Actual source code: ex2.c

petsc-master 2017-08-16
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  2: static char help[] ="Solves a time-dependent nonlinear PDE. Uses implicit\n\
  3: timestepping.  Runtime options include:\n\
  4:   -M <xg>, where <xg> = number of grid points\n\
  5:   -debug : Activate debugging printouts\n\
  6:   -nox   : Deactivate x-window graphics\n\n";

  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 "petscsys.h" and other lower-level
 39:    PETSc include files.

 41:    Include the "petscdmda.h" to allow us to use the distributed array data
 42:    structures to manage the parallel grid.
 43: */
 44:  #include <petscts.h>
 45:  #include <petscdm.h>
 46:  #include <petscdmda.h>
 47:  #include <petscdraw.h>

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

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

 73: int main(int argc,char **argv)
 74: {
 75:   AppCtx         appctx;                 /* user-defined application context */
 76:   TS             ts;                     /* timestepping context */
 77:   Mat            A;                      /* Jacobian matrix data structure */
 78:   Vec            u;                      /* approximate solution vector */
 79:   PetscInt       time_steps_max = 100;  /* default max timesteps */
 81:   PetscReal      dt;
 82:   PetscReal      time_total_max = 100.0; /* default max total time */
 83:   PetscBool      mymonitor      = PETSC_FALSE;
 84:   PetscReal      bounds[]       = {1.0, 3.3};

 86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 87:      Initialize program and set problem parameters
 88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 90:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 91:   PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,bounds);

 93:   appctx.comm = PETSC_COMM_WORLD;
 94:   appctx.m    = 60;

 96:   PetscOptionsGetInt(NULL,NULL,"-M",&appctx.m,NULL);
 97:   PetscOptionsHasName(NULL,NULL,"-debug",&appctx.debug);
 98:   PetscOptionsHasName(NULL,NULL,"-mymonitor",&mymonitor);

100:   appctx.h    = 1.0/(appctx.m-1.0);

102:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103:      Create vector data structures
104:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

106:   /*
107:      Create distributed array (DMDA) to manage parallel grid and vectors
108:      and to set up the ghost point communication pattern.  There are M
109:      total grid values spread equally among all the processors.
110:   */
111:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,appctx.m,1,1,NULL,&appctx.da);
112:   DMSetFromOptions(appctx.da);
113:   DMSetUp(appctx.da);

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

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

130:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
131:      Create timestepping solver context; set callback routine for
132:      right-hand-side function evaluation.
133:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

135:   TSCreate(PETSC_COMM_WORLD,&ts);
136:   TSSetProblemType(ts,TS_NONLINEAR);
137:   TSSetRHSFunction(ts,NULL,RHSFunction,&appctx);

139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140:      Set optional user-defined monitoring routine
141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

143:   if (mymonitor) {
144:     TSMonitorSet(ts,Monitor,&appctx,NULL);
145:   }

147:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148:      For nonlinear problems, the user can provide a Jacobian evaluation
149:      routine (or use a finite differencing approximation).

151:      Create matrix data structure; set Jacobian evaluation routine.
152:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

154:   MatCreate(PETSC_COMM_WORLD,&A);
155:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,appctx.m,appctx.m);
156:   MatSetFromOptions(A);
157:   MatSetUp(A);
158:   TSSetRHSJacobian(ts,A,A,RHSJacobian,&appctx);

160:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161:      Set solution vector and initial timestep
162:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

164:   dt   = appctx.h/2.0;
165:   TSSetTimeStep(ts,dt);

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_final_time <maxtime>
174:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
175:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

177:   TSSetType(ts,TSBEULER);
178:   TSSetMaxSteps(ts,time_steps_max);
179:   TSSetMaxTime(ts,time_total_max);
180:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
181:   TSSetFromOptions(ts);

183:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184:      Solve the problem
185:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

187:   /*
188:      Evaluate initial conditions
189:   */
190:   InitialConditions(u,&appctx);

192:   /*
193:      Run the timestepping solver
194:   */
195:   TSSolve(ts,u);

197:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198:      Free work space.  All PETSc objects should be destroyed when they
199:      are no longer needed.
200:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

202:   TSDestroy(&ts);
203:   VecDestroy(&u);
204:   MatDestroy(&A);
205:   DMDestroy(&appctx.da);
206:   VecDestroy(&appctx.localwork);
207:   VecDestroy(&appctx.solution);
208:   VecDestroy(&appctx.u_local);

210:   /*
211:      Always call PetscFinalize() before exiting a program.  This routine
212:        - finalizes the PETSc libraries as well as MPI
213:        - provides summary and diagnostic information if certain runtime
214:          options are chosen (e.g., -log_view).
215:   */
216:   PetscFinalize();
217:   return ierr;
218: }
219: /* --------------------------------------------------------------------- */
220: /*
221:    InitialConditions - Computes the solution at the initial time.

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

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

236:   /*
237:      Determine starting point of each processor's range of
238:      grid values.
239:   */
240:   VecGetOwnershipRange(u,&mybase,&myend);

242:   /*
243:     Get a pointer to vector data.
244:     - For default PETSc vectors, VecGetArray() returns a pointer to
245:       the data array.  Otherwise, the routine is implementation dependent.
246:     - You MUST call VecRestoreArray() when you no longer need access to
247:       the array.
248:     - Note that the Fortran interface to VecGetArray() differs from the
249:       C version.  See the users manual for details.
250:   */
251:   VecGetArray(u,&u_localptr);

253:   /*
254:      We initialize the solution array by simply writing the solution
255:      directly into the array locations.  Alternatively, we could use
256:      VecSetValues() or VecSetValuesLocal().
257:   */
258:   for (i=mybase; i<myend; i++) {
259:     x = h*(PetscReal)i; /* current location in global grid */
260:     u_localptr[i-mybase] = 1.0 + x*x;
261:   }

263:   /*
264:      Restore vector
265:   */
266:   VecRestoreArray(u,&u_localptr);

268:   /*
269:      Print debugging information if desired
270:   */
271:   if (appctx->debug) {
272:     PetscPrintf(appctx->comm,"initial guess vector\n");
273:     VecView(u,PETSC_VIEWER_STDOUT_WORLD);
274:   }

276:   return 0;
277: }
278: /* --------------------------------------------------------------------- */
279: /*
280:    ExactSolution - Computes the exact solution at a given time.

282:    Input Parameters:
283:    t - current time
284:    solution - vector in which exact solution will be computed
285:    appctx - user-defined application context

287:    Output Parameter:
288:    solution - vector with the newly computed exact solution
289: */
290: PetscErrorCode ExactSolution(PetscReal t,Vec solution,AppCtx *appctx)
291: {
292:   PetscScalar    *s_localptr,h = appctx->h,x;
293:   PetscInt       i,mybase,myend;

296:   /*
297:      Determine starting and ending points of each processor's
298:      range of grid values
299:   */
300:   VecGetOwnershipRange(solution,&mybase,&myend);

302:   /*
303:      Get a pointer to vector data.
304:   */
305:   VecGetArray(solution,&s_localptr);

307:   /*
308:      Simply write the solution directly into the array locations.
309:      Alternatively, we could use VecSetValues() or VecSetValuesLocal().
310:   */
311:   for (i=mybase; i<myend; i++) {
312:     x = h*(PetscReal)i;
313:     s_localptr[i-mybase] = (t + 1.0)*(1.0 + x*x);
314:   }

316:   /*
317:      Restore vector
318:   */
319:   VecRestoreArray(solution,&s_localptr);
320:   return 0;
321: }
322: /* --------------------------------------------------------------------- */
323: /*
324:    Monitor - User-provided routine to monitor the solution computed at
325:    each timestep.  This example plots the solution and computes the
326:    error in two different norms.

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

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

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

361:   /*
362:      Compute the exact solution at this timestep
363:   */
364:   ExactSolution(time,appctx->solution,appctx);

366:   /*
367:      Print debugging information if desired
368:   */
369:   if (appctx->debug) {
370:     PetscPrintf(appctx->comm,"Computed solution vector\n");
371:     VecView(u,PETSC_VIEWER_STDOUT_WORLD);
372:     PetscPrintf(appctx->comm,"Exact solution vector\n");
373:     VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD);
374:   }

376:   /*
377:      Compute the 2-norm and max-norm of the error
378:   */
379:   VecAXPY(appctx->solution,-1.0,u);
380:   VecNorm(appctx->solution,NORM_2,&en2);
381:   en2s = PetscSqrtReal(appctx->h)*en2;  /* scale the 2-norm by the grid spacing */
382:   VecNorm(appctx->solution,NORM_MAX,&enmax);

384:   /*
385:      PetscPrintf() causes only the first processor in this
386:      communicator to print the timestep information.
387:   */
388:   PetscPrintf(appctx->comm,"Timestep %D: time = %g 2-norm error = %g  max norm error = %g\n",step,(double)time,(double)en2s,(double)enmax);

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

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

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

428:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
429:      Get ready for local function computations
430:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
431:   /*
432:      Scatter ghost points to local vector, using the 2-step process
433:         DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
434:      By placing code between these two statements, computations can be
435:      done while messages are in transition.
436:   */
437:   DMGlobalToLocalBegin(da,global_in,INSERT_VALUES,local_in);
438:   DMGlobalToLocalEnd(da,global_in,INSERT_VALUES,local_in);

440:   /*
441:       Access directly the values in our local INPUT work array
442:   */
443:   VecGetArrayRead(local_in,&localptr);

445:   /*
446:       Access directly the values in our local OUTPUT work array
447:   */
448:   VecGetArray(localwork,&copyptr);

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

452:   /*
453:       Evaluate our function on the nodes owned by this processor
454:   */
455:   VecGetLocalSize(local_in,&localsize);

457:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
458:      Compute entries for the locally owned part
459:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

461:   /*
462:      Handle boundary conditions: This is done by using the boundary condition
463:         u(t,boundary) = g(t,boundary)
464:      for some function g. Now take the derivative with respect to t to obtain
465:         u_{t}(t,boundary) = g_{t}(t,boundary)

467:      In our case, u(t,0) = t + 1, so that u_{t}(t,0) = 1
468:              and  u(t,1) = 2t+ 2, so that u_{t}(t,1) = 2
469:   */
470:   MPI_Comm_rank(appctx->comm,&rank);
471:   MPI_Comm_size(appctx->comm,&size);
472:   if (!rank)          copyptr[0]           = 1.0;
473:   if (rank == size-1) copyptr[localsize-1] = 2.0;

475:   /*
476:      Handle the interior nodes where the PDE is replace by finite
477:      difference operators.
478:   */
479:   for (i=1; i<localsize-1; i++) copyptr[i] =  localptr[i] * sc * (localptr[i+1] + localptr[i-1] - 2.0*localptr[i]);

481:   /*
482:      Restore vectors
483:   */
484:   VecRestoreArrayRead(local_in,&localptr);
485:   VecRestoreArray(localwork,&copyptr);

487:   /*
488:      Insert values from the local OUTPUT vector into the global
489:      output vector
490:   */
491:   DMLocalToGlobalBegin(da,localwork,INSERT_VALUES,global_out);
492:   DMLocalToGlobalEnd(da,localwork,INSERT_VALUES,global_out);

494:   /* Print debugging information if desired */
495:   if (appctx->debug) {
496:     PetscPrintf(appctx->comm,"RHS function vector\n");
497:     VecView(global_out,PETSC_VIEWER_STDOUT_WORLD);
498:   }

500:   return 0;
501: }
502: /* --------------------------------------------------------------------- */
503: /*
504:    RHSJacobian - User-provided routine to compute the Jacobian of
505:    the nonlinear right-hand-side function of the ODE.

507:    Input Parameters:
508:    ts - the TS context
509:    t - current time
510:    global_in - global input vector
511:    dummy - optional user-defined context, as set by TSetRHSJacobian()

513:    Output Parameters:
514:    AA - Jacobian matrix
515:    BB - optionally different preconditioning matrix
516:    str - flag indicating matrix structure

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

541:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
542:      Get ready for local Jacobian computations
543:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
544:   /*
545:      Scatter ghost points to local vector, using the 2-step process
546:         DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
547:      By placing code between these two statements, computations can be
548:      done while messages are in transition.
549:   */
550:   DMGlobalToLocalBegin(da,global_in,INSERT_VALUES,local_in);
551:   DMGlobalToLocalEnd(da,global_in,INSERT_VALUES,local_in);

553:   /*
554:      Get pointer to vector data
555:   */
556:   VecGetArrayRead(local_in,&localptr);

558:   /*
559:      Get starting and ending locally owned rows of the matrix
560:   */
561:   MatGetOwnershipRange(BB,&mstarts,&mends);
562:   mstart = mstarts; mend = mends;

564:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
565:      Compute entries for the locally owned part of the Jacobian.
566:       - Currently, all PETSc parallel matrix formats are partitioned by
567:         contiguous chunks of rows across the processors.
568:       - Each processor needs to insert only elements that it owns
569:         locally (but any non-local elements will be sent to the
570:         appropriate processor during matrix assembly).
571:       - Here, we set all entries for a particular row at once.
572:       - We can set matrix entries either using either
573:         MatSetValuesLocal() or MatSetValues().
574:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

576:   /*
577:      Set matrix rows corresponding to boundary data
578:   */
579:   if (mstart == 0) {
580:     v[0] = 0.0;
581:     MatSetValues(BB,1,&mstart,1,&mstart,v,INSERT_VALUES);
582:     mstart++;
583:   }
584:   if (mend == appctx->m) {
585:     mend--;
586:     v[0] = 0.0;
587:     MatSetValues(BB,1,&mend,1,&mend,v,INSERT_VALUES);
588:   }

590:   /*
591:      Set matrix rows corresponding to interior data.  We construct the
592:      matrix one row at a time.
593:   */
594:   sc = 1.0/(appctx->h*appctx->h*2.0*(1.0+t)*(1.0+t));
595:   for (i=mstart; i<mend; i++) {
596:     idx[0] = i-1; idx[1] = i; idx[2] = i+1;
597:     is     = i - mstart + 1;
598:     v[0]   = sc*localptr[is];
599:     v[1]   = sc*(localptr[is+1] + localptr[is-1] - 4.0*localptr[is]);
600:     v[2]   = sc*localptr[is];
601:     MatSetValues(BB,1,&i,3,idx,v,INSERT_VALUES);
602:   }

604:   /*
605:      Restore vector
606:   */
607:   VecRestoreArrayRead(local_in,&localptr);

609:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
610:      Complete the matrix assembly process and set some options
611:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
612:   /*
613:      Assemble matrix, using the 2-step process:
614:        MatAssemblyBegin(), MatAssemblyEnd()
615:      Computations can be done while messages are in transition
616:      by placing code between these two statements.
617:   */
618:   MatAssemblyBegin(BB,MAT_FINAL_ASSEMBLY);
619:   MatAssemblyEnd(BB,MAT_FINAL_ASSEMBLY);
620:   if (BB != AA) {
621:     MatAssemblyBegin(AA,MAT_FINAL_ASSEMBLY);
622:     MatAssemblyEnd(AA,MAT_FINAL_ASSEMBLY);
623:   }

625:   /*
626:      Set and option to indicate that we will never add a new nonzero location
627:      to the matrix. If we do, it will generate an error.
628:   */
629:   MatSetOption(BB,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

631:   return 0;
632: }