Actual source code: ex10.c

petsc-3.9.3 2018-07-02
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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*/



 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_SELF,1,"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,1,"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:   PetscMalloc1(user.Nvglobal,&verticesmask);
307:   PetscMemzero(verticesmask,user.Nvglobal*sizeof(PetscInt));
308:   nvertices = 0;

310:   /*
311:     First load "owned vertices" into list
312:   */
313:   for (i=0; i < user.Nvlocal; i++) {
314:     vertices[nvertices++]        = user.locInd[i];
315:     verticesmask[user.locInd[i]] = nvertices;
316:   }

318:   /*
319:     Now load ghost vertices into list
320:   */
321:   for (i=0; i < user.Nvlocal; i++) {
322:     for (j=0; j < user.itot[i]; j++) {
323:       nb = user.AdjM[i][j];
324:       if (!verticesmask[nb]) {
325:         vertices[nvertices++] = nb;
326:         verticesmask[nb]      = nvertices;
327:       }
328:     }
329:   }

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

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

350:       PetscFPrintf(PETSC_COMM_SELF,fptr1,"%D ",user.AdjM[i][j]);
351:     }
352:     PetscFPrintf(PETSC_COMM_SELF,fptr1,"\n");
353:   }

355:   N = user.Nvglobal;

357:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
358:      Create vector and matrix data structures
359:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

397:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
398:      Create nonlinear solver context
399:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

416:     /* Get the data structure of Jac */
417:     FormJacobian(snes,x,Jac,Jac,&user);
418:     /* Create coloring context */
419:     MatColoringCreate(Jac,&mc);
420:     MatColoringSetType(mc,MATCOLORINGSL);
421:     MatColoringSetFromOptions(mc);
422:     MatColoringApply(mc,&iscoloring);
423:     MatColoringDestroy(&mc);
424:     MatFDColoringCreate(Jac,iscoloring,&matfdcoloring);
425:     MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))FormFunction,&user);
426:     MatFDColoringSetFromOptions(matfdcoloring);
427:     MatFDColoringSetUp(Jac,iscoloring,matfdcoloring);
428:     /* MatFDColoringView(matfdcoloring,PETSC_VIEWER_STDOUT_WORLD); */
429:     SNESSetJacobian(snes,Jac,Jac,SNESComputeJacobianDefaultColor,matfdcoloring);
430:     ISColoringDestroy(&iscoloring);
431:   }

433:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
434:      Customize nonlinear solver; set runtime options
435:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

437:   SNESSetFromOptions(snes);

439:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
440:      Evaluate initial guess; then solve nonlinear system
441:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

460:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
461:      Now solve the nonlinear system
462:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

468:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
469:     Print the output : solution vector and other information
470:      Each processor writes to the file output.<rank> where rank is the
471:      processor's rank.
472:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

613:   /*
614:     Now compute the f(x). As mentioned earlier, the computed Laplacian is just an
615:     approximate one chosen for illustrative purpose only. Another point to notice
616:     is that this is a local (completly parallel) calculation. In practical application
617:     codes, function calculation time is a dominat portion of the overall execution time.
618:   */
619:   for (i=0; i < Nvlocal; i++) {
620:     f[i] = (user->itot[i] - alpha)*x[i] - lambda*x[i]*x[i];
621:     for (j = 0; j < user->itot[i]; j++) f[i] -= x[user->AdjM[i][j]];
622:   }

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

631:   return 0;
632: }

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

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

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

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

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

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

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

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

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

690:   for (i=0; i < Nvlocal; i++) {
691:     col[0]   = i;
692:     value[0] = user->itot[i] - 2.0*lambda*x[i] - alpha;
693:     for (j = 0; j < user->itot[i]; j++) {
694:       col[j+1]   = user->AdjM[i][j];
695:       value[j+1] = -1.0;
696:     }

698:     /*
699:       Set the matrix values in the local ordering. Note that in order to use this
700:       feature we must call the routine MatSetLocalToGlobalMapping() after the
701:       matrix has been created.
702:     */
703:     MatSetValuesLocal(jac,1,&i,1+user->itot[i],col,value,INSERT_VALUES);
704:   }

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

716:   /*
717:      Tell the matrix we will never add a new nonzero location to the
718:      matrix. If we do, it will generate an error.
719:   */
720:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
721:   /* MatView(jac,PETSC_VIEWER_STDOUT_SELF); */
722:   return 0;
723: }



727: /*TEST

729:    build:
730:       requires: !complex

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

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

743: TEST*/