xref: /petsc/src/ksp/pc/impls/gasm/gasm.c (revision 4dbf25a8fa98e38799e7b47dcb2d8a9309975f41)
1 /*
2   This file defines an "generalized" additive Schwarz preconditioner for any Mat implementation.
3   In this version, each MPI process may intersect multiple subdomains and any subdomain may
4   intersect multiple MPI processes.  Intersections of subdomains with MPI processes are called *local
5   subdomains*.
6 
7        N    - total number of distinct global subdomains  (set explicitly in PCGASMSetTotalSubdomains() or implicitly PCGASMSetSubdomains() and then calculated in PCSetUp_GASM())
8        n    - actual number of local subdomains on this process (set in `PCGASMSetSubdomains()` or calculated in `PCGASMSetTotalSubdomains()`)
9        nmax - maximum number of local subdomains per process (calculated in PCSetUp_GASM())
10 */
11 #include <petsc/private/pcimpl.h> /*I "petscpc.h" I*/
12 #include <petscdm.h>
13 
14 typedef struct {
15   PetscInt   N, n, nmax;
16   PetscInt   overlap;                /* overlap requested by user */
17   PCGASMType type;                   /* use reduced interpolation, restriction or both */
18   PetscBool  type_set;               /* if user set this value (so won't change it for symmetric problems) */
19   PetscBool  same_subdomain_solvers; /* flag indicating whether all local solvers are same */
20   PetscBool  sort_indices;           /* flag to sort subdomain indices */
21   PetscBool  user_subdomains;        /* whether the user set explicit subdomain index sets -- keep them on PCReset() */
22   PetscBool  dm_subdomains;          /* whether DM is allowed to define subdomains */
23   PetscBool  hierarchicalpartitioning;
24   IS        *ois;           /* index sets that define the outer (conceptually, overlapping) subdomains */
25   IS        *iis;           /* index sets that define the inner (conceptually, nonoverlapping) subdomains */
26   KSP       *ksp;           /* linear solvers for each subdomain */
27   Mat       *pmat;          /* subdomain block matrices */
28   Vec        gx, gy;        /* Merged work vectors */
29   Vec       *x, *y;         /* Split work vectors; storage aliases pieces of storage of the above merged vectors. */
30   VecScatter gorestriction; /* merged restriction to disjoint union of outer subdomains */
31   VecScatter girestriction; /* merged restriction to disjoint union of inner subdomains */
32   VecScatter pctoouter;
33   IS         permutationIS;
34   Mat        permutationP;
35   Mat        pcmat;
36   Vec        pcx, pcy;
37 } PC_GASM;
38 
39 static PetscErrorCode PCGASMComputeGlobalSubdomainNumbering_Private(PC pc, PetscInt **numbering, PetscInt **permutation)
40 {
41   PC_GASM *osm = (PC_GASM *)pc->data;
42   PetscInt i;
43 
44   PetscFunctionBegin;
45   /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
46   PetscCall(PetscMalloc2(osm->n, numbering, osm->n, permutation));
47   PetscCall(PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc), osm->n, (PetscObject *)osm->iis, NULL, *numbering));
48   for (i = 0; i < osm->n; ++i) (*permutation)[i] = i;
49   PetscCall(PetscSortIntWithPermutation(osm->n, *numbering, *permutation));
50   PetscFunctionReturn(PETSC_SUCCESS);
51 }
52 
53 static PetscErrorCode PCGASMSubdomainView_Private(PC pc, PetscInt i, PetscViewer viewer)
54 {
55   PC_GASM        *osm = (PC_GASM *)pc->data;
56   PetscInt        j, nidx;
57   const PetscInt *idx;
58   PetscViewer     sviewer;
59   char           *cidx;
60 
61   PetscFunctionBegin;
62   PetscCheck(i >= -1 && i < osm->n, PetscObjectComm((PetscObject)viewer), PETSC_ERR_ARG_WRONG, "Invalid subdomain %" PetscInt_FMT ": must nonnegative and less than %" PetscInt_FMT, i, osm->n);
63 
64   /* Inner subdomains. */
65   /*
66    No more than 15 characters per index plus a space.
67    PetscViewerStringSPrintf requires a string of size at least 2, so use (nidx+1) instead of nidx,
68    in case nidx == 0. That will take care of the space for the trailing '\0' as well.
69    For nidx == 0, the whole string 16 '\0'.
70    */
71   PetscCall(PetscViewerASCIIPrintf(viewer, "Inner subdomain:\n"));
72   PetscCall(PetscViewerFlush(viewer));
73   PetscCall(PetscViewerASCIIPushSynchronized(viewer));
74   if (i > -1) {
75     PetscCall(ISGetLocalSize(osm->iis[i], &nidx));
76     PetscCall(PetscMalloc1(16 * (nidx + 1) + 1, &cidx));
77     PetscCall(PetscViewerStringOpen(PETSC_COMM_SELF, cidx, 16 * (nidx + 1) + 1, &sviewer));
78     PetscCall(ISGetIndices(osm->iis[i], &idx));
79     for (j = 0; j < nidx; ++j) PetscCall(PetscViewerStringSPrintf(sviewer, "%" PetscInt_FMT " ", idx[j]));
80     PetscCall(ISRestoreIndices(osm->iis[i], &idx));
81     PetscCall(PetscViewerDestroy(&sviewer));
82     PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx));
83     PetscCall(PetscFree(cidx));
84   }
85   PetscCall(PetscViewerFlush(viewer));
86   PetscCall(PetscViewerASCIIPopSynchronized(viewer));
87   PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
88   PetscCall(PetscViewerFlush(viewer));
89 
90   /* Outer subdomains. */
91   /*
92    No more than 15 characters per index plus a space.
93    PetscViewerStringSPrintf requires a string of size at least 2, so use (nidx+1) instead of nidx,
94    in case nidx == 0. That will take care of the space for the trailing '\0' as well.
95    For nidx == 0, the whole string 16 '\0'.
96    */
97   PetscCall(PetscViewerASCIIPrintf(viewer, "Outer subdomain:\n"));
98   PetscCall(PetscViewerFlush(viewer));
99   PetscCall(PetscViewerASCIIPushSynchronized(viewer));
100   if (i > -1) {
101     PetscCall(ISGetLocalSize(osm->ois[i], &nidx));
102     PetscCall(PetscMalloc1(16 * (nidx + 1) + 1, &cidx));
103     PetscCall(PetscViewerStringOpen(PETSC_COMM_SELF, cidx, 16 * (nidx + 1) + 1, &sviewer));
104     PetscCall(ISGetIndices(osm->ois[i], &idx));
105     for (j = 0; j < nidx; ++j) PetscCall(PetscViewerStringSPrintf(sviewer, "%" PetscInt_FMT " ", idx[j]));
106     PetscCall(PetscViewerDestroy(&sviewer));
107     PetscCall(ISRestoreIndices(osm->ois[i], &idx));
108     PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx));
109     PetscCall(PetscFree(cidx));
110   }
111   PetscCall(PetscViewerFlush(viewer));
112   PetscCall(PetscViewerASCIIPopSynchronized(viewer));
113   PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
114   PetscCall(PetscViewerFlush(viewer));
115   PetscFunctionReturn(PETSC_SUCCESS);
116 }
117 
118 static PetscErrorCode PCGASMPrintSubdomains(PC pc)
119 {
120   PC_GASM    *osm = (PC_GASM *)pc->data;
121   const char *prefix;
122   char        fname[PETSC_MAX_PATH_LEN + 1];
123   PetscInt    l, d, count;
124   PetscBool   found;
125   PetscViewer viewer;
126   PetscInt   *numbering, *permutation; /* global numbering of locally-supported subdomains and the permutation from the local ordering */
127 
128   PetscFunctionBegin;
129   PetscCall(PCGetOptionsPrefix(pc, &prefix));
130   PetscCall(PetscOptionsHasName(NULL, prefix, "-pc_gasm_print_subdomains", &found));
131   if (!found) PetscFunctionReturn(PETSC_SUCCESS);
132   PetscCall(PetscOptionsGetString(NULL, prefix, "-pc_gasm_print_subdomains", fname, sizeof(fname), &found));
133   if (!found) PetscCall(PetscStrncpy(fname, "stdout", sizeof(fname)));
134   PetscCall(PetscViewerASCIIOpen(PetscObjectComm((PetscObject)pc), fname, &viewer));
135   /*
136    Make sure the viewer has a name. Otherwise this may cause a deadlock or other weird errors when creating a subcomm viewer:
137    the subcomm viewer will attempt to inherit the viewer's name, which, if not set, will be constructed collectively on the comm.
138   */
139   PetscCall(PetscObjectName((PetscObject)viewer));
140   l = 0;
141   PetscCall(PCGASMComputeGlobalSubdomainNumbering_Private(pc, &numbering, &permutation));
142   for (count = 0; count < osm->N; ++count) {
143     /* Now let subdomains go one at a time in the global numbering order and print their subdomain/solver info. */
144     if (l < osm->n) {
145       d = permutation[l]; /* d is the local number of the l-th smallest (in the global ordering) among the locally supported subdomains */
146       if (numbering[d] == count) l++;
147       else d = -1;
148     } else d = -1;
149     PetscCall(PCGASMSubdomainView_Private(pc, d, viewer));
150   }
151   PetscCall(PetscFree2(numbering, permutation));
152   PetscCall(PetscViewerDestroy(&viewer));
153   PetscFunctionReturn(PETSC_SUCCESS);
154 }
155 
156 static PetscErrorCode PCView_GASM(PC pc, PetscViewer viewer)
157 {
158   PC_GASM    *osm = (PC_GASM *)pc->data;
159   const char *prefix;
160   PetscMPIInt rank, size;
161   PetscInt    bsz;
162   PetscBool   iascii, view_subdomains = PETSC_FALSE;
163   PetscViewer sviewer;
164   PetscInt    count, l;
165   char        overlap[256]     = "user-defined overlap";
166   char        gsubdomains[256] = "unknown total number of subdomains";
167   char        msubdomains[256] = "unknown max number of local subdomains";
168   PetscInt   *numbering, *permutation; /* global numbering of locally-supported subdomains and the permutation from the local ordering */
169 
170   PetscFunctionBegin;
171   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
172   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
173 
174   if (osm->overlap >= 0) PetscCall(PetscSNPrintf(overlap, sizeof(overlap), "requested amount of overlap = %" PetscInt_FMT, osm->overlap));
175   if (osm->N != PETSC_DETERMINE) PetscCall(PetscSNPrintf(gsubdomains, sizeof(gsubdomains), "total number of subdomains = %" PetscInt_FMT, osm->N));
176   if (osm->nmax != PETSC_DETERMINE) PetscCall(PetscSNPrintf(msubdomains, sizeof(msubdomains), "max number of local subdomains = %" PetscInt_FMT, osm->nmax));
177 
178   PetscCall(PCGetOptionsPrefix(pc, &prefix));
179   PetscCall(PetscOptionsGetBool(NULL, prefix, "-pc_gasm_view_subdomains", &view_subdomains, NULL));
180 
181   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
182   if (iascii) {
183     /*
184      Make sure the viewer has a name. Otherwise this may cause a deadlock when creating a subcomm viewer:
185      the subcomm viewer will attempt to inherit the viewer's name, which, if not set, will be constructed
186      collectively on the comm.
187      */
188     PetscCall(PetscObjectName((PetscObject)viewer));
189     PetscCall(PetscViewerASCIIPrintf(viewer, "  Restriction/interpolation type: %s\n", PCGASMTypes[osm->type]));
190     PetscCall(PetscViewerASCIIPrintf(viewer, "  %s\n", overlap));
191     PetscCall(PetscViewerASCIIPrintf(viewer, "  %s\n", gsubdomains));
192     PetscCall(PetscViewerASCIIPrintf(viewer, "  %s\n", msubdomains));
193     PetscCall(PetscViewerASCIIPushSynchronized(viewer));
194     PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "  [%d|%d] number of locally-supported subdomains = %" PetscInt_FMT "\n", rank, size, osm->n));
195     PetscCall(PetscViewerFlush(viewer));
196     PetscCall(PetscViewerASCIIPopSynchronized(viewer));
197     /* Cannot take advantage of osm->same_subdomain_solvers without a global numbering of subdomains. */
198     PetscCall(PetscViewerASCIIPrintf(viewer, "  Subdomain solver info is as follows:\n"));
199     PetscCall(PetscViewerASCIIPushTab(viewer));
200     PetscCall(PetscViewerASCIIPrintf(viewer, "  - - - - - - - - - - - - - - - - - -\n"));
201     /* Now let subdomains go one at a time in the global numbering order and print their subdomain/solver info. */
202     PetscCall(PCGASMComputeGlobalSubdomainNumbering_Private(pc, &numbering, &permutation));
203     l = 0;
204     for (count = 0; count < osm->N; ++count) {
205       PetscMPIInt srank, ssize;
206       if (l < osm->n) {
207         PetscInt d = permutation[l]; /* d is the local number of the l-th smallest (in the global ordering) among the locally supported subdomains */
208         if (numbering[d] == count) {
209           PetscCallMPI(MPI_Comm_size(((PetscObject)osm->ois[d])->comm, &ssize));
210           PetscCallMPI(MPI_Comm_rank(((PetscObject)osm->ois[d])->comm, &srank));
211           PetscCall(PetscViewerGetSubViewer(viewer, ((PetscObject)osm->ois[d])->comm, &sviewer));
212           PetscCall(ISGetLocalSize(osm->ois[d], &bsz));
213           PetscCall(PetscViewerASCIISynchronizedPrintf(sviewer, "  [%d|%d] (subcomm [%d|%d]) local subdomain number %" PetscInt_FMT ", local size = %" PetscInt_FMT "\n", rank, size, srank, ssize, d, bsz));
214           PetscCall(PetscViewerFlush(sviewer));
215           PetscCall(PetscViewerASCIIPushTab(sviewer));
216           if (view_subdomains) PetscCall(PCGASMSubdomainView_Private(pc, d, sviewer));
217           if (!pc->setupcalled) {
218             PetscCall(PetscViewerASCIISynchronizedPrintf(sviewer, "  Solver not set up yet: PCSetUp() not yet called\n"));
219           } else {
220             PetscCall(KSPView(osm->ksp[d], sviewer));
221           }
222           PetscCall(PetscViewerASCIIPopTab(sviewer));
223           PetscCall(PetscViewerASCIIPrintf(sviewer, "  - - - - - - - - - - - - - - - - - -\n"));
224           PetscCall(PetscViewerFlush(sviewer));
225           PetscCall(PetscViewerRestoreSubViewer(viewer, ((PetscObject)osm->ois[d])->comm, &sviewer));
226           ++l;
227         } else {
228           PetscCall(PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
229           PetscCall(PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
230         }
231       } else {
232         PetscCall(PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
233         PetscCall(PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
234       }
235     }
236     PetscCall(PetscFree2(numbering, permutation));
237     PetscCall(PetscViewerASCIIPopTab(viewer));
238     PetscCall(PetscViewerFlush(viewer));
239     /* this line is needed to match the extra PetscViewerASCIIPushSynchronized() in PetscViewerGetSubViewer() */
240     PetscCall(PetscViewerASCIIPopSynchronized(viewer));
241   }
242   PetscFunctionReturn(PETSC_SUCCESS);
243 }
244 
245 PETSC_INTERN PetscErrorCode PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[]);
246 
247 static PetscErrorCode PCGASMSetHierarchicalPartitioning(PC pc)
248 {
249   PC_GASM        *osm = (PC_GASM *)pc->data;
250   MatPartitioning part;
251   MPI_Comm        comm;
252   PetscMPIInt     size;
253   PetscInt        nlocalsubdomains, fromrows_localsize;
254   IS              partitioning, fromrows, isn;
255   Vec             outervec;
256 
257   PetscFunctionBegin;
258   PetscCall(PetscObjectGetComm((PetscObject)pc, &comm));
259   PetscCallMPI(MPI_Comm_size(comm, &size));
260   /* we do not need a hierarchical partitioning when
261     * the total number of subdomains is consistent with
262     * the number of MPI tasks.
263     * For the following cases, we do not need to use HP
264     * */
265   if (osm->N == PETSC_DETERMINE || osm->N >= size || osm->N == 1) PetscFunctionReturn(PETSC_SUCCESS);
266   PetscCheck(size % osm->N == 0, PETSC_COMM_WORLD, PETSC_ERR_ARG_INCOMP, "have to specify the total number of subdomains %" PetscInt_FMT " to be a factor of the number of ranks %d ", osm->N, size);
267   nlocalsubdomains = size / osm->N;
268   osm->n           = 1;
269   PetscCall(MatPartitioningCreate(comm, &part));
270   PetscCall(MatPartitioningSetAdjacency(part, pc->pmat));
271   PetscCall(MatPartitioningSetType(part, MATPARTITIONINGHIERARCH));
272   PetscCall(MatPartitioningHierarchicalSetNcoarseparts(part, osm->N));
273   PetscCall(MatPartitioningHierarchicalSetNfineparts(part, nlocalsubdomains));
274   PetscCall(MatPartitioningSetFromOptions(part));
275   /* get new rank owner number of each vertex */
276   PetscCall(MatPartitioningApply(part, &partitioning));
277   PetscCall(ISBuildTwoSided(partitioning, NULL, &fromrows));
278   PetscCall(ISPartitioningToNumbering(partitioning, &isn));
279   PetscCall(ISDestroy(&isn));
280   PetscCall(ISGetLocalSize(fromrows, &fromrows_localsize));
281   PetscCall(MatPartitioningDestroy(&part));
282   PetscCall(MatCreateVecs(pc->pmat, &outervec, NULL));
283   PetscCall(VecCreateMPI(comm, fromrows_localsize, PETSC_DETERMINE, &osm->pcx));
284   PetscCall(VecDuplicate(osm->pcx, &osm->pcy));
285   PetscCall(VecScatterCreate(osm->pcx, NULL, outervec, fromrows, &osm->pctoouter));
286   PetscCall(MatCreateSubMatrix(pc->pmat, fromrows, fromrows, MAT_INITIAL_MATRIX, &osm->permutationP));
287   PetscCall(PetscObjectReference((PetscObject)fromrows));
288   osm->permutationIS = fromrows;
289   osm->pcmat         = pc->pmat;
290   PetscCall(PetscObjectReference((PetscObject)osm->permutationP));
291   pc->pmat = osm->permutationP;
292   PetscCall(VecDestroy(&outervec));
293   PetscCall(ISDestroy(&fromrows));
294   PetscCall(ISDestroy(&partitioning));
295   osm->n = PETSC_DETERMINE;
296   PetscFunctionReturn(PETSC_SUCCESS);
297 }
298 
299 static PetscErrorCode PCSetUp_GASM(PC pc)
300 {
301   PC_GASM        *osm = (PC_GASM *)pc->data;
302   PetscInt        i, nInnerIndices, nTotalInnerIndices;
303   PetscMPIInt     rank, size;
304   MatReuse        scall = MAT_REUSE_MATRIX;
305   KSP             ksp;
306   PC              subpc;
307   const char     *prefix, *pprefix;
308   Vec             x, y;
309   PetscInt        oni;   /* Number of indices in the i-th local outer subdomain.               */
310   const PetscInt *oidxi; /* Indices from the i-th subdomain local outer subdomain.             */
311   PetscInt        on;    /* Number of indices in the disjoint union of local outer subdomains. */
312   PetscInt       *oidx;  /* Indices in the disjoint union of local outer subdomains. */
313   IS              gois;  /* Disjoint union the global indices of outer subdomains.             */
314   IS              goid;  /* Identity IS of the size of the disjoint union of outer subdomains. */
315   PetscScalar    *gxarray, *gyarray;
316   PetscInt        gostart; /* Start of locally-owned indices in the vectors -- osm->gx,osm->gy -- over the disjoint union of outer subdomains. */
317   PetscInt        num_subdomains  = 0;
318   DM             *subdomain_dm    = NULL;
319   char          **subdomain_names = NULL;
320   PetscInt       *numbering;
321 
322   PetscFunctionBegin;
323   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
324   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
325   if (!pc->setupcalled) {
326     /* use a hierarchical partitioning */
327     if (osm->hierarchicalpartitioning) PetscCall(PCGASMSetHierarchicalPartitioning(pc));
328     if (osm->n == PETSC_DETERMINE) {
329       if (osm->N != PETSC_DETERMINE) {
330         /* No local subdomains given, but the desired number of total subdomains is known, so construct them accordingly. */
331         PetscCall(PCGASMCreateSubdomains(pc->pmat, osm->N, &osm->n, &osm->iis));
332       } else if (osm->dm_subdomains && pc->dm) {
333         /* try pc->dm next, if allowed */
334         PetscInt d;
335         IS      *inner_subdomain_is, *outer_subdomain_is;
336         PetscCall(DMCreateDomainDecomposition(pc->dm, &num_subdomains, &subdomain_names, &inner_subdomain_is, &outer_subdomain_is, &subdomain_dm));
337         if (num_subdomains) PetscCall(PCGASMSetSubdomains(pc, num_subdomains, inner_subdomain_is, outer_subdomain_is));
338         for (d = 0; d < num_subdomains; ++d) {
339           if (inner_subdomain_is) PetscCall(ISDestroy(&inner_subdomain_is[d]));
340           if (outer_subdomain_is) PetscCall(ISDestroy(&outer_subdomain_is[d]));
341         }
342         PetscCall(PetscFree(inner_subdomain_is));
343         PetscCall(PetscFree(outer_subdomain_is));
344       } else {
345         /* still no subdomains; use one per rank */
346         osm->nmax = osm->n = 1;
347         PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
348         osm->N = size;
349         PetscCall(PCGASMCreateLocalSubdomains(pc->pmat, osm->n, &osm->iis));
350       }
351     }
352     if (!osm->iis) {
353       /*
354        osm->n was set in PCGASMSetSubdomains(), but the actual subdomains have not been supplied.
355        We create the requisite number of local inner subdomains and then expand them into
356        out subdomains, if necessary.
357        */
358       PetscCall(PCGASMCreateLocalSubdomains(pc->pmat, osm->n, &osm->iis));
359     }
360     if (!osm->ois) {
361       /*
362             Initially make outer subdomains the same as inner subdomains. If nonzero additional overlap
363             has been requested, copy the inner subdomains over so they can be modified.
364       */
365       PetscCall(PetscMalloc1(osm->n, &osm->ois));
366       for (i = 0; i < osm->n; ++i) {
367         if (osm->overlap > 0 && osm->N > 1) { /* With positive overlap, osm->iis[i] will be modified */
368           PetscCall(ISDuplicate(osm->iis[i], (osm->ois) + i));
369           PetscCall(ISCopy(osm->iis[i], osm->ois[i]));
370         } else {
371           PetscCall(PetscObjectReference((PetscObject)osm->iis[i]));
372           osm->ois[i] = osm->iis[i];
373         }
374       }
375       if (osm->overlap > 0 && osm->N > 1) {
376         /* Extend the "overlapping" regions by a number of steps */
377         PetscCall(MatIncreaseOverlapSplit(pc->pmat, osm->n, osm->ois, osm->overlap));
378       }
379     }
380 
381     /* Now the subdomains are defined.  Determine their global and max local numbers, if necessary. */
382     if (osm->nmax == PETSC_DETERMINE) {
383       PetscInt inwork, outwork;
384       /* determine global number of subdomains and the max number of local subdomains */
385       inwork = osm->n;
386       PetscCallMPI(MPIU_Allreduce(&inwork, &outwork, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)pc)));
387       osm->nmax = outwork;
388     }
389     if (osm->N == PETSC_DETERMINE) {
390       /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
391       PetscCall(PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc), osm->n, (PetscObject *)osm->ois, &osm->N, NULL));
392     }
393 
394     if (osm->sort_indices) {
395       for (i = 0; i < osm->n; i++) {
396         PetscCall(ISSort(osm->ois[i]));
397         PetscCall(ISSort(osm->iis[i]));
398       }
399     }
400     PetscCall(PCGetOptionsPrefix(pc, &prefix));
401     PetscCall(PCGASMPrintSubdomains(pc));
402 
403     /*
404        Merge the ISs, create merged vectors and restrictions.
405      */
406     /* Merge outer subdomain ISs and construct a restriction onto the disjoint union of local outer subdomains. */
407     on = 0;
408     for (i = 0; i < osm->n; i++) {
409       PetscCall(ISGetLocalSize(osm->ois[i], &oni));
410       on += oni;
411     }
412     PetscCall(PetscMalloc1(on, &oidx));
413     on = 0;
414     /* Merge local indices together */
415     for (i = 0; i < osm->n; i++) {
416       PetscCall(ISGetLocalSize(osm->ois[i], &oni));
417       PetscCall(ISGetIndices(osm->ois[i], &oidxi));
418       PetscCall(PetscArraycpy(oidx + on, oidxi, oni));
419       PetscCall(ISRestoreIndices(osm->ois[i], &oidxi));
420       on += oni;
421     }
422     PetscCall(ISCreateGeneral(((PetscObject)pc)->comm, on, oidx, PETSC_OWN_POINTER, &gois));
423     nTotalInnerIndices = 0;
424     for (i = 0; i < osm->n; i++) {
425       PetscCall(ISGetLocalSize(osm->iis[i], &nInnerIndices));
426       nTotalInnerIndices += nInnerIndices;
427     }
428     PetscCall(VecCreateMPI(((PetscObject)pc)->comm, nTotalInnerIndices, PETSC_DETERMINE, &x));
429     PetscCall(VecDuplicate(x, &y));
430 
431     PetscCall(VecCreateMPI(PetscObjectComm((PetscObject)pc), on, PETSC_DECIDE, &osm->gx));
432     PetscCall(VecDuplicate(osm->gx, &osm->gy));
433     PetscCall(VecGetOwnershipRange(osm->gx, &gostart, NULL));
434     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), on, gostart, 1, &goid));
435     /* gois might indices not on local */
436     PetscCall(VecScatterCreate(x, gois, osm->gx, goid, &osm->gorestriction));
437     PetscCall(PetscMalloc1(osm->n, &numbering));
438     PetscCall(PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc), osm->n, (PetscObject *)osm->ois, NULL, numbering));
439     PetscCall(VecDestroy(&x));
440     PetscCall(ISDestroy(&gois));
441 
442     /* Merge inner subdomain ISs and construct a restriction onto the disjoint union of local inner subdomains. */
443     {
444       PetscInt        ini;   /* Number of indices the i-th a local inner subdomain. */
445       PetscInt        in;    /* Number of indices in the disjoint union of local inner subdomains. */
446       PetscInt       *iidx;  /* Global indices in the merged local inner subdomain. */
447       PetscInt       *ioidx; /* Global indices of the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
448       IS              giis;  /* IS for the disjoint union of inner subdomains. */
449       IS              giois; /* IS for the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
450       PetscScalar    *array;
451       const PetscInt *indices;
452       PetscInt        k;
453       on = 0;
454       for (i = 0; i < osm->n; i++) {
455         PetscCall(ISGetLocalSize(osm->ois[i], &oni));
456         on += oni;
457       }
458       PetscCall(PetscMalloc1(on, &iidx));
459       PetscCall(PetscMalloc1(on, &ioidx));
460       PetscCall(VecGetArray(y, &array));
461       /* set communicator id to determine where overlap is */
462       in = 0;
463       for (i = 0; i < osm->n; i++) {
464         PetscCall(ISGetLocalSize(osm->iis[i], &ini));
465         for (k = 0; k < ini; ++k) array[in + k] = numbering[i];
466         in += ini;
467       }
468       PetscCall(VecRestoreArray(y, &array));
469       PetscCall(VecScatterBegin(osm->gorestriction, y, osm->gy, INSERT_VALUES, SCATTER_FORWARD));
470       PetscCall(VecScatterEnd(osm->gorestriction, y, osm->gy, INSERT_VALUES, SCATTER_FORWARD));
471       PetscCall(VecGetOwnershipRange(osm->gy, &gostart, NULL));
472       PetscCall(VecGetArray(osm->gy, &array));
473       on = 0;
474       in = 0;
475       for (i = 0; i < osm->n; i++) {
476         PetscCall(ISGetLocalSize(osm->ois[i], &oni));
477         PetscCall(ISGetIndices(osm->ois[i], &indices));
478         for (k = 0; k < oni; k++) {
479           /*  skip overlapping indices to get inner domain */
480           if (PetscRealPart(array[on + k]) != numbering[i]) continue;
481           iidx[in]    = indices[k];
482           ioidx[in++] = gostart + on + k;
483         }
484         PetscCall(ISRestoreIndices(osm->ois[i], &indices));
485         on += oni;
486       }
487       PetscCall(VecRestoreArray(osm->gy, &array));
488       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), in, iidx, PETSC_OWN_POINTER, &giis));
489       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), in, ioidx, PETSC_OWN_POINTER, &giois));
490       PetscCall(VecScatterCreate(y, giis, osm->gy, giois, &osm->girestriction));
491       PetscCall(VecDestroy(&y));
492       PetscCall(ISDestroy(&giis));
493       PetscCall(ISDestroy(&giois));
494     }
495     PetscCall(ISDestroy(&goid));
496     PetscCall(PetscFree(numbering));
497 
498     /* Create the subdomain work vectors. */
499     PetscCall(PetscMalloc1(osm->n, &osm->x));
500     PetscCall(PetscMalloc1(osm->n, &osm->y));
501     PetscCall(VecGetArray(osm->gx, &gxarray));
502     PetscCall(VecGetArray(osm->gy, &gyarray));
503     for (i = 0, on = 0; i < osm->n; ++i, on += oni) {
504       PetscInt oNi;
505       PetscCall(ISGetLocalSize(osm->ois[i], &oni));
506       /* on a sub communicator */
507       PetscCall(ISGetSize(osm->ois[i], &oNi));
508       PetscCall(VecCreateMPIWithArray(((PetscObject)osm->ois[i])->comm, 1, oni, oNi, gxarray + on, &osm->x[i]));
509       PetscCall(VecCreateMPIWithArray(((PetscObject)osm->ois[i])->comm, 1, oni, oNi, gyarray + on, &osm->y[i]));
510     }
511     PetscCall(VecRestoreArray(osm->gx, &gxarray));
512     PetscCall(VecRestoreArray(osm->gy, &gyarray));
513     /* Create the subdomain solvers */
514     PetscCall(PetscMalloc1(osm->n, &osm->ksp));
515     for (i = 0; i < osm->n; i++) {
516       char subprefix[PETSC_MAX_PATH_LEN + 1];
517       PetscCall(KSPCreate(((PetscObject)osm->ois[i])->comm, &ksp));
518       PetscCall(KSPSetNestLevel(ksp, pc->kspnestlevel));
519       PetscCall(KSPSetErrorIfNotConverged(ksp, pc->erroriffailure));
520       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ksp, (PetscObject)pc, 1));
521       PetscCall(KSPSetType(ksp, KSPPREONLY));
522       PetscCall(KSPGetPC(ksp, &subpc)); /* Why do we need this here? */
523       if (subdomain_dm) {
524         PetscCall(KSPSetDM(ksp, subdomain_dm[i]));
525         PetscCall(DMDestroy(subdomain_dm + i));
526       }
527       PetscCall(PCGetOptionsPrefix(pc, &prefix));
528       PetscCall(KSPSetOptionsPrefix(ksp, prefix));
529       if (subdomain_names && subdomain_names[i]) {
530         PetscCall(PetscSNPrintf(subprefix, PETSC_MAX_PATH_LEN, "sub_%s_", subdomain_names[i]));
531         PetscCall(KSPAppendOptionsPrefix(ksp, subprefix));
532         PetscCall(PetscFree(subdomain_names[i]));
533       }
534       PetscCall(KSPAppendOptionsPrefix(ksp, "sub_"));
535       osm->ksp[i] = ksp;
536     }
537     PetscCall(PetscFree(subdomain_dm));
538     PetscCall(PetscFree(subdomain_names));
539     scall = MAT_INITIAL_MATRIX;
540   } else { /* if (pc->setupcalled) */
541     /*
542        Destroy the submatrices from the previous iteration
543     */
544     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
545       PetscCall(MatDestroyMatrices(osm->n, &osm->pmat));
546       scall = MAT_INITIAL_MATRIX;
547     }
548     if (osm->permutationIS) {
549       PetscCall(MatCreateSubMatrix(pc->pmat, osm->permutationIS, osm->permutationIS, scall, &osm->permutationP));
550       PetscCall(PetscObjectReference((PetscObject)osm->permutationP));
551       osm->pcmat = pc->pmat;
552       pc->pmat   = osm->permutationP;
553     }
554   }
555 
556   /*
557      Extract the submatrices.
558   */
559   if (size > 1) {
560     PetscCall(MatCreateSubMatricesMPI(pc->pmat, osm->n, osm->ois, osm->ois, scall, &osm->pmat));
561   } else {
562     PetscCall(MatCreateSubMatrices(pc->pmat, osm->n, osm->ois, osm->ois, scall, &osm->pmat));
563   }
564   if (scall == MAT_INITIAL_MATRIX) {
565     PetscCall(PetscObjectGetOptionsPrefix((PetscObject)pc->pmat, &pprefix));
566     for (i = 0; i < osm->n; i++) PetscCall(PetscObjectSetOptionsPrefix((PetscObject)osm->pmat[i], pprefix));
567   }
568 
569   /* Return control to the user so that the submatrices can be modified (e.g., to apply
570      different boundary conditions for the submatrices than for the global problem) */
571   PetscCall(PCModifySubMatrices(pc, osm->n, osm->ois, osm->ois, osm->pmat, pc->modifysubmatricesP));
572 
573   /*
574      Loop over submatrices putting them into local ksps
575   */
576   for (i = 0; i < osm->n; i++) {
577     PetscCall(KSPSetOperators(osm->ksp[i], osm->pmat[i], osm->pmat[i]));
578     PetscCall(KSPGetOptionsPrefix(osm->ksp[i], &prefix));
579     PetscCall(MatSetOptionsPrefix(osm->pmat[i], prefix));
580     if (!pc->setupcalled) PetscCall(KSPSetFromOptions(osm->ksp[i]));
581   }
582   if (osm->pcmat) {
583     PetscCall(MatDestroy(&pc->pmat));
584     pc->pmat   = osm->pcmat;
585     osm->pcmat = NULL;
586   }
587   PetscFunctionReturn(PETSC_SUCCESS);
588 }
589 
590 static PetscErrorCode PCSetUpOnBlocks_GASM(PC pc)
591 {
592   PC_GASM *osm = (PC_GASM *)pc->data;
593   PetscInt i;
594 
595   PetscFunctionBegin;
596   for (i = 0; i < osm->n; i++) PetscCall(KSPSetUp(osm->ksp[i]));
597   PetscFunctionReturn(PETSC_SUCCESS);
598 }
599 
600 static PetscErrorCode PCApply_GASM(PC pc, Vec xin, Vec yout)
601 {
602   PC_GASM    *osm = (PC_GASM *)pc->data;
603   PetscInt    i;
604   Vec         x, y;
605   ScatterMode forward = SCATTER_FORWARD, reverse = SCATTER_REVERSE;
606 
607   PetscFunctionBegin;
608   if (osm->pctoouter) {
609     PetscCall(VecScatterBegin(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
610     PetscCall(VecScatterEnd(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
611     x = osm->pcx;
612     y = osm->pcy;
613   } else {
614     x = xin;
615     y = yout;
616   }
617   /*
618      support for limiting the restriction or interpolation only to the inner
619      subdomain values (leaving the other values 0).
620   */
621   if (!(osm->type & PC_GASM_RESTRICT)) {
622     /* have to zero the work RHS since scatter may leave some slots empty */
623     PetscCall(VecZeroEntries(osm->gx));
624     PetscCall(VecScatterBegin(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
625   } else {
626     PetscCall(VecScatterBegin(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
627   }
628   PetscCall(VecZeroEntries(osm->gy));
629   if (!(osm->type & PC_GASM_RESTRICT)) {
630     PetscCall(VecScatterEnd(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
631   } else {
632     PetscCall(VecScatterEnd(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
633   }
634   /* do the subdomain solves */
635   for (i = 0; i < osm->n; ++i) {
636     PetscCall(KSPSolve(osm->ksp[i], osm->x[i], osm->y[i]));
637     PetscCall(KSPCheckSolve(osm->ksp[i], pc, osm->y[i]));
638   }
639   /* do we need to zero y? */
640   PetscCall(VecZeroEntries(y));
641   if (!(osm->type & PC_GASM_INTERPOLATE)) {
642     PetscCall(VecScatterBegin(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
643     PetscCall(VecScatterEnd(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
644   } else {
645     PetscCall(VecScatterBegin(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
646     PetscCall(VecScatterEnd(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
647   }
648   if (osm->pctoouter) {
649     PetscCall(VecScatterBegin(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
650     PetscCall(VecScatterEnd(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
651   }
652   PetscFunctionReturn(PETSC_SUCCESS);
653 }
654 
655 static PetscErrorCode PCMatApply_GASM(PC pc, Mat Xin, Mat Yout)
656 {
657   PC_GASM    *osm = (PC_GASM *)pc->data;
658   Mat         X, Y, O = NULL, Z, W;
659   Vec         x, y;
660   PetscInt    i, m, M, N;
661   ScatterMode forward = SCATTER_FORWARD, reverse = SCATTER_REVERSE;
662 
663   PetscFunctionBegin;
664   PetscCheck(osm->n == 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Not yet implemented");
665   PetscCall(MatGetSize(Xin, NULL, &N));
666   if (osm->pctoouter) {
667     PetscCall(VecGetLocalSize(osm->pcx, &m));
668     PetscCall(VecGetSize(osm->pcx, &M));
669     PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &O));
670     for (i = 0; i < N; ++i) {
671       PetscCall(MatDenseGetColumnVecRead(Xin, i, &x));
672       PetscCall(MatDenseGetColumnVecWrite(O, i, &y));
673       PetscCall(VecScatterBegin(osm->pctoouter, x, y, INSERT_VALUES, SCATTER_REVERSE));
674       PetscCall(VecScatterEnd(osm->pctoouter, x, y, INSERT_VALUES, SCATTER_REVERSE));
675       PetscCall(MatDenseRestoreColumnVecWrite(O, i, &y));
676       PetscCall(MatDenseRestoreColumnVecRead(Xin, i, &x));
677     }
678     X = Y = O;
679   } else {
680     X = Xin;
681     Y = Yout;
682   }
683   /*
684      support for limiting the restriction or interpolation only to the inner
685      subdomain values (leaving the other values 0).
686   */
687   PetscCall(VecGetLocalSize(osm->x[0], &m));
688   PetscCall(VecGetSize(osm->x[0], &M));
689   PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &Z));
690   for (i = 0; i < N; ++i) {
691     PetscCall(MatDenseGetColumnVecRead(X, i, &x));
692     PetscCall(MatDenseGetColumnVecWrite(Z, i, &y));
693     if (!(osm->type & PC_GASM_RESTRICT)) {
694       /* have to zero the work RHS since scatter may leave some slots empty */
695       PetscCall(VecZeroEntries(y));
696       PetscCall(VecScatterBegin(osm->girestriction, x, y, INSERT_VALUES, forward));
697       PetscCall(VecScatterEnd(osm->girestriction, x, y, INSERT_VALUES, forward));
698     } else {
699       PetscCall(VecScatterBegin(osm->gorestriction, x, y, INSERT_VALUES, forward));
700       PetscCall(VecScatterEnd(osm->gorestriction, x, y, INSERT_VALUES, forward));
701     }
702     PetscCall(MatDenseRestoreColumnVecWrite(Z, i, &y));
703     PetscCall(MatDenseRestoreColumnVecRead(X, i, &x));
704   }
705   PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &W));
706   PetscCall(MatSetOption(Z, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
707   PetscCall(MatAssemblyBegin(Z, MAT_FINAL_ASSEMBLY));
708   PetscCall(MatAssemblyEnd(Z, MAT_FINAL_ASSEMBLY));
709   /* do the subdomain solve */
710   PetscCall(KSPMatSolve(osm->ksp[0], Z, W));
711   PetscCall(KSPCheckSolve(osm->ksp[0], pc, NULL));
712   PetscCall(MatDestroy(&Z));
713   /* do we need to zero y? */
714   PetscCall(MatZeroEntries(Y));
715   for (i = 0; i < N; ++i) {
716     PetscCall(MatDenseGetColumnVecWrite(Y, i, &y));
717     PetscCall(MatDenseGetColumnVecRead(W, i, &x));
718     if (!(osm->type & PC_GASM_INTERPOLATE)) {
719       PetscCall(VecScatterBegin(osm->girestriction, x, y, ADD_VALUES, reverse));
720       PetscCall(VecScatterEnd(osm->girestriction, x, y, ADD_VALUES, reverse));
721     } else {
722       PetscCall(VecScatterBegin(osm->gorestriction, x, y, ADD_VALUES, reverse));
723       PetscCall(VecScatterEnd(osm->gorestriction, x, y, ADD_VALUES, reverse));
724     }
725     PetscCall(MatDenseRestoreColumnVecRead(W, i, &x));
726     if (osm->pctoouter) {
727       PetscCall(MatDenseGetColumnVecWrite(Yout, i, &x));
728       PetscCall(VecScatterBegin(osm->pctoouter, y, x, INSERT_VALUES, SCATTER_FORWARD));
729       PetscCall(VecScatterEnd(osm->pctoouter, y, x, INSERT_VALUES, SCATTER_FORWARD));
730       PetscCall(MatDenseRestoreColumnVecRead(Yout, i, &x));
731     }
732     PetscCall(MatDenseRestoreColumnVecWrite(Y, i, &y));
733   }
734   PetscCall(MatDestroy(&W));
735   PetscCall(MatDestroy(&O));
736   PetscFunctionReturn(PETSC_SUCCESS);
737 }
738 
739 static PetscErrorCode PCApplyTranspose_GASM(PC pc, Vec xin, Vec yout)
740 {
741   PC_GASM    *osm = (PC_GASM *)pc->data;
742   PetscInt    i;
743   Vec         x, y;
744   ScatterMode forward = SCATTER_FORWARD, reverse = SCATTER_REVERSE;
745 
746   PetscFunctionBegin;
747   if (osm->pctoouter) {
748     PetscCall(VecScatterBegin(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
749     PetscCall(VecScatterEnd(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
750     x = osm->pcx;
751     y = osm->pcy;
752   } else {
753     x = xin;
754     y = yout;
755   }
756   /*
757      Support for limiting the restriction or interpolation to only local
758      subdomain values (leaving the other values 0).
759 
760      Note: these are reversed from the PCApply_GASM() because we are applying the
761      transpose of the three terms
762   */
763   if (!(osm->type & PC_GASM_INTERPOLATE)) {
764     /* have to zero the work RHS since scatter may leave some slots empty */
765     PetscCall(VecZeroEntries(osm->gx));
766     PetscCall(VecScatterBegin(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
767   } else {
768     PetscCall(VecScatterBegin(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
769   }
770   PetscCall(VecZeroEntries(osm->gy));
771   if (!(osm->type & PC_GASM_INTERPOLATE)) {
772     PetscCall(VecScatterEnd(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
773   } else {
774     PetscCall(VecScatterEnd(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
775   }
776   /* do the local solves */
777   for (i = 0; i < osm->n; ++i) { /* Note that the solves are local, so we can go to osm->n, rather than osm->nmax. */
778     PetscCall(KSPSolveTranspose(osm->ksp[i], osm->x[i], osm->y[i]));
779     PetscCall(KSPCheckSolve(osm->ksp[i], pc, osm->y[i]));
780   }
781   PetscCall(VecZeroEntries(y));
782   if (!(osm->type & PC_GASM_RESTRICT)) {
783     PetscCall(VecScatterBegin(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
784     PetscCall(VecScatterEnd(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
785   } else {
786     PetscCall(VecScatterBegin(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
787     PetscCall(VecScatterEnd(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
788   }
789   if (osm->pctoouter) {
790     PetscCall(VecScatterBegin(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
791     PetscCall(VecScatterEnd(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
792   }
793   PetscFunctionReturn(PETSC_SUCCESS);
794 }
795 
796 static PetscErrorCode PCReset_GASM(PC pc)
797 {
798   PC_GASM *osm = (PC_GASM *)pc->data;
799   PetscInt i;
800 
801   PetscFunctionBegin;
802   if (osm->ksp) {
803     for (i = 0; i < osm->n; i++) PetscCall(KSPReset(osm->ksp[i]));
804   }
805   if (osm->pmat) {
806     if (osm->n > 0) {
807       PetscMPIInt size;
808       PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
809       if (size > 1) {
810         /* osm->pmat is created by MatCreateSubMatricesMPI(), cannot use MatDestroySubMatrices() */
811         PetscCall(MatDestroyMatrices(osm->n, &osm->pmat));
812       } else {
813         PetscCall(MatDestroySubMatrices(osm->n, &osm->pmat));
814       }
815     }
816   }
817   if (osm->x) {
818     for (i = 0; i < osm->n; i++) {
819       PetscCall(VecDestroy(&osm->x[i]));
820       PetscCall(VecDestroy(&osm->y[i]));
821     }
822   }
823   PetscCall(VecDestroy(&osm->gx));
824   PetscCall(VecDestroy(&osm->gy));
825 
826   PetscCall(VecScatterDestroy(&osm->gorestriction));
827   PetscCall(VecScatterDestroy(&osm->girestriction));
828   if (!osm->user_subdomains) {
829     PetscCall(PCGASMDestroySubdomains(osm->n, &osm->ois, &osm->iis));
830     osm->N    = PETSC_DETERMINE;
831     osm->nmax = PETSC_DETERMINE;
832   }
833   if (osm->pctoouter) PetscCall(VecScatterDestroy(&osm->pctoouter));
834   if (osm->permutationIS) PetscCall(ISDestroy(&osm->permutationIS));
835   if (osm->pcx) PetscCall(VecDestroy(&osm->pcx));
836   if (osm->pcy) PetscCall(VecDestroy(&osm->pcy));
837   if (osm->permutationP) PetscCall(MatDestroy(&osm->permutationP));
838   if (osm->pcmat) PetscCall(MatDestroy(&osm->pcmat));
839   PetscFunctionReturn(PETSC_SUCCESS);
840 }
841 
842 static PetscErrorCode PCDestroy_GASM(PC pc)
843 {
844   PC_GASM *osm = (PC_GASM *)pc->data;
845   PetscInt i;
846 
847   PetscFunctionBegin;
848   PetscCall(PCReset_GASM(pc));
849   /* PCReset will not destroy subdomains, if user_subdomains is true. */
850   PetscCall(PCGASMDestroySubdomains(osm->n, &osm->ois, &osm->iis));
851   if (osm->ksp) {
852     for (i = 0; i < osm->n; i++) PetscCall(KSPDestroy(&osm->ksp[i]));
853     PetscCall(PetscFree(osm->ksp));
854   }
855   PetscCall(PetscFree(osm->x));
856   PetscCall(PetscFree(osm->y));
857   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSubdomains_C", NULL));
858   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetOverlap_C", NULL));
859   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetType_C", NULL));
860   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSortIndices_C", NULL));
861   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMGetSubKSP_C", NULL));
862   PetscCall(PetscFree(pc->data));
863   PetscFunctionReturn(PETSC_SUCCESS);
864 }
865 
866 static PetscErrorCode PCSetFromOptions_GASM(PC pc, PetscOptionItems PetscOptionsObject)
867 {
868   PC_GASM   *osm = (PC_GASM *)pc->data;
869   PetscInt   blocks, ovl;
870   PetscBool  flg;
871   PCGASMType gasmtype;
872 
873   PetscFunctionBegin;
874   PetscOptionsHeadBegin(PetscOptionsObject, "Generalized additive Schwarz options");
875   PetscCall(PetscOptionsBool("-pc_gasm_use_dm_subdomains", "If subdomains aren't set, use DMCreateDomainDecomposition() to define subdomains.", "PCGASMSetUseDMSubdomains", osm->dm_subdomains, &osm->dm_subdomains, &flg));
876   PetscCall(PetscOptionsInt("-pc_gasm_total_subdomains", "Total number of subdomains across communicator", "PCGASMSetTotalSubdomains", osm->N, &blocks, &flg));
877   if (flg) PetscCall(PCGASMSetTotalSubdomains(pc, blocks));
878   PetscCall(PetscOptionsInt("-pc_gasm_overlap", "Number of overlapping degrees of freedom", "PCGASMSetOverlap", osm->overlap, &ovl, &flg));
879   if (flg) {
880     PetscCall(PCGASMSetOverlap(pc, ovl));
881     osm->dm_subdomains = PETSC_FALSE;
882   }
883   flg = PETSC_FALSE;
884   PetscCall(PetscOptionsEnum("-pc_gasm_type", "Type of restriction/extension", "PCGASMSetType", PCGASMTypes, (PetscEnum)osm->type, (PetscEnum *)&gasmtype, &flg));
885   if (flg) PetscCall(PCGASMSetType(pc, gasmtype));
886   PetscCall(PetscOptionsBool("-pc_gasm_use_hierachical_partitioning", "use hierarchical partitioning", NULL, osm->hierarchicalpartitioning, &osm->hierarchicalpartitioning, &flg));
887   PetscOptionsHeadEnd();
888   PetscFunctionReturn(PETSC_SUCCESS);
889 }
890 
891 /*@
892   PCGASMSetTotalSubdomains - sets the total number of subdomains to use across the communicator for `PCGASM`
893 
894   Logically Collective
895 
896   Input Parameters:
897 + pc - the preconditioner
898 - N  - total number of subdomains
899 
900   Level: beginner
901 
902 .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMSetOverlap()`
903           `PCGASMCreateSubdomains2D()`
904 @*/
905 PetscErrorCode PCGASMSetTotalSubdomains(PC pc, PetscInt N)
906 {
907   PC_GASM    *osm = (PC_GASM *)pc->data;
908   PetscMPIInt size, rank;
909 
910   PetscFunctionBegin;
911   PetscCheck(N >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Total number of subdomains must be 1 or more, got N = %" PetscInt_FMT, N);
912   PetscCheck(!pc->setupcalled, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "PCGASMSetTotalSubdomains() should be called before calling PCSetUp().");
913 
914   PetscCall(PCGASMDestroySubdomains(osm->n, &osm->iis, &osm->ois));
915   osm->ois = osm->iis = NULL;
916 
917   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
918   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
919   osm->N             = N;
920   osm->n             = PETSC_DETERMINE;
921   osm->nmax          = PETSC_DETERMINE;
922   osm->dm_subdomains = PETSC_FALSE;
923   PetscFunctionReturn(PETSC_SUCCESS);
924 }
925 
926 static PetscErrorCode PCGASMSetSubdomains_GASM(PC pc, PetscInt n, IS iis[], IS ois[])
927 {
928   PC_GASM *osm = (PC_GASM *)pc->data;
929   PetscInt i;
930 
931   PetscFunctionBegin;
932   PetscCheck(n >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Each MPI rank must have 1 or more subdomains, got n = %" PetscInt_FMT, n);
933   PetscCheck(!pc->setupcalled, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "PCGASMSetSubdomains() should be called before calling PCSetUp().");
934 
935   PetscCall(PCGASMDestroySubdomains(osm->n, &osm->iis, &osm->ois));
936   osm->iis = osm->ois = NULL;
937   osm->n              = n;
938   osm->N              = PETSC_DETERMINE;
939   osm->nmax           = PETSC_DETERMINE;
940   if (ois) {
941     PetscCall(PetscMalloc1(n, &osm->ois));
942     for (i = 0; i < n; i++) {
943       PetscCall(PetscObjectReference((PetscObject)ois[i]));
944       osm->ois[i] = ois[i];
945     }
946     /*
947        Since the user set the outer subdomains, even if nontrivial overlap was requested via PCGASMSetOverlap(),
948        it will be ignored.  To avoid confusion later on (e.g., when viewing the PC), the overlap size is set to -1.
949     */
950     osm->overlap = -1;
951     /* inner subdomains must be provided  */
952     PetscCheck(iis, PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "inner indices have to be provided ");
953   } /* end if */
954   if (iis) {
955     PetscCall(PetscMalloc1(n, &osm->iis));
956     for (i = 0; i < n; i++) {
957       PetscCall(PetscObjectReference((PetscObject)iis[i]));
958       osm->iis[i] = iis[i];
959     }
960     if (!ois) {
961       osm->ois = NULL;
962       /* if user does not provide outer indices, we will create the corresponding outer indices using  osm->overlap =1 in PCSetUp_GASM */
963     }
964   }
965   if (PetscDefined(USE_DEBUG)) {
966     PetscInt        j, rstart, rend, *covered, lsize;
967     const PetscInt *indices;
968     /* check if the inner indices cover and only cover the local portion of the preconditioning matrix */
969     PetscCall(MatGetOwnershipRange(pc->pmat, &rstart, &rend));
970     PetscCall(PetscCalloc1(rend - rstart, &covered));
971     /* check if the current MPI process owns indices from others */
972     for (i = 0; i < n; i++) {
973       PetscCall(ISGetIndices(osm->iis[i], &indices));
974       PetscCall(ISGetLocalSize(osm->iis[i], &lsize));
975       for (j = 0; j < lsize; j++) {
976         PetscCheck(indices[j] >= rstart && indices[j] < rend, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "inner subdomains can not own an index %" PetscInt_FMT " from other ranks", indices[j]);
977         PetscCheck(covered[indices[j] - rstart] != 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "inner subdomains can not have an overlapping index %" PetscInt_FMT " ", indices[j]);
978         covered[indices[j] - rstart] = 1;
979       }
980       PetscCall(ISRestoreIndices(osm->iis[i], &indices));
981     }
982     /* check if we miss any indices */
983     for (i = rstart; i < rend; i++) PetscCheck(covered[i - rstart], PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "local entity %" PetscInt_FMT " was not covered by inner subdomains", i);
984     PetscCall(PetscFree(covered));
985   }
986   if (iis) osm->user_subdomains = PETSC_TRUE;
987   PetscFunctionReturn(PETSC_SUCCESS);
988 }
989 
990 static PetscErrorCode PCGASMSetOverlap_GASM(PC pc, PetscInt ovl)
991 {
992   PC_GASM *osm = (PC_GASM *)pc->data;
993 
994   PetscFunctionBegin;
995   PetscCheck(ovl >= 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Negative overlap value requested");
996   PetscCheck(!pc->setupcalled || ovl == osm->overlap, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "PCGASMSetOverlap() should be called before PCSetUp().");
997   if (!pc->setupcalled) osm->overlap = ovl;
998   PetscFunctionReturn(PETSC_SUCCESS);
999 }
1000 
1001 static PetscErrorCode PCGASMSetType_GASM(PC pc, PCGASMType type)
1002 {
1003   PC_GASM *osm = (PC_GASM *)pc->data;
1004 
1005   PetscFunctionBegin;
1006   osm->type     = type;
1007   osm->type_set = PETSC_TRUE;
1008   PetscFunctionReturn(PETSC_SUCCESS);
1009 }
1010 
1011 static PetscErrorCode PCGASMSetSortIndices_GASM(PC pc, PetscBool doSort)
1012 {
1013   PC_GASM *osm = (PC_GASM *)pc->data;
1014 
1015   PetscFunctionBegin;
1016   osm->sort_indices = doSort;
1017   PetscFunctionReturn(PETSC_SUCCESS);
1018 }
1019 
1020 /*
1021    FIXME: This routine might need to be modified now that multiple processes per subdomain are allowed.
1022         In particular, it would upset the global subdomain number calculation.
1023 */
1024 static PetscErrorCode PCGASMGetSubKSP_GASM(PC pc, PetscInt *n, PetscInt *first, KSP **ksp)
1025 {
1026   PC_GASM *osm = (PC_GASM *)pc->data;
1027 
1028   PetscFunctionBegin;
1029   PetscCheck(osm->n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ORDER, "Need to call PCSetUp() on PC (or KSPSetUp() on the outer KSP object) before calling here");
1030 
1031   if (n) *n = osm->n;
1032   if (first) {
1033     PetscCallMPI(MPI_Scan(&osm->n, first, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)pc)));
1034     *first -= osm->n;
1035   }
1036   if (ksp) {
1037     /* Assume that local solves are now different; not necessarily
1038        true, though!  This flag is used only for PCView_GASM() */
1039     *ksp                        = osm->ksp;
1040     osm->same_subdomain_solvers = PETSC_FALSE;
1041   }
1042   PetscFunctionReturn(PETSC_SUCCESS);
1043 } /* PCGASMGetSubKSP_GASM() */
1044 
1045 /*@
1046   PCGASMSetSubdomains - Sets the subdomains for this MPI process
1047   for the additive Schwarz preconditioner with multiple MPI processes per subdomain, `PCGASM`
1048 
1049   Collective
1050 
1051   Input Parameters:
1052 + pc  - the preconditioner object
1053 . n   - the number of subdomains for this MPI process
1054 . iis - the index sets that define the inner subdomains (or `NULL` for PETSc to determine subdomains), the `iis` array is
1055         copied so may be freed after this call.
1056 - ois - the index sets that define the outer subdomains (or `NULL` to use the same as `iis`, or to construct by expanding `iis` by
1057         the requested overlap), the `ois` array is copied so may be freed after this call.
1058 
1059   Level: advanced
1060 
1061   Notes:
1062   The `IS` indices use the parallel, global numbering of the vector entries.
1063 
1064   Inner subdomains are those where the correction is applied.
1065 
1066   Outer subdomains are those where the residual necessary to obtain the
1067   corrections is obtained (see `PCGASMType` for the use of inner/outer subdomains).
1068 
1069   Both inner and outer subdomains can extend over several MPI processes.
1070   This process' portion of a subdomain is known as a local subdomain.
1071 
1072   Inner subdomains can not overlap with each other, do not have any entities from remote processes,
1073   and  have to cover the entire local subdomain owned by the current process. The index sets on each
1074   process should be ordered such that the ith local subdomain is connected to the ith remote subdomain
1075   on another MPI process.
1076 
1077   By default the `PGASM` preconditioner uses 1 (local) subdomain per MPI process.
1078 
1079   The `iis` and `ois` arrays may be freed after this call using `PCGASMDestroySubdomains()`
1080 
1081 .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`, `PCGASMDestroySubdomains()`,
1082           `PCGASMCreateSubdomains2D()`, `PCGASMGetSubdomains()`
1083 @*/
1084 PetscErrorCode PCGASMSetSubdomains(PC pc, PetscInt n, IS iis[], IS ois[])
1085 {
1086   PC_GASM *osm = (PC_GASM *)pc->data;
1087 
1088   PetscFunctionBegin;
1089   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1090   PetscTryMethod(pc, "PCGASMSetSubdomains_C", (PC, PetscInt, IS[], IS[]), (pc, n, iis, ois));
1091   osm->dm_subdomains = PETSC_FALSE;
1092   PetscFunctionReturn(PETSC_SUCCESS);
1093 }
1094 
1095 /*@
1096   PCGASMSetOverlap - Sets the overlap between a pair of subdomains for the
1097   additive Schwarz preconditioner `PCGASM`.  Either all or no MPI processes in the
1098   pc communicator must call this routine.
1099 
1100   Logically Collective
1101 
1102   Input Parameters:
1103 + pc  - the preconditioner context
1104 - ovl - the amount of overlap between subdomains (ovl >= 0, default value = 0)
1105 
1106   Options Database Key:
1107 . -pc_gasm_overlap <overlap> - Sets overlap
1108 
1109   Level: intermediate
1110 
1111   Notes:
1112   By default the `PCGASM` preconditioner uses 1 subdomain per process.  To use
1113   multiple subdomain per perocessor or "straddling" subdomains that intersect
1114   multiple processes use `PCGASMSetSubdomains()` (or option `-pc_gasm_total_subdomains` <n>).
1115 
1116   The overlap defaults to 0, so if one desires that no additional
1117   overlap be computed beyond what may have been set with a call to
1118   `PCGASMSetSubdomains()`, then `ovl` must be set to be 0.  In particular, if one does
1119   not explicitly set the subdomains in application code, then all overlap would be computed
1120   internally by PETSc, and using an overlap of 0 would result in an `PCGASM`
1121   variant that is equivalent to the block Jacobi preconditioner.
1122 
1123   One can define initial index sets with any overlap via
1124   `PCGASMSetSubdomains()`; the routine `PCGASMSetOverlap()` merely allows
1125   PETSc to extend that overlap further, if desired.
1126 
1127 .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1128           `PCGASMCreateSubdomains2D()`, `PCGASMGetSubdomains()`
1129 @*/
1130 PetscErrorCode PCGASMSetOverlap(PC pc, PetscInt ovl)
1131 {
1132   PC_GASM *osm = (PC_GASM *)pc->data;
1133 
1134   PetscFunctionBegin;
1135   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1136   PetscValidLogicalCollectiveInt(pc, ovl, 2);
1137   PetscTryMethod(pc, "PCGASMSetOverlap_C", (PC, PetscInt), (pc, ovl));
1138   osm->dm_subdomains = PETSC_FALSE;
1139   PetscFunctionReturn(PETSC_SUCCESS);
1140 }
1141 
1142 /*@
1143   PCGASMSetType - Sets the type of restriction and interpolation used
1144   for local problems in the `PCGASM` additive Schwarz method.
1145 
1146   Logically Collective
1147 
1148   Input Parameters:
1149 + pc   - the preconditioner context
1150 - type - variant of `PCGASM`, one of
1151 .vb
1152       `PC_GASM_BASIC`       - full interpolation and restriction
1153       `PC_GASM_RESTRICT`    - full restriction, local MPI process interpolation
1154       `PC_GASM_INTERPOLATE` - full interpolation, local MPI process restriction
1155       `PC_GASM_NONE`        - local MPI process restriction and interpolation
1156 .ve
1157 
1158   Options Database Key:
1159 . -pc_gasm_type [basic,restrict,interpolate,none] - Sets `PCGASM` type
1160 
1161   Level: intermediate
1162 
1163 .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1164           `PCGASMCreateSubdomains2D()`, `PCASM`, `PCASMSetType()`
1165 @*/
1166 PetscErrorCode PCGASMSetType(PC pc, PCGASMType type)
1167 {
1168   PetscFunctionBegin;
1169   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1170   PetscValidLogicalCollectiveEnum(pc, type, 2);
1171   PetscTryMethod(pc, "PCGASMSetType_C", (PC, PCGASMType), (pc, type));
1172   PetscFunctionReturn(PETSC_SUCCESS);
1173 }
1174 
1175 /*@
1176   PCGASMSetSortIndices - Determines whether subdomain indices are sorted.
1177 
1178   Logically Collective
1179 
1180   Input Parameters:
1181 + pc     - the preconditioner context
1182 - doSort - sort the subdomain indices
1183 
1184   Level: intermediate
1185 
1186 .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1187           `PCGASMCreateSubdomains2D()`
1188 @*/
1189 PetscErrorCode PCGASMSetSortIndices(PC pc, PetscBool doSort)
1190 {
1191   PetscFunctionBegin;
1192   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1193   PetscValidLogicalCollectiveBool(pc, doSort, 2);
1194   PetscTryMethod(pc, "PCGASMSetSortIndices_C", (PC, PetscBool), (pc, doSort));
1195   PetscFunctionReturn(PETSC_SUCCESS);
1196 }
1197 
1198 /*@C
1199   PCGASMGetSubKSP - Gets the local `KSP` contexts for all subdomains on this MPI process.
1200 
1201   Collective iff first_local is requested
1202 
1203   Input Parameter:
1204 . pc - the preconditioner context
1205 
1206   Output Parameters:
1207 + n_local     - the number of blocks on this MPI process or `NULL`
1208 . first_local - the global number of the first block on this process or `NULL`, all processes must request or all must pass `NULL`
1209 - ksp         - the array of `KSP` contexts
1210 
1211   Level: advanced
1212 
1213   Note:
1214   After `PCGASMGetSubKSP()` the array of `KSP`es is not to be freed
1215 
1216   Currently for some matrix implementations only 1 block per MPI process
1217   is supported.
1218 
1219   You must call `KSPSetUp()` before calling `PCGASMGetSubKSP()`.
1220 
1221 .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMSetOverlap()`,
1222           `PCGASMCreateSubdomains2D()`,
1223 @*/
1224 PetscErrorCode PCGASMGetSubKSP(PC pc, PetscInt *n_local, PetscInt *first_local, KSP *ksp[])
1225 {
1226   PetscFunctionBegin;
1227   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1228   PetscUseMethod(pc, "PCGASMGetSubKSP_C", (PC, PetscInt *, PetscInt *, KSP **), (pc, n_local, first_local, ksp));
1229   PetscFunctionReturn(PETSC_SUCCESS);
1230 }
1231 
1232 /*MC
1233    PCGASM - Use the (restricted) additive Schwarz method, each block is (approximately) solved with
1234            its own `KSP` object on a subset of MPI processes
1235 
1236    Options Database Keys:
1237 +  -pc_gasm_total_subdomains <n>                   - Sets total number of local subdomains to be distributed among the MPI processes
1238 .  -pc_gasm_view_subdomains                        - activates the printing of subdomain indices in `PCView()`, -ksp_view or -snes_view
1239 .  -pc_gasm_print_subdomains                       - activates the printing of subdomain indices in `PCSetUp()`
1240 .  -pc_gasm_overlap <ovl>                          - Sets overlap by which to (automatically) extend local subdomains
1241 -  -pc_gasm_type [basic,restrict,interpolate,none] - Sets `PCGASMType`
1242 
1243    Level: beginner
1244 
1245    Notes:
1246    To set options on the solvers for each block append `-sub_` to all the `KSP`, and `PC`
1247    options database keys. For example, `-sub_pc_type ilu -sub_pc_factor_levels 1 -sub_ksp_type preonly`
1248 
1249    To set the options on the solvers separate for each block call `PCGASMGetSubKSP()`
1250    and set the options directly on the resulting `KSP` object (you can access its `PC`
1251    with `KSPGetPC()`)
1252 
1253    See {cite}`dryja1987additive` and {cite}`1sbg` for details on additive Schwarz algorithms
1254 
1255 .seealso: [](ch_ksp), `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCASM`, `PCGASMType`, `PCGASMSetType()`,
1256           `PCBJACOBI`, `PCGASMGetSubKSP()`, `PCGASMSetSubdomains()`,
1257           `PCSetModifySubMatrices()`, `PCGASMSetOverlap()`, `PCGASMSetType()`
1258 M*/
1259 
1260 PETSC_EXTERN PetscErrorCode PCCreate_GASM(PC pc)
1261 {
1262   PC_GASM *osm;
1263 
1264   PetscFunctionBegin;
1265   PetscCall(PetscNew(&osm));
1266 
1267   osm->N                        = PETSC_DETERMINE;
1268   osm->n                        = PETSC_DECIDE;
1269   osm->nmax                     = PETSC_DETERMINE;
1270   osm->overlap                  = 0;
1271   osm->ksp                      = NULL;
1272   osm->gorestriction            = NULL;
1273   osm->girestriction            = NULL;
1274   osm->pctoouter                = NULL;
1275   osm->gx                       = NULL;
1276   osm->gy                       = NULL;
1277   osm->x                        = NULL;
1278   osm->y                        = NULL;
1279   osm->pcx                      = NULL;
1280   osm->pcy                      = NULL;
1281   osm->permutationIS            = NULL;
1282   osm->permutationP             = NULL;
1283   osm->pcmat                    = NULL;
1284   osm->ois                      = NULL;
1285   osm->iis                      = NULL;
1286   osm->pmat                     = NULL;
1287   osm->type                     = PC_GASM_RESTRICT;
1288   osm->same_subdomain_solvers   = PETSC_TRUE;
1289   osm->sort_indices             = PETSC_TRUE;
1290   osm->dm_subdomains            = PETSC_FALSE;
1291   osm->hierarchicalpartitioning = PETSC_FALSE;
1292 
1293   pc->data                 = (void *)osm;
1294   pc->ops->apply           = PCApply_GASM;
1295   pc->ops->matapply        = PCMatApply_GASM;
1296   pc->ops->applytranspose  = PCApplyTranspose_GASM;
1297   pc->ops->setup           = PCSetUp_GASM;
1298   pc->ops->reset           = PCReset_GASM;
1299   pc->ops->destroy         = PCDestroy_GASM;
1300   pc->ops->setfromoptions  = PCSetFromOptions_GASM;
1301   pc->ops->setuponblocks   = PCSetUpOnBlocks_GASM;
1302   pc->ops->view            = PCView_GASM;
1303   pc->ops->applyrichardson = NULL;
1304 
1305   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSubdomains_C", PCGASMSetSubdomains_GASM));
1306   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetOverlap_C", PCGASMSetOverlap_GASM));
1307   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetType_C", PCGASMSetType_GASM));
1308   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSortIndices_C", PCGASMSetSortIndices_GASM));
1309   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMGetSubKSP_C", PCGASMGetSubKSP_GASM));
1310   PetscFunctionReturn(PETSC_SUCCESS);
1311 }
1312 
1313 PetscErrorCode PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[])
1314 {
1315   MatPartitioning mpart;
1316   const char     *prefix;
1317   PetscInt        i, j, rstart, rend, bs;
1318   PetscBool       hasop, isbaij = PETSC_FALSE, foundpart = PETSC_FALSE;
1319   Mat             Ad = NULL, adj;
1320   IS              ispart, isnumb, *is;
1321 
1322   PetscFunctionBegin;
1323   PetscCheck(nloc >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "number of local subdomains must > 0, got nloc = %" PetscInt_FMT, nloc);
1324 
1325   /* Get prefix, row distribution, and block size */
1326   PetscCall(MatGetOptionsPrefix(A, &prefix));
1327   PetscCall(MatGetOwnershipRange(A, &rstart, &rend));
1328   PetscCall(MatGetBlockSize(A, &bs));
1329   PetscCheck(rstart / bs * bs == rstart && rend / bs * bs == rend, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "bad row distribution [%" PetscInt_FMT ",%" PetscInt_FMT ") for matrix block size %" PetscInt_FMT, rstart, rend, bs);
1330 
1331   /* Get diagonal block from matrix if possible */
1332   PetscCall(MatHasOperation(A, MATOP_GET_DIAGONAL_BLOCK, &hasop));
1333   if (hasop) PetscCall(MatGetDiagonalBlock(A, &Ad));
1334   if (Ad) {
1335     PetscCall(PetscObjectBaseTypeCompare((PetscObject)Ad, MATSEQBAIJ, &isbaij));
1336     if (!isbaij) PetscCall(PetscObjectBaseTypeCompare((PetscObject)Ad, MATSEQSBAIJ, &isbaij));
1337   }
1338   if (Ad && nloc > 1) {
1339     PetscBool match, done;
1340     /* Try to setup a good matrix partitioning if available */
1341     PetscCall(MatPartitioningCreate(PETSC_COMM_SELF, &mpart));
1342     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)mpart, prefix));
1343     PetscCall(MatPartitioningSetFromOptions(mpart));
1344     PetscCall(PetscObjectTypeCompare((PetscObject)mpart, MATPARTITIONINGCURRENT, &match));
1345     if (!match) PetscCall(PetscObjectTypeCompare((PetscObject)mpart, MATPARTITIONINGSQUARE, &match));
1346     if (!match) { /* assume a "good" partitioner is available */
1347       PetscInt        na;
1348       const PetscInt *ia, *ja;
1349       PetscCall(MatGetRowIJ(Ad, 0, PETSC_TRUE, isbaij, &na, &ia, &ja, &done));
1350       if (done) {
1351         /* Build adjacency matrix by hand. Unfortunately a call to
1352            MatConvert(Ad,MATMPIADJ,MAT_INITIAL_MATRIX,&adj) will
1353            remove the block-aij structure and we cannot expect
1354            MatPartitioning to split vertices as we need */
1355         PetscInt        i, j, len, nnz, cnt, *iia = NULL, *jja = NULL;
1356         const PetscInt *row;
1357         nnz = 0;
1358         for (i = 0; i < na; i++) { /* count number of nonzeros */
1359           len = ia[i + 1] - ia[i];
1360           row = ja + ia[i];
1361           for (j = 0; j < len; j++) {
1362             if (row[j] == i) { /* don't count diagonal */
1363               len--;
1364               break;
1365             }
1366           }
1367           nnz += len;
1368         }
1369         PetscCall(PetscMalloc1(na + 1, &iia));
1370         PetscCall(PetscMalloc1(nnz, &jja));
1371         nnz    = 0;
1372         iia[0] = 0;
1373         for (i = 0; i < na; i++) { /* fill adjacency */
1374           cnt = 0;
1375           len = ia[i + 1] - ia[i];
1376           row = ja + ia[i];
1377           for (j = 0; j < len; j++) {
1378             if (row[j] != i) jja[nnz + cnt++] = row[j]; /* if not diagonal */
1379           }
1380           nnz += cnt;
1381           iia[i + 1] = nnz;
1382         }
1383         /* Partitioning of the adjacency matrix */
1384         PetscCall(MatCreateMPIAdj(PETSC_COMM_SELF, na, na, iia, jja, NULL, &adj));
1385         PetscCall(MatPartitioningSetAdjacency(mpart, adj));
1386         PetscCall(MatPartitioningSetNParts(mpart, nloc));
1387         PetscCall(MatPartitioningApply(mpart, &ispart));
1388         PetscCall(ISPartitioningToNumbering(ispart, &isnumb));
1389         PetscCall(MatDestroy(&adj));
1390         foundpart = PETSC_TRUE;
1391       }
1392       PetscCall(MatRestoreRowIJ(Ad, 0, PETSC_TRUE, isbaij, &na, &ia, &ja, &done));
1393     }
1394     PetscCall(MatPartitioningDestroy(&mpart));
1395   }
1396   PetscCall(PetscMalloc1(nloc, &is));
1397   if (!foundpart) {
1398     /* Partitioning by contiguous chunks of rows */
1399 
1400     PetscInt mbs   = (rend - rstart) / bs;
1401     PetscInt start = rstart;
1402     for (i = 0; i < nloc; i++) {
1403       PetscInt count = (mbs / nloc + ((mbs % nloc) > i)) * bs;
1404       PetscCall(ISCreateStride(PETSC_COMM_SELF, count, start, 1, &is[i]));
1405       start += count;
1406     }
1407 
1408   } else {
1409     /* Partitioning by adjacency of diagonal block  */
1410 
1411     const PetscInt *numbering;
1412     PetscInt       *count, nidx, *indices, *newidx, start = 0;
1413     /* Get node count in each partition */
1414     PetscCall(PetscMalloc1(nloc, &count));
1415     PetscCall(ISPartitioningCount(ispart, nloc, count));
1416     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1417       for (i = 0; i < nloc; i++) count[i] *= bs;
1418     }
1419     /* Build indices from node numbering */
1420     PetscCall(ISGetLocalSize(isnumb, &nidx));
1421     PetscCall(PetscMalloc1(nidx, &indices));
1422     for (i = 0; i < nidx; i++) indices[i] = i; /* needs to be initialized */
1423     PetscCall(ISGetIndices(isnumb, &numbering));
1424     PetscCall(PetscSortIntWithPermutation(nidx, numbering, indices));
1425     PetscCall(ISRestoreIndices(isnumb, &numbering));
1426     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1427       PetscCall(PetscMalloc1(nidx * bs, &newidx));
1428       for (i = 0; i < nidx; i++) {
1429         for (j = 0; j < bs; j++) newidx[i * bs + j] = indices[i] * bs + j;
1430       }
1431       PetscCall(PetscFree(indices));
1432       nidx *= bs;
1433       indices = newidx;
1434     }
1435     /* Shift to get global indices */
1436     for (i = 0; i < nidx; i++) indices[i] += rstart;
1437 
1438     /* Build the index sets for each block */
1439     for (i = 0; i < nloc; i++) {
1440       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count[i], &indices[start], PETSC_COPY_VALUES, &is[i]));
1441       PetscCall(ISSort(is[i]));
1442       start += count[i];
1443     }
1444 
1445     PetscCall(PetscFree(count));
1446     PetscCall(PetscFree(indices));
1447     PetscCall(ISDestroy(&isnumb));
1448     PetscCall(ISDestroy(&ispart));
1449   }
1450   *iis = is;
1451   PetscFunctionReturn(PETSC_SUCCESS);
1452 }
1453 
1454 PETSC_INTERN PetscErrorCode PCGASMCreateStraddlingSubdomains(Mat A, PetscInt N, PetscInt *n, IS *iis[])
1455 {
1456   PetscFunctionBegin;
1457   PetscCall(MatSubdomainsCreateCoalesce(A, N, n, iis));
1458   PetscFunctionReturn(PETSC_SUCCESS);
1459 }
1460 
1461 /*@C
1462   PCGASMCreateSubdomains - Creates `n` index sets defining `n` nonoverlapping subdomains on this MPI process for the `PCGASM` additive
1463   Schwarz preconditioner for a any problem based on its matrix.
1464 
1465   Collective
1466 
1467   Input Parameters:
1468 + A - The global matrix operator
1469 - N - the number of global subdomains requested
1470 
1471   Output Parameters:
1472 + n   - the number of subdomains created on this MPI process
1473 - iis - the array of index sets defining the local inner subdomains (on which the correction is applied)
1474 
1475   Level: advanced
1476 
1477   Notes:
1478   When `N` >= A's communicator size, each subdomain is local -- contained within a single MPI process.
1479   When `N` < size, the subdomains are 'straddling' (process boundaries) and are no longer local.
1480   The resulting subdomains can be use in `PCGASMSetSubdomains`(pc,n,iss,`NULL`).  The overlapping
1481   outer subdomains will be automatically generated from these according to the requested amount of
1482   overlap; this is currently supported only with local subdomains.
1483 
1484   Use `PCGASMDestroySubdomains()` to free the array and the list of index sets.
1485 
1486 .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMDestroySubdomains()`
1487 @*/
1488 PetscErrorCode PCGASMCreateSubdomains(Mat A, PetscInt N, PetscInt *n, IS *iis[])
1489 {
1490   PetscMPIInt size;
1491 
1492   PetscFunctionBegin;
1493   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
1494   PetscAssertPointer(iis, 4);
1495 
1496   PetscCheck(N >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of subdomains must be > 0, N = %" PetscInt_FMT, N);
1497   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
1498   if (N >= size) {
1499     *n = N / size + (N % size);
1500     PetscCall(PCGASMCreateLocalSubdomains(A, *n, iis));
1501   } else {
1502     PetscCall(PCGASMCreateStraddlingSubdomains(A, N, n, iis));
1503   }
1504   PetscFunctionReturn(PETSC_SUCCESS);
1505 }
1506 
1507 /*@C
1508   PCGASMDestroySubdomains - Destroys the index sets created with
1509   `PCGASMCreateSubdomains()` or `PCGASMCreateSubdomains2D()`. Should be
1510   called after setting subdomains with `PCGASMSetSubdomains()`.
1511 
1512   Collective
1513 
1514   Input Parameters:
1515 + n   - the number of index sets
1516 . iis - the array of inner subdomains
1517 - ois - the array of outer subdomains, can be `NULL`
1518 
1519   Level: intermediate
1520 
1521   Note:
1522   This is a convenience subroutine that walks each list,
1523   destroys each `IS` on the list, and then frees the list. At the end the
1524   list pointers are set to `NULL`.
1525 
1526 .seealso: [](ch_ksp), `PCGASM`, `PCGASMCreateSubdomains()`, `PCGASMSetSubdomains()`
1527 @*/
1528 PetscErrorCode PCGASMDestroySubdomains(PetscInt n, IS *iis[], IS *ois[])
1529 {
1530   PetscInt i;
1531 
1532   PetscFunctionBegin;
1533   if (n <= 0) PetscFunctionReturn(PETSC_SUCCESS);
1534   if (ois) {
1535     PetscAssertPointer(ois, 3);
1536     if (*ois) {
1537       PetscAssertPointer(*ois, 3);
1538       for (i = 0; i < n; i++) PetscCall(ISDestroy(&(*ois)[i]));
1539       PetscCall(PetscFree(*ois));
1540     }
1541   }
1542   if (iis) {
1543     PetscAssertPointer(iis, 2);
1544     if (*iis) {
1545       PetscAssertPointer(*iis, 2);
1546       for (i = 0; i < n; i++) PetscCall(ISDestroy(&(*iis)[i]));
1547       PetscCall(PetscFree(*iis));
1548     }
1549   }
1550   PetscFunctionReturn(PETSC_SUCCESS);
1551 }
1552 
1553 #define PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, xleft_loc, ylow_loc, xright_loc, yhigh_loc, n) \
1554   do { \
1555     PetscInt first_row = first / M, last_row = last / M + 1; \
1556     /*                                                                                                    \
1557      Compute ylow_loc and yhigh_loc so that (ylow_loc,xleft) and (yhigh_loc,xright) are the corners       \
1558      of the bounding box of the intersection of the subdomain with the local ownership range (local       \
1559      subdomain).                                                                                          \
1560      Also compute xleft_loc and xright_loc as the lower and upper bounds on the first and last rows       \
1561      of the intersection.                                                                                 \
1562     */ \
1563     /* ylow_loc is the grid row containing the first element of the local sumbdomain */ \
1564     *ylow_loc = PetscMax(first_row, ylow); \
1565     /* xleft_loc is the offset of first element of the local subdomain within its grid row (might actually be outside the local subdomain) */ \
1566     *xleft_loc = *ylow_loc == first_row ? PetscMax(first % M, xleft) : xleft; \
1567     /* yhigh_loc is the grid row above the last local subdomain element */ \
1568     *yhigh_loc = PetscMin(last_row, yhigh); \
1569     /* xright is the offset of the end of the  local subdomain within its grid row (might actually be outside the local subdomain) */ \
1570     *xright_loc = *yhigh_loc == last_row ? PetscMin(xright, last % M) : xright; \
1571     /* Now compute the size of the local subdomain n. */ \
1572     *n = 0; \
1573     if (*ylow_loc < *yhigh_loc) { \
1574       PetscInt width = xright - xleft; \
1575       *n += width * (*yhigh_loc - *ylow_loc - 1); \
1576       *n += PetscMin(PetscMax(*xright_loc - xleft, 0), width); \
1577       *n -= PetscMin(PetscMax(*xleft_loc - xleft, 0), width); \
1578     } \
1579   } while (0)
1580 
1581 /*@C
1582   PCGASMCreateSubdomains2D - Creates the index sets for the `PCGASM` overlapping Schwarz
1583   preconditioner for a two-dimensional problem on a regular grid.
1584 
1585   Collective
1586 
1587   Input Parameters:
1588 + pc       - the preconditioner context
1589 . M        - the global number of grid points in the x direction
1590 . N        - the global number of grid points in the y direction
1591 . Mdomains - the global number of subdomains in the x direction
1592 . Ndomains - the global number of subdomains in the y direction
1593 . dof      - degrees of freedom per node
1594 - overlap  - overlap in mesh lines
1595 
1596   Output Parameters:
1597 + nsub - the number of local subdomains created
1598 . iis  - array of index sets defining inner (nonoverlapping) subdomains
1599 - ois  - array of index sets defining outer (overlapping, if overlap > 0) subdomains
1600 
1601   Level: advanced
1602 
1603   Note:
1604   Use `PCGASMDestroySubdomains()` to free the index sets and the arrays
1605 
1606 .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`, `PCGASMSetOverlap()`, `PCASMCreateSubdomains2D()`,
1607           `PCGASMDestroySubdomains()`
1608 @*/
1609 PetscErrorCode PCGASMCreateSubdomains2D(PC pc, PetscInt M, PetscInt N, PetscInt Mdomains, PetscInt Ndomains, PetscInt dof, PetscInt overlap, PetscInt *nsub, IS *iis[], IS *ois[])
1610 {
1611   PetscMPIInt size, rank;
1612   PetscInt    i, j;
1613   PetscInt    maxheight, maxwidth;
1614   PetscInt    xstart, xleft, xright, xleft_loc, xright_loc;
1615   PetscInt    ystart, ylow, yhigh, ylow_loc, yhigh_loc;
1616   PetscInt    x[2][2], y[2][2], n[2];
1617   PetscInt    first, last;
1618   PetscInt    nidx, *idx;
1619   PetscInt    ii, jj, s, q, d;
1620   PetscInt    k, kk;
1621   PetscMPIInt color;
1622   MPI_Comm    comm, subcomm;
1623   IS        **xis = NULL, **is = ois, **is_local = iis;
1624 
1625   PetscFunctionBegin;
1626   PetscCall(PetscObjectGetComm((PetscObject)pc, &comm));
1627   PetscCallMPI(MPI_Comm_size(comm, &size));
1628   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1629   PetscCall(MatGetOwnershipRange(pc->pmat, &first, &last));
1630   PetscCheck((first % dof) == 0 && (last % dof) == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE,
1631              "Matrix row partitioning unsuitable for domain decomposition: local row range (%" PetscInt_FMT ",%" PetscInt_FMT ") "
1632              "does not respect the number of degrees of freedom per grid point %" PetscInt_FMT,
1633              first, last, dof);
1634 
1635   /* Determine the number of domains with nonzero intersections with the local ownership range. */
1636   s      = 0;
1637   ystart = 0;
1638   for (j = 0; j < Ndomains; ++j) {
1639     maxheight = N / Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1640     PetscCheck(maxheight >= 2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Too many %" PetscInt_FMT " subdomains in the vertical direction for mesh height %" PetscInt_FMT, Ndomains, N);
1641     /* Vertical domain limits with an overlap. */
1642     ylow   = PetscMax(ystart - overlap, 0);
1643     yhigh  = PetscMin(ystart + maxheight + overlap, N);
1644     xstart = 0;
1645     for (i = 0; i < Mdomains; ++i) {
1646       maxwidth = M / Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1647       PetscCheck(maxwidth >= 2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Too many %" PetscInt_FMT " subdomains in the horizontal direction for mesh width %" PetscInt_FMT, Mdomains, M);
1648       /* Horizontal domain limits with an overlap. */
1649       xleft  = PetscMax(xstart - overlap, 0);
1650       xright = PetscMin(xstart + maxwidth + overlap, M);
1651       /*
1652          Determine whether this subdomain intersects this rank's ownership range of pc->pmat.
1653       */
1654       PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, (&xleft_loc), (&ylow_loc), (&xright_loc), (&yhigh_loc), (&nidx));
1655       if (nidx) ++s;
1656       xstart += maxwidth;
1657     } /* for (i = 0; i < Mdomains; ++i) */
1658     ystart += maxheight;
1659   } /* for (j = 0; j < Ndomains; ++j) */
1660 
1661   /* Now we can allocate the necessary number of ISs. */
1662   *nsub = s;
1663   PetscCall(PetscMalloc1(*nsub, is));
1664   PetscCall(PetscMalloc1(*nsub, is_local));
1665   s      = 0;
1666   ystart = 0;
1667   for (j = 0; j < Ndomains; ++j) {
1668     maxheight = N / Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1669     PetscCheck(maxheight >= 2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Too many %" PetscInt_FMT " subdomains in the vertical direction for mesh height %" PetscInt_FMT, Ndomains, N);
1670     /* Vertical domain limits with an overlap. */
1671     y[0][0] = PetscMax(ystart - overlap, 0);
1672     y[0][1] = PetscMin(ystart + maxheight + overlap, N);
1673     /* Vertical domain limits without an overlap. */
1674     y[1][0] = ystart;
1675     y[1][1] = PetscMin(ystart + maxheight, N);
1676     xstart  = 0;
1677     for (i = 0; i < Mdomains; ++i) {
1678       maxwidth = M / Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1679       PetscCheck(maxwidth >= 2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Too many %" PetscInt_FMT " subdomains in the horizontal direction for mesh width %" PetscInt_FMT, Mdomains, M);
1680       /* Horizontal domain limits with an overlap. */
1681       x[0][0] = PetscMax(xstart - overlap, 0);
1682       x[0][1] = PetscMin(xstart + maxwidth + overlap, M);
1683       /* Horizontal domain limits without an overlap. */
1684       x[1][0] = xstart;
1685       x[1][1] = PetscMin(xstart + maxwidth, M);
1686       /*
1687          Determine whether this domain intersects this rank's ownership range of pc->pmat.
1688          Do this twice: first for the domains with overlaps, and once without.
1689          During the first pass create the subcommunicators, and use them on the second pass as well.
1690       */
1691       for (q = 0; q < 2; ++q) {
1692         PetscBool split = PETSC_FALSE;
1693         /*
1694           domain limits, (xleft, xright) and (ylow, yheigh) are adjusted
1695           according to whether the domain with an overlap or without is considered.
1696         */
1697         xleft  = x[q][0];
1698         xright = x[q][1];
1699         ylow   = y[q][0];
1700         yhigh  = y[q][1];
1701         PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, (&xleft_loc), (&ylow_loc), (&xright_loc), (&yhigh_loc), (&nidx));
1702         nidx *= dof;
1703         n[q] = nidx;
1704         /*
1705          Based on the counted number of indices in the local domain *with an overlap*,
1706          construct a subcommunicator of all the MPI ranks supporting this domain.
1707          Observe that a domain with an overlap might have nontrivial local support,
1708          while the domain without an overlap might not.  Hence, the decision to participate
1709          in the subcommunicator must be based on the domain with an overlap.
1710          */
1711         if (q == 0) {
1712           if (nidx) color = 1;
1713           else color = MPI_UNDEFINED;
1714           PetscCallMPI(MPI_Comm_split(comm, color, rank, &subcomm));
1715           split = PETSC_TRUE;
1716         }
1717         /*
1718          Proceed only if the number of local indices *with an overlap* is nonzero.
1719          */
1720         if (n[0]) {
1721           if (q == 0) xis = is;
1722           if (q == 1) {
1723             /*
1724              The IS for the no-overlap subdomain shares a communicator with the overlapping domain.
1725              Moreover, if the overlap is zero, the two ISs are identical.
1726              */
1727             if (overlap == 0) {
1728               (*is_local)[s] = (*is)[s];
1729               PetscCall(PetscObjectReference((PetscObject)(*is)[s]));
1730               continue;
1731             } else {
1732               xis     = is_local;
1733               subcomm = ((PetscObject)(*is)[s])->comm;
1734             }
1735           } /* if (q == 1) */
1736           idx = NULL;
1737           PetscCall(PetscMalloc1(nidx, &idx));
1738           if (nidx) {
1739             k = 0;
1740             for (jj = ylow_loc; jj < yhigh_loc; ++jj) {
1741               PetscInt x0 = (jj == ylow_loc) ? xleft_loc : xleft;
1742               PetscInt x1 = (jj == yhigh_loc - 1) ? xright_loc : xright;
1743               kk          = dof * (M * jj + x0);
1744               for (ii = x0; ii < x1; ++ii) {
1745                 for (d = 0; d < dof; ++d) idx[k++] = kk++;
1746               }
1747             }
1748           }
1749           PetscCall(ISCreateGeneral(subcomm, nidx, idx, PETSC_OWN_POINTER, (*xis) + s));
1750           if (split) PetscCallMPI(MPI_Comm_free(&subcomm));
1751         } /* if (n[0]) */
1752       } /* for (q = 0; q < 2; ++q) */
1753       if (n[0]) ++s;
1754       xstart += maxwidth;
1755     } /* for (i = 0; i < Mdomains; ++i) */
1756     ystart += maxheight;
1757   } /* for (j = 0; j < Ndomains; ++j) */
1758   PetscFunctionReturn(PETSC_SUCCESS);
1759 }
1760 
1761 /*@C
1762   PCGASMGetSubdomains - Gets the subdomains supported on this MPI process
1763   for the `PCGASM` additive Schwarz preconditioner.
1764 
1765   Not Collective
1766 
1767   Input Parameter:
1768 . pc - the preconditioner context
1769 
1770   Output Parameters:
1771 + n   - the number of subdomains for this MPI process (default value = 1)
1772 . iis - the index sets that define the inner subdomains (without overlap) supported on this process (can be `NULL`)
1773 - ois - the index sets that define the outer subdomains (with overlap) supported on this process (can be `NULL`)
1774 
1775   Level: advanced
1776 
1777   Notes:
1778   The user is responsible for destroying the `IS`s and freeing the returned arrays, this can be done with
1779   `PCGASMDestroySubdomains()`
1780 
1781   The `IS` numbering is in the parallel, global numbering of the vector.
1782 
1783 .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`, `PCGASMCreateSubdomains2D()`,
1784           `PCGASMSetSubdomains()`, `PCGASMGetSubmatrices()`, `PCGASMDestroySubdomains()`
1785 @*/
1786 PetscErrorCode PCGASMGetSubdomains(PC pc, PetscInt *n, IS *iis[], IS *ois[])
1787 {
1788   PC_GASM  *osm;
1789   PetscBool match;
1790   PetscInt  i;
1791 
1792   PetscFunctionBegin;
1793   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1794   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1795   PetscCheck(match, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Incorrect object type: expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1796   osm = (PC_GASM *)pc->data;
1797   if (n) *n = osm->n;
1798   if (iis) PetscCall(PetscMalloc1(osm->n, iis));
1799   if (ois) PetscCall(PetscMalloc1(osm->n, ois));
1800   if (iis || ois) {
1801     for (i = 0; i < osm->n; ++i) {
1802       if (iis) (*iis)[i] = osm->iis[i];
1803       if (ois) (*ois)[i] = osm->ois[i];
1804     }
1805   }
1806   PetscFunctionReturn(PETSC_SUCCESS);
1807 }
1808 
1809 /*@C
1810   PCGASMGetSubmatrices - Gets the local submatrices (for this MPI process
1811   only) for the `PCGASM` additive Schwarz preconditioner.
1812 
1813   Not Collective
1814 
1815   Input Parameter:
1816 . pc - the preconditioner context
1817 
1818   Output Parameters:
1819 + n   - the number of matrices for this MPI process (default value = 1)
1820 - mat - the matrices
1821 
1822   Level: advanced
1823 
1824   Note:
1825   Matrices returned by this routine have the same communicators as the index sets (`IS`)
1826   used to define subdomains in `PCGASMSetSubdomains()`
1827 
1828 .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`,
1829           `PCGASMCreateSubdomains2D()`, `PCGASMSetSubdomains()`, `PCGASMGetSubdomains()`
1830 @*/
1831 PetscErrorCode PCGASMGetSubmatrices(PC pc, PetscInt *n, Mat *mat[])
1832 {
1833   PC_GASM  *osm;
1834   PetscBool match;
1835 
1836   PetscFunctionBegin;
1837   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1838   PetscAssertPointer(n, 2);
1839   if (mat) PetscAssertPointer(mat, 3);
1840   PetscCheck(pc->setupcalled, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call after KSPSetUp() or PCSetUp().");
1841   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1842   PetscCheck(match, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1843   osm = (PC_GASM *)pc->data;
1844   if (n) *n = osm->n;
1845   if (mat) *mat = osm->pmat;
1846   PetscFunctionReturn(PETSC_SUCCESS);
1847 }
1848 
1849 /*@
1850   PCGASMSetUseDMSubdomains - Indicates whether to use `DMCreateDomainDecomposition()` to define the subdomains, whenever possible for `PCGASM`
1851 
1852   Logically Collective
1853 
1854   Input Parameters:
1855 + pc  - the preconditioner
1856 - flg - boolean indicating whether to use subdomains defined by the `DM`
1857 
1858   Options Database Key:
1859 + -pc_gasm_dm_subdomains    - configure subdomains
1860 . -pc_gasm_overlap          - set overlap
1861 - -pc_gasm_total_subdomains - set number of subdomains
1862 
1863   Level: intermediate
1864 
1865   Note:
1866   `PCGASMSetSubdomains()`, `PCGASMSetTotalSubdomains()` or `PCGASMSetOverlap()` take precedence over `PCGASMSetUseDMSubdomains()`,
1867   so setting `PCGASMSetSubdomains()` with nontrivial subdomain ISs or any of `PCGASMSetTotalSubdomains()` and `PCGASMSetOverlap()`
1868   automatically turns the latter off.
1869 
1870 .seealso: [](ch_ksp), `PCGASM`, `PCGASMGetUseDMSubdomains()`, `PCGASMSetSubdomains()`, `PCGASMSetOverlap()`
1871           `PCGASMCreateSubdomains2D()`
1872 @*/
1873 PetscErrorCode PCGASMSetUseDMSubdomains(PC pc, PetscBool flg)
1874 {
1875   PC_GASM  *osm = (PC_GASM *)pc->data;
1876   PetscBool match;
1877 
1878   PetscFunctionBegin;
1879   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1880   PetscValidLogicalCollectiveBool(pc, flg, 2);
1881   PetscCheck(!pc->setupcalled, ((PetscObject)pc)->comm, PETSC_ERR_ARG_WRONGSTATE, "Not for a setup PC.");
1882   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1883   if (match) {
1884     if (!osm->user_subdomains && osm->N == PETSC_DETERMINE && osm->overlap < 0) osm->dm_subdomains = flg;
1885   }
1886   PetscFunctionReturn(PETSC_SUCCESS);
1887 }
1888 
1889 /*@
1890   PCGASMGetUseDMSubdomains - Returns flag indicating whether to use `DMCreateDomainDecomposition()` to define the subdomains, whenever possible with `PCGASM`
1891 
1892   Not Collective
1893 
1894   Input Parameter:
1895 . pc - the preconditioner
1896 
1897   Output Parameter:
1898 . flg - boolean indicating whether to use subdomains defined by the `DM`
1899 
1900   Level: intermediate
1901 
1902 .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetUseDMSubdomains()`, `PCGASMSetOverlap()`
1903           `PCGASMCreateSubdomains2D()`
1904 @*/
1905 PetscErrorCode PCGASMGetUseDMSubdomains(PC pc, PetscBool *flg)
1906 {
1907   PC_GASM  *osm = (PC_GASM *)pc->data;
1908   PetscBool match;
1909 
1910   PetscFunctionBegin;
1911   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1912   PetscAssertPointer(flg, 2);
1913   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1914   if (match) {
1915     if (flg) *flg = osm->dm_subdomains;
1916   }
1917   PetscFunctionReturn(PETSC_SUCCESS);
1918 }
1919