Actual source code: ex10.c

petsc-3.8.0 2017-09-26
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  2: /*
  3:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
  4:    file automatically includes:
  5:      petscsys.h       - base PETSc routines   petscvec.h - vectors
  6:      petscmat.h - matrices
  7:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
  8:      petscviewer.h - viewers               petscpc.h  - preconditioners
  9:      petscksp.h   - linear solvers
 10: */
 11: #include <petscsnes.h>
 12: #include <petscao.h>

 14: static char help[] = "An Unstructured Grid Example.\n\
 15: This example demonstrates how to solve a nonlinear system in parallel\n\
 16: with SNES for an unstructured mesh. The mesh and partitioning information\n\
 17: is read in an application defined ordering,which is later transformed\n\
 18: into another convenient ordering (called the local ordering). The local\n\
 19: ordering, apart from being efficient on cpu cycles and memory, allows\n\
 20: the use of the SPMD model of parallel programming. After partitioning\n\
 21: is done, scatters are created between local (sequential)and global\n\
 22: (distributed) vectors. Finally, we set up the nonlinear solver context\n\
 23: in the usual way as a structured grid  (see\n\
 24: petsc/src/snes/examples/tutorials/ex5.c).\n\
 25: This example also illustrates the use of parallel matrix coloring.\n\
 26: The command line options include:\n\
 27:   -vert <Nv>, where Nv is the global number of nodes\n\
 28:   -elem <Ne>, where Ne is the global number of elements\n\
 29:   -nl_par <lambda>, where lambda is the multiplier for the non linear term (u*u) term\n\
 30:   -lin_par <alpha>, where alpha is the multiplier for the linear term (u)\n\
 31:   -fd_jacobian_coloring -mat_coloring_type lf\n";

 33: /*T
 34:    Concepts: SNES^unstructured grid
 35:    Concepts: AO^application to PETSc ordering or vice versa;
 36:    Concepts: VecScatter^using vector scatter operations;
 37:    Processors: n
 38: T*/

 40: /* ------------------------------------------------------------------------

 42:    PDE Solved : L(u) + lambda*u*u + alpha*u = 0 where L(u) is the Laplacian.

 44:    The Laplacian is approximated in the following way: each edge is given a weight
 45:    of one meaning that the diagonal term will have the weight equal to the degree
 46:    of a node. The off diagonal terms will get a weight of -1.

 48:    -----------------------------------------------------------------------*/


 51: #define MAX_ELEM      500  /* Maximum number of elements */
 52: #define MAX_VERT      100  /* Maximum number of vertices */
 53: #define MAX_VERT_ELEM   3  /* Vertices per element       */

 55: /*
 56:   Application-defined context for problem specific data
 57: */
 58: typedef struct {
 59:   PetscInt   Nvglobal,Nvlocal;              /* global and local number of vertices */
 60:   PetscInt   Neglobal,Nelocal;              /* global and local number of vertices */
 61:   PetscInt   AdjM[MAX_VERT][50];            /* adjacency list of a vertex */
 62:   PetscInt   itot[MAX_VERT];                /* total number of neighbors for a vertex */
 63:   PetscInt   icv[MAX_ELEM][MAX_VERT_ELEM];  /* vertices belonging to an element */
 64:   PetscInt   v2p[MAX_VERT];                 /* processor number for a vertex */
 65:   PetscInt   *locInd,*gloInd;               /* local and global orderings for a node */
 66:   Vec        localX,localF;                 /* local solution (u) and f(u) vectors */
 67:   PetscReal  non_lin_param;                 /* nonlinear parameter for the PDE */
 68:   PetscReal  lin_param;                     /* linear parameter for the PDE */
 69:   VecScatter scatter;                       /* scatter context for the local and
 70:                                                distributed vectors */
 71: } AppCtx;

 73: /*
 74:   User-defined routines
 75: */
 76: PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);
 77: PetscErrorCode FormFunction(SNES,Vec,Vec,void*);
 78: PetscErrorCode FormInitialGuess(AppCtx*,Vec);

 80: int main(int argc,char **argv)
 81: {
 82:   SNES                   snes;                 /* SNES context */
 83:   SNESType               type = SNESNEWTONLS;  /* default nonlinear solution method */
 84:   Vec                    x,r;                  /* solution, residual vectors */
 85:   Mat                    Jac;                  /* Jacobian matrix */
 86:   AppCtx                 user;                 /* user-defined application context */
 87:   AO                     ao;                   /* Application Ordering object */
 88:   IS                     isglobal,islocal;     /* global and local index sets */
 89:   PetscMPIInt            rank,size;            /* rank of a process, number of processors */
 90:   PetscInt               rstart;               /* starting index of PETSc ordering for a processor */
 91:   PetscInt               nfails;               /* number of unsuccessful Newton steps */
 92:   PetscInt               bs = 1;               /* block size for multicomponent systems */
 93:   PetscInt               nvertices;            /* number of local plus ghost nodes of a processor */
 94:   PetscInt               *pordering;           /* PETSc ordering */
 95:   PetscInt               *vertices;            /* list of all vertices (incl. ghost ones) on a processor */
 96:   PetscInt               *verticesmask;
 97:   PetscInt               *tmp;
 98:   PetscInt               i,j,jstart,inode,nb,nbrs,Nvneighborstotal = 0;
 99:   PetscErrorCode         ierr;
100:   PetscInt               its,N;
101:   PetscScalar            *xx;
102:   char                   str[256],form[256],part_name[256];
103:   FILE                   *fptr,*fptr1;
104:   ISLocalToGlobalMapping isl2g;
105:   int                    dtmp;
106: #if defined(UNUSED_VARIABLES)
107:   PetscDraw              draw;                 /* drawing context */
108:   PetscScalar            *ff,*gg;
109:   PetscReal              tiny = 1.0e-10,zero = 0.0,one = 1.0,big = 1.0e+10;
110:   PetscInt               *tmp1,*tmp2;
111: #endif
112:   MatFDColoring          matfdcoloring = 0;
113:   PetscBool              fd_jacobian_coloring = PETSC_FALSE;

115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116:      Initialize program
117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

119:    PetscInitialize(&argc,&argv,"options.inf",help);if (ierr) return ierr;
120:   MPI_Comm_rank(MPI_COMM_WORLD,&rank);
121:   MPI_Comm_size(MPI_COMM_WORLD,&size);

123:   /* The current input file options.inf is for 2 proc run only */
124:   if (size != 2) SETERRQ(PETSC_COMM_SELF,1,"This Example currently runs on 2 procs only.");

126:   /*
127:      Initialize problem parameters
128:   */
129:   user.Nvglobal = 16;      /*Global # of vertices  */
130:   user.Neglobal = 18;      /*Global # of elements  */

132:   PetscOptionsGetInt(NULL,NULL,"-vert",&user.Nvglobal,NULL);
133:   PetscOptionsGetInt(NULL,NULL,"-elem",&user.Neglobal,NULL);

135:   user.non_lin_param = 0.06;

137:   PetscOptionsGetReal(NULL,NULL,"-nl_par",&user.non_lin_param,NULL);

139:   user.lin_param = -1.0;

141:   PetscOptionsGetReal(NULL,NULL,"-lin_par",&user.lin_param,NULL);

143:   user.Nvlocal = 0;
144:   user.Nelocal = 0;

146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147:       Read the mesh and partitioning information
148:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

150:   /*
151:      Read the mesh and partitioning information from 'adj.in'.
152:      The file format is as follows.
153:      For each line the first entry is the processor rank where the
154:      current node belongs. The second entry is the number of
155:      neighbors of a node. The rest of the line is the adjacency
156:      list of a node. Currently this file is set up to work on two
157:      processors.

159:      This is not a very good example of reading input. In the future,
160:      we will put an example that shows the style that should be
161:      used in a real application, where partitioning will be done
162:      dynamically by calling partitioning routines (at present, we have
163:      a  ready interface to ParMeTiS).
164:    */
165:   fptr = fopen("adj.in","r");
166:   if (!fptr) SETERRQ(PETSC_COMM_SELF,0,"Could not open adj.in");

168:   /*
169:      Each processor writes to the file output.<rank> where rank is the
170:      processor's rank.
171:   */
172:   sprintf(part_name,"output.%d",rank);
173:   fptr1 = fopen(part_name,"w");
174:   if (!fptr1) SETERRQ(PETSC_COMM_SELF,0,"Could no open output file");
175:   PetscMalloc1(user.Nvglobal,&user.gloInd);
176:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"Rank is %D\n",rank);
177:   for (inode = 0; inode < user.Nvglobal; inode++) {
178:     if (!fgets(str,256,fptr)) SETERRQ(PETSC_COMM_SELF,1,"fgets read failed");
179:     sscanf(str,"%d",&dtmp);user.v2p[inode] = dtmp;
180:     if (user.v2p[inode] == rank) {
181:       PetscFPrintf(PETSC_COMM_SELF,fptr1,"Node %D belongs to processor %D\n",inode,user.v2p[inode]);

183:       user.gloInd[user.Nvlocal] = inode;
184:       sscanf(str,"%*d %d",&dtmp);
185:       nbrs = dtmp;
186:       PetscFPrintf(PETSC_COMM_SELF,fptr1,"Number of neighbors for the vertex %D is %D\n",inode,nbrs);

188:       user.itot[user.Nvlocal] = nbrs;
189:       Nvneighborstotal       += nbrs;
190:       for (i = 0; i < user.itot[user.Nvlocal]; i++) {
191:         form[0]='\0';
192:         for (j=0; j < i+2; j++) {
193:           PetscStrcat(form,"%*d ");
194:         }
195:         PetscStrcat(form,"%d");

197:         sscanf(str,form,&dtmp);
198:         user.AdjM[user.Nvlocal][i] = dtmp;

200:         PetscFPrintf(PETSC_COMM_SELF,fptr1,"%D ",user.AdjM[user.Nvlocal][i]);
201:       }
202:       PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
203:       user.Nvlocal++;
204:     }
205:   }
206:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"Total # of Local Vertices is %D \n",user.Nvlocal);

208:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209:      Create different orderings
210:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

212:   /*
213:     Create the local ordering list for vertices. First a list using the PETSc global
214:     ordering is created. Then we use the AO object to get the PETSc-to-application and
215:     application-to-PETSc mappings. Each vertex also gets a local index (stored in the
216:     locInd array).
217:   */
218:   MPI_Scan(&user.Nvlocal,&rstart,1,MPIU_INT,MPI_SUM,PETSC_COMM_WORLD);
219:   rstart -= user.Nvlocal;
220:   PetscMalloc1(user.Nvlocal,&pordering);

222:   for (i=0; i < user.Nvlocal; i++) pordering[i] = rstart + i;

224:   /*
225:     Create the AO object
226:   */
227:   AOCreateBasic(MPI_COMM_WORLD,user.Nvlocal,user.gloInd,pordering,&ao);
228:   PetscFree(pordering);

230:   /*
231:     Keep the global indices for later use
232:   */
233:   PetscMalloc1(user.Nvlocal,&user.locInd);
234:   PetscMalloc1(Nvneighborstotal,&tmp);

236:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
237:     Demonstrate the use of AO functionality
238:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

240:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"Before AOApplicationToPetsc, local indices are : \n");
241:   for (i=0; i < user.Nvlocal; i++) {
242:     PetscFPrintf(PETSC_COMM_SELF,fptr1," %D ",user.gloInd[i]);

244:     user.locInd[i] = user.gloInd[i];
245:   }
246:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
247:   jstart = 0;
248:   for (i=0; i < user.Nvlocal; i++) {
249:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"Neghbors of local vertex %D are : ",user.gloInd[i]);
250:     for (j=0; j < user.itot[i]; j++) {
251:       PetscFPrintf(PETSC_COMM_SELF,fptr1,"%D ",user.AdjM[i][j]);

253:       tmp[j + jstart] = user.AdjM[i][j];
254:     }
255:     jstart += user.itot[i];
256:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
257:   }

259:   /*
260:     Now map the vlocal and neighbor lists to the PETSc ordering
261:   */
262:   AOApplicationToPetsc(ao,user.Nvlocal,user.locInd);
263:   AOApplicationToPetsc(ao,Nvneighborstotal,tmp);
264:   AODestroy(&ao);

266:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"After AOApplicationToPetsc, local indices are : \n");
267:   for (i=0; i < user.Nvlocal; i++) {
268:     PetscFPrintf(PETSC_COMM_SELF,fptr1," %D ",user.locInd[i]);
269:   }
270:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");

272:   jstart = 0;
273:   for (i=0; i < user.Nvlocal; i++) {
274:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"Neghbors of local vertex %D are : ",user.locInd[i]);
275:     for (j=0; j < user.itot[i]; j++) {
276:       user.AdjM[i][j] = tmp[j+jstart];

278:       PetscFPrintf(PETSC_COMM_SELF,fptr1,"%D ",user.AdjM[i][j]);
279:     }
280:     jstart += user.itot[i];
281:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
282:   }

284:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
285:      Extract the ghost vertex information for each processor
286:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
287:   /*
288:    Next, we need to generate a list of vertices required for this processor
289:    and a local numbering scheme for all vertices required on this processor.
290:       vertices - integer array of all vertices needed on this processor in PETSc
291:                  global numbering; this list consists of first the "locally owned"
292:                  vertices followed by the ghost vertices.
293:       verticesmask - integer array that for each global vertex lists its local
294:                      vertex number (in vertices) + 1. If the global vertex is not
295:                      represented on this processor, then the corresponding
296:                      entry in verticesmask is zero

298:       Note: vertices and verticesmask are both Nvglobal in length; this may
299:     sound terribly non-scalable, but in fact is not so bad for a reasonable
300:     number of processors. Importantly, it allows us to use NO SEARCHING
301:     in setting up the data structures.
302:   */
303:   PetscMalloc1(user.Nvglobal,&vertices);
304:   PetscMalloc1(user.Nvglobal,&verticesmask);
305:   PetscMemzero(verticesmask,user.Nvglobal*sizeof(PetscInt));
306:   nvertices = 0;

308:   /*
309:     First load "owned vertices" into list
310:   */
311:   for (i=0; i < user.Nvlocal; i++) {
312:     vertices[nvertices++]        = user.locInd[i];
313:     verticesmask[user.locInd[i]] = nvertices;
314:   }

316:   /*
317:     Now load ghost vertices into list
318:   */
319:   for (i=0; i < user.Nvlocal; i++) {
320:     for (j=0; j < user.itot[i]; j++) {
321:       nb = user.AdjM[i][j];
322:       if (!verticesmask[nb]) {
323:         vertices[nvertices++] = nb;
324:         verticesmask[nb]      = nvertices;
325:       }
326:     }
327:   }

329:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
330:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"The array vertices is :\n");
331:   for (i=0; i < nvertices; i++) {
332:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"%D ",vertices[i]);
333:   }
334:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");

336:   /*
337:      Map the vertices listed in the neighbors to the local numbering from
338:     the global ordering that they contained initially.
339:   */
340:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
341:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"After mapping neighbors in the local contiguous ordering\n");
342:   for (i=0; i<user.Nvlocal; i++) {
343:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"Neghbors of local vertex %D are :\n",i);
344:     for (j = 0; j < user.itot[i]; j++) {
345:       nb              = user.AdjM[i][j];
346:       user.AdjM[i][j] = verticesmask[nb] - 1;

348:       PetscFPrintf(PETSC_COMM_SELF,fptr1,"%D ",user.AdjM[i][j]);
349:     }
350:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
351:   }

353:   N = user.Nvglobal;

355:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
356:      Create vector and matrix data structures
357:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

359:   /*
360:     Create vector data structures
361:   */
362:   VecCreate(MPI_COMM_WORLD,&x);
363:   VecSetSizes(x,user.Nvlocal,N);
364:   VecSetFromOptions(x);
365:   VecDuplicate(x,&r);
366:   VecCreateSeq(MPI_COMM_SELF,bs*nvertices,&user.localX);
367:   VecDuplicate(user.localX,&user.localF);

369:   /*
370:     Create the scatter between the global representation and the
371:     local representation
372:   */
373:   ISCreateStride(MPI_COMM_SELF,bs*nvertices,0,1,&islocal);
374:   ISCreateBlock(MPI_COMM_SELF,bs,nvertices,vertices,PETSC_COPY_VALUES,&isglobal);
375:   VecScatterCreate(x,isglobal,user.localX,islocal,&user.scatter);
376:   ISDestroy(&isglobal);
377:   ISDestroy(&islocal);

379:   /*
380:      Create matrix data structure; Just to keep the example simple, we have not done any
381:      preallocation of memory for the matrix. In real application code with big matrices,
382:      preallocation should always be done to expedite the matrix creation.
383:   */
384:   MatCreate(MPI_COMM_WORLD,&Jac);
385:   MatSetSizes(Jac,PETSC_DECIDE,PETSC_DECIDE,N,N);
386:   MatSetFromOptions(Jac);
387:   MatSetUp(Jac);

389:   /*
390:     The following routine allows us to set the matrix values in local ordering
391:   */
392:   ISLocalToGlobalMappingCreate(MPI_COMM_SELF,bs,nvertices,vertices,PETSC_COPY_VALUES,&isl2g);
393:   MatSetLocalToGlobalMapping(Jac,isl2g,isl2g);

395:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
396:      Create nonlinear solver context
397:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

399:   SNESCreate(MPI_COMM_WORLD,&snes);
400:   SNESSetType(snes,type);

402:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
403:     Set routines for function and Jacobian evaluation
404:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
405:   SNESSetFunction(snes,r,FormFunction,(void*)&user);

407:   PetscOptionsGetBool(NULL,NULL,"-fd_jacobian_coloring",&fd_jacobian_coloring,0);
408:   if (!fd_jacobian_coloring) {
409:     SNESSetJacobian(snes,Jac,Jac,FormJacobian,(void*)&user);
410:   } else {  /* Use matfdcoloring */
411:     ISColoring   iscoloring;
412:     MatColoring  mc;

414:     /* Get the data structure of Jac */
415:     FormJacobian(snes,x,Jac,Jac,&user);
416:     /* Create coloring context */
417:     MatColoringCreate(Jac,&mc);
418:     MatColoringSetType(mc,MATCOLORINGSL);
419:     MatColoringSetFromOptions(mc);
420:     MatColoringApply(mc,&iscoloring);
421:     MatColoringDestroy(&mc);
422:     MatFDColoringCreate(Jac,iscoloring,&matfdcoloring);
423:     MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))FormFunction,&user);
424:     MatFDColoringSetFromOptions(matfdcoloring);
425:     MatFDColoringSetUp(Jac,iscoloring,matfdcoloring);
426:     /* MatFDColoringView(matfdcoloring,PETSC_VIEWER_STDOUT_WORLD); */
427:     SNESSetJacobian(snes,Jac,Jac,SNESComputeJacobianDefaultColor,matfdcoloring);
428:     ISColoringDestroy(&iscoloring);
429:   }

431:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
432:      Customize nonlinear solver; set runtime options
433:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

435:   SNESSetFromOptions(snes);

437:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
438:      Evaluate initial guess; then solve nonlinear system
439:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

441:   /*
442:      Note: The user should initialize the vector, x, with the initial guess
443:      for the nonlinear solver prior to calling SNESSolve().  In particular,
444:      to employ an initial guess of zero, the user should explicitly set
445:      this vector to zero by calling VecSet().
446:   */
447:   FormInitialGuess(&user,x);

449:   /*
450:     Print the initial guess
451:   */
452:   VecGetArray(x,&xx);
453:   for (inode = 0; inode < user.Nvlocal; inode++) {
454:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"Initial Solution at node %D is %f \n",inode,xx[inode]);
455:   }
456:   VecRestoreArray(x,&xx);

458:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
459:      Now solve the nonlinear system
460:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

462:   SNESSolve(snes,NULL,x);
463:   SNESGetIterationNumber(snes,&its);
464:   SNESGetNonlinearStepFailures(snes,&nfails);

466:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
467:     Print the output : solution vector and other information
468:      Each processor writes to the file output.<rank> where rank is the
469:      processor's rank.
470:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

472:   VecGetArray(x,&xx);
473:   for (inode = 0; inode < user.Nvlocal; inode++) {
474:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"Solution at node %D is %f \n",inode,xx[inode]);
475:   }
476:   VecRestoreArray(x,&xx);
477:   fclose(fptr1);
478:   PetscPrintf(MPI_COMM_WORLD,"number of SNES iterations = %D, ",its);
479:   PetscPrintf(MPI_COMM_WORLD,"number of unsuccessful steps = %D\n",nfails);

481:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
482:      Free work space.  All PETSc objects should be destroyed when they
483:      are no longer needed.
484:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
485:   PetscFree(user.gloInd);
486:   PetscFree(user.locInd);
487:   PetscFree(vertices);
488:   PetscFree(verticesmask);
489:   PetscFree(tmp);
490:   VecScatterDestroy(&user.scatter);
491:   ISLocalToGlobalMappingDestroy(&isl2g);
492:   VecDestroy(&x);
493:   VecDestroy(&r);
494:   VecDestroy(&user.localX);
495:   VecDestroy(&user.localF);
496:   MatDestroy(&Jac);  SNESDestroy(&snes);
497:   /*PetscDrawDestroy(draw);*/
498:   if (fd_jacobian_coloring) {
499:     MatFDColoringDestroy(&matfdcoloring);
500:   }
501:   PetscFinalize();
502:   return ierr;
503: }
504: /* --------------------  Form initial approximation ----------------- */

506: /*
507:    FormInitialGuess - Forms initial approximation.

509:    Input Parameters:
510:    user - user-defined application context
511:    X - vector

513:    Output Parameter:
514:    X - vector
515:  */
516: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
517: {
518:   PetscInt    i,Nvlocal,ierr;
519:   PetscInt    *gloInd;
520:   PetscScalar *x;
521: #if defined(UNUSED_VARIABLES)
522:   PetscReal temp1,temp,hx,hy,hxdhy,hydhx,sc;
523:   PetscInt  Neglobal,Nvglobal,j,row;
524:   PetscReal alpha,lambda;

526:   Nvglobal = user->Nvglobal;
527:   Neglobal = user->Neglobal;
528:   lambda   = user->non_lin_param;
529:   alpha    = user->lin_param;
530: #endif

532:   Nvlocal = user->Nvlocal;
533:   gloInd  = user->gloInd;

535:   /*
536:      Get a pointer to vector data.
537:        - For default PETSc vectors, VecGetArray() returns a pointer to
538:          the data array.  Otherwise, the routine is implementation dependent.
539:        - You MUST call VecRestoreArray() when you no longer need access to
540:          the array.
541:   */
542:   VecGetArray(X,&x);

544:   /*
545:      Compute initial guess over the locally owned part of the grid
546:   */
547:   for (i=0; i < Nvlocal; i++) x[i] = (PetscReal)gloInd[i];

549:   /*
550:      Restore vector
551:   */
552:   VecRestoreArray(X,&x);
553:   return 0;
554: }
555: /* --------------------  Evaluate Function F(x) --------------------- */
556: /*
557:    FormFunction - Evaluates nonlinear function, F(x).

559:    Input Parameters:
560: .  snes - the SNES context
561: .  X - input vector
562: .  ptr - optional user-defined context, as set by SNESSetFunction()

564:    Output Parameter:
565: .  F - function vector
566:  */
567: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ptr)
568: {
569:   AppCtx         *user = (AppCtx*)ptr;
571:   PetscInt       i,j,Nvlocal;
572:   PetscReal      alpha,lambda;
573:   PetscScalar    *x,*f;
574:   VecScatter     scatter;
575:   Vec            localX = user->localX;
576: #if defined(UNUSED_VARIABLES)
577:   PetscScalar ut,ub,ul,ur,u,*g,sc,uyy,uxx;
578:   PetscReal   hx,hy,hxdhy,hydhx;
579:   PetscReal   two = 2.0,one = 1.0;
580:   PetscInt    Nvglobal,Neglobal,row;
581:   PetscInt    *gloInd;

583:   Nvglobal = user->Nvglobal;
584:   Neglobal = user->Neglobal;
585:   gloInd   = user->gloInd;
586: #endif

588:   Nvlocal = user->Nvlocal;
589:   lambda  = user->non_lin_param;
590:   alpha   = user->lin_param;
591:   scatter = user->scatter;

593:   /*
594:      PDE : L(u) + lambda*u*u +alpha*u = 0 where L(u) is the approximate Laplacian as
595:      described in the beginning of this code

597:      First scatter the distributed vector X into local vector localX (that includes
598:      values for ghost nodes. If we wish,we can put some other work between
599:      VecScatterBegin() and VecScatterEnd() to overlap the communication with
600:      computation.
601:  */
602:   VecScatterBegin(scatter,X,localX,INSERT_VALUES,SCATTER_FORWARD);
603:   VecScatterEnd(scatter,X,localX,INSERT_VALUES,SCATTER_FORWARD);

605:   /*
606:      Get pointers to vector data
607:   */
608:   VecGetArray(localX,&x);
609:   VecGetArray(F,&f);

611:   /*
612:     Now compute the f(x). As mentioned earlier, the computed Laplacian is just an
613:     approximate one chosen for illustrative purpose only. Another point to notice
614:     is that this is a local (completly parallel) calculation. In practical application
615:     codes, function calculation time is a dominat portion of the overall execution time.
616:   */
617:   for (i=0; i < Nvlocal; i++) {
618:     f[i] = (user->itot[i] - alpha)*x[i] - lambda*x[i]*x[i];
619:     for (j = 0; j < user->itot[i]; j++) f[i] -= x[user->AdjM[i][j]];
620:   }

622:   /*
623:      Restore vectors
624:   */
625:   VecRestoreArray(localX,&x);
626:   VecRestoreArray(F,&f);
627:   /*VecView(F,PETSC_VIEWER_STDOUT_WORLD);*/

629:   return 0;
630: }

632: /* --------------------  Evaluate Jacobian F'(x) -------------------- */
633: /*
634:    FormJacobian - Evaluates Jacobian matrix.

636:    Input Parameters:
637: .  snes - the SNES context
638: .  X - input vector
639: .  ptr - optional user-defined context, as set by SNESSetJacobian()

641:    Output Parameters:
642: .  A - Jacobian matrix
643: .  B - optionally different preconditioning matrix
644: .  flag - flag indicating matrix structure

646: */
647: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat J,Mat jac,void *ptr)
648: {
649:   AppCtx      *user = (AppCtx*)ptr;
650:   PetscInt    i,j,Nvlocal,col[50],ierr;
651:   PetscScalar alpha,lambda,value[50];
652:   Vec         localX = user->localX;
653:   VecScatter  scatter;
654:   PetscScalar *x;
655: #if defined(UNUSED_VARIABLES)
656:   PetscScalar two = 2.0,one = 1.0;
657:   PetscInt    row,Nvglobal,Neglobal;
658:   PetscInt    *gloInd;

660:   Nvglobal = user->Nvglobal;
661:   Neglobal = user->Neglobal;
662:   gloInd   = user->gloInd;
663: #endif

665:   /*printf("Entering into FormJacobian \n");*/
666:   Nvlocal = user->Nvlocal;
667:   lambda  = user->non_lin_param;
668:   alpha   =  user->lin_param;
669:   scatter = user->scatter;

671:   /*
672:      PDE : L(u) + lambda*u*u +alpha*u = 0 where L(u) is the approximate Laplacian as
673:      described in the beginning of this code

675:      First scatter the distributed vector X into local vector localX (that includes
676:      values for ghost nodes. If we wish, we can put some other work between
677:      VecScatterBegin() and VecScatterEnd() to overlap the communication with
678:      computation.
679:   */
680:   VecScatterBegin(scatter,X,localX,INSERT_VALUES,SCATTER_FORWARD);
681:   VecScatterEnd(scatter,X,localX,INSERT_VALUES,SCATTER_FORWARD);

683:   /*
684:      Get pointer to vector data
685:   */
686:   VecGetArray(localX,&x);

688:   for (i=0; i < Nvlocal; i++) {
689:     col[0]   = i;
690:     value[0] = user->itot[i] - 2.0*lambda*x[i] - alpha;
691:     for (j = 0; j < user->itot[i]; j++) {
692:       col[j+1]   = user->AdjM[i][j];
693:       value[j+1] = -1.0;
694:     }

696:     /*
697:       Set the matrix values in the local ordering. Note that in order to use this
698:       feature we must call the routine MatSetLocalToGlobalMapping() after the
699:       matrix has been created.
700:     */
701:     MatSetValuesLocal(jac,1,&i,1+user->itot[i],col,value,INSERT_VALUES);
702:   }

704:   /*
705:      Assemble matrix, using the 2-step process:
706:        MatAssemblyBegin(), MatAssemblyEnd().
707:      Between these two calls, the pointer to vector data has been restored to
708:      demonstrate the use of overlapping communicationn with computation.
709:   */
710:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
711:   VecRestoreArray(localX,&x);
712:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);

714:   /*
715:      Tell the matrix we will never add a new nonzero location to the
716:      matrix. If we do, it will generate an error.
717:   */
718:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
719:   /* MatView(jac,PETSC_VIEWER_STDOUT_SELF); */
720:   return 0;
721: }