Actual source code: ex10.c

petsc-3.14.1 2020-11-03
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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/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*/



 42: /* ------------------------------------------------------------------------

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

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

 50:    -----------------------------------------------------------------------*/


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

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

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

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

117:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
118:      Initialize program
119:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

125:   /* The current input file options.inf is for 2 proc run only */
126:   if (size != 2) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This example currently runs on 2 procs only.");

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

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

137:   user.non_lin_param = 0.06;

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

141:   user.lin_param = -1.0;

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

145:   user.Nvlocal = 0;
146:   user.Nelocal = 0;

148:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149:       Read the mesh and partitioning information
150:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

190:       user.itot[user.Nvlocal] = nbrs;
191:       Nvneighborstotal       += nbrs;
192:       for (i = 0; i < user.itot[user.Nvlocal]; i++) {
193:         form[0]='\0';
194:         for (j=0; j < i+2; j++) {
195:           PetscStrlcat(form,"%*d ",sizeof(form));
196:         }
197:         PetscStrlcat(form,"%d",sizeof(form));

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

202:         PetscFPrintf(PETSC_COMM_SELF,fptr1,"%D ",user.AdjM[user.Nvlocal][i]);
203:       }
204:       PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
205:       user.Nvlocal++;
206:     }
207:   }
208:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"Total # of Local Vertices is %D \n",user.Nvlocal);

210:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211:      Create different orderings
212:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

238:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
239:     Demonstrate the use of AO functionality
240:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

255:       tmp[j + jstart] = user.AdjM[i][j];
256:     }
257:     jstart += user.itot[i];
258:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
259:   }

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

268:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"After AOApplicationToPetsc, local indices are : \n");
269:   for (i=0; i < user.Nvlocal; i++) {
270:     PetscFPrintf(PETSC_COMM_SELF,fptr1," %D ",user.locInd[i]);
271:   }
272:   PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");

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

280:       PetscFPrintf(PETSC_COMM_SELF,fptr1,"%D ",user.AdjM[i][j]);
281:     }
282:     jstart += user.itot[i];
283:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
284:   }

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

300:       Note: vertices and verticesmask are both Nvglobal in length; this may
301:     sound terribly non-scalable, but in fact is not so bad for a reasonable
302:     number of processors. Importantly, it allows us to use NO SEARCHING
303:     in setting up the data structures.
304:   */
305:   PetscMalloc1(user.Nvglobal,&vertices);
306:   PetscCalloc1(user.Nvglobal,&verticesmask);
307:   nvertices = 0;

309:   /*
310:     First load "owned vertices" into list
311:   */
312:   for (i=0; i < user.Nvlocal; i++) {
313:     vertices[nvertices++]        = user.locInd[i];
314:     verticesmask[user.locInd[i]] = nvertices;
315:   }

317:   /*
318:     Now load ghost vertices into list
319:   */
320:   for (i=0; i < user.Nvlocal; i++) {
321:     for (j=0; j < user.itot[i]; j++) {
322:       nb = user.AdjM[i][j];
323:       if (!verticesmask[nb]) {
324:         vertices[nvertices++] = nb;
325:         verticesmask[nb]      = nvertices;
326:       }
327:     }
328:   }

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

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

349:       PetscFPrintf(PETSC_COMM_SELF,fptr1,"%D ",user.AdjM[i][j]);
350:     }
351:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
352:   }

354:   N = user.Nvglobal;

356:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
357:      Create vector and matrix data structures
358:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

396:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
397:      Create nonlinear solver context
398:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

415:     /* Get the data structure of Jac */
416:     FormJacobian(snes,x,Jac,Jac,&user);
417:     /* Create coloring context */
418:     MatColoringCreate(Jac,&mc);
419:     MatColoringSetType(mc,MATCOLORINGSL);
420:     MatColoringSetFromOptions(mc);
421:     MatColoringApply(mc,&iscoloring);
422:     MatColoringDestroy(&mc);
423:     MatFDColoringCreate(Jac,iscoloring,&matfdcoloring);
424:     MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))FormFunction,&user);
425:     MatFDColoringSetFromOptions(matfdcoloring);
426:     MatFDColoringSetUp(Jac,iscoloring,matfdcoloring);
427:     /* MatFDColoringView(matfdcoloring,PETSC_VIEWER_STDOUT_WORLD); */
428:     SNESSetJacobian(snes,Jac,Jac,SNESComputeJacobianDefaultColor,matfdcoloring);
429:     ISColoringDestroy(&iscoloring);
430:   }

432:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
433:      Customize nonlinear solver; set runtime options
434:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

436:   SNESSetFromOptions(snes);

438:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
439:      Evaluate initial guess; then solve nonlinear system
440:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

459:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
460:      Now solve the nonlinear system
461:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

467:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
468:     Print the output : solution vector and other information
469:      Each processor writes to the file output.<rank> where rank is the
470:      processor's rank.
471:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

612:   /*
613:     Now compute the f(x). As mentioned earlier, the computed Laplacian is just an
614:     approximate one chosen for illustrative purpose only. Another point to notice
615:     is that this is a local (completly parallel) calculation. In practical application
616:     codes, function calculation time is a dominat portion of the overall execution time.
617:   */
618:   for (i=0; i < Nvlocal; i++) {
619:     f[i] = (user->itot[i] - alpha)*x[i] - lambda*x[i]*x[i];
620:     for (j = 0; j < user->itot[i]; j++) f[i] -= x[user->AdjM[i][j]];
621:   }

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

630:   return 0;
631: }

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

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

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

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

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

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

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

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

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

689:   for (i=0; i < Nvlocal; i++) {
690:     col[0]   = i;
691:     value[0] = user->itot[i] - 2.0*lambda*x[i] - alpha;
692:     for (j = 0; j < user->itot[i]; j++) {
693:       col[j+1]   = user->AdjM[i][j];
694:       value[j+1] = -1.0;
695:     }

697:     /*
698:       Set the matrix values in the local ordering. Note that in order to use this
699:       feature we must call the routine MatSetLocalToGlobalMapping() after the
700:       matrix has been created.
701:     */
702:     MatSetValuesLocal(jac,1,&i,1+user->itot[i],col,value,INSERT_VALUES);
703:   }

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

715:   /*
716:      Tell the matrix we will never add a new nonzero location to the
717:      matrix. If we do, it will generate an error.
718:   */
719:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
720:   /* MatView(jac,PETSC_VIEWER_STDOUT_SELF); */
721:   return 0;
722: }



726: /*TEST

728:    build:
729:       requires: !complex

731:    test:
732:       nsize: 2
733:       args: -snes_monitor_short
734:       localrunfiles: options.inf adj.in

736:    test:
737:       suffix: 2
738:       nsize: 2
739:       args: -snes_monitor_short -fd_jacobian_coloring
740:       localrunfiles: options.inf adj.in

742: TEST*/