Actual source code: ex2.c

  1: /*$Id: ex2.c,v 1.46 2001/09/11 16:34:32 bsmith Exp $*/

  3: static char help[] = "Reads a a simple unstructured grid from a file. Partitions it,n
  4: and distributes the grid data accordinglynn";

  6: /*T
  7:    Concepts: Mat^partitioning a matrix;
  8:    Processors: n
  9: T*/

 11: /*
 12:     Updates of this example MAY be found at 
 13:        http://www.mcs.anl.gov/petsc/src/dm/ao/examples/tutorials/ex2.c

 15:     This is a very basic, even crude, example of managing an unstructured
 16:     grid in parallel.

 18:     This particular code is for a Galerkin-style finite element method. 

 20:     After the calls below, each processor will have 
 21:       1) a list of elements it "owns"; for each "owned" element it will have the global 
 22:          numbering of the three vertices; stored in gdata->ele;
 23:       2) a list of vertices it "owns". For each owned it will have the x and y 
 24:          coordinates; stored in gdata->vert

 26:     It will not have 
 27:       1) list of ghost elements (since they are not needed for traditional 
 28:          Galerkin style finite element methods). For various finite volume methods
 29:          you may need the ghost element lists, these may be generated using the 
 30:          element neighbor information given in the file database.

 32:     To compute the local element stiffness matrix and load vector, each processor
 33:     will need the vertex coordinates for all of the vertices on the locally 
 34:     "owned" elements.  This data could be obtained by doing the appropriate vector
 35:     scatter on the data stored in gdata->vert; we haven't had time to demonstrate this.

 37:     Clearly writing a complete parallel unstructured grid code with PETSc is still
 38:     a good deal of work and requires a lot of application level coding.  BUT, at least
 39:     PETSc can manage all of the nonlinear and linear solvers (including matrix assembly 
 40:     etc.), which allows the programmer to concentrate his or her efforts on managing 
 41:     the unstructured grid. The PETSc team is developing additional library objects
 42:     to help manage parallel unstructured grid computations.  Unfortunately we have 
 43:     not had time to complete these yet, so the application programmer still must
 44:     manage much of the parallel grid manipulation as indicated below.

 46: */

 48: /* 
 49:   Include "petscmat.h" so that we can use matrices.
 50:   automatically includes:
 51:      petsc.h       - base PETSc routines   petscvec.h    - vectors
 52:      petscsys.h    - system routines       petscmat.h    - matrices
 53:      petscis.h     - index sets            petscviewer.h - viewers               

 55:   Include "petscao.h" allows use of the AO (application ordering) commands,
 56:   used below for renumbering the vertex numbers after the partitioning.

 58:   Include "petscbt.h" for managing logical bit arrays that are used to 
 59:   conserve space. Note that the code does use order N bit arrays on each 
 60:   processor so is theoretically not scalable, but even with 64 million 
 61:   vertices it will only need temporarily 8 megabytes of memory for the 
 62:   bit array so one can still do very large problems with this approach, 
 63:   since the bit arrays are freed before the vectors and matrices are
 64:   created.
 65: */
 66:  #include petscmat.h
 67:  #include petscao.h
 68:  #include petscbt.h

 70: /* 
 71:     This is the user-defined grid data context 
 72: */
 73: typedef struct {
 74:   int    n_vert,n_ele;
 75:   int    mlocal_vert,mlocal_ele;
 76:   int    *ele;
 77:   PetscScalar *vert;
 78:   int    *ia,*ja;
 79:   IS     isnewproc;
 80:   int    *localvert,nlocal; /* used to stash temporarily old global vertex number of new vertex */
 81: } GridData;

 83: /*
 84:    Variables on all processors:
 85:       n_vert          - total number of vertices
 86:       mlocal_vert     - number of vertices on this processor
 87:       vert            - x,y coordinates of local vertices

 89:       n_ele           - total number of elements
 90:       mlocal_ele      - number of elements on this processor
 91:       ele             - vertices of elements on this processor

 93:       ia, ja          - adjacency graph of elements (for partitioning)
 94:     
 95:    Variables on processor 0 during data reading from file:
 96:       mmlocal_vert[i] - number of vertices on each processor
 97:       tmpvert         - x,y coordinates of vertices on any processor (as read in)

 99:       mmlocal_ele[i]  - number of elements on each processor

101:       tmpia, tmpja    - adjacency graph of elements for other processors

103:    Notes:
104:    The code below has a great deal of IO (print statements). This is to allow one to track 
105:    the renumbering and movement of data among processors. In an actual 
106:    production run, IO of this type would be deactivated.

108:    To use the ParMETIS partitioner run with the option -mat_partitioning_type parmetis
109:    otherwise it defaults to the initial element partitioning induced when the data 
110:    is read in.

112:    To understand the parallel performance of this type of code, it is important
113:    to profile the time spent in various events in the code; running with the
114:    option -log_summary will indicate how much time is spent in the routines 
115:    below.   Of course, for very small problems, such as the sample grid used here,
116:    the profiling results are meaningless.
117: */

119: extern int DataRead(GridData *);
120: extern int DataPartitionElements(GridData *);
121: extern int DataMoveElements(GridData *);
122: extern int DataPartitionVertices(GridData *);
123: extern int DataMoveVertices(GridData *);
124: extern int DataDestroy(GridData *);

126: int main(int argc,char **args)
127: {
128:   int          ierr;
129:   int          READ_EVENT,PARTITION_ELEMENT_EVENT,MOVE_ELEMENT_EVENT;
130:   int          PARTITION_VERTEX_EVENT,MOVE_VERTEX_EVENT;
131:   GridData     gdata;

133:   PetscInitialize(&argc,&args,(char *)0,help);

135:   PetscLogEventRegister(&READ_EVENT,             "Read Data",0);
136:   PetscLogEventRegister(&PARTITION_ELEMENT_EVENT,"Partition elemen",0);
137:   PetscLogEventRegister(&MOVE_ELEMENT_EVENT,     "Move elements",0);
138:   PetscLogEventRegister(&PARTITION_VERTEX_EVENT, "Partition vertic",0);
139:   PetscLogEventRegister(&MOVE_VERTEX_EVENT,      "Move vertices",0);

141:   PetscLogEventBegin(READ_EVENT,0,0,0,0);
142:   DataRead(&gdata);
143:   PetscLogEventEnd(READ_EVENT,0,0,0,0);
144:   PetscLogEventBegin(PARTITION_ELEMENT_EVENT,0,0,0,0);
145:   DataPartitionElements(&gdata);
146:   PetscLogEventEnd(PARTITION_ELEMENT_EVENT,0,0,0,0);
147:   PetscLogEventBegin(MOVE_ELEMENT_EVENT,0,0,0,0);
148:   DataMoveElements(&gdata);
149:   PetscLogEventEnd(MOVE_ELEMENT_EVENT,0,0,0,0);
150:   PetscLogEventBegin(PARTITION_VERTEX_EVENT,0,0,0,0);
151:   DataPartitionVertices(&gdata);
152:   PetscLogEventEnd(PARTITION_VERTEX_EVENT,0,0,0,0);
153:   PetscLogEventBegin(MOVE_VERTEX_EVENT,0,0,0,0);
154:   DataMoveVertices(&gdata);
155:   PetscLogEventEnd(MOVE_VERTEX_EVENT,0,0,0,0);
156:   DataDestroy(&gdata);

158:   PetscFinalize();
159:   return 0;
160: }


163: /*
164:      Reads in the grid data from a file; each processor is naively 
165:   assigned a continuous chunk of vertex and element data. Later the data
166:   will be partitioned and moved to the appropriate processor.
167: */
168: int DataRead(GridData *gdata)
169: {
170:   int          rank,size,n_vert,*mmlocal_vert,mlocal_vert,i,*ia,*ja,cnt,j;
171:   int          mlocal_ele,*mmlocal_ele,*ele,*tmpele,n_ele,net,a1,a2,a3;
172:   int          *iatmp,*jatmp,ierr;
173:   char         msg[128];
174:   PetscScalar  *vert,*tmpvert;
175:   MPI_Status   status;

178:   /*
179:      Processor 0 opens the file, reads in chunks of data and sends a portion off to
180:    each other processor.

182:      Note: For a truely scalable IO portion of the code, one would store
183:    the grid data in a binary file and use MPI-IO commands to have each 
184:    processor read in the parts that it needs. However in most circumstances
185:    involving up to a say a million nodes and 100 processors this approach 
186:    here is fine.
187:   */
188:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
189:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);

191:   if (!rank) {
192:     FILE *fd;
193:     fd = fopen("usgdata","r"); if (!fd) SETERRQ(1,"Cannot open grid file");

195:     /* read in number of vertices */
196:     fgets(msg,128,fd);
197:     printf("File msg:%s",msg);
198:     fscanf(fd,"Number Vertices = %dn",&n_vert);
199:     printf("Number of grid vertices %dn",n_vert);

201:     /* broadcast number of vertices to all processors */
202:     MPI_Bcast(&n_vert,1,MPI_INT,0,PETSC_COMM_WORLD);
203:     mlocal_vert  = n_vert/size + ((n_vert % size) > 0);

205:     /* 
206:       allocate enough room for the first processor to keep track of how many 
207:       vertices are assigned to each processor. Splitting vertices equally amoung
208:       all processors.
209:     */
210:     PetscMalloc(size*sizeof(int),&mmlocal_vert);
211:     for (i=0; i<size; i++) {
212:       mmlocal_vert[i] = n_vert/size + ((n_vert % size) > i);
213:       printf("Processor %d assigned %d verticesn",i,mmlocal_vert[i]);
214:     }

216:     /*
217:        Read in vertices assigned to first processor
218:     */
219:     PetscMalloc(2*mmlocal_vert[0]*sizeof(PetscScalar),&vert);
220:     printf("Vertices assigned to processor 0n");
221:     for (i=0; i<mlocal_vert; i++) {
222:       fscanf(fd,"%d %lf %lfn",&cnt,vert+2*i,vert+2*i+1);
223:       printf("%d %g %gn",cnt,PetscRealPart(vert[2*i]),PetscRealPart(vert[2*i+1]));
224:     }

226:     /* 
227:        Read in vertices for all the other processors 
228:     */
229:     PetscMalloc(2*mmlocal_vert[0]*sizeof(PetscScalar),&tmpvert);
230:     for (j=1; j<size; j++) {
231:       printf("Vertices assigned to processor %dn",j);
232:       for (i=0; i<mmlocal_vert[j]; i++) {
233:         fscanf(fd,"%d %lf %lfn",&cnt,tmpvert+2*i,tmpvert+2*i+1);
234:         printf("%d %g %gn",cnt,tmpvert[2*i],tmpvert[2*i+1]);
235:       }
236:       MPI_Send(tmpvert,2*mmlocal_vert[j],MPIU_SCALAR,j,0,PETSC_COMM_WORLD);
237:     }
238:     PetscFree(tmpvert);
239:     PetscFree(mmlocal_vert);

241:     fscanf(fd,"Number Elements = %dn",&n_ele);
242:     printf("Number of grid elements %dn",n_ele);

244:     /* 
245:        Broadcast number of elements to all processors
246:     */
247:     MPI_Bcast(&n_ele,1,MPI_INT,0,PETSC_COMM_WORLD);
248:     mlocal_ele  = n_ele/size + ((n_ele % size) > 0);

250:     /* 
251:       Allocate enough room for the first processor to keep track of how many 
252:       elements are assigned to each processor.
253:     */
254:     PetscMalloc(size*sizeof(int),&mmlocal_ele);
255:     for (i=0; i<size; i++) {
256:       mmlocal_ele[i] = n_ele/size + ((n_ele % size) > i);
257:       printf("Processor %d assigned %d elementsn",i,mmlocal_ele[i]);
258:     }
259: 
260:     /*
261:         read in element information for the first processor
262:     */
263:     PetscMalloc(3*mmlocal_ele[0]*sizeof(int),&ele);
264:     printf("Elements assigned to processor 0n");
265:     for (i=0; i<mlocal_ele; i++) {
266:       fscanf(fd,"%d %d %d %dn",&cnt,ele+3*i,ele+3*i+1,ele+3*i+2);
267:       printf("%d %d %d %dn",cnt,ele[3*i],ele[3*i+1],ele[3*i+2]);
268:     }

270:     /* 
271:        Read in elements for all the other processors 
272:     */
273:     PetscMalloc(3*mmlocal_ele[0]*sizeof(int),&tmpele);
274:     for (j=1; j<size; j++) {
275:       printf("Elements assigned to processor %dn",j);
276:       for (i=0; i<mmlocal_ele[j]; i++) {
277:         fscanf(fd,"%d %d %d %dn",&cnt,tmpele+3*i,tmpele+3*i+1,tmpele+3*i+2);
278:         printf("%d %d %d %dn",cnt,tmpele[3*i],tmpele[3*i+1],tmpele[3*i+2]);
279:       }
280:       MPI_Send(tmpele,3*mmlocal_ele[j],MPI_INT,j,0,PETSC_COMM_WORLD);
281:     }
282:     PetscFree(tmpele);

284:     /* 
285:          Read in element neighbors for processor 0 
286:          We don't know how many spaces in ja[] to allocate so we allocate 
287:        3*the number of local elements, this is the maximum it could be
288:     */
289:     PetscMalloc((mlocal_ele+1)*sizeof(int),&ia);
290:     PetscMalloc((3*mlocal_ele+1)*sizeof(int),&ja);
291:     net   = 0;
292:     ia[0] = 0;
293:     printf("Element neighbors on processor 0n");
294:     fgets(msg,128,fd);
295:     for (i=0; i<mlocal_ele; i++) {
296:       fscanf(fd,"%d %d %d %dn",&cnt,&a1,&a2,&a3);
297:       printf("%d %d %d %dn",cnt,a1,a2,a3);
298:       if (a1 >= 0) {ja[net++] = a1;}
299:       if (a2 >= 0) {ja[net++] = a2;}
300:       if (a3 >= 0) {ja[net++] = a3;}
301:       ia[i+1] = net;
302:     }

304:     printf("ia values for processor 0n");
305:     for (i=0; i<mlocal_ele+1; i++) {
306:       printf("%d ",ia[i]);
307:     }
308:     printf("n");
309:     printf("ja values for processor 0n");
310:     for (i=0; i<ia[mlocal_ele]; i++) {
311:       printf("%d ",ja[i]);
312:     }
313:     printf("n");

315:     /*
316:        Read in element neighbor information for all other processors
317:     */
318:     PetscMalloc((mlocal_ele+1)*sizeof(int),&iatmp);
319:     PetscMalloc((3*mlocal_ele+1)*sizeof(int),&jatmp);
320:     for (j=1; j<size; j++) {
321:       net   = 0;
322:       iatmp[0] = 0;
323:       printf("Element neighbors on processor %dn",j);
324:       for (i=0; i<mmlocal_ele[j]; i++) {
325:         fscanf(fd,"%d %d %d %dn",&cnt,&a1,&a2,&a3);
326:         printf("%d %d %d %dn",cnt,a1,a2,a3);
327:         if (a1 >= 0) {jatmp[net++] = a1;}
328:         if (a2 >= 0) {jatmp[net++] = a2;}
329:         if (a3 >= 0) {jatmp[net++] = a3;}
330:         iatmp[i+1] = net;
331:       }

333:       printf("ia values for processor %dn",j);
334:       for (i=0; i<mmlocal_ele[j]+1; i++) {
335:         printf("%d ",iatmp[i]);
336:       }
337:       printf("n");
338:       printf("ja values for processor %dn",j);
339:       for (i=0; i<iatmp[mmlocal_ele[j]]; i++) {
340:         printf("%d ",jatmp[i]);
341:       }
342:       printf("n");

344:       /* send graph off to appropriate processor */
345:       MPI_Send(iatmp,mmlocal_ele[j]+1,MPI_INT,j,0,PETSC_COMM_WORLD);
346:       MPI_Send(jatmp,iatmp[mmlocal_ele[j]],MPI_INT,j,0,PETSC_COMM_WORLD);
347:     }
348:     PetscFree(iatmp);
349:     PetscFree(jatmp);
350:     PetscFree(mmlocal_ele);

352:     fclose(fd);
353:   } else {
354:     /*
355:         We are not the zeroth processor so we do not open the file
356:       rather we wait for processor 0 to send us our data.
357:     */

359:     /* receive total number of vertices */
360:     MPI_Bcast(&n_vert,1,MPI_INT,0,PETSC_COMM_WORLD);
361:     mlocal_vert = n_vert/size + ((n_vert % size) > rank);

363:     /* receive vertices */
364:     PetscMalloc(2*(mlocal_vert+1)*sizeof(PetscScalar),&vert);
365:     MPI_Recv(vert,2*mlocal_vert,MPIU_SCALAR,0,0,PETSC_COMM_WORLD,&status);

367:     /* receive total number of elements */
368:     MPI_Bcast(&n_ele,1,MPI_INT,0,PETSC_COMM_WORLD);
369:     mlocal_ele = n_ele/size + ((n_ele % size) > rank);

371:     /* receive elements */
372:     PetscMalloc(3*(mlocal_ele+1)*sizeof(int),&ele);
373:     MPI_Recv(ele,3*mlocal_ele,MPI_INT,0,0,PETSC_COMM_WORLD,&status);

375:     /* receive element adjacency graph */
376:     PetscMalloc((mlocal_ele+1)*sizeof(int),&ia);
377:     MPI_Recv(ia,mlocal_ele+1,MPI_INT,0,0,PETSC_COMM_WORLD,&status);

379:     PetscMalloc((ia[mlocal_ele]+1)*sizeof(int),&ja);
380:     MPI_Recv(ja,ia[mlocal_ele],MPI_INT,0,0,PETSC_COMM_WORLD,&status);
381:   }

383:   gdata->n_vert      = n_vert;
384:   gdata->n_ele       = n_ele;
385:   gdata->mlocal_vert = mlocal_vert;
386:   gdata->mlocal_ele  = mlocal_ele;
387:   gdata->ele         = ele;
388:   gdata->vert        = vert;

390:   gdata->ia          = ia;
391:   gdata->ja          = ja;

393:   return(0);
394: }


397: /*
398:          Given the grid data spread across the processors, determines a
399:    new partitioning of the CELLS (elements) to reduce the number of cut edges between
400:    cells (elements).
401: */
402: int DataPartitionElements(GridData *gdata)
403: {
404:   Mat             Adj;                /* adjacency matrix */
405:   int             *ia,*ja;
406:   int             mlocal_ele,n_ele,ierr;
407:   MatPartitioning part;
408:   IS              isnewproc;

411:   n_ele       = gdata->n_ele;
412:   mlocal_ele  = gdata->mlocal_ele;

414:   ia          = gdata->ia;
415:   ja          = gdata->ja;

417:   /*
418:       Create the adjacency graph matrix
419:   */
420:   MatCreateMPIAdj(PETSC_COMM_WORLD,mlocal_ele,n_ele,ia,ja,PETSC_NULL,&Adj);

422:   /*
423:       Create the partioning object
424:   */
425:   MatPartitioningCreate(PETSC_COMM_WORLD,&part);
426:   MatPartitioningSetAdjacency(part,Adj);
427:   MatPartitioningSetFromOptions(part);
428:   MatPartitioningApply(part,&isnewproc);
429:   MatPartitioningDestroy(part);

431:   /*
432:        isnewproc - indicates for each local element the new processor it is assigned to
433:   */
434:   PetscPrintf(PETSC_COMM_WORLD,"New processor assignment for each elementn");
435:   ISView(isnewproc,PETSC_VIEWER_STDOUT_WORLD);
436:   gdata->isnewproc = isnewproc;

438:   /*
439:       Free the adjacency graph data structures
440:   */
441:   MatDestroy(Adj);


444:   return(0);
445: }

447: /*
448:       Moves the grid element data to be on the correct processor for the new
449:    element partitioning.
450: */
451: int DataMoveElements(GridData *gdata)
452: {
453:   int          ierr,*counts,rank,size,i,*idx;
454:   Vec          vele,veleold;
455:   PetscScalar  *array;
456:   IS           isscat,isnum;
457:   VecScatter   vecscat;


461:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
462:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);

464:   /* 
465:       Determine how many elements are assigned to each processor 
466:   */
467:   PetscMalloc(size*sizeof(int),&counts);
468:   ierr   = ISPartitioningCount(gdata->isnewproc,counts);

470:   /* 
471:      Create a vector to contain the newly ordered element information 

473:      Note: we use vectors to communicate this data since we can use the powerful
474:      VecScatter routines to get the data to the correct location. This is a little
475:      wasteful since the vectors hold double precision numbers instead of integers,
476:      but since this is just a setup phase in the entire numerical computation that 
477:      is only called once it is not a measureable performance bottleneck.
478:   */
479:   VecCreate(PETSC_COMM_WORLD,&vele);
480:   VecSetSizes(vele,3*counts[rank],PETSC_DECIDE);
481:   VecSetFromOptions(vele);

483:   /* 
484:       Create an index set from the isnewproc index set to indicate the mapping TO 
485:   */
486:   ISPartitioningToNumbering(gdata->isnewproc,&isnum);
487:   ISDestroy(gdata->isnewproc);
488:   /* 
489:       There are three data items per cell (element), the integer vertex numbers of its three 
490:     coordinates (we convert to double to use the scatter) (one can think 
491:     of the vectors of having a block size of 3 and there is one index in idx[] for each block)
492:   */
493:   ISGetIndices(isnum,&idx);
494:   for (i=0; i<gdata->mlocal_ele; i++) {
495:     idx[i] *= 3;
496:   }
497:   ISCreateBlock(PETSC_COMM_WORLD,3,gdata->mlocal_ele,idx,&isscat);
498:   ISRestoreIndices(isnum,&idx);
499:   ISDestroy(isnum);

501:   /* 
502:      Create a vector to contain the old ordered element information
503:   */
504:   VecCreateSeq(PETSC_COMM_SELF,3*gdata->mlocal_ele,&veleold);
505:   VecGetArray(veleold,&array);
506:   for (i=0; i<3*gdata->mlocal_ele; i++) {
507:     array[i] = gdata->ele[i];
508:   }
509:   VecRestoreArray(veleold,&array);
510: 
511:   /* 
512:      Scatter the element vertex information to the correct processor
513:   */
514:   VecScatterCreate(veleold,PETSC_NULL,vele,isscat,&vecscat);
515:   ISDestroy(isscat);
516:   VecScatterBegin(veleold,vele,INSERT_VALUES,SCATTER_FORWARD,vecscat);
517:   VecScatterEnd(veleold,vele,INSERT_VALUES,SCATTER_FORWARD,vecscat);
518:   VecScatterDestroy(vecscat);
519:   VecDestroy(veleold);

521:   /* 
522:      Put the element vertex data into a new allocation of the gdata->ele 
523:   */
524:   PetscFree(gdata->ele);
525:   gdata->mlocal_ele = counts[rank];
526:   PetscFree(counts);
527:   PetscMalloc(3*gdata->mlocal_ele*sizeof(int),&gdata->ele);
528:   VecGetArray(vele,&array);
529:   for (i=0; i<3*gdata->mlocal_ele; i++) {
530:     gdata->ele[i] = (int)PetscRealPart(array[i]);
531:   }
532:   VecRestoreArray(vele,&array);
533:   VecDestroy(vele);

535:   PetscPrintf(PETSC_COMM_WORLD,"Old vertex numbering in new element orderingn");
536:   PetscSynchronizedPrintf(PETSC_COMM_WORLD,"Processor %dn",rank);
537:   for (i=0; i<gdata->mlocal_ele; i++) {
538:     PetscSynchronizedPrintf(PETSC_COMM_WORLD,"%d %d %d %dn",i,gdata->ele[3*i],gdata->ele[3*i+1],
539:                             gdata->ele[3*i+2]);
540:   }
541:   PetscSynchronizedFlush(PETSC_COMM_WORLD);

543:   return(0);
544: }

546: /*
547:          Given the newly partitioned cells (elements), this routine partitions the 
548:      vertices.

550:      The code is not completely scalable since it requires
551:      1) O(n_vert) bits per processor memory
552:      2) uses O(size) stages of communication; each of size O(n_vert) bits
553:      3) it is sequential (each processor marks it vertices ONLY after all processors
554:         to the left have marked theirs.
555:      4) the amount of work on the last processor is O(n_vert)

557:      The algorithm also does not take advantage of vertices that are "interior" to a
558:      processors elements (that is; is not contained in any element on another processor).
559:      A better algorithm would first have all processors determine "interior" vertices and
560:      make sure they are retained on that processor before listing "boundary" vertices.

562:      The algorithm is:
563:      a) each processor waits for a message from the left containing mask of all marked vertices
564:      b) it loops over all local elements, generating a list of vertices it will 
565:         claim (not claiming ones that have already been marked in the bit-array)
566:         it claims at most n_vert/size vertices
567:      c) it sends to the right the mask

569:      This is a quick-and-dirty implementation; it should work fine for many problems,
570:      but will need to be replaced once profiling shows that it takes a large amount of
571:      time. An advantage is it requires no searching or sorting.
572:      
573: */
574: int DataPartitionVertices(GridData *gdata)
575: {
576:   int        n_vert = gdata->n_vert,ierr,*localvert;
577:   int        rank,size,mlocal_ele = gdata->mlocal_ele,*ele = gdata->ele,i,j,nlocal = 0,nmax;
578:   PetscBT    mask;
579:   MPI_Status status;

582:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
583:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

585:   /*
586:       Allocated space to store bit-array indicting vertices marked
587:   */
588:   PetscBTCreate(n_vert,mask);

590:   /*
591:      All processors except last can have a maximum of n_vert/size vertices assigned
592:      (because last processor needs to handle any leftovers)
593:   */
594:   nmax = n_vert/size;
595:   if (rank == size-1) {
596:     nmax = n_vert;
597:   }

599:   /* 
600:      Receive list of marked vertices from left 
601:   */
602:   if (rank) {
603:     MPI_Recv(mask,PetscBTLength(n_vert),MPI_CHAR,rank-1,0,PETSC_COMM_WORLD,&status);
604:   }

606:   if (rank == size-1) {
607:     /* last processor gets all the rest */
608:     for (i=0; i<n_vert; i++) {
609:       if (!PetscBTLookup(mask,i)) {
610:         nlocal++;
611:       }
612:     }
613:     nmax = nlocal;
614:   }

616:   /* 
617:      Now we know how many are local, allocated enough space for them and mark them 
618:   */
619:   PetscMalloc((nmax+1)*sizeof(int),&localvert);

621:   /* generate local list and fill in mask */
622:   nlocal = 0;
623:   if (rank < size-1) {
624:     /* count my vertices */
625:     for (i=0; i<mlocal_ele; i++) {
626:       for (j=0; j<3; j++) {
627:         if (!PetscBTLookupSet(mask,ele[3*i+j])) {
628:           localvert[nlocal++] = ele[3*i+j];
629:           if (nlocal >= nmax) goto foundenough2;
630:         }
631:       }
632:     }
633:     foundenough2:;
634:   } else {
635:     /* last processor gets all the rest */
636:     for (i=0; i<n_vert; i++) {
637:       if (!PetscBTLookup(mask,i)) {
638:         localvert[nlocal++] = i;
639:       }
640:     }
641:   }
642:   /* 
643:       Send bit mask on to next processor
644:   */
645:   if (rank < size-1) {
646:     MPI_Send(mask,PetscBTLength(n_vert),MPI_CHAR,rank+1,0,PETSC_COMM_WORLD);
647:   }
648:   PetscBTDestroy(mask);

650:   gdata->localvert = localvert;
651:   gdata->nlocal    = nlocal;

653:   /* print lists of owned vertices */
654:   PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d] Number vertices assigned %dn",rank,nlocal);
655:   PetscSynchronizedFlush(PETSC_COMM_WORLD);
656:   PetscIntView(nlocal,localvert,PETSC_VIEWER_STDOUT_WORLD);

658:   return(0);
659: }

661: /*
662:      Given the partitioning of the vertices; renumbers the element vertex lists for the 
663:      new vertex numbering and moves the vertex coordinate values to the correct processor
664: */
665: int DataMoveVertices(GridData *gdata)
666: {
667:   AO           ao;
668:   int          ierr,rank,i;
669:   Vec          vert,overt;
670:   VecScatter   vecscat;
671:   IS           isscat;
672:   PetscScalar  *avert;


676:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);

678:   /* ---------------------------------------------------------------------
679:       Create a global reodering of the vertex numbers
680:   */
681:   AOCreateBasic(PETSC_COMM_WORLD,gdata->nlocal,gdata->localvert,PETSC_NULL,&ao);

683:   /*
684:      Change the element vertex information to the new vertex numbering
685:   */
686:   AOApplicationToPetsc(ao,3*gdata->mlocal_ele,gdata->ele);
687:   PetscPrintf(PETSC_COMM_WORLD,"New vertex numbering in new element orderingn");
688:   PetscSynchronizedPrintf(PETSC_COMM_WORLD,"Processor %dn",rank);
689:   for (i=0; i<gdata->mlocal_ele; i++) {
690:     PetscSynchronizedPrintf(PETSC_COMM_WORLD,"%d %d %d %dn",i,gdata->ele[3*i],gdata->ele[3*i+1],
691:                             gdata->ele[3*i+2]);
692:   }
693:   PetscSynchronizedFlush(PETSC_COMM_WORLD);

695:   /*
696:      Destroy the AO that is no longer needed
697:   */
698:   AODestroy(ao);

700:   /* --------------------------------------------------------------------
701:       Finally ship the vertex coordinate information to its owning process
702:       note, we do this in a way very similar to what was done for the element info
703:   */
704:   /* create a vector to contain the newly ordered vertex information */
705:   VecCreateSeq(PETSC_COMM_SELF,2*gdata->nlocal,&vert);

707:   /* create a vector to contain the old ordered vertex information */
708:   VecCreateMPIWithArray(PETSC_COMM_WORLD,2*gdata->mlocal_vert,PETSC_DECIDE,gdata->vert,
709:                                &overt);

711:   /* 
712:       There are two data items per vertex, the x and y coordinates (i.e. one can think 
713:     of the vectors of having a block size of 2 and there is one index in localvert[] for each block)
714:   */
715:   for (i=0; i<gdata->nlocal; i++) gdata->localvert[i] *= 2;
716:   ISCreateBlock(PETSC_COMM_WORLD,2,gdata->nlocal,gdata->localvert,&isscat);
717:   PetscFree(gdata->localvert);

719:   /* 
720:       Scatter the element vertex information to the correct processor
721:   */
722:   VecScatterCreate(overt,isscat,vert,PETSC_NULL,&vecscat);
723:   ISDestroy(isscat);
724:   VecScatterBegin(overt,vert,INSERT_VALUES,SCATTER_FORWARD,vecscat);
725:   VecScatterEnd(overt,vert,INSERT_VALUES,SCATTER_FORWARD,vecscat);
726:   VecScatterDestroy(vecscat);

728:   VecDestroy(overt);
729:   PetscFree(gdata->vert);
730: 
731:   /*
732:         Put resulting vertex information into gdata->vert array
733:   */
734:   PetscMalloc(2*gdata->nlocal*sizeof(PetscScalar),&gdata->vert);
735:   VecGetArray(vert,&avert);
736:   PetscMemcpy(gdata->vert,avert,2*gdata->nlocal*sizeof(PetscScalar));
737:   VecRestoreArray(vert,&avert);
738:   gdata->mlocal_vert = gdata->nlocal;
739:   VecDestroy(vert);

741:   PetscPrintf(PETSC_COMM_WORLD,"Vertex coordinates in new numberingn");
742:   for (i=0; i<2*gdata->mlocal_vert; i++) {
743:     PetscSynchronizedPrintf(PETSC_COMM_WORLD,"%gn",gdata->vert[i]);
744:   }
745:   PetscSynchronizedFlush(PETSC_COMM_WORLD);

747:   return(0);
748: }


751: int DataDestroy(GridData *gdata)
752: {

756:   PetscFree(gdata->ele);
757:   PetscFree(gdata->vert);
758:   return(0);
759: }