Actual source code: gasm.c

  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*.

  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>
 12: #include <petscdm.h>

 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;

 39: static PetscErrorCode PCGASMComputeGlobalSubdomainNumbering_Private(PC pc, PetscInt **numbering, PetscInt **permutation)
 40: {
 41:   PC_GASM *osm = (PC_GASM *)pc->data;
 42:   PetscInt i;

 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: }

 53: static PetscErrorCode PCGASMSubdomainView_Private(PC pc, PetscInt i, PetscViewer viewer)
 54: {
 55:   PC_GASM        *osm = (PC_GASM *)pc->data;
 56:   PetscInt        nidx;
 57:   const PetscInt *idx;
 58:   PetscViewer     sviewer;
 59:   char           *cidx;

 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);

 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 (PetscInt 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));

 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 (PetscInt 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: }

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 */

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: }

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   isascii, view_subdomains = PETSC_FALSE;
163:   PetscViewer sviewer;
164:   PetscInt    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 */

170:   PetscFunctionBegin;
171:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
172:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));

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));

178:   PetscCall(PCGetOptionsPrefix(pc, &prefix));
179:   PetscCall(PetscOptionsGetBool(NULL, prefix, "-pc_gasm_view_subdomains", &view_subdomains, NULL));

181:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
182:   if (isascii) {
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:\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 (PetscInt 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: }

245: PETSC_INTERN PetscErrorCode PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[]);

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;

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: }

299: static PetscErrorCode PCSetUp_GASM(PC pc)
300: {
301:   PC_GASM        *osm = (PC_GASM *)pc->data;
302:   PetscInt        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:   PetscInt        gostart; /* Start of locally-owned indices in the vectors -- osm->gx,osm->gy -- over the disjoint union of outer subdomains. */
316:   PetscInt        num_subdomains  = 0;
317:   DM             *subdomain_dm    = NULL;
318:   char          **subdomain_names = NULL;
319:   PetscInt       *numbering;

321:   PetscFunctionBegin;
322:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
323:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
324:   if (!pc->setupcalled) {
325:     /* use a hierarchical partitioning */
326:     if (osm->hierarchicalpartitioning) PetscCall(PCGASMSetHierarchicalPartitioning(pc));
327:     if (osm->n == PETSC_DETERMINE) {
328:       if (osm->N != PETSC_DETERMINE) {
329:         /* No local subdomains given, but the desired number of total subdomains is known, so construct them accordingly. */
330:         PetscCall(PCGASMCreateSubdomains(pc->pmat, osm->N, &osm->n, &osm->iis));
331:       } else if (osm->dm_subdomains && pc->dm) {
332:         /* try pc->dm next, if allowed */
333:         IS *inner_subdomain_is, *outer_subdomain_is;
334:         PetscCall(DMCreateDomainDecomposition(pc->dm, &num_subdomains, &subdomain_names, &inner_subdomain_is, &outer_subdomain_is, &subdomain_dm));
335:         if (num_subdomains) PetscCall(PCGASMSetSubdomains(pc, num_subdomains, inner_subdomain_is, outer_subdomain_is));
336:         for (PetscInt d = 0; d < num_subdomains; ++d) {
337:           if (inner_subdomain_is) PetscCall(ISDestroy(&inner_subdomain_is[d]));
338:           if (outer_subdomain_is) PetscCall(ISDestroy(&outer_subdomain_is[d]));
339:         }
340:         PetscCall(PetscFree(inner_subdomain_is));
341:         PetscCall(PetscFree(outer_subdomain_is));
342:       } else {
343:         /* still no subdomains; use one per rank */
344:         osm->nmax = osm->n = 1;
345:         PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
346:         osm->N = size;
347:         PetscCall(PCGASMCreateLocalSubdomains(pc->pmat, osm->n, &osm->iis));
348:       }
349:     }
350:     if (!osm->iis) {
351:       /*
352:        osm->n was set in PCGASMSetSubdomains(), but the actual subdomains have not been supplied.
353:        We create the requisite number of local inner subdomains and then expand them into
354:        out subdomains, if necessary.
355:        */
356:       PetscCall(PCGASMCreateLocalSubdomains(pc->pmat, osm->n, &osm->iis));
357:     }
358:     if (!osm->ois) {
359:       /*
360:             Initially make outer subdomains the same as inner subdomains. If nonzero additional overlap
361:             has been requested, copy the inner subdomains over so they can be modified.
362:       */
363:       PetscCall(PetscMalloc1(osm->n, &osm->ois));
364:       for (PetscInt i = 0; i < osm->n; ++i) {
365:         if (osm->overlap > 0 && osm->N > 1) { /* With positive overlap, osm->iis[i] will be modified */
366:           PetscCall(ISDuplicate(osm->iis[i], (osm->ois) + i));
367:           PetscCall(ISCopy(osm->iis[i], osm->ois[i]));
368:         } else {
369:           PetscCall(PetscObjectReference((PetscObject)osm->iis[i]));
370:           osm->ois[i] = osm->iis[i];
371:         }
372:       }
373:       if (osm->overlap > 0 && osm->N > 1) {
374:         /* Extend the "overlapping" regions by a number of steps */
375:         PetscCall(MatIncreaseOverlapSplit(pc->pmat, osm->n, osm->ois, osm->overlap));
376:       }
377:     }

379:     /* Now the subdomains are defined.  Determine their global and max local numbers, if necessary. */
380:     if (osm->nmax == PETSC_DETERMINE) {
381:       PetscInt outwork;
382:       /* determine global number of subdomains and the max number of local subdomains */
383:       outwork = osm->n;
384:       PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &outwork, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)pc)));
385:       osm->nmax = outwork;
386:     }
387:     if (osm->N == PETSC_DETERMINE) {
388:       /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
389:       PetscCall(PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc), osm->n, (PetscObject *)osm->ois, &osm->N, NULL));
390:     }

392:     if (osm->sort_indices) {
393:       for (PetscInt i = 0; i < osm->n; i++) {
394:         PetscCall(ISSort(osm->ois[i]));
395:         PetscCall(ISSort(osm->iis[i]));
396:       }
397:     }
398:     PetscCall(PCGetOptionsPrefix(pc, &prefix));
399:     PetscCall(PCGASMPrintSubdomains(pc));

401:     /*
402:        Merge the ISs, create merged vectors and restrictions.
403:      */
404:     /* Merge outer subdomain ISs and construct a restriction onto the disjoint union of local outer subdomains. */
405:     on = 0;
406:     for (PetscInt i = 0; i < osm->n; i++) {
407:       PetscCall(ISGetLocalSize(osm->ois[i], &oni));
408:       on += oni;
409:     }
410:     PetscCall(PetscMalloc1(on, &oidx));
411:     on = 0;
412:     /* Merge local indices together */
413:     for (PetscInt i = 0; i < osm->n; i++) {
414:       PetscCall(ISGetLocalSize(osm->ois[i], &oni));
415:       PetscCall(ISGetIndices(osm->ois[i], &oidxi));
416:       PetscCall(PetscArraycpy(oidx + on, oidxi, oni));
417:       PetscCall(ISRestoreIndices(osm->ois[i], &oidxi));
418:       on += oni;
419:     }
420:     PetscCall(ISCreateGeneral(((PetscObject)pc)->comm, on, oidx, PETSC_OWN_POINTER, &gois));
421:     nTotalInnerIndices = 0;
422:     for (PetscInt i = 0; i < osm->n; i++) {
423:       PetscCall(ISGetLocalSize(osm->iis[i], &nInnerIndices));
424:       nTotalInnerIndices += nInnerIndices;
425:     }
426:     PetscCall(VecCreateMPI(((PetscObject)pc)->comm, nTotalInnerIndices, PETSC_DETERMINE, &x));
427:     PetscCall(VecDuplicate(x, &y));

429:     /* Keep the merged vectors on the host so that their arrays also work with host-only subdomain solvers. */
430:     PetscCall(VecCreateMPI(PetscObjectComm((PetscObject)pc), on, PETSC_DECIDE, &osm->gx));
431:     PetscCall(VecDuplicate(osm->gx, &osm->gy));
432:     PetscCall(VecGetOwnershipRange(osm->gx, &gostart, NULL));
433:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), on, gostart, 1, &goid));
434:     /* gois might indices not on local */
435:     PetscCall(VecScatterCreate(x, gois, osm->gx, goid, &osm->gorestriction));
436:     PetscCall(PetscMalloc1(osm->n, &numbering));
437:     PetscCall(PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc), osm->n, (PetscObject *)osm->ois, NULL, numbering));
438:     PetscCall(VecDestroy(&x));
439:     PetscCall(ISDestroy(&gois));

441:     /* Merge inner subdomain ISs and construct a restriction onto the disjoint union of local inner subdomains. */
442:     {
443:       PetscInt        ini;   /* Number of indices the i-th a local inner subdomain. */
444:       PetscInt        in;    /* Number of indices in the disjoint union of local inner subdomains. */
445:       PetscInt       *iidx;  /* Global indices in the merged local inner subdomain. */
446:       PetscInt       *ioidx; /* Global indices of the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
447:       IS              giis;  /* IS for the disjoint union of inner subdomains. */
448:       IS              giois; /* IS for the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
449:       PetscScalar    *array;
450:       const PetscInt *indices;
451:       on = 0;
452:       for (PetscInt i = 0; i < osm->n; i++) {
453:         PetscCall(ISGetLocalSize(osm->ois[i], &oni));
454:         on += oni;
455:       }
456:       PetscCall(PetscMalloc1(on, &iidx));
457:       PetscCall(PetscMalloc1(on, &ioidx));
458:       PetscCall(VecGetArray(y, &array));
459:       /* set communicator id to determine where overlap is */
460:       in = 0;
461:       for (PetscInt i = 0; i < osm->n; i++) {
462:         PetscCall(ISGetLocalSize(osm->iis[i], &ini));
463:         for (PetscInt k = 0; k < ini; ++k) array[in + k] = numbering[i];
464:         in += ini;
465:       }
466:       PetscCall(VecRestoreArray(y, &array));
467:       PetscCall(VecScatterBegin(osm->gorestriction, y, osm->gy, INSERT_VALUES, SCATTER_FORWARD));
468:       PetscCall(VecScatterEnd(osm->gorestriction, y, osm->gy, INSERT_VALUES, SCATTER_FORWARD));
469:       PetscCall(VecGetOwnershipRange(osm->gy, &gostart, NULL));
470:       PetscCall(VecGetArray(osm->gy, &array));
471:       on = 0;
472:       in = 0;
473:       for (PetscInt i = 0; i < osm->n; i++) {
474:         PetscCall(ISGetLocalSize(osm->ois[i], &oni));
475:         PetscCall(ISGetIndices(osm->ois[i], &indices));
476:         for (PetscInt k = 0; k < oni; k++) {
477:           /*  skip overlapping indices to get inner domain */
478:           if (PetscRealPart(array[on + k]) != numbering[i]) continue;
479:           iidx[in]    = indices[k];
480:           ioidx[in++] = gostart + on + k;
481:         }
482:         PetscCall(ISRestoreIndices(osm->ois[i], &indices));
483:         on += oni;
484:       }
485:       PetscCall(VecRestoreArray(osm->gy, &array));
486:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), in, iidx, PETSC_OWN_POINTER, &giis));
487:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), in, ioidx, PETSC_OWN_POINTER, &giois));
488:       PetscCall(VecScatterCreate(y, giis, osm->gy, giois, &osm->girestriction));
489:       PetscCall(VecDestroy(&y));
490:       PetscCall(ISDestroy(&giis));
491:       PetscCall(ISDestroy(&giois));
492:     }
493:     PetscCall(ISDestroy(&goid));
494:     PetscCall(PetscFree(numbering));

496:     /* Create the subdomain solvers */
497:     PetscCall(PetscMalloc1(osm->n, &osm->ksp));
498:     for (PetscInt i = 0; i < osm->n; i++) {
499:       char subprefix[PETSC_MAX_PATH_LEN + 1];
500:       PetscCall(KSPCreate(((PetscObject)osm->ois[i])->comm, &ksp));
501:       PetscCall(KSPSetNestLevel(ksp, pc->kspnestlevel));
502:       PetscCall(KSPSetErrorIfNotConverged(ksp, pc->erroriffailure));
503:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ksp, (PetscObject)pc, 1));
504:       PetscCall(KSPSetType(ksp, KSPPREONLY));
505:       PetscCall(KSPGetPC(ksp, &subpc)); /* Why do we need this here? */
506:       if (subdomain_dm) {
507:         PetscCall(KSPSetDM(ksp, subdomain_dm[i]));
508:         PetscCall(DMDestroy(subdomain_dm + i));
509:       }
510:       PetscCall(PCGetOptionsPrefix(pc, &prefix));
511:       PetscCall(KSPSetOptionsPrefix(ksp, prefix));
512:       if (subdomain_names && subdomain_names[i]) {
513:         PetscCall(PetscSNPrintf(subprefix, PETSC_MAX_PATH_LEN, "sub_%s_", subdomain_names[i]));
514:         PetscCall(KSPAppendOptionsPrefix(ksp, subprefix));
515:         PetscCall(PetscFree(subdomain_names[i]));
516:       }
517:       PetscCall(KSPAppendOptionsPrefix(ksp, "sub_"));
518:       osm->ksp[i] = ksp;
519:     }
520:     PetscCall(PetscFree(subdomain_dm));
521:     PetscCall(PetscFree(subdomain_names));
522:     scall = MAT_INITIAL_MATRIX;
523:   } else { /* if (pc->setupcalled) */
524:     /*
525:        Destroy the submatrices from the previous iteration
526:     */
527:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
528:       PetscCall(MatDestroyMatrices(osm->n, &osm->pmat));
529:       scall = MAT_INITIAL_MATRIX;
530:     }
531:     if (osm->permutationIS) {
532:       PetscCall(MatCreateSubMatrix(pc->pmat, osm->permutationIS, osm->permutationIS, scall, &osm->permutationP));
533:       PetscCall(PetscObjectReference((PetscObject)osm->permutationP));
534:       osm->pcmat = pc->pmat;
535:       pc->pmat   = osm->permutationP;
536:     }
537:   }

539:   /*
540:      Extract the submatrices.
541:   */
542:   if (size > 1) PetscCall(MatCreateSubMatricesMPI(pc->pmat, osm->n, osm->ois, osm->ois, scall, &osm->pmat));
543:   else PetscCall(MatCreateSubMatrices(pc->pmat, osm->n, osm->ois, osm->ois, scall, &osm->pmat));
544:   if (scall == MAT_INITIAL_MATRIX) {
545:     PetscCall(PetscObjectGetOptionsPrefix((PetscObject)pc->pmat, &pprefix));
546:     for (PetscInt i = 0; i < osm->n; i++) PetscCall(PetscObjectSetOptionsPrefix((PetscObject)osm->pmat[i], pprefix));
547:   }

549:   /* Return control to the user so that the submatrices can be modified (e.g., to apply
550:      different boundary conditions for the submatrices than for the global problem) */
551:   PetscCall(PCModifySubMatrices(pc, osm->n, osm->ois, osm->ois, osm->pmat, pc->modifysubmatricesP));

553:   /*
554:      Loop over submatrices putting them into local ksps
555:   */
556:   for (PetscInt i = 0; i < osm->n; i++) {
557:     PetscCall(KSPSetOperators(osm->ksp[i], osm->pmat[i], osm->pmat[i]));
558:     PetscCall(KSPGetOptionsPrefix(osm->ksp[i], &prefix));
559:     PetscCall(MatSetOptionsPrefix(osm->pmat[i], prefix));
560:     if (!pc->setupcalled) PetscCall(KSPSetFromOptions(osm->ksp[i]));
561:   }
562:   if (!pc->setupcalled) {
563:     /* MatCreateVecs() would allocate arrays before they are needed. Create arrayless work vectors where supported because
564:        PCApply_GASM() and PCApplyTranspose_GASM() place the merged vectors' arrays into them. */
565:     PetscCall(PetscMalloc1(osm->n, &osm->x));
566:     PetscCall(PetscMalloc1(osm->n, &osm->y));
567:     for (PetscInt i = 0; i < osm->n; ++i) {
568:       VecType     vtype;
569:       PetscInt    oNi, m, n, M, N;
570:       PetscMPIInt subsize;
571:       PetscBool   boundtocpu, bindingpropagates, iskok;

573:       PetscCall(MatGetVecType(osm->pmat[i], &vtype));
574:       PetscCall(PetscStrcmpAny(vtype, &iskok, VECKOKKOS, VECSEQKOKKOS, VECMPIKOKKOS, ""));
575:       PetscCall(ISGetLocalSize(osm->ois[i], &oni));
576:       PetscCall(ISGetSize(osm->ois[i], &oNi));
577:       PetscCall(MatGetLocalSize(osm->pmat[i], &m, &n));
578:       PetscCall(MatGetSize(osm->pmat[i], &M, &N));
579:       PetscCheck(m == oni && n == oni && M == oNi && N == oNi, PetscObjectComm((PetscObject)osm->pmat[i]), PETSC_ERR_ARG_SIZ, "Modified submatrix %" PetscInt_FMT " has size %" PetscInt_FMT " x %" PetscInt_FMT " (local %" PetscInt_FMT " x %" PetscInt_FMT "), but its outer index set has size %" PetscInt_FMT " (local %" PetscInt_FMT ")", i, M, N, m, n, oNi, oni);
580:       PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)osm->pmat[i]), &subsize));
581:       PetscCall(MatBoundToCPU(osm->pmat[i], &boundtocpu));
582:       PetscCall(MatGetBindingPropagates(osm->pmat[i], &bindingpropagates));
583:       for (PetscInt j = 0; j < 2; ++j) {
584:         Vec *v = j ? &osm->y[i] : &osm->x[i];

586:         if (iskok) {
587:           /* Kokkos vectors require valid host storage even when VecPlaceArray() will replace it. */
588:           PetscCall(VecCreate(PetscObjectComm((PetscObject)osm->pmat[i]), v));
589:           PetscCall(VecSetSizes(*v, oni, oNi));
590:           PetscCall(VecSetBlockSize(*v, 1));
591:         } else if (subsize == 1) PetscCall(VecCreateSeqWithArray(PetscObjectComm((PetscObject)osm->pmat[i]), 1, oni, NULL, v));
592:         else PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)osm->pmat[i]), 1, oni, oNi, NULL, v));
593:         PetscCall(VecSetType(*v, vtype));
594:         if (boundtocpu && bindingpropagates) {
595:           PetscCall(VecSetBindingPropagates(*v, PETSC_TRUE));
596:           PetscCall(VecBindToCPU(*v, PETSC_TRUE));
597:         }
598:       }
599:     }
600:   }
601:   if (osm->pcmat) {
602:     PetscCall(MatDestroy(&pc->pmat));
603:     pc->pmat   = osm->pcmat;
604:     osm->pcmat = NULL;
605:   }
606:   PetscFunctionReturn(PETSC_SUCCESS);
607: }

609: static PetscErrorCode PCSetUpOnBlocks_GASM(PC pc)
610: {
611:   PC_GASM *osm = (PC_GASM *)pc->data;
612:   PetscInt i;

614:   PetscFunctionBegin;
615:   for (i = 0; i < osm->n; i++) PetscCall(KSPSetUp(osm->ksp[i]));
616:   PetscFunctionReturn(PETSC_SUCCESS);
617: }

619: static PetscErrorCode PCApply_GASM(PC pc, Vec xin, Vec yout)
620: {
621:   PC_GASM           *osm = (PC_GASM *)pc->data;
622:   const PetscScalar *gxarray;
623:   PetscScalar       *gyarray;
624:   PetscInt           i, oni, on;
625:   Vec                x, y;
626:   ScatterMode        forward = SCATTER_FORWARD, reverse = SCATTER_REVERSE;

628:   PetscFunctionBegin;
629:   if (osm->pctoouter) {
630:     PetscCall(VecScatterBegin(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
631:     PetscCall(VecScatterEnd(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
632:     x = osm->pcx;
633:     y = osm->pcy;
634:   } else {
635:     x = xin;
636:     y = yout;
637:   }
638:   /*
639:      support for limiting the restriction or interpolation only to the inner
640:      subdomain values (leaving the other values 0).
641:   */
642:   if (!(osm->type & PC_GASM_RESTRICT)) {
643:     /* have to zero the work RHS since scatter may leave some slots empty */
644:     PetscCall(VecZeroEntries(osm->gx));
645:     PetscCall(VecScatterBegin(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
646:   } else {
647:     PetscCall(VecScatterBegin(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
648:   }
649:   PetscCall(VecZeroEntries(osm->gy));
650:   if (!(osm->type & PC_GASM_RESTRICT)) {
651:     PetscCall(VecScatterEnd(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
652:   } else {
653:     PetscCall(VecScatterEnd(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
654:   }
655:   /* do the subdomain solves */
656:   PetscCall(VecGetArrayRead(osm->gx, &gxarray));
657:   PetscCall(VecGetArray(osm->gy, &gyarray));
658:   for (i = 0, on = 0; i < osm->n; ++i, on += oni) {
659:     PetscCall(ISGetLocalSize(osm->ois[i], &oni));
660:     PetscCall(VecPlaceArray(osm->x[i], PetscSafePointerPlusOffset(gxarray, on)));
661:     PetscCall(VecPlaceArray(osm->y[i], PetscSafePointerPlusOffset(gyarray, on)));
662:     PetscCall(KSPSolve(osm->ksp[i], osm->x[i], osm->y[i]));
663:     PetscCall(KSPCheckSolve(osm->ksp[i], pc, osm->y[i]));
664:     PetscCall(VecResetArray(osm->x[i]));
665:     PetscCall(VecResetArray(osm->y[i]));
666:   }
667:   PetscCall(VecRestoreArrayRead(osm->gx, &gxarray));
668:   PetscCall(VecRestoreArray(osm->gy, &gyarray));
669:   /* do we need to zero y? */
670:   PetscCall(VecZeroEntries(y));
671:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
672:     PetscCall(VecScatterBegin(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
673:     PetscCall(VecScatterEnd(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
674:   } else {
675:     PetscCall(VecScatterBegin(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
676:     PetscCall(VecScatterEnd(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
677:   }
678:   if (osm->pctoouter) {
679:     PetscCall(VecScatterBegin(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
680:     PetscCall(VecScatterEnd(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
681:   }
682:   PetscFunctionReturn(PETSC_SUCCESS);
683: }

685: static PetscErrorCode PCMatApply_GASM(PC pc, Mat Xin, Mat Yout)
686: {
687:   PC_GASM    *osm = (PC_GASM *)pc->data;
688:   Mat         X, Y, O = NULL, Z, W;
689:   Vec         x, y;
690:   PetscInt    i, m, M, N;
691:   ScatterMode forward = SCATTER_FORWARD, reverse = SCATTER_REVERSE;

693:   PetscFunctionBegin;
694:   PetscCheck(osm->n == 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Not yet implemented");
695:   PetscCall(MatGetSize(Xin, NULL, &N));
696:   if (osm->pctoouter) {
697:     PetscCall(VecGetLocalSize(osm->pcx, &m));
698:     PetscCall(VecGetSize(osm->pcx, &M));
699:     PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &O));
700:     for (i = 0; i < N; ++i) {
701:       PetscCall(MatDenseGetColumnVecRead(Xin, i, &x));
702:       PetscCall(MatDenseGetColumnVecWrite(O, i, &y));
703:       PetscCall(VecScatterBegin(osm->pctoouter, x, y, INSERT_VALUES, SCATTER_REVERSE));
704:       PetscCall(VecScatterEnd(osm->pctoouter, x, y, INSERT_VALUES, SCATTER_REVERSE));
705:       PetscCall(MatDenseRestoreColumnVecWrite(O, i, &y));
706:       PetscCall(MatDenseRestoreColumnVecRead(Xin, i, &x));
707:     }
708:     X = Y = O;
709:   } else {
710:     X = Xin;
711:     Y = Yout;
712:   }
713:   /*
714:      support for limiting the restriction or interpolation only to the inner
715:      subdomain values (leaving the other values 0).
716:   */
717:   PetscCall(VecGetLocalSize(osm->x[0], &m));
718:   PetscCall(VecGetSize(osm->x[0], &M));
719:   PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &Z));
720:   for (i = 0; i < N; ++i) {
721:     PetscCall(MatDenseGetColumnVecRead(X, i, &x));
722:     PetscCall(MatDenseGetColumnVecWrite(Z, i, &y));
723:     if (!(osm->type & PC_GASM_RESTRICT)) {
724:       /* have to zero the work RHS since scatter may leave some slots empty */
725:       PetscCall(VecZeroEntries(y));
726:       PetscCall(VecScatterBegin(osm->girestriction, x, y, INSERT_VALUES, forward));
727:       PetscCall(VecScatterEnd(osm->girestriction, x, y, INSERT_VALUES, forward));
728:     } else {
729:       PetscCall(VecScatterBegin(osm->gorestriction, x, y, INSERT_VALUES, forward));
730:       PetscCall(VecScatterEnd(osm->gorestriction, x, y, INSERT_VALUES, forward));
731:     }
732:     PetscCall(MatDenseRestoreColumnVecWrite(Z, i, &y));
733:     PetscCall(MatDenseRestoreColumnVecRead(X, i, &x));
734:   }
735:   PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &W));
736:   PetscCall(MatSetOption(Z, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
737:   PetscCall(MatAssemblyBegin(Z, MAT_FINAL_ASSEMBLY));
738:   PetscCall(MatAssemblyEnd(Z, MAT_FINAL_ASSEMBLY));
739:   /* do the subdomain solve */
740:   PetscCall(KSPMatSolve(osm->ksp[0], Z, W));
741:   PetscCall(KSPCheckSolve(osm->ksp[0], pc, NULL));
742:   PetscCall(MatDestroy(&Z));
743:   /* do we need to zero y? */
744:   PetscCall(MatZeroEntries(Y));
745:   for (i = 0; i < N; ++i) {
746:     PetscCall(MatDenseGetColumnVecWrite(Y, i, &y));
747:     PetscCall(MatDenseGetColumnVecRead(W, i, &x));
748:     if (!(osm->type & PC_GASM_INTERPOLATE)) {
749:       PetscCall(VecScatterBegin(osm->girestriction, x, y, ADD_VALUES, reverse));
750:       PetscCall(VecScatterEnd(osm->girestriction, x, y, ADD_VALUES, reverse));
751:     } else {
752:       PetscCall(VecScatterBegin(osm->gorestriction, x, y, ADD_VALUES, reverse));
753:       PetscCall(VecScatterEnd(osm->gorestriction, x, y, ADD_VALUES, reverse));
754:     }
755:     PetscCall(MatDenseRestoreColumnVecRead(W, i, &x));
756:     if (osm->pctoouter) {
757:       PetscCall(MatDenseGetColumnVecWrite(Yout, i, &x));
758:       PetscCall(VecScatterBegin(osm->pctoouter, y, x, INSERT_VALUES, SCATTER_FORWARD));
759:       PetscCall(VecScatterEnd(osm->pctoouter, y, x, INSERT_VALUES, SCATTER_FORWARD));
760:       PetscCall(MatDenseRestoreColumnVecRead(Yout, i, &x));
761:     }
762:     PetscCall(MatDenseRestoreColumnVecWrite(Y, i, &y));
763:   }
764:   PetscCall(MatDestroy(&W));
765:   PetscCall(MatDestroy(&O));
766:   PetscFunctionReturn(PETSC_SUCCESS);
767: }

769: static PetscErrorCode PCApplyTranspose_GASM(PC pc, Vec xin, Vec yout)
770: {
771:   PC_GASM           *osm = (PC_GASM *)pc->data;
772:   const PetscScalar *gxarray;
773:   PetscScalar       *gyarray;
774:   PetscInt           i, oni, on;
775:   Vec                x, y;
776:   ScatterMode        forward = SCATTER_FORWARD, reverse = SCATTER_REVERSE;

778:   PetscFunctionBegin;
779:   if (osm->pctoouter) {
780:     PetscCall(VecScatterBegin(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
781:     PetscCall(VecScatterEnd(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
782:     x = osm->pcx;
783:     y = osm->pcy;
784:   } else {
785:     x = xin;
786:     y = yout;
787:   }
788:   /*
789:      Support for limiting the restriction or interpolation to only local
790:      subdomain values (leaving the other values 0).

792:      Note: these are reversed from the PCApply_GASM() because we are applying the
793:      transpose of the three terms
794:   */
795:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
796:     /* have to zero the work RHS since scatter may leave some slots empty */
797:     PetscCall(VecZeroEntries(osm->gx));
798:     PetscCall(VecScatterBegin(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
799:   } else {
800:     PetscCall(VecScatterBegin(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
801:   }
802:   PetscCall(VecZeroEntries(osm->gy));
803:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
804:     PetscCall(VecScatterEnd(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
805:   } else {
806:     PetscCall(VecScatterEnd(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
807:   }
808:   /* do the local solves */
809:   PetscCall(VecGetArrayRead(osm->gx, &gxarray));
810:   PetscCall(VecGetArray(osm->gy, &gyarray));
811:   for (i = 0, on = 0; i < osm->n; ++i, on += oni) { /* Note that the solves are local, so we can go to osm->n, rather than osm->nmax. */
812:     PetscCall(ISGetLocalSize(osm->ois[i], &oni));
813:     PetscCall(VecPlaceArray(osm->x[i], PetscSafePointerPlusOffset(gxarray, on)));
814:     PetscCall(VecPlaceArray(osm->y[i], PetscSafePointerPlusOffset(gyarray, on)));
815:     PetscCall(KSPSolveTranspose(osm->ksp[i], osm->x[i], osm->y[i]));
816:     PetscCall(KSPCheckSolve(osm->ksp[i], pc, osm->y[i]));
817:     PetscCall(VecResetArray(osm->x[i]));
818:     PetscCall(VecResetArray(osm->y[i]));
819:   }
820:   PetscCall(VecRestoreArrayRead(osm->gx, &gxarray));
821:   PetscCall(VecRestoreArray(osm->gy, &gyarray));
822:   PetscCall(VecZeroEntries(y));
823:   if (!(osm->type & PC_GASM_RESTRICT)) {
824:     PetscCall(VecScatterBegin(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
825:     PetscCall(VecScatterEnd(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
826:   } else {
827:     PetscCall(VecScatterBegin(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
828:     PetscCall(VecScatterEnd(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
829:   }
830:   if (osm->pctoouter) {
831:     PetscCall(VecScatterBegin(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
832:     PetscCall(VecScatterEnd(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
833:   }
834:   PetscFunctionReturn(PETSC_SUCCESS);
835: }

837: static PetscErrorCode PCReset_GASM(PC pc)
838: {
839:   PC_GASM *osm = (PC_GASM *)pc->data;

841:   PetscFunctionBegin;
842:   if (osm->ksp) {
843:     for (PetscInt i = 0; i < osm->n; i++) PetscCall(KSPReset(osm->ksp[i]));
844:   }
845:   if (osm->pmat) {
846:     if (osm->n > 0) {
847:       PetscMPIInt size;

849:       PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
850:       if (size > 1) {
851:         /* osm->pmat is created by MatCreateSubMatricesMPI(), cannot use MatDestroySubMatrices() */
852:         PetscCall(MatDestroyMatrices(osm->n, &osm->pmat));
853:       } else {
854:         PetscCall(MatDestroySubMatrices(osm->n, &osm->pmat));
855:       }
856:     }
857:   }
858:   if (osm->x) {
859:     for (PetscInt i = 0; i < osm->n; i++) {
860:       PetscCall(VecDestroy(&osm->x[i]));
861:       PetscCall(VecDestroy(&osm->y[i]));
862:     }
863:   }
864:   PetscCall(PetscFree(osm->x));
865:   PetscCall(PetscFree(osm->y));
866:   PetscCall(VecDestroy(&osm->gx));
867:   PetscCall(VecDestroy(&osm->gy));

869:   PetscCall(VecScatterDestroy(&osm->gorestriction));
870:   PetscCall(VecScatterDestroy(&osm->girestriction));
871:   if (!osm->user_subdomains) {
872:     PetscCall(PCGASMDestroySubdomains(osm->n, &osm->ois, &osm->iis));
873:     osm->N    = PETSC_DETERMINE;
874:     osm->nmax = PETSC_DETERMINE;
875:   }
876:   PetscCall(VecScatterDestroy(&osm->pctoouter));
877:   PetscCall(ISDestroy(&osm->permutationIS));
878:   PetscCall(VecDestroy(&osm->pcx));
879:   PetscCall(VecDestroy(&osm->pcy));
880:   PetscCall(MatDestroy(&osm->permutationP));
881:   PetscCall(MatDestroy(&osm->pcmat));
882:   PetscFunctionReturn(PETSC_SUCCESS);
883: }

885: static PetscErrorCode PCDestroy_GASM(PC pc)
886: {
887:   PC_GASM *osm = (PC_GASM *)pc->data;

889:   PetscFunctionBegin;
890:   PetscCall(PCReset_GASM(pc));
891:   /* PCReset will not destroy subdomains, if user_subdomains is true. */
892:   PetscCall(PCGASMDestroySubdomains(osm->n, &osm->ois, &osm->iis));
893:   if (osm->ksp) {
894:     for (PetscInt i = 0; i < osm->n; i++) PetscCall(KSPDestroy(&osm->ksp[i]));
895:     PetscCall(PetscFree(osm->ksp));
896:   }
897:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSubdomains_C", NULL));
898:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetOverlap_C", NULL));
899:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetType_C", NULL));
900:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSortIndices_C", NULL));
901:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMGetSubKSP_C", NULL));
902:   PetscCall(PetscFree(pc->data));
903:   PetscFunctionReturn(PETSC_SUCCESS);
904: }

906: static PetscErrorCode PCSetFromOptions_GASM(PC pc, PetscOptionItems PetscOptionsObject)
907: {
908:   PC_GASM   *osm = (PC_GASM *)pc->data;
909:   PetscInt   blocks, ovl;
910:   PetscBool  flg;
911:   PCGASMType gasmtype;

913:   PetscFunctionBegin;
914:   PetscOptionsHeadBegin(PetscOptionsObject, "Generalized additive Schwarz options");
915:   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));
916:   PetscCall(PetscOptionsInt("-pc_gasm_total_subdomains", "Total number of subdomains across communicator", "PCGASMSetTotalSubdomains", osm->N, &blocks, &flg));
917:   if (flg) PetscCall(PCGASMSetTotalSubdomains(pc, blocks));
918:   PetscCall(PetscOptionsInt("-pc_gasm_overlap", "Number of overlapping degrees of freedom", "PCGASMSetOverlap", osm->overlap, &ovl, &flg));
919:   if (flg) {
920:     PetscCall(PCGASMSetOverlap(pc, ovl));
921:     osm->dm_subdomains = PETSC_FALSE;
922:   }
923:   flg = PETSC_FALSE;
924:   PetscCall(PetscOptionsEnum("-pc_gasm_type", "Type of restriction/extension", "PCGASMSetType", PCGASMTypes, (PetscEnum)osm->type, (PetscEnum *)&gasmtype, &flg));
925:   if (flg) PetscCall(PCGASMSetType(pc, gasmtype));
926:   PetscCall(PetscOptionsBool("-pc_gasm_use_hierachical_partitioning", "use hierarchical partitioning", NULL, osm->hierarchicalpartitioning, &osm->hierarchicalpartitioning, &flg));
927:   PetscOptionsHeadEnd();
928:   PetscFunctionReturn(PETSC_SUCCESS);
929: }

931: /*@
932:   PCGASMSetTotalSubdomains - sets the total number of subdomains to use across the communicator for `PCGASM`

934:   Logically Collective

936:   Input Parameters:
937: + pc - the preconditioner
938: - N  - total number of subdomains

940:   Level: beginner

942: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMSetOverlap()`,
943:           `PCGASMCreateSubdomains2D()`
944: @*/
945: PetscErrorCode PCGASMSetTotalSubdomains(PC pc, PetscInt N)
946: {
947:   PC_GASM    *osm = (PC_GASM *)pc->data;
948:   PetscMPIInt size, rank;

950:   PetscFunctionBegin;
951:   PetscCheck(N >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Total number of subdomains must be 1 or more, got N = %" PetscInt_FMT, N);
952:   PetscCheck(!pc->setupcalled, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "PCGASMSetTotalSubdomains() should be called before calling PCSetUp().");

954:   PetscCall(PCGASMDestroySubdomains(osm->n, &osm->iis, &osm->ois));
955:   osm->ois = osm->iis = NULL;

957:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
958:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
959:   osm->N             = N;
960:   osm->n             = PETSC_DETERMINE;
961:   osm->nmax          = PETSC_DETERMINE;
962:   osm->dm_subdomains = PETSC_FALSE;
963:   PetscFunctionReturn(PETSC_SUCCESS);
964: }

966: static PetscErrorCode PCGASMSetSubdomains_GASM(PC pc, PetscInt n, IS iis[], IS ois[])
967: {
968:   PC_GASM *osm = (PC_GASM *)pc->data;

970:   PetscFunctionBegin;
971:   PetscCheck(n >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Each MPI rank must have 1 or more subdomains, got n = %" PetscInt_FMT, n);
972:   PetscCheck(!pc->setupcalled, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "PCGASMSetSubdomains() should be called before calling PCSetUp().");

974:   PetscCall(PCGASMDestroySubdomains(osm->n, &osm->iis, &osm->ois));
975:   osm->iis = osm->ois = NULL;
976:   osm->n              = n;
977:   osm->N              = PETSC_DETERMINE;
978:   osm->nmax           = PETSC_DETERMINE;
979:   if (ois) {
980:     PetscCall(PetscMalloc1(n, &osm->ois));
981:     for (PetscInt i = 0; i < n; i++) {
982:       PetscCall(PetscObjectReference((PetscObject)ois[i]));
983:       osm->ois[i] = ois[i];
984:     }
985:     /*
986:        Since the user set the outer subdomains, even if nontrivial overlap was requested via PCGASMSetOverlap(),
987:        it will be ignored.  To avoid confusion later on (e.g., when viewing the PC), the overlap size is set to -1.
988:     */
989:     osm->overlap = -1;
990:     /* inner subdomains must be provided  */
991:     PetscCheck(iis, PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "inner indices have to be provided ");
992:   } /* end if */
993:   if (iis) {
994:     PetscCall(PetscMalloc1(n, &osm->iis));
995:     for (PetscInt i = 0; i < n; i++) {
996:       PetscCall(PetscObjectReference((PetscObject)iis[i]));
997:       osm->iis[i] = iis[i];
998:     }
999:     if (!ois) {
1000:       osm->ois = NULL;
1001:       /* if user does not provide outer indices, we will create the corresponding outer indices using  osm->overlap =1 in PCSetUp_GASM */
1002:     }
1003:   }
1004:   if (PetscDefined(USE_DEBUG)) {
1005:     PetscInt        j, rstart, rend, *covered, lsize;
1006:     const PetscInt *indices;

1008:     if (osm->iis) {
1009:       /* check if the inner indices cover and only cover the local portion of the matrix */
1010:       PetscCall(MatGetOwnershipRange(pc->pmat, &rstart, &rend));
1011:       PetscCall(PetscCalloc1(rend - rstart, &covered));
1012:       /* check if the current MPI process owns indices from others */
1013:       for (PetscInt i = 0; i < n; i++) {
1014:         PetscCall(ISGetIndices(osm->iis[i], &indices));
1015:         PetscCall(ISGetLocalSize(osm->iis[i], &lsize));
1016:         for (j = 0; j < lsize; j++) {
1017:           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]);
1018:           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]);
1019:           covered[indices[j] - rstart] = 1;
1020:         }
1021:         PetscCall(ISRestoreIndices(osm->iis[i], &indices));
1022:       }
1023:       /* check if we miss any indices */
1024:       for (PetscInt 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);
1025:       PetscCall(PetscFree(covered));
1026:     }
1027:   }
1028:   if (iis) osm->user_subdomains = PETSC_TRUE;
1029:   PetscFunctionReturn(PETSC_SUCCESS);
1030: }

1032: static PetscErrorCode PCGASMSetOverlap_GASM(PC pc, PetscInt ovl)
1033: {
1034:   PC_GASM *osm = (PC_GASM *)pc->data;

1036:   PetscFunctionBegin;
1037:   PetscCheck(ovl >= 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Negative overlap value requested");
1038:   PetscCheck(!pc->setupcalled || ovl == osm->overlap, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "PCGASMSetOverlap() should be called before PCSetUp().");
1039:   if (!pc->setupcalled) osm->overlap = ovl;
1040:   PetscFunctionReturn(PETSC_SUCCESS);
1041: }

1043: static PetscErrorCode PCGASMSetType_GASM(PC pc, PCGASMType type)
1044: {
1045:   PC_GASM *osm = (PC_GASM *)pc->data;

1047:   PetscFunctionBegin;
1048:   osm->type     = type;
1049:   osm->type_set = PETSC_TRUE;
1050:   PetscFunctionReturn(PETSC_SUCCESS);
1051: }

1053: static PetscErrorCode PCGASMSetSortIndices_GASM(PC pc, PetscBool doSort)
1054: {
1055:   PC_GASM *osm = (PC_GASM *)pc->data;

1057:   PetscFunctionBegin;
1058:   osm->sort_indices = doSort;
1059:   PetscFunctionReturn(PETSC_SUCCESS);
1060: }

1062: /*
1063:    FIXME: This routine might need to be modified now that multiple processes per subdomain are allowed.
1064:         In particular, it would upset the global subdomain number calculation.
1065: */
1066: static PetscErrorCode PCGASMGetSubKSP_GASM(PC pc, PetscInt *n, PetscInt *first, KSP **ksp)
1067: {
1068:   PC_GASM *osm = (PC_GASM *)pc->data;

1070:   PetscFunctionBegin;
1071:   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");

1073:   if (n) *n = osm->n;
1074:   if (first) {
1075:     PetscCallMPI(MPI_Scan(&osm->n, first, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)pc)));
1076:     *first -= osm->n;
1077:   }
1078:   if (ksp) {
1079:     /* Assume that local solves are now different; not necessarily
1080:        true, though!  This flag is used only for PCView_GASM() */
1081:     *ksp                        = osm->ksp;
1082:     osm->same_subdomain_solvers = PETSC_FALSE;
1083:   }
1084:   PetscFunctionReturn(PETSC_SUCCESS);
1085: } /* PCGASMGetSubKSP_GASM() */

1087: /*@
1088:   PCGASMSetSubdomains - Sets the subdomains for this MPI process
1089:   for the additive Schwarz preconditioner with multiple MPI processes per subdomain, `PCGASM`

1091:   Collective

1093:   Input Parameters:
1094: + pc  - the preconditioner object
1095: . n   - the number of subdomains for this MPI process
1096: . iis - the index sets that define the inner subdomains (or `NULL` for PETSc to determine subdomains), the `iis` array is
1097:         copied so may be freed after this call.
1098: - ois - the index sets that define the outer subdomains (or `NULL` to use the same as `iis`, or to construct by expanding `iis` by
1099:         the requested overlap), the `ois` array is copied so may be freed after this call.

1101:   Level: advanced

1103:   Notes:
1104:   The `IS` indices use the parallel, global numbering of the vector entries.

1106:   Inner subdomains are those where the correction is applied.

1108:   Outer subdomains are those where the residual necessary to obtain the
1109:   corrections is obtained (see `PCGASMType` for the use of inner/outer subdomains).

1111:   Both inner and outer subdomains can extend over several MPI processes.
1112:   This process' portion of a subdomain is known as a local subdomain.

1114:   Inner subdomains can not overlap with each other, do not have any entities from remote processes,
1115:   and  have to cover the entire local subdomain owned by the current process. The index sets on each
1116:   process should be ordered such that the ith local subdomain is connected to the ith remote subdomain
1117:   on another MPI process.

1119:   By default the `PGASM` preconditioner uses 1 (local) subdomain per MPI process.

1121:   The `iis` and `ois` arrays may be freed after this call using `PCGASMDestroySubdomains()`

1123: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`, `PCGASMDestroySubdomains()`,
1124:           `PCGASMCreateSubdomains2D()`, `PCGASMGetSubdomains()`
1125: @*/
1126: PetscErrorCode PCGASMSetSubdomains(PC pc, PetscInt n, IS iis[], IS ois[])
1127: {
1128:   PC_GASM *osm = (PC_GASM *)pc->data;

1130:   PetscFunctionBegin;
1132:   PetscTryMethod(pc, "PCGASMSetSubdomains_C", (PC, PetscInt, IS[], IS[]), (pc, n, iis, ois));
1133:   osm->dm_subdomains = PETSC_FALSE;
1134:   PetscFunctionReturn(PETSC_SUCCESS);
1135: }

1137: /*@
1138:   PCGASMSetOverlap - Sets the overlap between a pair of subdomains for the
1139:   additive Schwarz preconditioner `PCGASM`.  Either all or no MPI processes in the
1140:   pc communicator must call this routine.

1142:   Logically Collective

1144:   Input Parameters:
1145: + pc  - the preconditioner context
1146: - ovl - the amount of overlap between subdomains (ovl >= 0, default value = 0)

1148:   Options Database Key:
1149: . -pc_gasm_overlap overlap - Sets overlap

1151:   Level: intermediate

1153:   Notes:
1154:   By default the `PCGASM` preconditioner uses 1 subdomain per process.  To use
1155:   multiple subdomain per perocessor or "straddling" subdomains that intersect
1156:   multiple processes use `PCGASMSetSubdomains()` (or option `-pc_gasm_total_subdomains` <n>).

1158:   The overlap defaults to 0, so if one desires that no additional
1159:   overlap be computed beyond what may have been set with a call to
1160:   `PCGASMSetSubdomains()`, then `ovl` must be set to be 0.  In particular, if one does
1161:   not explicitly set the subdomains in application code, then all overlap would be computed
1162:   internally by PETSc, and using an overlap of 0 would result in an `PCGASM`
1163:   variant that is equivalent to the block Jacobi preconditioner.

1165:   One can define initial index sets with any overlap via
1166:   `PCGASMSetSubdomains()`; the routine `PCGASMSetOverlap()` merely allows
1167:   PETSc to extend that overlap further, if desired.

1169: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1170:           `PCGASMCreateSubdomains2D()`, `PCGASMGetSubdomains()`
1171: @*/
1172: PetscErrorCode PCGASMSetOverlap(PC pc, PetscInt ovl)
1173: {
1174:   PC_GASM *osm = (PC_GASM *)pc->data;

1176:   PetscFunctionBegin;
1179:   PetscTryMethod(pc, "PCGASMSetOverlap_C", (PC, PetscInt), (pc, ovl));
1180:   osm->dm_subdomains = PETSC_FALSE;
1181:   PetscFunctionReturn(PETSC_SUCCESS);
1182: }

1184: /*@
1185:   PCGASMSetType - Sets the type of restriction and interpolation used
1186:   for local problems in the `PCGASM` additive Schwarz method.

1188:   Logically Collective

1190:   Input Parameters:
1191: + pc   - the preconditioner context
1192: - type - variant of `PCGASM`, one of
1193: .vb
1194:       `PC_GASM_BASIC`       - full interpolation and restriction
1195:       `PC_GASM_RESTRICT`    - full restriction, local MPI process interpolation
1196:       `PC_GASM_INTERPOLATE` - full interpolation, local MPI process restriction
1197:       `PC_GASM_NONE`        - local MPI process restriction and interpolation
1198: .ve

1200:   Options Database Key:
1201: . -pc_gasm_type [basic,restrict,interpolate,none] - Sets `PCGASM` type

1203:   Level: intermediate

1205: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1206:           `PCGASMCreateSubdomains2D()`, `PCASM`, `PCASMSetType()`
1207: @*/
1208: PetscErrorCode PCGASMSetType(PC pc, PCGASMType type)
1209: {
1210:   PetscFunctionBegin;
1213:   PetscTryMethod(pc, "PCGASMSetType_C", (PC, PCGASMType), (pc, type));
1214:   PetscFunctionReturn(PETSC_SUCCESS);
1215: }

1217: /*@
1218:   PCGASMSetSortIndices - Determines whether subdomain indices are sorted.

1220:   Logically Collective

1222:   Input Parameters:
1223: + pc     - the preconditioner context
1224: - doSort - sort the subdomain indices

1226:   Level: intermediate

1228: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1229:           `PCGASMCreateSubdomains2D()`
1230: @*/
1231: PetscErrorCode PCGASMSetSortIndices(PC pc, PetscBool doSort)
1232: {
1233:   PetscFunctionBegin;
1236:   PetscTryMethod(pc, "PCGASMSetSortIndices_C", (PC, PetscBool), (pc, doSort));
1237:   PetscFunctionReturn(PETSC_SUCCESS);
1238: }

1240: /*@
1241:   PCGASMGetSubKSP - Gets the local `KSP` contexts for all subdomains on this MPI process.

1243:   Collective iff first_local is requested

1245:   Input Parameter:
1246: . pc - the preconditioner context

1248:   Output Parameters:
1249: + n_local     - the number of blocks on this MPI process or `NULL`
1250: . first_local - the global number of the first block on this process or `NULL`, all processes must request or all must pass `NULL`
1251: - ksp         - the array of `KSP` contexts

1253:   Level: advanced

1255:   Note:
1256:   After `PCGASMGetSubKSP()` the array of `KSP`es is not to be freed

1258:   Currently for some matrix implementations only 1 block per MPI process
1259:   is supported.

1261:   You must call `KSPSetUp()` before calling `PCGASMGetSubKSP()`.

1263:   Fortran Note:
1264:   Call `PCGASMRestoreSubKSP()` when the array of `KSP` is no longer needed

1266: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMSetOverlap()`,
1267:           `PCGASMCreateSubdomains2D()`
1268: @*/
1269: PetscErrorCode PCGASMGetSubKSP(PC pc, PetscInt *n_local, PetscInt *first_local, KSP *ksp[])
1270: {
1271:   PetscFunctionBegin;
1273:   PetscUseMethod(pc, "PCGASMGetSubKSP_C", (PC, PetscInt *, PetscInt *, KSP **), (pc, n_local, first_local, ksp));
1274:   PetscFunctionReturn(PETSC_SUCCESS);
1275: }

1277: /*MC
1278:    PCGASM - Use the (restricted) additive Schwarz method, each block is (approximately) solved with
1279:            its own `KSP` object on a subset of MPI processes

1281:    Options Database Keys:
1282: +  -pc_gasm_total_subdomains n                     - Sets total number of local subdomains to be distributed among the MPI processes
1283: .  -pc_gasm_view_subdomains                        - activates the printing of subdomain indices in `PCView()`, -ksp_view or -snes_view
1284: .  -pc_gasm_print_subdomains                       - activates the printing of subdomain indices in `PCSetUp()`
1285: .  -pc_gasm_overlap ovl                            - Sets overlap by which to (automatically) extend local subdomains
1286: -  -pc_gasm_type (basic|restrict|interpolate|none) - Sets `PCGASMType`

1288:    Level: beginner

1290:    Notes:
1291:    To set options on the solvers for each block append `-sub_` to all the `KSP`, and `PC`
1292:    options database keys. For example, `-sub_pc_type ilu -sub_pc_factor_levels 1 -sub_ksp_type preonly`

1294:    To set the options on the solvers separate for each block call `PCGASMGetSubKSP()`
1295:    and set the options directly on the resulting `KSP` object (you can access its `PC`
1296:    with `KSPGetPC()`)

1298:    `PCGASM` uses host memory for the merged subdomain vectors so that host-only subdomain solvers work with device global vectors.
1299:    Device subdomain solvers therefore copy each right-hand side to the device and each solution back to the host during every application.

1301:    See {cite}`dryja1987additive` and {cite}`1sbg` for details on additive Schwarz algorithms

1303: .seealso: [](ch_ksp), `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCASM`, `PCGASMType`, `PCGASMSetType()`,
1304:           `PCBJACOBI`, `PCGASMGetSubKSP()`, `PCGASMSetSubdomains()`,
1305:           `PCSetModifySubMatrices()`, `PCGASMSetOverlap()`, `PCASMSetType()`
1306: M*/

1308: PETSC_EXTERN PetscErrorCode PCCreate_GASM(PC pc)
1309: {
1310:   PC_GASM *osm;

1312:   PetscFunctionBegin;
1313:   PetscCall(PetscNew(&osm));

1315:   osm->N                        = PETSC_DETERMINE;
1316:   osm->n                        = PETSC_DECIDE;
1317:   osm->nmax                     = PETSC_DETERMINE;
1318:   osm->overlap                  = 0;
1319:   osm->ksp                      = NULL;
1320:   osm->gorestriction            = NULL;
1321:   osm->girestriction            = NULL;
1322:   osm->pctoouter                = NULL;
1323:   osm->gx                       = NULL;
1324:   osm->gy                       = NULL;
1325:   osm->x                        = NULL;
1326:   osm->y                        = NULL;
1327:   osm->pcx                      = NULL;
1328:   osm->pcy                      = NULL;
1329:   osm->permutationIS            = NULL;
1330:   osm->permutationP             = NULL;
1331:   osm->pcmat                    = NULL;
1332:   osm->ois                      = NULL;
1333:   osm->iis                      = NULL;
1334:   osm->pmat                     = NULL;
1335:   osm->type                     = PC_GASM_RESTRICT;
1336:   osm->same_subdomain_solvers   = PETSC_TRUE;
1337:   osm->sort_indices             = PETSC_TRUE;
1338:   osm->dm_subdomains            = PETSC_FALSE;
1339:   osm->hierarchicalpartitioning = PETSC_FALSE;

1341:   pc->data                 = (void *)osm;
1342:   pc->ops->apply           = PCApply_GASM;
1343:   pc->ops->matapply        = PCMatApply_GASM;
1344:   pc->ops->applytranspose  = PCApplyTranspose_GASM;
1345:   pc->ops->setup           = PCSetUp_GASM;
1346:   pc->ops->reset           = PCReset_GASM;
1347:   pc->ops->destroy         = PCDestroy_GASM;
1348:   pc->ops->setfromoptions  = PCSetFromOptions_GASM;
1349:   pc->ops->setuponblocks   = PCSetUpOnBlocks_GASM;
1350:   pc->ops->view            = PCView_GASM;
1351:   pc->ops->applyrichardson = NULL;

1353:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSubdomains_C", PCGASMSetSubdomains_GASM));
1354:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetOverlap_C", PCGASMSetOverlap_GASM));
1355:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetType_C", PCGASMSetType_GASM));
1356:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSortIndices_C", PCGASMSetSortIndices_GASM));
1357:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMGetSubKSP_C", PCGASMGetSubKSP_GASM));
1358:   PetscFunctionReturn(PETSC_SUCCESS);
1359: }

1361: PetscErrorCode PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[])
1362: {
1363:   MatPartitioning mpart;
1364:   const char     *prefix;
1365:   PetscInt        i, j, rstart, rend, bs;
1366:   PetscBool       hasop, isbaij = PETSC_FALSE, foundpart = PETSC_FALSE;
1367:   Mat             Ad = NULL, adj;
1368:   IS              ispart, isnumb, *is;

1370:   PetscFunctionBegin;
1371:   PetscCheck(nloc >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "number of local subdomains must > 0, got nloc = %" PetscInt_FMT, nloc);

1373:   /* Get prefix, row distribution, and block size */
1374:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1375:   PetscCall(MatGetOwnershipRange(A, &rstart, &rend));
1376:   PetscCall(MatGetBlockSize(A, &bs));
1377:   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);

1379:   /* Get diagonal block from matrix if possible */
1380:   PetscCall(MatHasOperation(A, MATOP_GET_DIAGONAL_BLOCK, &hasop));
1381:   if (hasop) PetscCall(MatGetDiagonalBlock(A, &Ad));
1382:   if (Ad) {
1383:     PetscCall(PetscObjectBaseTypeCompare((PetscObject)Ad, MATSEQBAIJ, &isbaij));
1384:     if (!isbaij) PetscCall(PetscObjectBaseTypeCompare((PetscObject)Ad, MATSEQSBAIJ, &isbaij));
1385:   }
1386:   if (Ad && nloc > 1) {
1387:     PetscBool match, done;
1388:     /* Try to setup a good matrix partitioning if available */
1389:     PetscCall(MatPartitioningCreate(PETSC_COMM_SELF, &mpart));
1390:     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)mpart, prefix));
1391:     PetscCall(MatPartitioningSetFromOptions(mpart));
1392:     PetscCall(PetscObjectTypeCompare((PetscObject)mpart, MATPARTITIONINGCURRENT, &match));
1393:     if (!match) PetscCall(PetscObjectTypeCompare((PetscObject)mpart, MATPARTITIONINGSQUARE, &match));
1394:     if (!match) { /* assume a "good" partitioner is available */
1395:       PetscInt        na;
1396:       const PetscInt *ia, *ja;
1397:       PetscCall(MatGetRowIJ(Ad, 0, PETSC_TRUE, isbaij, &na, &ia, &ja, &done));
1398:       if (done) {
1399:         /* Build adjacency matrix by hand. Unfortunately a call to
1400:            MatConvert(Ad,MATMPIADJ,MAT_INITIAL_MATRIX,&adj) will
1401:            remove the block-aij structure and we cannot expect
1402:            MatPartitioning to split vertices as we need */
1403:         PetscInt        i, j, len, nnz, cnt, *iia = NULL, *jja = NULL;
1404:         const PetscInt *row;
1405:         nnz = 0;
1406:         for (i = 0; i < na; i++) { /* count number of nonzeros */
1407:           len = ia[i + 1] - ia[i];
1408:           row = ja + ia[i];
1409:           for (j = 0; j < len; j++) {
1410:             if (row[j] == i) { /* don't count diagonal */
1411:               len--;
1412:               break;
1413:             }
1414:           }
1415:           nnz += len;
1416:         }
1417:         PetscCall(PetscMalloc1(na + 1, &iia));
1418:         PetscCall(PetscMalloc1(nnz, &jja));
1419:         nnz    = 0;
1420:         iia[0] = 0;
1421:         for (i = 0; i < na; i++) { /* fill adjacency */
1422:           cnt = 0;
1423:           len = ia[i + 1] - ia[i];
1424:           row = ja + ia[i];
1425:           for (j = 0; j < len; j++) {
1426:             if (row[j] != i) jja[nnz + cnt++] = row[j]; /* if not diagonal */
1427:           }
1428:           nnz += cnt;
1429:           iia[i + 1] = nnz;
1430:         }
1431:         /* Partitioning of the adjacency matrix */
1432:         PetscCall(MatCreateMPIAdj(PETSC_COMM_SELF, na, na, iia, jja, NULL, &adj));
1433:         PetscCall(MatPartitioningSetAdjacency(mpart, adj));
1434:         PetscCall(MatPartitioningSetNParts(mpart, nloc));
1435:         PetscCall(MatPartitioningApply(mpart, &ispart));
1436:         PetscCall(ISPartitioningToNumbering(ispart, &isnumb));
1437:         PetscCall(MatDestroy(&adj));
1438:         foundpart = PETSC_TRUE;
1439:       }
1440:       PetscCall(MatRestoreRowIJ(Ad, 0, PETSC_TRUE, isbaij, &na, &ia, &ja, &done));
1441:     }
1442:     PetscCall(MatPartitioningDestroy(&mpart));
1443:   }
1444:   PetscCall(PetscMalloc1(nloc, &is));
1445:   if (!foundpart) {
1446:     /* Partitioning by contiguous chunks of rows */

1448:     PetscInt mbs   = (rend - rstart) / bs;
1449:     PetscInt start = rstart;
1450:     for (i = 0; i < nloc; i++) {
1451:       PetscInt count = (mbs / nloc + ((mbs % nloc) > i)) * bs;
1452:       PetscCall(ISCreateStride(PETSC_COMM_SELF, count, start, 1, &is[i]));
1453:       start += count;
1454:     }

1456:   } else {
1457:     /* Partitioning by adjacency of diagonal block  */

1459:     const PetscInt *numbering;
1460:     PetscInt       *count, nidx, *indices, *newidx, start = 0;
1461:     /* Get node count in each partition */
1462:     PetscCall(PetscMalloc1(nloc, &count));
1463:     PetscCall(ISPartitioningCount(ispart, nloc, count));
1464:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1465:       for (i = 0; i < nloc; i++) count[i] *= bs;
1466:     }
1467:     /* Build indices from node numbering */
1468:     PetscCall(ISGetLocalSize(isnumb, &nidx));
1469:     PetscCall(PetscMalloc1(nidx, &indices));
1470:     for (i = 0; i < nidx; i++) indices[i] = i; /* needs to be initialized */
1471:     PetscCall(ISGetIndices(isnumb, &numbering));
1472:     PetscCall(PetscSortIntWithPermutation(nidx, numbering, indices));
1473:     PetscCall(ISRestoreIndices(isnumb, &numbering));
1474:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1475:       PetscCall(PetscMalloc1(nidx * bs, &newidx));
1476:       for (i = 0; i < nidx; i++) {
1477:         for (j = 0; j < bs; j++) newidx[i * bs + j] = indices[i] * bs + j;
1478:       }
1479:       PetscCall(PetscFree(indices));
1480:       nidx *= bs;
1481:       indices = newidx;
1482:     }
1483:     /* Shift to get global indices */
1484:     for (i = 0; i < nidx; i++) indices[i] += rstart;

1486:     /* Build the index sets for each block */
1487:     for (i = 0; i < nloc; i++) {
1488:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count[i], &indices[start], PETSC_COPY_VALUES, &is[i]));
1489:       PetscCall(ISSort(is[i]));
1490:       start += count[i];
1491:     }

1493:     PetscCall(PetscFree(count));
1494:     PetscCall(PetscFree(indices));
1495:     PetscCall(ISDestroy(&isnumb));
1496:     PetscCall(ISDestroy(&ispart));
1497:   }
1498:   *iis = is;
1499:   PetscFunctionReturn(PETSC_SUCCESS);
1500: }

1502: PETSC_INTERN PetscErrorCode PCGASMCreateStraddlingSubdomains(Mat A, PetscInt N, PetscInt *n, IS *iis[])
1503: {
1504:   PetscFunctionBegin;
1505:   PetscCall(MatSubdomainsCreateCoalesce(A, N, n, iis));
1506:   PetscFunctionReturn(PETSC_SUCCESS);
1507: }

1509: /*@
1510:   PCGASMCreateSubdomains - Creates `n` index sets defining `n` nonoverlapping subdomains on this MPI process for the `PCGASM` additive
1511:   Schwarz preconditioner for a any problem based on its matrix.

1513:   Collective

1515:   Input Parameters:
1516: + A - The global matrix operator
1517: - N - the number of global subdomains requested

1519:   Output Parameters:
1520: + n   - the number of subdomains created on this MPI process
1521: - iis - the array of index sets defining the local inner subdomains (on which the correction is applied)

1523:   Level: advanced

1525:   Notes:
1526:   When `N` >= A's communicator size, each subdomain is local -- contained within a single MPI process.
1527:   When `N` < size, the subdomains are 'straddling' (process boundaries) and are no longer local.
1528:   The resulting subdomains can be use in `PCGASMSetSubdomains`(pc,n,iss,`NULL`).  The overlapping
1529:   outer subdomains will be automatically generated from these according to the requested amount of
1530:   overlap; this is currently supported only with local subdomains.

1532:   Use `PCGASMDestroySubdomains()` to free the array and the list of index sets.

1534: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMDestroySubdomains()`
1535: @*/
1536: PetscErrorCode PCGASMCreateSubdomains(Mat A, PetscInt N, PetscInt *n, IS *iis[])
1537: {
1538:   PetscMPIInt size;

1540:   PetscFunctionBegin;
1542:   PetscAssertPointer(iis, 4);

1544:   PetscCheck(N >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of subdomains must be > 0, N = %" PetscInt_FMT, N);
1545:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
1546:   if (N >= size) {
1547:     *n = N / size + (N % size);
1548:     PetscCall(PCGASMCreateLocalSubdomains(A, *n, iis));
1549:   } else {
1550:     PetscCall(PCGASMCreateStraddlingSubdomains(A, N, n, iis));
1551:   }
1552:   PetscFunctionReturn(PETSC_SUCCESS);
1553: }

1555: /*@
1556:   PCGASMDestroySubdomains - Destroys the index sets created with
1557:   `PCGASMCreateSubdomains()` or `PCGASMCreateSubdomains2D()`. Should be
1558:   called after setting subdomains with `PCGASMSetSubdomains()`.

1560:   Collective

1562:   Input Parameters:
1563: + n   - the number of index sets
1564: . iis - the array of inner subdomains
1565: - ois - the array of outer subdomains, can be `NULL`

1567:   Level: intermediate

1569:   Note:
1570:   This is a convenience subroutine that walks each list,
1571:   destroys each `IS` on the list, and then frees the list. At the end the
1572:   list pointers are set to `NULL`.

1574: .seealso: [](ch_ksp), `PCGASM`, `PCGASMCreateSubdomains()`, `PCGASMSetSubdomains()`
1575: @*/
1576: PetscErrorCode PCGASMDestroySubdomains(PetscInt n, IS *iis[], IS *ois[])
1577: {
1578:   PetscFunctionBegin;
1579:   if (n <= 0) PetscFunctionReturn(PETSC_SUCCESS);
1580:   if (ois) {
1581:     PetscAssertPointer(ois, 3);
1582:     if (*ois) {
1583:       PetscAssertPointer(*ois, 3);
1584:       for (PetscInt i = 0; i < n; i++) PetscCall(ISDestroy(&(*ois)[i]));
1585:       PetscCall(PetscFree(*ois));
1586:     }
1587:   }
1588:   if (iis) {
1589:     PetscAssertPointer(iis, 2);
1590:     if (*iis) {
1591:       PetscAssertPointer(*iis, 2);
1592:       for (PetscInt i = 0; i < n; i++) PetscCall(ISDestroy(&(*iis)[i]));
1593:       PetscCall(PetscFree(*iis));
1594:     }
1595:   }
1596:   PetscFunctionReturn(PETSC_SUCCESS);
1597: }

1599: #define PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, xleft_loc, ylow_loc, xright_loc, yhigh_loc, n) \
1600:   do { \
1601:     PetscInt first_row = first / M, last_row = last / M + 1; \
1602:     /*                                                                                                    \
1603:      Compute ylow_loc and yhigh_loc so that (ylow_loc,xleft) and (yhigh_loc,xright) are the corners       \
1604:      of the bounding box of the intersection of the subdomain with the local ownership range (local       \
1605:      subdomain).                                                                                          \
1606:      Also compute xleft_loc and xright_loc as the lower and upper bounds on the first and last rows       \
1607:      of the intersection.                                                                                 \
1608:     */ \
1609:     /* ylow_loc is the grid row containing the first element of the local sumbdomain */ \
1610:     *ylow_loc = PetscMax(first_row, ylow); \
1611:     /* xleft_loc is the offset of first element of the local subdomain within its grid row (might actually be outside the local subdomain) */ \
1612:     *xleft_loc = *ylow_loc == first_row ? PetscMax(first % M, xleft) : xleft; \
1613:     /* yhigh_loc is the grid row above the last local subdomain element */ \
1614:     *yhigh_loc = PetscMin(last_row, yhigh); \
1615:     /* xright is the offset of the end of the  local subdomain within its grid row (might actually be outside the local subdomain) */ \
1616:     *xright_loc = *yhigh_loc == last_row ? PetscMin(xright, last % M) : xright; \
1617:     /* Now compute the size of the local subdomain n. */ \
1618:     *n = 0; \
1619:     if (*ylow_loc < *yhigh_loc) { \
1620:       PetscInt width = xright - xleft; \
1621:       *n += width * (*yhigh_loc - *ylow_loc - 1); \
1622:       *n += PetscMin(PetscMax(*xright_loc - xleft, 0), width); \
1623:       *n -= PetscMin(PetscMax(*xleft_loc - xleft, 0), width); \
1624:     } \
1625:   } while (0)

1627: /*@
1628:   PCGASMCreateSubdomains2D - Creates the index sets for the `PCGASM` overlapping Schwarz
1629:   preconditioner for a two-dimensional problem on a regular grid.

1631:   Collective

1633:   Input Parameters:
1634: + pc       - the preconditioner context
1635: . M        - the global number of grid points in the x direction
1636: . N        - the global number of grid points in the y direction
1637: . Mdomains - the global number of subdomains in the x direction
1638: . Ndomains - the global number of subdomains in the y direction
1639: . dof      - degrees of freedom per node
1640: - overlap  - overlap in mesh lines

1642:   Output Parameters:
1643: + nsub - the number of local subdomains created
1644: . iis  - array of index sets defining inner (nonoverlapping) subdomains
1645: - ois  - array of index sets defining outer (overlapping, if overlap > 0) subdomains

1647:   Level: advanced

1649:   Note:
1650:   Use `PCGASMDestroySubdomains()` to free the index sets and the arrays

1652: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`, `PCGASMSetOverlap()`, `PCASMCreateSubdomains2D()`,
1653:           `PCGASMDestroySubdomains()`
1654: @*/
1655: PetscErrorCode PCGASMCreateSubdomains2D(PC pc, PetscInt M, PetscInt N, PetscInt Mdomains, PetscInt Ndomains, PetscInt dof, PetscInt overlap, PetscInt *nsub, IS *iis[], IS *ois[])
1656: {
1657:   PetscMPIInt size, rank;
1658:   PetscInt    maxheight, maxwidth;
1659:   PetscInt    xstart, xleft, xright, xleft_loc, xright_loc;
1660:   PetscInt    ystart, ylow, yhigh, ylow_loc, yhigh_loc;
1661:   PetscInt    x[2][2], y[2][2], n[2];
1662:   PetscInt    first, last;
1663:   PetscInt    nidx, *idx;
1664:   PetscInt    ii, jj, s, q, d;
1665:   PetscInt    k, kk;
1666:   PetscMPIInt color;
1667:   MPI_Comm    comm, subcomm;
1668:   IS        **xis = NULL, **is = ois, **is_local = iis;

1670:   PetscFunctionBegin;
1671:   PetscCall(PetscObjectGetComm((PetscObject)pc, &comm));
1672:   PetscCallMPI(MPI_Comm_size(comm, &size));
1673:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1674:   PetscCall(MatGetOwnershipRange(pc->pmat, &first, &last));
1675:   PetscCheck((first % dof) == 0 && (last % dof) == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE,
1676:              "Matrix row partitioning unsuitable for domain decomposition: local row range (%" PetscInt_FMT ",%" PetscInt_FMT ") "
1677:              "does not respect the number of degrees of freedom per grid point %" PetscInt_FMT,
1678:              first, last, dof);

1680:   /* Determine the number of domains with nonzero intersections with the local ownership range. */
1681:   s      = 0;
1682:   ystart = 0;
1683:   for (PetscInt j = 0; j < Ndomains; ++j) {
1684:     maxheight = N / Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1685:     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);
1686:     /* Vertical domain limits with an overlap. */
1687:     ylow   = PetscMax(ystart - overlap, 0);
1688:     yhigh  = PetscMin(ystart + maxheight + overlap, N);
1689:     xstart = 0;
1690:     for (PetscInt i = 0; i < Mdomains; ++i) {
1691:       maxwidth = M / Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1692:       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);
1693:       /* Horizontal domain limits with an overlap. */
1694:       xleft  = PetscMax(xstart - overlap, 0);
1695:       xright = PetscMin(xstart + maxwidth + overlap, M);
1696:       /*
1697:          Determine whether this subdomain intersects this rank's ownership range of pc->pmat.
1698:       */
1699:       PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, (&xleft_loc), (&ylow_loc), (&xright_loc), (&yhigh_loc), (&nidx));
1700:       if (nidx) ++s;
1701:       xstart += maxwidth;
1702:     } /* for (PetscInt i = 0; i < Mdomains; ++i) */
1703:     ystart += maxheight;
1704:   } /* for (PetscInt j = 0; j < Ndomains; ++j) */

1706:   /* Now we can allocate the necessary number of ISs. */
1707:   *nsub = s;
1708:   PetscCall(PetscMalloc1(*nsub, is));
1709:   PetscCall(PetscMalloc1(*nsub, is_local));
1710:   s      = 0;
1711:   ystart = 0;
1712:   for (PetscInt j = 0; j < Ndomains; ++j) {
1713:     maxheight = N / Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1714:     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);
1715:     /* Vertical domain limits with an overlap. */
1716:     y[0][0] = PetscMax(ystart - overlap, 0);
1717:     y[0][1] = PetscMin(ystart + maxheight + overlap, N);
1718:     /* Vertical domain limits without an overlap. */
1719:     y[1][0] = ystart;
1720:     y[1][1] = PetscMin(ystart + maxheight, N);
1721:     xstart  = 0;
1722:     for (PetscInt i = 0; i < Mdomains; ++i) {
1723:       maxwidth = M / Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1724:       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);
1725:       /* Horizontal domain limits with an overlap. */
1726:       x[0][0] = PetscMax(xstart - overlap, 0);
1727:       x[0][1] = PetscMin(xstart + maxwidth + overlap, M);
1728:       /* Horizontal domain limits without an overlap. */
1729:       x[1][0] = xstart;
1730:       x[1][1] = PetscMin(xstart + maxwidth, M);
1731:       /*
1732:          Determine whether this domain intersects this rank's ownership range of pc->pmat.
1733:          Do this twice: first for the domains with overlaps, and once without.
1734:          During the first pass create the subcommunicators, and use them on the second pass as well.
1735:       */
1736:       for (q = 0; q < 2; ++q) {
1737:         PetscBool split = PETSC_FALSE;
1738:         /*
1739:           domain limits, (xleft, xright) and (ylow, yheigh) are adjusted
1740:           according to whether the domain with an overlap or without is considered.
1741:         */
1742:         xleft  = x[q][0];
1743:         xright = x[q][1];
1744:         ylow   = y[q][0];
1745:         yhigh  = y[q][1];
1746:         PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, (&xleft_loc), (&ylow_loc), (&xright_loc), (&yhigh_loc), (&nidx));
1747:         nidx *= dof;
1748:         n[q] = nidx;
1749:         /*
1750:          Based on the counted number of indices in the local domain *with an overlap*,
1751:          construct a subcommunicator of all the MPI ranks supporting this domain.
1752:          Observe that a domain with an overlap might have nontrivial local support,
1753:          while the domain without an overlap might not.  Hence, the decision to participate
1754:          in the subcommunicator must be based on the domain with an overlap.
1755:          */
1756:         if (q == 0) {
1757:           if (nidx) color = 1;
1758:           else color = MPI_UNDEFINED;
1759:           PetscCallMPI(MPI_Comm_split(comm, color, rank, &subcomm));
1760:           split = PETSC_TRUE;
1761:         }
1762:         /*
1763:          Proceed only if the number of local indices *with an overlap* is nonzero.
1764:          */
1765:         if (n[0]) {
1766:           if (q == 0) xis = is;
1767:           if (q == 1) {
1768:             /*
1769:              The IS for the no-overlap subdomain shares a communicator with the overlapping domain.
1770:              Moreover, if the overlap is zero, the two ISs are identical.
1771:              */
1772:             if (overlap == 0) {
1773:               (*is_local)[s] = (*is)[s];
1774:               PetscCall(PetscObjectReference((PetscObject)(*is)[s]));
1775:               continue;
1776:             } else {
1777:               xis     = is_local;
1778:               subcomm = ((PetscObject)(*is)[s])->comm;
1779:             }
1780:           } /* if (q == 1) */
1781:           idx = NULL;
1782:           PetscCall(PetscMalloc1(nidx, &idx));
1783:           if (nidx) {
1784:             k = 0;
1785:             for (jj = ylow_loc; jj < yhigh_loc; ++jj) {
1786:               PetscInt x0 = (jj == ylow_loc) ? xleft_loc : xleft;
1787:               PetscInt x1 = (jj == yhigh_loc - 1) ? xright_loc : xright;
1788:               kk          = dof * (M * jj + x0);
1789:               for (ii = x0; ii < x1; ++ii) {
1790:                 for (d = 0; d < dof; ++d) idx[k++] = kk++;
1791:               }
1792:             }
1793:           }
1794:           PetscCall(ISCreateGeneral(subcomm, nidx, idx, PETSC_OWN_POINTER, (*xis) + s));
1795:           if (split) PetscCallMPI(MPI_Comm_free(&subcomm));
1796:         } /* if (n[0]) */
1797:       } /* for (q = 0; q < 2; ++q) */
1798:       if (n[0]) ++s;
1799:       xstart += maxwidth;
1800:     } /* for (PetscInt i = 0; i < Mdomains; ++i) */
1801:     ystart += maxheight;
1802:   } /* for (PetscInt j = 0; j < Ndomains; ++j) */
1803:   PetscFunctionReturn(PETSC_SUCCESS);
1804: }

1806: /*@
1807:   PCGASMGetSubdomains - Gets the subdomains supported on this MPI process
1808:   for the `PCGASM` additive Schwarz preconditioner.

1810:   Not Collective

1812:   Input Parameter:
1813: . pc - the preconditioner context

1815:   Output Parameters:
1816: + n   - the number of subdomains for this MPI process (default value = 1)
1817: . iis - the index sets that define the inner subdomains (without overlap) supported on this process (can be `NULL`)
1818: - ois - the index sets that define the outer subdomains (with overlap) supported on this process (can be `NULL`)

1820:   Level: advanced

1822:   Notes:
1823:   The user is responsible for destroying the `IS`s and freeing the returned arrays, this can be done with
1824:   `PCGASMDestroySubdomains()`

1826:   The `IS` numbering is in the parallel, global numbering of the vector.

1828: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`, `PCGASMCreateSubdomains2D()`,
1829:           `PCGASMSetSubdomains()`, `PCGASMGetSubmatrices()`, `PCGASMDestroySubdomains()`
1830: @*/
1831: PetscErrorCode PCGASMGetSubdomains(PC pc, PetscInt *n, IS *iis[], IS *ois[])
1832: {
1833:   PC_GASM  *osm;
1834:   PetscBool match;

1836:   PetscFunctionBegin;
1838:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1839:   PetscCheck(match, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Incorrect object type: expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1840:   osm = (PC_GASM *)pc->data;
1841:   if (n) *n = osm->n;
1842:   if (iis) PetscCall(PetscMalloc1(osm->n, iis));
1843:   if (ois) PetscCall(PetscMalloc1(osm->n, ois));
1844:   if (iis || ois) {
1845:     for (PetscInt i = 0; i < osm->n; ++i) {
1846:       if (iis) (*iis)[i] = osm->iis[i];
1847:       if (ois) (*ois)[i] = osm->ois[i];
1848:     }
1849:   }
1850:   PetscFunctionReturn(PETSC_SUCCESS);
1851: }

1853: /*@
1854:   PCGASMGetSubmatrices - Gets the local submatrices (for this MPI process
1855:   only) for the `PCGASM` additive Schwarz preconditioner.

1857:   Not Collective

1859:   Input Parameter:
1860: . pc - the preconditioner context

1862:   Output Parameters:
1863: + n   - the number of matrices for this MPI process (default value = 1)
1864: - mat - the matrices

1866:   Level: advanced

1868:   Note:
1869:   Matrices returned by this routine have the same communicators as the index sets (`IS`)
1870:   used to define subdomains in `PCGASMSetSubdomains()`

1872: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`,
1873:           `PCGASMCreateSubdomains2D()`, `PCGASMSetSubdomains()`, `PCGASMGetSubdomains()`
1874: @*/
1875: PetscErrorCode PCGASMGetSubmatrices(PC pc, PetscInt *n, Mat *mat[])
1876: {
1877:   PC_GASM  *osm;
1878:   PetscBool match;

1880:   PetscFunctionBegin;
1882:   PetscAssertPointer(n, 2);
1883:   if (mat) PetscAssertPointer(mat, 3);
1884:   PetscCheck(pc->setupcalled, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call after KSPSetUp() or PCSetUp().");
1885:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1886:   PetscCheck(match, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1887:   osm = (PC_GASM *)pc->data;
1888:   if (n) *n = osm->n;
1889:   if (mat) *mat = osm->pmat;
1890:   PetscFunctionReturn(PETSC_SUCCESS);
1891: }

1893: /*@
1894:   PCGASMSetUseDMSubdomains - Indicates whether to use `DMCreateDomainDecomposition()` to define the subdomains, whenever possible for `PCGASM`

1896:   Logically Collective

1898:   Input Parameters:
1899: + pc  - the preconditioner
1900: - flg - boolean indicating whether to use subdomains defined by the `DM`

1902:   Options Database Key:
1903: + -pc_gasm_dm_subdomains    - configure subdomains
1904: . -pc_gasm_overlap          - set overlap
1905: - -pc_gasm_total_subdomains - set number of subdomains

1907:   Level: intermediate

1909:   Note:
1910:   `PCGASMSetSubdomains()`, `PCGASMSetTotalSubdomains()` or `PCGASMSetOverlap()` take precedence over `PCGASMSetUseDMSubdomains()`,
1911:   so setting `PCGASMSetSubdomains()` with nontrivial subdomain ISs or any of `PCGASMSetTotalSubdomains()` and `PCGASMSetOverlap()`
1912:   automatically turns the latter off.

1914: .seealso: [](ch_ksp), `PCGASM`, `PCGASMGetUseDMSubdomains()`, `PCGASMSetSubdomains()`, `PCGASMSetOverlap()`,
1915:           `PCGASMCreateSubdomains2D()`
1916: @*/
1917: PetscErrorCode PCGASMSetUseDMSubdomains(PC pc, PetscBool flg)
1918: {
1919:   PC_GASM  *osm = (PC_GASM *)pc->data;
1920:   PetscBool match;

1922:   PetscFunctionBegin;
1925:   PetscCheck(!pc->setupcalled, ((PetscObject)pc)->comm, PETSC_ERR_ARG_WRONGSTATE, "Not for a setup PC.");
1926:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1927:   if (match && !osm->user_subdomains && osm->N == PETSC_DETERMINE && osm->overlap < 0) osm->dm_subdomains = flg;
1928:   PetscFunctionReturn(PETSC_SUCCESS);
1929: }

1931: /*@
1932:   PCGASMGetUseDMSubdomains - Returns flag indicating whether to use `DMCreateDomainDecomposition()` to define the subdomains, whenever possible with `PCGASM`

1934:   Not Collective

1936:   Input Parameter:
1937: . pc - the preconditioner

1939:   Output Parameter:
1940: . flg - boolean indicating whether to use subdomains defined by the `DM`

1942:   Level: intermediate

1944: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetUseDMSubdomains()`, `PCGASMSetOverlap()`,
1945:           `PCGASMCreateSubdomains2D()`
1946: @*/
1947: PetscErrorCode PCGASMGetUseDMSubdomains(PC pc, PetscBool *flg)
1948: {
1949:   PC_GASM  *osm = (PC_GASM *)pc->data;
1950:   PetscBool match;

1952:   PetscFunctionBegin;
1954:   PetscAssertPointer(flg, 2);
1955:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1956:   if (match) {
1957:     if (flg) *flg = osm->dm_subdomains;
1958:   }
1959:   PetscFunctionReturn(PETSC_SUCCESS);
1960: }