Actual source code: da2.c


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

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

 16:   MPI_Comm_rank(PetscObjectComm((PetscObject)da),&rank);

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

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

 71:     PetscViewerDrawGetDraw(viewer,0,&draw);
 72:     PetscDrawIsNull(draw,&isnull);
 73:     if (isnull) return(0);

 75:     PetscDrawCheckResizedWindow(draw);
 76:     PetscDrawClear(draw);
 77:     PetscDrawSetCoordinates(draw,xmin,ymin,xmax,ymax);

 79:     PetscDrawCollectiveBegin(draw);
 80:     /* first processor draw all node lines */
 81:     if (rank == 0) {
 82:       ymin = 0.0; ymax = dd->N - 1;
 83:       for (xmin=0; xmin<dd->M; xmin++) {
 84:         PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_BLACK);
 85:       }
 86:       xmin = 0.0; xmax = dd->M - 1;
 87:       for (ymin=0; ymin<dd->N; ymin++) {
 88:         PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_BLACK);
 89:       }
 90:     }
 91:     PetscDrawCollectiveEnd(draw);
 92:     PetscDrawFlush(draw);
 93:     PetscDrawPause(draw);

 95:     PetscDrawCollectiveBegin(draw);
 96:     /* draw my box */
 97:     xmin = dd->xs/dd->w; xmax =(dd->xe-1)/dd->w; ymin = dd->ys; ymax = dd->ye - 1;
 98:     PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_RED);
 99:     PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_RED);
100:     PetscDrawLine(draw,xmin,ymax,xmax,ymax,PETSC_DRAW_RED);
101:     PetscDrawLine(draw,xmax,ymin,xmax,ymax,PETSC_DRAW_RED);
102:     /* put in numbers */
103:     base = (dd->base)/dd->w;
104:     for (y=ymin; y<=ymax; y++) {
105:       for (x=xmin; x<=xmax; x++) {
106:         PetscSNPrintf(node,sizeof(node),"%d",(int)base++);
107:         PetscDrawString(draw,x,y,PETSC_DRAW_BLACK,node);
108:       }
109:     }
110:     PetscDrawCollectiveEnd(draw);
111:     PetscDrawFlush(draw);
112:     PetscDrawPause(draw);

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

164:   (*ctx->func)(0,U,a,ctx->funcctx);
165:   (*ctx->funcisetbase)(U,ctx->funcctx);

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

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

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

183:   VecRestoreArray(U,&ww);
184:   VecRestoreArray(a,&aa);
185:   return(0);
186: }
187: #endif

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

216:   if (stencil_type == DMDA_STENCIL_BOX && (bx == DM_BOUNDARY_MIRROR || by == DM_BOUNDARY_MIRROR)) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Mirror boundary and box stencil");
217:   PetscObjectGetComm((PetscObject)da,&comm);
218: #if !defined(PETSC_USE_64BIT_INDICES)
219:   if (((PetscInt64) M)*((PetscInt64) N)*((PetscInt64) dof) > (PetscInt64) PETSC_MPI_INT_MAX) SETERRQ3(comm,PETSC_ERR_INT_OVERFLOW,"Mesh of %D by %D by %D (dof) is too large for 32 bit indices",M,N,dof);
220: #endif

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

225:   dd->p = 1;
226:   if (m != PETSC_DECIDE) {
227:     if (m < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in X direction: %D",m);
228:     else if (m > size) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in X direction: %D %d",m,size);
229:   }
230:   if (n != PETSC_DECIDE) {
231:     if (n < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in Y direction: %D",n);
232:     else if (n > size) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in Y direction: %D %d",n,size);
233:   }

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

254:   if (M < m) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Partition in x direction is too fine! %D %D",M,m);
255:   if (N < n) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Partition in y direction is too fine! %D %D",N,n);

257:   /*
258:      Determine locally owned region
259:      xs is the first local node number, x is the number of local nodes
260:   */
261:   if (!lx) {
262:     PetscMalloc1(m, &dd->lx);
263:     lx   = dd->lx;
264:     for (i=0; i<m; i++) {
265:       lx[i] = M/m + ((M % m) > i);
266:     }
267:   }
268:   x  = lx[rank % m];
269:   xs = 0;
270:   for (i=0; i<(rank % m); i++) {
271:     xs += lx[i];
272:   }
273:   if (PetscDefined(USE_DEBUG)) {
274:     left = xs;
275:     for (i=(rank % m); i<m; i++) {
276:       left += lx[i];
277:     }
278:     if (left != M) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Sum of lx across processors not equal to M: %D %D",left,M);
279:   }

281:   /*
282:      Determine locally owned region
283:      ys is the first local node number, y is the number of local nodes
284:   */
285:   if (!ly) {
286:     PetscMalloc1(n, &dd->ly);
287:     ly   = dd->ly;
288:     for (i=0; i<n; i++) {
289:       ly[i] = N/n + ((N % n) > i);
290:     }
291:   }
292:   y  = ly[rank/m];
293:   ys = 0;
294:   for (i=0; i<(rank/m); i++) {
295:     ys += ly[i];
296:   }
297:   if (PetscDefined(USE_DEBUG)) {
298:     left = ys;
299:     for (i=(rank/m); i<n; i++) {
300:       left += ly[i];
301:     }
302:     if (left != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Sum of ly across processors not equal to N: %D %D",left,N);
303:   }

305:   /*
306:    check if the scatter requires more than one process neighbor or wraps around
307:    the domain more than once
308:   */
309:   if ((x < s) && ((m > 1) || (bx == DM_BOUNDARY_PERIODIC))) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local x-width of domain x %D is smaller than stencil width s %D",x,s);
310:   if ((y < s) && ((n > 1) || (by == DM_BOUNDARY_PERIODIC))) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local y-width of domain y %D is smaller than stencil width s %D",y,s);
311:   xe = xs + x;
312:   ye = ys + y;

314:   /* determine ghost region (Xs) and region scattered into (IXs)  */
315:   if (xs-s > 0) {
316:     Xs = xs - s; IXs = xs - s;
317:   } else {
318:     if (bx) {
319:       Xs = xs - s;
320:     } else {
321:       Xs = 0;
322:     }
323:     IXs = 0;
324:   }
325:   if (xe+s <= M) {
326:     Xe = xe + s; IXe = xe + s;
327:   } else {
328:     if (bx) {
329:       Xs = xs - s; Xe = xe + s;
330:     } else {
331:       Xe = M;
332:     }
333:     IXe = M;
334:   }

336:   if (bx == DM_BOUNDARY_PERIODIC || bx == DM_BOUNDARY_MIRROR) {
337:     IXs = xs - s;
338:     IXe = xe + s;
339:     Xs  = xs - s;
340:     Xe  = xe + s;
341:   }

343:   if (ys-s > 0) {
344:     Ys = ys - s; IYs = ys - s;
345:   } else {
346:     if (by) {
347:       Ys = ys - s;
348:     } else {
349:       Ys = 0;
350:     }
351:     IYs = 0;
352:   }
353:   if (ye+s <= N) {
354:     Ye = ye + s; IYe = ye + s;
355:   } else {
356:     if (by) {
357:       Ye = ye + s;
358:     } else {
359:       Ye = N;
360:     }
361:     IYe = N;
362:   }

364:   if (by == DM_BOUNDARY_PERIODIC || by == DM_BOUNDARY_MIRROR) {
365:     IYs = ys - s;
366:     IYe = ye + s;
367:     Ys  = ys - s;
368:     Ye  = ye + s;
369:   }

371:   /* stencil length in each direction */
372:   s_x = s;
373:   s_y = s;

375:   /* determine starting point of each processor */
376:   nn       = x*y;
377:   PetscMalloc2(size+1,&bases,size,&ldims);
378:   MPI_Allgather(&nn,1,MPIU_INT,ldims,1,MPIU_INT,comm);
379:   bases[0] = 0;
380:   for (i=1; i<=size; i++) {
381:     bases[i] = ldims[i-1];
382:   }
383:   for (i=1; i<=size; i++) {
384:     bases[i] += bases[i-1];
385:   }
386:   base = bases[rank]*dof;

388:   /* allocate the base parallel and sequential vectors */
389:   dd->Nlocal = x*y*dof;
390:   VecCreateMPIWithArray(comm,dof,dd->Nlocal,PETSC_DECIDE,NULL,&global);
391:   dd->nlocal = (Xe-Xs)*(Ye-Ys)*dof;
392:   VecCreateSeqWithArray(PETSC_COMM_SELF,dof,dd->nlocal,NULL,&local);

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

396:   /* global to local must include ghost points within the domain,
397:      but not ghost points outside the domain that aren't periodic */
398:   PetscMalloc1((IXe-IXs)*(IYe-IYs),&idx);
399:   if (stencil_type == DMDA_STENCIL_BOX) {
400:     left  = IXs - Xs; right = left + (IXe-IXs);
401:     down  = IYs - Ys; up = down + (IYe-IYs);
402:     count = 0;
403:     for (i=down; i<up; i++) {
404:       for (j=left; j<right; j++) {
405:         idx[count++] = j + i*(Xe-Xs);
406:       }
407:     }
408:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);

410:   } else {
411:     /* must drop into cross shape region */
412:     /*       ---------|
413:             |  top    |
414:          |---         ---| up
415:          |   middle      |
416:          |               |
417:          ----         ---- down
418:             | bottom  |
419:             -----------
420:          Xs xs        xe Xe */
421:     left  = xs - Xs; right = left + x;
422:     down  = ys - Ys; up = down + y;
423:     count = 0;
424:     /* bottom */
425:     for (i=(IYs-Ys); i<down; i++) {
426:       for (j=left; j<right; j++) {
427:         idx[count++] = j + i*(Xe-Xs);
428:       }
429:     }
430:     /* middle */
431:     for (i=down; i<up; i++) {
432:       for (j=(IXs-Xs); j<(IXe-Xs); j++) {
433:         idx[count++] = j + i*(Xe-Xs);
434:       }
435:     }
436:     /* top */
437:     for (i=up; i<up+IYe-ye; i++) {
438:       for (j=left; j<right; j++) {
439:         idx[count++] = j + i*(Xe-Xs);
440:       }
441:     }
442:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);
443:   }

445:   /* determine who lies on each side of us stored in    n6 n7 n8
446:                                                         n3    n5
447:                                                         n0 n1 n2
448:   */

450:   /* Assume the Non-Periodic Case */
451:   n1 = rank - m;
452:   if (rank % m) {
453:     n0 = n1 - 1;
454:   } else {
455:     n0 = -1;
456:   }
457:   if ((rank+1) % m) {
458:     n2 = n1 + 1;
459:     n5 = rank + 1;
460:     n8 = rank + m + 1; if (n8 >= m*n) n8 = -1;
461:   } else {
462:     n2 = -1; n5 = -1; n8 = -1;
463:   }
464:   if (rank % m) {
465:     n3 = rank - 1;
466:     n6 = n3 + m; if (n6 >= m*n) n6 = -1;
467:   } else {
468:     n3 = -1; n6 = -1;
469:   }
470:   n7 = rank + m; if (n7 >= m*n) n7 = -1;

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

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

488:     /* Handle Left and Right Sides */
489:     if (n3 < 0) n3 = rank + (m-1);
490:     if (n5 < 0) n5 = rank - (m-1);
491:     if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
492:     if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
493:     if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
494:     if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
495:   } else if (by == DM_BOUNDARY_PERIODIC) {  /* Handle Top and Bottom Sides */
496:     if (n1 < 0) n1 = rank + m * (n-1);
497:     if (n7 < 0) n7 = rank - m * (n-1);
498:     if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
499:     if ((n3 >= 0) && (n6 < 0)) n6 = (rank%m)-1;
500:     if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
501:     if ((n5 >= 0) && (n8 < 0)) n8 = (rank%m)+1;
502:   } else if (bx == DM_BOUNDARY_PERIODIC) { /* Handle Left and Right Sides */
503:     if (n3 < 0) n3 = rank + (m-1);
504:     if (n5 < 0) n5 = rank - (m-1);
505:     if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
506:     if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
507:     if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
508:     if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
509:   }

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

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

523:   if (stencil_type == DMDA_STENCIL_STAR) {
524:     /* save corner processor numbers */
525:     sn0 = n0; sn2 = n2; sn6 = n6; sn8 = n8;
526:     n0  = n2 = n6 = n8 = -1;
527:   }

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

531:   nn = 0;
532:   xbase = bases[rank];
533:   for (i=1; i<=s_y; i++) {
534:     if (n0 >= 0) { /* left below */
535:       x_t = lx[n0 % m];
536:       y_t = ly[(n0/m)];
537:       s_t = bases[n0] + x_t*y_t - (s_y-i)*x_t - s_x;
538:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
539:     }

541:     if (n1 >= 0) { /* directly below */
542:       x_t = x;
543:       y_t = ly[(n1/m)];
544:       s_t = bases[n1] + x_t*y_t - (s_y+1-i)*x_t;
545:       for (j=0; j<x_t; j++) idx[nn++] = s_t++;
546:     } else if (by == DM_BOUNDARY_MIRROR) {
547:       for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(s_y - i + 1)  + j;
548:     }

550:     if (n2 >= 0) { /* right below */
551:       x_t = lx[n2 % m];
552:       y_t = ly[(n2/m)];
553:       s_t = bases[n2] + x_t*y_t - (s_y+1-i)*x_t;
554:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
555:     }
556:   }

558:   for (i=0; i<y; i++) {
559:     if (n3 >= 0) { /* directly left */
560:       x_t = lx[n3 % m];
561:       /* y_t = y; */
562:       s_t = bases[n3] + (i+1)*x_t - s_x;
563:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
564:     } else if (bx == DM_BOUNDARY_MIRROR) {
565:       for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*i + s_x - j;
566:     }

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

570:     if (n5 >= 0) { /* directly right */
571:       x_t = lx[n5 % m];
572:       /* y_t = y; */
573:       s_t = bases[n5] + (i)*x_t;
574:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
575:     } else if (bx == DM_BOUNDARY_MIRROR) {
576:       for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*(i + 1) - 2 - j;
577:     }
578:   }

580:   for (i=1; i<=s_y; i++) {
581:     if (n6 >= 0) { /* left above */
582:       x_t = lx[n6 % m];
583:       /* y_t = ly[(n6/m)]; */
584:       s_t = bases[n6] + (i)*x_t - s_x;
585:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
586:     }

588:     if (n7 >= 0) { /* directly above */
589:       x_t = x;
590:       /* y_t = ly[(n7/m)]; */
591:       s_t = bases[n7] + (i-1)*x_t;
592:       for (j=0; j<x_t; j++) idx[nn++] = s_t++;
593:     } else if (by == DM_BOUNDARY_MIRROR) {
594:       for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(y - i - 1)  + j;
595:     }

597:     if (n8 >= 0) { /* right above */
598:       x_t = lx[n8 % m];
599:       /* y_t = ly[(n8/m)]; */
600:       s_t = bases[n8] + (i-1)*x_t;
601:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
602:     }
603:   }

605:   ISCreateBlock(comm,dof,nn,idx,PETSC_USE_POINTER,&from);
606:   VecScatterCreate(global,from,local,to,&gtol);
607:   PetscLogObjectParent((PetscObject)da,(PetscObject)gtol);
608:   ISDestroy(&to);
609:   ISDestroy(&from);

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

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

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

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

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

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

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

728:   VecDestroy(&local);
729:   VecDestroy(&global);

731:   dd->gtol      = gtol;
732:   dd->base      = base;
733:   da->ops->view = DMView_DA_2d;
734:   dd->ltol      = NULL;
735:   dd->ao        = NULL;
736:   return(0);
737: }

739: /*@C
740:    DMDACreate2d -  Creates an object that will manage the communication of  two-dimensional
741:    regular array data that is distributed across some processors.

743:    Collective

745:    Input Parameters:
746: +  comm - MPI communicator
747: .  bx,by - type of ghost nodes the array have.
748:          Use one of DM_BOUNDARY_NONE, DM_BOUNDARY_GHOSTED, DM_BOUNDARY_PERIODIC.
749: .  stencil_type - stencil type.  Use either DMDA_STENCIL_BOX or DMDA_STENCIL_STAR.
750: .  M,N - global dimension in each direction of the array
751: .  m,n - corresponding number of processors in each dimension
752:          (or PETSC_DECIDE to have calculated)
753: .  dof - number of degrees of freedom per node
754: .  s - stencil width
755: -  lx, ly - arrays containing the number of nodes in each cell along
756:            the x and y coordinates, or NULL. If non-null, these
757:            must be of length as m and n, and the corresponding
758:            m and n cannot be PETSC_DECIDE. The sum of the lx[] entries
759:            must be M, and the sum of the ly[] entries must be N.

761:    Output Parameter:
762: .  da - the resulting distributed array object

764:    Options Database Key:
765: +  -dm_view - Calls DMView() at the conclusion of DMDACreate2d()
766: .  -da_grid_x <nx> - number of grid points in x direction
767: .  -da_grid_y <ny> - number of grid points in y direction
768: .  -da_processors_x <nx> - number of processors in x direction
769: .  -da_processors_y <ny> - number of processors in y direction
770: .  -da_refine_x <rx> - refinement ratio in x direction
771: .  -da_refine_y <ry> - refinement ratio in y direction
772: -  -da_refine <n> - refine the DMDA n times before creating

774:    Level: beginner

776:    Notes:
777:    The stencil type DMDA_STENCIL_STAR with width 1 corresponds to the
778:    standard 5-pt stencil, while DMDA_STENCIL_BOX with width 1 denotes
779:    the standard 9-pt stencil.

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

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

787:    If you wish to use the options database to change values in the DMDA call DMSetFromOptions() after this call
788:    but before DMSetUp().

790: .seealso: DMDestroy(), DMView(), DMDACreate1d(), DMDACreate3d(), DMGlobalToLocalBegin(), DMDAGetRefinementFactor(),
791:           DMGlobalToLocalEnd(), DMLocalToGlobalBegin(), DMLocalToLocalBegin(), DMLocalToLocalEnd(), DMDASetRefinementFactor(),
792:           DMDAGetInfo(), DMCreateGlobalVector(), DMCreateLocalVector(), DMDACreateNaturalVector(), DMLoad(), DMDAGetOwnershipRanges(),
793:           DMStagCreate2d()

795: @*/

797: PetscErrorCode  DMDACreate2d(MPI_Comm comm,DMBoundaryType bx,DMBoundaryType by,DMDAStencilType stencil_type,
798:                              PetscInt M,PetscInt N,PetscInt m,PetscInt n,PetscInt dof,PetscInt s,const PetscInt lx[],const PetscInt ly[],DM *da)
799: {

803:   DMDACreate(comm, da);
804:   DMSetDimension(*da, 2);
805:   DMDASetSizes(*da, M, N, 1);
806:   DMDASetNumProcs(*da, m, n, PETSC_DECIDE);
807:   DMDASetBoundaryType(*da, bx, by, DM_BOUNDARY_NONE);
808:   DMDASetDof(*da, dof);
809:   DMDASetStencilType(*da, stencil_type);
810:   DMDASetStencilWidth(*da, s);
811:   DMDASetOwnershipRanges(*da, lx, ly, NULL);
812:   return(0);
813: }