Actual source code: da2.c

  1: #include <petsc/private/dmdaimpl.h>
  2: #include <petscdraw.h>

  4: static PetscErrorCode DMView_DA_2d(DM da, PetscViewer viewer)
  5: {
  6:   PetscMPIInt rank;
  7:   PetscBool   iascii, isdraw, isglvis, isbinary;
  8:   DM_DA      *dd = (DM_DA *)da->data;
  9: #if defined(PETSC_HAVE_MATLAB)
 10:   PetscBool ismatlab;
 11: #endif

 13:   PetscFunctionBegin;
 14:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)da), &rank));

 16:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
 17:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
 18:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERGLVIS, &isglvis));
 19:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
 20: #if defined(PETSC_HAVE_MATLAB)
 21:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERMATLAB, &ismatlab));
 22: #endif
 23:   if (iascii) {
 24:     PetscViewerFormat format;

 26:     PetscCall(PetscViewerGetFormat(viewer, &format));
 27:     if (format == PETSC_VIEWER_LOAD_BALANCE) {
 28:       PetscInt      i, nmax = 0, nmin = PETSC_INT_MAX, navg = 0, *nz, nzlocal;
 29:       DMDALocalInfo info;
 30:       PetscMPIInt   size;
 31:       PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)da), &size));
 32:       PetscCall(DMDAGetLocalInfo(da, &info));
 33:       nzlocal = info.xm * info.ym;
 34:       PetscCall(PetscMalloc1(size, &nz));
 35:       PetscCallMPI(MPI_Allgather(&nzlocal, 1, MPIU_INT, nz, 1, MPIU_INT, PetscObjectComm((PetscObject)da)));
 36:       for (i = 0; i < (PetscInt)size; i++) {
 37:         nmax = PetscMax(nmax, nz[i]);
 38:         nmin = PetscMin(nmin, nz[i]);
 39:         navg += nz[i];
 40:       }
 41:       PetscCall(PetscFree(nz));
 42:       navg = navg / size;
 43:       PetscCall(PetscViewerASCIIPrintf(viewer, "  Load Balance - Grid Points: Min %" PetscInt_FMT "  avg %" PetscInt_FMT "  max %" PetscInt_FMT "\n", nmin, navg, nmax));
 44:       PetscFunctionReturn(PETSC_SUCCESS);
 45:     }
 46:     if (format != PETSC_VIEWER_ASCII_VTK_DEPRECATED && format != PETSC_VIEWER_ASCII_VTK_CELL_DEPRECATED && format != PETSC_VIEWER_ASCII_GLVIS) {
 47:       DMDALocalInfo info;
 48:       PetscCall(DMDAGetLocalInfo(da, &info));
 49:       PetscCall(PetscViewerASCIIPushSynchronized(viewer));
 50:       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Processor [%d] M %" PetscInt_FMT " N %" PetscInt_FMT " m %" PetscInt_FMT " n %" PetscInt_FMT " w %" PetscInt_FMT " s %" PetscInt_FMT "\n", rank, dd->M, dd->N, dd->m, dd->n, dd->w, dd->s));
 51:       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "X range of indices: %" PetscInt_FMT " %" PetscInt_FMT ", Y range of indices: %" PetscInt_FMT " %" PetscInt_FMT "\n", info.xs, info.xs + info.xm, info.ys, info.ys + info.ym));
 52:       PetscCall(PetscViewerFlush(viewer));
 53:       PetscCall(PetscViewerASCIIPopSynchronized(viewer));
 54:     } else if (format == PETSC_VIEWER_ASCII_GLVIS) PetscCall(DMView_DA_GLVis(da, viewer));
 55:     else PetscCall(DMView_DA_VTK(da, viewer));
 56:   } else if (isdraw) {
 57:     PetscDraw       draw;
 58:     double          ymin = -1 * dd->s - 1, ymax = dd->N + dd->s;
 59:     double          xmin = -1 * dd->s - 1, xmax = dd->M + dd->s;
 60:     double          x, y;
 61:     PetscInt        base;
 62:     const PetscInt *idx;
 63:     char            node[10];
 64:     PetscBool       isnull;

 66:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
 67:     PetscCall(PetscDrawIsNull(draw, &isnull));
 68:     if (isnull) PetscFunctionReturn(PETSC_SUCCESS);

 70:     PetscCall(PetscDrawCheckResizedWindow(draw));
 71:     PetscCall(PetscDrawClear(draw));
 72:     PetscCall(PetscDrawSetCoordinates(draw, xmin, ymin, xmax, ymax));

 74:     PetscDrawCollectiveBegin(draw);
 75:     /* first processor draw all node lines */
 76:     if (rank == 0) {
 77:       ymin = 0.0;
 78:       ymax = dd->N - 1;
 79:       for (xmin = 0; xmin < dd->M; xmin++) PetscCall(PetscDrawLine(draw, xmin, ymin, xmin, ymax, PETSC_DRAW_BLACK));
 80:       xmin = 0.0;
 81:       xmax = dd->M - 1;
 82:       for (ymin = 0; ymin < dd->N; ymin++) PetscCall(PetscDrawLine(draw, xmin, ymin, xmax, ymin, PETSC_DRAW_BLACK));
 83:     }
 84:     PetscDrawCollectiveEnd(draw);
 85:     PetscCall(PetscDrawFlush(draw));
 86:     PetscCall(PetscDrawPause(draw));

 88:     PetscDrawCollectiveBegin(draw);
 89:     /* draw my box */
 90:     xmin = dd->xs / dd->w;
 91:     xmax = (dd->xe - 1) / dd->w;
 92:     ymin = dd->ys;
 93:     ymax = dd->ye - 1;
 94:     PetscCall(PetscDrawLine(draw, xmin, ymin, xmax, ymin, PETSC_DRAW_RED));
 95:     PetscCall(PetscDrawLine(draw, xmin, ymin, xmin, ymax, PETSC_DRAW_RED));
 96:     PetscCall(PetscDrawLine(draw, xmin, ymax, xmax, ymax, PETSC_DRAW_RED));
 97:     PetscCall(PetscDrawLine(draw, xmax, ymin, xmax, ymax, PETSC_DRAW_RED));
 98:     /* put in numbers */
 99:     base = (dd->base) / dd->w;
100:     for (y = ymin; y <= ymax; y++) {
101:       for (x = xmin; x <= xmax; x++) {
102:         PetscCall(PetscSNPrintf(node, sizeof(node), "%d", (int)base++));
103:         PetscCall(PetscDrawString(draw, x, y, PETSC_DRAW_BLACK, node));
104:       }
105:     }
106:     PetscDrawCollectiveEnd(draw);
107:     PetscCall(PetscDrawFlush(draw));
108:     PetscCall(PetscDrawPause(draw));

110:     PetscDrawCollectiveBegin(draw);
111:     /* overlay ghost numbers, useful for error checking */
112:     PetscCall(ISLocalToGlobalMappingGetBlockIndices(da->ltogmap, &idx));
113:     base = 0;
114:     xmin = dd->Xs;
115:     xmax = dd->Xe;
116:     ymin = dd->Ys;
117:     ymax = dd->Ye;
118:     for (y = ymin; y < ymax; y++) {
119:       for (x = xmin; x < xmax; x++) {
120:         if ((base % dd->w) == 0) {
121:           PetscCall(PetscSNPrintf(node, sizeof(node), "%d", (int)(idx[base / dd->w])));
122:           PetscCall(PetscDrawString(draw, x / dd->w, y, PETSC_DRAW_BLUE, node));
123:         }
124:         base++;
125:       }
126:     }
127:     PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(da->ltogmap, &idx));
128:     PetscDrawCollectiveEnd(draw);
129:     PetscCall(PetscDrawFlush(draw));
130:     PetscCall(PetscDrawPause(draw));
131:     PetscCall(PetscDrawSave(draw));
132:   } else if (isglvis) {
133:     PetscCall(DMView_DA_GLVis(da, viewer));
134:   } else if (isbinary) {
135:     PetscCall(DMView_DA_Binary(da, viewer));
136: #if defined(PETSC_HAVE_MATLAB)
137:   } else if (ismatlab) {
138:     PetscCall(DMView_DA_Matlab(da, viewer));
139: #endif
140:   }
141:   PetscFunctionReturn(PETSC_SUCCESS);
142: }

144: #if defined(new)
145: /*
146:   DMDAGetDiagonal_MFFD - Gets the diagonal for a matrix-free matrix where local
147:     function lives on a DMDA

149:         y ~= (F(u + ha) - F(u))/h,
150:   where F = nonlinear function, as set by SNESSetFunction()
151:         u = current iterate
152:         h = difference interval
153: */
154: PetscErrorCode DMDAGetDiagonal_MFFD(DM da, Vec U, Vec a)
155: {
156:   PetscScalar   h, *aa, *ww, v;
157:   PetscReal     epsilon = PETSC_SQRT_MACHINE_EPSILON, umin = 100.0 * PETSC_SQRT_MACHINE_EPSILON;
158:   PetscInt      gI, nI;
159:   MatStencil    stencil;
160:   DMDALocalInfo info;

162:   PetscFunctionBegin;
163:   PetscCall((*ctx->func)(0, U, a, ctx->funcctx));
164:   PetscCall((*ctx->funcisetbase)(U, ctx->funcctx));

166:   PetscCall(VecGetArray(U, &ww));
167:   PetscCall(VecGetArray(a, &aa));

169:   nI = 0;
170:   h  = ww[gI];
171:   if (h == 0.0) h = 1.0;
172:   if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0) h = umin;
173:   else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
174:   h *= epsilon;

176:   ww[gI] += h;
177:   PetscCall((*ctx->funci)(i, w, &v, ctx->funcctx));
178:   aa[nI] = (v - aa[nI]) / h;
179:   ww[gI] -= h;
180:   nI++;

182:   PetscCall(VecRestoreArray(U, &ww));
183:   PetscCall(VecRestoreArray(a, &aa));
184:   PetscFunctionReturn(PETSC_SUCCESS);
185: }
186: #endif

188: PetscErrorCode DMSetUp_DA_2D(DM da)
189: {
190:   DM_DA          *dd = (DM_DA *)da->data;
191:   const PetscInt  M  = dd->M;
192:   const PetscInt  N  = dd->N;
193:   PetscMPIInt     m, n;
194:   const PetscInt  dof          = dd->w;
195:   const PetscInt  s            = dd->s;
196:   DMBoundaryType  bx           = dd->bx;
197:   DMBoundaryType  by           = dd->by;
198:   DMDAStencilType stencil_type = dd->stencil_type;
199:   PetscInt       *lx           = dd->lx;
200:   PetscInt       *ly           = dd->ly;
201:   MPI_Comm        comm;
202:   PetscMPIInt     rank, size, n0, n1, n2, n3, n5, n6, n7, n8;
203:   PetscInt        xs, xe, ys, ye, x, y, Xs, Xe, Ys, Ye, IXs, IXe, IYs, IYe;
204:   PetscInt        up, down, left, right, i, *idx, nn;
205:   PetscInt        xbase, *bases, *ldims, j, x_t, y_t, s_t, base, count;
206:   PetscInt        s_x, s_y; /* s proportionalized to w */
207:   PetscMPIInt     sn0 = 0, sn2 = 0, sn6 = 0, sn8 = 0;
208:   Vec             local, global;
209:   VecScatter      gtol;
210:   IS              to, from;

212:   PetscFunctionBegin;
213:   PetscCheck(stencil_type != DMDA_STENCIL_BOX || (bx != DM_BOUNDARY_MIRROR && by != DM_BOUNDARY_MIRROR), PetscObjectComm((PetscObject)da), PETSC_ERR_SUP, "Mirror boundary and box stencil");
214:   PetscCall(PetscObjectGetComm((PetscObject)da, &comm));
215: #if !defined(PETSC_USE_64BIT_INDICES)
216:   PetscCheck(((PetscInt64)M) * ((PetscInt64)N) * ((PetscInt64)dof) <= (PetscInt64)PETSC_MPI_INT_MAX, comm, PETSC_ERR_INT_OVERFLOW, "Mesh of %" PetscInt_FMT " by %" PetscInt_FMT " by %" PetscInt_FMT " (dof) is too large for 32-bit indices", M, N, dof);
217: #endif
218:   PetscCall(PetscMPIIntCast(dd->m, &m));
219:   PetscCall(PetscMPIIntCast(dd->n, &n));

221:   PetscCallMPI(MPI_Comm_size(comm, &size));
222:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

224:   dd->p = 1;
225:   if (m != PETSC_DECIDE) {
226:     PetscCheck(m >= 1, comm, PETSC_ERR_ARG_OUTOFRANGE, "Non-positive number of processors in X direction: %d", m);
227:     PetscCheck(m <= size, comm, PETSC_ERR_ARG_OUTOFRANGE, "Too many processors in X direction: %d %d", m, size);
228:   }
229:   if (n != PETSC_DECIDE) {
230:     PetscCheck(n >= 1, comm, PETSC_ERR_ARG_OUTOFRANGE, "Non-positive number of processors in Y direction: %d", n);
231:     PetscCheck(n <= size, comm, PETSC_ERR_ARG_OUTOFRANGE, "Too many processors in Y direction: %d %d", n, size);
232:   }

234:   if (m == PETSC_DECIDE || n == PETSC_DECIDE) {
235:     if (n != PETSC_DECIDE) {
236:       m = size / n;
237:     } else if (m != PETSC_DECIDE) {
238:       n = size / m;
239:     } else {
240:       /* try for squarish distribution */
241:       m = (PetscMPIInt)(0.5 + PetscSqrtReal(((PetscReal)M) * ((PetscReal)size) / ((PetscReal)N)));
242:       if (!m) m = 1;
243:       while (m > 0) {
244:         n = size / m;
245:         if (m * n == size) break;
246:         m--;
247:       }
248:       if (M > N && m < n) {
249:         PetscMPIInt _m = m;
250:         m              = n;
251:         n              = _m;
252:       }
253:     }
254:     PetscCheck(m * n == size, comm, PETSC_ERR_PLIB, "Unable to create partition, check the size of the communicator and input m and n ");
255:   } else PetscCheck(m * n == size, comm, PETSC_ERR_ARG_OUTOFRANGE, "Given Bad partition");

257:   PetscCheck(M >= m, comm, PETSC_ERR_ARG_OUTOFRANGE, "Partition in x direction is too fine! %" PetscInt_FMT " %d", M, m);
258:   PetscCheck(N >= n, comm, PETSC_ERR_ARG_OUTOFRANGE, "Partition in y direction is too fine! %" PetscInt_FMT " %d", N, n);

260:   /*
261:      Determine locally owned region
262:      xs is the first local node number, x is the number of local nodes
263:   */
264:   if (!lx) {
265:     PetscCall(PetscMalloc1(m, &dd->lx));
266:     lx = dd->lx;
267:     for (i = 0; i < m; i++) lx[i] = M / m + ((M % m) > i);
268:   }
269:   x  = lx[rank % m];
270:   xs = 0;
271:   for (i = 0; i < (rank % m); i++) xs += lx[i];
272:   if (PetscDefined(USE_DEBUG)) {
273:     left = xs;
274:     for (i = (rank % m); i < m; i++) left += lx[i];
275:     PetscCheck(left == M, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Sum of lx across processors not equal to M: %" PetscInt_FMT " %" PetscInt_FMT, left, M);
276:   }

278:   /*
279:      Determine locally owned region
280:      ys is the first local node number, y is the number of local nodes
281:   */
282:   if (!ly) {
283:     PetscCall(PetscMalloc1(n, &dd->ly));
284:     ly = dd->ly;
285:     for (i = 0; i < n; i++) ly[i] = N / n + ((N % n) > i);
286:   }
287:   y  = ly[rank / m];
288:   ys = 0;
289:   for (i = 0; i < (rank / m); i++) ys += ly[i];
290:   if (PetscDefined(USE_DEBUG)) {
291:     left = ys;
292:     for (i = (rank / m); i < n; i++) left += ly[i];
293:     PetscCheck(left == N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Sum of ly across processors not equal to N: %" PetscInt_FMT " %" PetscInt_FMT, left, N);
294:   }

296:   /*
297:    check if the scatter requires more than one process neighbor or wraps around
298:    the domain more than once
299:   */
300:   PetscCheck((x >= s) || ((m <= 1) && (bx != DM_BOUNDARY_PERIODIC)), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local x-width of domain x %" PetscInt_FMT " is smaller than stencil width s %" PetscInt_FMT, x, s);
301:   PetscCheck((y >= s) || ((n <= 1) && (by != DM_BOUNDARY_PERIODIC)), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local y-width of domain y %" PetscInt_FMT " is smaller than stencil width s %" PetscInt_FMT, y, s);
302:   PetscCheck((x > s) || (bx != DM_BOUNDARY_MIRROR), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local x-width of domain x %" PetscInt_FMT " is smaller than stencil width s %" PetscInt_FMT " with mirror", x, s);
303:   PetscCheck((y > s) || (by != DM_BOUNDARY_MIRROR), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local y-width of domain y %" PetscInt_FMT " is smaller than stencil width s %" PetscInt_FMT " with mirror", y, s);
304:   xe = xs + x;
305:   ye = ys + y;

307:   /* determine ghost region (Xs) and region scattered into (IXs)  */
308:   if (xs - s > 0) {
309:     Xs  = xs - s;
310:     IXs = xs - s;
311:   } else {
312:     if (bx) {
313:       Xs = xs - s;
314:     } else {
315:       Xs = 0;
316:     }
317:     IXs = 0;
318:   }
319:   if (xe + s <= M) {
320:     Xe  = xe + s;
321:     IXe = xe + s;
322:   } else {
323:     if (bx) {
324:       Xs = xs - s;
325:       Xe = xe + s;
326:     } else {
327:       Xe = M;
328:     }
329:     IXe = M;
330:   }

332:   if (bx == DM_BOUNDARY_PERIODIC || bx == DM_BOUNDARY_MIRROR) {
333:     IXs = xs - s;
334:     IXe = xe + s;
335:     Xs  = xs - s;
336:     Xe  = xe + s;
337:   }

339:   if (ys - s > 0) {
340:     Ys  = ys - s;
341:     IYs = ys - s;
342:   } else {
343:     if (by) {
344:       Ys = ys - s;
345:     } else {
346:       Ys = 0;
347:     }
348:     IYs = 0;
349:   }
350:   if (ye + s <= N) {
351:     Ye  = ye + s;
352:     IYe = ye + s;
353:   } else {
354:     if (by) {
355:       Ye = ye + s;
356:     } else {
357:       Ye = N;
358:     }
359:     IYe = N;
360:   }

362:   if (by == DM_BOUNDARY_PERIODIC || by == DM_BOUNDARY_MIRROR) {
363:     IYs = ys - s;
364:     IYe = ye + s;
365:     Ys  = ys - s;
366:     Ye  = ye + s;
367:   }

369:   /* stencil length in each direction */
370:   s_x = s;
371:   s_y = s;

373:   /* determine starting point of each processor */
374:   nn = x * y;
375:   PetscCall(PetscMalloc2(size + 1, &bases, size, &ldims));
376:   PetscCallMPI(MPI_Allgather(&nn, 1, MPIU_INT, ldims, 1, MPIU_INT, comm));
377:   bases[0] = 0;
378:   for (i = 1; i <= size; i++) bases[i] = ldims[i - 1];
379:   for (i = 1; i <= size; i++) bases[i] += bases[i - 1];
380:   base = bases[rank] * dof;

382:   /* allocate the base parallel and sequential vectors */
383:   dd->Nlocal = x * y * dof;
384:   PetscCall(VecCreateMPIWithArray(comm, dof, dd->Nlocal, PETSC_DECIDE, NULL, &global));
385:   dd->nlocal = (Xe - Xs) * (Ye - Ys) * dof;
386:   PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, dof, dd->nlocal, NULL, &local));

388:   /* generate global to local vector scatter and local to global mapping*/

390:   /* global to local must include ghost points within the domain,
391:      but not ghost points outside the domain that aren't periodic */
392:   PetscCall(PetscMalloc1((IXe - IXs) * (IYe - IYs), &idx));
393:   if (stencil_type == DMDA_STENCIL_BOX) {
394:     left  = IXs - Xs;
395:     right = left + (IXe - IXs);
396:     down  = IYs - Ys;
397:     up    = down + (IYe - IYs);
398:     count = 0;
399:     for (i = down; i < up; i++) {
400:       for (j = left; j < right; j++) idx[count++] = j + i * (Xe - Xs);
401:     }
402:     PetscCall(ISCreateBlock(comm, dof, count, idx, PETSC_OWN_POINTER, &to));

404:   } else {
405:     /* must drop into cross shape region */
406:     /*       ---------|
407:             |  top    |
408:          |---         ---| up
409:          |   middle      |
410:          |               |
411:          ----         ---- down
412:             | bottom  |
413:             -----------
414:          Xs xs        xe Xe */
415:     left  = xs - Xs;
416:     right = left + x;
417:     down  = ys - Ys;
418:     up    = down + y;
419:     count = 0;
420:     /* bottom */
421:     for (i = (IYs - Ys); i < down; i++) {
422:       for (j = left; j < right; j++) idx[count++] = j + i * (Xe - Xs);
423:     }
424:     /* middle */
425:     for (i = down; i < up; i++) {
426:       for (j = (IXs - Xs); j < (IXe - Xs); j++) idx[count++] = j + i * (Xe - Xs);
427:     }
428:     /* top */
429:     for (i = up; i < up + IYe - ye; i++) {
430:       for (j = left; j < right; j++) idx[count++] = j + i * (Xe - Xs);
431:     }
432:     PetscCall(ISCreateBlock(comm, dof, count, idx, PETSC_OWN_POINTER, &to));
433:   }

435:   /* determine who lies on each side of us stored in    n6 n7 n8
436:                                                         n3    n5
437:                                                         n0 n1 n2
438:   */

440:   /* Assume the Non-Periodic Case */
441:   n1 = rank - m;
442:   if (rank % m) {
443:     n0 = n1 - 1;
444:   } else {
445:     n0 = -1;
446:   }
447:   if ((rank + 1) % m) {
448:     n2 = n1 + 1;
449:     n5 = rank + 1;
450:     n8 = rank + m + 1;
451:     if (n8 >= m * n) n8 = -1;
452:   } else {
453:     n2 = -1;
454:     n5 = -1;
455:     n8 = -1;
456:   }
457:   if (rank % m) {
458:     n3 = rank - 1;
459:     n6 = n3 + m;
460:     if (n6 >= m * n) n6 = -1;
461:   } else {
462:     n3 = -1;
463:     n6 = -1;
464:   }
465:   n7 = rank + m;
466:   if (n7 >= m * n) n7 = -1;

468:   if (bx == DM_BOUNDARY_PERIODIC && by == DM_BOUNDARY_PERIODIC) {
469:     /* Modify for Periodic Cases */
470:     /* Handle all four corners */
471:     if ((n6 < 0) && (n7 < 0) && (n3 < 0)) n6 = m - 1;
472:     if ((n8 < 0) && (n7 < 0) && (n5 < 0)) n8 = 0;
473:     if ((n2 < 0) && (n5 < 0) && (n1 < 0)) n2 = size - m;
474:     if ((n0 < 0) && (n3 < 0) && (n1 < 0)) n0 = size - 1;

476:     /* Handle Top and Bottom Sides */
477:     if (n1 < 0) n1 = rank + m * (n - 1);
478:     if (n7 < 0) n7 = rank - m * (n - 1);
479:     if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
480:     if ((n3 >= 0) && (n6 < 0)) n6 = (rank % m) - 1;
481:     if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
482:     if ((n5 >= 0) && (n8 < 0)) n8 = (rank % m) + 1;

484:     /* Handle Left and Right Sides */
485:     if (n3 < 0) n3 = rank + (m - 1);
486:     if (n5 < 0) n5 = rank - (m - 1);
487:     if ((n1 >= 0) && (n0 < 0)) n0 = rank - 1;
488:     if ((n1 >= 0) && (n2 < 0)) n2 = rank - 2 * m + 1;
489:     if ((n7 >= 0) && (n6 < 0)) n6 = rank + 2 * m - 1;
490:     if ((n7 >= 0) && (n8 < 0)) n8 = rank + 1;
491:   } else if (by == DM_BOUNDARY_PERIODIC) { /* Handle Top and Bottom Sides */
492:     if (n1 < 0) n1 = rank + m * (n - 1);
493:     if (n7 < 0) n7 = rank - m * (n - 1);
494:     if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
495:     if ((n3 >= 0) && (n6 < 0)) n6 = (rank % m) - 1;
496:     if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
497:     if ((n5 >= 0) && (n8 < 0)) n8 = (rank % m) + 1;
498:   } else if (bx == DM_BOUNDARY_PERIODIC) { /* Handle Left and Right Sides */
499:     if (n3 < 0) n3 = rank + (m - 1);
500:     if (n5 < 0) n5 = rank - (m - 1);
501:     if ((n1 >= 0) && (n0 < 0)) n0 = rank - 1;
502:     if ((n1 >= 0) && (n2 < 0)) n2 = rank - 2 * m + 1;
503:     if ((n7 >= 0) && (n6 < 0)) n6 = rank + 2 * m - 1;
504:     if ((n7 >= 0) && (n8 < 0)) n8 = rank + 1;
505:   }

507:   PetscCall(PetscMalloc1(9, &dd->neighbors));

509:   dd->neighbors[0] = n0;
510:   dd->neighbors[1] = n1;
511:   dd->neighbors[2] = n2;
512:   dd->neighbors[3] = n3;
513:   dd->neighbors[4] = rank;
514:   dd->neighbors[5] = n5;
515:   dd->neighbors[6] = n6;
516:   dd->neighbors[7] = n7;
517:   dd->neighbors[8] = n8;

519:   if (stencil_type == DMDA_STENCIL_STAR) {
520:     /* save corner processor numbers */
521:     sn0 = n0;
522:     sn2 = n2;
523:     sn6 = n6;
524:     sn8 = n8;
525:     n0 = n2 = n6 = n8 = -1;
526:   }

528:   PetscCall(PetscMalloc1((Xe - Xs) * (Ye - Ys), &idx));

530:   nn    = 0;
531:   xbase = bases[rank];
532:   for (i = 1; i <= s_y; i++) {
533:     if (n0 >= 0) { /* left below */
534:       x_t = lx[n0 % m];
535:       y_t = ly[n0 / m];
536:       s_t = bases[n0] + x_t * y_t - (s_y - i) * x_t - s_x;
537:       for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
538:     }

540:     if (n1 >= 0) { /* directly below */
541:       x_t = x;
542:       y_t = ly[n1 / m];
543:       s_t = bases[n1] + x_t * y_t - (s_y + 1 - i) * x_t;
544:       for (j = 0; j < x_t; j++) idx[nn++] = s_t++;
545:     } else if (by == DM_BOUNDARY_MIRROR) {
546:       for (j = 0; j < x; j++) idx[nn++] = bases[rank] + x * (s_y - i + 1) + j;
547:     }

549:     if (n2 >= 0) { /* right below */
550:       x_t = lx[n2 % m];
551:       y_t = ly[n2 / m];
552:       s_t = bases[n2] + x_t * y_t - (s_y + 1 - i) * x_t;
553:       for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
554:     }
555:   }

557:   for (i = 0; i < y; i++) {
558:     if (n3 >= 0) { /* directly left */
559:       x_t = lx[n3 % m];
560:       /* y_t = y; */
561:       s_t = bases[n3] + (i + 1) * x_t - s_x;
562:       for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
563:     } else if (bx == DM_BOUNDARY_MIRROR) {
564:       for (j = 0; j < s_x; j++) idx[nn++] = bases[rank] + x * i + s_x - j;
565:     }

567:     for (j = 0; j < x; j++) idx[nn++] = xbase++; /* interior */

569:     if (n5 >= 0) { /* directly right */
570:       x_t = lx[n5 % m];
571:       /* y_t = y; */
572:       s_t = bases[n5] + (i)*x_t;
573:       for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
574:     } else if (bx == DM_BOUNDARY_MIRROR) {
575:       for (j = 0; j < s_x; j++) idx[nn++] = bases[rank] + x * (i + 1) - 2 - j;
576:     }
577:   }

579:   for (i = 1; i <= s_y; i++) {
580:     if (n6 >= 0) { /* left above */
581:       x_t = lx[n6 % m];
582:       /* y_t = ly[n6 / m]; */
583:       s_t = bases[n6] + (i)*x_t - s_x;
584:       for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
585:     }

587:     if (n7 >= 0) { /* directly above */
588:       x_t = x;
589:       /* y_t = ly[n7 / m]; */
590:       s_t = bases[n7] + (i - 1) * x_t;
591:       for (j = 0; j < x_t; j++) idx[nn++] = s_t++;
592:     } else if (by == DM_BOUNDARY_MIRROR) {
593:       for (j = 0; j < x; j++) idx[nn++] = bases[rank] + x * (y - i - 1) + j;
594:     }

596:     if (n8 >= 0) { /* right above */
597:       x_t = lx[n8 % m];
598:       /* y_t = ly[n8 / m]; */
599:       s_t = bases[n8] + (i - 1) * x_t;
600:       for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
601:     }
602:   }

604:   PetscCall(ISCreateBlock(comm, dof, nn, idx, PETSC_USE_POINTER, &from));
605:   PetscCall(VecScatterCreate(global, from, local, to, &gtol));
606:   PetscCall(ISDestroy(&to));
607:   PetscCall(ISDestroy(&from));

609:   if (stencil_type == DMDA_STENCIL_STAR) {
610:     n0 = sn0;
611:     n2 = sn2;
612:     n6 = sn6;
613:     n8 = sn8;
614:   }

616:   if ((stencil_type == DMDA_STENCIL_STAR) || (bx && bx != DM_BOUNDARY_PERIODIC) || (by && by != DM_BOUNDARY_PERIODIC)) {
617:     /*
618:         Recompute the local to global mappings, this time keeping the
619:       information about the cross corner processor numbers and any ghosted
620:       but not periodic indices.
621:     */
622:     nn    = 0;
623:     xbase = bases[rank];
624:     for (i = 1; i <= s_y; i++) {
625:       if (n0 >= 0) { /* left below */
626:         x_t = lx[n0 % m];
627:         y_t = ly[n0 / m];
628:         s_t = bases[n0] + x_t * y_t - (s_y - i) * x_t - s_x;
629:         for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
630:       } else if (xs - Xs > 0 && ys - Ys > 0) {
631:         for (j = 0; j < s_x; j++) idx[nn++] = -1;
632:       }
633:       if (n1 >= 0) { /* directly below */
634:         x_t = x;
635:         y_t = ly[n1 / m];
636:         s_t = bases[n1] + x_t * y_t - (s_y + 1 - i) * x_t;
637:         for (j = 0; j < x_t; j++) idx[nn++] = s_t++;
638:       } else if (ys - Ys > 0) {
639:         if (by == DM_BOUNDARY_MIRROR) {
640:           for (j = 0; j < x; j++) idx[nn++] = bases[rank] + x * (s_y - i + 1) + j;
641:         } else {
642:           for (j = 0; j < x; j++) idx[nn++] = -1;
643:         }
644:       }
645:       if (n2 >= 0) { /* right below */
646:         x_t = lx[n2 % m];
647:         y_t = ly[n2 / m];
648:         s_t = bases[n2] + x_t * y_t - (s_y + 1 - i) * x_t;
649:         for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
650:       } else if (Xe - xe > 0 && ys - Ys > 0) {
651:         for (j = 0; j < s_x; j++) idx[nn++] = -1;
652:       }
653:     }

655:     for (i = 0; i < y; i++) {
656:       if (n3 >= 0) { /* directly left */
657:         x_t = lx[n3 % m];
658:         /* y_t = y; */
659:         s_t = bases[n3] + (i + 1) * x_t - s_x;
660:         for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
661:       } else if (xs - Xs > 0) {
662:         if (bx == DM_BOUNDARY_MIRROR) {
663:           for (j = 0; j < s_x; j++) idx[nn++] = bases[rank] + x * i + s_x - j;
664:         } else {
665:           for (j = 0; j < s_x; j++) idx[nn++] = -1;
666:         }
667:       }

669:       for (j = 0; j < x; j++) idx[nn++] = xbase++; /* interior */

671:       if (n5 >= 0) { /* directly right */
672:         x_t = lx[n5 % m];
673:         /* y_t = y; */
674:         s_t = bases[n5] + (i)*x_t;
675:         for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
676:       } else if (Xe - xe > 0) {
677:         if (bx == DM_BOUNDARY_MIRROR) {
678:           for (j = 0; j < s_x; j++) idx[nn++] = bases[rank] + x * (i + 1) - 2 - j;
679:         } else {
680:           for (j = 0; j < s_x; j++) idx[nn++] = -1;
681:         }
682:       }
683:     }

685:     for (i = 1; i <= s_y; i++) {
686:       if (n6 >= 0) { /* left above */
687:         x_t = lx[n6 % m];
688:         /* y_t = ly[n6 / m]; */
689:         s_t = bases[n6] + (i)*x_t - s_x;
690:         for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
691:       } else if (xs - Xs > 0 && Ye - ye > 0) {
692:         for (j = 0; j < s_x; j++) idx[nn++] = -1;
693:       }
694:       if (n7 >= 0) { /* directly above */
695:         x_t = x;
696:         /* y_t = ly[n7 / m]; */
697:         s_t = bases[n7] + (i - 1) * x_t;
698:         for (j = 0; j < x_t; j++) idx[nn++] = s_t++;
699:       } else if (Ye - ye > 0) {
700:         if (by == DM_BOUNDARY_MIRROR) {
701:           for (j = 0; j < x; j++) idx[nn++] = bases[rank] + x * (y - i - 1) + j;
702:         } else {
703:           for (j = 0; j < x; j++) idx[nn++] = -1;
704:         }
705:       }
706:       if (n8 >= 0) { /* right above */
707:         x_t = lx[n8 % m];
708:         /* y_t = ly[n8 / m]; */
709:         s_t = bases[n8] + (i - 1) * x_t;
710:         for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
711:       } else if (Xe - xe > 0 && Ye - ye > 0) {
712:         for (j = 0; j < s_x; j++) idx[nn++] = -1;
713:       }
714:     }
715:   }
716:   /*
717:      Set the local to global ordering in the global vector, this allows use
718:      of VecSetValuesLocal().
719:   */
720:   PetscCall(ISLocalToGlobalMappingCreate(comm, dof, nn, idx, PETSC_OWN_POINTER, &da->ltogmap));

722:   PetscCall(PetscFree2(bases, ldims));
723:   dd->m = m;
724:   dd->n = n;
725:   /* note petsc expects xs/xe/Xs/Xe to be multiplied by #dofs in many places */
726:   dd->xs = xs * dof;
727:   dd->xe = xe * dof;
728:   dd->ys = ys;
729:   dd->ye = ye;
730:   dd->zs = 0;
731:   dd->ze = 1;
732:   dd->Xs = Xs * dof;
733:   dd->Xe = Xe * dof;
734:   dd->Ys = Ys;
735:   dd->Ye = Ye;
736:   dd->Zs = 0;
737:   dd->Ze = 1;

739:   PetscCall(VecDestroy(&local));
740:   PetscCall(VecDestroy(&global));

742:   dd->gtol      = gtol;
743:   dd->base      = base;
744:   da->ops->view = DMView_DA_2d;
745:   dd->ltol      = NULL;
746:   dd->ao        = NULL;
747:   PetscFunctionReturn(PETSC_SUCCESS);
748: }

750: /*@
751:   DMDACreate2d -  Creates an object that will manage the communication of two-dimensional
752:   regular array data that is distributed across one or more MPI processes.

754:   Collective

756:   Input Parameters:
757: + comm         - MPI communicator
758: . bx           - type of ghost nodes the x array have. Use one of `DM_BOUNDARY_NONE`, `DM_BOUNDARY_GHOSTED`, `DM_BOUNDARY_PERIODIC`.
759: . by           - type of ghost nodes the y array have. Use one of `DM_BOUNDARY_NONE`, `DM_BOUNDARY_GHOSTED`, `DM_BOUNDARY_PERIODIC`.
760: . stencil_type - stencil type.  Use either `DMDA_STENCIL_BOX` or `DMDA_STENCIL_STAR`.
761: . M            - global dimension in x direction of the array
762: . N            - global dimension in y direction of the array
763: . m            - corresponding number of processors in x dimension (or `PETSC_DECIDE` to have calculated)
764: . n            - corresponding number of processors in y dimension (or `PETSC_DECIDE` to have calculated)
765: . dof          - number of degrees of freedom per node
766: . s            - stencil width
767: . lx           - arrays containing the number of nodes in each cell along the x coordinates, or `NULL`.
768: - ly           - arrays containing the number of nodes in each cell along the y coordinates, or `NULL`.

770:   Output Parameter:
771: . da - the resulting distributed array object

773:   Options Database Keys:
774: + -dm_view              - Calls `DMView()` at the conclusion of `DMDACreate2d()`
775: . -da_grid_x <nx>       - number of grid points in x direction
776: . -da_grid_y <ny>       - number of grid points in y direction
777: . -da_processors_x <nx> - number of processors in x direction
778: . -da_processors_y <ny> - number of processors in y direction
779: . -da_bd_x <bx>         - boundary type in x direction
780: . -da_bd_y <by>         - boundary type in y direction
781: . -da_bd_all <bt>       - boundary type in all directions
782: . -da_refine_x <rx>     - refinement ratio in x direction
783: . -da_refine_y <ry>     - refinement ratio in y direction
784: - -da_refine <n>        - refine the `DMDA` n times before creating

786:   Level: beginner

788:   Notes:
789:   If `lx` or `ly` are non-null, these must be of length as `m` and `n`, and the corresponding
790:   `m` and `n` cannot be `PETSC_DECIDE`. The sum of the `lx` entries must be `M`, and the sum of
791:   the `ly` entries must be `N`.

793:   The stencil type `DMDA_STENCIL_STAR` with width 1 corresponds to the
794:   standard 5-pt stencil, while `DMDA_STENCIL_BOX` with width 1 denotes
795:   the standard 9-pt stencil.

797:   The array data itself is NOT stored in the `DMDA`, it is stored in `Vec` objects;
798:   The appropriate vector objects can be obtained with calls to `DMCreateGlobalVector()`
799:   and DMCreateLocalVector() and calls to `VecDuplicate()` if more are needed.

801:   You must call `DMSetUp()` after this call before using this `DM`.

803:   To use the options database to change values in the `DMDA` call `DMSetFromOptions()` after this call
804:   but before `DMSetUp()`.

806: .seealso: [](sec_struct), `DM`, `DMDA`, `DMDestroy()`, `DMView()`, `DMDACreate1d()`, `DMDACreate3d()`, `DMGlobalToLocalBegin()`, `DMDAGetRefinementFactor()`,
807:           `DMGlobalToLocalEnd()`, `DMLocalToGlobalBegin()`, `DMLocalToLocalBegin()`, `DMLocalToLocalEnd()`, `DMDASetRefinementFactor()`,
808:           `DMDAGetInfo()`, `DMCreateGlobalVector()`, `DMCreateLocalVector()`, `DMDACreateNaturalVector()`, `DMLoad()`, `DMDAGetOwnershipRanges()`,
809:           `DMStagCreate2d()`, `DMBoundaryType`
810: @*/
811: PetscErrorCode DMDACreate2d(MPI_Comm comm, DMBoundaryType bx, DMBoundaryType by, DMDAStencilType stencil_type, PetscInt M, PetscInt N, PetscInt m, PetscInt n, PetscInt dof, PetscInt s, const PetscInt lx[], const PetscInt ly[], DM *da)
812: {
813:   PetscFunctionBegin;
814:   PetscCall(DMDACreate(comm, da));
815:   PetscCall(DMSetDimension(*da, 2));
816:   PetscCall(DMDASetSizes(*da, M, N, 1));
817:   PetscCall(DMDASetNumProcs(*da, m, n, PETSC_DECIDE));
818:   PetscCall(DMDASetBoundaryType(*da, bx, by, DM_BOUNDARY_NONE));
819:   PetscCall(DMDASetDof(*da, dof));
820:   PetscCall(DMDASetStencilType(*da, stencil_type));
821:   PetscCall(DMDASetStencilWidth(*da, s));
822:   PetscCall(DMDASetOwnershipRanges(*da, lx, ly, NULL));
823:   PetscFunctionReturn(PETSC_SUCCESS);
824: }