
1011 - locA   - A local vector with auxiliary fields, or NULL
1012 
1013   Output Parameters:
1014 + u   - The field coefficients
1015 . u_t - The fields derivative coefficients
1016 - a   - The auxiliary field coefficients
1017 
1018   Level: developer
1019 
1020 .seealso: DMPlexGetFaceFields()
1021 @*/
1022 PetscErrorCode DMPlexRestoreCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1023 {
1024   PetscErrorCode ierr;
1025 
1026   PetscFunctionBegin;
1027   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u);CHKERRQ(ierr);
1028   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u_t);CHKERRQ(ierr);
1029   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, a);CHKERRQ(ierr);
1030   PetscFunctionReturn(0);
1031 }
1032 
1033 #undef __FUNCT__
1034 #define __FUNCT__ "DMPlexGetFaceFields"
1035 /*@C
1036   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces
1037 
1038   Input Parameters:
1039 + dm     - The DM
1040 . fStart - The first face to include
1041 . fEnd   - The first face to exclude
1042 . locX   - A local vector with the solution fields
1043 . locX_t - A local vector with solution field time derivatives, or NULL
1044 . faceGeometry - A local vector with face geometry
1045 . cellGeometry - A local vector with cell geometry
1046 - locaGrad - A local vector with field gradients, or NULL
1047 
1048   Output Parameters:
1049 + uL - The field coefficients at the left side of the face
1050 - uR - The field coefficients at the right side of the face
1051 
1052   Level: developer
1053 
1054 .seealso: DMPlexGetCellFields()
1055 @*/
1056 PetscErrorCode DMPlexGetFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscScalar **uL, PetscScalar **uR)
1057 {
1058   DM                 dmFace, dmCell, dmGrad = NULL;
1059   PetscDS            prob;
1060   DMLabel            ghostLabel;
1061   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
1062   PetscInt           dim, totDim, numFaces = fEnd - fStart, iface, face;
1063   PetscErrorCode     ierr;
1064 
1065   PetscFunctionBegin;
1066   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1067   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1068   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1069   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 6);
1070   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 7);
1071   if (locGrad) {PetscValidHeaderSpecific(locGrad, VEC_CLASSID, 8);}
1072   PetscValidPointer(uL, 9);
1073   PetscValidPointer(uR, 10);
1074   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1075   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1076   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1077   ierr = DMPlexGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1078   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1079   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1080   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1081   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1082   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1083   if (locGrad) {
1084     ierr = VecGetDM(locGrad, &dmGrad);CHKERRQ(ierr);
1085     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1086   }
1087   ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, uL);CHKERRQ(ierr);
1088   ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, uR);CHKERRQ(ierr);
1089   for (face = fStart, iface = 0; face < fEnd; ++face) {
1090     const PetscInt        *cells;
1091     const PetscFVFaceGeom *fg;
1092     const PetscFVCellGeom *cgL, *cgR;
1093     const PetscScalar     *xL, *xR, *gL, *gR;
1094     PetscScalar           *uLl = *uL, *uRl = *uR;
1095     PetscInt               ghost, d;
1096 
1097     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1098     if (ghost >= 0) continue;
1099     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1100     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1101     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1102     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1103     ierr = DMPlexPointLocalRead(dm, cells[0], x, &xL);CHKERRQ(ierr);
1104     ierr = DMPlexPointLocalRead(dm, cells[1], x, &xR);CHKERRQ(ierr);
1105     if (dmGrad) {
1106       PetscReal dxL[3], dxR[3];
1107 
1108       ierr = DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);CHKERRQ(ierr);
1109       ierr = DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);CHKERRQ(ierr);
1110       DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
1111       DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
1112       for (d = 0; d < totDim; ++d) {
1113         uLl[iface*totDim+d] = xL[d] + DMPlex_DotD_Internal(dim, &gL[d*dim], dxL);
1114         uRl[iface*totDim+d] = xR[d] + DMPlex_DotD_Internal(dim, &gR[d*dim], dxR);
1115       }
1116     } else {
1117       for (d = 0; d < totDim; ++d) {
1118         uLl[iface*totDim+d] = xL[d];
1119         uRl[iface*totDim+d] = xR[d];
1120       }
1121     }
1122     ++iface;
1123   }
1124   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1125   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1126   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1127   if (locGrad) {
1128     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1129   }
1130   PetscFunctionReturn(0);
1131 }
1132 
1133 #undef __FUNCT__
1134 #define __FUNCT__ "DMPlexRestoreFaceFields"
1135 /*@C
1136   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces
1137 
1138   Input Parameters:
1139 + dm     - The DM
1140 . fStart - The first face to include
1141 . fEnd   - The first face to exclude
1142 . locX   - A local vector with the solution fields
1143 . locX_t - A local vector with solution field time derivatives, or NULL
1144 . faceGeometry - A local vector with face geometry
1145 . cellGeometry - A local vector with cell geometry
1146 - locaGrad - A local vector with field gradients, or NULL
1147 
1148   Output Parameters:
1149 + uL - The field coefficients at the left side of the face
1150 - uR - The field coefficients at the right side of the face
1151 
1152   Level: developer
1153 
1154 .seealso: DMPlexGetFaceFields()
1155 @*/
1156 PetscErrorCode DMPlexRestoreFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscScalar **uL, PetscScalar **uR)
1157 {
1158   PetscErrorCode ierr;
1159 
1160   PetscFunctionBegin;
1161   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uL);CHKERRQ(ierr);
1162   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uR);CHKERRQ(ierr);
1163   PetscFunctionReturn(0);
1164 }
1165 
1166 #undef __FUNCT__
1167 #define __FUNCT__ "DMPlexGetFaceGeometry"
1168 /*@C
1169   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces
1170 
1171   Input Parameters:
1172 + dm     - The DM
1173 . fStart - The first face to include
1174 . fEnd   - The first face to exclude
1175 . faceGeometry - A local vector with face geometry
1176 - cellGeometry - A local vector with cell geometry
1177 
1178   Output Parameters:
1179 + fgeom - The extract the face centroid and normal
1180 - vol   - The cell volume
1181 
1182   Level: developer
1183 
1184 .seealso: DMPlexGetCellFields()
1185 @*/
1186 PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscFVFaceGeom **fgeom, PetscReal **vol)
1187 {
1188   DM                 dmFace, dmCell;
1189   DMLabel            ghostLabel;
1190   const PetscScalar *facegeom, *cellgeom;
1191   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
1192   PetscErrorCode     ierr;
1193 
1194   PetscFunctionBegin;
1195   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1196   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 4);
1197   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 5);
1198   PetscValidPointer(fgeom, 6);
1199   PetscValidPointer(vol, 7);
1200   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1201   ierr = DMPlexGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1202   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1203   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1204   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1205   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1206   ierr = PetscMalloc1(numFaces, fgeom);CHKERRQ(ierr);
1207   ierr = DMGetWorkArray(dm, numFaces*2, PETSC_SCALAR, vol);CHKERRQ(ierr);
1208   for (face = fStart, iface = 0; face < fEnd; ++face) {
1209     const PetscInt        *cells;
1210     const PetscFVFaceGeom *fg;
1211     const PetscFVCellGeom *cgL, *cgR;
1212     PetscFVFaceGeom       *fgeoml = *fgeom;
1213     PetscReal             *voll   = *vol;
1214     PetscInt               ghost, d;
1215 
1216     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1217     if (ghost >= 0) continue;
1218     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1219     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1220     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1221     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1222     for (d = 0; d < dim; ++d) {
1223       fgeoml[iface].centroid[d] = fg->centroid[d];
1224       fgeoml[iface].normal[d]   = fg->normal[d];
1225     }
1226     voll[iface*2+0] = cgL->volume;
1227     voll[iface*2+1] = cgR->volume;
1228     ++iface;
1229   }
1230   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1231   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1232   PetscFunctionReturn(0);
1233 }
1234 
1235 #undef __FUNCT__
1236 #define __FUNCT__ "DMPlexRestoreFaceGeometry"
1237 /*@C
1238   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces
1239 
1240   Input Parameters:
1241 + dm     - The DM
1242 . fStart - The first face to include
1243 . fEnd   - The first face to exclude
1244 . faceGeometry - A local vector with face geometry
1245 - cellGeometry - A local vector with cell geometry
1246 
1247   Output Parameters:
1248 + fgeom - The extract the face centroid and normal
1249 - vol   - The cell volume
1250 
1251   Level: developer
1252 
1253 .seealso: DMPlexGetFaceFields()
1254 @*/
1255 PetscErrorCode DMPlexRestoreFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscFVFaceGeom **fgeom, PetscReal **vol)
1256 {
1257   PetscErrorCode ierr;
1258 
1259   PetscFunctionBegin;
1260   ierr = PetscFree(*fgeom);CHKERRQ(ierr);
1261   ierr = DMRestoreWorkArray(dm, 0, PETSC_REAL, vol);CHKERRQ(ierr);
1262   PetscFunctionReturn(0);
1263 }
1264 
1265 #undef __FUNCT__
1266 #define __FUNCT__ "DMPlexReconstructGradients_Internal"
1267 PetscErrorCode DMPlexReconstructGradients_Internal(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, Vec locX, Vec grad)
1268 {
1269   DM                 dmFace, dmCell, dmGrad;
1270   DMLabel            ghostLabel;
1271   PetscDS            prob;
1272   PetscFV            fvm;
1273   PetscLimiter       lim;
1274   const PetscScalar *facegeom, *cellgeom, *x;
1275   PetscScalar       *gr;
1276   PetscReal         *cellPhi;
1277   PetscInt           dim, face, cell, totDim, cStart, cEnd, cEndInterior;
1278   PetscErrorCode     ierr;
1279 
1280   PetscFunctionBegin;
1281   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1282   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1283   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1284   ierr = DMPlexGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1285   ierr = PetscDSGetDiscretization(prob, 0, (PetscObject *) &fvm);CHKERRQ(ierr);
1286   ierr = PetscFVGetLimiter(fvm, &lim);CHKERRQ(ierr);
1287   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1288   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1289   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1290   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1291   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1292   ierr = VecGetDM(grad, &dmGrad);CHKERRQ(ierr);
1293   ierr = VecZeroEntries(grad);CHKERRQ(ierr);
1294   ierr = VecGetArray(grad, &gr);CHKERRQ(ierr);
1295   /* Reconstruct gradients */
1296   for (face = fStart; face < fEnd; ++face) {
1297     const PetscInt        *cells;
1298     const PetscFVFaceGeom *fg;
1299     const PetscScalar     *cx[2];
1300     PetscScalar           *cgrad[2];
1301     PetscBool              boundary;
1302     PetscInt               ghost, c, pd, d;
1303 
1304     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1305     if (ghost >= 0) continue;
1306     ierr = DMPlexIsBoundaryPoint(dm, face, &boundary);CHKERRQ(ierr);
1307     if (boundary) continue;
1308     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1309     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1310     for (c = 0; c < 2; ++c) {
1311       ierr = DMPlexPointLocalRead(dm, cells[c], x, &cx[c]);CHKERRQ(ierr);
1312       ierr = DMPlexPointGlobalRef(dmGrad, cells[c], gr, &cgrad[c]);CHKERRQ(ierr);
1313     }
1314     for (pd = 0; pd < totDim; ++pd) {
1315       PetscScalar delta = cx[1][pd] - cx[0][pd];
1316 
1317       for (d = 0; d < dim; ++d) {
1318         if (cgrad[0]) cgrad[0][pd*dim+d] += fg->grad[0][d] * delta;
1319         if (cgrad[1]) cgrad[1][pd*dim+d] -= fg->grad[1][d] * delta;
1320       }
1321     }
1322   }
1323   /* Limit interior gradients (using cell-based loop because it generalizes better to vector limiters) */
1324   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1325   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1326   cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
1327   ierr = DMGetWorkArray(dm, totDim, PETSC_REAL, &cellPhi);CHKERRQ(ierr);
1328   for (cell = dmGrad && lim ? cStart : cEnd; cell < cEndInterior; ++cell) {
1329     const PetscInt        *faces;
1330     const PetscScalar     *cx;
1331     const PetscFVCellGeom *cg;
1332     PetscScalar           *cgrad;
1333     PetscInt               coneSize, f, pd, d;
1334 
1335     ierr = DMPlexGetConeSize(dm, cell, &coneSize);CHKERRQ(ierr);
1336     ierr = DMPlexGetCone(dm, cell, &faces);CHKERRQ(ierr);
1337     ierr = DMPlexPointLocalRead(dm, cell, x, &cx);CHKERRQ(ierr);
1338     ierr = DMPlexPointLocalRead(dmCell, cell, cellgeom, &cg);CHKERRQ(ierr);
1339     ierr = DMPlexPointGlobalRef(dmGrad, cell, gr, &cgrad);CHKERRQ(ierr);
1340     if (!cgrad) continue; /* Unowned overlap cell, we do not compute */
1341     /* Limiter will be minimum value over all neighbors */
1342     for (d = 0; d < totDim; ++d) cellPhi[d] = PETSC_MAX_REAL;
1343     for (f = 0; f < coneSize; ++f) {
1344       const PetscScalar     *ncx;
1345       const PetscFVCellGeom *ncg;
1346       const PetscInt        *fcells;
1347       PetscInt               face = faces[f], ncell, ghost;
1348       PetscReal              v[3];
1349       PetscBool              boundary;
1350 
1351       ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1352       ierr = DMPlexIsBoundaryPoint(dm, face, &boundary);CHKERRQ(ierr);
1353       if ((ghost >= 0) || boundary) continue;
1354       ierr  = DMPlexGetSupport(dm, face, &fcells);CHKERRQ(ierr);
1355       ncell = cell == fcells[0] ? fcells[1] : fcells[0];
1356       ierr  = DMPlexPointLocalRead(dm, ncell, x, &ncx);CHKERRQ(ierr);
1357       ierr  = DMPlexPointLocalRead(dmCell, ncell, cellgeom, &ncg);CHKERRQ(ierr);
1358       DMPlex_WaxpyD_Internal(dim, -1, cg->centroid, ncg->centroid, v);
1359       for (d = 0; d < totDim; ++d) {
1360         /* We use the symmetric slope limited form of Berger, Aftosmis, and Murman 2005 */
1361         PetscReal phi, flim = 0.5 * PetscRealPart(ncx[d] - cx[d]) / DMPlex_DotD_Internal(dim, &cgrad[d*dim], v);
1362 
1363         ierr = PetscLimiterLimit(lim, flim, &phi);CHKERRQ(ierr);
1364         cellPhi[d] = PetscMin(cellPhi[d], phi);
1365       }
1366     }
1367     /* Apply limiter to gradient */
1368     for (pd = 0; pd < totDim; ++pd)
1369       /* Scalar limiter applied to each component separately */
1370       for (d = 0; d < dim; ++d) cgrad[pd*dim+d] *= cellPhi[pd];
1371   }
1372   ierr = DMRestoreWorkArray(dm, totDim, PETSC_REAL, &cellPhi);CHKERRQ(ierr);
1373   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1374   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1375   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1376   ierr = VecRestoreArray(grad, &gr);CHKERRQ(ierr);
1377   PetscFunctionReturn(0);
1378 }
1379 
1380 #undef __FUNCT__
1381 #define __FUNCT__ "DMPlexComputeBdResidual_Internal"
1382 PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, Vec locF, void *user)
1383 {
1384   DM_Plex         *mesh = (DM_Plex *) dm->data;
1385   PetscSection     section;
1386   PetscDS          prob;
1387   DMLabel          depth;
1388   PetscFECellGeom *cgeom;
1389   PetscScalar     *u = NULL, *u_t = NULL, *elemVec = NULL;
1390   PetscInt         dim, Nf, f, totDimBd, numBd, bd;
1391   PetscErrorCode   ierr;
1392 
1393   PetscFunctionBegin;
1394   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1395   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1396   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1397   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1398   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
1399   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1400   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1401   for (bd = 0; bd < numBd; ++bd) {
1402     const char     *bdLabel;
1403     DMLabel         label;
1404     IS              pointIS;
1405     const PetscInt *points;
1406     const PetscInt *values;
1407     PetscInt        field, numValues, numPoints, p, dep, numFaces;
1408     PetscBool       isEssential;
1409 
1410     ierr = DMPlexGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1411     if (isEssential) continue;
1412     if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
1413     ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1414     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1415     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1416     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1417     for (p = 0, numFaces = 0; p < numPoints; ++p) {
1418       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1419       if (dep == dim-1) ++numFaces;
1420     }
1421     ierr = PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd,&elemVec);CHKERRQ(ierr);
1422     if (locX_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
1423     for (p = 0, f = 0; p < numPoints; ++p) {
1424       const PetscInt point = points[p];
1425       PetscScalar   *x     = NULL;
1426       PetscInt       i;
1427 
1428       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1429       if (dep != dim-1) continue;
1430       ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
1431       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);
1432       if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
1433       ierr = DMPlexVecGetClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1434       for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
1435       ierr = DMPlexVecRestoreClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1436       if (locX_t) {
1437         ierr = DMPlexVecGetClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1438         for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
1439         ierr = DMPlexVecRestoreClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1440       }
1441       ++f;
1442     }
1443     for (f = 0; f < Nf; ++f) {
1444       PetscFE         fe;
1445       PetscQuadrature q;
1446       PetscInt        numQuadPoints, Nb;
1447       /* Conforming batches */
1448       PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1449       /* Remainder */
1450       PetscInt        Nr, offset;
1451 
1452       ierr = PetscDSGetBdDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1453       ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1454       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1455       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1456       ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1457       blockSize = Nb*numQuadPoints;
1458       batchSize = numBlocks * blockSize;
1459       ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1460       numChunks = numFaces / (numBatches*batchSize);
1461       Ne        = numChunks*numBatches*batchSize;
1462       Nr        = numFaces % (numBatches*batchSize);
1463       offset    = numFaces - Nr;
1464       ierr = PetscFEIntegrateBdResidual(fe, prob, f, Ne, cgeom, u, u_t, NULL, NULL, elemVec);CHKERRQ(ierr);
1465       ierr = PetscFEIntegrateBdResidual(fe, prob, f, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, &elemVec[offset*totDimBd]);CHKERRQ(ierr);
1466     }
1467     for (p = 0, f = 0; p < numPoints; ++p) {
1468       const PetscInt point = points[p];
1469 
1470       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1471       if (dep != dim-1) continue;
1472       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDimBd, &elemVec[f*totDimBd]);CHKERRQ(ierr);}
1473       ierr = DMPlexVecSetClosure(dm, NULL, locF, point, &elemVec[f*totDimBd], ADD_VALUES);CHKERRQ(ierr);
1474       ++f;
1475     }
1476     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1477     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1478     ierr = PetscFree3(u,cgeom,elemVec);CHKERRQ(ierr);
1479     if (locX_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
1480   }
1481   PetscFunctionReturn(0);
1482 }
1483 
1484 #undef __FUNCT__
1485 #define __FUNCT__ "DMPlexComputeResidual_Internal"
1486 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, PetscReal time, Vec locX, Vec locX_t, Vec locF, void *user)
1487 {
1488   DM_Plex          *mesh       = (DM_Plex *) dm->data;
1489   const char       *name       = "Residual";
1490   DM                dmAux      = NULL;
1491   DM                dmGrad     = NULL;
1492   DMLabel           ghostLabel = NULL;
1493   PetscDS           prob       = NULL;
1494   PetscDS           probAux    = NULL;
1495   PetscSection      section    = NULL;
1496   PetscBool         useFEM     = PETSC_FALSE;
1497   PetscBool         useFVM     = PETSC_FALSE;
1498   PetscFV           fvm        = NULL;
1499   PetscFECellGeom  *cgeomFEM   = NULL;
1500   PetscFVCellGeom  *cgeomFVM   = NULL;
1501   PetscFVFaceGeom  *fgeomFVM   = NULL;
1502   Vec               locA, cellGeometryFEM = NULL, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1503   PetscScalar      *u, *u_t, *a, *uL, *uR;
1504   PetscInt          Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, cStart, cEnd, fStart, fEnd;
1505   PetscErrorCode    ierr;
1506 
1507   PetscFunctionBegin;
1508   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1509   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1510   /* TODO The FVM geometry is over-manipulated. Make the preclac functions return exactly what we need */
1511   /* FEM+FVM */
1512   /* 1: Get sizes from dm and dmAux */
1513   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1514   ierr = DMPlexGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1515   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1516   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1517   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1518   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1519   if (locA) {
1520     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1521     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1522     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1523   }
1524   /* 2: Get geometric data */
1525   for (f = 0; f < Nf; ++f) {
1526     PetscObject  obj;
1527     PetscClassId id;
1528 
1529     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1530     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1531     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1532     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1533   }
1534   if (useFEM) {
1535     ierr = DMPlexSNESGetGeometryFEM(dm, &cellGeometryFEM);CHKERRQ(ierr);
1536     ierr = VecGetArrayRead(cellGeometryFEM, (const PetscScalar **) &cgeomFEM);CHKERRQ(ierr);
1537   }
1538   if (useFVM) {
1539     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1540     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1541     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1542     /* Reconstruct and limit cell gradients */
1543     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1544     if (dmGrad) {
1545       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1546       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1547       ierr = DMPlexReconstructGradients_Internal(dm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1548       /* Communicate gradient values */
1549       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1550       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1551       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1552       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1553     }
1554   }
1555   /* Handle boundary values */
1556   ierr = DMPlexInsertBoundaryValues(dm, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1557   /* Loop over chunks */
1558   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1559   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1560   numChunks     = 1;
1561   cellChunkSize = (cEnd - cStart)/numChunks;
1562   faceChunkSize = (fEnd - fStart)/numChunks;
1563   for (chunk = 0; chunk < numChunks; ++chunk) {
1564     PetscScalar     *elemVec, *fluxL, *fluxR;
1565     PetscReal       *vol;
1566     PetscFVFaceGeom *fgeom;
1567     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, cell;
1568     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = fE - fS, face;
1569 
1570     /* Extract field coefficients */
1571     if (useFEM) {
1572       ierr = DMPlexGetCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1573       ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1574     }
1575     if (useFVM) {
1576       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &uL, &uR);CHKERRQ(ierr);
1577       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &fgeom, &vol);CHKERRQ(ierr);
1578       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1579       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1580     }
1581     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1582     /* Loop over fields */
1583     for (f = 0; f < Nf; ++f) {
1584       PetscObject  obj;
1585       PetscClassId id;
1586       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1587 
1588       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1589       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1590       if (id == PETSCFE_CLASSID) {
1591         PetscFE         fe = (PetscFE) obj;
1592         PetscQuadrature q;
1593         PetscInt        Nq, Nb;
1594 
1595         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1596 
1597         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1598         ierr = PetscQuadratureGetData(q, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1599         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1600         blockSize = Nb*Nq;
1601         batchSize = numBlocks * blockSize;
1602         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1603         numChunks = numCells / (numBatches*batchSize);
1604         Ne        = numChunks*numBatches*batchSize;
1605         Nr        = numCells % (numBatches*batchSize);
1606         offset    = numCells - Nr;
1607         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1608         /*   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) */
1609         ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeomFEM, u, u_t, probAux, a, elemVec);CHKERRQ(ierr);
1610         ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, &cgeomFEM[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVec[offset*totDim]);CHKERRQ(ierr);
1611       } else if (id == PETSCFV_CLASSID) {
1612         PetscFV fv = (PetscFV) obj;
1613 
1614         Ne = numFaces;
1615         Nr = 0;
1616         /* Riemann solve over faces (need fields at face centroids) */
1617         /*   We need to evaluate FE fields at those coordinates */
1618         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1619       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1620     }
1621     /* Loop over domain */
1622     if (useFEM) {
1623       /* Add elemVec to locX */
1624       for (cell = cS; cell < cE; ++cell) {
1625         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cell*totDim]);CHKERRQ(ierr);}
1626         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cell*totDim], ADD_VALUES);CHKERRQ(ierr);
1627       }
1628     }
1629     if (useFVM) {
1630       PetscScalar *fa;
1631       PetscInt     iface;
1632 
1633       /* Accumulate fluxes to cells */
1634       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1635       for (face = fS, iface = 0; face < fE; ++face) {
1636         const PetscInt *cells;
1637         PetscScalar    *fL, *fR;
1638         PetscInt        ghost, d;
1639 
1640         ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1641         if (ghost >= 0) continue;
1642         ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1643         ierr = DMPlexPointGlobalRef(dm, cells[0], fa, &fL);CHKERRQ(ierr);
1644         ierr = DMPlexPointGlobalRef(dm, cells[1], fa, &fR);CHKERRQ(ierr);
1645         for (d = 0; d < totDim; ++d) {
1646           if (fL) fL[d] -= fluxL[iface*totDim+d];
1647           if (fR) fR[d] += fluxR[iface*totDim+d];
1648         }
1649         ++iface;
1650       }
1651       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1652     }
1653     if (useFEM) {
1654       ierr = DMPlexRestoreCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1655       ierr = DMRestoreWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1656     }
1657     if (useFVM) {
1658       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &uL, &uR);CHKERRQ(ierr);
1659       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &fgeom, &vol);CHKERRQ(ierr);
1660       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1661       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1662       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1663     }
1664   }
1665 
1666   if (useFEM) {ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, locF, user);CHKERRQ(ierr);}
1667 
1668   /* FEM */
1669   /* 1: Get sizes from dm and dmAux */
1670   /* 2: Get geometric data */
1671   /* 3: Handle boundary values */
1672   /* 4: Loop over domain */
1673   /*   Extract coefficients */
1674   /* Loop over fields */
1675   /*   Set tiling for FE*/
1676   /*   Integrate FE residual to get elemVec */
1677   /*     Loop over subdomain */
1678   /*       Loop over quad points */
1679   /*         Transform coords to real space */
1680   /*         Evaluate field and aux fields at point */
1681   /*         Evaluate residual at point */
1682   /*         Transform residual to real space */
1683   /*       Add residual to elemVec */
1684   /* Loop over domain */
1685   /*   Add elemVec to locX */
1686 
1687   /* FVM */
1688   /* Get geometric data */
1689   /* If using gradients */
1690   /*   Compute gradient data */
1691   /*   Loop over domain faces */
1692   /*     Count computational faces */
1693   /*     Reconstruct cell gradient */
1694   /*   Loop over domain cells */
1695   /*     Limit cell gradients */
1696   /* Handle boundary values */
1697   /* Loop over domain faces */
1698   /*   Read out field, centroid, normal, volume for each side of face */
1699   /* Riemann solve over faces */
1700   /* Loop over domain faces */
1701   /*   Accumulate fluxes to cells */
1702   /* TODO Change printFEM to printDisc here */
1703   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, locF);CHKERRQ(ierr);}
1704   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1705   PetscFunctionReturn(0);
1706 }
1707 
1708 #undef __FUNCT__
1709 #define __FUNCT__ "DMPlexComputeResidualFEM_Check_Internal"
1710 static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, Vec F, void *user)
1711 {
1712   DM                dmCh, dmAux;
1713   Vec               A, cellgeom;
1714   PetscDS           prob, probCh, probAux = NULL;
1715   PetscQuadrature   q;
1716   PetscSection      section, sectionAux;
1717   PetscFECellGeom  *cgeom;
1718   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
1719   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
1720   PetscInt          totDim, totDimAux, diffCell = 0;
1721   PetscErrorCode    ierr;
1722 
1723   PetscFunctionBegin;
1724   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1725   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1726   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1727   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1728   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1729   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1730   numCells = cEnd - cStart;
1731   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
1732   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
1733   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1734   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1735   if (dmAux) {
1736     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1737     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1738     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1739   }
1740   ierr = DMPlexInsertBoundaryValues(dm, X, 0.0, NULL, NULL, NULL);CHKERRQ(ierr);
1741   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1742   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);CHKERRQ(ierr);
1743   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
1744   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1745   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
1746   ierr = VecGetArray(cellgeom, (PetscScalar **) &cgeom);CHKERRQ(ierr);
1747   for (c = cStart; c < cEnd; ++c) {
1748     PetscScalar *x = NULL, *x_t = NULL;
1749     PetscInt     i;
1750 
1751     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1752     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1753     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1754     if (X_t) {
1755       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1756       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1757       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1758     }
1759     if (dmAux) {
1760       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1761       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1762       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1763     }
1764   }
1765   for (f = 0; f < Nf; ++f) {
1766     PetscFE  fe, feCh;
1767     PetscInt numQuadPoints, Nb;
1768     /* Conforming batches */
1769     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1770     /* Remainder */
1771     PetscInt Nr, offset;
1772 
1773     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1774     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
1775     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1776     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1777     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1778     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1779     blockSize = Nb*numQuadPoints;
1780     batchSize = numBlocks * blockSize;
1781     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1782     numChunks = numCells / (numBatches*batchSize);
1783     Ne        = numChunks*numBatches*batchSize;
1784     Nr        = numCells % (numBatches*batchSize);
1785     offset    = numCells - Nr;
1786     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeom, u, u_t, probAux, a, elemVec);CHKERRQ(ierr);
1787     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, cgeom, u, u_t, probAux, a, elemVecCh);CHKERRQ(ierr);
1788     ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVec[offset*totDim]);CHKERRQ(ierr);
1789     ierr = PetscFEIntegrateResidual(feCh, prob, f, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVecCh[offset*totDim]);CHKERRQ(ierr);
1790   }
1791   for (c = cStart; c < cEnd; ++c) {
1792     PetscBool diff = PETSC_FALSE;
1793     PetscInt  d;
1794 
1795     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
1796     if (diff) {
1797       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
1798       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
1799       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
1800       ++diffCell;
1801     }
1802     if (diffCell > 9) break;
1803     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_VALUES);CHKERRQ(ierr);
1804   }
1805   ierr = VecRestoreArray(cellgeom, (PetscScalar **) &cgeom);CHKERRQ(ierr);
1806   ierr = PetscFree3(u,u_t,elemVec);CHKERRQ(ierr);
1807   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
1808   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1809   PetscFunctionReturn(0);
1810 }
1811 
1812 #undef __FUNCT__
1813 #define __FUNCT__ "DMPlexSNESComputeResidualFEM"
1814 /*@
1815   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1816 
1817   Input Parameters:
1818 + dm - The mesh
1819 . X  - Local solution
1820 - user - The user context
1821 
1822   Output Parameter:
1823 . F  - Local output vector
1824 
1825   Level: developer
1826 
1827 .seealso: DMPlexComputeJacobianActionFEM()
1828 @*/
1829 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
1830 {
1831   PetscObject    check;
1832   PetscErrorCode ierr;
1833 
1834   PetscFunctionBegin;
1835   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
1836   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", &check);CHKERRQ(ierr);
1837   if (check) {ierr = DMPlexComputeResidualFEM_Check_Internal(dm, X, NULL, F, user);CHKERRQ(ierr);}
1838   else       {ierr = DMPlexComputeResidual_Internal(dm, 0.0, X, NULL, F, user);CHKERRQ(ierr);}
1839   PetscFunctionReturn(0);
1840 }
1841 
1842 #undef __FUNCT__
1843 #define __FUNCT__ "DMPlexComputeJacobianFEM_Internal"
1844 PetscErrorCode DMPlexComputeJacobianFEM_Internal(DM dm, Vec X, Vec X_t, Mat Jac, Mat JacP,void *user)
1845 {
1846   DM_Plex          *mesh  = (DM_Plex *) dm->data;
1847   const char       *name  = "Jacobian";
1848   DM                dmAux;
1849   DMLabel           depth;
1850   Vec               A, cellgeom;
1851   PetscDS           prob, probAux = NULL;
1852   PetscQuadrature   quad;
1853   PetscSection      section, globalSection, sectionAux;
1854   PetscFECellGeom  *cgeom;
1855   PetscScalar      *elemMat, *u, *u_t, *a = NULL;
1856   PetscInt          dim, Nf, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
1857   PetscInt          totDim, totDimBd, totDimAux, numBd, bd;
1858   PetscBool         isShell;
1859   PetscErrorCode    ierr;
1860 
1861   PetscFunctionBegin;
1862   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1863   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1864   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1865   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
1866   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1867   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1868   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
1869   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1870   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1871   numCells = cEnd - cStart;
1872   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1873   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1874   if (dmAux) {
1875     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1876     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1877     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1878   }
1879   ierr = DMPlexInsertBoundaryValues(dm, X, 0.0, NULL, NULL, NULL);CHKERRQ(ierr);
1880   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
1881   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim*totDim,&elemMat);CHKERRQ(ierr);
1882   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1883   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
1884   ierr = VecGetArray(cellgeom, (PetscScalar **) &cgeom);CHKERRQ(ierr);
1885   for (c = cStart; c < cEnd; ++c) {
1886     PetscScalar *x = NULL,  *x_t = NULL;
1887     PetscInt     i;
1888 
1889     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1890     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1891     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1892     if (X_t) {
1893       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1894       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1895       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1896     }
1897     if (dmAux) {
1898       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1899       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1900       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1901     }
1902   }
1903   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1904   for (fieldI = 0; fieldI < Nf; ++fieldI) {
1905     PetscFE  fe;
1906     PetscInt numQuadPoints, Nb;
1907     /* Conforming batches */
1908     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1909     /* Remainder */
1910     PetscInt Nr, offset;
1911 
1912     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
1913     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1914     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1915     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1916     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1917     blockSize = Nb*numQuadPoints;
1918     batchSize = numBlocks * blockSize;
1919     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1920     numChunks = numCells / (numBatches*batchSize);
1921     Ne        = numChunks*numBatches*batchSize;
1922     Nr        = numCells % (numBatches*batchSize);
1923     offset    = numCells - Nr;
1924     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1925       ierr = PetscFEIntegrateJacobian(fe, prob, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, elemMat);CHKERRQ(ierr);
1926       ierr = PetscFEIntegrateJacobian(fe, prob, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
1927     }
1928   }
1929   for (c = cStart; c < cEnd; ++c) {
1930     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[c*totDim*totDim]);CHKERRQ(ierr);}
1931     ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[c*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
1932   }
1933   ierr = VecGetArray(cellgeom, (PetscScalar **) &cgeom);CHKERRQ(ierr);
1934   ierr = PetscFree3(u,u_t,elemMat);CHKERRQ(ierr);
1935   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1936   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1937   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1938   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1939   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1940   for (bd = 0; bd < numBd; ++bd) {
1941     const char     *bdLabel;
1942     DMLabel         label;
1943     IS              pointIS;
1944     const PetscInt *points;
1945     const PetscInt *values;
1946     PetscInt        field, numValues, numPoints, p, dep, numFaces;
1947     PetscBool       isEssential;
1948 
1949     ierr = DMPlexGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1950     if (isEssential) continue;
1951     if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
1952     ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1953     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1954     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1955     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1956     for (p = 0, numFaces = 0; p < numPoints; ++p) {
1957       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1958       if (dep == dim-1) ++numFaces;
1959     }
1960     ierr = PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd*totDimBd,&elemMat);CHKERRQ(ierr);
1961     if (X_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
1962     for (p = 0, f = 0; p < numPoints; ++p) {
1963       const PetscInt point = points[p];
1964       PetscScalar   *x     = NULL;
1965       PetscInt       i;
1966 
1967       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1968       if (dep != dim-1) continue;
1969       ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
1970       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);
1971       if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
1972       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1973       for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
1974       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1975       if (X_t) {
1976         ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1977         for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
1978         ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1979       }
1980       ++f;
1981     }
1982     ierr = PetscMemzero(elemMat, numFaces*totDimBd*totDimBd * sizeof(PetscScalar));CHKERRQ(ierr);
1983     for (fieldI = 0; fieldI < Nf; ++fieldI) {
1984       PetscFE  fe;
1985       PetscInt numQuadPoints, Nb;
1986       /* Conforming batches */
1987       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1988       /* Remainder */
1989       PetscInt Nr, offset;
1990 
1991       ierr = PetscDSGetBdDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
1992       ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1993       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1994       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1995       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1996       blockSize = Nb*numQuadPoints;
1997       batchSize = numBlocks * blockSize;
1998       ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1999       numChunks = numFaces / (numBatches*batchSize);
2000       Ne        = numChunks*numBatches*batchSize;
2001       Nr        = numFaces % (numBatches*batchSize);
2002       offset    = numFaces - Nr;
2003       for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2004         ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, cgeom, u, u_t, NULL, NULL, elemMat);CHKERRQ(ierr);
2005         ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, &elemMat[offset*totDimBd*totDimBd]);CHKERRQ(ierr);
2006       }
2007     }
2008     for (p = 0, f = 0; p < numPoints; ++p) {
2009       const PetscInt point = points[p];
2010 
2011       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
2012       if (dep != dim-1) continue;
2013       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDimBd, totDimBd, &elemMat[f*totDimBd*totDimBd]);CHKERRQ(ierr);}
2014       ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*totDimBd*totDimBd], ADD_VALUES);CHKERRQ(ierr);
2015       ++f;
2016     }
2017     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2018     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2019     ierr = PetscFree3(u,cgeom,elemMat);CHKERRQ(ierr);
2020     if (X_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
2021   }
2022   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2023   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2024   if (mesh->printFEM) {
2025     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
2026     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
2027     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2028   }
2029   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2030   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
2031   if (isShell) {
2032     JacActionCtx *jctx;
2033 
2034     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
2035     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
2036   }
2037   PetscFunctionReturn(0);
2038 }
2039 
2040 #undef __FUNCT__
2041 #define __FUNCT__ "DMPlexSNESComputeJacobianFEM"
2042 /*@
2043   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2044 
2045   Input Parameters:
2046 + dm - The mesh
2047 . X  - Local input vector
2048 - user - The user context
2049 
2050   Output Parameter:
2051 . Jac  - Jacobian matrix
2052 
2053   Note:
2054   The first member of the user context must be an FEMContext.
2055 
2056   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2057   like a GPU, or vectorize on a multicore machine.
2058 
2059   Level: developer
2060 
2061 .seealso: FormFunctionLocal()
2062 @*/
2063 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2064 {
2065   PetscErrorCode ierr;
2066 
2067   PetscFunctionBegin;
2068   ierr = DMPlexComputeJacobianFEM_Internal(dm, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2069   PetscFunctionReturn(0);
2070 }
2071