Actual source code: gasm.c
petsc-3.13.6 2020-09-29
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      1: /*
      2:   This file defines an "generalized" additive Schwarz preconditioner for any Mat implementation.
      3:   In this version each processor may intersect multiple subdomains and any subdomain may
      4:   intersect multiple processors.  Intersections of subdomains with processors 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 processor (set in PCGASMSetSubdomains() or calculated in PCGASMSetTotalSubdomains())
      9:        nmax - maximum number of local subdomains per processor    (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;

     46:   /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
     47:   PetscMalloc2(osm->n,numbering,osm->n,permutation);
     48:   PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc),osm->n,(PetscObject*)osm->iis,NULL,*numbering);
     49:   for (i = 0; i < osm->n; ++i) (*permutation)[i] = i;
     50:   PetscSortIntWithPermutation(osm->n,*numbering,*permutation);
     51:   return(0);
     52: }

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

     64:   if (i < 0 || i > osm->n) SETERRQ2(PetscObjectComm((PetscObject)viewer), PETSC_ERR_ARG_WRONG, "Invalid subdomain %D: must nonnegative and less than %D", i, osm->n);
     65:   /* Inner subdomains. */
     66:   ISGetLocalSize(osm->iis[i], &nidx);
     67:   /*
     68:    No more than 15 characters per index plus a space.
     69:    PetscViewerStringSPrintf requires a string of size at least 2, so use (nidx+1) instead of nidx,
     70:    in case nidx == 0. That will take care of the space for the trailing '\0' as well.
     71:    For nidx == 0, the whole string 16 '\0'.
     72:    */
     73: #define len  16*(nidx+1)+1
     74:   PetscMalloc1(len, &cidx);
     75:   PetscViewerStringOpen(PETSC_COMM_SELF, cidx, len, &sviewer);
     76: #undef len
     77:   ISGetIndices(osm->iis[i], &idx);
     78:   for (j = 0; j < nidx; ++j) {
     79:     PetscViewerStringSPrintf(sviewer, "%D ", idx[j]);
     80:   }
     81:   ISRestoreIndices(osm->iis[i],&idx);
     82:   PetscViewerDestroy(&sviewer);
     83:   PetscViewerASCIIPrintf(viewer, "Inner subdomain:\n");
     84:   PetscViewerFlush(viewer);
     85:   PetscViewerASCIIPushSynchronized(viewer);
     86:   PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx);
     87:   PetscViewerFlush(viewer);
     88:   PetscViewerASCIIPopSynchronized(viewer);
     89:   PetscViewerASCIIPrintf(viewer, "\n");
     90:   PetscViewerFlush(viewer);
     91:   PetscFree(cidx);
     92:   /* Outer subdomains. */
     93:   ISGetLocalSize(osm->ois[i], &nidx);
     94:   /*
     95:    No more than 15 characters per index plus a space.
     96:    PetscViewerStringSPrintf requires a string of size at least 2, so use (nidx+1) instead of nidx,
     97:    in case nidx == 0. That will take care of the space for the trailing '\0' as well.
     98:    For nidx == 0, the whole string 16 '\0'.
     99:    */
    100: #define len  16*(nidx+1)+1
    101:   PetscMalloc1(len, &cidx);
    102:   PetscViewerStringOpen(PETSC_COMM_SELF, cidx, len, &sviewer);
    103: #undef len
    104:   ISGetIndices(osm->ois[i], &idx);
    105:   for (j = 0; j < nidx; ++j) {
    106:     PetscViewerStringSPrintf(sviewer,"%D ", idx[j]);
    107:   }
    108:   PetscViewerDestroy(&sviewer);
    109:   ISRestoreIndices(osm->ois[i],&idx);
    110:   PetscViewerASCIIPrintf(viewer, "Outer subdomain:\n");
    111:   PetscViewerFlush(viewer);
    112:   PetscViewerASCIIPushSynchronized(viewer);
    113:   PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx);
    114:   PetscViewerFlush(viewer);
    115:   PetscViewerASCIIPopSynchronized(viewer);
    116:   PetscViewerASCIIPrintf(viewer, "\n");
    117:   PetscViewerFlush(viewer);
    118:   PetscFree(cidx);
    119:   return(0);
    120: }

    122: static PetscErrorCode  PCGASMPrintSubdomains(PC pc)
    123: {
    124:   PC_GASM        *osm = (PC_GASM*)pc->data;
    125:   const char     *prefix;
    126:   char           fname[PETSC_MAX_PATH_LEN+1];
    127:   PetscInt       l, d, count;
    128:   PetscBool      doprint,found;
    129:   PetscViewer    viewer, sviewer = NULL;
    130:   PetscInt       *numbering,*permutation;/* global numbering of locally-supported subdomains and the permutation from the local ordering */

    134:   PCGetOptionsPrefix(pc,&prefix);
    135:   doprint  = PETSC_FALSE;
    136:   PetscOptionsGetBool(NULL,prefix,"-pc_gasm_print_subdomains",&doprint,NULL);
    137:   if (!doprint) return(0);
    138:   PetscOptionsGetString(NULL,prefix,"-pc_gasm_print_subdomains",fname,PETSC_MAX_PATH_LEN,&found);
    139:   if (!found) { PetscStrcpy(fname,"stdout"); };
    140:   PetscViewerASCIIOpen(PetscObjectComm((PetscObject)pc),fname,&viewer);
    141:   /*
    142:    Make sure the viewer has a name. Otherwise this may cause a deadlock or other weird errors when creating a subcomm viewer:
    143:    the subcomm viewer will attempt to inherit the viewer's name, which, if not set, will be constructed collectively on the comm.
    144:   */
    145:   PetscObjectName((PetscObject)viewer);
    146:   l    = 0;
    147:   PCGASMComputeGlobalSubdomainNumbering_Private(pc,&numbering,&permutation);
    148:   for (count = 0; count < osm->N; ++count) {
    149:     /* Now let subdomains go one at a time in the global numbering order and print their subdomain/solver info. */
    150:     if (l<osm->n) {
    151:       d = permutation[l]; /* d is the local number of the l-th smallest (in the global ordering) among the locally supported subdomains */
    152:       if (numbering[d] == count) {
    153:         PetscViewerGetSubViewer(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
    154:         PCGASMSubdomainView_Private(pc,d,sviewer);
    155:         PetscViewerRestoreSubViewer(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
    156:         ++l;
    157:       }
    158:     }
    159:     MPI_Barrier(PetscObjectComm((PetscObject)pc));
    160:   }
    161:   PetscFree2(numbering,permutation);
    162:   PetscViewerDestroy(&viewer);
    163:   return(0);
    164: }

    167: static PetscErrorCode PCView_GASM(PC pc,PetscViewer viewer)
    168: {
    169:   PC_GASM        *osm = (PC_GASM*)pc->data;
    170:   const char     *prefix;
    172:   PetscMPIInt    rank, size;
    173:   PetscInt       bsz;
    174:   PetscBool      iascii,view_subdomains=PETSC_FALSE;
    175:   PetscViewer    sviewer;
    176:   PetscInt       count, l;
    177:   char           overlap[256]     = "user-defined overlap";
    178:   char           gsubdomains[256] = "unknown total number of subdomains";
    179:   char           msubdomains[256] = "unknown max number of local subdomains";
    180:   PetscInt       *numbering,*permutation;/* global numbering of locally-supported subdomains and the permutation from the local ordering */

    183:   MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size);
    184:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank);

    186:   if (osm->overlap >= 0) {
    187:     PetscSNPrintf(overlap,sizeof(overlap),"requested amount of overlap = %D",osm->overlap);
    188:   }
    189:   if (osm->N != PETSC_DETERMINE) {
    190:     PetscSNPrintf(gsubdomains, sizeof(gsubdomains), "total number of subdomains = %D",osm->N);
    191:   }
    192:   if (osm->nmax != PETSC_DETERMINE) {
    193:     PetscSNPrintf(msubdomains,sizeof(msubdomains),"max number of local subdomains = %D",osm->nmax);
    194:   }

    196:   PCGetOptionsPrefix(pc,&prefix);
    197:   PetscOptionsGetBool(NULL,prefix,"-pc_gasm_view_subdomains",&view_subdomains,NULL);

    199:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    200:   if (iascii) {
    201:     /*
    202:      Make sure the viewer has a name. Otherwise this may cause a deadlock when creating a subcomm viewer:
    203:      the subcomm viewer will attempt to inherit the viewer's name, which, if not set, will be constructed
    204:      collectively on the comm.
    205:      */
    206:     PetscObjectName((PetscObject)viewer);
    207:     PetscViewerASCIIPrintf(viewer,"  Restriction/interpolation type: %s\n",PCGASMTypes[osm->type]);
    208:     PetscViewerASCIIPrintf(viewer,"  %s\n",overlap);
    209:     PetscViewerASCIIPrintf(viewer,"  %s\n",gsubdomains);
    210:     PetscViewerASCIIPrintf(viewer,"  %s\n",msubdomains);
    211:     PetscViewerASCIIPushSynchronized(viewer);
    212:     PetscViewerASCIISynchronizedPrintf(viewer,"  [%d|%d] number of locally-supported subdomains = %D\n",rank,size,osm->n);
    213:     PetscViewerFlush(viewer);
    214:     PetscViewerASCIIPopSynchronized(viewer);
    215:     /* Cannot take advantage of osm->same_subdomain_solvers without a global numbering of subdomains. */
    216:     PetscViewerASCIIPrintf(viewer,"  Subdomain solver info is as follows:\n");
    217:     PetscViewerASCIIPushTab(viewer);
    218:     PetscViewerASCIIPrintf(viewer,"  - - - - - - - - - - - - - - - - - -\n");
    219:     /* Make sure that everybody waits for the banner to be printed. */
    220:     MPI_Barrier(PetscObjectComm((PetscObject)viewer));
    221:     /* Now let subdomains go one at a time in the global numbering order and print their subdomain/solver info. */
    222:     PCGASMComputeGlobalSubdomainNumbering_Private(pc,&numbering,&permutation);
    223:     l = 0;
    224:     for (count = 0; count < osm->N; ++count) {
    225:       PetscMPIInt srank, ssize;
    226:       if (l<osm->n) {
    227:         PetscInt d = permutation[l]; /* d is the local number of the l-th smallest (in the global ordering) among the locally supported subdomains */
    228:         if (numbering[d] == count) {
    229:           MPI_Comm_size(((PetscObject)osm->ois[d])->comm, &ssize);
    230:           MPI_Comm_rank(((PetscObject)osm->ois[d])->comm, &srank);
    231:           PetscViewerGetSubViewer(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
    232:           ISGetLocalSize(osm->ois[d],&bsz);
    233:           PetscViewerASCIISynchronizedPrintf(sviewer,"  [%d|%d] (subcomm [%d|%d]) local subdomain number %D, local size = %D\n",rank,size,srank,ssize,d,bsz);
    234:           PetscViewerFlush(sviewer);
    235:           if (view_subdomains) {
    236:             PCGASMSubdomainView_Private(pc,d,sviewer);
    237:           }
    238:           if (!pc->setupcalled) {
    239:             PetscViewerASCIIPrintf(sviewer, "  Solver not set up yet: PCSetUp() not yet called\n");
    240:           } else {
    241:             KSPView(osm->ksp[d],sviewer);
    242:           }
    243:           PetscViewerASCIIPrintf(sviewer,"  - - - - - - - - - - - - - - - - - -\n");
    244:           PetscViewerFlush(sviewer);
    245:           PetscViewerRestoreSubViewer(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
    246:           ++l;
    247:         }
    248:       }
    249:       MPI_Barrier(PetscObjectComm((PetscObject)pc));
    250:     }
    251:     PetscFree2(numbering,permutation);
    252:     PetscViewerASCIIPopTab(viewer);
    253:   }
    254:   PetscViewerFlush(viewer);
    255:   PetscViewerASCIIPopSynchronized(viewer);
    256:   return(0);
    257: }

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

    263: PetscErrorCode PCGASMSetHierarchicalPartitioning(PC pc)
    264: {
    265:    PC_GASM              *osm = (PC_GASM*)pc->data;
    266:    MatPartitioning       part;
    267:    MPI_Comm              comm;
    268:    PetscMPIInt           size;
    269:    PetscInt              nlocalsubdomains,fromrows_localsize;
    270:    IS                    partitioning,fromrows,isn;
    271:    Vec                   outervec;
    272:    PetscErrorCode        ierr;

    275:    PetscObjectGetComm((PetscObject)pc,&comm);
    276:    MPI_Comm_size(comm,&size);
    277:    /* we do not need a hierarchical partitioning when
    278:     * the total number of subdomains is consistent with
    279:     * the number of MPI tasks.
    280:     * For the following cases, we do not need to use HP
    281:     * */
    282:    if(osm->N==PETSC_DETERMINE || osm->N>=size || osm->N==1) return(0);
    283:    if(size%osm->N != 0) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_ARG_INCOMP,"have to specify the total number of subdomains %D to be a factor of the number of processors %d \n",osm->N,size);
    284:    nlocalsubdomains = size/osm->N;
    285:    osm->n           = 1;
    286:    MatPartitioningCreate(comm,&part);
    287:    MatPartitioningSetAdjacency(part,pc->pmat);
    288:    MatPartitioningSetType(part,MATPARTITIONINGHIERARCH);
    289:    MatPartitioningHierarchicalSetNcoarseparts(part,osm->N);
    290:    MatPartitioningHierarchicalSetNfineparts(part,nlocalsubdomains);
    291:    MatPartitioningSetFromOptions(part);
    292:    /* get new processor owner number of each vertex */
    293:    MatPartitioningApply(part,&partitioning);
    294:    ISBuildTwoSided(partitioning,NULL,&fromrows);
    295:    ISPartitioningToNumbering(partitioning,&isn);
    296:    ISDestroy(&isn);
    297:    ISGetLocalSize(fromrows,&fromrows_localsize);
    298:    MatPartitioningDestroy(&part);
    299:    MatCreateVecs(pc->pmat,&outervec,NULL);
    300:    VecCreateMPI(comm,fromrows_localsize,PETSC_DETERMINE,&(osm->pcx));
    301:    VecDuplicate(osm->pcx,&(osm->pcy));
    302:    VecScatterCreate(osm->pcx,NULL,outervec,fromrows,&(osm->pctoouter));
    303:    MatCreateSubMatrix(pc->pmat,fromrows,fromrows,MAT_INITIAL_MATRIX,&(osm->permutationP));
    304:    PetscObjectReference((PetscObject)fromrows);
    305:    osm->permutationIS = fromrows;
    306:    osm->pcmat =  pc->pmat;
    307:    PetscObjectReference((PetscObject)osm->permutationP);
    308:    pc->pmat = osm->permutationP;
    309:    VecDestroy(&outervec);
    310:    ISDestroy(&fromrows);
    311:    ISDestroy(&partitioning);
    312:    osm->n           = PETSC_DETERMINE;
    313:    return(0);
    314: }

    318: static PetscErrorCode PCSetUp_GASM(PC pc)
    319: {
    320:   PC_GASM        *osm = (PC_GASM*)pc->data;
    322:   PetscInt       i,nInnerIndices,nTotalInnerIndices;
    323:   PetscMPIInt    rank, size;
    324:   MatReuse       scall = MAT_REUSE_MATRIX;
    325:   KSP            ksp;
    326:   PC             subpc;
    327:   const char     *prefix,*pprefix;
    328:   Vec            x,y;
    329:   PetscInt       oni;       /* Number of indices in the i-th local outer subdomain.               */
    330:   const PetscInt *oidxi;    /* Indices from the i-th subdomain local outer subdomain.             */
    331:   PetscInt       on;        /* Number of indices in the disjoint union of local outer subdomains. */
    332:   PetscInt       *oidx;     /* Indices in the disjoint union of local outer subdomains. */
    333:   IS             gois;      /* Disjoint union the global indices of outer subdomains.             */
    334:   IS             goid;      /* Identity IS of the size of the disjoint union of outer subdomains. */
    335:   PetscScalar    *gxarray, *gyarray;
    336:   PetscInt       gostart;   /* Start of locally-owned indices in the vectors -- osm->gx,osm->gy -- over the disjoint union of outer subdomains. */
    337:   PetscInt       num_subdomains    = 0;
    338:   DM             *subdomain_dm     = NULL;
    339:   char           **subdomain_names = NULL;
    340:   PetscInt       *numbering;

    344:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
    345:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
    346:   if (!pc->setupcalled) {
    347:         /* use a hierarchical partitioning */
    348:     if(osm->hierarchicalpartitioning){
    349:       PCGASMSetHierarchicalPartitioning(pc);
    350:     }
    351:     if (osm->n == PETSC_DETERMINE) {
    352:       if (osm->N != PETSC_DETERMINE) {
    353:            /* No local subdomains given, but the desired number of total subdomains is known, so construct them accordingly. */
    354:            PCGASMCreateSubdomains(pc->pmat,osm->N,&osm->n,&osm->iis);
    355:       } else if (osm->dm_subdomains && pc->dm) {
    356:         /* try pc->dm next, if allowed */
    357:         PetscInt  d;
    358:         IS       *inner_subdomain_is, *outer_subdomain_is;
    359:         DMCreateDomainDecomposition(pc->dm, &num_subdomains, &subdomain_names, &inner_subdomain_is, &outer_subdomain_is, &subdomain_dm);
    360:         if (num_subdomains) {
    361:           PCGASMSetSubdomains(pc, num_subdomains, inner_subdomain_is, outer_subdomain_is);
    362:         }
    363:         for (d = 0; d < num_subdomains; ++d) {
    364:           if (inner_subdomain_is) {ISDestroy(&inner_subdomain_is[d]);}
    365:           if (outer_subdomain_is) {ISDestroy(&outer_subdomain_is[d]);}
    366:         }
    367:         PetscFree(inner_subdomain_is);
    368:         PetscFree(outer_subdomain_is);
    369:       } else {
    370:         /* still no subdomains; use one per processor */
    371:         osm->nmax = osm->n = 1;
    372:         MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
    373:         osm->N    = size;
    374:         PCGASMCreateLocalSubdomains(pc->pmat,osm->n,&osm->iis);
    375:       }
    376:     }
    377:     if (!osm->iis) {
    378:       /*
    379:        osm->n was set in PCGASMSetSubdomains(), but the actual subdomains have not been supplied.
    380:        We create the requisite number of local inner subdomains and then expand them into
    381:        out subdomains, if necessary.
    382:        */
    383:       PCGASMCreateLocalSubdomains(pc->pmat,osm->n,&osm->iis);
    384:     }
    385:     if (!osm->ois) {
    386:       /*
    387:             Initially make outer subdomains the same as inner subdomains. If nonzero additional overlap
    388:             has been requested, copy the inner subdomains over so they can be modified.
    389:       */
    390:       PetscMalloc1(osm->n,&osm->ois);
    391:       for (i=0; i<osm->n; ++i) {
    392:         if (osm->overlap > 0 && osm->N>1) { /* With positive overlap, osm->iis[i] will be modified */
    393:           ISDuplicate(osm->iis[i],(osm->ois)+i);
    394:           ISCopy(osm->iis[i],osm->ois[i]);
    395:         } else {
    396:           PetscObjectReference((PetscObject)((osm->iis)[i]));
    397:           osm->ois[i] = osm->iis[i];
    398:         }
    399:       }
    400:       if (osm->overlap>0 && osm->N>1) {
    401:            /* Extend the "overlapping" regions by a number of steps */
    402:            MatIncreaseOverlapSplit(pc->pmat,osm->n,osm->ois,osm->overlap);
    403:       }
    404:     }

    406:     /* Now the subdomains are defined.  Determine their global and max local numbers, if necessary. */
    407:     if (osm->nmax == PETSC_DETERMINE) {
    408:       PetscMPIInt inwork,outwork;
    409:       /* determine global number of subdomains and the max number of local subdomains */
    410:       inwork = osm->n;
    411:       MPIU_Allreduce(&inwork,&outwork,1,MPI_INT,MPI_MAX,PetscObjectComm((PetscObject)pc));
    412:       osm->nmax  = outwork;
    413:     }
    414:     if (osm->N == PETSC_DETERMINE) {
    415:       /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
    416:       PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc),osm->n,(PetscObject*)osm->ois,&osm->N,NULL);
    417:     }

    420:     if (osm->sort_indices) {
    421:       for (i=0; i<osm->n; i++) {
    422:         ISSort(osm->ois[i]);
    423:         ISSort(osm->iis[i]);
    424:       }
    425:     }
    426:     PCGetOptionsPrefix(pc,&prefix);
    427:     PCGASMPrintSubdomains(pc);

    429:     /*
    430:        Merge the ISs, create merged vectors and restrictions.
    431:      */
    432:     /* Merge outer subdomain ISs and construct a restriction onto the disjoint union of local outer subdomains. */
    433:     on = 0;
    434:     for (i=0; i<osm->n; i++) {
    435:       ISGetLocalSize(osm->ois[i],&oni);
    436:       on  += oni;
    437:     }
    438:     PetscMalloc1(on, &oidx);
    439:     on   = 0;
    440:     /* Merge local indices together */
    441:     for (i=0; i<osm->n; i++) {
    442:       ISGetLocalSize(osm->ois[i],&oni);
    443:       ISGetIndices(osm->ois[i],&oidxi);
    444:       PetscArraycpy(oidx+on,oidxi,oni);
    445:       ISRestoreIndices(osm->ois[i],&oidxi);
    446:       on  += oni;
    447:     }
    448:     ISCreateGeneral(((PetscObject)(pc))->comm,on,oidx,PETSC_OWN_POINTER,&gois);
    449:     nTotalInnerIndices = 0;
    450:     for(i=0; i<osm->n; i++){
    451:       ISGetLocalSize(osm->iis[i],&nInnerIndices);
    452:       nTotalInnerIndices += nInnerIndices;
    453:     }
    454:     VecCreateMPI(((PetscObject)(pc))->comm,nTotalInnerIndices,PETSC_DETERMINE,&x);
    455:     VecDuplicate(x,&y);

    457:     VecCreateMPI(PetscObjectComm((PetscObject)pc),on,PETSC_DECIDE,&osm->gx);
    458:     VecDuplicate(osm->gx,&osm->gy);
    459:     VecGetOwnershipRange(osm->gx, &gostart, NULL);
    460:     ISCreateStride(PetscObjectComm((PetscObject)pc),on,gostart,1, &goid);
    461:     /* gois might indices not on local */
    462:     VecScatterCreate(x,gois,osm->gx,goid, &(osm->gorestriction));
    463:     PetscMalloc1(osm->n,&numbering);
    464:     PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc),osm->n,(PetscObject*)osm->ois,NULL,numbering);
    465:     VecDestroy(&x);
    466:     ISDestroy(&gois);

    468:     /* Merge inner subdomain ISs and construct a restriction onto the disjoint union of local inner subdomains. */
    469:     {
    470:       PetscInt        ini;           /* Number of indices the i-th a local inner subdomain. */
    471:       PetscInt        in;            /* Number of indices in the disjoint union of local inner subdomains. */
    472:       PetscInt       *iidx;          /* Global indices in the merged local inner subdomain. */
    473:       PetscInt       *ioidx;         /* Global indices of the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
    474:       IS              giis;          /* IS for the disjoint union of inner subdomains. */
    475:       IS              giois;         /* IS for the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
    476:       PetscScalar    *array;
    477:       const PetscInt *indices;
    478:       PetscInt        k;
    479:       on = 0;
    480:       for (i=0; i<osm->n; i++) {
    481:         ISGetLocalSize(osm->ois[i],&oni);
    482:         on  += oni;
    483:       }
    484:       PetscMalloc1(on, &iidx);
    485:       PetscMalloc1(on, &ioidx);
    486:       VecGetArray(y,&array);
    487:       /* set communicator id to determine where overlap is */
    488:       in   = 0;
    489:       for (i=0; i<osm->n; i++) {
    490:         ISGetLocalSize(osm->iis[i],&ini);
    491:         for (k = 0; k < ini; ++k){
    492:           array[in+k] = numbering[i];
    493:         }
    494:         in += ini;
    495:       }
    496:       VecRestoreArray(y,&array);
    497:       VecScatterBegin(osm->gorestriction,y,osm->gy,INSERT_VALUES,SCATTER_FORWARD);
    498:       VecScatterEnd(osm->gorestriction,y,osm->gy,INSERT_VALUES,SCATTER_FORWARD);
    499:       VecGetOwnershipRange(osm->gy,&gostart, NULL);
    500:       VecGetArray(osm->gy,&array);
    501:       on  = 0;
    502:       in  = 0;
    503:       for (i=0; i<osm->n; i++) {
    504:             ISGetLocalSize(osm->ois[i],&oni);
    505:             ISGetIndices(osm->ois[i],&indices);
    506:             for (k=0; k<oni; k++) {
    507:           /*  skip overlapping indices to get inner domain */
    508:           if(PetscRealPart(array[on+k]) != numbering[i]) continue;
    509:           iidx[in]    = indices[k];
    510:           ioidx[in++] = gostart+on+k;
    511:             }
    512:             ISRestoreIndices(osm->ois[i], &indices);
    513:             on += oni;
    514:       }
    515:       VecRestoreArray(osm->gy,&array);
    516:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),in,iidx,PETSC_OWN_POINTER,&giis);
    517:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),in,ioidx,PETSC_OWN_POINTER,&giois);
    518:       VecScatterCreate(y,giis,osm->gy,giois,&osm->girestriction);
    519:       VecDestroy(&y);
    520:       ISDestroy(&giis);
    521:       ISDestroy(&giois);
    522:     }
    523:     ISDestroy(&goid);
    524:     PetscFree(numbering);

    526:     /* Create the subdomain work vectors. */
    527:     PetscMalloc1(osm->n,&osm->x);
    528:     PetscMalloc1(osm->n,&osm->y);
    529:     VecGetArray(osm->gx, &gxarray);
    530:     VecGetArray(osm->gy, &gyarray);
    531:     for (i=0, on=0; i<osm->n; ++i, on += oni) {
    532:       PetscInt oNi;
    533:       ISGetLocalSize(osm->ois[i],&oni);
    534:       /* on a sub communicator */
    535:       ISGetSize(osm->ois[i],&oNi);
    536:       VecCreateMPIWithArray(((PetscObject)(osm->ois[i]))->comm,1,oni,oNi,gxarray+on,&osm->x[i]);
    537:       VecCreateMPIWithArray(((PetscObject)(osm->ois[i]))->comm,1,oni,oNi,gyarray+on,&osm->y[i]);
    538:     }
    539:     VecRestoreArray(osm->gx, &gxarray);
    540:     VecRestoreArray(osm->gy, &gyarray);
    541:     /* Create the subdomain solvers */
    542:     PetscMalloc1(osm->n,&osm->ksp);
    543:     for (i=0; i<osm->n; i++) {
    544:       char subprefix[PETSC_MAX_PATH_LEN+1];
    545:       KSPCreate(((PetscObject)(osm->ois[i]))->comm,&ksp);
    546:       KSPSetErrorIfNotConverged(ksp,pc->erroriffailure);
    547:       PetscLogObjectParent((PetscObject)pc,(PetscObject)ksp);
    548:       PetscObjectIncrementTabLevel((PetscObject)ksp,(PetscObject)pc,1);
    549:       KSPSetType(ksp,KSPPREONLY);
    550:       KSPGetPC(ksp,&subpc); /* Why do we need this here? */
    551:       if (subdomain_dm) {
    552:             KSPSetDM(ksp,subdomain_dm[i]);
    553:             DMDestroy(subdomain_dm+i);
    554:       }
    555:       PCGetOptionsPrefix(pc,&prefix);
    556:       KSPSetOptionsPrefix(ksp,prefix);
    557:       if (subdomain_names && subdomain_names[i]) {
    558:              PetscSNPrintf(subprefix,PETSC_MAX_PATH_LEN,"sub_%s_",subdomain_names[i]);
    559:              KSPAppendOptionsPrefix(ksp,subprefix);
    560:              PetscFree(subdomain_names[i]);
    561:       }
    562:       KSPAppendOptionsPrefix(ksp,"sub_");
    563:       osm->ksp[i] = ksp;
    564:     }
    565:     PetscFree(subdomain_dm);
    566:     PetscFree(subdomain_names);
    567:     scall = MAT_INITIAL_MATRIX;

    569:   } else { /* if (pc->setupcalled) */
    570:     /*
    571:        Destroy the submatrices from the previous iteration
    572:     */
    573:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
    574:       MatDestroyMatrices(osm->n,&osm->pmat);
    575:       scall = MAT_INITIAL_MATRIX;
    576:     }
    577:     if(osm->permutationIS){
    578:       MatCreateSubMatrix(pc->pmat,osm->permutationIS,osm->permutationIS,scall,&osm->permutationP);
    579:       PetscObjectReference((PetscObject)osm->permutationP);
    580:       osm->pcmat = pc->pmat;
    581:       pc->pmat   = osm->permutationP;
    582:     }

    584:   }

    587:   /*
    588:      Extract out the submatrices.
    589:   */
    590:   if (size > 1) {
    591:     MatCreateSubMatricesMPI(pc->pmat,osm->n,osm->ois,osm->ois,scall,&osm->pmat);
    592:   } else {
    593:     MatCreateSubMatrices(pc->pmat,osm->n,osm->ois,osm->ois,scall,&osm->pmat);
    594:   }
    595:   if (scall == MAT_INITIAL_MATRIX) {
    596:     PetscObjectGetOptionsPrefix((PetscObject)pc->pmat,&pprefix);
    597:     for (i=0; i<osm->n; i++) {
    598:       PetscLogObjectParent((PetscObject)pc,(PetscObject)osm->pmat[i]);
    599:       PetscObjectSetOptionsPrefix((PetscObject)osm->pmat[i],pprefix);
    600:     }
    601:   }

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

    607:   /*
    608:      Loop over submatrices putting them into local ksps
    609:   */
    610:   for (i=0; i<osm->n; i++) {
    611:     KSPSetOperators(osm->ksp[i],osm->pmat[i],osm->pmat[i]);
    612:     if (!pc->setupcalled) {
    613:       KSPSetFromOptions(osm->ksp[i]);
    614:     }
    615:   }
    616:   if(osm->pcmat){
    617:     MatDestroy(&pc->pmat);
    618:     pc->pmat   = osm->pcmat;
    619:     osm->pcmat = 0;
    620:   }
    621:   return(0);
    622: }

    624: static PetscErrorCode PCSetUpOnBlocks_GASM(PC pc)
    625: {
    626:   PC_GASM        *osm = (PC_GASM*)pc->data;
    628:   PetscInt       i;

    631:   for (i=0; i<osm->n; i++) {
    632:     KSPSetUp(osm->ksp[i]);
    633:   }
    634:   return(0);
    635: }

    637: static PetscErrorCode PCApply_GASM(PC pc,Vec xin,Vec yout)
    638: {
    639:   PC_GASM        *osm = (PC_GASM*)pc->data;
    641:   PetscInt       i;
    642:   Vec            x,y;
    643:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

    646:   if(osm->pctoouter){
    647:     VecScatterBegin(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
    648:     VecScatterEnd(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
    649:     x = osm->pcx;
    650:     y = osm->pcy;
    651:   }else{
    652:         x = xin;
    653:         y = yout;
    654:   }
    655:   /*
    656:      Support for limiting the restriction or interpolation only to the inner
    657:      subdomain values (leaving the other values 0).
    658:   */
    659:   if (!(osm->type & PC_GASM_RESTRICT)) {
    660:     /* have to zero the work RHS since scatter may leave some slots empty */
    661:     VecZeroEntries(osm->gx);
    662:     VecScatterBegin(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
    663:   } else {
    664:     VecScatterBegin(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
    665:   }
    666:   VecZeroEntries(osm->gy);
    667:   if (!(osm->type & PC_GASM_RESTRICT)) {
    668:     VecScatterEnd(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
    669:   } else {
    670:     VecScatterEnd(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
    671:   }
    672:   /* do the subdomain solves */
    673:   for (i=0; i<osm->n; ++i) {
    674:     KSPSolve(osm->ksp[i],osm->x[i],osm->y[i]);
    675:     KSPCheckSolve(osm->ksp[i],pc,osm->y[i]);
    676:   }
    677:   /* Do we need to zero y ?? */
    678:   VecZeroEntries(y);
    679:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
    680:     VecScatterBegin(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
    681:     VecScatterEnd(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
    682:   } else {
    683:     VecScatterBegin(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
    684:     VecScatterEnd(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
    685:   }
    686:   if(osm->pctoouter){
    687:     VecScatterBegin(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
    688:     VecScatterEnd(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
    689:   }
    690:   return(0);
    691: }

    693: static PetscErrorCode PCApplyTranspose_GASM(PC pc,Vec xin,Vec yout)
    694: {
    695:   PC_GASM        *osm = (PC_GASM*)pc->data;
    697:   PetscInt       i;
    698:   Vec            x,y;
    699:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

    702:   if(osm->pctoouter){
    703:    VecScatterBegin(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
    704:    VecScatterEnd(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
    705:    x = osm->pcx;
    706:    y = osm->pcy;
    707:   }else{
    708:         x = xin;
    709:         y = yout;
    710:   }
    711:   /*
    712:      Support for limiting the restriction or interpolation to only local
    713:      subdomain values (leaving the other values 0).

    715:      Note: these are reversed from the PCApply_GASM() because we are applying the
    716:      transpose of the three terms
    717:   */
    718:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
    719:     /* have to zero the work RHS since scatter may leave some slots empty */
    720:     VecZeroEntries(osm->gx);
    721:     VecScatterBegin(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
    722:   } else {
    723:     VecScatterBegin(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
    724:   }
    725:   VecZeroEntries(osm->gy);
    726:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
    727:     VecScatterEnd(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
    728:   } else {
    729:     VecScatterEnd(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
    730:   }
    731:   /* do the local solves */
    732:   for (i=0; i<osm->n; ++i) { /* Note that the solves are local, so we can go to osm->n, rather than osm->nmax. */
    733:     KSPSolveTranspose(osm->ksp[i],osm->x[i],osm->y[i]);
    734:     KSPCheckSolve(osm->ksp[i],pc,osm->y[i]);
    735:   }
    736:   VecZeroEntries(y);
    737:   if (!(osm->type & PC_GASM_RESTRICT)) {
    738:     VecScatterBegin(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
    739:     VecScatterEnd(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
    740:   } else {
    741:     VecScatterBegin(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
    742:     VecScatterEnd(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
    743:   }
    744:   if(osm->pctoouter){
    745:    VecScatterBegin(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
    746:    VecScatterEnd(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
    747:   }
    748:   return(0);
    749: }

    751: static PetscErrorCode PCReset_GASM(PC pc)
    752: {
    753:   PC_GASM        *osm = (PC_GASM*)pc->data;
    755:   PetscInt       i;

    758:   if (osm->ksp) {
    759:     for (i=0; i<osm->n; i++) {
    760:       KSPReset(osm->ksp[i]);
    761:     }
    762:   }
    763:   if (osm->pmat) {
    764:     if (osm->n > 0) {
    765:       PetscMPIInt size;
    766:       MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
    767:       if (size > 1) {
    768:         /* osm->pmat is created by MatCreateSubMatricesMPI(), cannot use MatDestroySubMatrices() */
    769:         MatDestroyMatrices(osm->n,&osm->pmat);
    770:       } else {
    771:         MatDestroySubMatrices(osm->n,&osm->pmat);
    772:       }
    773:     }
    774:   }
    775:   if (osm->x) {
    776:     for (i=0; i<osm->n; i++) {
    777:       VecDestroy(&osm->x[i]);
    778:       VecDestroy(&osm->y[i]);
    779:     }
    780:   }
    781:   VecDestroy(&osm->gx);
    782:   VecDestroy(&osm->gy);

    784:   VecScatterDestroy(&osm->gorestriction);
    785:   VecScatterDestroy(&osm->girestriction);
    786:   if (!osm->user_subdomains) {
    787:     PCGASMDestroySubdomains(osm->n,&osm->ois,&osm->iis);
    788:     osm->N    = PETSC_DETERMINE;
    789:     osm->nmax = PETSC_DETERMINE;
    790:   }
    791:   if(osm->pctoouter){
    792:         VecScatterDestroy(&(osm->pctoouter));
    793:   }
    794:   if(osm->permutationIS){
    795:         ISDestroy(&(osm->permutationIS));
    796:   }
    797:   if(osm->pcx){
    798:         VecDestroy(&(osm->pcx));
    799:   }
    800:   if(osm->pcy){
    801:         VecDestroy(&(osm->pcy));
    802:   }
    803:   if(osm->permutationP){
    804:     MatDestroy(&(osm->permutationP));
    805:   }
    806:   if(osm->pcmat){
    807:         MatDestroy(&osm->pcmat);
    808:   }
    809:   return(0);
    810: }

    812: static PetscErrorCode PCDestroy_GASM(PC pc)
    813: {
    814:   PC_GASM        *osm = (PC_GASM*)pc->data;
    816:   PetscInt       i;

    819:   PCReset_GASM(pc);
    820:   /* PCReset will not destroy subdomains, if user_subdomains is true. */
    821:   PCGASMDestroySubdomains(osm->n,&osm->ois,&osm->iis);
    822:   if (osm->ksp) {
    823:     for (i=0; i<osm->n; i++) {
    824:       KSPDestroy(&osm->ksp[i]);
    825:     }
    826:     PetscFree(osm->ksp);
    827:   }
    828:   PetscFree(osm->x);
    829:   PetscFree(osm->y);
    830:   PetscFree(pc->data);
    831:   return(0);
    832: }

    834: static PetscErrorCode PCSetFromOptions_GASM(PetscOptionItems *PetscOptionsObject,PC pc)
    835: {
    836:   PC_GASM        *osm = (PC_GASM*)pc->data;
    838:   PetscInt       blocks,ovl;
    839:   PetscBool      flg;
    840:   PCGASMType     gasmtype;

    843:   PetscOptionsHead(PetscOptionsObject,"Generalized additive Schwarz options");
    844:   PetscOptionsBool("-pc_gasm_use_dm_subdomains","If subdomains aren't set, use DMCreateDomainDecomposition() to define subdomains.","PCGASMSetUseDMSubdomains",osm->dm_subdomains,&osm->dm_subdomains,&flg);
    845:   PetscOptionsInt("-pc_gasm_total_subdomains","Total number of subdomains across communicator","PCGASMSetTotalSubdomains",osm->N,&blocks,&flg);
    846:   if (flg) {
    847:     PCGASMSetTotalSubdomains(pc,blocks);
    848:   }
    849:   PetscOptionsInt("-pc_gasm_overlap","Number of overlapping degrees of freedom","PCGASMSetOverlap",osm->overlap,&ovl,&flg);
    850:   if (flg) {
    851:     PCGASMSetOverlap(pc,ovl);
    852:     osm->dm_subdomains = PETSC_FALSE;
    853:   }
    854:   flg  = PETSC_FALSE;
    855:   PetscOptionsEnum("-pc_gasm_type","Type of restriction/extension","PCGASMSetType",PCGASMTypes,(PetscEnum)osm->type,(PetscEnum*)&gasmtype,&flg);
    856:   if (flg) {PCGASMSetType(pc,gasmtype);}
    857:   PetscOptionsBool("-pc_gasm_use_hierachical_partitioning","use hierarchical partitioning",NULL,osm->hierarchicalpartitioning,&osm->hierarchicalpartitioning,&flg);
    858:   PetscOptionsTail();
    859:   return(0);
    860: }

    862: /*------------------------------------------------------------------------------------*/

    864: /*@
    865:     PCGASMSetTotalSubdomains - sets the total number of subdomains to use across the
    866:                                communicator.
    867:     Logically collective on pc

    869:     Input Parameters:
    870: +   pc  - the preconditioner
    871: -   N   - total number of subdomains

    874:     Level: beginner

    876: .seealso: PCGASMSetSubdomains(), PCGASMSetOverlap()
    877:           PCGASMCreateSubdomains2D()
    878: @*/
    879: PetscErrorCode  PCGASMSetTotalSubdomains(PC pc,PetscInt N)
    880: {
    881:   PC_GASM        *osm = (PC_GASM*)pc->data;
    882:   PetscMPIInt    size,rank;

    886:   if (N < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Total number of subdomains must be 1 or more, got N = %D",N);
    887:   if (pc->setupcalled) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"PCGASMSetTotalSubdomains() should be called before calling PCSetUp().");

    889:   PCGASMDestroySubdomains(osm->n,&osm->iis,&osm->ois);
    890:   osm->ois = osm->iis = NULL;

    892:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
    893:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
    894:   osm->N    = N;
    895:   osm->n    = PETSC_DETERMINE;
    896:   osm->nmax = PETSC_DETERMINE;
    897:   osm->dm_subdomains = PETSC_FALSE;
    898:   return(0);
    899: }

    902: static PetscErrorCode  PCGASMSetSubdomains_GASM(PC pc,PetscInt n,IS iis[],IS ois[])
    903: {
    904:   PC_GASM         *osm = (PC_GASM*)pc->data;
    905:   PetscErrorCode  ierr;
    906:   PetscInt        i;

    909:   if (n < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Each process must have 1 or more subdomains, got n = %D",n);
    910:   if (pc->setupcalled) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"PCGASMSetSubdomains() should be called before calling PCSetUp().");

    912:   PCGASMDestroySubdomains(osm->n,&osm->iis,&osm->ois);
    913:   osm->iis  = osm->ois = NULL;
    914:   osm->n    = n;
    915:   osm->N    = PETSC_DETERMINE;
    916:   osm->nmax = PETSC_DETERMINE;
    917:   if (ois) {
    918:     PetscMalloc1(n,&osm->ois);
    919:     for (i=0; i<n; i++) {
    920:       PetscObjectReference((PetscObject)ois[i]);
    921:       osm->ois[i] = ois[i];
    922:     }
    923:     /*
    924:        Since the user set the outer subdomains, even if nontrivial overlap was requested via PCGASMSetOverlap(),
    925:        it will be ignored.  To avoid confusion later on (e.g., when viewing the PC), the overlap size is set to -1.
    926:     */
    927:     osm->overlap = -1;
    928:     /* inner subdomains must be provided  */
    929:     if (!iis) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"inner indices have to be provided \n");
    930:   }/* end if */
    931:   if (iis) {
    932:     PetscMalloc1(n,&osm->iis);
    933:     for (i=0; i<n; i++) {
    934:       PetscObjectReference((PetscObject)iis[i]);
    935:       osm->iis[i] = iis[i];
    936:     }
    937:     if (!ois) {
    938:       osm->ois = NULL;
    939:       /* if user does not provide outer indices, we will create the corresponding outer indices using  osm->overlap =1 in PCSetUp_GASM */
    940:     }
    941:   }
    942: #if defined(PETSC_USE_DEBUG)
    943:   {
    944:     PetscInt        j,rstart,rend,*covered,lsize;
    945:     const PetscInt  *indices;
    946:     /* check if the inner indices cover and only cover the local portion of the preconditioning matrix */
    947:     MatGetOwnershipRange(pc->pmat,&rstart,&rend);
    948:     PetscCalloc1(rend-rstart,&covered);
    949:     /* check if the current processor owns indices from others */
    950:     for (i=0; i<n; i++) {
    951:       ISGetIndices(osm->iis[i],&indices);
    952:       ISGetLocalSize(osm->iis[i],&lsize);
    953:       for (j=0; j<lsize; j++) {
    954:         if (indices[j]<rstart || indices[j]>=rend) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"inner subdomains can not own an index %d from other processors", indices[j]);
    955:         else if (covered[indices[j]-rstart]==1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"inner subdomains can not have an overlapping index %d ",indices[j]);
    956:         else covered[indices[j]-rstart] = 1;
    957:       }
    958:     ISRestoreIndices(osm->iis[i],&indices);
    959:     }
    960:     /* check if we miss any indices */
    961:     for (i=rstart; i<rend; i++) {
    962:       if (!covered[i-rstart]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"local entity %d was not covered by inner subdomains",i);
    963:     }
    964:     PetscFree(covered);
    965:   }
    966: #endif
    967:   if (iis)  osm->user_subdomains = PETSC_TRUE;
    968:   return(0);
    969: }

    972: static PetscErrorCode  PCGASMSetOverlap_GASM(PC pc,PetscInt ovl)
    973: {
    974:   PC_GASM *osm = (PC_GASM*)pc->data;

    977:   if (ovl < 0) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap value requested");
    978:   if (pc->setupcalled && ovl != osm->overlap) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"PCGASMSetOverlap() should be called before PCSetUp().");
    979:   if (!pc->setupcalled) osm->overlap = ovl;
    980:   return(0);
    981: }

    983: static PetscErrorCode  PCGASMSetType_GASM(PC pc,PCGASMType type)
    984: {
    985:   PC_GASM *osm = (PC_GASM*)pc->data;

    988:   osm->type     = type;
    989:   osm->type_set = PETSC_TRUE;
    990:   return(0);
    991: }

    993: static PetscErrorCode  PCGASMSetSortIndices_GASM(PC pc,PetscBool doSort)
    994: {
    995:   PC_GASM *osm = (PC_GASM*)pc->data;

    998:   osm->sort_indices = doSort;
    999:   return(0);
    1000: }

    1002: /*
    1003:    FIXME: This routine might need to be modified now that multiple ranks per subdomain are allowed.
    1004:         In particular, it would upset the global subdomain number calculation.
    1005: */
    1006: static PetscErrorCode  PCGASMGetSubKSP_GASM(PC pc,PetscInt *n,PetscInt *first,KSP **ksp)
    1007: {
    1008:   PC_GASM        *osm = (PC_GASM*)pc->data;

    1012:   if (osm->n < 1) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ORDER,"Need to call PCSetUp() on PC (or KSPSetUp() on the outer KSP object) before calling here");

    1014:   if (n) *n = osm->n;
    1015:   if (first) {
    1016:     MPI_Scan(&osm->n,first,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
    1017:     *first -= osm->n;
    1018:   }
    1019:   if (ksp) {
    1020:     /* Assume that local solves are now different; not necessarily
    1021:        true, though!  This flag is used only for PCView_GASM() */
    1022:     *ksp                        = osm->ksp;
    1023:     osm->same_subdomain_solvers = PETSC_FALSE;
    1024:   }
    1025:   return(0);
    1026: } /* PCGASMGetSubKSP_GASM() */

    1028: /*@C
    1029:     PCGASMSetSubdomains - Sets the subdomains for this processor
    1030:     for the additive Schwarz preconditioner.

    1032:     Collective on pc

    1034:     Input Parameters:
    1035: +   pc  - the preconditioner object
    1036: .   n   - the number of subdomains for this processor
    1037: .   iis - the index sets that define the inner subdomains (or NULL for PETSc to determine subdomains)
    1038: -   ois - the index sets that define the outer subdomains (or NULL to use the same as iis, or to construct by expanding iis by the requested overlap)

    1040:     Notes:
    1041:     The IS indices use the parallel, global numbering of the vector entries.
    1042:     Inner subdomains are those where the correction is applied.
    1043:     Outer subdomains are those where the residual necessary to obtain the
    1044:     corrections is obtained (see PCGASMType for the use of inner/outer subdomains).
    1045:     Both inner and outer subdomains can extend over several processors.
    1046:     This processor's portion of a subdomain is known as a local subdomain.

    1048:     Inner subdomains can not overlap with each other, do not have any entities from remote processors,
    1049:     and  have to cover the entire local subdomain owned by the current processor. The index sets on each
    1050:     process should be ordered such that the ith local subdomain is connected to the ith remote subdomain
    1051:     on another MPI process.

    1053:     By default the GASM preconditioner uses 1 (local) subdomain per processor.

    1056:     Level: advanced

    1058: .seealso: PCGASMSetNumSubdomains(), PCGASMSetOverlap(), PCGASMGetSubKSP(),
    1059:           PCGASMCreateSubdomains2D(), PCGASMGetSubdomains()
    1060: @*/
    1061: PetscErrorCode  PCGASMSetSubdomains(PC pc,PetscInt n,IS iis[],IS ois[])
    1062: {
    1063:   PC_GASM *osm = (PC_GASM*)pc->data;

    1068:   PetscTryMethod(pc,"PCGASMSetSubdomains_C",(PC,PetscInt,IS[],IS[]),(pc,n,iis,ois));
    1069:   osm->dm_subdomains = PETSC_FALSE;
    1070:   return(0);
    1071: }

    1074: /*@
    1075:     PCGASMSetOverlap - Sets the overlap between a pair of subdomains for the
    1076:     additive Schwarz preconditioner.  Either all or no processors in the
    1077:     pc communicator must call this routine.

    1079:     Logically Collective on pc

    1081:     Input Parameters:
    1082: +   pc  - the preconditioner context
    1083: -   ovl - the amount of overlap between subdomains (ovl >= 0, default value = 0)

    1085:     Options Database Key:
    1086: .   -pc_gasm_overlap <overlap> - Sets overlap

    1088:     Notes:
    1089:     By default the GASM preconditioner uses 1 subdomain per processor.  To use
    1090:     multiple subdomain per perocessor or "straddling" subdomains that intersect
    1091:     multiple processors use PCGASMSetSubdomains() (or option -pc_gasm_total_subdomains <n>).

    1093:     The overlap defaults to 0, so if one desires that no additional
    1094:     overlap be computed beyond what may have been set with a call to
    1095:     PCGASMSetSubdomains(), then ovl must be set to be 0.  In particular, if one does
    1096:     not explicitly set the subdomains in Section 1.5 Writing Application Codes with PETSc code, then all overlap would be computed
    1097:     internally by PETSc, and using an overlap of 0 would result in an GASM
    1098:     variant that is equivalent to the block Jacobi preconditioner.

    1100:     Note that one can define initial index sets with any overlap via
    1101:     PCGASMSetSubdomains(); the routine PCGASMSetOverlap() merely allows
    1102:     PETSc to extend that overlap further, if desired.

    1104:     Level: intermediate

    1106: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
    1107:           PCGASMCreateSubdomains2D(), PCGASMGetSubdomains()
    1108: @*/
    1109: PetscErrorCode  PCGASMSetOverlap(PC pc,PetscInt ovl)
    1110: {
    1112:   PC_GASM *osm = (PC_GASM*)pc->data;

    1117:   PetscTryMethod(pc,"PCGASMSetOverlap_C",(PC,PetscInt),(pc,ovl));
    1118:   osm->dm_subdomains = PETSC_FALSE;
    1119:   return(0);
    1120: }

    1122: /*@
    1123:     PCGASMSetType - Sets the type of restriction and interpolation used
    1124:     for local problems in the additive Schwarz method.

    1126:     Logically Collective on PC

    1128:     Input Parameters:
    1129: +   pc  - the preconditioner context
    1130: -   type - variant of GASM, one of
    1131: .vb
    1132:       PC_GASM_BASIC       - full interpolation and restriction
    1133:       PC_GASM_RESTRICT    - full restriction, local processor interpolation
    1134:       PC_GASM_INTERPOLATE - full interpolation, local processor restriction
    1135:       PC_GASM_NONE        - local processor restriction and interpolation
    1136: .ve

    1138:     Options Database Key:
    1139: .   -pc_gasm_type [basic,restrict,interpolate,none] - Sets GASM type

    1141:     Level: intermediate

    1143: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
    1144:           PCGASMCreateSubdomains2D()
    1145: @*/
    1146: PetscErrorCode  PCGASMSetType(PC pc,PCGASMType type)
    1147: {

    1153:   PetscTryMethod(pc,"PCGASMSetType_C",(PC,PCGASMType),(pc,type));
    1154:   return(0);
    1155: }

    1157: /*@
    1158:     PCGASMSetSortIndices - Determines whether subdomain indices are sorted.

    1160:     Logically Collective on PC

    1162:     Input Parameters:
    1163: +   pc  - the preconditioner context
    1164: -   doSort - sort the subdomain indices

    1166:     Level: intermediate

    1168: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
    1169:           PCGASMCreateSubdomains2D()
    1170: @*/
    1171: PetscErrorCode  PCGASMSetSortIndices(PC pc,PetscBool doSort)
    1172: {

    1178:   PetscTryMethod(pc,"PCGASMSetSortIndices_C",(PC,PetscBool),(pc,doSort));
    1179:   return(0);
    1180: }

    1182: /*@C
    1183:    PCGASMGetSubKSP - Gets the local KSP contexts for all blocks on
    1184:    this processor.

    1186:    Collective on PC iff first_local is requested

    1188:    Input Parameter:
    1189: .  pc - the preconditioner context

    1191:    Output Parameters:
    1192: +  n_local - the number of blocks on this processor or NULL
    1193: .  first_local - the global number of the first block on this processor or NULL,
    1194:                  all processors must request or all must pass NULL
    1195: -  ksp - the array of KSP contexts

    1197:    Note:
    1198:    After PCGASMGetSubKSP() the array of KSPes is not to be freed

    1200:    Currently for some matrix implementations only 1 block per processor
    1201:    is supported.

    1203:    You must call KSPSetUp() before calling PCGASMGetSubKSP().

    1205:    Level: advanced

    1207: .seealso: PCGASMSetSubdomains(), PCGASMSetOverlap(),
    1208:           PCGASMCreateSubdomains2D(),
    1209: @*/
    1210: PetscErrorCode  PCGASMGetSubKSP(PC pc,PetscInt *n_local,PetscInt *first_local,KSP *ksp[])
    1211: {

    1216:   PetscUseMethod(pc,"PCGASMGetSubKSP_C",(PC,PetscInt*,PetscInt*,KSP **),(pc,n_local,first_local,ksp));
    1217:   return(0);
    1218: }

    1220: /* -------------------------------------------------------------------------------------*/
    1221: /*MC
    1222:    PCGASM - Use the (restricted) additive Schwarz method, each block is (approximately) solved with
    1223:            its own KSP object.

    1225:    Options Database Keys:
    1226: +  -pc_gasm_total_subdomains <n>  - Sets total number of local subdomains to be distributed among processors
    1227: .  -pc_gasm_view_subdomains       - activates the printing of subdomain indices in PCView(), -ksp_view or -snes_view
    1228: .  -pc_gasm_print_subdomains      - activates the printing of subdomain indices in PCSetUp()
    1229: .  -pc_gasm_overlap <ovl>         - Sets overlap by which to (automatically) extend local subdomains
    1230: -  -pc_gasm_type [basic,restrict,interpolate,none] - Sets GASM type

    1232:      IMPORTANT: If you run with, for example, 3 blocks on 1 processor or 3 blocks on 3 processors you
    1233:       will get a different convergence rate due to the default option of -pc_gasm_type restrict. Use
    1234:       -pc_gasm_type basic to use the standard GASM.

    1236:    Notes:
    1237:     Blocks can be shared by multiple processes.

    1239:      To set options on the solvers for each block append -sub_ to all the KSP, and PC
    1240:         options database keys. For example, -sub_pc_type ilu -sub_pc_factor_levels 1 -sub_ksp_type preonly

    1242:      To set the options on the solvers separate for each block call PCGASMGetSubKSP()
    1243:          and set the options directly on the resulting KSP object (you can access its PC
    1244:          with KSPGetPC())

    1247:    Level: beginner

    1249:     References:
    1250: +   1. - M Dryja, OB Widlund, An additive variant of the Schwarz alternating method for the case of many subregions
    1251:      Courant Institute, New York University Technical report
    1252: -   2. - Barry Smith, Petter Bjorstad, and William Gropp, Domain Decompositions: Parallel Multilevel Methods for Elliptic Partial Differential Equations,
    1253:     Cambridge University Press.

    1255: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,
    1256:            PCBJACOBI,  PCGASMGetSubKSP(), PCGASMSetSubdomains(),
    1257:            PCSetModifySubMatrices(), PCGASMSetOverlap(), PCGASMSetType()

    1259: M*/

    1261: PETSC_EXTERN PetscErrorCode PCCreate_GASM(PC pc)
    1262: {
    1264:   PC_GASM        *osm;

    1267:   PetscNewLog(pc,&osm);

    1269:   osm->N                        = PETSC_DETERMINE;
    1270:   osm->n                        = PETSC_DECIDE;
    1271:   osm->nmax                     = PETSC_DETERMINE;
    1272:   osm->overlap                  = 0;
    1273:   osm->ksp                      = 0;
    1274:   osm->gorestriction            = 0;
    1275:   osm->girestriction            = 0;
    1276:   osm->pctoouter                = 0;
    1277:   osm->gx                       = 0;
    1278:   osm->gy                       = 0;
    1279:   osm->x                        = 0;
    1280:   osm->y                        = 0;
    1281:   osm->pcx                      = 0;
    1282:   osm->pcy                      = 0;
    1283:   osm->permutationIS            = 0;
    1284:   osm->permutationP             = 0;
    1285:   osm->pcmat                    = 0;
    1286:   osm->ois                      = 0;
    1287:   osm->iis                      = 0;
    1288:   osm->pmat                     = 0;
    1289:   osm->type                     = PC_GASM_RESTRICT;
    1290:   osm->same_subdomain_solvers   = PETSC_TRUE;
    1291:   osm->sort_indices             = PETSC_TRUE;
    1292:   osm->dm_subdomains            = PETSC_FALSE;
    1293:   osm->hierarchicalpartitioning = PETSC_FALSE;

    1295:   pc->data                 = (void*)osm;
    1296:   pc->ops->apply           = PCApply_GASM;
    1297:   pc->ops->applytranspose  = PCApplyTranspose_GASM;
    1298:   pc->ops->setup           = PCSetUp_GASM;
    1299:   pc->ops->reset           = PCReset_GASM;
    1300:   pc->ops->destroy         = PCDestroy_GASM;
    1301:   pc->ops->setfromoptions  = PCSetFromOptions_GASM;
    1302:   pc->ops->setuponblocks   = PCSetUpOnBlocks_GASM;
    1303:   pc->ops->view            = PCView_GASM;
    1304:   pc->ops->applyrichardson = 0;

    1306:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetSubdomains_C",PCGASMSetSubdomains_GASM);
    1307:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetOverlap_C",PCGASMSetOverlap_GASM);
    1308:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetType_C",PCGASMSetType_GASM);
    1309:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetSortIndices_C",PCGASMSetSortIndices_GASM);
    1310:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMGetSubKSP_C",PCGASMGetSubKSP_GASM);
    1311:   return(0);
    1312: }

    1315: PetscErrorCode  PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[])
    1316: {
    1317:   MatPartitioning mpart;
    1318:   const char      *prefix;
    1319:   PetscInt        i,j,rstart,rend,bs;
    1320:   PetscBool       hasop, isbaij = PETSC_FALSE,foundpart = PETSC_FALSE;
    1321:   Mat             Ad     = NULL, adj;
    1322:   IS              ispart,isnumb,*is;
    1323:   PetscErrorCode  ierr;

    1326:   if (nloc < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"number of local subdomains must > 0, got nloc = %D",nloc);

    1328:   /* Get prefix, row distribution, and block size */
    1329:   MatGetOptionsPrefix(A,&prefix);
    1330:   MatGetOwnershipRange(A,&rstart,&rend);
    1331:   MatGetBlockSize(A,&bs);
    1332:   if (rstart/bs*bs != rstart || rend/bs*bs != rend) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"bad row distribution [%D,%D) for matrix block size %D",rstart,rend,bs);

    1334:   /* Get diagonal block from matrix if possible */
    1335:   MatHasOperation(A,MATOP_GET_DIAGONAL_BLOCK,&hasop);
    1336:   if (hasop) {
    1337:     MatGetDiagonalBlock(A,&Ad);
    1338:   }
    1339:   if (Ad) {
    1340:     PetscObjectBaseTypeCompare((PetscObject)Ad,MATSEQBAIJ,&isbaij);
    1341:     if (!isbaij) {PetscObjectBaseTypeCompare((PetscObject)Ad,MATSEQSBAIJ,&isbaij);}
    1342:   }
    1343:   if (Ad && nloc > 1) {
    1344:     PetscBool  match,done;
    1345:     /* Try to setup a good matrix partitioning if available */
    1346:     MatPartitioningCreate(PETSC_COMM_SELF,&mpart);
    1347:     PetscObjectSetOptionsPrefix((PetscObject)mpart,prefix);
    1348:     MatPartitioningSetFromOptions(mpart);
    1349:     PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGCURRENT,&match);
    1350:     if (!match) {
    1351:       PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGSQUARE,&match);
    1352:     }
    1353:     if (!match) { /* assume a "good" partitioner is available */
    1354:       PetscInt       na;
    1355:       const PetscInt *ia,*ja;
    1356:       MatGetRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
    1357:       if (done) {
    1358:         /* Build adjacency matrix by hand. Unfortunately a call to
    1359:            MatConvert(Ad,MATMPIADJ,MAT_INITIAL_MATRIX,&adj) will
    1360:            remove the block-aij structure and we cannot expect
    1361:            MatPartitioning to split vertices as we need */
    1362:         PetscInt       i,j,len,nnz,cnt,*iia=0,*jja=0;
    1363:         const PetscInt *row;
    1364:         nnz = 0;
    1365:         for (i=0; i<na; i++) { /* count number of nonzeros */
    1366:           len = ia[i+1] - ia[i];
    1367:           row = ja + ia[i];
    1368:           for (j=0; j<len; j++) {
    1369:             if (row[j] == i) { /* don't count diagonal */
    1370:               len--; break;
    1371:             }
    1372:           }
    1373:           nnz += len;
    1374:         }
    1375:         PetscMalloc1(na+1,&iia);
    1376:         PetscMalloc1(nnz,&jja);
    1377:         nnz    = 0;
    1378:         iia[0] = 0;
    1379:         for (i=0; i<na; i++) { /* fill adjacency */
    1380:           cnt = 0;
    1381:           len = ia[i+1] - ia[i];
    1382:           row = ja + ia[i];
    1383:           for (j=0; j<len; j++) {
    1384:             if (row[j] != i) jja[nnz+cnt++] = row[j]; /* if not diagonal */
    1385:           }
    1386:           nnz += cnt;
    1387:           iia[i+1] = nnz;
    1388:         }
    1389:         /* Partitioning of the adjacency matrix */
    1390:         MatCreateMPIAdj(PETSC_COMM_SELF,na,na,iia,jja,NULL,&adj);
    1391:         MatPartitioningSetAdjacency(mpart,adj);
    1392:         MatPartitioningSetNParts(mpart,nloc);
    1393:         MatPartitioningApply(mpart,&ispart);
    1394:         ISPartitioningToNumbering(ispart,&isnumb);
    1395:         MatDestroy(&adj);
    1396:         foundpart = PETSC_TRUE;
    1397:       }
    1398:       MatRestoreRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
    1399:     }
    1400:     MatPartitioningDestroy(&mpart);
    1401:   }
    1402:   PetscMalloc1(nloc,&is);
    1403:   if (!foundpart) {

    1405:     /* Partitioning by contiguous chunks of rows */

    1407:     PetscInt mbs   = (rend-rstart)/bs;
    1408:     PetscInt start = rstart;
    1409:     for (i=0; i<nloc; i++) {
    1410:       PetscInt count = (mbs/nloc + ((mbs % nloc) > i)) * bs;
    1411:       ISCreateStride(PETSC_COMM_SELF,count,start,1,&is[i]);
    1412:       start += count;
    1413:     }

    1415:   } else {

    1417:     /* Partitioning by adjacency of diagonal block  */

    1419:     const PetscInt *numbering;
    1420:     PetscInt       *count,nidx,*indices,*newidx,start=0;
    1421:     /* Get node count in each partition */
    1422:     PetscMalloc1(nloc,&count);
    1423:     ISPartitioningCount(ispart,nloc,count);
    1424:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
    1425:       for (i=0; i<nloc; i++) count[i] *= bs;
    1426:     }
    1427:     /* Build indices from node numbering */
    1428:     ISGetLocalSize(isnumb,&nidx);
    1429:     PetscMalloc1(nidx,&indices);
    1430:     for (i=0; i<nidx; i++) indices[i] = i; /* needs to be initialized */
    1431:     ISGetIndices(isnumb,&numbering);
    1432:     PetscSortIntWithPermutation(nidx,numbering,indices);
    1433:     ISRestoreIndices(isnumb,&numbering);
    1434:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
    1435:       PetscMalloc1(nidx*bs,&newidx);
    1436:       for (i=0; i<nidx; i++) {
    1437:         for (j=0; j<bs; j++) newidx[i*bs+j] = indices[i]*bs + j;
    1438:       }
    1439:       PetscFree(indices);
    1440:       nidx   *= bs;
    1441:       indices = newidx;
    1442:     }
    1443:     /* Shift to get global indices */
    1444:     for (i=0; i<nidx; i++) indices[i] += rstart;

    1446:     /* Build the index sets for each block */
    1447:     for (i=0; i<nloc; i++) {
    1448:       ISCreateGeneral(PETSC_COMM_SELF,count[i],&indices[start],PETSC_COPY_VALUES,&is[i]);
    1449:       ISSort(is[i]);
    1450:       start += count[i];
    1451:     }

    1453:     PetscFree(count);
    1454:     PetscFree(indices);
    1455:     ISDestroy(&isnumb);
    1456:     ISDestroy(&ispart);
    1457:   }
    1458:   *iis = is;
    1459:   return(0);
    1460: }

    1462: PETSC_INTERN PetscErrorCode  PCGASMCreateStraddlingSubdomains(Mat A,PetscInt N,PetscInt *n,IS *iis[])
    1463: {
    1464:   PetscErrorCode  ierr;

    1467:   MatSubdomainsCreateCoalesce(A,N,n,iis);
    1468:   return(0);
    1469: }

    1473: /*@C
    1474:    PCGASMCreateSubdomains - Creates n index sets defining n nonoverlapping subdomains for the additive
    1475:    Schwarz preconditioner for a any problem based on its matrix.

    1477:    Collective

    1479:    Input Parameters:
    1480: +  A       - The global matrix operator
    1481: -  N       - the number of global subdomains requested

    1483:    Output Parameters:
    1484: +  n   - the number of subdomains created on this processor
    1485: -  iis - the array of index sets defining the local inner subdomains (on which the correction is applied)

    1487:    Level: advanced

    1489:    Note: When N >= A's communicator size, each subdomain is local -- contained within a single processor.
    1490:          When N < size, the subdomains are 'straddling' (processor boundaries) and are no longer local.
    1491:          The resulting subdomains can be use in PCGASMSetSubdomains(pc,n,iss,NULL).  The overlapping
    1492:          outer subdomains will be automatically generated from these according to the requested amount of
    1493:          overlap; this is currently supported only with local subdomains.

    1496: .seealso: PCGASMSetSubdomains(), PCGASMDestroySubdomains()
    1497: @*/
    1498: PetscErrorCode  PCGASMCreateSubdomains(Mat A,PetscInt N,PetscInt *n,IS *iis[])
    1499: {
    1500:   PetscMPIInt     size;
    1501:   PetscErrorCode  ierr;

    1507:   if (N < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Number of subdomains must be > 0, N = %D",N);
    1508:   MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
    1509:   if (N >= size) {
    1510:     *n = N/size + (N%size);
    1511:     PCGASMCreateLocalSubdomains(A,*n,iis);
    1512:   } else {
    1513:     PCGASMCreateStraddlingSubdomains(A,N,n,iis);
    1514:   }
    1515:   return(0);
    1516: }

    1518: /*@C
    1519:    PCGASMDestroySubdomains - Destroys the index sets created with
    1520:    PCGASMCreateSubdomains() or PCGASMCreateSubdomains2D. Should be
    1521:    called after setting subdomains with PCGASMSetSubdomains().

    1523:    Collective

    1525:    Input Parameters:
    1526: +  n   - the number of index sets
    1527: .  iis - the array of inner subdomains,
    1528: -  ois - the array of outer subdomains, can be NULL

    1530:    Level: intermediate

    1532:    Notes:
    1533:     this is merely a convenience subroutine that walks each list,
    1534:    destroys each IS on the list, and then frees the list. At the end the
    1535:    list pointers are set to NULL.

    1537: .seealso: PCGASMCreateSubdomains(), PCGASMSetSubdomains()
    1538: @*/
    1539: PetscErrorCode  PCGASMDestroySubdomains(PetscInt n,IS **iis,IS **ois)
    1540: {
    1541:   PetscInt       i;

    1545:   if (n <= 0) return(0);
    1546:   if (ois) {
    1548:     if (*ois) {
    1550:       for (i=0; i<n; i++) {
    1551:         ISDestroy(&(*ois)[i]);
    1552:       }
    1553:       PetscFree((*ois));
    1554:     }
    1555:   }
    1556:   if (iis) {
    1558:     if (*iis) {
    1560:       for (i=0; i<n; i++) {
    1561:         ISDestroy(&(*iis)[i]);
    1562:       }
    1563:       PetscFree((*iis));
    1564:     }
    1565:   }
    1566:   return(0);
    1567: }

    1570: #define PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,xleft_loc,ylow_loc,xright_loc,yhigh_loc,n) \
    1571:   {                                                                                                       \
    1572:     PetscInt first_row = first/M, last_row = last/M+1;                                                     \
    1573:     /*                                                                                                    \
    1574:      Compute ylow_loc and yhigh_loc so that (ylow_loc,xleft) and (yhigh_loc,xright) are the corners       \
    1575:      of the bounding box of the intersection of the subdomain with the local ownership range (local       \
    1576:      subdomain).                                                                                          \
    1577:      Also compute xleft_loc and xright_loc as the lower and upper bounds on the first and last rows       \
    1578:      of the intersection.                                                                                 \
    1579:     */                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \
    1580:     /* ylow_loc is the grid row containing the first element of the local sumbdomain */                   \
    1581:     *ylow_loc = PetscMax(first_row,ylow);                                                                    \
    1582:     /* xleft_loc is the offset of first element of the local subdomain within its grid row (might actually be outside the local subdomain) */ \
    1583:     *xleft_loc = *ylow_loc==first_row ? PetscMax(first%M,xleft) : xleft;                                                                            \
    1584:     /* yhigh_loc is the grid row above the last local subdomain element */                                                                    \
    1585:     *yhigh_loc = PetscMin(last_row,yhigh);                                                                                                     \
    1586:     /* xright is the offset of the end of the  local subdomain within its grid row (might actually be outside the local subdomain) */         \
    1587:     *xright_loc = *yhigh_loc==last_row ? PetscMin(xright,last%M) : xright;                                                                          \
    1588:     /* Now compute the size of the local subdomain n. */ \
    1589:     *n = 0;                                               \
    1590:     if (*ylow_loc < *yhigh_loc) {                           \
    1591:       PetscInt width = xright-xleft;                     \
    1592:       *n += width*(*yhigh_loc-*ylow_loc-1);                 \
    1593:       *n += PetscMin(PetscMax(*xright_loc-xleft,0),width); \
    1594:       *n -= PetscMin(PetscMax(*xleft_loc-xleft,0), width); \
    1595:     } \
    1596:   }

    1600: /*@
    1601:    PCGASMCreateSubdomains2D - Creates the index sets for the overlapping Schwarz
    1602:    preconditioner for a two-dimensional problem on a regular grid.

    1604:    Collective

    1606:    Input Parameters:
    1607: +  M, N               - the global number of grid points in the x and y directions
    1608: .  Mdomains, Ndomains - the global number of subdomains in the x and y directions
    1609: .  dof                - degrees of freedom per node
    1610: -  overlap            - overlap in mesh lines

    1612:    Output Parameters:
    1613: +  Nsub - the number of local subdomains created
    1614: .  iis  - array of index sets defining inner (nonoverlapping) subdomains
    1615: -  ois  - array of index sets defining outer (overlapping, if overlap > 0) subdomains

    1618:    Level: advanced

    1620: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(), PCGASMSetOverlap()
    1621: @*/
    1622: PetscErrorCode  PCGASMCreateSubdomains2D(PC pc,PetscInt M,PetscInt N,PetscInt Mdomains,PetscInt Ndomains,PetscInt dof,PetscInt overlap,PetscInt *nsub,IS **iis,IS **ois)
    1623: {
    1625:   PetscMPIInt    size, rank;
    1626:   PetscInt       i, j;
    1627:   PetscInt       maxheight, maxwidth;
    1628:   PetscInt       xstart, xleft, xright, xleft_loc, xright_loc;
    1629:   PetscInt       ystart, ylow,  yhigh,  ylow_loc,  yhigh_loc;
    1630:   PetscInt       x[2][2], y[2][2], n[2];
    1631:   PetscInt       first, last;
    1632:   PetscInt       nidx, *idx;
    1633:   PetscInt       ii,jj,s,q,d;
    1634:   PetscInt       k,kk;
    1635:   PetscMPIInt    color;
    1636:   MPI_Comm       comm, subcomm;
    1637:   IS             **xis = 0, **is = ois, **is_local = iis;

    1640:   PetscObjectGetComm((PetscObject)pc, &comm);
    1641:   MPI_Comm_size(comm, &size);
    1642:   MPI_Comm_rank(comm, &rank);
    1643:   MatGetOwnershipRange(pc->pmat, &first, &last);
    1644:   if (first%dof || last%dof) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Matrix row partitioning unsuitable for domain decomposition: local row range (%D,%D) "
    1645:                                       "does not respect the number of degrees of freedom per grid point %D", first, last, dof);

    1647:   /* Determine the number of domains with nonzero intersections with the local ownership range. */
    1648:   s      = 0;
    1649:   ystart = 0;
    1650:   for (j=0; j<Ndomains; ++j) {
    1651:     maxheight = N/Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
    1652:     if (maxheight < 2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many %D subdomains in the vertical directon for mesh height %D", Ndomains, N);
    1653:     /* Vertical domain limits with an overlap. */
    1654:     ylow   = PetscMax(ystart - overlap,0);
    1655:     yhigh  = PetscMin(ystart + maxheight + overlap,N);
    1656:     xstart = 0;
    1657:     for (i=0; i<Mdomains; ++i) {
    1658:       maxwidth = M/Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
    1659:       if (maxwidth < 2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many %D subdomains in the horizontal direction for mesh width %D", Mdomains, M);
    1660:       /* Horizontal domain limits with an overlap. */
    1661:       xleft  = PetscMax(xstart - overlap,0);
    1662:       xright = PetscMin(xstart + maxwidth + overlap,M);
    1663:       /*
    1664:          Determine whether this subdomain intersects this processor's ownership range of pc->pmat.
    1665:       */
    1666:       PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,(&xleft_loc),(&ylow_loc),(&xright_loc),(&yhigh_loc),(&nidx));
    1667:       if (nidx) ++s;
    1668:       xstart += maxwidth;
    1669:     } /* for (i = 0; i < Mdomains; ++i) */
    1670:     ystart += maxheight;
    1671:   } /* for (j = 0; j < Ndomains; ++j) */

    1673:   /* Now we can allocate the necessary number of ISs. */
    1674:   *nsub  = s;
    1675:   PetscMalloc1(*nsub,is);
    1676:   PetscMalloc1(*nsub,is_local);
    1677:   s      = 0;
    1678:   ystart = 0;
    1679:   for (j=0; j<Ndomains; ++j) {
    1680:     maxheight = N/Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
    1681:     if (maxheight < 2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many %D subdomains in the vertical directon for mesh height %D", Ndomains, N);
    1682:     /* Vertical domain limits with an overlap. */
    1683:     y[0][0] = PetscMax(ystart - overlap,0);
    1684:     y[0][1] = PetscMin(ystart + maxheight + overlap,N);
    1685:     /* Vertical domain limits without an overlap. */
    1686:     y[1][0] = ystart;
    1687:     y[1][1] = PetscMin(ystart + maxheight,N);
    1688:     xstart  = 0;
    1689:     for (i=0; i<Mdomains; ++i) {
    1690:       maxwidth = M/Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
    1691:       if (maxwidth < 2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many %D subdomains in the horizontal direction for mesh width %D", Mdomains, M);
    1692:       /* Horizontal domain limits with an overlap. */
    1693:       x[0][0] = PetscMax(xstart - overlap,0);
    1694:       x[0][1] = PetscMin(xstart + maxwidth + overlap,M);
    1695:       /* Horizontal domain limits without an overlap. */
    1696:       x[1][0] = xstart;
    1697:       x[1][1] = PetscMin(xstart+maxwidth,M);
    1698:       /*
    1699:          Determine whether this domain intersects this processor's ownership range of pc->pmat.
    1700:          Do this twice: first for the domains with overlaps, and once without.
    1701:          During the first pass create the subcommunicators, and use them on the second pass as well.
    1702:       */
    1703:       for (q = 0; q < 2; ++q) {
    1704:         PetscBool split = PETSC_FALSE;
    1705:         /*
    1706:           domain limits, (xleft, xright) and (ylow, yheigh) are adjusted
    1707:           according to whether the domain with an overlap or without is considered.
    1708:         */
    1709:         xleft = x[q][0]; xright = x[q][1];
    1710:         ylow  = y[q][0]; yhigh  = y[q][1];
    1711:         PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,(&xleft_loc),(&ylow_loc),(&xright_loc),(&yhigh_loc),(&nidx));
    1712:         nidx *= dof;
    1713:         n[q]  = nidx;
    1714:         /*
    1715:          Based on the counted number of indices in the local domain *with an overlap*,
    1716:          construct a subcommunicator of all the processors supporting this domain.
    1717:          Observe that a domain with an overlap might have nontrivial local support,
    1718:          while the domain without an overlap might not.  Hence, the decision to participate
    1719:          in the subcommunicator must be based on the domain with an overlap.
    1720:          */
    1721:         if (q == 0) {
    1722:           if (nidx) color = 1;
    1723:           else color = MPI_UNDEFINED;
    1724:           MPI_Comm_split(comm, color, rank, &subcomm);
    1725:           split = PETSC_TRUE;
    1726:         }
    1727:         /*
    1728:          Proceed only if the number of local indices *with an overlap* is nonzero.
    1729:          */
    1730:         if (n[0]) {
    1731:           if (q == 0) xis = is;
    1732:           if (q == 1) {
    1733:             /*
    1734:              The IS for the no-overlap subdomain shares a communicator with the overlapping domain.
    1735:              Moreover, if the overlap is zero, the two ISs are identical.
    1736:              */
    1737:             if (overlap == 0) {
    1738:               (*is_local)[s] = (*is)[s];
    1739:               PetscObjectReference((PetscObject)(*is)[s]);
    1740:               continue;
    1741:             } else {
    1742:               xis     = is_local;
    1743:               subcomm = ((PetscObject)(*is)[s])->comm;
    1744:             }
    1745:           } /* if (q == 1) */
    1746:           idx  = NULL;
    1747:           PetscMalloc1(nidx,&idx);
    1748:           if (nidx) {
    1749:             k = 0;
    1750:             for (jj=ylow_loc; jj<yhigh_loc; ++jj) {
    1751:               PetscInt x0 = (jj==ylow_loc) ? xleft_loc : xleft;
    1752:               PetscInt x1 = (jj==yhigh_loc-1) ? xright_loc : xright;
    1753:               kk = dof*(M*jj + x0);
    1754:               for (ii=x0; ii<x1; ++ii) {
    1755:                 for (d = 0; d < dof; ++d) {
    1756:                   idx[k++] = kk++;
    1757:                 }
    1758:               }
    1759:             }
    1760:           }
    1761:           ISCreateGeneral(subcomm,nidx,idx,PETSC_OWN_POINTER,(*xis)+s);
    1762:           if (split) {
    1763:             MPI_Comm_free(&subcomm);
    1764:           }
    1765:         }/* if (n[0]) */
    1766:       }/* for (q = 0; q < 2; ++q) */
    1767:       if (n[0]) ++s;
    1768:       xstart += maxwidth;
    1769:     } /* for (i = 0; i < Mdomains; ++i) */
    1770:     ystart += maxheight;
    1771:   } /* for (j = 0; j < Ndomains; ++j) */
    1772:   return(0);
    1773: }

    1775: /*@C
    1776:     PCGASMGetSubdomains - Gets the subdomains supported on this processor
    1777:     for the additive Schwarz preconditioner.

    1779:     Not Collective

    1781:     Input Parameter:
    1782: .   pc - the preconditioner context

    1784:     Output Parameters:
    1785: +   n   - the number of subdomains for this processor (default value = 1)
    1786: .   iis - the index sets that define the inner subdomains (without overlap) supported on this processor (can be NULL)
    1787: -   ois - the index sets that define the outer subdomains (with overlap) supported on this processor (can be NULL)

    1790:     Notes:
    1791:     The user is responsible for destroying the ISs and freeing the returned arrays.
    1792:     The IS numbering is in the parallel, global numbering of the vector.

    1794:     Level: advanced

    1796: .seealso: PCGASMSetOverlap(), PCGASMGetSubKSP(), PCGASMCreateSubdomains2D(),
    1797:           PCGASMSetSubdomains(), PCGASMGetSubmatrices()
    1798: @*/
    1799: PetscErrorCode  PCGASMGetSubdomains(PC pc,PetscInt *n,IS *iis[],IS *ois[])
    1800: {
    1801:   PC_GASM        *osm;
    1803:   PetscBool      match;
    1804:   PetscInt       i;

    1808:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
    1809:   if (!match) SETERRQ2(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Incorrect object type: expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
    1810:   osm = (PC_GASM*)pc->data;
    1811:   if (n) *n = osm->n;
    1812:   if (iis) {
    1813:     PetscMalloc1(osm->n, iis);
    1814:   }
    1815:   if (ois) {
    1816:     PetscMalloc1(osm->n, ois);
    1817:   }
    1818:   if (iis || ois) {
    1819:     for (i = 0; i < osm->n; ++i) {
    1820:       if (iis) (*iis)[i] = osm->iis[i];
    1821:       if (ois) (*ois)[i] = osm->ois[i];
    1822:     }
    1823:   }
    1824:   return(0);
    1825: }

    1827: /*@C
    1828:     PCGASMGetSubmatrices - Gets the local submatrices (for this processor
    1829:     only) for the additive Schwarz preconditioner.

    1831:     Not Collective

    1833:     Input Parameter:
    1834: .   pc - the preconditioner context

    1836:     Output Parameters:
    1837: +   n   - the number of matrices for this processor (default value = 1)
    1838: -   mat - the matrices

    1840:     Notes:
    1841:     matrices returned by this routine have the same communicators as the index sets (IS)
    1842:            used to define subdomains in PCGASMSetSubdomains()
    1843:     Level: advanced

    1845: .seealso: PCGASMSetOverlap(), PCGASMGetSubKSP(),
    1846:           PCGASMCreateSubdomains2D(), PCGASMSetSubdomains(), PCGASMGetSubdomains()
    1847: @*/
    1848: PetscErrorCode  PCGASMGetSubmatrices(PC pc,PetscInt *n,Mat *mat[])
    1849: {
    1850:   PC_GASM        *osm;
    1852:   PetscBool      match;

    1858:   if (!pc->setupcalled) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must call after KSPSetUp() or PCSetUp().");
    1859:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
    1860:   if (!match) SETERRQ2(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
    1861:   osm = (PC_GASM*)pc->data;
    1862:   if (n) *n = osm->n;
    1863:   if (mat) *mat = osm->pmat;
    1864:   return(0);
    1865: }

    1867: /*@
    1868:     PCGASMSetUseDMSubdomains - Indicates whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.
    1869:     Logically Collective

    1871:     Input Parameter:
    1872: +   pc  - the preconditioner
    1873: -   flg - boolean indicating whether to use subdomains defined by the DM

    1875:     Options Database Key:
    1876: .   -pc_gasm_dm_subdomains -pc_gasm_overlap -pc_gasm_total_subdomains

    1878:     Level: intermediate

    1880:     Notes:
    1881:     PCGASMSetSubdomains(), PCGASMSetTotalSubdomains() or PCGASMSetOverlap() take precedence over PCGASMSetUseDMSubdomains(),
    1882:     so setting PCGASMSetSubdomains() with nontrivial subdomain ISs or any of PCGASMSetTotalSubdomains() and PCGASMSetOverlap()
    1883:     automatically turns the latter off.

    1885: .seealso: PCGASMGetUseDMSubdomains(), PCGASMSetSubdomains(), PCGASMSetOverlap()
    1886:           PCGASMCreateSubdomains2D()
    1887: @*/
    1888: PetscErrorCode  PCGASMSetUseDMSubdomains(PC pc,PetscBool flg)
    1889: {
    1890:   PC_GASM        *osm = (PC_GASM*)pc->data;
    1892:   PetscBool      match;

    1897:   if (pc->setupcalled) SETERRQ(((PetscObject)pc)->comm,PETSC_ERR_ARG_WRONGSTATE,"Not for a setup PC.");
    1898:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
    1899:   if (match) {
    1900:     if (!osm->user_subdomains && osm->N == PETSC_DETERMINE && osm->overlap < 0) {
    1901:       osm->dm_subdomains = flg;
    1902:     }
    1903:   }
    1904:   return(0);
    1905: }

    1907: /*@
    1908:     PCGASMGetUseDMSubdomains - Returns flag indicating whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.
    1909:     Not Collective

    1911:     Input Parameter:
    1912: .   pc  - the preconditioner

    1914:     Output Parameter:
    1915: .   flg - boolean indicating whether to use subdomains defined by the DM

    1917:     Level: intermediate

    1919: .seealso: PCGASMSetUseDMSubdomains(), PCGASMSetOverlap()
    1920:           PCGASMCreateSubdomains2D()
    1921: @*/
    1922: PetscErrorCode  PCGASMGetUseDMSubdomains(PC pc,PetscBool* flg)
    1923: {
    1924:   PC_GASM        *osm = (PC_GASM*)pc->data;
    1926:   PetscBool      match;

    1931:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
    1932:   if (match) {
    1933:     if (flg) *flg = osm->dm_subdomains;
    1934:   }
    1935:   return(0);
    1936: }