Actual source code: ex10.c
1: /*$Id: ex10.c,v 1.29 2001/09/11 16:34:10 bsmith Exp $*/
3: /*
4: Program usage: mpirun -np <procs> usg [-help] [all PETSc options]
5: */
7: #if !defined(PETSC_USE_COMPLEX)
9: static char help[] = "An Unstructured Grid Example.\n\
10: This example demonstrates how to solve a nonlinear system in parallel\n\
11: with SNES for an unstructured mesh. The mesh and partitioning information\n\
12: is read in an application defined ordering,which is later transformed\n\
13: into another convenient ordering (called the local ordering). The local\n\
14: ordering, apart from being efficient on cpu cycles and memory, allows\n\
15: the use of the SPMD model of parallel programming. After partitioning\n\
16: is done, scatters are created between local (sequential)and global\n\
17: (distributed) vectors. Finally, we set up the nonlinear solver context\n\
18: in the usual way as a structured grid (see\n\
19: petsc/src/snes/examples/tutorials/ex5.c).\n\
20: The command line options include:\n\
21: -vert <Nv>, where Nv is the global number of nodes\n\
22: -elem <Ne>, where Ne is the global number of elements\n\
23: -nl_par <lambda>, where lambda is the multiplier for the non linear term (u*u) term\n\
24: -lin_par <alpha>, where alpha is the multiplier for the linear term (u) \n";
26: /*T
27: Concepts: SNES^unstructured grid
28: Concepts: AO^application to PETSc ordering or vice versa;
29: Concepts: VecScatter^using vector scatter operations;
30: Processors: n
31: T*/
33: /* ------------------------------------------------------------------------
35: PDE Solved : L(u) + lambda*u*u + alpha*u = 0 where L(u) is the Laplacian.
37: The Laplacian is approximated in the following way: each edge is given a weight
38: of one meaning that the diagonal term will have the weight equal to the degree
39: of a node. The off diagonal terms will get a weight of -1.
41: -----------------------------------------------------------------------*/
43: /*
44: Include petscao.h so that we can use AO (Application Ordering) object's services.
45: Include "petscsnes.h" so that we can use SNES solvers. Note that this
46: file automatically includes:
47: petsc.h - base PETSc routines petscvec.h - vectors
48: petscsys.h - system routines petscmat.h - matrices
49: petscis.h - index sets petscksp.h - Krylov subspace methods
50: petscviewer.h - viewers petscpc.h - preconditioners
51: petscsles.h - linear solvers
52: */
53: #include "petscao.h"
54: #include "petscsnes.h"
57: #define MAX_ELEM 500 /* Maximum number of elements */
58: #define MAX_VERT 100 /* Maximum number of vertices */
59: #define MAX_VERT_ELEM 3 /* Vertices per element */
61: /*
62: Application-defined context for problem specific data
63: */
64: typedef struct {
65: int Nvglobal,Nvlocal; /* global and local number of vertices */
66: int Neglobal,Nelocal; /* global and local number of vertices */
67: int AdjM[MAX_VERT][50]; /* adjacency list of a vertex */
68: int itot[MAX_VERT]; /* total number of neighbors for a vertex */
69: int icv[MAX_ELEM][MAX_VERT_ELEM]; /* vertices belonging to an element */
70: int v2p[MAX_VERT]; /* processor number for a vertex */
71: int *locInd,*gloInd; /* local and global orderings for a node */
72: Vec localX,localF; /* local solution (u) and f(u) vectors */
73: PetscReal non_lin_param; /* nonlinear parameter for the PDE */
74: PetscReal lin_param; /* linear parameter for the PDE */
75: VecScatter scatter; /* scatter context for the local and
76: distributed vectors */
77: } AppCtx;
79: /*
80: User-defined routines
81: */
82: int FormJacobian(SNES,Vec,Mat*,Mat*,MatStructure*,void*),
83: FormFunction(SNES,Vec,Vec,void*),
84: FormInitialGuess(AppCtx*,Vec);
88: int main(int argc,char **argv)
89: {
90: SNES snes; /* SNES context */
91: SNESType type = SNESLS; /* default nonlinear solution method */
92: Vec x,r; /* solution, residual vectors */
93: Mat Jac; /* Jacobian matrix */
94: AppCtx user; /* user-defined application context */
95: AO ao; /* Application Ordering object */
96: IS isglobal,islocal; /* global and local index sets */
97: int rank,size; /* rank of a process, number of processors */
98: int rstart; /* starting index of PETSc ordering for a processor */
99: int nfails; /* number of unsuccessful Newton steps */
100: int bs = 1; /* block size for multicomponent systems */
101: int nvertices; /* number of local plus ghost nodes of a processor */
102: int *pordering; /* PETSc ordering */
103: int *vertices; /* list of all vertices (incl. ghost ones)
104: on a processor */
105: int *verticesmask,*svertices;
106: int *tmp;
107: int i,j,jstart,inode,nb,nbrs,Nvneighborstotal = 0;
108: int ierr,its,N;
109: PetscScalar *xx;
110: char str[256],form[256],part_name[256];
111: FILE *fptr,*fptr1;
112: ISLocalToGlobalMapping isl2g;
113: #if defined (UNUSED_VARIABLES)
114: PetscDraw draw; /* drawing context */
115: PetscScalar *ff,*gg;
116: PetscReal tiny = 1.0e-10,zero = 0.0,one = 1.0,big = 1.0e+10;
117: int *tmp1,*tmp2;
118: #endif
119: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
120: Initialize program
121: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
123: PetscInitialize(&argc,&argv,"options.inf",help);
124: MPI_Comm_rank(MPI_COMM_WORLD,&rank);
125: MPI_Comm_size(MPI_COMM_WORLD,&size);
127: /* The current input file options.inf is for 2 proc run only */
128: if (size != 2) SETERRQ(1,"This Example currently runs on 2 procs only.");
130: /*
131: Initialize problem parameters
132: */
133: user.Nvglobal = 16; /*Global # of vertices */
134: user.Neglobal = 18; /*Global # of elements */
135: PetscOptionsGetInt(PETSC_NULL,"-vert",&user.Nvglobal,PETSC_NULL);
136: PetscOptionsGetInt(PETSC_NULL,"-elem",&user.Neglobal,PETSC_NULL);
137: user.non_lin_param = 0.06;
138: PetscOptionsGetReal(PETSC_NULL,"-nl_par",&user.non_lin_param,PETSC_NULL);
139: user.lin_param = -1.0;
140: PetscOptionsGetReal(PETSC_NULL,"-lin_par",&user.lin_param,PETSC_NULL);
141: user.Nvlocal = 0;
142: user.Nelocal = 0;
144: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145: Read the mesh and partitioning information
146: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147:
148: /*
149: Read the mesh and partitioning information from 'adj.in'.
150: The file format is as follows.
151: For each line the first entry is the processor rank where the
152: current node belongs. The second entry is the number of
153: neighbors of a node. The rest of the line is the adjacency
154: list of a node. Currently this file is set up to work on two
155: processors.
157: This is not a very good example of reading input. In the future,
158: we will put an example that shows the style that should be
159: used in a real application, where partitioning will be done
160: dynamically by calling partitioning routines (at present, we have
161: a ready interface to ParMeTiS).
162: */
163: fptr = fopen("adj.in","r");
164: if (!fptr) {
165: SETERRQ(0,"Could not open adj.in")
166: }
167:
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) {
175: SETERRQ(0,"Could no open output file");
176: }
177: PetscMalloc(user.Nvglobal*sizeof(int),&user.gloInd);
178: fprintf(fptr1,"Rank is %d\n",rank);
179: for (inode = 0; inode < user.Nvglobal; inode++) {
180: fgets(str,256,fptr);
181: sscanf(str,"%d",&user.v2p[inode]);
182: if (user.v2p[inode] == rank) {
183: fprintf(fptr1,"Node %d belongs to processor %d\n",inode,user.v2p[inode]);
184: user.gloInd[user.Nvlocal] = inode;
185: sscanf(str,"%*d %d",&nbrs);
186: fprintf(fptr1,"Number of neighbors for the vertex %d is %d\n",inode,nbrs);
187: user.itot[user.Nvlocal] = nbrs;
188: Nvneighborstotal += nbrs;
189: for (i = 0; i < user.itot[user.Nvlocal]; i++){
190: form[0]='\0';
191: for (j=0; j < i+2; j++){
192: PetscStrcat(form,"%*d ");
193: }
194: PetscStrcat(form,"%d");
195: sscanf(str,form,&user.AdjM[user.Nvlocal][i]);
196: fprintf(fptr1,"%d ",user.AdjM[user.Nvlocal][i]);
197: }
198: fprintf(fptr1,"\n");
199: user.Nvlocal++;
200: }
201: }
202: fprintf(fptr1,"Total # of Local Vertices is %d \n",user.Nvlocal);
204: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205: Create different orderings
206: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
208: /*
209: Create the local ordering list for vertices. First a list using the PETSc global
210: ordering is created. Then we use the AO object to get the PETSc-to-application and
211: application-to-PETSc mappings. Each vertex also gets a local index (stored in the
212: locInd array).
213: */
214: MPI_Scan(&user.Nvlocal,&rstart,1,MPI_INT,MPI_SUM,MPI_COMM_WORLD);
215: rstart -= user.Nvlocal;
216: PetscMalloc(user.Nvlocal*sizeof(int),&pordering);
218: for (i=0; i < user.Nvlocal; i++) {
219: pordering[i] = rstart + i;
220: }
222: /*
223: Create the AO object
224: */
225: AOCreateBasic(MPI_COMM_WORLD,user.Nvlocal,user.gloInd,pordering,&ao);
226: PetscFree(pordering);
227:
228: /*
229: Keep the global indices for later use
230: */
231: PetscMalloc(user.Nvlocal*sizeof(int),&user.locInd);
232: PetscMalloc(Nvneighborstotal*sizeof(int),&tmp);
233:
234: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
235: Demonstrate the use of AO functionality
236: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
238: fprintf(fptr1,"Before AOApplicationToPetsc, local indices are : \n");
239: for (i=0; i < user.Nvlocal; i++) {
240: fprintf(fptr1," %d ",user.gloInd[i]);
241: user.locInd[i] = user.gloInd[i];
242: }
243: fprintf(fptr1,"\n");
244: jstart = 0;
245: for (i=0; i < user.Nvlocal; i++) {
246: fprintf(fptr1,"Neghbors of local vertex %d are : ",user.gloInd[i]);
247: for (j=0; j < user.itot[i]; j++) {
248: fprintf(fptr1,"%d ",user.AdjM[i][j]);
249: tmp[j + jstart] = user.AdjM[i][j];
250: }
251: jstart += user.itot[i];
252: fprintf(fptr1,"\n");
253: }
255: /*
256: Now map the vlocal and neighbor lists to the PETSc ordering
257: */
258: AOApplicationToPetsc(ao,user.Nvlocal,user.locInd);
259: AOApplicationToPetsc(ao,Nvneighborstotal,tmp);
260: AODestroy(ao);
262: fprintf(fptr1,"After AOApplicationToPetsc, local indices are : \n");
263: for (i=0; i < user.Nvlocal; i++) {
264: fprintf(fptr1," %d ",user.locInd[i]);
265: }
266: fprintf(fptr1,"\n");
268: jstart = 0;
269: for (i=0; i < user.Nvlocal; i++) {
270: fprintf(fptr1,"Neghbors of local vertex %d are : ",user.locInd[i]);
271: for (j=0; j < user.itot[i]; j++) {
272: user.AdjM[i][j] = tmp[j+jstart];
273: fprintf(fptr1,"%d ",user.AdjM[i][j]);
274: }
275: jstart += user.itot[i];
276: fprintf(fptr1,"\n");
277: }
279: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
280: Extract the ghost vertex information for each processor
281: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
282: /*
283: Next, we need to generate a list of vertices required for this processor
284: and a local numbering scheme for all vertices required on this processor.
285: vertices - integer array of all vertices needed on this processor in PETSc
286: global numbering; this list consists of first the "locally owned"
287: vertices followed by the ghost vertices.
288: verticesmask - integer array that for each global vertex lists its local
289: vertex number (in vertices) + 1. If the global vertex is not
290: represented on this processor, then the corresponding
291: entry in verticesmask is zero
292:
293: Note: vertices and verticesmask are both Nvglobal in length; this may
294: sound terribly non-scalable, but in fact is not so bad for a reasonable
295: number of processors. Importantly, it allows us to use NO SEARCHING
296: in setting up the data structures.
297: */
298: PetscMalloc(user.Nvglobal*sizeof(int),&vertices);
299: PetscMalloc(user.Nvglobal*sizeof(int),&verticesmask);
300: PetscMemzero(verticesmask,user.Nvglobal*sizeof(int));
301: nvertices = 0;
302:
303: /*
304: First load "owned vertices" into list
305: */
306: for (i=0; i < user.Nvlocal; i++) {
307: vertices[nvertices++] = user.locInd[i];
308: verticesmask[user.locInd[i]] = nvertices;
309: }
310:
311: /*
312: Now load ghost vertices into list
313: */
314: for (i=0; i < user.Nvlocal; i++) {
315: for (j=0; j < user.itot[i]; j++) {
316: nb = user.AdjM[i][j];
317: if (!verticesmask[nb]) {
318: vertices[nvertices++] = nb;
319: verticesmask[nb] = nvertices;
320: }
321: }
322: }
324: fprintf(fptr1,"\n");
325: fprintf(fptr1,"The array vertices is :\n");
326: for (i=0; i < nvertices; i++) {
327: fprintf(fptr1,"%d ",vertices[i]);
328: }
329: fprintf(fptr1,"\n");
330:
331: /*
332: Map the vertices listed in the neighbors to the local numbering from
333: the global ordering that they contained initially.
334: */
335: fprintf(fptr1,"\n");
336: fprintf(fptr1,"After mapping neighbors in the local contiguous ordering\n");
337: for (i=0; i<user.Nvlocal; i++) {
338: fprintf(fptr1,"Neghbors of local vertex %d are :\n",i);
339: for (j = 0; j < user.itot[i]; j++) {
340: nb = user.AdjM[i][j];
341: user.AdjM[i][j] = verticesmask[nb] - 1;
342: fprintf(fptr1,"%d ",user.AdjM[i][j]);
343: }
344: fprintf(fptr1,"\n");
345: }
347: N = user.Nvglobal;
348:
349: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
350: Create vector and matrix data structures
351: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
353: /*
354: Create vector data structures
355: */
356: VecCreate(MPI_COMM_WORLD,&x);
357: VecSetSizes(x,user.Nvlocal,N);
358: VecSetFromOptions(x);
359: VecDuplicate(x,&r);
360: VecCreateSeq(MPI_COMM_SELF,bs*nvertices,&user.localX);
361: VecDuplicate(user.localX,&user.localF);
363: /*
364: Create the scatter between the global representation and the
365: local representation
366: */
367: ISCreateStride(MPI_COMM_SELF,bs*nvertices,0,1,&islocal);
368: PetscMalloc(nvertices*sizeof(int),&svertices);
369: for (i=0; i<nvertices; i++) svertices[i] = bs*vertices[i];
370: ISCreateBlock(MPI_COMM_SELF,bs,nvertices,svertices,&isglobal);
371: PetscFree(svertices);
372: VecScatterCreate(x,isglobal,user.localX,islocal,&user.scatter);
374: /*
375: Create matrix data structure; Just to keep the example simple, we have not done any
376: preallocation of memory for the matrix. In real application code with big matrices,
377: preallocation should always be done to expedite the matrix creation.
378: */
379: MatCreate(MPI_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,&Jac);
380: MatSetFromOptions(Jac);
382: /*
383: The following routine allows us to set the matrix values in local ordering
384: */
385: ISLocalToGlobalMappingCreate(MPI_COMM_SELF,bs*nvertices,vertices,&isl2g);
386: MatSetLocalToGlobalMapping(Jac,isl2g);
388: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
389: Create nonlinear solver context
390: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
392: SNESCreate(MPI_COMM_WORLD,&snes);
393: SNESSetType(snes,type);
395: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
396: Set routines for function and Jacobian evaluation
397: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
399: FormInitialGuess(&user,x);
400: SNESSetFunction(snes,r,FormFunction,(void *)&user);
401: SNESSetJacobian(snes,Jac,Jac,FormJacobian,(void *)&user);
403: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
404: Customize nonlinear solver; set runtime options
405: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
407: SNESSetFromOptions(snes);
409: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
410: Evaluate initial guess; then solve nonlinear system
411: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
413: /*
414: Note: The user should initialize the vector, x, with the initial guess
415: for the nonlinear solver prior to calling SNESSolve(). In particular,
416: to employ an initial guess of zero, the user should explicitly set
417: this vector to zero by calling VecSet().
418: */
419: FormInitialGuess(&user,x);
421: /*
422: Print the initial guess
423: */
424: VecGetArray(x,&xx);
425: for (inode = 0; inode < user.Nvlocal; inode++)
426: fprintf(fptr1,"Initial Solution at node %d is %f \n",inode,xx[inode]);
427: VecRestoreArray(x,&xx);
429: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
430: Now solve the nonlinear system
431: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
433: SNESSolve(snes,x,&its);
434: SNESGetNumberUnsuccessfulSteps(snes,&nfails);
435:
436: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
437: Print the output : solution vector and other information
438: Each processor writes to the file output.<rank> where rank is the
439: processor's rank.
440: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
442: VecGetArray(x,&xx);
443: for (inode = 0; inode < user.Nvlocal; inode++)
444: fprintf(fptr1,"Solution at node %d is %f \n",inode,xx[inode]);
445: VecRestoreArray(x,&xx);
446: fclose(fptr1);
447: PetscPrintf(MPI_COMM_WORLD,"number of Newton iterations = %d, ",its);
448: PetscPrintf(MPI_COMM_WORLD,"number of unsuccessful steps = %d\n",nfails);
450: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
451: Free work space. All PETSc objects should be destroyed when they
452: are no longer needed.
453: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
455: VecDestroy(x);
456: VecDestroy(r);
457: VecDestroy(user.localX);
458: VecDestroy(user.localF);
459: MatDestroy(Jac); SNESDestroy(snes);
460: /*PetscDrawDestroy(draw);*/
461: PetscFinalize();
463: return 0;
464: }
467: /* -------------------- Form initial approximation ----------------- */
469: /*
470: FormInitialGuess - Forms initial approximation.
472: Input Parameters:
473: user - user-defined application context
474: X - vector
476: Output Parameter:
477: X - vector
478: */
479: int FormInitialGuess(AppCtx *user,Vec X)
480: {
481: int i,Nvlocal,ierr;
482: int *gloInd;
483: PetscScalar *x;
484: #if defined (UNUSED_VARIABLES)
485: PetscReal temp1,temp,hx,hy,hxdhy,hydhx,sc;
486: int Neglobal,Nvglobal,j,row;
487: PetscReal alpha,lambda;
489: Nvglobal = user->Nvglobal;
490: Neglobal = user->Neglobal;
491: lambda = user->non_lin_param;
492: alpha = user->lin_param;
493: #endif
495: Nvlocal = user->Nvlocal;
496: gloInd = user->gloInd;
498: /*
499: Get a pointer to vector data.
500: - For default PETSc vectors, VecGetArray() returns a pointer to
501: the data array. Otherwise, the routine is implementation dependent.
502: - You MUST call VecRestoreArray() when you no longer need access to
503: the array.
504: */
505: VecGetArray(X,&x);
507: /*
508: Compute initial guess over the locally owned part of the grid
509: */
510: for (i=0; i < Nvlocal; i++) {
511: x[i] = (PetscReal)gloInd[i];
512: }
514: /*
515: Restore vector
516: */
517: VecRestoreArray(X,&x);
518: return 0;
519: }
522: /* -------------------- Evaluate Function F(x) --------------------- */
523: /*
524: FormFunction - Evaluates nonlinear function, F(x).
526: Input Parameters:
527: . snes - the SNES context
528: . X - input vector
529: . ptr - optional user-defined context, as set by SNESSetFunction()
531: Output Parameter:
532: . F - function vector
533: */
534: int FormFunction(SNES snes,Vec X,Vec F,void *ptr)
535: {
536: AppCtx *user = (AppCtx*)ptr;
537: int ierr,i,j,Nvlocal;
538: PetscReal alpha,lambda;
539: PetscScalar *x,*f;
540: VecScatter scatter;
541: Vec localX = user->localX;
542: #if defined (UNUSED_VARIABLES)
543: PetscScalar ut,ub,ul,ur,u,*g,sc,uyy,uxx;
544: PetscReal hx,hy,hxdhy,hydhx;
545: PetscReal two = 2.0,one = 1.0;
546: int Nvglobal,Neglobal,row;
547: int *gloInd;
549: Nvglobal = user->Nvglobal;
550: Neglobal = user->Neglobal;
551: gloInd = user->gloInd;
552: #endif
554: Nvlocal = user->Nvlocal;
555: lambda = user->non_lin_param;
556: alpha = user->lin_param;
557: scatter = user->scatter;
559: /*
560: PDE : L(u) + lambda*u*u +alpha*u = 0 where L(u) is the approximate Laplacian as
561: described in the beginning of this code
562:
563: First scatter the distributed vector X into local vector localX (that includes
564: values for ghost nodes. If we wish,we can put some other work between
565: VecScatterBegin() and VecScatterEnd() to overlap the communication with
566: computation.
567: */
568: VecScatterBegin(X,localX,INSERT_VALUES,SCATTER_FORWARD,scatter);
569: VecScatterEnd(X,localX,INSERT_VALUES,SCATTER_FORWARD,scatter);
571: /*
572: Get pointers to vector data
573: */
574: VecGetArray(localX,&x);
575: VecGetArray(F,&f);
577: /*
578: Now compute the f(x). As mentioned earlier, the computed Laplacian is just an
579: approximate one chosen for illustrative purpose only. Another point to notice
580: is that this is a local (completly parallel) calculation. In practical application
581: codes, function calculation time is a dominat portion of the overall execution time.
582: */
583: for (i=0; i < Nvlocal; i++) {
584: f[i] = (user->itot[i] - alpha)*x[i] - lambda*x[i]*x[i];
585: for (j = 0; j < user->itot[i]; j++) {
586: f[i] -= x[user->AdjM[i][j]];
587: }
588: }
590: /*
591: Restore vectors
592: */
593: VecRestoreArray(localX,&x);
594: VecRestoreArray(F,&f);
595: /*VecView(F,PETSC_VIEWER_STDOUT_WORLD);*/
597: return 0;
598: }
602: /* -------------------- Evaluate Jacobian F'(x) -------------------- */
603: /*
604: FormJacobian - Evaluates Jacobian matrix.
606: Input Parameters:
607: . snes - the SNES context
608: . X - input vector
609: . ptr - optional user-defined context, as set by SNESSetJacobian()
611: Output Parameters:
612: . A - Jacobian matrix
613: . B - optionally different preconditioning matrix
614: . flag - flag indicating matrix structure
616: */
617: int FormJacobian(SNES snes,Vec X,Mat *J,Mat *B,MatStructure *flag,void *ptr)
618: {
619: AppCtx *user = (AppCtx*)ptr;
620: Mat jac = *B;
621: int i,j,Nvlocal,col[50],ierr;
622: PetscScalar alpha,lambda,value[50];
623: Vec localX = user->localX;
624: VecScatter scatter;
625: PetscScalar *x;
626: #if defined (UNUSED_VARIABLES)
627: PetscScalar two = 2.0,one = 1.0;
628: int row,Nvglobal,Neglobal;
629: int *gloInd;
631: Nvglobal = user->Nvglobal;
632: Neglobal = user->Neglobal;
633: gloInd = user->gloInd;
634: #endif
635:
636: /*printf("Entering into FormJacobian \n");*/
637: Nvlocal = user->Nvlocal;
638: lambda = user->non_lin_param;
639: alpha = user->lin_param;
640: scatter = user->scatter;
642: /*
643: PDE : L(u) + lambda*u*u +alpha*u = 0 where L(u) is the approximate Laplacian as
644: described in the beginning of this code
645:
646: First scatter the distributed vector X into local vector localX (that includes
647: values for ghost nodes. If we wish, we can put some other work between
648: VecScatterBegin() and VecScatterEnd() to overlap the communication with
649: computation.
650: */
651: VecScatterBegin(X,localX,INSERT_VALUES,SCATTER_FORWARD,scatter);
652: VecScatterEnd(X,localX,INSERT_VALUES,SCATTER_FORWARD,scatter);
653:
654: /*
655: Get pointer to vector data
656: */
657: VecGetArray(localX,&x);
659: for (i=0; i < Nvlocal; i++) {
660: col[0] = i;
661: value[0] = user->itot[i] - 2.0*lambda*x[i] - alpha;
662: for (j = 0; j < user->itot[i]; j++) {
663: col[j+1] = user->AdjM[i][j];
664: value[j+1] = -1.0;
665: }
667: /*
668: Set the matrix values in the local ordering. Note that in order to use this
669: feature we must call the routine MatSetLocalToGlobalMapping() after the
670: matrix has been created.
671: */
672: MatSetValuesLocal(jac,1,&i,1+user->itot[i],col,value,INSERT_VALUES);
673: }
675: /*
676: Assemble matrix, using the 2-step process:
677: MatAssemblyBegin(), MatAssemblyEnd().
678: Between these two calls, the pointer to vector data has been restored to
679: demonstrate the use of overlapping communicationn with computation.
680: */
681: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
682: VecRestoreArray(localX,&x);
683: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
685: /*
686: Set flag to indicate that the Jacobian matrix retains an identical
687: nonzero structure throughout all nonlinear iterations (although the
688: values of the entries change). Thus, we can save some work in setting
689: up the preconditioner (e.g., no need to redo symbolic factorization for
690: ILU/ICC preconditioners).
691: - If the nonzero structure of the matrix is different during
692: successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
693: must be used instead. If you are unsure whether the matrix
694: structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
695: - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
696: believes your assertion and does not check the structure
697: of the matrix. If you erroneously claim that the structure
698: is the same when it actually is not, the new preconditioner
699: will not function correctly. Thus, use this optimization
700: feature with caution!
701: */
702: *flag = SAME_NONZERO_PATTERN;
704: /*
705: Tell the matrix we will never add a new nonzero location to the
706: matrix. If we do, it will generate an error.
707: */
708: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR);
709: /* MatView(jac,PETSC_VIEWER_STDOUT_SELF); */
710: return 0;
711: }
712: #else
713: #include <stdio.h>
714: int main(int argc,char **args)
715: {
716: fprintf(stdout,"This example does not work for complex numbers.\n");
717: return 0;
718: }
719: #endif