Date: 2025-03-29T05:58:31+00:00

Actual source code: wb.c

      1: #include <petscdmda.h>
      2: #include <petsc/private/pcmgimpl.h>
      3: #include <petsc/private/hashmapi.h>

      5: typedef struct {
      6:   PCExoticType type;
      7:   Mat          P;           /* the constructed interpolation matrix */
      8:   PetscBool    directSolve; /* use direct LU factorization to construct interpolation */
      9:   KSP          ksp;
     10: } PC_Exotic;

     12: const char *const PCExoticTypes[] = {"face", "wirebasket", "PCExoticType", "PC_Exotic", NULL};

     14: /*
     15:       DMDAGetWireBasketInterpolation - Gets the interpolation for a wirebasket based coarse space
     16: */
     17: static PetscErrorCode DMDAGetWireBasketInterpolation(PC pc, DM da, PC_Exotic *exotic, Mat Aglobal, MatReuse reuse, Mat *P)
     18: {
     19:   PetscInt               dim, i, j, k, m, n, p, dof, Nint, Nface, Nwire, Nsurf, *Iint, *Isurf, cint = 0, csurf = 0, istart, jstart, kstart, *II, N, c = 0;
     20:   PetscInt               mwidth, nwidth, pwidth, cnt, mp, np, pp, Ntotal, gl[26], *globals, Ng, *IIint, *IIsurf;
     21:   Mat                    Xint, Xsurf, Xint_tmp;
     22:   IS                     isint, issurf, is, row, col;
     23:   ISLocalToGlobalMapping ltg;
     24:   MPI_Comm               comm;
     25:   Mat                    A, Aii, Ais, Asi, *Aholder, iAii;
     26:   MatFactorInfo          info;
     27:   PetscScalar           *xsurf, *xint;
     28:   const PetscScalar     *rxint;
     29: #if defined(PETSC_USE_DEBUG_foo)
     30:   PetscScalar tmp;
     31: #endif
     32:   PetscHMapI ht = NULL;

     34:   PetscFunctionBegin;
     35:   PetscCall(DMDAGetInfo(da, &dim, NULL, NULL, NULL, &mp, &np, &pp, &dof, NULL, NULL, NULL, NULL, NULL));
     36:   PetscCheck(dof == 1, PetscObjectComm((PetscObject)da), PETSC_ERR_SUP, "Only for single field problems");
     37:   PetscCheck(dim == 3, PetscObjectComm((PetscObject)da), PETSC_ERR_SUP, "Only coded for 3d problems");
     38:   PetscCall(DMDAGetCorners(da, NULL, NULL, NULL, &m, &n, &p));
     39:   PetscCall(DMDAGetGhostCorners(da, &istart, &jstart, &kstart, &mwidth, &nwidth, &pwidth));
     40:   istart = istart ? -1 : 0;
     41:   jstart = jstart ? -1 : 0;
     42:   kstart = kstart ? -1 : 0;

     44:   /*
     45:     the columns of P are the interpolation of each coarse (wirebasket) grid point (one for each face, vertex and edge)
     46:     to all the local degrees of freedom (this includes the vertices, edges and faces).

     48:     Xint are the subset of the interpolation into the interior

     50:     Xface are the interpolation onto faces but not into the interior

     52:     Xsurf are the interpolation onto the vertices and edges (the wirebasket)
     53:                                       Xint
     54:     Symbolically one could write P = (Xface) after interchanging the rows to match the natural ordering on the domain
     55:                                       Xsurf
     56:   */
     57:   N     = (m - istart) * (n - jstart) * (p - kstart);
     58:   Nint  = (m - 2 - istart) * (n - 2 - jstart) * (p - 2 - kstart);
     59:   Nface = 2 * ((m - 2 - istart) * (n - 2 - jstart) + (m - 2 - istart) * (p - 2 - kstart) + (n - 2 - jstart) * (p - 2 - kstart));
     60:   Nwire = 4 * ((m - 2 - istart) + (n - 2 - jstart) + (p - 2 - kstart)) + 8;
     61:   Nsurf = Nface + Nwire;
     62:   PetscCall(MatCreateSeqDense(MPI_COMM_SELF, Nint, 26, NULL, &Xint));
     63:   PetscCall(MatCreateSeqDense(MPI_COMM_SELF, Nsurf, 26, NULL, &Xsurf));
     64:   PetscCall(MatDenseGetArray(Xsurf, &xsurf));

     66:   /*
     67:      Require that all 12 edges and 6 faces have at least one grid point. Otherwise some of the columns of
     68:      Xsurf will be all zero (thus making the coarse matrix singular).
     69:   */
     70:   PetscCheck(m - istart >= 3, PETSC_COMM_SELF, PETSC_ERR_SUP, "Number of grid points per process in X direction must be at least 3");
     71:   PetscCheck(n - jstart >= 3, PETSC_COMM_SELF, PETSC_ERR_SUP, "Number of grid points per process in Y direction must be at least 3");
     72:   PetscCheck(p - kstart >= 3, PETSC_COMM_SELF, PETSC_ERR_SUP, "Number of grid points per process in Z direction must be at least 3");

     74:   cnt = 0;

     76:   xsurf[cnt++] = 1;
     77:   for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + Nsurf] = 1;
     78:   xsurf[cnt++ + 2 * Nsurf] = 1;

     80:   for (j = 1; j < n - 1 - jstart; j++) {
     81:     xsurf[cnt++ + 3 * Nsurf] = 1;
     82:     for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + 4 * Nsurf] = 1;
     83:     xsurf[cnt++ + 5 * Nsurf] = 1;
     84:   }

     86:   xsurf[cnt++ + 6 * Nsurf] = 1;
     87:   for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + 7 * Nsurf] = 1;
     88:   xsurf[cnt++ + 8 * Nsurf] = 1;

     90:   for (k = 1; k < p - 1 - kstart; k++) {
     91:     xsurf[cnt++ + 9 * Nsurf] = 1;
     92:     for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + 10 * Nsurf] = 1;
     93:     xsurf[cnt++ + 11 * Nsurf] = 1;

     95:     for (j = 1; j < n - 1 - jstart; j++) {
     96:       xsurf[cnt++ + 12 * Nsurf] = 1;
     97:       /* these are the interior nodes */
     98:       xsurf[cnt++ + 13 * Nsurf] = 1;
     99:     }

    101:     xsurf[cnt++ + 14 * Nsurf] = 1;
    102:     for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + 15 * Nsurf] = 1;
    103:     xsurf[cnt++ + 16 * Nsurf] = 1;
    104:   }

    106:   xsurf[cnt++ + 17 * Nsurf] = 1;
    107:   for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + 18 * Nsurf] = 1;
    108:   xsurf[cnt++ + 19 * Nsurf] = 1;

    110:   for (j = 1; j < n - 1 - jstart; j++) {
    111:     xsurf[cnt++ + 20 * Nsurf] = 1;
    112:     for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + 21 * Nsurf] = 1;
    113:     xsurf[cnt++ + 22 * Nsurf] = 1;
    114:   }

    116:   xsurf[cnt++ + 23 * Nsurf] = 1;
    117:   for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + 24 * Nsurf] = 1;
    118:   xsurf[cnt++ + 25 * Nsurf] = 1;

    120:   /* interpolations only sum to 1 when using direct solver */
    121: #if defined(PETSC_USE_DEBUG_foo)
    122:   for (i = 0; i < Nsurf; i++) {
    123:     tmp = 0.0;
    124:     for (j = 0; j < 26; j++) tmp += xsurf[i + j * Nsurf];
    125:     PetscCheck(PetscAbsScalar(tmp - 1.0) <= 1.e-10, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Wrong Xsurf interpolation at i %" PetscInt_FMT " value %g", i, (double)PetscAbsScalar(tmp));
    126:   }
    127: #endif
    128:   PetscCall(MatDenseRestoreArray(Xsurf, &xsurf));
    129:   /* PetscCall(MatView(Xsurf,PETSC_VIEWER_STDOUT_WORLD));*/

    131:   /*
    132:        I are the indices for all the needed vertices (in global numbering)
    133:        Iint are the indices for the interior values, I surf for the surface values
    134:             (This is just for the part of the global matrix obtained with MatCreateSubMatrix(), it
    135:              is NOT the local DMDA ordering.)
    136:        IIint and IIsurf are the same as the Iint, Isurf except they are in the global numbering
    137:   */
    138: #define Endpoint(a, start, b) (a == 0 || a == (b - 1 - start))
    139:   PetscCall(PetscMalloc3(N, &II, Nint, &Iint, Nsurf, &Isurf));
    140:   PetscCall(PetscMalloc2(Nint, &IIint, Nsurf, &IIsurf));
    141:   for (k = 0; k < p - kstart; k++) {
    142:     for (j = 0; j < n - jstart; j++) {
    143:       for (i = 0; i < m - istart; i++) {
    144:         II[c++] = i + j * mwidth + k * mwidth * nwidth;

    146:         if (!Endpoint(i, istart, m) && !Endpoint(j, jstart, n) && !Endpoint(k, kstart, p)) {
    147:           IIint[cint]  = i + j * mwidth + k * mwidth * nwidth;
    148:           Iint[cint++] = i + j * (m - istart) + k * (m - istart) * (n - jstart);
    149:         } else {
    150:           IIsurf[csurf]  = i + j * mwidth + k * mwidth * nwidth;
    151:           Isurf[csurf++] = i + j * (m - istart) + k * (m - istart) * (n - jstart);
    152:         }
    153:       }
    154:     }
    155:   }
    156: #undef Endpoint
    157:   PetscCheck(c == N, PETSC_COMM_SELF, PETSC_ERR_PLIB, "c != N");
    158:   PetscCheck(cint == Nint, PETSC_COMM_SELF, PETSC_ERR_PLIB, "cint != Nint");
    159:   PetscCheck(csurf == Nsurf, PETSC_COMM_SELF, PETSC_ERR_PLIB, "csurf != Nsurf");
    160:   PetscCall(DMGetLocalToGlobalMapping(da, &ltg));
    161:   PetscCall(ISLocalToGlobalMappingApply(ltg, N, II, II));
    162:   PetscCall(ISLocalToGlobalMappingApply(ltg, Nint, IIint, IIint));
    163:   PetscCall(ISLocalToGlobalMappingApply(ltg, Nsurf, IIsurf, IIsurf));
    164:   PetscCall(PetscObjectGetComm((PetscObject)da, &comm));
    165:   PetscCall(ISCreateGeneral(comm, N, II, PETSC_COPY_VALUES, &is));
    166:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, Nint, Iint, PETSC_COPY_VALUES, &isint));
    167:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, Nsurf, Isurf, PETSC_COPY_VALUES, &issurf));
    168:   PetscCall(PetscFree3(II, Iint, Isurf));

    170:   PetscCall(MatCreateSubMatrices(Aglobal, 1, &is, &is, MAT_INITIAL_MATRIX, &Aholder));
    171:   A = *Aholder;
    172:   PetscCall(PetscFree(Aholder));

    174:   PetscCall(MatCreateSubMatrix(A, isint, isint, MAT_INITIAL_MATRIX, &Aii));
    175:   PetscCall(MatCreateSubMatrix(A, isint, issurf, MAT_INITIAL_MATRIX, &Ais));
    176:   PetscCall(MatCreateSubMatrix(A, issurf, isint, MAT_INITIAL_MATRIX, &Asi));

    178:   /*
    179:      Solve for the interpolation onto the interior Xint
    180:   */
    181:   PetscCall(MatMatMult(Ais, Xsurf, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &Xint_tmp));
    182:   PetscCall(MatScale(Xint_tmp, -1.0));
    183:   if (exotic->directSolve) {
    184:     PetscCall(MatGetFactor(Aii, MATSOLVERPETSC, MAT_FACTOR_LU, &iAii));
    185:     PetscCall(MatFactorInfoInitialize(&info));
    186:     PetscCall(MatGetOrdering(Aii, MATORDERINGND, &row, &col));
    187:     PetscCall(MatLUFactorSymbolic(iAii, Aii, row, col, &info));
    188:     PetscCall(ISDestroy(&row));
    189:     PetscCall(ISDestroy(&col));
    190:     PetscCall(MatLUFactorNumeric(iAii, Aii, &info));
    191:     PetscCall(MatMatSolve(iAii, Xint_tmp, Xint));
    192:     PetscCall(MatDestroy(&iAii));
    193:   } else {
    194:     Vec          b, x;
    195:     PetscScalar *xint_tmp;

    197:     PetscCall(MatDenseGetArray(Xint, &xint));
    198:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, Nint, NULL, &x));
    199:     PetscCall(MatDenseGetArray(Xint_tmp, &xint_tmp));
    200:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, Nint, NULL, &b));
    201:     PetscCall(KSPSetOperators(exotic->ksp, Aii, Aii));
    202:     for (i = 0; i < 26; i++) {
    203:       PetscCall(VecPlaceArray(x, xint + i * Nint));
    204:       PetscCall(VecPlaceArray(b, xint_tmp + i * Nint));
    205:       PetscCall(KSPSolve(exotic->ksp, b, x));
    206:       PetscCall(KSPCheckSolve(exotic->ksp, pc, x));
    207:       PetscCall(VecResetArray(x));
    208:       PetscCall(VecResetArray(b));
    209:     }
    210:     PetscCall(MatDenseRestoreArray(Xint, &xint));
    211:     PetscCall(MatDenseRestoreArray(Xint_tmp, &xint_tmp));
    212:     PetscCall(VecDestroy(&x));
    213:     PetscCall(VecDestroy(&b));
    214:   }
    215:   PetscCall(MatDestroy(&Xint_tmp));

    217: #if defined(PETSC_USE_DEBUG_foo)
    218:   PetscCall(MatDenseGetArrayRead(Xint, &rxint));
    219:   for (i = 0; i < Nint; i++) {
    220:     tmp = 0.0;
    221:     for (j = 0; j < 26; j++) tmp += rxint[i + j * Nint];

    223:     PetscCheck(PetscAbsScalar(tmp - 1.0) <= 1.e-10, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Wrong Xint interpolation at i %" PetscInt_FMT " value %g", i, (double)PetscAbsScalar(tmp));
    224:   }
    225:   PetscCall(MatDenseRestoreArrayRead(Xint, &rxint));
    226:   /* PetscCall(MatView(Xint,PETSC_VIEWER_STDOUT_WORLD)); */
    227: #endif

    229:   /*         total vertices             total faces                                  total edges */
    230:   Ntotal = (mp + 1) * (np + 1) * (pp + 1) + mp * np * (pp + 1) + mp * pp * (np + 1) + np * pp * (mp + 1) + mp * (np + 1) * (pp + 1) + np * (mp + 1) * (pp + 1) + pp * (mp + 1) * (np + 1);

    232:   /*
    233:       For each vertex, edge, face on process (in the same orderings as used above) determine its local number including ghost points
    234:   */
    235:   cnt = 0;

    237:   gl[cnt++] = 0;
    238:   {
    239:     gl[cnt++] = 1;
    240:   }
    241:   gl[cnt++] = m - istart - 1;
    242:   {
    243:     gl[cnt++] = mwidth;
    244:     {
    245:       gl[cnt++] = mwidth + 1;
    246:     }
    247:     gl[cnt++] = mwidth + m - istart - 1;
    248:   }
    249:   gl[cnt++] = mwidth * (n - jstart - 1);
    250:   {
    251:     gl[cnt++] = mwidth * (n - jstart - 1) + 1;
    252:   }
    253:   gl[cnt++] = mwidth * (n - jstart - 1) + m - istart - 1;
    254:   {
    255:     gl[cnt++] = mwidth * nwidth;
    256:     {
    257:       gl[cnt++] = mwidth * nwidth + 1;
    258:     }
    259:     gl[cnt++] = mwidth * nwidth + m - istart - 1;
    260:     {
    261:       gl[cnt++] = mwidth * nwidth + mwidth; /* these are the interior nodes */
    262:       gl[cnt++] = mwidth * nwidth + mwidth + m - istart - 1;
    263:     }
    264:     gl[cnt++] = mwidth * nwidth + mwidth * (n - jstart - 1);
    265:     {
    266:       gl[cnt++] = mwidth * nwidth + mwidth * (n - jstart - 1) + 1;
    267:     }
    268:     gl[cnt++] = mwidth * nwidth + mwidth * (n - jstart - 1) + m - istart - 1;
    269:   }
    270:   gl[cnt++] = mwidth * nwidth * (p - kstart - 1);
    271:   {
    272:     gl[cnt++] = mwidth * nwidth * (p - kstart - 1) + 1;
    273:   }
    274:   gl[cnt++] = mwidth * nwidth * (p - kstart - 1) + m - istart - 1;
    275:   {
    276:     gl[cnt++] = mwidth * nwidth * (p - kstart - 1) + mwidth;
    277:     {
    278:       gl[cnt++] = mwidth * nwidth * (p - kstart - 1) + mwidth + 1;
    279:     }
    280:     gl[cnt++] = mwidth * nwidth * (p - kstart - 1) + mwidth + m - istart - 1;
    281:   }
    282:   gl[cnt++] = mwidth * nwidth * (p - kstart - 1) + mwidth * (n - jstart - 1);
    283:   {
    284:     gl[cnt++] = mwidth * nwidth * (p - kstart - 1) + mwidth * (n - jstart - 1) + 1;
    285:   }
    286:   gl[cnt++] = mwidth * nwidth * (p - kstart - 1) + mwidth * (n - jstart - 1) + m - istart - 1;

    288:   /* PetscIntView(26,gl,PETSC_VIEWER_STDOUT_WORLD); */
    289:   /* convert that to global numbering and get them on all processes */
    290:   PetscCall(ISLocalToGlobalMappingApply(ltg, 26, gl, gl));
    291:   /* PetscIntView(26,gl,PETSC_VIEWER_STDOUT_WORLD); */
    292:   PetscCall(PetscMalloc1(26 * mp * np * pp, &globals));
    293:   PetscCallMPI(MPI_Allgather(gl, 26, MPIU_INT, globals, 26, MPIU_INT, PetscObjectComm((PetscObject)da)));

    295:   /* Number the coarse grid points from 0 to Ntotal */
    296:   PetscCall(PetscHMapICreateWithSize(Ntotal / 3, &ht));
    297:   for (i = 0, cnt = 0; i < 26 * mp * np * pp; i++) {
    298:     PetscHashIter it      = 0;
    299:     PetscBool     missing = PETSC_TRUE;

    301:     PetscCall(PetscHMapIPut(ht, globals[i] + 1, &it, &missing));
    302:     if (missing) {
    303:       ++cnt;
    304:       PetscCall(PetscHMapIIterSet(ht, it, cnt));
    305:     }
    306:   }
    307:   PetscCheck(cnt == Ntotal, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Hash table size %" PetscInt_FMT " not equal to total number coarse grid points %" PetscInt_FMT, cnt, Ntotal);
    308:   PetscCall(PetscFree(globals));
    309:   for (i = 0; i < 26; i++) {
    310:     PetscCall(PetscHMapIGetWithDefault(ht, gl[i] + 1, 0, gl + i));
    311:     --(gl[i]);
    312:   }
    313:   PetscCall(PetscHMapIDestroy(&ht));
    314:   /* PetscIntView(26,gl,PETSC_VIEWER_STDOUT_WORLD); */

    316:   /* construct global interpolation matrix */
    317:   PetscCall(MatGetLocalSize(Aglobal, &Ng, NULL));
    318:   if (reuse == MAT_INITIAL_MATRIX) {
    319:     PetscCall(MatCreateAIJ(PetscObjectComm((PetscObject)da), Ng, PETSC_DECIDE, PETSC_DECIDE, Ntotal, Nint + Nsurf, NULL, Nint + Nsurf, NULL, P));
    320:   } else {
    321:     PetscCall(MatZeroEntries(*P));
    322:   }
    323:   PetscCall(MatSetOption(*P, MAT_ROW_ORIENTED, PETSC_FALSE));
    324:   PetscCall(MatDenseGetArrayRead(Xint, &rxint));
    325:   PetscCall(MatSetValues(*P, Nint, IIint, 26, gl, rxint, INSERT_VALUES));
    326:   PetscCall(MatDenseRestoreArrayRead(Xint, &rxint));
    327:   PetscCall(MatDenseGetArrayRead(Xsurf, &rxint));
    328:   PetscCall(MatSetValues(*P, Nsurf, IIsurf, 26, gl, rxint, INSERT_VALUES));
    329:   PetscCall(MatDenseRestoreArrayRead(Xsurf, &rxint));
    330:   PetscCall(MatAssemblyBegin(*P, MAT_FINAL_ASSEMBLY));
    331:   PetscCall(MatAssemblyEnd(*P, MAT_FINAL_ASSEMBLY));
    332:   PetscCall(PetscFree2(IIint, IIsurf));

    334: #if defined(PETSC_USE_DEBUG_foo)
    335:   {
    336:     Vec          x, y;
    337:     PetscScalar *yy;
    338:     PetscCall(VecCreateMPI(PetscObjectComm((PetscObject)da), Ng, PETSC_DETERMINE, &y));
    339:     PetscCall(VecCreateMPI(PetscObjectComm((PetscObject)da), PETSC_DETERMINE, Ntotal, &x));
    340:     PetscCall(VecSet(x, 1.0));
    341:     PetscCall(MatMult(*P, x, y));
    342:     PetscCall(VecGetArray(y, &yy));
    343:     for (i = 0; i < Ng; i++) PetscCheck(PetscAbsScalar(yy[i] - 1.0) <= 1.e-10, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Wrong p interpolation at i %" PetscInt_FMT " value %g", i, (double)PetscAbsScalar(yy[i]));
    344:     PetscCall(VecRestoreArray(y, &yy));
    345:     PetscCall(VecDestroy(x));
    346:     PetscCall(VecDestroy(y));
    347:   }
    348: #endif

    350:   PetscCall(MatDestroy(&Aii));
    351:   PetscCall(MatDestroy(&Ais));
    352:   PetscCall(MatDestroy(&Asi));
    353:   PetscCall(MatDestroy(&A));
    354:   PetscCall(ISDestroy(&is));
    355:   PetscCall(ISDestroy(&isint));
    356:   PetscCall(ISDestroy(&issurf));
    357:   PetscCall(MatDestroy(&Xint));
    358:   PetscCall(MatDestroy(&Xsurf));
    359:   PetscFunctionReturn(PETSC_SUCCESS);
    360: }

    362: /*
    363:       DMDAGetFaceInterpolation - Gets the interpolation for a face based coarse space
    364: */
    365: static PetscErrorCode DMDAGetFaceInterpolation(PC pc, DM da, PC_Exotic *exotic, Mat Aglobal, MatReuse reuse, Mat *P)
    366: {
    367:   PetscInt               dim, i, j, k, m, n, p, dof, Nint, Nface, Nwire, Nsurf, *Iint, *Isurf, cint = 0, csurf = 0, istart, jstart, kstart, *II, N, c = 0;
    368:   PetscInt               mwidth, nwidth, pwidth, cnt, mp, np, pp, Ntotal, gl[6], *globals, Ng, *IIint, *IIsurf;
    369:   Mat                    Xint, Xsurf, Xint_tmp;
    370:   IS                     isint, issurf, is, row, col;
    371:   ISLocalToGlobalMapping ltg;
    372:   MPI_Comm               comm;
    373:   Mat                    A, Aii, Ais, Asi, *Aholder, iAii;
    374:   MatFactorInfo          info;
    375:   PetscScalar           *xsurf, *xint;
    376:   const PetscScalar     *rxint;
    377: #if defined(PETSC_USE_DEBUG_foo)
    378:   PetscScalar tmp;
    379: #endif
    380:   PetscHMapI ht;

    382:   PetscFunctionBegin;
    383:   PetscCall(DMDAGetInfo(da, &dim, NULL, NULL, NULL, &mp, &np, &pp, &dof, NULL, NULL, NULL, NULL, NULL));
    384:   PetscCheck(dof == 1, PetscObjectComm((PetscObject)da), PETSC_ERR_SUP, "Only for single field problems");
    385:   PetscCheck(dim == 3, PetscObjectComm((PetscObject)da), PETSC_ERR_SUP, "Only coded for 3d problems");
    386:   PetscCall(DMDAGetCorners(da, NULL, NULL, NULL, &m, &n, &p));
    387:   PetscCall(DMDAGetGhostCorners(da, &istart, &jstart, &kstart, &mwidth, &nwidth, &pwidth));
    388:   istart = istart ? -1 : 0;
    389:   jstart = jstart ? -1 : 0;
    390:   kstart = kstart ? -1 : 0;

    392:   /*
    393:     the columns of P are the interpolation of each coarse (face) grid point (one for each face)
    394:     to all the local degrees of freedom (this includes the vertices, edges and faces).

    396:     Xint are the subset of the interpolation into the interior

    398:     Xface are the interpolation onto faces but not into the interior

    400:     Xsurf are the interpolation onto the vertices and edges (the wirebasket)
    401:                                       Xint
    402:     Symbolically one could write P = (Xface) after interchanging the rows to match the natural ordering on the domain
    403:                                       Xsurf
    404:   */
    405:   N     = (m - istart) * (n - jstart) * (p - kstart);
    406:   Nint  = (m - 2 - istart) * (n - 2 - jstart) * (p - 2 - kstart);
    407:   Nface = 2 * ((m - 2 - istart) * (n - 2 - jstart) + (m - 2 - istart) * (p - 2 - kstart) + (n - 2 - jstart) * (p - 2 - kstart));
    408:   Nwire = 4 * ((m - 2 - istart) + (n - 2 - jstart) + (p - 2 - kstart)) + 8;
    409:   Nsurf = Nface + Nwire;
    410:   PetscCall(MatCreateSeqDense(MPI_COMM_SELF, Nint, 6, NULL, &Xint));
    411:   PetscCall(MatCreateSeqDense(MPI_COMM_SELF, Nsurf, 6, NULL, &Xsurf));
    412:   PetscCall(MatDenseGetArray(Xsurf, &xsurf));

    414:   /*
    415:      Require that all 12 edges and 6 faces have at least one grid point. Otherwise some of the columns of
    416:      Xsurf will be all zero (thus making the coarse matrix singular).
    417:   */
    418:   PetscCheck(m - istart >= 3, PETSC_COMM_SELF, PETSC_ERR_SUP, "Number of grid points per process in X direction must be at least 3");
    419:   PetscCheck(n - jstart >= 3, PETSC_COMM_SELF, PETSC_ERR_SUP, "Number of grid points per process in Y direction must be at least 3");
    420:   PetscCheck(p - kstart >= 3, PETSC_COMM_SELF, PETSC_ERR_SUP, "Number of grid points per process in Z direction must be at least 3");

    422:   cnt = 0;
    423:   for (j = 1; j < n - 1 - jstart; j++) {
    424:     for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + 0 * Nsurf] = 1;
    425:   }

    427:   for (k = 1; k < p - 1 - kstart; k++) {
    428:     for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + 1 * Nsurf] = 1;
    429:     for (j = 1; j < n - 1 - jstart; j++) {
    430:       xsurf[cnt++ + 2 * Nsurf] = 1;
    431:       /* these are the interior nodes */
    432:       xsurf[cnt++ + 3 * Nsurf] = 1;
    433:     }
    434:     for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + 4 * Nsurf] = 1;
    435:   }
    436:   for (j = 1; j < n - 1 - jstart; j++) {
    437:     for (i = 1; i < m - istart - 1; i++) xsurf[cnt++ + 5 * Nsurf] = 1;
    438:   }

    440: #if defined(PETSC_USE_DEBUG_foo)
    441:   for (i = 0; i < Nsurf; i++) {
    442:     tmp = 0.0;
    443:     for (j = 0; j < 6; j++) tmp += xsurf[i + j * Nsurf];

    445:     PetscCheck(PetscAbsScalar(tmp - 1.0) <= 1.e-10, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Wrong Xsurf interpolation at i %" PetscInt_FMT " value %g", i, (double)PetscAbsScalar(tmp));
    446:   }
    447: #endif
    448:   PetscCall(MatDenseRestoreArray(Xsurf, &xsurf));
    449:   /* PetscCall(MatView(Xsurf,PETSC_VIEWER_STDOUT_WORLD));*/

    451:   /*
    452:        I are the indices for all the needed vertices (in global numbering)
    453:        Iint are the indices for the interior values, I surf for the surface values
    454:             (This is just for the part of the global matrix obtained with MatCreateSubMatrix(), it
    455:              is NOT the local DMDA ordering.)
    456:        IIint and IIsurf are the same as the Iint, Isurf except they are in the global numbering
    457:   */
    458: #define Endpoint(a, start, b) (a == 0 || a == (b - 1 - start))
    459:   PetscCall(PetscMalloc3(N, &II, Nint, &Iint, Nsurf, &Isurf));
    460:   PetscCall(PetscMalloc2(Nint, &IIint, Nsurf, &IIsurf));
    461:   for (k = 0; k < p - kstart; k++) {
    462:     for (j = 0; j < n - jstart; j++) {
    463:       for (i = 0; i < m - istart; i++) {
    464:         II[c++] = i + j * mwidth + k * mwidth * nwidth;

    466:         if (!Endpoint(i, istart, m) && !Endpoint(j, jstart, n) && !Endpoint(k, kstart, p)) {
    467:           IIint[cint]  = i + j * mwidth + k * mwidth * nwidth;
    468:           Iint[cint++] = i + j * (m - istart) + k * (m - istart) * (n - jstart);
    469:         } else {
    470:           IIsurf[csurf]  = i + j * mwidth + k * mwidth * nwidth;
    471:           Isurf[csurf++] = i + j * (m - istart) + k * (m - istart) * (n - jstart);
    472:         }
    473:       }
    474:     }
    475:   }
    476: #undef Endpoint
    477:   PetscCheck(c == N, PETSC_COMM_SELF, PETSC_ERR_PLIB, "c != N");
    478:   PetscCheck(cint == Nint, PETSC_COMM_SELF, PETSC_ERR_PLIB, "cint != Nint");
    479:   PetscCheck(csurf == Nsurf, PETSC_COMM_SELF, PETSC_ERR_PLIB, "csurf != Nsurf");
    480:   PetscCall(DMGetLocalToGlobalMapping(da, &ltg));
    481:   PetscCall(ISLocalToGlobalMappingApply(ltg, N, II, II));
    482:   PetscCall(ISLocalToGlobalMappingApply(ltg, Nint, IIint, IIint));
    483:   PetscCall(ISLocalToGlobalMappingApply(ltg, Nsurf, IIsurf, IIsurf));
    484:   PetscCall(PetscObjectGetComm((PetscObject)da, &comm));
    485:   PetscCall(ISCreateGeneral(comm, N, II, PETSC_COPY_VALUES, &is));
    486:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, Nint, Iint, PETSC_COPY_VALUES, &isint));
    487:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, Nsurf, Isurf, PETSC_COPY_VALUES, &issurf));
    488:   PetscCall(PetscFree3(II, Iint, Isurf));

    490:   PetscCall(ISSort(is));
    491:   PetscCall(MatCreateSubMatrices(Aglobal, 1, &is, &is, MAT_INITIAL_MATRIX, &Aholder));
    492:   A = *Aholder;
    493:   PetscCall(PetscFree(Aholder));

    495:   PetscCall(MatCreateSubMatrix(A, isint, isint, MAT_INITIAL_MATRIX, &Aii));
    496:   PetscCall(MatCreateSubMatrix(A, isint, issurf, MAT_INITIAL_MATRIX, &Ais));
    497:   PetscCall(MatCreateSubMatrix(A, issurf, isint, MAT_INITIAL_MATRIX, &Asi));

    499:   /*
    500:      Solve for the interpolation onto the interior Xint
    501:   */
    502:   PetscCall(MatMatMult(Ais, Xsurf, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &Xint_tmp));
    503:   PetscCall(MatScale(Xint_tmp, -1.0));

    505:   if (exotic->directSolve) {
    506:     PetscCall(MatGetFactor(Aii, MATSOLVERPETSC, MAT_FACTOR_LU, &iAii));
    507:     PetscCall(MatFactorInfoInitialize(&info));
    508:     PetscCall(MatGetOrdering(Aii, MATORDERINGND, &row, &col));
    509:     PetscCall(MatLUFactorSymbolic(iAii, Aii, row, col, &info));
    510:     PetscCall(ISDestroy(&row));
    511:     PetscCall(ISDestroy(&col));
    512:     PetscCall(MatLUFactorNumeric(iAii, Aii, &info));
    513:     PetscCall(MatMatSolve(iAii, Xint_tmp, Xint));
    514:     PetscCall(MatDestroy(&iAii));
    515:   } else {
    516:     Vec          b, x;
    517:     PetscScalar *xint_tmp;

    519:     PetscCall(MatDenseGetArray(Xint, &xint));
    520:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, Nint, NULL, &x));
    521:     PetscCall(MatDenseGetArray(Xint_tmp, &xint_tmp));
    522:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, Nint, NULL, &b));
    523:     PetscCall(KSPSetOperators(exotic->ksp, Aii, Aii));
    524:     for (i = 0; i < 6; i++) {
    525:       PetscCall(VecPlaceArray(x, xint + i * Nint));
    526:       PetscCall(VecPlaceArray(b, xint_tmp + i * Nint));
    527:       PetscCall(KSPSolve(exotic->ksp, b, x));
    528:       PetscCall(KSPCheckSolve(exotic->ksp, pc, x));
    529:       PetscCall(VecResetArray(x));
    530:       PetscCall(VecResetArray(b));
    531:     }
    532:     PetscCall(MatDenseRestoreArray(Xint, &xint));
    533:     PetscCall(MatDenseRestoreArray(Xint_tmp, &xint_tmp));
    534:     PetscCall(VecDestroy(&x));
    535:     PetscCall(VecDestroy(&b));
    536:   }
    537:   PetscCall(MatDestroy(&Xint_tmp));

    539: #if defined(PETSC_USE_DEBUG_foo)
    540:   PetscCall(MatDenseGetArrayRead(Xint, &rxint));
    541:   for (i = 0; i < Nint; i++) {
    542:     tmp = 0.0;
    543:     for (j = 0; j < 6; j++) tmp += rxint[i + j * Nint];

    545:     PetscCheck(PetscAbsScalar(tmp - 1.0) <= 1.e-10, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Wrong Xint interpolation at i %" PetscInt_FMT " value %g", i, (double)PetscAbsScalar(tmp));
    546:   }
    547:   PetscCall(MatDenseRestoreArrayRead(Xint, &rxint));
    548:   /* PetscCall(MatView(Xint,PETSC_VIEWER_STDOUT_WORLD)); */
    549: #endif

    551:   /*         total faces    */
    552:   Ntotal = mp * np * (pp + 1) + mp * pp * (np + 1) + np * pp * (mp + 1);

    554:   /*
    555:       For each vertex, edge, face on process (in the same orderings as used above) determine its local number including ghost points
    556:   */
    557:   cnt = 0;
    558:   {
    559:     gl[cnt++] = mwidth + 1;
    560:   }
    561:   {
    562:     {
    563:       gl[cnt++] = mwidth * nwidth + 1;
    564:     }
    565:     {
    566:       gl[cnt++] = mwidth * nwidth + mwidth; /* these are the interior nodes */
    567:       gl[cnt++] = mwidth * nwidth + mwidth + m - istart - 1;
    568:     }
    569:     {
    570:       gl[cnt++] = mwidth * nwidth + mwidth * (n - jstart - 1) + 1;
    571:     }
    572:   }
    573:   {
    574:     gl[cnt++] = mwidth * nwidth * (p - kstart - 1) + mwidth + 1;
    575:   }

    577:   /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
    578:   /* convert that to global numbering and get them on all processes */
    579:   PetscCall(ISLocalToGlobalMappingApply(ltg, 6, gl, gl));
    580:   /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
    581:   PetscCall(PetscMalloc1(6 * mp * np * pp, &globals));
    582:   PetscCallMPI(MPI_Allgather(gl, 6, MPIU_INT, globals, 6, MPIU_INT, PetscObjectComm((PetscObject)da)));

    584:   /* Number the coarse grid points from 0 to Ntotal */
    585:   PetscCall(PetscHMapICreateWithSize(Ntotal / 3, &ht));
    586:   for (i = 0, cnt = 0; i < 6 * mp * np * pp; i++) {
    587:     PetscHashIter it      = 0;
    588:     PetscBool     missing = PETSC_TRUE;

    590:     PetscCall(PetscHMapIPut(ht, globals[i] + 1, &it, &missing));
    591:     if (missing) {
    592:       ++cnt;
    593:       PetscCall(PetscHMapIIterSet(ht, it, cnt));
    594:     }
    595:   }
    596:   PetscCheck(cnt == Ntotal, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Hash table size %" PetscInt_FMT " not equal to total number coarse grid points %" PetscInt_FMT, cnt, Ntotal);
    597:   PetscCall(PetscFree(globals));
    598:   for (i = 0; i < 6; i++) {
    599:     PetscCall(PetscHMapIGetWithDefault(ht, gl[i] + 1, 0, gl + i));
    600:     --(gl[i]);
    601:   }
    602:   PetscCall(PetscHMapIDestroy(&ht));
    603:   /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */

    605:   /* construct global interpolation matrix */
    606:   PetscCall(MatGetLocalSize(Aglobal, &Ng, NULL));
    607:   if (reuse == MAT_INITIAL_MATRIX) {
    608:     PetscCall(MatCreateAIJ(PetscObjectComm((PetscObject)da), Ng, PETSC_DECIDE, PETSC_DECIDE, Ntotal, Nint + Nsurf, NULL, Nint, NULL, P));
    609:   } else {
    610:     PetscCall(MatZeroEntries(*P));
    611:   }
    612:   PetscCall(MatSetOption(*P, MAT_ROW_ORIENTED, PETSC_FALSE));
    613:   PetscCall(MatDenseGetArrayRead(Xint, &rxint));
    614:   PetscCall(MatSetValues(*P, Nint, IIint, 6, gl, rxint, INSERT_VALUES));
    615:   PetscCall(MatDenseRestoreArrayRead(Xint, &rxint));
    616:   PetscCall(MatDenseGetArrayRead(Xsurf, &rxint));
    617:   PetscCall(MatSetValues(*P, Nsurf, IIsurf, 6, gl, rxint, INSERT_VALUES));
    618:   PetscCall(MatDenseRestoreArrayRead(Xsurf, &rxint));
    619:   PetscCall(MatAssemblyBegin(*P, MAT_FINAL_ASSEMBLY));
    620:   PetscCall(MatAssemblyEnd(*P, MAT_FINAL_ASSEMBLY));
    621:   PetscCall(PetscFree2(IIint, IIsurf));

    623: #if defined(PETSC_USE_DEBUG_foo)
    624:   {
    625:     Vec          x, y;
    626:     PetscScalar *yy;
    627:     PetscCall(VecCreateMPI(PetscObjectComm((PetscObject)da), Ng, PETSC_DETERMINE, &y));
    628:     PetscCall(VecCreateMPI(PetscObjectComm((PetscObject)da), PETSC_DETERMINE, Ntotal, &x));
    629:     PetscCall(VecSet(x, 1.0));
    630:     PetscCall(MatMult(*P, x, y));
    631:     PetscCall(VecGetArray(y, &yy));
    632:     for (i = 0; i < Ng; i++) PetscCheck(PetscAbsScalar(yy[i] - 1.0) <= 1.e-10, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Wrong p interpolation at i %" PetscInt_FMT " value %g", i, (double)PetscAbsScalar(yy[i]));
    633:     PetscCall(VecRestoreArray(y, &yy));
    634:     PetscCall(VecDestroy(x));
    635:     PetscCall(VecDestroy(y));
    636:   }
    637: #endif

    639:   PetscCall(MatDestroy(&Aii));
    640:   PetscCall(MatDestroy(&Ais));
    641:   PetscCall(MatDestroy(&Asi));
    642:   PetscCall(MatDestroy(&A));
    643:   PetscCall(ISDestroy(&is));
    644:   PetscCall(ISDestroy(&isint));
    645:   PetscCall(ISDestroy(&issurf));
    646:   PetscCall(MatDestroy(&Xint));
    647:   PetscCall(MatDestroy(&Xsurf));
    648:   PetscFunctionReturn(PETSC_SUCCESS);
    649: }

    651: /*@
    652:   PCExoticSetType - Sets the type of coarse grid interpolation to use

    654:   Logically Collective

    656:   Input Parameters:
    657: + pc   - the preconditioner context
    658: - type - either `PC_EXOTIC_FACE` or `PC_EXOTIC_WIREBASKET` (defaults to face)

    660:   Options Database Keys:
    661: . -pc_exotic_type <face,wirebasket> - use a coarse grid point for each face, or edge and vertex

    663:   Notes:
    664:   The face based interpolation has 1 degree of freedom per face and ignores the
    665:   edge and vertex values completely in the coarse problem. For any seven point
    666:   stencil the interpolation of a constant on all faces into the interior is that constant.

    668:   The wirebasket interpolation has 1 degree of freedom per vertex, per edge and
    669:   per face. A constant on the subdomain boundary is interpolated as that constant
    670:   in the interior of the domain.

    672:   The coarse grid matrix is obtained via the Galerkin computation $A_c = R A R^T$, hence
    673:   if $A$ is nonsingular $A_c$ is also nonsingular.

    675:   Both interpolations are suitable for only scalar problems.

    677:   Level: intermediate

    679: .seealso: [](ch_ksp), `PCEXOTIC`, `PCExoticType()`
    680: @*/
    681: PetscErrorCode PCExoticSetType(PC pc, PCExoticType type)
    682: {
    683:   PetscFunctionBegin;
    686:   PetscTryMethod(pc, "PCExoticSetType_C", (PC, PCExoticType), (pc, type));
    687:   PetscFunctionReturn(PETSC_SUCCESS);
    688: }

    690: static PetscErrorCode PCExoticSetType_Exotic(PC pc, PCExoticType type)
    691: {
    692:   PC_MG     *mg  = (PC_MG *)pc->data;
    693:   PC_Exotic *ctx = (PC_Exotic *)mg->innerctx;

    695:   PetscFunctionBegin;
    696:   ctx->type = type;
    697:   PetscFunctionReturn(PETSC_SUCCESS);
    698: }

    700: static PetscErrorCode PCSetUp_Exotic(PC pc)
    701: {
    702:   Mat        A;
    703:   PC_MG     *mg    = (PC_MG *)pc->data;
    704:   PC_Exotic *ex    = (PC_Exotic *)mg->innerctx;
    705:   MatReuse   reuse = (ex->P) ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX;

    707:   PetscFunctionBegin;
    708:   PetscCheck(pc->dm, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Need to call PCSetDM() before using this PC");
    709:   PetscCall(PCGetOperators(pc, NULL, &A));
    710:   PetscCheck(ex->type == PC_EXOTIC_FACE || ex->type == PC_EXOTIC_WIREBASKET, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unknown exotic coarse space %d", ex->type);
    711:   if (ex->type == PC_EXOTIC_FACE) {
    712:     PetscCall(DMDAGetFaceInterpolation(pc, pc->dm, ex, A, reuse, &ex->P));
    713:   } else /* if (ex->type == PC_EXOTIC_WIREBASKET) */ {
    714:     PetscCall(DMDAGetWireBasketInterpolation(pc, pc->dm, ex, A, reuse, &ex->P));
    715:   }
    716:   PetscCall(PCMGSetInterpolation(pc, 1, ex->P));
    717:   /* if PC has attached DM we must remove it or the PCMG will use it to compute incorrect sized vectors and interpolations */
    718:   PetscCall(PCSetDM(pc, NULL));
    719:   PetscCall(PCSetUp_MG(pc));
    720:   PetscFunctionReturn(PETSC_SUCCESS);
    721: }

    723: static PetscErrorCode PCDestroy_Exotic(PC pc)
    724: {
    725:   PC_MG     *mg  = (PC_MG *)pc->data;
    726:   PC_Exotic *ctx = (PC_Exotic *)mg->innerctx;

    728:   PetscFunctionBegin;
    729:   PetscCall(MatDestroy(&ctx->P));
    730:   PetscCall(KSPDestroy(&ctx->ksp));
    731:   PetscCall(PetscFree(ctx));
    732:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCExoticSetType_C", NULL));
    733:   PetscCall(PCDestroy_MG(pc));
    734:   PetscFunctionReturn(PETSC_SUCCESS);
    735: }

    737: static PetscErrorCode PCView_Exotic(PC pc, PetscViewer viewer)
    738: {
    739:   PC_MG     *mg = (PC_MG *)pc->data;
    740:   PetscBool  iascii;
    741:   PC_Exotic *ctx = (PC_Exotic *)mg->innerctx;

    743:   PetscFunctionBegin;
    744:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
    745:   if (iascii) {
    746:     PetscCall(PetscViewerASCIIPrintf(viewer, "    Exotic type = %s\n", PCExoticTypes[ctx->type]));
    747:     if (ctx->directSolve) {
    748:       PetscCall(PetscViewerASCIIPrintf(viewer, "      Using direct solver to construct interpolation\n"));
    749:     } else {
    750:       PetscViewer sviewer;
    751:       PetscMPIInt rank;

    753:       PetscCall(PetscViewerASCIIPrintf(viewer, "      Using iterative solver to construct interpolation\n"));
    754:       PetscCall(PetscViewerASCIIPushTab(viewer));
    755:       PetscCall(PetscViewerASCIIPushTab(viewer)); /* should not need to push this twice? */
    756:       PetscCall(PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    757:       PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
    758:       if (rank == 0) PetscCall(KSPView(ctx->ksp, sviewer));
    759:       PetscCall(PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    760:       PetscCall(PetscViewerASCIIPopTab(viewer));
    761:       PetscCall(PetscViewerASCIIPopTab(viewer));
    762:     }
    763:   }
    764:   PetscCall(PCView_MG(pc, viewer));
    765:   PetscFunctionReturn(PETSC_SUCCESS);
    766: }

    768: static PetscErrorCode PCSetFromOptions_Exotic(PC pc, PetscOptionItems PetscOptionsObject)
    769: {
    770:   PetscBool    flg;
    771:   PC_MG       *mg = (PC_MG *)pc->data;
    772:   PCExoticType mgctype;
    773:   PC_Exotic   *ctx = (PC_Exotic *)mg->innerctx;

    775:   PetscFunctionBegin;
    776:   PetscOptionsHeadBegin(PetscOptionsObject, "Exotic coarse space options");
    777:   PetscCall(PetscOptionsEnum("-pc_exotic_type", "face or wirebasket", "PCExoticSetType", PCExoticTypes, (PetscEnum)ctx->type, (PetscEnum *)&mgctype, &flg));
    778:   if (flg) PetscCall(PCExoticSetType(pc, mgctype));
    779:   PetscCall(PetscOptionsBool("-pc_exotic_direct_solver", "use direct solver to construct interpolation", "None", ctx->directSolve, &ctx->directSolve, NULL));
    780:   if (!ctx->directSolve) {
    781:     if (!ctx->ksp) {
    782:       const char *prefix;
    783:       PetscCall(KSPCreate(PETSC_COMM_SELF, &ctx->ksp));
    784:       PetscCall(KSPSetNestLevel(ctx->ksp, pc->kspnestlevel));
    785:       PetscCall(KSPSetErrorIfNotConverged(ctx->ksp, pc->erroriffailure));
    786:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ctx->ksp, (PetscObject)pc, 1));
    787:       PetscCall(PCGetOptionsPrefix(pc, &prefix));
    788:       PetscCall(KSPSetOptionsPrefix(ctx->ksp, prefix));
    789:       PetscCall(KSPAppendOptionsPrefix(ctx->ksp, "exotic_"));
    790:     }
    791:     PetscCall(KSPSetFromOptions(ctx->ksp));
    792:   }
    793:   PetscOptionsHeadEnd();
    794:   PetscFunctionReturn(PETSC_SUCCESS);
    795: }

    797: /*MC
    798:    PCEXOTIC - Two level overlapping Schwarz preconditioner with exotic (non-standard) coarse grid spaces

    800:    This uses the `PCMG` infrastructure restricted to two levels and the face and wirebasket based coarse
    801:    grid spaces.

    803:    Options Database Keys:
    804: +  -pc_exotic_type <face,wirebasket> - use a coarse grid point for each face, or edge and vertex
    805: -  -pc_exotic_direct_solver          - use a direct solver to construct interpolation instead of an iterative solver

    807:    Level: advanced

    809:    Notes:
    810:    Must be used with `DMDA` in three dimensions

    812:    By default this uses `KSPGMRES` on the fine grid smoother so this should be used with `KSPFGMRES` or the smoother changed to not use `KSPGMRES`

    814:    These coarse grid spaces originate in the work of Bramble, Pasciak  and Schatz {cite}`bramble1989construction`.
    815:    They were generalized slightly in "Domain Decomposition Method for Linear Elasticity", Ph. D. thesis, Barry Smith, {cite}`smith1990domain`.
    816:    They were then explored in great detail in Dryja, Smith, Widlund {cite}`dryja1994schwarz`. These were developed in the context of iterative substructuring preconditioners.

    818:    They were then ingeniously applied as coarse grid spaces for overlapping Schwarz methods by Dohrmann and Widlund.
    819:    They refer to them as GDSW (generalized Dryja, Smith, Widlund preconditioners). See, for example, {cite}`dohrmann2008extending`, {cite}`dohrmann2008family`,
    820:    {cite}`dohrmann2008domain`, {cite}`dohrmann2009overlapping`.

    822:    In this code the wirebasket includes a constant for each face, as well as the true "wirebasket". Other wirebasket algorithms exist that
    823:    only have constants for edges and vertices.

    825:    The usual `PCMG` options are supported, such as `-mg_levels_pc_type` <type> `-mg_coarse_pc_type` <type> `-mg_fine_pc_type` <type> and `-pc_mg_type` <type>

    827: .seealso: [](ch_ksp), `PCMG`, `PCSetDM()`, `PCExoticType`, `PCExoticSetType()`
    828: M*/

    830: PETSC_EXTERN PetscErrorCode PCCreate_Exotic(PC pc)
    831: {
    832:   PC_Exotic *ex;
    833:   PC_MG     *mg;

    835:   PetscFunctionBegin;
    836:   /* if type was previously mg; must manually destroy it because call to PCSetType(pc,PCMG) will not destroy it */
    837:   PetscTryTypeMethod(pc, destroy);
    838:   pc->data = NULL;

    840:   PetscCall(PetscFree(((PetscObject)pc)->type_name));
    841:   ((PetscObject)pc)->type_name = NULL;

    843:   PetscCall(PCSetType(pc, PCMG));
    844:   PetscCall(PCMGSetLevels(pc, 2, NULL));
    845:   PetscCall(PCMGSetGalerkin(pc, PC_MG_GALERKIN_PMAT));
    846:   PetscCall(PetscNew(&ex));
    847:   ex->type     = PC_EXOTIC_FACE;
    848:   mg           = (PC_MG *)pc->data;
    849:   mg->innerctx = ex;

    851:   pc->ops->setfromoptions = PCSetFromOptions_Exotic;
    852:   pc->ops->view           = PCView_Exotic;
    853:   pc->ops->destroy        = PCDestroy_Exotic;
    854:   pc->ops->setup          = PCSetUp_Exotic;

    856:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCExoticSetType_C", PCExoticSetType_Exotic));
    857:   PetscFunctionReturn(PETSC_SUCCESS);
    858: }