Actual source code: ex10.c

      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*/