Actual source code: da2.c

petsc-3.7.2 2016-06-05
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  2: #include <petsc/private/dmdaimpl.h>    /*I   "petscdmda.h"   I*/
  3: #include <petscdraw.h>

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

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

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

 29:     PetscViewerGetFormat(viewer, &format);
 30:     if (format != PETSC_VIEWER_ASCII_VTK && format != PETSC_VIEWER_ASCII_VTK_CELL) {
 31:       DMDALocalInfo info;
 32:       DMDAGetLocalInfo(da,&info);
 33:       PetscViewerASCIIPushSynchronized(viewer);
 34:       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);
 35:       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);
 36:       PetscViewerFlush(viewer);
 37:       PetscViewerASCIIPopSynchronized(viewer);
 38:     } else {
 39:       DMView_DA_VTK(da,viewer);
 40:     }
 41:   } else if (isdraw) {
 42:     PetscDraw      draw;
 43:     double         ymin = -1*dd->s-1,ymax = dd->N+dd->s;
 44:     double         xmin = -1*dd->s-1,xmax = dd->M+dd->s;
 45:     double         x,y;
 46:     PetscInt       base;
 47:     const PetscInt *idx;
 48:     char           node[10];
 49:     PetscBool      isnull;

 51:     PetscViewerDrawGetDraw(viewer,0,&draw);
 52:     PetscDrawIsNull(draw,&isnull);
 53:     if (isnull) return(0);

 55:     PetscDrawCheckResizedWindow(draw);
 56:     PetscDrawClear(draw);
 57:     PetscDrawSetCoordinates(draw,xmin,ymin,xmax,ymax);

 59:     PetscDrawCollectiveBegin(draw);
 60:     /* first processor draw all node lines */
 61:     if (!rank) {
 62:       ymin = 0.0; ymax = dd->N - 1;
 63:       for (xmin=0; xmin<dd->M; xmin++) {
 64:         PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_BLACK);
 65:       }
 66:       xmin = 0.0; xmax = dd->M - 1;
 67:       for (ymin=0; ymin<dd->N; ymin++) {
 68:         PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_BLACK);
 69:       }
 70:     }
 71:     PetscDrawCollectiveEnd(draw);
 72:     PetscDrawFlush(draw);
 73:     PetscDrawPause(draw);

 75:     PetscDrawCollectiveBegin(draw);
 76:     /* draw my box */
 77:     xmin = dd->xs/dd->w; xmax =(dd->xe-1)/dd->w; ymin = dd->ys; ymax = dd->ye - 1;
 78:     PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_RED);
 79:     PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_RED);
 80:     PetscDrawLine(draw,xmin,ymax,xmax,ymax,PETSC_DRAW_RED);
 81:     PetscDrawLine(draw,xmax,ymin,xmax,ymax,PETSC_DRAW_RED);
 82:     /* put in numbers */
 83:     base = (dd->base)/dd->w;
 84:     for (y=ymin; y<=ymax; y++) {
 85:       for (x=xmin; x<=xmax; x++) {
 86:         PetscSNPrintf(node,sizeof(node),"%d",(int)base++);
 87:         PetscDrawString(draw,x,y,PETSC_DRAW_BLACK,node);
 88:       }
 89:     }
 90:     PetscDrawCollectiveEnd(draw);
 91:     PetscDrawFlush(draw);
 92:     PetscDrawPause(draw);

 94:     PetscDrawCollectiveBegin(draw);
 95:     /* overlay ghost numbers, useful for error checking */
 96:     ISLocalToGlobalMappingGetBlockIndices(da->ltogmap,&idx);
 97:     base = 0; xmin = dd->Xs; xmax = dd->Xe; ymin = dd->Ys; ymax = dd->Ye;
 98:     for (y=ymin; y<ymax; y++) {
 99:       for (x=xmin; x<xmax; x++) {
100:         if ((base % dd->w) == 0) {
101:           PetscSNPrintf(node,sizeof(node),"%d",(int)(idx[base/dd->w]));
102:           PetscDrawString(draw,x/dd->w,y,PETSC_DRAW_BLUE,node);
103:         }
104:         base++;
105:       }
106:     }
107:     ISLocalToGlobalMappingRestoreBlockIndices(da->ltogmap,&idx);
108:     PetscDrawCollectiveEnd(draw);
109:     PetscDrawFlush(draw);
110:     PetscDrawPause(draw);
111:     PetscDrawSave(draw);
112:   } else if (isbinary) {
113:     DMView_DA_Binary(da,viewer);
114: #if defined(PETSC_HAVE_MATLAB_ENGINE)
115:   } else if (ismatlab) {
116:     DMView_DA_Matlab(da,viewer);
117: #endif
118:   }
119:   return(0);
120: }

122: /*
123:       M is number of grid points
124:       m is number of processors

126: */
129: PetscErrorCode  DMDASplitComm2d(MPI_Comm comm,PetscInt M,PetscInt N,PetscInt sw,MPI_Comm *outcomm)
130: {
132:   PetscInt       m,n = 0,x = 0,y = 0;
133:   PetscMPIInt    size,csize,rank;

136:   MPI_Comm_size(comm,&size);
137:   MPI_Comm_rank(comm,&rank);

139:   csize = 4*size;
140:   do {
141:     if (csize % 4) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cannot split communicator of size %d tried %d %D %D",size,csize,x,y);
142:     csize = csize/4;

144:     m = (PetscInt)(0.5 + PetscSqrtReal(((PetscReal)M)*((PetscReal)csize)/((PetscReal)N)));
145:     if (!m) m = 1;
146:     while (m > 0) {
147:       n = csize/m;
148:       if (m*n == csize) break;
149:       m--;
150:     }
151:     if (M > N && m < n) {PetscInt _m = m; m = n; n = _m;}

153:     x = M/m + ((M % m) > ((csize-1) % m));
154:     y = (N + (csize-1)/m)/n;
155:   } while ((x < 4 || y < 4) && csize > 1);
156:   if (size != csize) {
157:     MPI_Group   entire_group,sub_group;
158:     PetscMPIInt i,*groupies;

160:     MPI_Comm_group(comm,&entire_group);
161:     PetscMalloc1(csize,&groupies);
162:     for (i=0; i<csize; i++) {
163:       groupies[i] = (rank/csize)*csize + i;
164:     }
165:     MPI_Group_incl(entire_group,csize,groupies,&sub_group);
166:     PetscFree(groupies);
167:     MPI_Comm_create(comm,sub_group,outcomm);
168:     MPI_Group_free(&entire_group);
169:     MPI_Group_free(&sub_group);
170:     PetscInfo1(0,"DMDASplitComm2d:Creating redundant coarse problems of size %d\n",csize);
171:   } else {
172:     *outcomm = comm;
173:   }
174:   return(0);
175: }

177: #if defined(new)
180: /*
181:   DMDAGetDiagonal_MFFD - Gets the diagonal for a matrix free matrix where local
182:     function lives on a DMDA

184:         y ~= (F(u + ha) - F(u))/h,
185:   where F = nonlinear function, as set by SNESSetFunction()
186:         u = current iterate
187:         h = difference interval
188: */
189: PetscErrorCode DMDAGetDiagonal_MFFD(DM da,Vec U,Vec a)
190: {
191:   PetscScalar    h,*aa,*ww,v;
192:   PetscReal      epsilon = PETSC_SQRT_MACHINE_EPSILON,umin = 100.0*PETSC_SQRT_MACHINE_EPSILON;
194:   PetscInt       gI,nI;
195:   MatStencil     stencil;
196:   DMDALocalInfo  info;

199:   (*ctx->func)(0,U,a,ctx->funcctx);
200:   (*ctx->funcisetbase)(U,ctx->funcctx);

202:   VecGetArray(U,&ww);
203:   VecGetArray(a,&aa);

205:   nI = 0;
206:   h  = ww[gI];
207:   if (h == 0.0) h = 1.0;
208:   if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0) h = umin;
209:   else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
210:   h *= epsilon;

212:   ww[gI] += h;
213:   (*ctx->funci)(i,w,&v,ctx->funcctx);
214:   aa[nI]  = (v - aa[nI])/h;
215:   ww[gI] -= h;
216:   nI++;

218:   VecRestoreArray(U,&ww);
219:   VecRestoreArray(a,&aa);
220:   return(0);
221: }
222: #endif

226: PetscErrorCode  DMSetUp_DA_2D(DM da)
227: {
228:   DM_DA            *dd = (DM_DA*)da->data;
229:   const PetscInt   M            = dd->M;
230:   const PetscInt   N            = dd->N;
231:   PetscInt         m            = dd->m;
232:   PetscInt         n            = dd->n;
233:   const PetscInt   dof          = dd->w;
234:   const PetscInt   s            = dd->s;
235:   DMBoundaryType   bx           = dd->bx;
236:   DMBoundaryType   by           = dd->by;
237:   DMDAStencilType  stencil_type = dd->stencil_type;
238:   PetscInt         *lx          = dd->lx;
239:   PetscInt         *ly          = dd->ly;
240:   MPI_Comm         comm;
241:   PetscMPIInt      rank,size;
242:   PetscInt         xs,xe,ys,ye,x,y,Xs,Xe,Ys,Ye,IXs,IXe,IYs,IYe;
243:   PetscInt         up,down,left,right,i,n0,n1,n2,n3,n5,n6,n7,n8,*idx,nn;
244:   PetscInt         xbase,*bases,*ldims,j,x_t,y_t,s_t,base,count;
245:   PetscInt         s_x,s_y; /* s proportionalized to w */
246:   PetscInt         sn0 = 0,sn2 = 0,sn6 = 0,sn8 = 0;
247:   Vec              local,global;
248:   VecScatter       gtol;
249:   IS               to,from;
250:   PetscErrorCode   ierr;

253:   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");
254:   PetscObjectGetComm((PetscObject)da,&comm);
255: #if !defined(PETSC_USE_64BIT_INDICES)
256:   if (((Petsc64bitInt) M)*((Petsc64bitInt) N)*((Petsc64bitInt) dof) > (Petsc64bitInt) 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);
257: #endif

259:   if (dof < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Must have 1 or more degrees of freedom per node: %D",dof);
260:   if (s < 0) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Stencil width cannot be negative: %D",s);

262:   MPI_Comm_size(comm,&size);
263:   MPI_Comm_rank(comm,&rank);

265:   dd->p = 1;
266:   if (m != PETSC_DECIDE) {
267:     if (m < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in X direction: %D",m);
268:     else if (m > size) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in X direction: %D %d",m,size);
269:   }
270:   if (n != PETSC_DECIDE) {
271:     if (n < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in Y direction: %D",n);
272:     else if (n > size) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in Y direction: %D %d",n,size);
273:   }

275:   if (m == PETSC_DECIDE || n == PETSC_DECIDE) {
276:     if (n != PETSC_DECIDE) {
277:       m = size/n;
278:     } else if (m != PETSC_DECIDE) {
279:       n = size/m;
280:     } else {
281:       /* try for squarish distribution */
282:       m = (PetscInt)(0.5 + PetscSqrtReal(((PetscReal)M)*((PetscReal)size)/((PetscReal)N)));
283:       if (!m) m = 1;
284:       while (m > 0) {
285:         n = size/m;
286:         if (m*n == size) break;
287:         m--;
288:       }
289:       if (M > N && m < n) {PetscInt _m = m; m = n; n = _m;}
290:     }
291:     if (m*n != size) SETERRQ(comm,PETSC_ERR_PLIB,"Unable to create partition, check the size of the communicator and input m and n ");
292:   } else if (m*n != size) SETERRQ(comm,PETSC_ERR_ARG_OUTOFRANGE,"Given Bad partition");

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

297:   /*
298:      Determine locally owned region
299:      xs is the first local node number, x is the number of local nodes
300:   */
301:   if (!lx) {
302:     PetscMalloc1(m, &dd->lx);
303:     lx   = dd->lx;
304:     for (i=0; i<m; i++) {
305:       lx[i] = M/m + ((M % m) > i);
306:     }
307:   }
308:   x  = lx[rank % m];
309:   xs = 0;
310:   for (i=0; i<(rank % m); i++) {
311:     xs += lx[i];
312:   }
313: #if defined(PETSC_USE_DEBUG)
314:   left = xs;
315:   for (i=(rank % m); i<m; i++) {
316:     left += lx[i];
317:   }
318:   if (left != M) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Sum of lx across processors not equal to M: %D %D",left,M);
319: #endif

321:   /*
322:      Determine locally owned region
323:      ys is the first local node number, y is the number of local nodes
324:   */
325:   if (!ly) {
326:     PetscMalloc1(n, &dd->ly);
327:     ly   = dd->ly;
328:     for (i=0; i<n; i++) {
329:       ly[i] = N/n + ((N % n) > i);
330:     }
331:   }
332:   y  = ly[rank/m];
333:   ys = 0;
334:   for (i=0; i<(rank/m); i++) {
335:     ys += ly[i];
336:   }
337: #if defined(PETSC_USE_DEBUG)
338:   left = ys;
339:   for (i=(rank/m); i<n; i++) {
340:     left += ly[i];
341:   }
342:   if (left != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Sum of ly across processors not equal to N: %D %D",left,N);
343: #endif

345:   /*
346:    check if the scatter requires more than one process neighbor or wraps around
347:    the domain more than once
348:   */
349:   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);
350:   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);
351:   xe = xs + x;
352:   ye = ys + y;

354:   /* determine ghost region (Xs) and region scattered into (IXs)  */
355:   if (xs-s > 0) {
356:     Xs = xs - s; IXs = xs - s;
357:   } else {
358:     if (bx) {
359:       Xs = xs - s;
360:     } else {
361:       Xs = 0;
362:     }
363:     IXs = 0;
364:   }
365:   if (xe+s <= M) {
366:     Xe = xe + s; IXe = xe + s;
367:   } else {
368:     if (bx) {
369:       Xs = xs - s; Xe = xe + s;
370:     } else {
371:       Xe = M;
372:     }
373:     IXe = M;
374:   }

376:   if (bx == DM_BOUNDARY_PERIODIC || bx == DM_BOUNDARY_MIRROR) {
377:     IXs = xs - s;
378:     IXe = xe + s;
379:     Xs  = xs - s;
380:     Xe  = xe + s;
381:   }

383:   if (ys-s > 0) {
384:     Ys = ys - s; IYs = ys - s;
385:   } else {
386:     if (by) {
387:       Ys = ys - s;
388:     } else {
389:       Ys = 0;
390:     }
391:     IYs = 0;
392:   }
393:   if (ye+s <= N) {
394:     Ye = ye + s; IYe = ye + s;
395:   } else {
396:     if (by) {
397:       Ye = ye + s;
398:     } else {
399:       Ye = N;
400:     }
401:     IYe = N;
402:   }

404:   if (by == DM_BOUNDARY_PERIODIC || by == DM_BOUNDARY_MIRROR) {
405:     IYs = ys - s;
406:     IYe = ye + s;
407:     Ys  = ys - s;
408:     Ye  = ye + s;
409:   }

411:   /* stencil length in each direction */
412:   s_x = s;
413:   s_y = s;

415:   /* determine starting point of each processor */
416:   nn       = x*y;
417:   PetscMalloc2(size+1,&bases,size,&ldims);
418:   MPI_Allgather(&nn,1,MPIU_INT,ldims,1,MPIU_INT,comm);
419:   bases[0] = 0;
420:   for (i=1; i<=size; i++) {
421:     bases[i] = ldims[i-1];
422:   }
423:   for (i=1; i<=size; i++) {
424:     bases[i] += bases[i-1];
425:   }
426:   base = bases[rank]*dof;

428:   /* allocate the base parallel and sequential vectors */
429:   dd->Nlocal = x*y*dof;
430:   VecCreateMPIWithArray(comm,dof,dd->Nlocal,PETSC_DECIDE,NULL,&global);
431:   dd->nlocal = (Xe-Xs)*(Ye-Ys)*dof;
432:   VecCreateSeqWithArray(PETSC_COMM_SELF,dof,dd->nlocal,NULL,&local);

434:   /* generate appropriate vector scatters */
435:   /* local to global inserts non-ghost point region into global */
436:   PetscMalloc1((IXe-IXs)*(IYe-IYs),&idx);
437:   left  = xs - Xs; right = left + x;
438:   down  = ys - Ys; up = down + y;
439:   count = 0;
440:   for (i=down; i<up; i++) {
441:     for (j=left; j<right; j++) {
442:       idx[count++] = i*(Xe-Xs) + j;
443:     }
444:   }

446:   /* global to local must include ghost points within the domain,
447:      but not ghost points outside the domain that aren't periodic */
448:   if (stencil_type == DMDA_STENCIL_BOX) {
449:     left  = IXs - Xs; right = left + (IXe-IXs);
450:     down  = IYs - Ys; up = down + (IYe-IYs);
451:     count = 0;
452:     for (i=down; i<up; i++) {
453:       for (j=left; j<right; j++) {
454:         idx[count++] = j + i*(Xe-Xs);
455:       }
456:     }
457:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);

459:   } else {
460:     /* must drop into cross shape region */
461:     /*       ---------|
462:             |  top    |
463:          |---         ---| up
464:          |   middle      |
465:          |               |
466:          ----         ---- down
467:             | bottom  |
468:             -----------
469:          Xs xs        xe Xe */
470:     left  = xs - Xs; right = left + x;
471:     down  = ys - Ys; up = down + y;
472:     count = 0;
473:     /* bottom */
474:     for (i=(IYs-Ys); i<down; i++) {
475:       for (j=left; j<right; j++) {
476:         idx[count++] = j + i*(Xe-Xs);
477:       }
478:     }
479:     /* middle */
480:     for (i=down; i<up; i++) {
481:       for (j=(IXs-Xs); j<(IXe-Xs); j++) {
482:         idx[count++] = j + i*(Xe-Xs);
483:       }
484:     }
485:     /* top */
486:     for (i=up; i<up+IYe-ye; i++) {
487:       for (j=left; j<right; j++) {
488:         idx[count++] = j + i*(Xe-Xs);
489:       }
490:     }
491:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);
492:   }


495:   /* determine who lies on each side of us stored in    n6 n7 n8
496:                                                         n3    n5
497:                                                         n0 n1 n2
498:   */

500:   /* Assume the Non-Periodic Case */
501:   n1 = rank - m;
502:   if (rank % m) {
503:     n0 = n1 - 1;
504:   } else {
505:     n0 = -1;
506:   }
507:   if ((rank+1) % m) {
508:     n2 = n1 + 1;
509:     n5 = rank + 1;
510:     n8 = rank + m + 1; if (n8 >= m*n) n8 = -1;
511:   } else {
512:     n2 = -1; n5 = -1; n8 = -1;
513:   }
514:   if (rank % m) {
515:     n3 = rank - 1;
516:     n6 = n3 + m; if (n6 >= m*n) n6 = -1;
517:   } else {
518:     n3 = -1; n6 = -1;
519:   }
520:   n7 = rank + m; if (n7 >= m*n) n7 = -1;

522:   if (bx == DM_BOUNDARY_PERIODIC && by == DM_BOUNDARY_PERIODIC) {
523:     /* Modify for Periodic Cases */
524:     /* Handle all four corners */
525:     if ((n6 < 0) && (n7 < 0) && (n3 < 0)) n6 = m-1;
526:     if ((n8 < 0) && (n7 < 0) && (n5 < 0)) n8 = 0;
527:     if ((n2 < 0) && (n5 < 0) && (n1 < 0)) n2 = size-m;
528:     if ((n0 < 0) && (n3 < 0) && (n1 < 0)) n0 = size-1;

530:     /* Handle Top and Bottom Sides */
531:     if (n1 < 0) n1 = rank + m * (n-1);
532:     if (n7 < 0) n7 = rank - m * (n-1);
533:     if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
534:     if ((n3 >= 0) && (n6 < 0)) n6 = (rank%m)-1;
535:     if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
536:     if ((n5 >= 0) && (n8 < 0)) n8 = (rank%m)+1;

538:     /* Handle Left and Right Sides */
539:     if (n3 < 0) n3 = rank + (m-1);
540:     if (n5 < 0) n5 = rank - (m-1);
541:     if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
542:     if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
543:     if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
544:     if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
545:   } else if (by == DM_BOUNDARY_PERIODIC) {  /* Handle Top and Bottom Sides */
546:     if (n1 < 0) n1 = rank + m * (n-1);
547:     if (n7 < 0) n7 = rank - m * (n-1);
548:     if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
549:     if ((n3 >= 0) && (n6 < 0)) n6 = (rank%m)-1;
550:     if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
551:     if ((n5 >= 0) && (n8 < 0)) n8 = (rank%m)+1;
552:   } else if (bx == DM_BOUNDARY_PERIODIC) { /* Handle Left and Right Sides */
553:     if (n3 < 0) n3 = rank + (m-1);
554:     if (n5 < 0) n5 = rank - (m-1);
555:     if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
556:     if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
557:     if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
558:     if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
559:   }

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

563:   dd->neighbors[0] = n0;
564:   dd->neighbors[1] = n1;
565:   dd->neighbors[2] = n2;
566:   dd->neighbors[3] = n3;
567:   dd->neighbors[4] = rank;
568:   dd->neighbors[5] = n5;
569:   dd->neighbors[6] = n6;
570:   dd->neighbors[7] = n7;
571:   dd->neighbors[8] = n8;

573:   if (stencil_type == DMDA_STENCIL_STAR) {
574:     /* save corner processor numbers */
575:     sn0 = n0; sn2 = n2; sn6 = n6; sn8 = n8;
576:     n0  = n2 = n6 = n8 = -1;
577:   }

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

581:   nn = 0;
582:   xbase = bases[rank];
583:   for (i=1; i<=s_y; i++) {
584:     if (n0 >= 0) { /* left below */
585:       x_t = lx[n0 % m];
586:       y_t = ly[(n0/m)];
587:       s_t = bases[n0] + x_t*y_t - (s_y-i)*x_t - s_x;
588:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
589:     }

591:     if (n1 >= 0) { /* directly below */
592:       x_t = x;
593:       y_t = ly[(n1/m)];
594:       s_t = bases[n1] + x_t*y_t - (s_y+1-i)*x_t;
595:       for (j=0; j<x_t; j++) idx[nn++] = s_t++;
596:     } else if (by == DM_BOUNDARY_MIRROR) {
597:       for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(s_y - i + 1)  + j;
598:     }

600:     if (n2 >= 0) { /* right below */
601:       x_t = lx[n2 % m];
602:       y_t = ly[(n2/m)];
603:       s_t = bases[n2] + x_t*y_t - (s_y+1-i)*x_t;
604:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
605:     }
606:   }

608:   for (i=0; i<y; i++) {
609:     if (n3 >= 0) { /* directly left */
610:       x_t = lx[n3 % m];
611:       /* y_t = y; */
612:       s_t = bases[n3] + (i+1)*x_t - s_x;
613:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
614:     } else if (bx == DM_BOUNDARY_MIRROR) {
615:       for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*i + s_x - j;
616:     }

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

620:     if (n5 >= 0) { /* directly right */
621:       x_t = lx[n5 % m];
622:       /* y_t = y; */
623:       s_t = bases[n5] + (i)*x_t;
624:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
625:     } else if (bx == DM_BOUNDARY_MIRROR) {
626:       for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*(i + 1) - 2 - j;
627:     }
628:   }

630:   for (i=1; i<=s_y; i++) {
631:     if (n6 >= 0) { /* left above */
632:       x_t = lx[n6 % m];
633:       /* y_t = ly[(n6/m)]; */
634:       s_t = bases[n6] + (i)*x_t - s_x;
635:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
636:     }

638:     if (n7 >= 0) { /* directly above */
639:       x_t = x;
640:       /* y_t = ly[(n7/m)]; */
641:       s_t = bases[n7] + (i-1)*x_t;
642:       for (j=0; j<x_t; j++) idx[nn++] = s_t++;
643:     } else if (by == DM_BOUNDARY_MIRROR) {
644:       for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(y - i - 1)  + j;
645:     }

647:     if (n8 >= 0) { /* right above */
648:       x_t = lx[n8 % m];
649:       /* y_t = ly[(n8/m)]; */
650:       s_t = bases[n8] + (i-1)*x_t;
651:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
652:     }
653:   }

655:   ISCreateBlock(comm,dof,nn,idx,PETSC_USE_POINTER,&from);
656:   VecScatterCreate(global,from,local,to,&gtol);
657:   PetscLogObjectParent((PetscObject)da,(PetscObject)gtol);
658:   ISDestroy(&to);
659:   ISDestroy(&from);

661:   if (stencil_type == DMDA_STENCIL_STAR) {
662:     n0 = sn0; n2 = sn2; n6 = sn6; n8 = sn8;
663:   }

665:   if (((stencil_type == DMDA_STENCIL_STAR)  ||
666:        (bx && bx != DM_BOUNDARY_PERIODIC) ||
667:        (by && by != DM_BOUNDARY_PERIODIC))) {
668:     /*
669:         Recompute the local to global mappings, this time keeping the
670:       information about the cross corner processor numbers and any ghosted
671:       but not periodic indices.
672:     */
673:     nn    = 0;
674:     xbase = bases[rank];
675:     for (i=1; i<=s_y; i++) {
676:       if (n0 >= 0) { /* left below */
677:         x_t = lx[n0 % m];
678:         y_t = ly[(n0/m)];
679:         s_t = bases[n0] + x_t*y_t - (s_y-i)*x_t - s_x;
680:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
681:       } else if (xs-Xs > 0 && ys-Ys > 0) {
682:         for (j=0; j<s_x; j++) idx[nn++] = -1;
683:       }
684:       if (n1 >= 0) { /* directly below */
685:         x_t = x;
686:         y_t = ly[(n1/m)];
687:         s_t = bases[n1] + x_t*y_t - (s_y+1-i)*x_t;
688:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
689:       } else if (ys-Ys > 0) {
690:         if (by == DM_BOUNDARY_MIRROR) {
691:           for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(s_y - i + 1)  + j;
692:         } else {
693:           for (j=0; j<x; j++) idx[nn++] = -1;
694:         }
695:       }
696:       if (n2 >= 0) { /* right below */
697:         x_t = lx[n2 % m];
698:         y_t = ly[(n2/m)];
699:         s_t = bases[n2] + x_t*y_t - (s_y+1-i)*x_t;
700:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
701:       } else if (Xe-xe> 0 && ys-Ys > 0) {
702:         for (j=0; j<s_x; j++) idx[nn++] = -1;
703:       }
704:     }

706:     for (i=0; i<y; i++) {
707:       if (n3 >= 0) { /* directly left */
708:         x_t = lx[n3 % m];
709:         /* y_t = y; */
710:         s_t = bases[n3] + (i+1)*x_t - s_x;
711:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
712:       } else if (xs-Xs > 0) {
713:         if (bx == DM_BOUNDARY_MIRROR) {
714:           for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*i + s_x - j;
715:         } else {
716:           for (j=0; j<s_x; j++) idx[nn++] = -1;
717:         }
718:       }

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

722:       if (n5 >= 0) { /* directly right */
723:         x_t = lx[n5 % m];
724:         /* y_t = y; */
725:         s_t = bases[n5] + (i)*x_t;
726:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
727:       } else if (Xe-xe > 0) {
728:         if (bx == DM_BOUNDARY_MIRROR) {
729:           for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*(i + 1) - 2 - j;
730:         } else {
731:           for (j=0; j<s_x; j++) idx[nn++] = -1;
732:         }
733:       }
734:     }

736:     for (i=1; i<=s_y; i++) {
737:       if (n6 >= 0) { /* left above */
738:         x_t = lx[n6 % m];
739:         /* y_t = ly[(n6/m)]; */
740:         s_t = bases[n6] + (i)*x_t - s_x;
741:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
742:       } else if (xs-Xs > 0 && Ye-ye > 0) {
743:         for (j=0; j<s_x; j++) idx[nn++] = -1;
744:       }
745:       if (n7 >= 0) { /* directly above */
746:         x_t = x;
747:         /* y_t = ly[(n7/m)]; */
748:         s_t = bases[n7] + (i-1)*x_t;
749:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
750:       } else if (Ye-ye > 0) {
751:         if (by == DM_BOUNDARY_MIRROR) {
752:           for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(y - i - 1)  + j;
753:         } else {
754:           for (j=0; j<x; j++) idx[nn++] = -1;
755:         }
756:       }
757:       if (n8 >= 0) { /* right above */
758:         x_t = lx[n8 % m];
759:         /* y_t = ly[(n8/m)]; */
760:         s_t = bases[n8] + (i-1)*x_t;
761:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
762:       } else if (Xe-xe > 0 && Ye-ye > 0) {
763:         for (j=0; j<s_x; j++) idx[nn++] = -1;
764:       }
765:     }
766:   }
767:   /*
768:      Set the local to global ordering in the global vector, this allows use
769:      of VecSetValuesLocal().
770:   */
771:   ISLocalToGlobalMappingCreate(comm,dof,nn,idx,PETSC_OWN_POINTER,&da->ltogmap);
772:   PetscLogObjectParent((PetscObject)da,(PetscObject)da->ltogmap);

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

780:   VecDestroy(&local);
781:   VecDestroy(&global);

783:   dd->gtol      = gtol;
784:   dd->base      = base;
785:   da->ops->view = DMView_DA_2d;
786:   dd->ltol      = NULL;
787:   dd->ao        = NULL;
788:   return(0);
789: }

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

797:    Collective on MPI_Comm

799:    Input Parameters:
800: +  comm - MPI communicator
801: .  bx,by - type of ghost nodes the array have.
802:          Use one of DM_BOUNDARY_NONE, DM_BOUNDARY_GHOSTED, DM_BOUNDARY_PERIODIC.
803: .  stencil_type - stencil type.  Use either DMDA_STENCIL_BOX or DMDA_STENCIL_STAR.
804: .  M,N - global dimension in each direction of the array (use -M and or -N to indicate that it may be set to a different value
805:             from the command line with -da_grid_x <M> -da_grid_y <N>)
806: .  m,n - corresponding number of processors in each dimension
807:          (or PETSC_DECIDE to have calculated)
808: .  dof - number of degrees of freedom per node
809: .  s - stencil width
810: -  lx, ly - arrays containing the number of nodes in each cell along
811:            the x and y coordinates, or NULL. If non-null, these
812:            must be of length as m and n, and the corresponding
813:            m and n cannot be PETSC_DECIDE. The sum of the lx[] entries
814:            must be M, and the sum of the ly[] entries must be N.

816:    Output Parameter:
817: .  da - the resulting distributed array object

819:    Options Database Key:
820: +  -dm_view - Calls DMView() at the conclusion of DMDACreate2d()
821: .  -da_grid_x <nx> - number of grid points in x direction, if M < 0
822: .  -da_grid_y <ny> - number of grid points in y direction, if N < 0
823: .  -da_processors_x <nx> - number of processors in x direction
824: .  -da_processors_y <ny> - number of processors in y direction
825: .  -da_refine_x <rx> - refinement ratio in x direction
826: .  -da_refine_y <ry> - refinement ratio in y direction
827: -  -da_refine <n> - refine the DMDA n times before creating, if M or N < 0


830:    Level: beginner

832:    Notes:
833:    The stencil type DMDA_STENCIL_STAR with width 1 corresponds to the
834:    standard 5-pt stencil, while DMDA_STENCIL_BOX with width 1 denotes
835:    the standard 9-pt stencil.

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

841: .keywords: distributed array, create, two-dimensional

843: .seealso: DMDestroy(), DMView(), DMDACreate1d(), DMDACreate3d(), DMGlobalToLocalBegin(), DMDAGetRefinementFactor(),
844:           DMGlobalToLocalEnd(), DMLocalToGlobalBegin(), DMLocalToLocalBegin(), DMLocalToLocalEnd(), DMDASetRefinementFactor(),
845:           DMDAGetInfo(), DMCreateGlobalVector(), DMCreateLocalVector(), DMDACreateNaturalVector(), DMLoad(), DMDAGetOwnershipRanges()

847: @*/

849: PetscErrorCode  DMDACreate2d(MPI_Comm comm,DMBoundaryType bx,DMBoundaryType by,DMDAStencilType stencil_type,
850:                           PetscInt M,PetscInt N,PetscInt m,PetscInt n,PetscInt dof,PetscInt s,const PetscInt lx[],const PetscInt ly[],DM *da)
851: {

855:   DMDACreate(comm, da);
856:   DMSetDimension(*da, 2);
857:   DMDASetSizes(*da, M, N, 1);
858:   DMDASetNumProcs(*da, m, n, PETSC_DECIDE);
859:   DMDASetBoundaryType(*da, bx, by, DM_BOUNDARY_NONE);
860:   DMDASetDof(*da, dof);
861:   DMDASetStencilType(*da, stencil_type);
862:   DMDASetStencilWidth(*da, s);
863:   DMDASetOwnershipRanges(*da, lx, ly, NULL);
864:   /* This violates the behavior for other classes, but right now users expect negative dimensions to be handled this way */
865:   DMSetFromOptions(*da);
866:   DMSetUp(*da);
867:   return(0);
868: }