Date: 2026-05-01T06:11:48+00:00

Actual source code: ex6.c

      1: static char help[] = "Spectral element access patterns with Plex\n\n";

      3: #include <petscdmplex.h>

      5: typedef struct {
      6:   PetscInt  Nf; /* Number of fields */
      7:   PetscInt *Nc; /* Number of components per field */
      8:   PetscInt *k;  /* Spectral order per field */
      9: } AppCtx;

     11: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
     12: {
     13:   PetscInt  len;
     14:   PetscBool flg;

     16:   PetscFunctionBeginUser;
     17:   options->Nf = 0;
     18:   options->Nc = NULL;
     19:   options->k  = NULL;

     21:   PetscOptionsBegin(comm, "", "SEM Problem Options", "DMPLEX");
     22:   PetscCall(PetscOptionsBoundedInt("-num_fields", "The number of fields", "ex6.c", options->Nf, &options->Nf, NULL, 0));
     23:   if (options->Nf) {
     24:     len = options->Nf;
     25:     PetscCall(PetscMalloc1(len, &options->Nc));
     26:     PetscCall(PetscOptionsIntArray("-num_components", "The number of components per field", "ex6.c", options->Nc, &len, &flg));
     27:     PetscCheck(!flg || !(len != options->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Length of components array is %" PetscInt_FMT " should be %" PetscInt_FMT, len, options->Nf);
     28:     len = options->Nf;
     29:     PetscCall(PetscMalloc1(len, &options->k));
     30:     PetscCall(PetscOptionsIntArray("-order", "The spectral order per field", "ex6.c", options->k, &len, &flg));
     31:     PetscCheck(!flg || !(len != options->Nf), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Length of order array is %" PetscInt_FMT " should be %" PetscInt_FMT, len, options->Nf);
     32:   }
     33:   PetscOptionsEnd();
     34:   PetscFunctionReturn(PETSC_SUCCESS);
     35: }

     37: static PetscErrorCode LoadData2D(DM dm, PetscInt Ni, PetscInt Nj, PetscInt clSize, Vec u, AppCtx *user)
     38: {
     39:   PetscInt     i, j, f, c;
     40:   PetscScalar *closure;

     42:   PetscFunctionBeginUser;
     43:   PetscCall(PetscMalloc1(clSize, &closure));
     44:   for (j = 0; j < Nj; ++j) {
     45:     for (i = 0; i < Ni; ++i) {
     46:       PetscInt ki, kj, o = 0;
     47:       PetscCall(PetscArrayzero(closure, clSize));

     49:       for (f = 0; f < user->Nf; ++f) {
     50:         PetscInt ioff = i * user->k[f], joff = j * user->k[f];

     52:         for (kj = 0; kj <= user->k[f]; ++kj) {
     53:           for (ki = 0; ki <= user->k[f]; ++ki) {
     54:             for (c = 0; c < user->Nc[f]; ++c) closure[o++] = ((kj + joff) * (Ni * user->k[f] + 1) + ki + ioff) * user->Nc[f] + c;
     55:           }
     56:         }
     57:       }
     58:       PetscCall(DMPlexVecSetClosure(dm, NULL, u, j * Ni + i, closure, INSERT_VALUES));
     59:     }
     60:   }
     61:   PetscCall(PetscFree(closure));
     62:   PetscFunctionReturn(PETSC_SUCCESS);
     63: }

     65: static PetscErrorCode LoadData3D(DM dm, PetscInt Ni, PetscInt Nj, PetscInt Nk, PetscInt clSize, Vec u, AppCtx *user)
     66: {
     67:   PetscInt     i, j, k, f, c;
     68:   PetscScalar *closure;

     70:   PetscFunctionBeginUser;
     71:   PetscCall(PetscMalloc1(clSize, &closure));
     72:   for (k = 0; k < Nk; ++k) {
     73:     for (j = 0; j < Nj; ++j) {
     74:       for (i = 0; i < Ni; ++i) {
     75:         PetscInt ki, kj, kk, o = 0;
     76:         PetscCall(PetscArrayzero(closure, clSize));

     78:         for (f = 0; f < user->Nf; ++f) {
     79:           PetscInt ioff = i * user->k[f], joff = j * user->k[f], koff = k * user->k[f];

     81:           for (kk = 0; kk <= user->k[f]; ++kk) {
     82:             for (kj = 0; kj <= user->k[f]; ++kj) {
     83:               for (ki = 0; ki <= user->k[f]; ++ki) {
     84:                 for (c = 0; c < user->Nc[f]; ++c) closure[o++] = (((kk + koff) * (Nj * user->k[f] + 1) + kj + joff) * (Ni * user->k[f] + 1) + ki + ioff) * user->Nc[f] + c;
     85:               }
     86:             }
     87:           }
     88:         }
     89:         PetscCall(DMPlexVecSetClosure(dm, NULL, u, (k * Nj + j) * Ni + i, closure, INSERT_VALUES));
     90:       }
     91:     }
     92:   }
     93:   PetscCall(PetscFree(closure));
     94:   PetscFunctionReturn(PETSC_SUCCESS);
     95: }

     97: static PetscErrorCode CheckPoint(DM dm, Vec u, PetscInt point, AppCtx *user)
     98: {
     99:   PetscSection       s;
    100:   PetscScalar       *a;
    101:   const PetscScalar *array;
    102:   PetscInt           dof, d;

    104:   PetscFunctionBeginUser;
    105:   PetscCall(DMGetLocalSection(dm, &s));
    106:   PetscCall(VecGetArrayRead(u, &array));
    107:   PetscCall(DMPlexPointLocalRead(dm, point, array, &a));
    108:   PetscCall(PetscSectionGetDof(s, point, &dof));
    109:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "Point %" PetscInt_FMT ": ", point));
    110:   for (d = 0; d < dof; ++d) {
    111:     if (d > 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, ", "));
    112:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "%2.0f", (double)PetscRealPart(a[d])));
    113:   }
    114:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
    115:   PetscCall(VecRestoreArrayRead(u, &array));
    116:   PetscFunctionReturn(PETSC_SUCCESS);
    117: }

    119: static PetscErrorCode ReadData2D(DM dm, Vec u, AppCtx *user)
    120: {
    121:   PetscInt cStart, cEnd, cell;

    123:   PetscFunctionBeginUser;
    124:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    125:   for (cell = cStart; cell < cEnd; ++cell) {
    126:     PetscScalar *closure = NULL;
    127:     PetscInt     closureSize, ki, kj, f, c, foff = 0;

    129:     PetscCall(DMPlexVecGetClosure(dm, NULL, u, cell, &closureSize, &closure));
    130:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Cell %" PetscInt_FMT "\n", cell));
    131:     for (f = 0; f < user->Nf; ++f) {
    132:       PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Field %" PetscInt_FMT "\n", f));
    133:       for (kj = user->k[f]; kj >= 0; --kj) {
    134:         for (ki = 0; ki <= user->k[f]; ++ki) {
    135:           if (ki > 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  "));
    136:           for (c = 0; c < user->Nc[f]; ++c) {
    137:             if (c > 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, ","));
    138:             PetscCall(PetscPrintf(PETSC_COMM_SELF, "%2.0f", (double)PetscRealPart(closure[(kj * (user->k[f] + 1) + ki) * user->Nc[f] + c + foff])));
    139:           }
    140:         }
    141:         PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
    142:       }
    143:       PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n\n"));
    144:       foff += PetscSqr(user->k[f] + 1);
    145:     }
    146:     PetscCall(DMPlexVecRestoreClosure(dm, NULL, u, cell, &closureSize, &closure));
    147:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n\n"));
    148:   }
    149:   PetscFunctionReturn(PETSC_SUCCESS);
    150: }

    152: static PetscErrorCode ReadData3D(DM dm, Vec u, AppCtx *user)
    153: {
    154:   PetscInt cStart, cEnd, cell;

    156:   PetscFunctionBeginUser;
    157:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    158:   for (cell = cStart; cell < cEnd; ++cell) {
    159:     PetscScalar *closure = NULL;
    160:     PetscInt     closureSize, ki, kj, kk, f, c, foff = 0;

    162:     PetscCall(DMPlexVecGetClosure(dm, NULL, u, cell, &closureSize, &closure));
    163:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Cell %" PetscInt_FMT "\n", cell));
    164:     for (f = 0; f < user->Nf; ++f) {
    165:       PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Field %" PetscInt_FMT "\n", f));
    166:       for (kk = user->k[f]; kk >= 0; --kk) {
    167:         for (kj = user->k[f]; kj >= 0; --kj) {
    168:           for (ki = 0; ki <= user->k[f]; ++ki) {
    169:             if (ki > 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  "));
    170:             for (c = 0; c < user->Nc[f]; ++c) {
    171:               if (c > 0) PetscCall(PetscPrintf(PETSC_COMM_SELF, ","));
    172:               PetscCall(PetscPrintf(PETSC_COMM_SELF, "%2.0f", (double)PetscRealPart(closure[((kk * (user->k[f] + 1) + kj) * (user->k[f] + 1) + ki) * user->Nc[f] + c + foff])));
    173:             }
    174:           }
    175:           PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
    176:         }
    177:         PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
    178:       }
    179:       PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n\n"));
    180:       foff += PetscSqr(user->k[f] + 1);
    181:     }
    182:     PetscCall(DMPlexVecRestoreClosure(dm, NULL, u, cell, &closureSize, &closure));
    183:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n\n"));
    184:   }
    185:   PetscFunctionReturn(PETSC_SUCCESS);
    186: }

    188: static PetscErrorCode SetSymmetries(DM dm, PetscSection s, AppCtx *user)
    189: {
    190:   PetscInt dim, f, o, i, j, k, c, d;
    191:   DMLabel  depthLabel;

    193:   PetscFunctionBegin;
    194:   PetscCall(DMGetDimension(dm, &dim));
    195:   PetscCall(DMGetLabel(dm, "depth", &depthLabel));
    196:   for (f = 0; f < user->Nf; f++) {
    197:     PetscSectionSym sym;

    199:     if (user->k[f] < 3) continue; /* No symmetries needed for order < 3, because no cell, facet, edge or vertex has more than one node */
    200:     PetscCall(PetscSectionSymCreateLabel(PetscObjectComm((PetscObject)s), depthLabel, &sym));

    202:     for (d = 0; d <= dim; d++) {
    203:       if (d == 1) {
    204:         PetscInt   numDof  = user->k[f] - 1;
    205:         PetscInt   numComp = user->Nc[f];
    206:         PetscInt   minOrnt = -1;
    207:         PetscInt   maxOrnt = 1;
    208:         PetscInt **perms;

    210:         PetscCall(PetscCalloc1(maxOrnt - minOrnt, &perms));
    211:         for (o = minOrnt; o < maxOrnt; o++) {
    212:           PetscInt *perm;

    214:           if (!o) { /* identity */
    215:             perms[o - minOrnt] = NULL;
    216:           } else {
    217:             PetscCall(PetscMalloc1(numDof * numComp, &perm));
    218:             for (i = numDof - 1, k = 0; i >= 0; i--) {
    219:               for (j = 0; j < numComp; j++, k++) perm[k] = i * numComp + j;
    220:             }
    221:             perms[o - minOrnt] = perm;
    222:           }
    223:         }
    224:         PetscCall(PetscSectionSymLabelSetStratum(sym, d, numDof * numComp, minOrnt, maxOrnt, PETSC_OWN_POINTER, (const PetscInt **)perms, NULL));
    225:       } else if (d == 2) {
    226:         PetscInt   perEdge = user->k[f] - 1;
    227:         PetscInt   numDof  = perEdge * perEdge;
    228:         PetscInt   numComp = user->Nc[f];
    229:         PetscInt   minOrnt = -4;
    230:         PetscInt   maxOrnt = 4;
    231:         PetscInt **perms;

    233:         PetscCall(PetscCalloc1(maxOrnt - minOrnt, &perms));
    234:         for (o = minOrnt; o < maxOrnt; o++) {
    235:           PetscInt *perm;

    237:           if (!o) continue; /* identity */
    238:           PetscCall(PetscMalloc1(numDof * numComp, &perm));
    239:           /* We want to perm[k] to list which *localArray* position the *sectionArray* position k should go to for the given orientation*/
    240:           switch (o) {
    241:           case 0:
    242:             break; /* identity */
    243:           case -2: /* flip along (-1,-1)--( 1, 1), which swaps edges 0 and 3 and edges 1 and 2.  This swaps the i and j variables */
    244:             for (i = 0, k = 0; i < perEdge; i++) {
    245:               for (j = 0; j < perEdge; j++, k++) {
    246:                 for (c = 0; c < numComp; c++) perm[k * numComp + c] = (perEdge * j + i) * numComp + c;
    247:               }
    248:             }
    249:             break;
    250:           case -1: /* flip along (-1, 0)--( 1, 0), which swaps edges 0 and 2.  This reverses the i variable */
    251:             for (i = 0, k = 0; i < perEdge; i++) {
    252:               for (j = 0; j < perEdge; j++, k++) {
    253:                 for (c = 0; c < numComp; c++) perm[k * numComp + c] = (perEdge * (perEdge - 1 - i) + j) * numComp + c;
    254:               }
    255:             }
    256:             break;
    257:           case -4: /* flip along ( 1,-1)--(-1, 1), which swaps edges 0 and 1 and edges 2 and 3.  This swaps the i and j variables and reverse both */
    258:             for (i = 0, k = 0; i < perEdge; i++) {
    259:               for (j = 0; j < perEdge; j++, k++) {
    260:                 for (c = 0; c < numComp; c++) perm[k * numComp + c] = (perEdge * (perEdge - 1 - j) + (perEdge - 1 - i)) * numComp + c;
    261:               }
    262:             }
    263:             break;
    264:           case -3: /* flip along ( 0,-1)--( 0, 1), which swaps edges 3 and 1.  This reverses the j variable */
    265:             for (i = 0, k = 0; i < perEdge; i++) {
    266:               for (j = 0; j < perEdge; j++, k++) {
    267:                 for (c = 0; c < numComp; c++) perm[k * numComp + c] = (perEdge * i + (perEdge - 1 - j)) * numComp + c;
    268:               }
    269:             }
    270:             break;
    271:           case 1: /* rotate section edge 1 to local edge 0.  This swaps the i and j variables and then reverses the j variable */
    272:             for (i = 0, k = 0; i < perEdge; i++) {
    273:               for (j = 0; j < perEdge; j++, k++) {
    274:                 for (c = 0; c < numComp; c++) perm[k * numComp + c] = (perEdge * (perEdge - 1 - j) + i) * numComp + c;
    275:               }
    276:             }
    277:             break;
    278:           case 2: /* rotate section edge 2 to local edge 0.  This reverse both i and j variables */
    279:             for (i = 0, k = 0; i < perEdge; i++) {
    280:               for (j = 0; j < perEdge; j++, k++) {
    281:                 for (c = 0; c < numComp; c++) perm[k * numComp + c] = (perEdge * (perEdge - 1 - i) + (perEdge - 1 - j)) * numComp + c;
    282:               }
    283:             }
    284:             break;
    285:           case 3: /* rotate section edge 3 to local edge 0.  This swaps the i and j variables and then reverses the i variable */
    286:             for (i = 0, k = 0; i < perEdge; i++) {
    287:               for (j = 0; j < perEdge; j++, k++) {
    288:                 for (c = 0; c < numComp; c++) perm[k * numComp + c] = (perEdge * j + (perEdge - 1 - i)) * numComp + c;
    289:               }
    290:             }
    291:             break;
    292:           default:
    293:             break;
    294:           }
    295:           perms[o - minOrnt] = perm;
    296:         }
    297:         PetscCall(PetscSectionSymLabelSetStratum(sym, d, numDof * numComp, minOrnt, maxOrnt, PETSC_OWN_POINTER, (const PetscInt **)perms, NULL));
    298:       }
    299:     }
    300:     PetscCall(PetscSectionSetFieldSym(s, f, sym));
    301:     PetscCall(PetscSectionSymDestroy(&sym));
    302:   }
    303:   PetscCall(PetscSectionViewFromOptions(s, NULL, "-section_with_sym_view"));
    304:   PetscFunctionReturn(PETSC_SUCCESS);
    305: }

    307: int main(int argc, char **argv)
    308: {
    309:   DM           dm;
    310:   PetscSection s;
    311:   Vec          u;
    312:   AppCtx       user;
    313:   PetscInt     dim, size = 0, f;

    315:   PetscFunctionBeginUser;
    316:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
    317:   PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
    318:   PetscCall(DMCreate(PETSC_COMM_WORLD, &dm));
    319:   PetscCall(DMSetType(dm, DMPLEX));
    320:   PetscCall(DMSetFromOptions(dm));
    321:   PetscCall(DMViewFromOptions(dm, NULL, "-dm_view"));
    322:   PetscCall(DMGetDimension(dm, &dim));
    323:   /* Create a section for SEM order k */
    324:   {
    325:     PetscInt *numDof, d;

    327:     PetscCall(PetscMalloc1(user.Nf * (dim + 1), &numDof));
    328:     for (f = 0; f < user.Nf; ++f) {
    329:       for (d = 0; d <= dim; ++d) numDof[f * (dim + 1) + d] = PetscPowInt(user.k[f] - 1, d) * user.Nc[f];
    330:       size += PetscPowInt(user.k[f] + 1, d) * user.Nc[f];
    331:     }
    332:     PetscCall(DMSetNumFields(dm, user.Nf));
    333:     PetscCall(DMPlexCreateSection(dm, NULL, user.Nc, numDof, 0, NULL, NULL, NULL, NULL, &s));
    334:     PetscCall(SetSymmetries(dm, s, &user));
    335:     PetscCall(PetscFree(numDof));
    336:   }
    337:   PetscCall(DMSetLocalSection(dm, s));
    338:   /* Create spectral ordering and load in data */
    339:   PetscCall(DMPlexSetClosurePermutationTensor(dm, PETSC_DETERMINE, NULL));
    340:   PetscCall(DMGetLocalVector(dm, &u));
    341:   switch (dim) {
    342:   case 2:
    343:     PetscCall(LoadData2D(dm, 2, 2, size, u, &user));
    344:     break;
    345:   case 3:
    346:     PetscCall(LoadData3D(dm, 2, 2, 2, size, u, &user));
    347:     break;
    348:   }
    349:   /* Remove ordering and check some values */
    350:   PetscCall(PetscSectionSetClosurePermutation(s, (PetscObject)dm, dim, NULL));
    351:   switch (dim) {
    352:   case 2:
    353:     PetscCall(CheckPoint(dm, u, 0, &user));
    354:     PetscCall(CheckPoint(dm, u, 13, &user));
    355:     PetscCall(CheckPoint(dm, u, 15, &user));
    356:     PetscCall(CheckPoint(dm, u, 19, &user));
    357:     break;
    358:   case 3:
    359:     PetscCall(CheckPoint(dm, u, 0, &user));
    360:     PetscCall(CheckPoint(dm, u, 13, &user));
    361:     PetscCall(CheckPoint(dm, u, 15, &user));
    362:     PetscCall(CheckPoint(dm, u, 19, &user));
    363:     break;
    364:   }
    365:   /* Recreate spectral ordering and read out data */
    366:   PetscCall(DMPlexSetClosurePermutationTensor(dm, PETSC_DETERMINE, s));
    367:   switch (dim) {
    368:   case 2:
    369:     PetscCall(ReadData2D(dm, u, &user));
    370:     break;
    371:   case 3:
    372:     PetscCall(ReadData3D(dm, u, &user));
    373:     break;
    374:   }
    375:   PetscCall(DMRestoreLocalVector(dm, &u));
    376:   PetscCall(PetscSectionDestroy(&s));
    377:   PetscCall(DMDestroy(&dm));
    378:   PetscCall(PetscFree(user.Nc));
    379:   PetscCall(PetscFree(user.k));
    380:   PetscCall(PetscFinalize());
    381:   return 0;
    382: }

    384: /*TEST

    386:   # Spectral ordering 2D 0-5
    387:   testset:
    388:     args: -dm_plex_simplex 0 -dm_plex_box_faces 2,2

    390:     test:
    391:       suffix: 0
    392:       args: -num_fields 1 -num_components 1 -order 2
    393:     test:
    394:       suffix: 1
    395:       args: -num_fields 1 -num_components 1 -order 3
    396:     test:
    397:       suffix: 2
    398:       args: -num_fields 1 -num_components 1 -order 5
    399:     test:
    400:       suffix: 3
    401:       args: -num_fields 1 -num_components 2 -order 2
    402:     test:
    403:       suffix: 4
    404:       args: -num_fields 2 -num_components 1,1 -order 2,2
    405:     test:
    406:       suffix: 5
    407:       args: -num_fields 2 -num_components 1,2 -order 2,3

    409:   # Spectral ordering 3D 6-11
    410:   testset:
    411:     args: -dm_plex_dim 3 -dm_plex_simplex 0 -dm_plex_box_faces 2,2,2

    413:     test:
    414:       suffix: 6
    415:       args: -num_fields 1 -num_components 1 -order 2
    416:     test:
    417:       suffix: 7
    418:       args: -num_fields 1 -num_components 1 -order 3
    419:     test:
    420:       suffix: 8
    421:       args: -num_fields 1 -num_components 1 -order 5
    422:     test:
    423:       suffix: 9
    424:       args: -num_fields 1 -num_components 2 -order 2
    425:     test:
    426:       suffix: 10
    427:       args: -num_fields 2 -num_components 1,1 -order 2,2
    428:     test:
    429:       suffix: 11
    430:       args: -num_fields 2 -num_components 1,2 -order 2,3

    432: TEST*/