Actual source code: ex2.c

  1: /*$Id: ex2.c,v 1.41 2001/08/10 03:34:17 bsmith Exp $*/
  2: static char help[] ="Solves a time-dependent nonlinear PDE. Uses implicitn
  3: timestepping.  Runtime options include:n
  4:   -M <xg>, where <xg> = number of grid pointsn
  5:   -debug : Activate debugging printoutsn
  6:   -nox   : Deactivate x-window graphicsnn";

  8: /*
  9:    Concepts: TS^time-dependent nonlinear problems
 10:    Processors: n
 11: */

 13: /* ------------------------------------------------------------------------

 15:    This program solves the PDE

 17:                u * u_xx 
 18:          u_t = ---------
 19:                2*(t+1)^2 

 21:     on the domain 0 <= x <= 1, with boundary conditions
 22:          u(t,0) = t + 1,  u(t,1) = 2*t + 2,
 23:     and initial condition
 24:          u(0,x) = 1 + x*x.

 26:     The exact solution is:
 27:          u(t,x) = (1 + x*x) * (1 + t)

 29:     Note that since the solution is linear in time and quadratic in x,
 30:     the finite difference scheme actually computes the "exact" solution.

 32:     We use by default the backward Euler method.

 34:   ------------------------------------------------------------------------- */

 36: /*
 37:    Include "petscts.h" to use the PETSc timestepping routines. Note that
 38:    this file automatically includes "petsc.h" and other lower-level
 39:    PETSc include files.

 41:    Include the "petscda.h" to allow us to use the distributed array data 
 42:    structures to manage the parallel grid.
 43: */
 44:  #include petscts.h
 45:  #include petscda.h

 47: /* 
 48:    User-defined application context - contains data needed by the 
 49:    application-provided callback routines.
 50: */
 51: typedef struct {
 52:   MPI_Comm   comm;          /* communicator */
 53:   DA         da;            /* distributed array data structure */
 54:   Vec        localwork;     /* local ghosted work vector */
 55:   Vec        u_local;       /* local ghosted approximate solution vector */
 56:   Vec        solution;      /* global exact solution vector */
 57:   int        m;             /* total number of grid points */
 58:   PetscReal  h;             /* mesh width: h = 1/(m-1) */
 59:   PetscTruth debug;         /* flag (1 indicates activation of debugging printouts) */
 60: } AppCtx;

 62: /* 
 63:    User-defined routines, provided below.
 64: */
 65: extern int InitialConditions(Vec,AppCtx*);
 66: extern int RHSFunction(TS,PetscReal,Vec,Vec,void*);
 67: extern int RHSJacobian(TS,PetscReal,Vec,Mat*,Mat*,MatStructure*,void*);
 68: extern int Monitor(TS,int,PetscReal,Vec,void*);
 69: extern int ExactSolution(PetscReal,Vec,AppCtx*);

 71: /*
 72:    Utility routine for finite difference Jacobian approximation
 73: */
 74: extern int RHSJacobianFD(TS,PetscReal,Vec,Mat*,Mat*,MatStructure*,void*);

 76: int main(int argc,char **argv)
 77: {
 78:   AppCtx     appctx;                 /* user-defined application context */
 79:   TS         ts;                     /* timestepping context */
 80:   Mat        A;                      /* Jacobian matrix data structure */
 81:   Vec        u;                      /* approximate solution vector */
 82:   int        time_steps_max = 1000;  /* default max timesteps */
 83:   int        ierr,steps;
 84:   PetscReal  ftime;                  /* final time */
 85:   PetscReal  dt;
 86:   PetscReal  time_total_max = 100.0; /* default max total time */
 87:   PetscTruth flg;

 89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 90:      Initialize program and set problem parameters
 91:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 92: 
 93:   PetscInitialize(&argc,&argv,(char*)0,help);

 95:   appctx.comm = PETSC_COMM_WORLD;
 96:   appctx.m    = 60;
 97:   PetscOptionsGetInt(PETSC_NULL,"-M",&appctx.m,PETSC_NULL);
 98:   PetscOptionsHasName(PETSC_NULL,"-debug",&appctx.debug);
 99:   appctx.h    = 1.0/(appctx.m-1.0);

101:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102:      Create vector data structures
103:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

105:   /*
106:      Create distributed array (DA) to manage parallel grid and vectors
107:      and to set up the ghost point communication pattern.  There are M 
108:      total grid values spread equally among all the processors.
109:   */
110:   DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,appctx.m,1,1,PETSC_NULL,
111:                     &appctx.da);

113:   /*
114:      Extract global and local vectors from DA; we use these to store the
115:      approximate solution.  Then duplicate these for remaining vectors that
116:      have the same types.
117:   */
118:   DACreateGlobalVector(appctx.da,&u);
119:   DACreateLocalVector(appctx.da,&appctx.u_local);

121:   /*
122:      Create local work vector for use in evaluating right-hand-side function;
123:      create global work vector for storing exact solution.
124:   */
125:   VecDuplicate(appctx.u_local,&appctx.localwork);
126:   VecDuplicate(u,&appctx.solution);

128:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129:      Create timestepping solver context; set callback routine for
130:      right-hand-side function evaluation.
131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

133:   TSCreate(PETSC_COMM_WORLD,&ts);
134:   TSSetProblemType(ts,TS_NONLINEAR);
135:   TSSetRHSFunction(ts,RHSFunction,&appctx);

137:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
138:      Set optional user-defined monitoring routine
139:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

141:   TSSetMonitor(ts,Monitor,&appctx,PETSC_NULL);

143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144:      For nonlinear problems, the user can provide a Jacobian evaluation
145:      routine (or use a finite differencing approximation).

147:      Create matrix data structure; set Jacobian evaluation routine.
148:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

150:   MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,appctx.m,appctx.m,&A);
151:   MatSetFromOptions(A);
152:   PetscOptionsHasName(PETSC_NULL,"-fdjac",&flg);
153:   if (flg) {
154:     TSSetRHSJacobian(ts,A,A,RHSJacobianFD,&appctx);
155:   } else {
156:     TSSetRHSJacobian(ts,A,A,RHSJacobian,&appctx);
157:   }

159:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160:      Set solution vector and initial timestep
161:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

163:   dt   = appctx.h/2.0;
164:   TSSetInitialTimeStep(ts,0.0,dt);
165:   TSSetSolution(ts,u);

167:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
168:      Customize timestepping solver:  
169:        - Set the solution method to be the Backward Euler method.
170:        - Set timestepping duration info 
171:      Then set runtime options, which can override these defaults.
172:      For example,
173:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
174:      to override the defaults set by TSSetDuration().
175:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

177:   TSSetType(ts,TS_BEULER);
178:   TSSetDuration(ts,time_steps_max,time_total_max);
179:   TSSetFromOptions(ts);

181:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182:      Solve the problem
183:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

185:   /*
186:      Evaluate initial conditions
187:   */
188:   InitialConditions(u,&appctx);

190:   /*
191:      Run the timestepping solver
192:   */
193:   TSStep(ts,&steps,&ftime);

195:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196:      Free work space.  All PETSc objects should be destroyed when they
197:      are no longer needed.
198:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

200:   TSDestroy(ts);
201:   VecDestroy(u);
202:   MatDestroy(A);
203:   DADestroy(appctx.da);
204:   VecDestroy(appctx.localwork);
205:   VecDestroy(appctx.solution);
206:   VecDestroy(appctx.u_local);

208:   /*
209:      Always call PetscFinalize() before exiting a program.  This routine
210:        - finalizes the PETSc libraries as well as MPI
211:        - provides summary and diagnostic information if certain runtime
212:          options are chosen (e.g., -log_summary). 
213:   */
214:   PetscFinalize();
215:   return 0;
216: }
217: /* --------------------------------------------------------------------- */
218: /*
219:    InitialConditions - Computes the solution at the initial time. 

221:    Input Parameters:
222:    u - uninitialized solution vector (global)
223:    appctx - user-defined application context

225:    Output Parameter:
226:    u - vector with solution at initial time (global)
227: */
228: int InitialConditions(Vec u,AppCtx *appctx)
229: {
230:   PetscScalar *u_localptr,h = appctx->h,x;
231:   int    i,mybase,myend,ierr;

233:   /* 
234:      Determine starting point of each processor's range of
235:      grid values.
236:   */
237:   VecGetOwnershipRange(u,&mybase,&myend);

239:   /* 
240:     Get a pointer to vector data.
241:     - For default PETSc vectors, VecGetArray() returns a pointer to
242:       the data array.  Otherwise, the routine is implementation dependent.
243:     - You MUST call VecRestoreArray() when you no longer need access to
244:       the array.
245:     - Note that the Fortran interface to VecGetArray() differs from the
246:       C version.  See the users manual for details.
247:   */
248:   VecGetArray(u,&u_localptr);

250:   /* 
251:      We initialize the solution array by simply writing the solution
252:      directly into the array locations.  Alternatively, we could use
253:      VecSetValues() or VecSetValuesLocal().
254:   */
255:   for (i=mybase; i<myend; i++) {
256:     x = h*(PetscReal)i; /* current location in global grid */
257:     u_localptr[i-mybase] = 1.0 + x*x;
258:   }

260:   /* 
261:      Restore vector
262:   */
263:   VecRestoreArray(u,&u_localptr);

265:   /* 
266:      Print debugging information if desired
267:   */
268:   if (appctx->debug) {
269:      PetscPrintf(appctx->comm,"initial guess vectorn");
270:      VecView(u,PETSC_VIEWER_STDOUT_WORLD);
271:   }

273:   return 0;
274: }
275: /* --------------------------------------------------------------------- */
276: /*
277:    ExactSolution - Computes the exact solution at a given time.

279:    Input Parameters:
280:    t - current time
281:    solution - vector in which exact solution will be computed
282:    appctx - user-defined application context

284:    Output Parameter:
285:    solution - vector with the newly computed exact solution
286: */
287: int ExactSolution(PetscReal t,Vec solution,AppCtx *appctx)
288: {
289:   PetscScalar *s_localptr,h = appctx->h,x;
290:   int    i,mybase,myend,ierr;

292:   /* 
293:      Determine starting and ending points of each processor's 
294:      range of grid values
295:   */
296:   VecGetOwnershipRange(solution,&mybase,&myend);

298:   /*
299:      Get a pointer to vector data.
300:   */
301:   VecGetArray(solution,&s_localptr);

303:   /* 
304:      Simply write the solution directly into the array locations.
305:      Alternatively, we could use VecSetValues() or VecSetValuesLocal().
306:   */
307:   for (i=mybase; i<myend; i++) {
308:     x = h*(PetscReal)i;
309:     s_localptr[i-mybase] = (t + 1.0)*(1.0 + x*x);
310:   }

312:   /* 
313:      Restore vector
314:   */
315:   VecRestoreArray(solution,&s_localptr);
316:   return 0;
317: }
318: /* --------------------------------------------------------------------- */
319: /*
320:    Monitor - User-provided routine to monitor the solution computed at 
321:    each timestep.  This example plots the solution and computes the
322:    error in two different norms.

324:    Input Parameters:
325:    ts     - the timestep context
326:    step   - the count of the current step (with 0 meaning the
327:             initial condition)
328:    time   - the current time
329:    u      - the solution at this timestep
330:    ctx    - the user-provided context for this monitoring routine.
331:             In this case we use the application context which contains 
332:             information about the problem size, workspace and the exact 
333:             solution.
334: */
335: int Monitor(TS ts,int step,PetscReal time,Vec u,void *ctx)
336: {
337:   AppCtx       *appctx = (AppCtx*) ctx;   /* user-defined application context */
338:   int          ierr;
339:   PetscReal    en2,en2s,enmax;
340:   PetscScalar  mone = -1.0;
341:   PetscDraw    draw;

343:   /*
344:      We use the default X windows viewer
345:              PETSC_VIEWER_DRAW_(appctx->comm)
346:      that is associated with the current communicator. This saves
347:      the effort of calling PetscViewerDrawOpen() to create the window.
348:      Note that if we wished to plot several items in separate windows we
349:      would create each viewer with PetscViewerDrawOpen() and store them in
350:      the application context, appctx.

352:      PetscReal buffering makes graphics look better.
353:   */
354:   PetscViewerDrawGetDraw(PETSC_VIEWER_DRAW_(appctx->comm),0,&draw);
355:   PetscDrawSetDoubleBuffer(draw);
356:   VecView(u,PETSC_VIEWER_DRAW_(appctx->comm));

358:   /*
359:      Compute the exact solution at this timestep
360:   */
361:   ExactSolution(time,appctx->solution,appctx);

363:   /*
364:      Print debugging information if desired
365:   */
366:   if (appctx->debug) {
367:      PetscPrintf(appctx->comm,"Computed solution vectorn");
368:      VecView(u,PETSC_VIEWER_STDOUT_WORLD);
369:      PetscPrintf(appctx->comm,"Exact solution vectorn");
370:      VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD);
371:   }

373:   /*
374:      Compute the 2-norm and max-norm of the error
375:   */
376:   VecAXPY(&mone,u,appctx->solution);
377:   VecNorm(appctx->solution,NORM_2,&en2);
378:   en2s  = sqrt(appctx->h)*en2; /* scale the 2-norm by the grid spacing */
379:   VecNorm(appctx->solution,NORM_MAX,&enmax);

381:   /*
382:      PetscPrintf() causes only the first processor in this 
383:      communicator to print the timestep information.
384:   */
385:   PetscPrintf(appctx->comm,"Timestep %d: time = %g,2-norm error = %g, max norm error = %gn",
386:               step,time,en2s,enmax);

388:   /*
389:      Print debugging information if desired
390:   */
391:   if (appctx->debug) {
392:      PetscPrintf(appctx->comm,"Error vectorn");
393:      VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD);
394:   }
395:   return 0;
396: }
397: /* --------------------------------------------------------------------- */
398: /*
399:    RHSFunction - User-provided routine that evalues the right-hand-side
400:    function of the ODE.  This routine is set in the main program by 
401:    calling TSSetRHSFunction().  We compute:
402:           global_out = F(global_in)

404:    Input Parameters:
405:    ts         - timesteping context
406:    t          - current time
407:    global_in  - vector containing the current iterate
408:    ctx        - (optional) user-provided context for function evaluation.
409:                 In this case we use the appctx defined above.

411:    Output Parameter:
412:    global_out - vector containing the newly evaluated function
413: */
414: int RHSFunction(TS ts,PetscReal t,Vec global_in,Vec global_out,void *ctx)
415: {
416:   AppCtx *appctx = (AppCtx*) ctx;       /* user-defined application context */
417:   DA     da = appctx->da;               /* distributed array */
418:   Vec    local_in = appctx->u_local;    /* local ghosted input vector */
419:   Vec    localwork = appctx->localwork; /* local ghosted work vector */
420:   int    ierr,i,localsize,rank,size;
421:   PetscScalar *copyptr,*localptr,sc;

423:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
424:      Get ready for local function computations
425:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
426:   /*
427:      Scatter ghost points to local vector, using the 2-step process
428:         DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
429:      By placing code between these two statements, computations can be
430:      done while messages are in transition.
431:   */
432:   DAGlobalToLocalBegin(da,global_in,INSERT_VALUES,local_in);
433:   DAGlobalToLocalEnd(da,global_in,INSERT_VALUES,local_in);

435:   /*
436:       Access directly the values in our local INPUT work array
437:   */
438:   VecGetArray(local_in,&localptr);

440:   /*
441:       Access directly the values in our local OUTPUT work array
442:   */
443:   VecGetArray(localwork,&copyptr);

445:   sc = 1.0/(appctx->h*appctx->h*2.0*(1.0+t)*(1.0+t));

447:   /*
448:       Evaluate our function on the nodes owned by this processor
449:   */
450:   VecGetLocalSize(local_in,&localsize);

452:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
453:      Compute entries for the locally owned part 
454:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

456:   /*
457:      Handle boundary conditions: This is done by using the boundary condition 
458:         u(t,boundary) = g(t,boundary) 
459:      for some function g. Now take the derivative with respect to t to obtain
460:         u_{t}(t,boundary) = g_{t}(t,boundary)

462:      In our case, u(t,0) = t + 1, so that u_{t}(t,0) = 1 
463:              and  u(t,1) = 2t+ 1, so that u_{t}(t,1) = 2
464:   */
465:   MPI_Comm_rank(appctx->comm,&rank);
466:   MPI_Comm_size(appctx->comm,&size);
467:   if (!rank)          copyptr[0]           = 1.0;
468:   if (rank == size-1) copyptr[localsize-1] = 2.0;

470:   /*
471:      Handle the interior nodes where the PDE is replace by finite 
472:      difference operators.
473:   */
474:   for (i=1; i<localsize-1; i++) {
475:     copyptr[i] =  localptr[i] * sc * (localptr[i+1] + localptr[i-1] - 2.0*localptr[i]);
476:   }

478:   /* 
479:      Restore vectors
480:   */
481:   VecRestoreArray(local_in,&localptr);
482:   VecRestoreArray(localwork,&copyptr);

484:   /*
485:      Insert values from the local OUTPUT vector into the global 
486:      output vector
487:   */
488:   DALocalToGlobal(da,localwork,INSERT_VALUES,global_out);

490:   /* Print debugging information if desired */
491:   if (appctx->debug) {
492:      PetscPrintf(appctx->comm,"RHS function vectorn");
493:      VecView(global_out,PETSC_VIEWER_STDOUT_WORLD);
494:   }

496:   return 0;
497: }
498: /* --------------------------------------------------------------------- */
499: /*
500:    RHSJacobian - User-provided routine to compute the Jacobian of
501:    the nonlinear right-hand-side function of the ODE.

503:    Input Parameters:
504:    ts - the TS context
505:    t - current time
506:    global_in - global input vector
507:    dummy - optional user-defined context, as set by TSetRHSJacobian()

509:    Output Parameters:
510:    AA - Jacobian matrix
511:    BB - optionally different preconditioning matrix
512:    str - flag indicating matrix structure

514:   Notes:
515:   RHSJacobian computes entries for the locally owned part of the Jacobian.
516:    - Currently, all PETSc parallel matrix formats are partitioned by
517:      contiguous chunks of rows across the processors. 
518:    - Each processor needs to insert only elements that it owns
519:      locally (but any non-local elements will be sent to the
520:      appropriate processor during matrix assembly). 
521:    - Always specify global row and columns of matrix entries when
522:      using MatSetValues().
523:    - Here, we set all entries for a particular row at once.
524:    - Note that MatSetValues() uses 0-based row and column numbers
525:      in Fortran as well as in C.
526: */
527: int RHSJacobian(TS ts,PetscReal t,Vec global_in,Mat *AA,Mat *BB,MatStructure *str,void *ctx)
528: {
529:   Mat    A = *AA;                      /* Jacobian matrix */
530:   AppCtx *appctx = (AppCtx*)ctx;     /* user-defined application context */
531:   Vec    local_in = appctx->u_local;   /* local ghosted input vector */
532:   DA     da = appctx->da;              /* distributed array */
533:   PetscScalar v[3],*localptr,sc;
534:   int    ierr,i,mstart,mend,mstarts,mends,idx[3],is;

536:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
537:      Get ready for local Jacobian computations
538:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
539:   /*
540:      Scatter ghost points to local vector, using the 2-step process
541:         DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
542:      By placing code between these two statements, computations can be
543:      done while messages are in transition.
544:   */
545:   DAGlobalToLocalBegin(da,global_in,INSERT_VALUES,local_in);
546:   DAGlobalToLocalEnd(da,global_in,INSERT_VALUES,local_in);

548:   /*
549:      Get pointer to vector data
550:   */
551:   VecGetArray(local_in,&localptr);

553:   /* 
554:      Get starting and ending locally owned rows of the matrix
555:   */
556:   MatGetOwnershipRange(A,&mstarts,&mends);
557:   mstart = mstarts; mend = mends;

559:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
560:      Compute entries for the locally owned part of the Jacobian.
561:       - Currently, all PETSc parallel matrix formats are partitioned by
562:         contiguous chunks of rows across the processors. 
563:       - Each processor needs to insert only elements that it owns
564:         locally (but any non-local elements will be sent to the
565:         appropriate processor during matrix assembly). 
566:       - Here, we set all entries for a particular row at once.
567:       - We can set matrix entries either using either
568:         MatSetValuesLocal() or MatSetValues().
569:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

571:   /* 
572:      Set matrix rows corresponding to boundary data
573:   */
574:   if (mstart == 0) {
575:     v[0] = 0.0;
576:     MatSetValues(A,1,&mstart,1,&mstart,v,INSERT_VALUES);
577:     mstart++;
578:   }
579:   if (mend == appctx->m) {
580:     mend--;
581:     v[0] = 0.0;
582:     MatSetValues(A,1,&mend,1,&mend,v,INSERT_VALUES);
583:   }

585:   /*
586:      Set matrix rows corresponding to interior data.  We construct the 
587:      matrix one row at a time.
588:   */
589:   sc = 1.0/(appctx->h*appctx->h*2.0*(1.0+t)*(1.0+t));
590:   for (i=mstart; i<mend; i++) {
591:     idx[0] = i-1; idx[1] = i; idx[2] = i+1;
592:     is     = i - mstart + 1;
593:     v[0]   = sc*localptr[is];
594:     v[1]   = sc*(localptr[is+1] + localptr[is-1] - 4.0*localptr[is]);
595:     v[2]   = sc*localptr[is];
596:     MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
597:   }

599:   /* 
600:      Restore vector
601:   */
602:   VecRestoreArray(local_in,&localptr);

604:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
605:      Complete the matrix assembly process and set some options
606:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
607:   /*
608:      Assemble matrix, using the 2-step process:
609:        MatAssemblyBegin(), MatAssemblyEnd()
610:      Computations can be done while messages are in transition
611:      by placing code between these two statements.
612:   */
613:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
614:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

616:   /*
617:      Set flag to indicate that the Jacobian matrix retains an identical
618:      nonzero structure throughout all timestepping iterations (although the
619:      values of the entries change). Thus, we can save some work in setting
620:      up the preconditioner (e.g., no need to redo symbolic factorization for
621:      ILU/ICC preconditioners).
622:       - If the nonzero structure of the matrix is different during
623:         successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
624:         must be used instead.  If you are unsure whether the matrix
625:         structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
626:       - Caution:  If you specify SAME_NONZERO_PATTERN, PETSc
627:         believes your assertion and does not check the structure
628:         of the matrix.  If you erroneously claim that the structure
629:         is the same when it actually is not, the new preconditioner
630:         will not function correctly.  Thus, use this optimization
631:         feature with caution!
632:   */
633:   *str = SAME_NONZERO_PATTERN;

635:   /*
636:      Set and option to indicate that we will never add a new nonzero location 
637:      to the matrix. If we do, it will generate an error.
638:   */
639:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR);

641:   return 0;
642: }