xref: /petsc/src/ksp/pc/impls/patch/pcpatch.c (revision 1b68eb51b88e1230a9acd500dca328a6f38ec4c7)
1 #include <petsc/private/pcpatchimpl.h>     /*I "petscpc.h" I*/
2 #include <petsc/private/dmpleximpl.h> /* For DMPlexComputeJacobian_Patch_Internal() */
3 #include <petscsf.h>
4 #include <petscbt.h>
5 #include <petscds.h>
6 
7 PetscLogEvent PC_Patch_CreatePatches, PC_Patch_ComputeOp, PC_Patch_Solve, PC_Patch_Scatter, PC_Patch_Apply, PC_Patch_Prealloc;
8 
9 PETSC_STATIC_INLINE PetscErrorCode ObjectView(PetscObject obj, PetscViewer viewer, PetscViewerFormat format)
10 {
11   PetscErrorCode ierr;
12 
13   ierr = PetscViewerPushFormat(viewer, format);CHKERRQ(ierr);
14   ierr = PetscObjectView(obj, viewer);CHKERRQ(ierr);
15   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
16   return(0);
17 }
18 
19 static PetscErrorCode PCPatchConstruct_Star(void *vpatch, DM dm, PetscInt point, PetscHSetI ht)
20 {
21   PetscInt       starSize;
22   PetscInt      *star = NULL, si;
23   PetscErrorCode ierr;
24 
25   PetscFunctionBegin;
26   PetscHSetIClear(ht);
27   /* To start with, add the point we care about */
28   ierr = PetscHSetIAdd(ht, point);CHKERRQ(ierr);
29   /* Loop over all the points that this point connects to */
30   ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
31   for (si = 0; si < starSize*2; si += 2) {ierr = PetscHSetIAdd(ht, star[si]);CHKERRQ(ierr);}
32   ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
33   PetscFunctionReturn(0);
34 }
35 
36 static PetscErrorCode PCPatchConstruct_Vanka(void *vpatch, DM dm, PetscInt point, PetscHSetI ht)
37 {
38   PC_PATCH      *patch = (PC_PATCH *) vpatch;
39   PetscInt       starSize;
40   PetscInt      *star = NULL;
41   PetscBool      shouldIgnore = PETSC_FALSE;
42   PetscInt       cStart, cEnd, iStart, iEnd, si;
43   PetscErrorCode ierr;
44 
45   PetscFunctionBegin;
46   ierr = PetscHSetIClear(ht);CHKERRQ(ierr);
47   /* To start with, add the point we care about */
48   ierr = PetscHSetIAdd(ht, point);CHKERRQ(ierr);
49   /* Should we ignore any points of a certain dimension? */
50   if (patch->vankadim >= 0) {
51     shouldIgnore = PETSC_TRUE;
52     ierr = DMPlexGetDepthStratum(dm, patch->vankadim, &iStart, &iEnd);CHKERRQ(ierr);
53   }
54   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
55   /* Loop over all the cells that this point connects to */
56   ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
57   for (si = 0; si < starSize*2; si += 2) {
58     const PetscInt cell = star[si];
59     PetscInt       closureSize;
60     PetscInt      *closure = NULL, ci;
61 
62     if (cell < cStart || cell >= cEnd) continue;
63     /* now loop over all entities in the closure of that cell */
64     ierr = DMPlexGetTransitiveClosure(dm, cell, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
65     for (ci = 0; ci < closureSize*2; ci += 2) {
66       const PetscInt newpoint = closure[ci];
67 
68       /* We've been told to ignore entities of this type.*/
69       if (shouldIgnore && newpoint >= iStart && newpoint < iEnd) continue;
70       ierr = PetscHSetIAdd(ht, newpoint);CHKERRQ(ierr);
71     }
72     ierr = DMPlexRestoreTransitiveClosure(dm, cell, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
73   }
74   ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
75   PetscFunctionReturn(0);
76 }
77 
78 /* The user's already set the patches in patch->userIS. Build the hash tables */
79 static PetscErrorCode PCPatchConstruct_User(void *vpatch, DM dm, PetscInt point, PetscHSetI ht)
80 {
81   PC_PATCH       *patch   = (PC_PATCH *) vpatch;
82   IS              patchis = patch->userIS[point];
83   PetscInt        n;
84   const PetscInt *patchdata;
85   PetscInt        pStart, pEnd, i;
86   PetscErrorCode  ierr;
87 
88   PetscFunctionBegin;
89   ierr = PetscHSetIClear(ht);CHKERRQ(ierr);
90   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
91   ierr = ISGetLocalSize(patchis, &n);CHKERRQ(ierr);
92   ierr = ISGetIndices(patchis, &patchdata);CHKERRQ(ierr);
93   for (i = 0; i < n; ++i) {
94     const PetscInt ownedpoint = patchdata[i];
95 
96     if (ownedpoint < pStart || ownedpoint >= pEnd) {
97       SETERRQ3(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %D was not in [%D, %D)", ownedpoint, pStart, pEnd);
98     }
99     ierr = PetscHSetIAdd(ht, ownedpoint);CHKERRQ(ierr);
100   }
101   ierr = ISRestoreIndices(patchis, &patchdata);CHKERRQ(ierr);
102   PetscFunctionReturn(0);
103 }
104 
105 static PetscErrorCode PCPatchCreateDefaultSF_Private(PC pc, PetscInt n, const PetscSF *sf, const PetscInt *bs)
106 {
107   PC_PATCH      *patch = (PC_PATCH *) pc->data;
108   PetscInt       i;
109   PetscErrorCode ierr;
110 
111   PetscFunctionBegin;
112   if (n == 1 && bs[0] == 1) {
113     patch->defaultSF = sf[0];
114     ierr = PetscObjectReference((PetscObject) patch->defaultSF);CHKERRQ(ierr);
115   } else {
116     PetscInt     allRoots = 0, allLeaves = 0;
117     PetscInt     leafOffset = 0;
118     PetscInt    *ilocal = NULL;
119     PetscSFNode *iremote = NULL;
120     PetscInt    *remoteOffsets = NULL;
121     PetscInt     index = 0;
122     PetscHMapI   rankToIndex;
123     PetscInt     numRanks = 0;
124     PetscSFNode *remote = NULL;
125     PetscSF      rankSF;
126     PetscInt    *ranks = NULL;
127     PetscInt    *offsets = NULL;
128     MPI_Datatype contig;
129     PetscHSetI   ranksUniq;
130 
131     /* First figure out how many dofs there are in the concatenated numbering.
132      * allRoots: number of owned global dofs;
133      * allLeaves: number of visible dofs (global + ghosted).
134      */
135     for (i = 0; i < n; ++i) {
136       PetscInt nroots, nleaves;
137 
138       ierr = PetscSFGetGraph(sf[i], &nroots, &nleaves, NULL, NULL);CHKERRQ(ierr);
139       allRoots  += nroots * bs[i];
140       allLeaves += nleaves * bs[i];
141     }
142     ierr = PetscMalloc1(allLeaves, &ilocal);CHKERRQ(ierr);
143     ierr = PetscMalloc1(allLeaves, &iremote);CHKERRQ(ierr);
144     /* Now build an SF that just contains process connectivity. */
145     ierr = PetscHSetICreate(&ranksUniq);CHKERRQ(ierr);
146     for (i = 0; i < n; ++i) {
147       const PetscMPIInt *ranks = NULL;
148       PetscInt           nranks, j;
149 
150       ierr = PetscSFSetUp(sf[i]);CHKERRQ(ierr);
151       ierr = PetscSFGetRanks(sf[i], &nranks, &ranks, NULL, NULL, NULL);CHKERRQ(ierr);
152       /* These are all the ranks who communicate with me. */
153       for (j = 0; j < nranks; ++j) {
154         ierr = PetscHSetIAdd(ranksUniq, (PetscInt) ranks[j]);CHKERRQ(ierr);
155       }
156     }
157     ierr = PetscHSetIGetSize(ranksUniq, &numRanks);CHKERRQ(ierr);
158     ierr = PetscMalloc1(numRanks, &remote);CHKERRQ(ierr);
159     ierr = PetscMalloc1(numRanks, &ranks);CHKERRQ(ierr);
160     ierr = PetscHSetIGetElems(ranksUniq, &index, ranks);CHKERRQ(ierr);
161 
162     ierr = PetscHMapICreate(&rankToIndex);CHKERRQ(ierr);
163     for (i = 0; i < numRanks; ++i) {
164       remote[i].rank  = ranks[i];
165       remote[i].index = 0;
166       ierr = PetscHMapISet(rankToIndex, ranks[i], i);CHKERRQ(ierr);
167     }
168     ierr = PetscFree(ranks);CHKERRQ(ierr);
169     ierr = PetscHSetIDestroy(&ranksUniq);CHKERRQ(ierr);
170     ierr = PetscSFCreate(PetscObjectComm((PetscObject) pc), &rankSF);CHKERRQ(ierr);
171     ierr = PetscSFSetGraph(rankSF, 1, numRanks, NULL, PETSC_OWN_POINTER, remote, PETSC_OWN_POINTER);CHKERRQ(ierr);
172     ierr = PetscSFSetUp(rankSF);CHKERRQ(ierr);
173     /* OK, use it to communicate the root offset on the remote
174      * processes for each subspace. */
175     ierr = PetscMalloc1(n, &offsets);CHKERRQ(ierr);
176     ierr = PetscMalloc1(n*numRanks, &remoteOffsets);CHKERRQ(ierr);
177 
178     offsets[0] = 0;
179     for (i = 1; i < n; ++i) {
180       PetscInt nroots;
181 
182       ierr = PetscSFGetGraph(sf[i-1], &nroots, NULL, NULL, NULL);CHKERRQ(ierr);
183       offsets[i] = offsets[i-1] + nroots*bs[i-1];
184     }
185     /* Offsets are the offsets on the current process of the
186      * global dof numbering for the subspaces. */
187     ierr = MPI_Type_contiguous(n, MPIU_INT, &contig);CHKERRQ(ierr);
188     ierr = MPI_Type_commit(&contig);CHKERRQ(ierr);
189 
190     ierr = PetscSFBcastBegin(rankSF, contig, offsets, remoteOffsets);CHKERRQ(ierr);
191     ierr = PetscSFBcastEnd(rankSF, contig, offsets, remoteOffsets);CHKERRQ(ierr);
192     ierr = MPI_Type_free(&contig);CHKERRQ(ierr);
193     ierr = PetscFree(offsets);CHKERRQ(ierr);
194     ierr = PetscSFDestroy(&rankSF);CHKERRQ(ierr);
195     /* Now remoteOffsets contains the offsets on the remote
196      * processes who communicate with me.  So now we can
197      * concatenate the list of SFs into a single one. */
198     index = 0;
199     for (i = 0; i < n; ++i) {
200       const PetscSFNode *remote = NULL;
201       const PetscInt    *local  = NULL;
202       PetscInt           nroots, nleaves, j;
203 
204       ierr = PetscSFGetGraph(sf[i], &nroots, &nleaves, &local, &remote);CHKERRQ(ierr);
205       for (j = 0; j < nleaves; ++j) {
206         PetscInt rank = remote[j].rank;
207         PetscInt idx, rootOffset, k;
208 
209         ierr = PetscHMapIGet(rankToIndex, rank, &idx);CHKERRQ(ierr);
210         if (idx == -1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Didn't find rank, huh?");
211         /* Offset on given rank for ith subspace */
212         rootOffset = remoteOffsets[n*idx + i];
213         for (k = 0; k < bs[i]; ++k) {
214           ilocal[index]        = (local ? local[j] : j)*bs[i] + k + leafOffset;
215           iremote[index].rank  = remote[j].rank;
216           iremote[index].index = remote[j].index*bs[i] + k + rootOffset;
217           ++index;
218         }
219       }
220       leafOffset += nleaves * bs[i];
221     }
222     ierr = PetscHMapIDestroy(&rankToIndex);CHKERRQ(ierr);
223     ierr = PetscFree(remoteOffsets);CHKERRQ(ierr);
224     ierr = PetscSFCreate(PetscObjectComm((PetscObject)pc), &patch->defaultSF);CHKERRQ(ierr);
225     ierr = PetscSFSetGraph(patch->defaultSF, allRoots, allLeaves, ilocal, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER);CHKERRQ(ierr);
226   }
227   PetscFunctionReturn(0);
228 }
229 
230 /* TODO: Docs */
231 PetscErrorCode PCPatchSetIgnoreDim(PC pc, PetscInt dim)
232 {
233   PC_PATCH *patch = (PC_PATCH *) pc->data;
234   PetscFunctionBegin;
235   patch->ignoredim = dim;
236   PetscFunctionReturn(0);
237 }
238 
239 /* TODO: Docs */
240 PetscErrorCode PCPatchGetIgnoreDim(PC pc, PetscInt *dim)
241 {
242   PC_PATCH *patch = (PC_PATCH *) pc->data;
243   PetscFunctionBegin;
244   *dim = patch->ignoredim;
245   PetscFunctionReturn(0);
246 }
247 
248 /* TODO: Docs */
249 PetscErrorCode PCPatchSetSaveOperators(PC pc, PetscBool flg)
250 {
251   PC_PATCH *patch = (PC_PATCH *) pc->data;
252   PetscFunctionBegin;
253   patch->save_operators = flg;
254   PetscFunctionReturn(0);
255 }
256 
257 /* TODO: Docs */
258 PetscErrorCode PCPatchGetSaveOperators(PC pc, PetscBool *flg)
259 {
260   PC_PATCH *patch = (PC_PATCH *) pc->data;
261   PetscFunctionBegin;
262   *flg = patch->save_operators;
263   PetscFunctionReturn(0);
264 }
265 
266 /* TODO: Docs */
267 PetscErrorCode PCPatchSetPartitionOfUnity(PC pc, PetscBool flg)
268 {
269     PC_PATCH *patch = (PC_PATCH *) pc->data;
270     PetscFunctionBegin;
271     patch->partition_of_unity = flg;
272     PetscFunctionReturn(0);
273 }
274 
275 /* TODO: Docs */
276 PetscErrorCode PCPatchGetPartitionOfUnity(PC pc, PetscBool *flg)
277 {
278     PC_PATCH *patch = (PC_PATCH *) pc->data;
279     PetscFunctionBegin;
280     *flg = patch->partition_of_unity;
281     PetscFunctionReturn(0);
282 }
283 
284 /* TODO: Docs */
285 PetscErrorCode PCPatchSetSubMatType(PC pc, MatType sub_mat_type)
286 {
287   PC_PATCH      *patch = (PC_PATCH *) pc->data;
288   PetscErrorCode ierr;
289 
290   PetscFunctionBegin;
291   if (patch->sub_mat_type) {ierr = PetscFree(patch->sub_mat_type);CHKERRQ(ierr);}
292   ierr = PetscStrallocpy(sub_mat_type, (char **) &patch->sub_mat_type);CHKERRQ(ierr);
293   PetscFunctionReturn(0);
294 }
295 
296 /* TODO: Docs */
297 PetscErrorCode PCPatchGetSubMatType(PC pc, MatType *sub_mat_type)
298 {
299   PC_PATCH *patch = (PC_PATCH *) pc->data;
300   PetscFunctionBegin;
301   *sub_mat_type = patch->sub_mat_type;
302   PetscFunctionReturn(0);
303 }
304 
305 /* TODO: Docs */
306 PetscErrorCode PCPatchSetCellNumbering(PC pc, PetscSection cellNumbering)
307 {
308   PC_PATCH      *patch = (PC_PATCH *) pc->data;
309   PetscErrorCode ierr;
310 
311   PetscFunctionBegin;
312   patch->cellNumbering = cellNumbering;
313   ierr = PetscObjectReference((PetscObject) cellNumbering);CHKERRQ(ierr);
314   PetscFunctionReturn(0);
315 }
316 
317 /* TODO: Docs */
318 PetscErrorCode PCPatchGetCellNumbering(PC pc, PetscSection *cellNumbering)
319 {
320   PC_PATCH *patch = (PC_PATCH *) pc->data;
321   PetscFunctionBegin;
322   *cellNumbering = patch->cellNumbering;
323   PetscFunctionReturn(0);
324 }
325 
326 /* TODO: Docs */
327 PetscErrorCode PCPatchSetConstructType(PC pc, PCPatchConstructType ctype, PetscErrorCode (*func)(PC, PetscInt *, IS **, IS *, void *), void *ctx)
328 {
329   PC_PATCH *patch = (PC_PATCH *) pc->data;
330 
331   PetscFunctionBegin;
332   patch->ctype = ctype;
333   switch (ctype) {
334   case PC_PATCH_STAR:
335     patch->user_patches     = PETSC_FALSE;
336     patch->patchconstructop = PCPatchConstruct_Star;
337     break;
338   case PC_PATCH_VANKA:
339     patch->user_patches     = PETSC_FALSE;
340     patch->patchconstructop = PCPatchConstruct_Vanka;
341     break;
342   case PC_PATCH_USER:
343   case PC_PATCH_PYTHON:
344     patch->user_patches     = PETSC_TRUE;
345     patch->patchconstructop = PCPatchConstruct_User;
346     if (func) {
347       patch->userpatchconstructionop = func;
348       patch->userpatchconstructctx   = ctx;
349     }
350     break;
351   default:
352     SETERRQ1(PetscObjectComm((PetscObject) pc), PETSC_ERR_USER, "Unknown patch construction type %D", (PetscInt) patch->ctype);
353   }
354   PetscFunctionReturn(0);
355 }
356 
357 /* TODO: Docs */
358 PetscErrorCode PCPatchGetConstructType(PC pc, PCPatchConstructType *ctype, PetscErrorCode (**func)(PC, PetscInt *, IS **, IS *, void *), void **ctx)
359 {
360   PC_PATCH *patch = (PC_PATCH *) pc->data;
361 
362   PetscFunctionBegin;
363   *ctype = patch->ctype;
364   switch (patch->ctype) {
365   case PC_PATCH_STAR:
366   case PC_PATCH_VANKA:
367     break;
368   case PC_PATCH_USER:
369   case PC_PATCH_PYTHON:
370     *func = patch->userpatchconstructionop;
371     *ctx  = patch->userpatchconstructctx;
372     break;
373   default:
374     SETERRQ1(PetscObjectComm((PetscObject) pc), PETSC_ERR_USER, "Unknown patch construction type %D", (PetscInt) patch->ctype);
375   }
376   PetscFunctionReturn(0);
377 }
378 
379 /* TODO: Docs */
380 PetscErrorCode PCPatchSetDiscretisationInfo(PC pc, PetscInt nsubspaces, DM *dms, PetscInt *bs, PetscInt *nodesPerCell, const PetscInt **cellNodeMap,
381                                             const PetscInt *subspaceOffsets, PetscInt numGhostBcs, const PetscInt *ghostBcNodes, PetscInt numGlobalBcs, const PetscInt *globalBcNodes)
382 {
383   PC_PATCH      *patch = (PC_PATCH *) pc->data;
384   DM             dm;
385   PetscSF       *sfs;
386   PetscInt       cStart, cEnd, i, j;
387   PetscErrorCode ierr;
388 
389   PetscFunctionBegin;
390   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
391   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
392   ierr = PetscMalloc1(nsubspaces, &sfs);CHKERRQ(ierr);
393   ierr = PetscMalloc1(nsubspaces, &patch->dofSection);CHKERRQ(ierr);
394   ierr = PetscMalloc1(nsubspaces, &patch->bs);CHKERRQ(ierr);
395   ierr = PetscMalloc1(nsubspaces, &patch->nodesPerCell);CHKERRQ(ierr);
396   ierr = PetscMalloc1(nsubspaces, &patch->cellNodeMap);CHKERRQ(ierr);
397   ierr = PetscMalloc1(nsubspaces+1, &patch->subspaceOffsets);CHKERRQ(ierr);
398 
399   patch->nsubspaces       = nsubspaces;
400   patch->totalDofsPerCell = 0;
401   for (i = 0; i < nsubspaces; ++i) {
402     ierr = DMGetDefaultSection(dms[i], &patch->dofSection[i]);CHKERRQ(ierr);
403     ierr = PetscObjectReference((PetscObject) patch->dofSection[i]);CHKERRQ(ierr);
404     ierr = DMGetDefaultSF(dms[i], &sfs[i]);CHKERRQ(ierr);
405     patch->bs[i]              = bs[i];
406     patch->nodesPerCell[i]    = nodesPerCell[i];
407     patch->totalDofsPerCell  += nodesPerCell[i]*bs[i];
408     ierr = PetscMalloc1((cEnd-cStart)*nodesPerCell[i]*bs[i], &patch->cellNodeMap[i]);CHKERRQ(ierr);
409     for (j = 0; j < (cEnd-cStart)*nodesPerCell[i]*bs[i]; ++j) patch->cellNodeMap[i][j] = cellNodeMap[i][j];
410     patch->subspaceOffsets[i] = subspaceOffsets[i];
411   }
412   ierr = PCPatchCreateDefaultSF_Private(pc, nsubspaces, sfs, patch->bs);CHKERRQ(ierr);
413   ierr = PetscFree(sfs);CHKERRQ(ierr);
414 
415   patch->subspaceOffsets[nsubspaces] = subspaceOffsets[nsubspaces];
416   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGhostBcs, ghostBcNodes, PETSC_COPY_VALUES, &patch->ghostBcNodes);CHKERRQ(ierr);
417   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalBcs, globalBcNodes, PETSC_COPY_VALUES, &patch->globalBcNodes);CHKERRQ(ierr);
418   PetscFunctionReturn(0);
419 }
420 
421 /* TODO: Docs */
422 PetscErrorCode PCPatchSetDiscretisationInfoCombined(PC pc, DM dm, PetscInt *nodesPerCell, const PetscInt **cellNodeMap, PetscInt numGhostBcs, const PetscInt *ghostBcNodes, PetscInt numGlobalBcs, const PetscInt *globalBcNodes)
423 {
424   PC_PATCH      *patch = (PC_PATCH *) pc->data;
425   PetscInt       cStart, cEnd, i, j;
426   PetscErrorCode ierr;
427 
428   PetscFunctionBegin;
429   patch->combined = PETSC_TRUE;
430   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
431   ierr = DMGetNumFields(dm, &patch->nsubspaces);CHKERRQ(ierr);
432   ierr = PetscCalloc1(patch->nsubspaces, &patch->dofSection);CHKERRQ(ierr);
433   ierr = PetscMalloc1(patch->nsubspaces, &patch->bs);CHKERRQ(ierr);
434   ierr = PetscMalloc1(patch->nsubspaces, &patch->nodesPerCell);CHKERRQ(ierr);
435   ierr = PetscMalloc1(patch->nsubspaces, &patch->cellNodeMap);CHKERRQ(ierr);
436   ierr = PetscCalloc1(patch->nsubspaces+1, &patch->subspaceOffsets);CHKERRQ(ierr);
437   ierr = DMGetDefaultSection(dm, &patch->dofSection[0]);CHKERRQ(ierr);
438   ierr = PetscObjectReference((PetscObject) patch->dofSection[0]);CHKERRQ(ierr);
439   ierr = PetscSectionGetStorageSize(patch->dofSection[0], &patch->subspaceOffsets[patch->nsubspaces]);CHKERRQ(ierr);
440   patch->totalDofsPerCell = 0;
441   for (i = 0; i < patch->nsubspaces; ++i) {
442     patch->bs[i]             = 1;
443     patch->nodesPerCell[i]   = nodesPerCell[i];
444     patch->totalDofsPerCell += nodesPerCell[i];
445     ierr = PetscMalloc1((cEnd-cStart)*nodesPerCell[i], &patch->cellNodeMap[i]);CHKERRQ(ierr);
446     for (j = 0; j < (cEnd-cStart)*nodesPerCell[i]; ++j) patch->cellNodeMap[i][j] = cellNodeMap[i][j];
447   }
448   ierr = DMGetDefaultSF(dm, &patch->defaultSF);CHKERRQ(ierr);
449   ierr = PetscObjectReference((PetscObject) patch->defaultSF);CHKERRQ(ierr);
450   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGhostBcs, ghostBcNodes, PETSC_COPY_VALUES, &patch->ghostBcNodes);CHKERRQ(ierr);
451   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalBcs, globalBcNodes, PETSC_COPY_VALUES, &patch->globalBcNodes);CHKERRQ(ierr);
452   PetscFunctionReturn(0);
453 }
454 
455 /*@C
456 
457   PCPatchSetComputeOperator - Set the callback used to compute patch matrices
458 
459   Input Parameters:
460 + pc   - The PC
461 . func - The callback
462 - ctx  - The user context
463 
464   Level: advanced
465 
466   Note:
467   The callback has signature:
468 +  usercomputeop(pc, point, mat, cellIS, n, u, ctx)
469 +  pc     - The PC
470 +  point  - The point
471 +  mat    - The patch matrix
472 +  cellIS - An array of the cell numbers
473 +  n      - The size of g2l
474 +  g2l    - The global to local dof translation table
475 +  ctx    - The user context
476   and can assume that the matrix entries have been set to zero before the call.
477 
478 .seealso: PCPatchGetComputeOperator(), PCPatchSetDiscretisationInfo()
479 @*/
480 PetscErrorCode PCPatchSetComputeOperator(PC pc, PetscErrorCode (*func)(PC, PetscInt, Mat, IS, PetscInt, const PetscInt *, void *), void *ctx)
481 {
482   PC_PATCH *patch = (PC_PATCH *) pc->data;
483 
484   PetscFunctionBegin;
485   patch->usercomputeop  = func;
486   patch->usercomputectx = ctx;
487   PetscFunctionReturn(0);
488 }
489 
490 /* On entry, ht contains the topological entities whose dofs we are responsible for solving for;
491    on exit, cht contains all the topological entities we need to compute their residuals.
492    In full generality this should incorporate knowledge of the sparsity pattern of the matrix;
493    here we assume a standard FE sparsity pattern.*/
494 /* TODO: Use DMPlexGetAdjacency() */
495 /* TODO: Look at temp buffer management for GetClosure() */
496 static PetscErrorCode PCPatchCompleteCellPatch(PC pc, PetscHSetI ht, PetscHSetI cht)
497 {
498   DM             dm;
499   PetscHashIter  hi;
500   PetscInt       point;
501   PetscInt      *star = NULL, *closure = NULL;
502   PetscInt       ignoredim, iStart = 0, iEnd = -1, starSize, closureSize, si, ci;
503   PetscErrorCode ierr;
504 
505   PetscFunctionBegin;
506   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
507   ierr = PCPatchGetIgnoreDim(pc, &ignoredim);CHKERRQ(ierr);
508   if (ignoredim >= 0) {ierr = DMPlexGetDepthStratum(dm, ignoredim, &iStart, &iEnd);CHKERRQ(ierr);}
509   ierr = PetscHSetIClear(cht);CHKERRQ(ierr);
510   PetscHashIterBegin(ht, hi);
511   while (!PetscHashIterAtEnd(ht, hi)) {
512 
513     PetscHashIterGetKey(ht, hi, point);
514     PetscHashIterNext(ht, hi);
515 
516     /* Loop over all the cells that this point connects to */
517     ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
518     for (si = 0; si < starSize*2; si += 2) {
519       const PetscInt ownedpoint = star[si];
520       /* TODO Check for point in cht before running through closure again */
521       /* now loop over all entities in the closure of that cell */
522       ierr = DMPlexGetTransitiveClosure(dm, ownedpoint, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
523       for (ci = 0; ci < closureSize*2; ci += 2) {
524         const PetscInt seenpoint = closure[ci];
525         if (ignoredim >= 0 && seenpoint >= iStart && seenpoint < iEnd) continue;
526         ierr = PetscHSetIAdd(cht, seenpoint);CHKERRQ(ierr);
527       }
528     }
529   }
530   ierr = DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, NULL, &closure);CHKERRQ(ierr);
531   ierr = DMPlexRestoreTransitiveClosure(dm, 0, PETSC_FALSE, NULL, &star);CHKERRQ(ierr);
532   PetscFunctionReturn(0);
533 }
534 
535 static PetscErrorCode PCPatchGetGlobalDofs(PC pc, PetscSection dofSection[], PetscInt f, PetscBool combined, PetscInt p, PetscInt *dof, PetscInt *off)
536 {
537   PetscErrorCode ierr;
538 
539   PetscFunctionBegin;
540   if (combined) {
541     if (f < 0) {
542       if (dof) {ierr = PetscSectionGetDof(dofSection[0], p, dof);CHKERRQ(ierr);}
543       if (off) {ierr = PetscSectionGetOffset(dofSection[0], p, off);CHKERRQ(ierr);}
544     } else {
545       if (dof) {ierr = PetscSectionGetFieldDof(dofSection[0], p, f, dof);CHKERRQ(ierr);}
546       if (off) {ierr = PetscSectionGetFieldOffset(dofSection[0], p, f, off);CHKERRQ(ierr);}
547     }
548   } else {
549     if (f < 0) {
550       PC_PATCH *patch = (PC_PATCH *) pc->data;
551       PetscInt  fdof, g;
552 
553       if (dof) {
554         *dof = 0;
555         for (g = 0; g < patch->nsubspaces; ++g) {
556           ierr = PetscSectionGetDof(dofSection[g], p, &fdof);CHKERRQ(ierr);
557           *dof += fdof;
558         }
559       }
560       if (off) {ierr = PetscSectionGetOffset(dofSection[0], p, off);CHKERRQ(ierr);}
561     } else {
562       if (dof) {ierr = PetscSectionGetDof(dofSection[f], p, dof);CHKERRQ(ierr);}
563       if (off) {ierr = PetscSectionGetOffset(dofSection[f], p, off);CHKERRQ(ierr);}
564     }
565   }
566   PetscFunctionReturn(0);
567 }
568 
569 /* Given a hash table with a set of topological entities (pts), compute the degrees of
570    freedom in global concatenated numbering on those entities.
571    For Vanka smoothing, this needs to do something special: ignore dofs of the
572    constraint subspace on entities that aren't the base entity we're building the patch
573    around. */
574 static PetscErrorCode PCPatchGetPointDofs(PC pc, PetscHSetI pts, PetscHSetI dofs, PetscInt base, PetscInt exclude_subspace)
575 {
576   PC_PATCH      *patch = (PC_PATCH *) pc->data;
577   PetscHashIter  hi;
578   PetscInt       ldof, loff;
579   PetscInt       k, p;
580   PetscErrorCode ierr;
581 
582   PetscFunctionBegin;
583   ierr = PetscHSetIClear(dofs);CHKERRQ(ierr);
584   for (k = 0; k < patch->nsubspaces; ++k) {
585     PetscInt subspaceOffset = patch->subspaceOffsets[k];
586     PetscInt bs             = patch->bs[k];
587     PetscInt j, l;
588 
589     if (k == exclude_subspace) {
590       /* only get this subspace dofs at the base entity, not any others */
591       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, base, &ldof, &loff);CHKERRQ(ierr);
592       if (0 == ldof) continue;
593       for (j = loff; j < ldof + loff; ++j) {
594         for (l = 0; l < bs; ++l) {
595           PetscInt dof = bs*j + l + subspaceOffset;
596           ierr = PetscHSetIAdd(dofs, dof);CHKERRQ(ierr);
597         }
598       }
599       continue; /* skip the other dofs of this subspace */
600     }
601 
602     PetscHashIterBegin(pts, hi);
603     while (!PetscHashIterAtEnd(pts, hi)) {
604       PetscHashIterGetKey(pts, hi, p);
605       PetscHashIterNext(pts, hi);
606       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, p, &ldof, &loff);CHKERRQ(ierr);
607       if (0 == ldof) continue;
608       for (j = loff; j < ldof + loff; ++j) {
609         for (l = 0; l < bs; ++l) {
610           PetscInt dof = bs*j + l + subspaceOffset;
611           ierr = PetscHSetIAdd(dofs, dof);CHKERRQ(ierr);
612         }
613       }
614     }
615   }
616   PetscFunctionReturn(0);
617 }
618 
619 /* Given two hash tables A and B, compute the keys in B that are not in A, and put them in C */
620 static PetscErrorCode PCPatchComputeSetDifference_Private(PetscHSetI A, PetscHSetI B, PetscHSetI C)
621 {
622   PetscHashIter  hi;
623   PetscInt       key;
624   PetscBool      flg;
625   PetscErrorCode ierr;
626 
627   PetscFunctionBegin;
628   ierr = PetscHSetIClear(C);CHKERRQ(ierr);
629   PetscHashIterBegin(B, hi);
630   while (!PetscHashIterAtEnd(B, hi)) {
631     PetscHashIterGetKey(B, hi, key);
632     PetscHashIterNext(B, hi);
633     ierr = PetscHSetIHas(A, key, &flg);CHKERRQ(ierr);
634     if (!flg) {ierr = PetscHSetIAdd(C, key);CHKERRQ(ierr);}
635   }
636   PetscFunctionReturn(0);
637 }
638 
639 /*
640  * PCPatchCreateCellPatches - create patches.
641  *
642  * Input Parameters:
643  * + dm - The DMPlex object defining the mesh
644  *
645  * Output Parameters:
646  * + cellCounts  - Section with counts of cells around each vertex
647  * . cells       - IS of the cell point indices of cells in each patch
648  * . pointCounts - Section with counts of cells around each vertex
649  * - point       - IS of the cell point indices of cells in each patch
650  */
651 static PetscErrorCode PCPatchCreateCellPatches(PC pc)
652 {
653   PC_PATCH       *patch = (PC_PATCH *) pc->data;
654   DMLabel         ghost = NULL;
655   DM              dm, plex;
656   PetscHSetI      ht, cht;
657   PetscSection    cellCounts,  pointCounts;
658   PetscInt       *cellsArray, *pointsArray;
659   PetscInt        numCells,    numPoints;
660   const PetscInt *leaves;
661   PetscInt        nleaves, pStart, pEnd, cStart, cEnd, vStart, vEnd, v;
662   PetscBool       isFiredrake;
663   PetscErrorCode  ierr;
664 
665   PetscFunctionBegin;
666   /* Used to keep track of the cells in the patch. */
667   ierr = PetscHSetICreate(&ht);CHKERRQ(ierr);
668   ierr = PetscHSetICreate(&cht);CHKERRQ(ierr);
669 
670   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
671   if (!dm) SETERRQ(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_WRONGSTATE, "DM not yet set on patch PC\n");
672   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
673   ierr = DMPlexGetChart(plex, &pStart, &pEnd);CHKERRQ(ierr);
674   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
675 
676   if (patch->user_patches) {
677     ierr = patch->userpatchconstructionop(pc, &patch->npatch, &patch->userIS, &patch->iterationSet, patch->userpatchconstructctx);CHKERRQ(ierr);
678     vStart = 0; vEnd = patch->npatch;
679   } else if (patch->codim < 0) {
680     if (patch->dim < 0) {ierr = DMPlexGetDepthStratum(plex,  0,            &vStart, &vEnd);CHKERRQ(ierr);}
681     else                {ierr = DMPlexGetDepthStratum(plex,  patch->dim,   &vStart, &vEnd);CHKERRQ(ierr);}
682   } else                {ierr = DMPlexGetHeightStratum(plex, patch->codim, &vStart, &vEnd);CHKERRQ(ierr);}
683   patch->npatch = vEnd - vStart;
684 
685   /* These labels mark the owned points.  We only create patches around points that this process owns. */
686   ierr = DMHasLabel(dm, "pyop2_ghost", &isFiredrake);CHKERRQ(ierr);
687   if (isFiredrake) {
688     ierr = DMGetLabel(dm, "pyop2_ghost", &ghost);CHKERRQ(ierr);
689     ierr = DMLabelCreateIndex(ghost, pStart, pEnd);CHKERRQ(ierr);
690   } else {
691     PetscSF sf;
692 
693     ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
694     ierr = PetscSFGetGraph(sf, NULL, &nleaves, &leaves, NULL);CHKERRQ(ierr);
695     nleaves = PetscMax(nleaves, 0);
696   }
697 
698   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->cellCounts);CHKERRQ(ierr);
699   ierr = PetscObjectSetName((PetscObject) patch->cellCounts, "Patch Cell Layout");CHKERRQ(ierr);
700   cellCounts = patch->cellCounts;
701   ierr = PetscSectionSetChart(cellCounts, vStart, vEnd);CHKERRQ(ierr);
702   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->pointCounts);CHKERRQ(ierr);
703   ierr = PetscObjectSetName((PetscObject) patch->pointCounts, "Patch Point Layout");CHKERRQ(ierr);
704   pointCounts = patch->pointCounts;
705   ierr = PetscSectionSetChart(pointCounts, vStart, vEnd);CHKERRQ(ierr);
706   /* Count cells and points in the patch surrounding each entity */
707   for (v = vStart; v < vEnd; ++v) {
708     PetscHashIter hi;
709     PetscInt       chtSize, loc = -1;
710     PetscBool      flg;
711 
712     if (!patch->user_patches) {
713       if (ghost) {ierr = DMLabelHasPoint(ghost, v, &flg);CHKERRQ(ierr);}
714       else       {ierr = PetscFindInt(v, nleaves, leaves, &loc); flg = loc >=0 ? PETSC_TRUE : PETSC_FALSE;}
715       /* Not an owned entity, don't make a cell patch. */
716       if (flg) continue;
717     }
718 
719     ierr = patch->patchconstructop((void *) patch, dm, v, ht);CHKERRQ(ierr);
720     ierr = PCPatchCompleteCellPatch(pc, ht, cht);CHKERRQ(ierr);
721     ierr = PetscHSetIGetSize(cht, &chtSize);CHKERRQ(ierr);
722     /* empty patch, continue */
723     if (chtSize == 0) continue;
724 
725     /* safe because size(cht) > 0 from above */
726     PetscHashIterBegin(cht, hi);
727     while (!PetscHashIterAtEnd(cht, hi)) {
728       PetscInt point, pdof;
729 
730       PetscHashIterGetKey(cht, hi, point);
731       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, -1, patch->combined, point, &pdof, NULL);CHKERRQ(ierr);
732       if (pdof)                            {ierr = PetscSectionAddDof(pointCounts, v, 1);CHKERRQ(ierr);}
733       if (point >= cStart && point < cEnd) {ierr = PetscSectionAddDof(cellCounts, v, 1);CHKERRQ(ierr);}
734       PetscHashIterNext(cht, hi);
735     }
736   }
737   if (isFiredrake) {ierr = DMLabelDestroyIndex(ghost);CHKERRQ(ierr);}
738 
739   ierr = PetscSectionSetUp(cellCounts);CHKERRQ(ierr);
740   ierr = PetscSectionGetStorageSize(cellCounts, &numCells);CHKERRQ(ierr);
741   ierr = PetscMalloc1(numCells, &cellsArray);CHKERRQ(ierr);
742   ierr = PetscSectionSetUp(pointCounts);CHKERRQ(ierr);
743   ierr = PetscSectionGetStorageSize(pointCounts, &numPoints);CHKERRQ(ierr);
744   ierr = PetscMalloc1(numPoints, &pointsArray);CHKERRQ(ierr);
745 
746   /* Now that we know how much space we need, run through again and actually remember the cells. */
747   for (v = vStart; v < vEnd; v++ ) {
748     PetscHashIter hi;
749     PetscInt       dof, off, cdof, coff, pdof, n = 0, cn = 0;
750 
751     ierr = PetscSectionGetDof(pointCounts, v, &dof);CHKERRQ(ierr);
752     ierr = PetscSectionGetOffset(pointCounts, v, &off);CHKERRQ(ierr);
753     ierr = PetscSectionGetDof(cellCounts, v, &cdof);CHKERRQ(ierr);
754     ierr = PetscSectionGetOffset(cellCounts, v, &coff);CHKERRQ(ierr);
755     if (dof <= 0) continue;
756     ierr = patch->patchconstructop((void *) patch, dm, v, ht);CHKERRQ(ierr);
757     ierr = PCPatchCompleteCellPatch(pc, ht, cht);CHKERRQ(ierr);
758     PetscHashIterBegin(cht, hi);
759     while (!PetscHashIterAtEnd(cht, hi)) {
760       PetscInt point;
761 
762       PetscHashIterGetKey(cht, hi, point);
763       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, -1, patch->combined, point, &pdof, NULL);CHKERRQ(ierr);
764       if (pdof)                            {pointsArray[off + n++] = point;}
765       if (point >= cStart && point < cEnd) {cellsArray[coff + cn++] = point;}
766       PetscHashIterNext(cht, hi);
767     }
768     if (cn != cdof) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of cells in patch %D is %D, but should be %D", v, cn, cdof);
769     if (n  != dof)  SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of points in patch %D is %D, but should be %D", v, n, dof);
770   }
771   ierr = PetscHSetIDestroy(&ht);CHKERRQ(ierr);
772   ierr = PetscHSetIDestroy(&cht);CHKERRQ(ierr);
773   ierr = DMDestroy(&plex);CHKERRQ(ierr);
774 
775   ierr = ISCreateGeneral(PETSC_COMM_SELF, numCells,  cellsArray,  PETSC_OWN_POINTER, &patch->cells);CHKERRQ(ierr);
776   ierr = PetscObjectSetName((PetscObject) patch->cells,  "Patch Cells");CHKERRQ(ierr);
777   if (patch->viewCells) {
778     ierr = ObjectView((PetscObject) patch->cellCounts, patch->viewerCells, patch->formatCells);CHKERRQ(ierr);
779     ierr = ObjectView((PetscObject) patch->cells,      patch->viewerCells, patch->formatCells);CHKERRQ(ierr);
780   }
781   ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints, pointsArray, PETSC_OWN_POINTER, &patch->points);CHKERRQ(ierr);
782   ierr = PetscObjectSetName((PetscObject) patch->points, "Patch Points");CHKERRQ(ierr);
783   if (patch->viewPoints) {
784     ierr = ObjectView((PetscObject) patch->pointCounts, patch->viewerPoints, patch->formatPoints);CHKERRQ(ierr);
785     ierr = ObjectView((PetscObject) patch->points,      patch->viewerPoints, patch->formatPoints);CHKERRQ(ierr);
786   }
787   PetscFunctionReturn(0);
788 }
789 
790 /*
791  * PCPatchCreateCellPatchDiscretisationInfo - Build the dof maps for cell patches
792  *
793  * Input Parameters:
794  * + dm - The DMPlex object defining the mesh
795  * . cellCounts - Section with counts of cells around each vertex
796  * . cells - IS of the cell point indices of cells in each patch
797  * . cellNumbering - Section mapping plex cell points to Firedrake cell indices.
798  * . nodesPerCell - number of nodes per cell.
799  * - cellNodeMap - map from cells to node indices (nodesPerCell * numCells)
800  *
801  * Output Parameters:
802  * + dofs - IS of local dof numbers of each cell in the patch, where local is a patch local numbering
803  * . gtolCounts - Section with counts of dofs per cell patch
804  * - gtol - IS mapping from global dofs to local dofs for each patch.
805  */
806 static PetscErrorCode PCPatchCreateCellPatchDiscretisationInfo(PC pc)
807 {
808   PC_PATCH       *patch           = (PC_PATCH *) pc->data;
809   PetscSection    cellCounts      = patch->cellCounts;
810   PetscSection    pointCounts     = patch->pointCounts;
811   PetscSection    gtolCounts;
812   IS              cells           = patch->cells;
813   IS              points          = patch->points;
814   PetscSection    cellNumbering   = patch->cellNumbering;
815   PetscInt        Nf              = patch->nsubspaces;
816   PetscInt        numCells, numPoints;
817   PetscInt        numDofs;
818   PetscInt        numGlobalDofs;
819   PetscInt        totalDofsPerCell = patch->totalDofsPerCell;
820   PetscInt        vStart, vEnd, v;
821   const PetscInt *cellsArray, *pointsArray;
822   PetscInt       *newCellsArray   = NULL;
823   PetscInt       *dofsArray       = NULL;
824   PetscInt       *offsArray       = NULL;
825   PetscInt       *asmArray        = NULL;
826   PetscInt       *globalDofsArray = NULL;
827   PetscInt        globalIndex     = 0;
828   PetscInt        key             = 0;
829   PetscInt        asmKey          = 0;
830   DM              dm              = NULL;
831   const PetscInt *bcNodes         = NULL;
832   PetscHMapI      ht;
833   PetscHSetI      globalBcs;
834   PetscInt        numBcs;
835   PetscHSetI      ownedpts, seenpts, owneddofs, seendofs, artificialbcs;
836   PetscInt        pStart, pEnd, p;
837   PetscErrorCode  ierr;
838 
839   PetscFunctionBegin;
840 
841   ierr = PCGetDM(pc, &dm); CHKERRQ(ierr);
842   /* dofcounts section is cellcounts section * dofPerCell */
843   ierr = PetscSectionGetStorageSize(cellCounts, &numCells);CHKERRQ(ierr);
844   ierr = PetscSectionGetStorageSize(patch->pointCounts, &numPoints);CHKERRQ(ierr);
845   numDofs = numCells * totalDofsPerCell;
846   ierr = PetscMalloc1(numDofs, &dofsArray);CHKERRQ(ierr);
847   ierr = PetscMalloc1(numPoints*Nf, &offsArray);CHKERRQ(ierr);
848   ierr = PetscMalloc1(numDofs, &asmArray);CHKERRQ(ierr);
849   ierr = PetscMalloc1(numCells, &newCellsArray);CHKERRQ(ierr);
850   ierr = PetscSectionGetChart(cellCounts, &vStart, &vEnd);CHKERRQ(ierr);
851   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->gtolCounts);CHKERRQ(ierr);
852   gtolCounts = patch->gtolCounts;
853   ierr = PetscSectionSetChart(gtolCounts, vStart, vEnd);CHKERRQ(ierr);
854   ierr = PetscObjectSetName((PetscObject) patch->gtolCounts, "Patch Global Index Section");CHKERRQ(ierr);
855 
856   /* Outside the patch loop, get the dofs that are globally-enforced Dirichlet
857    conditions */
858   ierr = PetscHSetICreate(&globalBcs);CHKERRQ(ierr);
859   ierr = ISGetIndices(patch->ghostBcNodes, &bcNodes); CHKERRQ(ierr);
860   ierr = ISGetSize(patch->ghostBcNodes, &numBcs); CHKERRQ(ierr);
861   for ( PetscInt i = 0; i < numBcs; i++ ) {
862     ierr = PetscHSetIAdd(globalBcs, bcNodes[i]);CHKERRQ(ierr); /* these are already in concatenated numbering */
863   }
864   ierr = ISRestoreIndices(patch->ghostBcNodes, &bcNodes); CHKERRQ(ierr);
865   ierr = ISDestroy(&patch->ghostBcNodes); CHKERRQ(ierr); /* memory optimisation */
866 
867   /* Hash tables for artificial BC construction */
868   ierr = PetscHSetICreate(&ownedpts);CHKERRQ(ierr);
869   ierr = PetscHSetICreate(&seenpts);CHKERRQ(ierr);
870   ierr = PetscHSetICreate(&owneddofs);CHKERRQ(ierr);
871   ierr = PetscHSetICreate(&seendofs);CHKERRQ(ierr);
872   ierr = PetscHSetICreate(&artificialbcs);CHKERRQ(ierr);
873 
874   ierr = ISGetIndices(cells, &cellsArray);CHKERRQ(ierr);
875   ierr = ISGetIndices(points, &pointsArray);CHKERRQ(ierr);
876   ierr = PetscHMapICreate(&ht);CHKERRQ(ierr);
877   for (v = vStart; v < vEnd; ++v) {
878     PetscInt localIndex = 0;
879     PetscInt dof, off, i, j, k, l;
880 
881     ierr = PetscHMapIClear(ht);CHKERRQ(ierr);
882     ierr = PetscSectionGetDof(cellCounts, v, &dof);CHKERRQ(ierr);
883     ierr = PetscSectionGetOffset(cellCounts, v, &off);CHKERRQ(ierr);
884     if (dof <= 0) continue;
885 
886     /* Calculate the global numbers of the artificial BC dofs here first */
887     ierr = patch->patchconstructop((void*)patch, dm, v, ownedpts); CHKERRQ(ierr);
888     ierr = PCPatchCompleteCellPatch(pc, ownedpts, seenpts); CHKERRQ(ierr);
889     ierr = PCPatchGetPointDofs(pc, ownedpts, owneddofs, v, patch->exclude_subspace); CHKERRQ(ierr);
890     ierr = PCPatchGetPointDofs(pc, seenpts, seendofs, v, -1); CHKERRQ(ierr);
891     ierr = PCPatchComputeSetDifference_Private(owneddofs, seendofs, artificialbcs); CHKERRQ(ierr);
892     if (patch->viewPatches) {
893       PetscHSetI globalbcdofs;
894       PetscHashIter hi;
895       MPI_Comm comm = PetscObjectComm((PetscObject)pc);
896 
897       ierr = PetscHSetICreate(&globalbcdofs);CHKERRQ(ierr);
898       ierr = PetscSynchronizedPrintf(comm, "Patch %d: owned dofs:\n", v); CHKERRQ(ierr);
899       PetscHashIterBegin(owneddofs, hi);
900       while (!PetscHashIterAtEnd(owneddofs, hi)) {
901         PetscInt globalDof;
902 
903         PetscHashIterGetKey(owneddofs, hi, globalDof);
904         PetscHashIterNext(owneddofs, hi);
905         ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
906       }
907       ierr = PetscSynchronizedPrintf(comm, "\n"); CHKERRQ(ierr);
908       ierr = PetscSynchronizedPrintf(comm, "Patch %d: seen dofs:\n", v); CHKERRQ(ierr);
909       PetscHashIterBegin(seendofs, hi);
910       while (!PetscHashIterAtEnd(seendofs, hi)) {
911         PetscInt globalDof;
912         PetscBool flg;
913 
914         PetscHashIterGetKey(seendofs, hi, globalDof);
915         PetscHashIterNext(seendofs, hi);
916         ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
917 
918         ierr = PetscHSetIHas(globalBcs, globalDof, &flg);CHKERRQ(ierr);
919         if (flg) {ierr = PetscHSetIAdd(globalbcdofs, globalDof);CHKERRQ(ierr);}
920       }
921       ierr = PetscSynchronizedPrintf(comm, "\n"); CHKERRQ(ierr);
922       ierr = PetscSynchronizedPrintf(comm, "Patch %d: global BCs:\n", v); CHKERRQ(ierr);
923       ierr = PetscHSetIGetSize(globalbcdofs, &numBcs);CHKERRQ(ierr);
924       if (numBcs > 0) {
925         PetscHashIterBegin(globalbcdofs, hi);
926         while (!PetscHashIterAtEnd(globalbcdofs, hi)) {
927           PetscInt globalDof;
928           PetscHashIterGetKey(globalbcdofs, hi, globalDof);
929           PetscHashIterNext(globalbcdofs, hi);
930           ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof);CHKERRQ(ierr);
931         }
932       }
933       ierr = PetscSynchronizedPrintf(comm, "\n");CHKERRQ(ierr);
934       ierr = PetscSynchronizedPrintf(comm, "Patch %d: artificial BCs:\n", v);CHKERRQ(ierr);
935       ierr = PetscHSetIGetSize(artificialbcs, &numBcs);CHKERRQ(ierr);
936       if (numBcs > 0) {
937         PetscHashIterBegin(artificialbcs, hi);
938         while (!PetscHashIterAtEnd(artificialbcs, hi)) {
939           PetscInt globalDof;
940           PetscHashIterGetKey(artificialbcs, hi, globalDof);
941           PetscHashIterNext(artificialbcs, hi);
942           ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
943         }
944       }
945       ierr = PetscSynchronizedPrintf(comm, "\n\n"); CHKERRQ(ierr);
946       ierr = PetscHSetIDestroy(&globalbcdofs);CHKERRQ(ierr);
947     }
948    for (k = 0; k < patch->nsubspaces; ++k) {
949       const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
950       PetscInt        nodesPerCell   = patch->nodesPerCell[k];
951       PetscInt        subspaceOffset = patch->subspaceOffsets[k];
952       PetscInt        bs             = patch->bs[k];
953 
954       for (i = off; i < off + dof; ++i) {
955         /* Walk over the cells in this patch. */
956         const PetscInt c    = cellsArray[i];
957         PetscInt       cell = c;
958 
959         /* TODO Change this to an IS */
960         if (cellNumbering) {
961           ierr = PetscSectionGetDof(cellNumbering, c, &cell);CHKERRQ(ierr);
962           if (cell <= 0) SETERRQ1(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_OUTOFRANGE, "Cell %D doesn't appear in cell numbering map", c);
963           ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);
964         }
965         newCellsArray[i] = cell;
966         for (j = 0; j < nodesPerCell; ++j) {
967           /* For each global dof, map it into contiguous local storage. */
968           const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + subspaceOffset;
969           /* finally, loop over block size */
970           for (l = 0; l < bs; ++l) {
971             PetscInt  localDof;
972             PetscBool isGlobalBcDof, isArtificialBcDof;
973 
974             /* first, check if this is either a globally enforced or locally enforced BC dof */
975             ierr = PetscHSetIHas(globalBcs, globalDof + l, &isGlobalBcDof);CHKERRQ(ierr);
976             ierr = PetscHSetIHas(artificialbcs, globalDof + l, &isArtificialBcDof);CHKERRQ(ierr);
977 
978             /* if it's either, don't ever give it a local dof number */
979             if (isGlobalBcDof || isArtificialBcDof) {
980               dofsArray[globalIndex++] = -1; /* don't use this in assembly in this patch */
981             } else {
982               ierr = PetscHMapIGet(ht, globalDof + l, &localDof);CHKERRQ(ierr);
983               if (localDof == -1) {
984                 localDof = localIndex++;
985                 ierr = PetscHMapISet(ht, globalDof + l, localDof);CHKERRQ(ierr);
986               }
987               if ( globalIndex >= numDofs ) SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Found more dofs %D than expected %D", globalIndex+1, numDofs);
988               /* And store. */
989               dofsArray[globalIndex++] = localDof;
990             }
991           }
992         }
993       }
994     }
995     /* How many local dofs in this patch? */
996     ierr = PetscHMapIGetSize(ht, &dof);CHKERRQ(ierr);
997     ierr = PetscSectionSetDof(gtolCounts, v, dof);CHKERRQ(ierr);
998   }
999   if (globalIndex != numDofs) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Expected number of dofs (%d) doesn't match found number (%d)", numDofs, globalIndex);
1000   ierr = PetscSectionSetUp(gtolCounts);CHKERRQ(ierr);
1001   ierr = PetscSectionGetStorageSize(gtolCounts, &numGlobalDofs);CHKERRQ(ierr);
1002   ierr = PetscMalloc1(numGlobalDofs, &globalDofsArray);CHKERRQ(ierr);
1003 
1004   /* Now populate the global to local map.  This could be merged into the above loop if we were willing to deal with reallocs. */
1005   for (v = vStart; v < vEnd; ++v) {
1006     PetscHashIter hi;
1007     PetscInt       dof, off, Np, ooff, i, j, k, l;
1008 
1009     ierr = PetscHMapIClear(ht);CHKERRQ(ierr);
1010     ierr = PetscSectionGetDof(cellCounts, v, &dof);CHKERRQ(ierr);
1011     ierr = PetscSectionGetOffset(cellCounts, v, &off);CHKERRQ(ierr);
1012     ierr = PetscSectionGetDof(pointCounts, v, &Np);CHKERRQ(ierr);
1013     ierr = PetscSectionGetOffset(pointCounts, v, &ooff);CHKERRQ(ierr);
1014     if (dof <= 0) continue;
1015 
1016     for (k = 0; k < patch->nsubspaces; ++k) {
1017       const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
1018       PetscInt        nodesPerCell   = patch->nodesPerCell[k];
1019       PetscInt        subspaceOffset = patch->subspaceOffsets[k];
1020       PetscInt        bs             = patch->bs[k];
1021 
1022       for (i = off; i < off + dof; ++i) {
1023         /* Reconstruct mapping of global-to-local on this patch. */
1024         const PetscInt c    = cellsArray[i];
1025         PetscInt       cell = c;
1026 
1027         if (cellNumbering) {ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);}
1028         for (j = 0; j < nodesPerCell; ++j) {
1029           for (l = 0; l < bs; ++l) {
1030             const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + l + subspaceOffset;
1031             const PetscInt localDof  = dofsArray[key++];
1032 
1033             if (localDof >= 0) {ierr = PetscHMapISet(ht, globalDof, localDof);CHKERRQ(ierr);}
1034           }
1035         }
1036       }
1037 
1038       /* Shove it in the output data structure. */
1039       PetscInt goff;
1040 
1041       ierr = PetscSectionGetOffset(gtolCounts, v, &goff);CHKERRQ(ierr);
1042       PetscHashIterBegin(ht, hi);
1043       while (!PetscHashIterAtEnd(ht, hi)) {
1044         PetscInt globalDof, localDof;
1045 
1046         PetscHashIterGetKey(ht, hi, globalDof);
1047         PetscHashIterGetVal(ht, hi, localDof);
1048         if (globalDof >= 0) globalDofsArray[goff + localDof] = globalDof;
1049         PetscHashIterNext(ht, hi);
1050       }
1051 
1052       for (p = 0; p < Np; ++p) {
1053         const PetscInt point = pointsArray[ooff + p];
1054         PetscInt       globalDof, localDof;
1055 
1056         ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, point, NULL, &globalDof);CHKERRQ(ierr);
1057         ierr = PetscHMapIGet(ht, globalDof, &localDof);CHKERRQ(ierr);
1058         offsArray[(ooff + p)*Nf + k] = localDof;
1059       }
1060     }
1061 
1062     ierr = PetscHSetIDestroy(&ownedpts);CHKERRQ(ierr);
1063     ierr = PetscHSetIDestroy(&seenpts);CHKERRQ(ierr);
1064     ierr = PetscHSetIDestroy(&owneddofs);CHKERRQ(ierr);
1065     ierr = PetscHSetIDestroy(&seendofs);CHKERRQ(ierr);
1066     ierr = PetscHSetIDestroy(&artificialbcs);CHKERRQ(ierr);
1067 
1068       /* At this point, we have a hash table ht built that maps globalDof -> localDof.
1069      We need to create the dof table laid out cellwise first, then by subspace,
1070      as the assembler assembles cell-wise and we need to stuff the different
1071      contributions of the different function spaces to the right places. So we loop
1072      over cells, then over subspaces. */
1073     if (patch->nsubspaces > 1) { /* for nsubspaces = 1, data we need is already in dofsArray */
1074       for (i = off; i < off + dof; ++i) {
1075         const PetscInt c    = cellsArray[i];
1076         PetscInt       cell = c;
1077 
1078         if (cellNumbering) {ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);}
1079         for (k = 0; k < patch->nsubspaces; ++k) {
1080           const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
1081           PetscInt        nodesPerCell   = patch->nodesPerCell[k];
1082           PetscInt        subspaceOffset = patch->subspaceOffsets[k];
1083           PetscInt        bs             = patch->bs[k];
1084 
1085           for (j = 0; j < nodesPerCell; ++j) {
1086             for (l = 0; l < bs; ++l) {
1087               const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + l + subspaceOffset;
1088               PetscInt       localDof;
1089 
1090               ierr = PetscHMapIGet(ht, globalDof, &localDof);CHKERRQ(ierr);
1091               /* If it's not in the hash table, i.e. is a BC dof,
1092                then the PetscHSetIMap above gives -1, which matches
1093                exactly the convention for PETSc's matrix assembly to
1094                ignore the dof. So we don't need to do anything here */
1095               asmArray[asmKey++] = localDof;
1096             }
1097           }
1098         }
1099       }
1100     }
1101   }
1102   if (1 == patch->nsubspaces) {ierr = PetscMemcpy(asmArray, dofsArray, numDofs * sizeof(PetscInt));CHKERRQ(ierr);}
1103 
1104   ierr = PetscHMapIDestroy(&ht);CHKERRQ(ierr);
1105   ierr = ISRestoreIndices(cells, &cellsArray);CHKERRQ(ierr);
1106   ierr = ISRestoreIndices(points, &pointsArray);CHKERRQ(ierr);
1107   ierr = PetscFree(dofsArray);CHKERRQ(ierr);
1108   /* Create placeholder section for map from points to patch dofs */
1109   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->patchSection);CHKERRQ(ierr);
1110   ierr = PetscSectionSetNumFields(patch->patchSection, patch->nsubspaces);CHKERRQ(ierr);
1111   ierr = PetscSectionGetChart(patch->dofSection[0], &pStart, &pEnd);CHKERRQ(ierr);
1112   ierr = PetscSectionSetChart(patch->patchSection, pStart, pEnd);CHKERRQ(ierr);
1113   for (p = pStart; p < pEnd; ++p) {
1114     PetscInt dof, fdof, f;
1115 
1116     ierr = PetscSectionGetDof(patch->dofSection[0], p, &dof);CHKERRQ(ierr);
1117     ierr = PetscSectionSetDof(patch->patchSection, p, dof);CHKERRQ(ierr);
1118     for (f = 0; f < patch->nsubspaces; ++f) {
1119       ierr = PetscSectionGetFieldDof(patch->dofSection[0], p, f, &fdof);
1120       if (ierr == 0) {
1121         ierr = PetscSectionSetFieldDof(patch->patchSection, p, f, fdof);CHKERRQ(ierr);
1122       }
1123       else {
1124         /* assume only one field */
1125         ierr = PetscSectionSetFieldDof(patch->patchSection, p, f, dof);CHKERRQ(ierr);
1126       }
1127     }
1128   }
1129   ierr = PetscSectionSetUp(patch->patchSection);CHKERRQ(ierr);
1130   ierr = PetscSectionSetUseFieldOffsets(patch->patchSection, PETSC_TRUE);CHKERRQ(ierr);
1131   /* Replace cell indices with firedrake-numbered ones. */
1132   ierr = ISGeneralSetIndices(cells, numCells, (const PetscInt *) newCellsArray, PETSC_OWN_POINTER);CHKERRQ(ierr);
1133   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalDofs, globalDofsArray, PETSC_OWN_POINTER, &patch->gtol);CHKERRQ(ierr);
1134   ierr = PetscObjectSetName((PetscObject) patch->gtol, "Global Indices");CHKERRQ(ierr);
1135   ierr = PetscSectionViewFromOptions(patch->gtolCounts, (PetscObject) pc, "-pc_patch_g2l_view");CHKERRQ(ierr);
1136   ierr = ISViewFromOptions(patch->gtol, (PetscObject) pc, "-pc_patch_g2l_view");CHKERRQ(ierr);
1137   ierr = ISCreateGeneral(PETSC_COMM_SELF, numDofs, asmArray, PETSC_OWN_POINTER, &patch->dofs);CHKERRQ(ierr);
1138   ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints*Nf, offsArray, PETSC_OWN_POINTER, &patch->offs);CHKERRQ(ierr);
1139   PetscFunctionReturn(0);
1140 }
1141 
1142 static PetscErrorCode PCPatchZeroFillMatrix_Private(Mat mat, const PetscInt ncell, const PetscInt ndof, const PetscInt *dof)
1143 {
1144   const PetscScalar *values = NULL;
1145   PetscInt           rows, c, i;
1146   PetscErrorCode     ierr;
1147 
1148   PetscFunctionBegin;
1149   ierr = PetscCalloc1(ndof*ndof, &values);CHKERRQ(ierr);
1150   for (c = 0; c < ncell; ++c) {
1151     const PetscInt *idx = &dof[ndof*c];
1152     ierr = MatSetValues(mat, ndof, idx, ndof, idx, values, INSERT_VALUES);CHKERRQ(ierr);
1153   }
1154   ierr = MatGetLocalSize(mat, &rows, NULL);CHKERRQ(ierr);
1155   for (i = 0; i < rows; ++i) {
1156     ierr = MatSetValues(mat, 1, &i, 1, &i, values, INSERT_VALUES);CHKERRQ(ierr);
1157   }
1158   ierr = MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1159   ierr = MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1160   ierr = PetscFree(values);CHKERRQ(ierr);
1161   PetscFunctionReturn(0);
1162 }
1163 
1164 static PetscErrorCode PCPatchCreateMatrix_Private(PC pc, PetscInt point, Mat *mat)
1165 {
1166   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1167   Vec            x, y;
1168   PetscBool      flg;
1169   PetscInt       csize, rsize;
1170   const char    *prefix = NULL;
1171   PetscErrorCode ierr;
1172 
1173   PetscFunctionBegin;
1174   x = patch->patchX[point];
1175   y = patch->patchY[point];
1176   ierr = VecGetSize(x, &csize);CHKERRQ(ierr);
1177   ierr = VecGetSize(y, &rsize);CHKERRQ(ierr);
1178   ierr = MatCreate(PETSC_COMM_SELF, mat);CHKERRQ(ierr);
1179   ierr = PCGetOptionsPrefix(pc, &prefix);CHKERRQ(ierr);
1180   ierr = MatSetOptionsPrefix(*mat, prefix);CHKERRQ(ierr);
1181   ierr = MatAppendOptionsPrefix(*mat, "pc_patch_sub_");CHKERRQ(ierr);
1182   if (patch->sub_mat_type)       {ierr = MatSetType(*mat, patch->sub_mat_type);CHKERRQ(ierr);}
1183   else if (!patch->sub_mat_type) {ierr = MatSetType(*mat, MATDENSE);CHKERRQ(ierr);}
1184   ierr = MatSetSizes(*mat, rsize, csize, rsize, csize);CHKERRQ(ierr);
1185   ierr = PetscObjectTypeCompare((PetscObject) *mat, MATDENSE, &flg);CHKERRQ(ierr);
1186   if (!flg) {ierr = PetscObjectTypeCompare((PetscObject)*mat, MATSEQDENSE, &flg);CHKERRQ(ierr);}
1187   /* Sparse patch matrices */
1188   if (!flg) {
1189     PetscBT         bt;
1190     PetscInt       *dnnz      = NULL;
1191     const PetscInt *dofsArray = NULL;
1192     PetscInt        pStart, pEnd, ncell, offset, c, i, j;
1193 
1194     ierr = ISGetIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1195     ierr = PetscSectionGetChart(patch->cellCounts, &pStart, &pEnd);CHKERRQ(ierr);
1196     point += pStart;
1197     if (point >= pEnd) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Operator point %D not in [%D, %D)\n", point, pStart, pEnd);CHKERRQ(ierr);
1198     ierr = PetscSectionGetDof(patch->cellCounts, point, &ncell);CHKERRQ(ierr);
1199     ierr = PetscSectionGetOffset(patch->cellCounts, point, &offset);CHKERRQ(ierr);
1200     ierr = PetscCalloc1(rsize, &dnnz);CHKERRQ(ierr);
1201     ierr = PetscLogEventBegin(PC_Patch_Prealloc, pc, 0, 0, 0);CHKERRQ(ierr);
1202     /* XXX: This uses N^2 bits to store the sparsity pattern on a
1203      * patch.  This is probably OK if the patches are not too big,
1204      * but could use quite a bit of memory for planes in 3D.
1205      * Should we switch based on the value of rsize to a
1206      * hash-table (slower, but more memory efficient) approach? */
1207     ierr = PetscBTCreate(rsize*rsize, &bt);CHKERRQ(ierr);
1208     for (c = 0; c < ncell; ++c) {
1209       const PetscInt *idx = dofsArray + (offset + c)*patch->totalDofsPerCell;
1210       for (i = 0; i < patch->totalDofsPerCell; ++i) {
1211         const PetscInt row = idx[i];
1212         if (row < 0) continue;
1213         for (j = 0; j < patch->totalDofsPerCell; ++j) {
1214           const PetscInt col = idx[j];
1215           const PetscInt key = row*rsize + col;
1216           if (col < 0) continue;
1217           if (!PetscBTLookupSet(bt, key)) ++dnnz[row];
1218         }
1219       }
1220     }
1221     ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
1222     ierr = MatXAIJSetPreallocation(*mat, 1, dnnz, NULL, NULL, NULL);CHKERRQ(ierr);
1223     ierr = PetscFree(dnnz);CHKERRQ(ierr);
1224     ierr = PCPatchZeroFillMatrix_Private(*mat, ncell, patch->totalDofsPerCell, &dofsArray[offset*patch->totalDofsPerCell]);CHKERRQ(ierr);
1225     ierr = PetscLogEventEnd(PC_Patch_Prealloc, pc, 0, 0, 0);CHKERRQ(ierr);
1226     ierr = ISRestoreIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1227   }
1228   ierr = MatSetUp(*mat);CHKERRQ(ierr);
1229   PetscFunctionReturn(0);
1230 }
1231 
1232 static PetscErrorCode PCPatchComputeOperator_DMPlex_Private(PC pc, PetscInt patchNum, Mat J, IS cellIS, PetscInt n, const PetscInt *l2p, void *ctx)
1233 {
1234   PC_PATCH       *patch = (PC_PATCH *) pc->data;
1235   DM              dm;
1236   PetscSection    s;
1237   const PetscInt *parray, *oarray;
1238   PetscInt        Nf = patch->nsubspaces, Np, poff, p, f;
1239   PetscErrorCode  ierr;
1240 
1241   PetscFunctionBegin;
1242   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
1243   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
1244   /* Set offset into patch */
1245   ierr = PetscSectionGetDof(patch->pointCounts, patchNum, &Np);CHKERRQ(ierr);
1246   ierr = PetscSectionGetOffset(patch->pointCounts, patchNum, &poff);CHKERRQ(ierr);
1247   ierr = ISGetIndices(patch->points, &parray);CHKERRQ(ierr);
1248   ierr = ISGetIndices(patch->offs,   &oarray);CHKERRQ(ierr);
1249   for (f = 0; f < Nf; ++f) {
1250     for (p = 0; p < Np; ++p) {
1251       const PetscInt point = parray[poff+p];
1252       PetscInt       dof;
1253 
1254       ierr = PetscSectionGetFieldDof(patch->patchSection, point, f, &dof);CHKERRQ(ierr);
1255       ierr = PetscSectionSetFieldOffset(patch->patchSection, point, f, oarray[(poff+p)*Nf+f]);CHKERRQ(ierr);
1256       if (patch->nsubspaces == 1) {ierr = PetscSectionSetOffset(patch->patchSection, point, oarray[(poff+p)*Nf+f]);CHKERRQ(ierr);}
1257       else                        {ierr = PetscSectionSetOffset(patch->patchSection, point, -1);CHKERRQ(ierr);}
1258     }
1259   }
1260   ierr = ISRestoreIndices(patch->points, &parray);CHKERRQ(ierr);
1261   ierr = ISRestoreIndices(patch->offs,   &oarray);CHKERRQ(ierr);
1262   if (patch->viewSection) {ierr = ObjectView((PetscObject) patch->patchSection, patch->viewerSection, patch->formatSection);CHKERRQ(ierr);}
1263   /* TODO Shut off MatViewFromOptions() in MatAssemblyEnd() here */
1264   ierr = DMPlexComputeJacobian_Patch_Internal(pc->dm, patch->patchSection, patch->patchSection, cellIS, 0.0, 0.0, NULL, NULL, J, J, ctx);CHKERRQ(ierr);
1265   PetscFunctionReturn(0);
1266 }
1267 
1268 static PetscErrorCode PCPatchComputeOperator_Private(PC pc, Mat mat, PetscInt point)
1269 {
1270   PC_PATCH       *patch = (PC_PATCH *) pc->data;
1271   const PetscInt *dofsArray;
1272   const PetscInt *cellsArray;
1273   PetscInt        ncell, offset, pStart, pEnd;
1274   PetscErrorCode  ierr;
1275 
1276   PetscFunctionBegin;
1277   ierr = PetscLogEventBegin(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1278   if (!patch->usercomputeop) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Must call PCPatchSetComputeOperator() to set user callback\n");
1279   ierr = ISGetIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1280   ierr = ISGetIndices(patch->cells, &cellsArray);CHKERRQ(ierr);
1281   ierr = PetscSectionGetChart(patch->cellCounts, &pStart, &pEnd);CHKERRQ(ierr);
1282 
1283   point += pStart;
1284   if (point >= pEnd) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Operator point %D not in [%D, %D)\n", point, pStart, pEnd);CHKERRQ(ierr);
1285 
1286   ierr = PetscSectionGetDof(patch->cellCounts, point, &ncell);CHKERRQ(ierr);
1287   ierr = PetscSectionGetOffset(patch->cellCounts, point, &offset);CHKERRQ(ierr);
1288   if (ncell <= 0) {
1289     ierr = PetscLogEventEnd(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1290     PetscFunctionReturn(0);
1291   }
1292   PetscStackPush("PCPatch user callback");
1293   /* Cannot reuse the same IS because the geometry info is being cached in it */
1294   ierr = ISCreateGeneral(PETSC_COMM_SELF, ncell, cellsArray + offset, PETSC_USE_POINTER, &patch->cellIS);CHKERRQ(ierr);
1295   ierr = patch->usercomputeop(pc, point, mat, patch->cellIS, ncell*patch->totalDofsPerCell, dofsArray + offset*patch->totalDofsPerCell, patch->usercomputectx);CHKERRQ(ierr);
1296   PetscStackPop;
1297   ierr = ISDestroy(&patch->cellIS);CHKERRQ(ierr);
1298   ierr = ISRestoreIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1299   ierr = ISRestoreIndices(patch->cells, &cellsArray);CHKERRQ(ierr);
1300   if (patch->viewMatrix) {
1301     char name[PETSC_MAX_PATH_LEN];
1302 
1303     ierr = PetscSNPrintf(name, PETSC_MAX_PATH_LEN-1, "Patch matrix for Point %D", point);CHKERRQ(ierr);
1304     ierr = PetscObjectSetName((PetscObject) mat, name);CHKERRQ(ierr);
1305     ierr = ObjectView((PetscObject) mat, patch->viewerMatrix, patch->formatMatrix);CHKERRQ(ierr);
1306   }
1307   ierr = PetscLogEventEnd(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1308   PetscFunctionReturn(0);
1309 }
1310 
1311 static PetscErrorCode PCPatch_ScatterLocal_Private(PC pc, PetscInt p, Vec x, Vec y, InsertMode mode, ScatterMode scat)
1312 {
1313   PC_PATCH          *patch     = (PC_PATCH *) pc->data;
1314   const PetscScalar *xArray    = NULL;
1315   PetscScalar       *yArray    = NULL;
1316   const PetscInt    *gtolArray = NULL;
1317   PetscInt           dof, offset, lidx;
1318   PetscErrorCode     ierr;
1319 
1320   PetscFunctionBeginHot;
1321   ierr = PetscLogEventBegin(PC_Patch_Scatter, pc, 0, 0, 0);CHKERRQ(ierr);
1322   ierr = VecGetArrayRead(x, &xArray);CHKERRQ(ierr);
1323   ierr = VecGetArray(y, &yArray);CHKERRQ(ierr);
1324   ierr = PetscSectionGetDof(patch->gtolCounts, p, &dof);CHKERRQ(ierr);
1325   ierr = PetscSectionGetOffset(patch->gtolCounts, p, &offset);CHKERRQ(ierr);
1326   ierr = ISGetIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
1327   if (mode == INSERT_VALUES && scat != SCATTER_FORWARD) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Can't insert if not scattering forward\n");
1328   if (mode == ADD_VALUES    && scat != SCATTER_REVERSE) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Can't add if not scattering reverse\n");
1329   for (lidx = 0; lidx < dof; ++lidx) {
1330     const PetscInt gidx = gtolArray[offset+lidx];
1331 
1332     if (mode == INSERT_VALUES) yArray[lidx]  = xArray[gidx]; /* Forward */
1333     else                       yArray[gidx] += xArray[lidx]; /* Reverse */
1334   }
1335   ierr = ISRestoreIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
1336   ierr = VecRestoreArrayRead(x, &xArray);CHKERRQ(ierr);
1337   ierr = VecRestoreArray(y, &yArray);CHKERRQ(ierr);
1338   ierr = PetscLogEventEnd(PC_Patch_Scatter, pc, 0, 0, 0);CHKERRQ(ierr);
1339   PetscFunctionReturn(0);
1340 }
1341 
1342 static PetscErrorCode PCSetUp_PATCH(PC pc)
1343 {
1344   PC_PATCH       *patch   = (PC_PATCH *) pc->data;
1345   PetscInt        i;
1346   const char     *prefix;
1347   PetscErrorCode  ierr;
1348 
1349   PetscFunctionBegin;
1350   if (!pc->setupcalled) {
1351     PetscInt pStart, pEnd, p;
1352     PetscInt localSize;
1353 
1354     ierr = PetscLogEventBegin(PC_Patch_CreatePatches, pc, 0, 0, 0);CHKERRQ(ierr);
1355 
1356     if (!patch->nsubspaces) {
1357       DM           dm;
1358       PetscDS      prob;
1359       PetscSection s;
1360       PetscInt     cStart, cEnd, c, Nf, f, numGlobalBcs = 0, *globalBcs, *Nb, totNb = 0, **cellDofs;
1361 
1362       ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
1363       if (!dm) SETERRQ(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_WRONG, "Must set DM for PCPATCH or call PCPatchSetDiscretisationInfo()");
1364       ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
1365       ierr = PetscSectionGetNumFields(s, &Nf);CHKERRQ(ierr);
1366       ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
1367       for (p = pStart; p < pEnd; ++p) {
1368         PetscInt cdof;
1369         ierr = PetscSectionGetConstraintDof(s, p, &cdof);CHKERRQ(ierr);
1370         numGlobalBcs += cdof;
1371       }
1372       ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1373       ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1374       ierr = PetscMalloc3(Nf, &Nb, Nf, &cellDofs, numGlobalBcs, &globalBcs);CHKERRQ(ierr);
1375       for (f = 0; f < Nf; ++f) {
1376         PetscFE        fe;
1377         PetscDualSpace sp;
1378         PetscInt       cdoff = 0;
1379 
1380         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1381         /* ierr = PetscFEGetNumComponents(fe, &Nc[f]);CHKERRQ(ierr); */
1382         ierr = PetscFEGetDualSpace(fe, &sp);CHKERRQ(ierr);
1383         ierr = PetscDualSpaceGetDimension(sp, &Nb[f]);CHKERRQ(ierr);
1384         totNb += Nb[f];
1385 
1386         ierr = PetscMalloc1((cEnd-cStart)*Nb[f], &cellDofs[f]);CHKERRQ(ierr);
1387         for (c = cStart; c < cEnd; ++c) {
1388           PetscInt *closure = NULL;
1389           PetscInt  clSize  = 0, cl;
1390 
1391           ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &clSize, &closure);CHKERRQ(ierr);
1392           for (cl = 0; cl < clSize*2; cl += 2) {
1393             const PetscInt p = closure[cl];
1394             PetscInt       fdof, d, foff;
1395 
1396             ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
1397             ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
1398             for (d = 0; d < fdof; ++d, ++cdoff) cellDofs[f][cdoff] = foff + d;
1399           }
1400           ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &clSize, &closure);CHKERRQ(ierr);
1401         }
1402         if (cdoff != (cEnd-cStart)*Nb[f]) SETERRQ4(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_SIZ, "Total number of cellDofs %D for field %D should be Nc (%D) * cellDof (%D)", cdoff, f, cEnd-cStart, Nb[f]);
1403       }
1404       numGlobalBcs = 0;
1405       for (p = pStart; p < pEnd; ++p) {
1406         const PetscInt *ind;
1407         PetscInt        off, cdof, d;
1408 
1409         ierr = PetscSectionGetOffset(s, p, &off);CHKERRQ(ierr);
1410         ierr = PetscSectionGetConstraintDof(s, p, &cdof);CHKERRQ(ierr);
1411         ierr = PetscSectionGetConstraintIndices(s, p, &ind);CHKERRQ(ierr);
1412         for (d = 0; d < cdof; ++d) globalBcs[numGlobalBcs++] = off + ind[d];
1413       }
1414 
1415       ierr = PCPatchSetDiscretisationInfoCombined(pc, dm, Nb, (const PetscInt **) cellDofs, numGlobalBcs, globalBcs, numGlobalBcs, globalBcs);CHKERRQ(ierr);
1416       for (f = 0; f < Nf; ++f) {
1417         ierr = PetscFree(cellDofs[f]);CHKERRQ(ierr);
1418       }
1419       ierr = PetscFree3(Nb, cellDofs, globalBcs);CHKERRQ(ierr);
1420       ierr = PCPatchSetComputeOperator(pc, PCPatchComputeOperator_DMPlex_Private, NULL);CHKERRQ(ierr);
1421     }
1422 
1423     localSize = patch->subspaceOffsets[patch->nsubspaces];
1424     ierr = VecCreateSeq(PETSC_COMM_SELF, localSize, &patch->localX);CHKERRQ(ierr);
1425     ierr = VecSetUp(patch->localX);CHKERRQ(ierr);
1426     ierr = VecDuplicate(patch->localX, &patch->localY);CHKERRQ(ierr);
1427     ierr = PCPatchCreateCellPatches(pc);CHKERRQ(ierr);
1428     ierr = PCPatchCreateCellPatchDiscretisationInfo(pc);CHKERRQ(ierr);
1429 
1430     /* OK, now build the work vectors */
1431     ierr = PetscSectionGetChart(patch->gtolCounts, &pStart, &pEnd);CHKERRQ(ierr);
1432     ierr = PetscMalloc1(patch->npatch, &patch->patchX);CHKERRQ(ierr);
1433     ierr = PetscMalloc1(patch->npatch, &patch->patchY);CHKERRQ(ierr);
1434     for (p = pStart; p < pEnd; ++p) {
1435       PetscInt dof;
1436 
1437       ierr = PetscSectionGetDof(patch->gtolCounts, p, &dof);CHKERRQ(ierr);
1438       ierr = VecCreateSeq(PETSC_COMM_SELF, dof, &patch->patchX[p-pStart]);CHKERRQ(ierr);
1439       ierr = VecSetUp(patch->patchX[p-pStart]);CHKERRQ(ierr);
1440       ierr = VecCreateSeq(PETSC_COMM_SELF, dof, &patch->patchY[p-pStart]);CHKERRQ(ierr);
1441       ierr = VecSetUp(patch->patchY[p-pStart]);CHKERRQ(ierr);
1442     }
1443     ierr = PetscMalloc1(patch->npatch, &patch->ksp);CHKERRQ(ierr);
1444     ierr = PCGetOptionsPrefix(pc, &prefix);CHKERRQ(ierr);
1445     for (i = 0; i < patch->npatch; ++i) {
1446       PC subpc;
1447 
1448       ierr = KSPCreate(PETSC_COMM_SELF, &patch->ksp[i]);CHKERRQ(ierr);
1449       ierr = KSPSetOptionsPrefix(patch->ksp[i], prefix);CHKERRQ(ierr);
1450       ierr = KSPAppendOptionsPrefix(patch->ksp[i], "sub_");CHKERRQ(ierr);
1451       ierr = PetscObjectIncrementTabLevel((PetscObject) patch->ksp[i], (PetscObject) pc, 1);CHKERRQ(ierr);
1452       ierr = KSPGetPC(patch->ksp[i], &subpc);CHKERRQ(ierr);
1453       ierr = PetscObjectIncrementTabLevel((PetscObject) subpc, (PetscObject) pc, 1);CHKERRQ(ierr);
1454       ierr = PetscLogObjectParent((PetscObject) pc, (PetscObject) patch->ksp[i]);CHKERRQ(ierr);
1455     }
1456     if (patch->save_operators) {
1457       ierr = PetscMalloc1(patch->npatch, &patch->mat);CHKERRQ(ierr);
1458       for (i = 0; i < patch->npatch; ++i) {
1459         ierr = PCPatchCreateMatrix_Private(pc, i, &patch->mat[i]);CHKERRQ(ierr);
1460       }
1461     }
1462     ierr = PetscLogEventEnd(PC_Patch_CreatePatches, pc, 0, 0, 0);CHKERRQ(ierr);
1463 
1464     /* If desired, calculate weights for dof multiplicity */
1465     if (patch->partition_of_unity) {
1466       ierr = VecDuplicate(patch->localX, &patch->dof_weights);CHKERRQ(ierr);
1467       for (i = 0; i < patch->npatch; ++i) {
1468         PetscInt dof;
1469 
1470         ierr = PetscSectionGetDof(patch->gtolCounts, i+pStart, &dof);CHKERRQ(ierr);
1471         if (dof <= 0) continue;
1472         ierr = VecSet(patch->patchX[i], 1.0);CHKERRQ(ierr);
1473         ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->patchX[i], patch->dof_weights, ADD_VALUES, SCATTER_REVERSE);CHKERRQ(ierr);
1474       }
1475       ierr = VecReciprocal(patch->dof_weights);CHKERRQ(ierr);
1476     }
1477   }
1478   if (patch->save_operators) {
1479     for (i = 0; i < patch->npatch; ++i) {
1480       ierr = MatZeroEntries(patch->mat[i]);CHKERRQ(ierr);
1481       ierr = PCPatchComputeOperator_Private(pc, patch->mat[i], i);CHKERRQ(ierr);
1482       ierr = KSPSetOperators(patch->ksp[i], patch->mat[i], patch->mat[i]);CHKERRQ(ierr);
1483     }
1484   }
1485   if (!pc->setupcalled && patch->optionsSet) for (i = 0; i < patch->npatch; ++i) {ierr = KSPSetFromOptions(patch->ksp[i]);CHKERRQ(ierr);}
1486   PetscFunctionReturn(0);
1487 }
1488 
1489 static PetscErrorCode PCApply_PATCH(PC pc, Vec x, Vec y)
1490 {
1491   PC_PATCH          *patch    = (PC_PATCH *) pc->data;
1492   const PetscScalar *globalX  = NULL;
1493   PetscScalar       *localX   = NULL;
1494   PetscScalar       *globalY  = NULL;
1495   const PetscInt    *bcNodes  = NULL;
1496   PetscInt           nsweep   = patch->symmetrise_sweep ? 2 : 1;
1497   PetscInt           start[2] = {0, 0};
1498   PetscInt           end[2]   = {-1, -1};
1499   const PetscInt     inc[2]   = {1, -1};
1500   const PetscScalar *localY;
1501   const PetscInt    *iterationSet;
1502   PetscInt           pStart, numBcs, n, sweep, bc, j;
1503   PetscErrorCode     ierr;
1504 
1505   PetscFunctionBegin;
1506   ierr = PetscLogEventBegin(PC_Patch_Apply, pc, 0, 0, 0);CHKERRQ(ierr);
1507   ierr = PetscOptionsPushGetViewerOff(PETSC_TRUE);CHKERRQ(ierr);
1508   end[0]   = patch->npatch;
1509   start[1] = patch->npatch-1;
1510   if (patch->user_patches) {
1511     ierr = ISGetLocalSize(patch->iterationSet, &end[0]);CHKERRQ(ierr);
1512     start[1] = end[0] - 1;
1513     ierr = ISGetIndices(patch->iterationSet, &iterationSet);CHKERRQ(ierr);
1514   }
1515   /* Scatter from global space into overlapped local spaces */
1516   ierr = VecGetArrayRead(x, &globalX);CHKERRQ(ierr);
1517   ierr = VecGetArray(patch->localX, &localX);CHKERRQ(ierr);
1518   ierr = PetscSFBcastBegin(patch->defaultSF, MPIU_SCALAR, globalX, localX);CHKERRQ(ierr);
1519   ierr = PetscSFBcastEnd(patch->defaultSF, MPIU_SCALAR, globalX, localX);CHKERRQ(ierr);
1520   ierr = VecRestoreArrayRead(x, &globalX);CHKERRQ(ierr);
1521   ierr = VecRestoreArray(patch->localX, &localX);CHKERRQ(ierr);
1522 
1523   ierr = VecSet(patch->localY, 0.0);CHKERRQ(ierr);
1524   ierr = PetscSectionGetChart(patch->gtolCounts, &pStart, NULL);CHKERRQ(ierr);
1525   for (sweep = 0; sweep < nsweep; sweep++) {
1526     for (j = start[sweep]; j*inc[sweep] < end[sweep]*inc[sweep]; j += inc[sweep]) {
1527       PetscInt i       = patch->user_patches ? iterationSet[j] : j;
1528       PetscInt start, len;
1529 
1530       ierr = PetscSectionGetDof(patch->gtolCounts, i+pStart, &len);CHKERRQ(ierr);
1531       ierr = PetscSectionGetOffset(patch->gtolCounts, i+pStart, &start);CHKERRQ(ierr);
1532       /* TODO: Squash out these guys in the setup as well. */
1533       if (len <= 0) continue;
1534       /* TODO: Do we need different scatters for X and Y? */
1535       ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->localX, patch->patchX[i], INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
1536       if (!patch->save_operators) {
1537         Mat mat;
1538 
1539         ierr = PCPatchCreateMatrix_Private(pc, i, &mat);CHKERRQ(ierr);
1540         /* Populate operator here. */
1541         ierr = PCPatchComputeOperator_Private(pc, mat, i);CHKERRQ(ierr);
1542         ierr = KSPSetOperators(patch->ksp[i], mat, mat);
1543         /* Drop reference so the KSPSetOperators below will blow it away. */
1544         ierr = MatDestroy(&mat);CHKERRQ(ierr);
1545       }
1546       ierr = PetscLogEventBegin(PC_Patch_Solve, pc, 0, 0, 0);CHKERRQ(ierr);
1547       ierr = KSPSolve(patch->ksp[i], patch->patchX[i], patch->patchY[i]);CHKERRQ(ierr);
1548       ierr = PetscLogEventEnd(PC_Patch_Solve, pc, 0, 0, 0);CHKERRQ(ierr);
1549 
1550       if (!patch->save_operators) {
1551         PC pc;
1552         ierr = KSPSetOperators(patch->ksp[i], NULL, NULL);CHKERRQ(ierr);
1553         ierr = KSPGetPC(patch->ksp[i], &pc);CHKERRQ(ierr);
1554         /* Destroy PC context too, otherwise the factored matrix hangs around. */
1555         ierr = PCReset(pc);CHKERRQ(ierr);
1556       }
1557 
1558       ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->patchY[i], patch->localY, ADD_VALUES, SCATTER_REVERSE);CHKERRQ(ierr);
1559     }
1560   }
1561   if (patch->user_patches) {ierr = ISRestoreIndices(patch->iterationSet, &iterationSet);CHKERRQ(ierr);}
1562   /* XXX: should we do this on the global vector? */
1563   if (patch->partition_of_unity) {
1564     ierr = VecPointwiseMult(patch->localY, patch->localY, patch->dof_weights);CHKERRQ(ierr);
1565   }
1566   /* Now patch->localY contains the solution of the patch solves, so we need to combine them all. */
1567   ierr = VecSet(y, 0.0);CHKERRQ(ierr);
1568   ierr = VecGetArray(y, &globalY);CHKERRQ(ierr);
1569   ierr = VecGetArrayRead(patch->localY, &localY);CHKERRQ(ierr);
1570   ierr = PetscSFReduceBegin(patch->defaultSF, MPIU_SCALAR, localY, globalY, MPI_SUM);CHKERRQ(ierr);
1571   ierr = PetscSFReduceEnd(patch->defaultSF, MPIU_SCALAR, localY, globalY, MPI_SUM);CHKERRQ(ierr);
1572   ierr = VecRestoreArrayRead(patch->localY, &localY);CHKERRQ(ierr);
1573 
1574   /* Now we need to send the global BC values through */
1575   ierr = VecGetArrayRead(x, &globalX);CHKERRQ(ierr);
1576   ierr = ISGetSize(patch->globalBcNodes, &numBcs);CHKERRQ(ierr);
1577   ierr = ISGetIndices(patch->globalBcNodes, &bcNodes);CHKERRQ(ierr);
1578   ierr = VecGetLocalSize(x, &n);CHKERRQ(ierr);
1579   for (bc = 0; bc < numBcs; ++bc) {
1580     const PetscInt idx = bcNodes[bc];
1581     if (idx < n) globalY[idx] = globalX[idx];
1582   }
1583 
1584   ierr = ISRestoreIndices(patch->globalBcNodes, &bcNodes);CHKERRQ(ierr);
1585   ierr = VecRestoreArrayRead(x, &globalX);CHKERRQ(ierr);
1586   ierr = VecRestoreArray(y, &globalY);CHKERRQ(ierr);
1587 
1588   ierr = PetscOptionsPopGetViewerOff();CHKERRQ(ierr);
1589   ierr = PetscLogEventEnd(PC_Patch_Apply, pc, 0, 0, 0);CHKERRQ(ierr);
1590   PetscFunctionReturn(0);
1591 }
1592 
1593 static PetscErrorCode PCReset_PATCH(PC pc)
1594 {
1595   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1596   PetscInt       i;
1597   PetscErrorCode ierr;
1598 
1599   PetscFunctionBegin;
1600   /* TODO: Get rid of all these ifs */
1601   ierr = PetscSFDestroy(&patch->defaultSF);CHKERRQ(ierr);
1602   ierr = PetscSectionDestroy(&patch->cellCounts);CHKERRQ(ierr);
1603   ierr = PetscSectionDestroy(&patch->pointCounts);CHKERRQ(ierr);
1604   ierr = PetscSectionDestroy(&patch->cellNumbering);CHKERRQ(ierr);
1605   ierr = PetscSectionDestroy(&patch->gtolCounts);CHKERRQ(ierr);
1606   ierr = ISDestroy(&patch->gtol);CHKERRQ(ierr);
1607   ierr = ISDestroy(&patch->cells);CHKERRQ(ierr);
1608   ierr = ISDestroy(&patch->points);CHKERRQ(ierr);
1609   ierr = ISDestroy(&patch->dofs);CHKERRQ(ierr);
1610   ierr = ISDestroy(&patch->offs);CHKERRQ(ierr);
1611   ierr = PetscSectionDestroy(&patch->patchSection);CHKERRQ(ierr);
1612   ierr = ISDestroy(&patch->ghostBcNodes);CHKERRQ(ierr);
1613   ierr = ISDestroy(&patch->globalBcNodes);CHKERRQ(ierr);
1614 
1615   if (patch->dofSection) for (i = 0; i < patch->nsubspaces; i++) {ierr = PetscSectionDestroy(&patch->dofSection[i]);CHKERRQ(ierr);}
1616   ierr = PetscFree(patch->dofSection);CHKERRQ(ierr);
1617   ierr = PetscFree(patch->bs);CHKERRQ(ierr);
1618   ierr = PetscFree(patch->nodesPerCell);CHKERRQ(ierr);
1619   if (patch->cellNodeMap) for (i = 0; i < patch->nsubspaces; i++) {ierr = PetscFree(patch->cellNodeMap[i]);CHKERRQ(ierr);}
1620   ierr = PetscFree(patch->cellNodeMap);CHKERRQ(ierr);
1621   ierr = PetscFree(patch->subspaceOffsets);CHKERRQ(ierr);
1622 
1623   if (patch->ksp) {
1624     for (i = 0; i < patch->npatch; ++i) {ierr = KSPReset(patch->ksp[i]);CHKERRQ(ierr);}
1625   }
1626 
1627   ierr = VecDestroy(&patch->localX);CHKERRQ(ierr);
1628   ierr = VecDestroy(&patch->localY);CHKERRQ(ierr);
1629   if (patch->patchX) {
1630     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patchX[i]);CHKERRQ(ierr);}
1631     ierr = PetscFree(patch->patchX);CHKERRQ(ierr);
1632   }
1633   if (patch->patchY) {
1634     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patchY[i]);CHKERRQ(ierr);}
1635     ierr = PetscFree(patch->patchY);CHKERRQ(ierr);
1636   }
1637   ierr = VecDestroy(&patch->dof_weights);CHKERRQ(ierr);
1638   if (patch->patch_dof_weights) {
1639     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patch_dof_weights[i]);CHKERRQ(ierr);}
1640     ierr = PetscFree(patch->patch_dof_weights);CHKERRQ(ierr);
1641   }
1642   if (patch->mat) {
1643     for (i = 0; i < patch->npatch; ++i) {ierr = MatDestroy(&patch->mat[i]);CHKERRQ(ierr);}
1644     ierr = PetscFree(patch->mat);CHKERRQ(ierr);
1645   }
1646   ierr = PetscFree(patch->sub_mat_type);CHKERRQ(ierr);
1647   if (patch->userIS) {
1648     for (i = 0; i < patch->npatch; ++i) {ierr = ISDestroy(&patch->userIS[i]);CHKERRQ(ierr);}
1649     ierr = PetscFree(patch->userIS);CHKERRQ(ierr);
1650   }
1651   patch->bs          = 0;
1652   patch->cellNodeMap = NULL;
1653   patch->nsubspaces  = 0;
1654   ierr = ISDestroy(&patch->iterationSet);CHKERRQ(ierr);
1655 
1656   ierr = PetscViewerDestroy(&patch->viewerSection);CHKERRQ(ierr);
1657   PetscFunctionReturn(0);
1658 }
1659 
1660 static PetscErrorCode PCDestroy_PATCH(PC pc)
1661 {
1662   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1663   PetscInt       i;
1664   PetscErrorCode ierr;
1665 
1666   PetscFunctionBegin;
1667   ierr = PCReset_PATCH(pc);CHKERRQ(ierr);
1668   if (patch->ksp) {
1669     for (i = 0; i < patch->npatch; ++i) {ierr = KSPDestroy(&patch->ksp[i]);CHKERRQ(ierr);}
1670     ierr = PetscFree(patch->ksp);CHKERRQ(ierr);
1671   }
1672   ierr = PetscFree(pc->data);CHKERRQ(ierr);
1673   PetscFunctionReturn(0);
1674 }
1675 
1676 static PetscErrorCode PCSetFromOptions_PATCH(PetscOptionItems *PetscOptionsObject, PC pc)
1677 {
1678   PC_PATCH            *patch = (PC_PATCH *) pc->data;
1679   PCPatchConstructType patchConstructionType = PC_PATCH_STAR;
1680   char                 sub_mat_type[PETSC_MAX_PATH_LEN];
1681   const char          *prefix;
1682   PetscBool            flg, dimflg, codimflg;
1683   MPI_Comm             comm;
1684   PetscErrorCode       ierr;
1685 
1686   PetscFunctionBegin;
1687   ierr = PetscObjectGetComm((PetscObject) pc, &comm);CHKERRQ(ierr);
1688   ierr = PetscObjectGetOptionsPrefix((PetscObject) pc, &prefix);CHKERRQ(ierr);
1689   ierr = PetscOptionsHead(PetscOptionsObject, "Vertex-patch Additive Schwarz options");CHKERRQ(ierr);
1690   ierr = PetscOptionsBool("-pc_patch_save_operators",  "Store all patch operators for lifetime of PC?", "PCPatchSetSaveOperators", patch->save_operators, &patch->save_operators, &flg);CHKERRQ(ierr);
1691   ierr = PetscOptionsBool("-pc_patch_partition_of_unity", "Weight contributions by dof multiplicity?", "PCPatchSetPartitionOfUnity", patch->partition_of_unity, &patch->partition_of_unity, &flg);CHKERRQ(ierr);
1692   ierr = PetscOptionsInt("-pc_patch_construct_dim", "What dimension of mesh point to construct patches by? (0 = vertices)", "PCPATCH", patch->dim, &patch->dim, &dimflg);CHKERRQ(ierr);
1693   ierr = PetscOptionsInt("-pc_patch_construct_codim", "What co-dimension of mesh point to construct patches by? (0 = cells)", "PCPATCH", patch->codim, &patch->codim, &codimflg);CHKERRQ(ierr);
1694   if (dimflg && codimflg) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Can only set one of dimension or co-dimension");CHKERRQ(ierr);
1695   ierr = PetscOptionsEnum("-pc_patch_construct_type", "How should the patches be constructed?", "PCPatchSetConstructType", PCPatchConstructTypes, (PetscEnum) patchConstructionType, (PetscEnum *) &patchConstructionType, &flg);CHKERRQ(ierr);
1696   if (flg) {ierr = PCPatchSetConstructType(pc, patchConstructionType, NULL, NULL);CHKERRQ(ierr);}
1697   ierr = PetscOptionsInt("-pc_patch_vanka_dim", "Topological dimension of entities for Vanka to ignore", "PCPATCH", patch->vankadim, &patch->vankadim, &flg);CHKERRQ(ierr);
1698   ierr = PetscOptionsInt("-pc_patch_ignore_dim", "Topological dimension of entities for completion to ignore", "PCPATCH", patch->ignoredim, &patch->ignoredim, &flg);CHKERRQ(ierr);
1699   ierr = PetscOptionsFList("-pc_patch_sub_mat_type", "Matrix type for patch solves", "PCPatchSetSubMatType", MatList, NULL, sub_mat_type, PETSC_MAX_PATH_LEN, &flg);CHKERRQ(ierr);
1700   if (flg) {ierr = PCPatchSetSubMatType(pc, sub_mat_type);CHKERRQ(ierr);}
1701   ierr = PetscOptionsBool("-pc_patch_symmetrise_sweep", "Go start->end, end->start?", "PCPATCH", patch->symmetrise_sweep, &patch->symmetrise_sweep, &flg);CHKERRQ(ierr);
1702   ierr = PetscOptionsInt("-pc_patch_exclude_subspace", "What subspace (if any) to exclude in construction?", "PCPATCH", patch->exclude_subspace, &patch->exclude_subspace, &flg);CHKERRQ(ierr);
1703 
1704   ierr = PetscOptionsBool("-pc_patch_patches_view", "Print out information during patch construction", "PCPATCH", patch->viewPatches, &patch->viewPatches, &flg);CHKERRQ(ierr);
1705   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_cells_view",   &patch->viewerCells,   &patch->formatCells,   &patch->viewCells);CHKERRQ(ierr);
1706   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_points_view",  &patch->viewerPoints,  &patch->formatPoints,  &patch->viewPoints);CHKERRQ(ierr);
1707   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_section_view", &patch->viewerSection, &patch->formatSection, &patch->viewSection);CHKERRQ(ierr);
1708   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_mat_view",     &patch->viewerMatrix,  &patch->formatMatrix,  &patch->viewMatrix);CHKERRQ(ierr);
1709   ierr = PetscOptionsTail();CHKERRQ(ierr);
1710   patch->optionsSet = PETSC_TRUE;
1711   PetscFunctionReturn(0);
1712 }
1713 
1714 static PetscErrorCode PCSetUpOnBlocks_PATCH(PC pc)
1715 {
1716   PC_PATCH          *patch = (PC_PATCH*) pc->data;
1717   KSPConvergedReason reason;
1718   PetscInt           i;
1719   PetscErrorCode     ierr;
1720 
1721   PetscFunctionBegin;
1722   for (i = 0; i < patch->npatch; ++i) {
1723     ierr = KSPSetUp(patch->ksp[i]);CHKERRQ(ierr);
1724     ierr = KSPGetConvergedReason(patch->ksp[i], &reason);CHKERRQ(ierr);
1725     if (reason == KSP_DIVERGED_PCSETUP_FAILED) pc->failedreason = PC_SUBPC_ERROR;
1726   }
1727   PetscFunctionReturn(0);
1728 }
1729 
1730 static PetscErrorCode PCView_PATCH(PC pc, PetscViewer viewer)
1731 {
1732   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1733   PetscViewer    sviewer;
1734   PetscBool      isascii;
1735   PetscMPIInt    rank;
1736   PetscErrorCode ierr;
1737 
1738   PetscFunctionBegin;
1739   /* TODO Redo tabbing with set tbas in new style */
1740   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &isascii);CHKERRQ(ierr);
1741   if (!isascii) PetscFunctionReturn(0);
1742   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) pc), &rank);CHKERRQ(ierr);
1743   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1744   ierr = PetscViewerASCIIPrintf(viewer, "Subspace Correction preconditioner with %d patches\n", patch->npatch);CHKERRQ(ierr);
1745   ierr = PetscViewerASCIIPrintf(viewer, "Schwarz type: additive\n");CHKERRQ(ierr);
1746   if (patch->partition_of_unity) {ierr = PetscViewerASCIIPrintf(viewer, "Weighting by partition of unity\n");CHKERRQ(ierr);}
1747   else                           {ierr = PetscViewerASCIIPrintf(viewer, "Not weighting by partition of unity\n");CHKERRQ(ierr);}
1748   if (patch->symmetrise_sweep) {ierr = PetscViewerASCIIPrintf(viewer, "Symmetrising sweep (start->end, then end->start)\n");CHKERRQ(ierr);}
1749   else                         {ierr = PetscViewerASCIIPrintf(viewer, "Not symmetrising sweep\n");CHKERRQ(ierr);}
1750   if (!patch->save_operators) {ierr = PetscViewerASCIIPrintf(viewer, "Not saving patch operators (rebuilt every PCApply)\n");CHKERRQ(ierr);}
1751   else                        {ierr = PetscViewerASCIIPrintf(viewer, "Saving patch operators (rebuilt every PCSetUp)\n");CHKERRQ(ierr);}
1752   if (patch->patchconstructop == PCPatchConstruct_Star)       {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: star\n");CHKERRQ(ierr);}
1753   else if (patch->patchconstructop == PCPatchConstruct_Vanka) {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: Vanka\n");CHKERRQ(ierr);}
1754   else if (patch->patchconstructop == PCPatchConstruct_User)  {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: user-specified\n");CHKERRQ(ierr);}
1755   else                                                        {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: unknown\n");CHKERRQ(ierr);}
1756   ierr = PetscViewerASCIIPrintf(viewer, "KSP on patches (all same):\n");CHKERRQ(ierr);
1757   if (patch->ksp) {
1758     ierr = PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer);CHKERRQ(ierr);
1759     if (!rank) {
1760       ierr = PetscViewerASCIIPushTab(sviewer);CHKERRQ(ierr);
1761       ierr = KSPView(patch->ksp[0], sviewer);CHKERRQ(ierr);
1762       ierr = PetscViewerASCIIPopTab(sviewer);CHKERRQ(ierr);
1763     }
1764     ierr = PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer);CHKERRQ(ierr);
1765   } else {
1766     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1767     ierr = PetscViewerASCIIPrintf(viewer, "KSP not yet set.\n");CHKERRQ(ierr);
1768     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1769   }
1770   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1771   PetscFunctionReturn(0);
1772 }
1773 
1774 /*MC
1775   PCPATCH = "patch" - A PC object that encapsulates flexible definition of blocks for overlapping and non-overlapping
1776                       small block additive and multiplicative preconditioners. Block definition is based on topology from
1777                       a DM and equation numbering from a PetscSection.
1778 
1779   Options Database Keys:
1780 + -pc_patch_cells_view   - Views the process local cell numbers for each patch
1781 . -pc_patch_points_view  - Views the process local mesh point numbers for each patch
1782 . -pc_patch_g2l_view     - Views the map between global dofs and patch local dofs for each patch
1783 . -pc_patch_patches_view - Views the global dofs associated with each patch and its boundary
1784 - -pc_patch_sub_mat_view - Views the matrix associated with each patch
1785 
1786   Level: intermediate
1787 
1788 .seealso: PCType, PCCreate(), PCSetType()
1789 M*/
1790 PETSC_EXTERN PetscErrorCode PCCreate_Patch(PC pc)
1791 {
1792   PC_PATCH      *patch;
1793   PetscErrorCode ierr;
1794 
1795   PetscFunctionBegin;
1796   ierr = PetscNewLog(pc, &patch);CHKERRQ(ierr);
1797 
1798   /* Set some defaults */
1799   patch->combined           = PETSC_FALSE;
1800   patch->save_operators     = PETSC_TRUE;
1801   patch->partition_of_unity = PETSC_FALSE;
1802   patch->codim              = -1;
1803   patch->dim                = -1;
1804   patch->exclude_subspace   = -1;
1805   patch->vankadim           = -1;
1806   patch->ignoredim          = -1;
1807   patch->patchconstructop   = PCPatchConstruct_Star;
1808   patch->symmetrise_sweep   = PETSC_FALSE;
1809   patch->npatch             = 0;
1810   patch->userIS             = NULL;
1811   patch->optionsSet         = PETSC_FALSE;
1812   patch->iterationSet       = NULL;
1813   patch->user_patches       = PETSC_FALSE;
1814   ierr = PetscStrallocpy(MATDENSE, (char **) &patch->sub_mat_type);CHKERRQ(ierr);
1815   patch->viewPatches        = PETSC_FALSE;
1816   patch->viewCells          = PETSC_FALSE;
1817   patch->viewPoints         = PETSC_FALSE;
1818   patch->viewSection        = PETSC_FALSE;
1819   patch->viewMatrix         = PETSC_FALSE;
1820 
1821   pc->data                 = (void *) patch;
1822   pc->ops->apply           = PCApply_PATCH;
1823   pc->ops->applytranspose  = 0; /* PCApplyTranspose_PATCH; */
1824   pc->ops->setup           = PCSetUp_PATCH;
1825   pc->ops->reset           = PCReset_PATCH;
1826   pc->ops->destroy         = PCDestroy_PATCH;
1827   pc->ops->setfromoptions  = PCSetFromOptions_PATCH;
1828   pc->ops->setuponblocks   = PCSetUpOnBlocks_PATCH;
1829   pc->ops->view            = PCView_PATCH;
1830   pc->ops->applyrichardson = 0;
1831 
1832   PetscFunctionReturn(0);
1833 }
1834