Actual source code: ex21.c
petsc-3.7.5 2017-01-01
2: static char help[] ="Solves a time-dependent nonlinear PDE with lower and upper bounds on the interior grid points. 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\
7: -ul : lower bound\n\
8: -uh : upper bound\n\n";
10: /*
11: Concepts: TS^time-dependent nonlinear problems
12: Concepts: TS^Variational inequality nonlinear solver
13: Processors: n
14: */
16: /* ------------------------------------------------------------------------
18: This is a variation of ex2.c to solve the PDE
20: u * u_xx
21: u_t = ---------
22: 2*(t+1)^2
24: with box constraints on the interior grid points
25: ul <= u(t,x) <= uh with x != 0,1
26: on the domain 0 <= x <= 1, with boundary conditions
27: u(t,0) = t + 1, u(t,1) = 2*t + 2,
28: and initial condition
29: u(0,x) = 1 + x*x.
31: The exact solution is:
32: u(t,x) = (1 + x*x) * (1 + t)
34: We use by default the backward Euler method.
36: ------------------------------------------------------------------------- */
38: /*
39: Include "petscts.h" to use the PETSc timestepping routines. Note that
40: this file automatically includes "petscsys.h" and other lower-level
41: PETSc include files.
43: Include the "petscdmda.h" to allow us to use the distributed array data
44: structures to manage the parallel grid.
45: */
46: #include <petscts.h>
47: #include <petscdm.h>
48: #include <petscdmda.h>
49: #include <petscdraw.h>
51: /*
52: User-defined application context - contains data needed by the
53: application-provided callback routines.
54: */
55: typedef struct {
56: MPI_Comm comm; /* communicator */
57: DM da; /* distributed array data structure */
58: Vec localwork; /* local ghosted work vector */
59: Vec u_local; /* local ghosted approximate solution vector */
60: Vec solution; /* global exact solution vector */
61: PetscInt m; /* total number of grid points */
62: PetscReal h; /* mesh width: h = 1/(m-1) */
63: PetscBool debug; /* flag (1 indicates activation of debugging printouts) */
64: } AppCtx;
66: /*
67: User-defined routines, provided below.
68: */
69: extern PetscErrorCode InitialConditions(Vec,AppCtx*);
70: extern PetscErrorCode RHSFunction(TS,PetscReal,Vec,Vec,void*);
71: extern PetscErrorCode RHSJacobian(TS,PetscReal,Vec,Mat,Mat,void*);
72: extern PetscErrorCode Monitor(TS,PetscInt,PetscReal,Vec,void*);
73: extern PetscErrorCode ExactSolution(PetscReal,Vec,AppCtx*);
74: extern PetscErrorCode SetBounds(Vec,Vec,PetscScalar,PetscScalar,AppCtx*);
78: int main(int argc,char **argv)
79: {
80: AppCtx appctx; /* user-defined application context */
81: TS ts; /* timestepping context */
82: Mat A; /* Jacobian matrix data structure */
83: Vec u; /* approximate solution vector */
84: Vec r; /* residual vector */
85: PetscInt time_steps_max = 1000; /* default max timesteps */
87: PetscReal dt;
88: PetscReal time_total_max = 100.0; /* default max total time */
89: Vec xl,xu; /* Lower and upper bounds on variables */
90: PetscScalar ul=0.0,uh = 3.0;
91: PetscBool mymonitor;
92: PetscReal bounds[] = {1.0, 3.3};
94: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
95: Initialize program and set problem parameters
96: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
98: PetscInitialize(&argc,&argv,(char*)0,help);
99: PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,bounds);
101: appctx.comm = PETSC_COMM_WORLD;
102: appctx.m = 60;
103: PetscOptionsGetInt(NULL,NULL,"-M",&appctx.m,NULL);
104: PetscOptionsGetScalar(NULL,NULL,"-ul",&ul,NULL);
105: PetscOptionsGetScalar(NULL,NULL,"-uh",&uh,NULL);
106: PetscOptionsHasName(NULL,NULL,"-debug",&appctx.debug);
107: PetscOptionsHasName(NULL,NULL,"-mymonitor",&mymonitor);
108: appctx.h = 1.0/(appctx.m-1.0);
110: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
111: Create vector data structures
112: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
114: /*
115: Create distributed array (DMDA) to manage parallel grid and vectors
116: and to set up the ghost point communication pattern. There are M
117: total grid values spread equally among all the processors.
118: */
119: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,appctx.m,1,1,NULL,
120: &appctx.da);
122: /*
123: Extract global and local vectors from DMDA; we use these to store the
124: approximate solution. Then duplicate these for remaining vectors that
125: have the same types.
126: */
127: DMCreateGlobalVector(appctx.da,&u);
128: DMCreateLocalVector(appctx.da,&appctx.u_local);
130: /*
131: Create local work vector for use in evaluating right-hand-side function;
132: create global work vector for storing exact solution.
133: */
134: VecDuplicate(appctx.u_local,&appctx.localwork);
135: VecDuplicate(u,&appctx.solution);
137: /* Create residual vector */
138: VecDuplicate(u,&r);
139: /* Create lower and upper bound vectors */
140: VecDuplicate(u,&xl);
141: VecDuplicate(u,&xu);
142: SetBounds(xl,xu,ul,uh,&appctx);
144: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145: Create timestepping solver context; set callback routine for
146: right-hand-side function evaluation.
147: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149: TSCreate(PETSC_COMM_WORLD,&ts);
150: TSSetProblemType(ts,TS_NONLINEAR);
151: TSSetRHSFunction(ts,r,RHSFunction,&appctx);
153: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
154: Set optional user-defined monitoring routine
155: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
157: if (mymonitor) {
158: TSMonitorSet(ts,Monitor,&appctx,NULL);
159: }
161: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: For nonlinear problems, the user can provide a Jacobian evaluation
163: routine (or use a finite differencing approximation).
165: Create matrix data structure; set Jacobian evaluation routine.
166: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
168: MatCreate(PETSC_COMM_WORLD,&A);
169: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,appctx.m,appctx.m);
170: MatSetFromOptions(A);
171: MatSetUp(A);
172: TSSetRHSJacobian(ts,A,A,RHSJacobian,&appctx);
174: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: Set solution vector and initial timestep
176: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
178: dt = appctx.h/2.0;
179: TSSetInitialTimeStep(ts,0.0,dt);
181: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182: Customize timestepping solver:
183: - Set the solution method to be the Backward Euler method.
184: - Set timestepping duration info
185: Then set runtime options, which can override these defaults.
186: For example,
187: -ts_max_steps <maxsteps> -ts_final_time <maxtime>
188: to override the defaults set by TSSetDuration().
189: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
191: TSSetType(ts,TSBEULER);
192: TSSetDuration(ts,time_steps_max,time_total_max);
193: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
194: /* Set lower and upper bound on the solution vector for each time step */
195: TSVISetVariableBounds(ts,xl,xu);
196: TSSetFromOptions(ts);
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Solve the problem
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
202: /*
203: Evaluate initial conditions
204: */
205: InitialConditions(u,&appctx);
207: /*
208: Run the timestepping solver
209: */
210: TSSolve(ts,u);
212: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
213: Free work space. All PETSc objects should be destroyed when they
214: are no longer needed.
215: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
217: VecDestroy(&r);
218: VecDestroy(&xl);
219: VecDestroy(&xu);
220: TSDestroy(&ts);
221: VecDestroy(&u);
222: MatDestroy(&A);
223: DMDestroy(&appctx.da);
224: VecDestroy(&appctx.localwork);
225: VecDestroy(&appctx.solution);
226: VecDestroy(&appctx.u_local);
228: /*
229: Always call PetscFinalize() before exiting a program. This routine
230: - finalizes the PETSc libraries as well as MPI
231: - provides summary and diagnostic information if certain runtime
232: options are chosen (e.g., -log_summary).
233: */
234: PetscFinalize();
235: return 0;
236: }
237: /* --------------------------------------------------------------------- */
240: /*
241: InitialConditions - Computes the solution at the initial time.
243: Input Parameters:
244: u - uninitialized solution vector (global)
245: appctx - user-defined application context
247: Output Parameter:
248: u - vector with solution at initial time (global)
249: */
250: PetscErrorCode InitialConditions(Vec u,AppCtx *appctx)
251: {
252: PetscScalar *u_localptr,h = appctx->h,x;
253: PetscInt i,mybase,myend;
256: /*
257: Determine starting point of each processor's range of
258: grid values.
259: */
260: VecGetOwnershipRange(u,&mybase,&myend);
262: /*
263: Get a pointer to vector data.
264: - For default PETSc vectors, VecGetArray() returns a pointer to
265: the data array. Otherwise, the routine is implementation dependent.
266: - You MUST call VecRestoreArray() when you no longer need access to
267: the array.
268: - Note that the Fortran interface to VecGetArray() differs from the
269: C version. See the users manual for details.
270: */
271: VecGetArray(u,&u_localptr);
273: /*
274: We initialize the solution array by simply writing the solution
275: directly into the array locations. Alternatively, we could use
276: VecSetValues() or VecSetValuesLocal().
277: */
278: for (i=mybase; i<myend; i++) {
279: x = h*(PetscReal)i; /* current location in global grid */
280: u_localptr[i-mybase] = 1.0 + x*x;
281: }
283: /*
284: Restore vector
285: */
286: VecRestoreArray(u,&u_localptr);
288: /*
289: Print debugging information if desired
290: */
291: if (appctx->debug) {
292: PetscPrintf(appctx->comm,"initial guess vector\n");
293: VecView(u,PETSC_VIEWER_STDOUT_WORLD);
294: }
296: return 0;
297: }
299: /* --------------------------------------------------------------------- */
302: /*
303: SetBounds - Sets the lower and uper bounds on the interior points
305: Input parameters:
306: xl - vector of lower bounds
307: xu - vector of upper bounds
308: ul - constant lower bound for all variables
309: uh - constant upper bound for all variables
310: appctx - Application context
311: */
312: PetscErrorCode SetBounds(Vec xl, Vec xu, PetscScalar ul, PetscScalar uh,AppCtx *appctx)
313: {
314: PetscErrorCode ierr;
315: const PetscScalar *l,*u;
316: PetscMPIInt rank,size;
317: PetscInt localsize;
320: VecSet(xl,ul);
321: VecSet(xu,uh);
322: VecGetLocalSize(xl,&localsize);
323: VecGetArrayRead(xl,&l);
324: VecGetArrayRead(xu,&u);
326: MPI_Comm_rank(appctx->comm,&rank);
327: MPI_Comm_size(appctx->comm,&size);
328: if (!rank) {
329: l[0] = -PETSC_INFINITY;
330: u[0] = PETSC_INFINITY;
331: }
332: if (rank == size-1) {
333: l[localsize-1] = -PETSC_INFINITY;
334: u[localsize-1] = PETSC_INFINITY;
335: }
336: VecRestoreArrayRead(xl,&l);
337: VecRestoreArrayRead(xu,&u);
338: return(0);
339: }
341: /* --------------------------------------------------------------------- */
344: /*
345: ExactSolution - Computes the exact solution at a given time.
347: Input Parameters:
348: t - current time
349: solution - vector in which exact solution will be computed
350: appctx - user-defined application context
352: Output Parameter:
353: solution - vector with the newly computed exact solution
354: */
355: PetscErrorCode ExactSolution(PetscReal t,Vec solution,AppCtx *appctx)
356: {
357: PetscScalar *s_localptr,h = appctx->h,x;
358: PetscInt i,mybase,myend;
361: /*
362: Determine starting and ending points of each processor's
363: range of grid values
364: */
365: VecGetOwnershipRange(solution,&mybase,&myend);
367: /*
368: Get a pointer to vector data.
369: */
370: VecGetArray(solution,&s_localptr);
372: /*
373: Simply write the solution directly into the array locations.
374: Alternatively, we could use VecSetValues() or VecSetValuesLocal().
375: */
376: for (i=mybase; i<myend; i++) {
377: x = h*(PetscReal)i;
378: s_localptr[i-mybase] = (t + 1.0)*(1.0 + x*x);
379: }
381: /*
382: Restore vector
383: */
384: VecRestoreArray(solution,&s_localptr);
385: return 0;
386: }
387: /* --------------------------------------------------------------------- */
390: /*
391: Monitor - User-provided routine to monitor the solution computed at
392: each timestep. This example plots the solution and computes the
393: error in two different norms.
395: Input Parameters:
396: ts - the timestep context
397: step - the count of the current step (with 0 meaning the
398: initial condition)
399: time - the current time
400: u - the solution at this timestep
401: ctx - the user-provided context for this monitoring routine.
402: In this case we use the application context which contains
403: information about the problem size, workspace and the exact
404: solution.
405: */
406: PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec u,void *ctx)
407: {
408: AppCtx *appctx = (AppCtx*) ctx; /* user-defined application context */
410: PetscReal en2,en2s,enmax;
411: PetscDraw draw;
413: /*
414: We use the default X windows viewer
415: PETSC_VIEWER_DRAW_(appctx->comm)
416: that is associated with the current communicator. This saves
417: the effort of calling PetscViewerDrawOpen() to create the window.
418: Note that if we wished to plot several items in separate windows we
419: would create each viewer with PetscViewerDrawOpen() and store them in
420: the application context, appctx.
422: PetscReal buffering makes graphics look better.
423: */
424: PetscViewerDrawGetDraw(PETSC_VIEWER_DRAW_(appctx->comm),0,&draw);
425: PetscDrawSetDoubleBuffer(draw);
426: VecView(u,PETSC_VIEWER_DRAW_(appctx->comm));
428: /*
429: Compute the exact solution at this timestep
430: */
431: ExactSolution(time,appctx->solution,appctx);
433: /*
434: Print debugging information if desired
435: */
436: if (appctx->debug) {
437: PetscPrintf(appctx->comm,"Computed solution vector\n");
438: VecView(u,PETSC_VIEWER_STDOUT_WORLD);
439: PetscPrintf(appctx->comm,"Exact solution vector\n");
440: VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD);
441: }
443: /*
444: Compute the 2-norm and max-norm of the error
445: */
446: VecAXPY(appctx->solution,-1.0,u);
447: VecNorm(appctx->solution,NORM_2,&en2);
448: en2s = PetscSqrtReal(appctx->h)*en2; /* scale the 2-norm by the grid spacing */
449: VecNorm(appctx->solution,NORM_MAX,&enmax);
451: /*
452: PetscPrintf() causes only the first processor in this
453: communicator to print the timestep information.
454: */
455: PetscPrintf(appctx->comm,"Timestep %D: time = %g,2-norm error = %g, max norm error = %g\n",step,(double)time,(double)en2s,(double)enmax);
457: /*
458: Print debugging information if desired
459: */
460: /* if (appctx->debug) {
461: PetscPrintf(appctx->comm,"Error vector\n");
462: VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD);
463: } */
464: return 0;
465: }
466: /* --------------------------------------------------------------------- */
469: /*
470: RHSFunction - User-provided routine that evalues the right-hand-side
471: function of the ODE. This routine is set in the main program by
472: calling TSSetRHSFunction(). We compute:
473: global_out = F(global_in)
475: Input Parameters:
476: ts - timesteping context
477: t - current time
478: global_in - vector containing the current iterate
479: ctx - (optional) user-provided context for function evaluation.
480: In this case we use the appctx defined above.
482: Output Parameter:
483: global_out - vector containing the newly evaluated function
484: */
485: PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec global_in,Vec global_out,void *ctx)
486: {
487: AppCtx *appctx = (AppCtx*) ctx; /* user-defined application context */
488: DM da = appctx->da; /* distributed array */
489: Vec local_in = appctx->u_local; /* local ghosted input vector */
490: Vec localwork = appctx->localwork; /* local ghosted work vector */
491: PetscErrorCode ierr;
492: PetscInt i,localsize;
493: PetscMPIInt rank,size;
494: PetscScalar *copyptr,sc;
495: const PetscScalar *localptr;
497: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
498: Get ready for local function computations
499: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
500: /*
501: Scatter ghost points to local vector, using the 2-step process
502: DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
503: By placing code between these two statements, computations can be
504: done while messages are in transition.
505: */
506: DMGlobalToLocalBegin(da,global_in,INSERT_VALUES,local_in);
507: DMGlobalToLocalEnd(da,global_in,INSERT_VALUES,local_in);
509: /*
510: Access directly the values in our local INPUT work array
511: */
512: VecGetArrayRead(local_in,&localptr);
514: /*
515: Access directly the values in our local OUTPUT work array
516: */
517: VecGetArray(localwork,©ptr);
519: sc = 1.0/(appctx->h*appctx->h*2.0*(1.0+t)*(1.0+t));
521: /*
522: Evaluate our function on the nodes owned by this processor
523: */
524: VecGetLocalSize(local_in,&localsize);
526: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
527: Compute entries for the locally owned part
528: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
530: /*
531: Handle boundary conditions: This is done by using the boundary condition
532: u(t,boundary) = g(t,boundary)
533: for some function g. Now take the derivative with respect to t to obtain
534: u_{t}(t,boundary) = g_{t}(t,boundary)
536: In our case, u(t,0) = t + 1, so that u_{t}(t,0) = 1
537: and u(t,1) = 2t+ 2, so that u_{t}(t,1) = 2
538: */
539: MPI_Comm_rank(appctx->comm,&rank);
540: MPI_Comm_size(appctx->comm,&size);
541: if (!rank) copyptr[0] = 1.0;
542: if (rank == size-1) copyptr[localsize-1] = (t < .5) ? 2.0 : 0.0;
544: /*
545: Handle the interior nodes where the PDE is replace by finite
546: difference operators.
547: */
548: for (i=1; i<localsize-1; i++) copyptr[i] = localptr[i] * sc * (localptr[i+1] + localptr[i-1] - 2.0*localptr[i]);
550: /*
551: Restore vectors
552: */
553: VecRestoreArrayRead(local_in,&localptr);
554: VecRestoreArray(localwork,©ptr);
556: /*
557: Insert values from the local OUTPUT vector into the global
558: output vector
559: */
560: DMLocalToGlobalBegin(da,localwork,INSERT_VALUES,global_out);
561: DMLocalToGlobalEnd(da,localwork,INSERT_VALUES,global_out);
563: /* Print debugging information if desired */
564: /* if (appctx->debug) {
565: PetscPrintf(appctx->comm,"RHS function vector\n");
566: VecView(global_out,PETSC_VIEWER_STDOUT_WORLD);
567: } */
569: return 0;
570: }
571: /* --------------------------------------------------------------------- */
574: /*
575: RHSJacobian - User-provided routine to compute the Jacobian of
576: the nonlinear right-hand-side function of the ODE.
578: Input Parameters:
579: ts - the TS context
580: t - current time
581: global_in - global input vector
582: dummy - optional user-defined context, as set by TSetRHSJacobian()
584: Output Parameters:
585: AA - Jacobian matrix
586: BB - optionally different preconditioning matrix
587: str - flag indicating matrix structure
589: Notes:
590: RHSJacobian computes entries for the locally owned part of the Jacobian.
591: - Currently, all PETSc parallel matrix formats are partitioned by
592: contiguous chunks of rows across the processors.
593: - Each processor needs to insert only elements that it owns
594: locally (but any non-local elements will be sent to the
595: appropriate processor during matrix assembly).
596: - Always specify global row and columns of matrix entries when
597: using MatSetValues().
598: - Here, we set all entries for a particular row at once.
599: - Note that MatSetValues() uses 0-based row and column numbers
600: in Fortran as well as in C.
601: */
602: PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec global_in,Mat AA,Mat B,void *ctx)
603: {
604: AppCtx *appctx = (AppCtx*)ctx; /* user-defined application context */
605: Vec local_in = appctx->u_local; /* local ghosted input vector */
606: DM da = appctx->da; /* distributed array */
607: PetscScalar v[3],sc;
608: const PetscScalar *localptr;
609: PetscErrorCode ierr;
610: PetscInt i,mstart,mend,mstarts,mends,idx[3],is;
612: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
613: Get ready for local Jacobian computations
614: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
615: /*
616: Scatter ghost points to local vector, using the 2-step process
617: DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
618: By placing code between these two statements, computations can be
619: done while messages are in transition.
620: */
621: DMGlobalToLocalBegin(da,global_in,INSERT_VALUES,local_in);
622: DMGlobalToLocalEnd(da,global_in,INSERT_VALUES,local_in);
624: /*
625: Get pointer to vector data
626: */
627: VecGetArrayRead(local_in,&localptr);
629: /*
630: Get starting and ending locally owned rows of the matrix
631: */
632: MatGetOwnershipRange(B,&mstarts,&mends);
633: mstart = mstarts; mend = mends;
635: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
636: Compute entries for the locally owned part of the Jacobian.
637: - Currently, all PETSc parallel matrix formats are partitioned by
638: contiguous chunks of rows across the processors.
639: - Each processor needs to insert only elements that it owns
640: locally (but any non-local elements will be sent to the
641: appropriate processor during matrix assembly).
642: - Here, we set all entries for a particular row at once.
643: - We can set matrix entries either using either
644: MatSetValuesLocal() or MatSetValues().
645: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
647: /*
648: Set matrix rows corresponding to boundary data
649: */
650: if (mstart == 0) {
651: v[0] = 0.0;
652: MatSetValues(B,1,&mstart,1,&mstart,v,INSERT_VALUES);
653: mstart++;
654: }
655: if (mend == appctx->m) {
656: mend--;
657: v[0] = 0.0;
658: MatSetValues(B,1,&mend,1,&mend,v,INSERT_VALUES);
659: }
661: /*
662: Set matrix rows corresponding to interior data. We construct the
663: matrix one row at a time.
664: */
665: sc = 1.0/(appctx->h*appctx->h*2.0*(1.0+t)*(1.0+t));
666: for (i=mstart; i<mend; i++) {
667: idx[0] = i-1; idx[1] = i; idx[2] = i+1;
668: is = i - mstart + 1;
669: v[0] = sc*localptr[is];
670: v[1] = sc*(localptr[is+1] + localptr[is-1] - 4.0*localptr[is]);
671: v[2] = sc*localptr[is];
672: MatSetValues(B,1,&i,3,idx,v,INSERT_VALUES);
673: }
675: /*
676: Restore vector
677: */
678: VecRestoreArrayRead(local_in,&localptr);
680: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
681: Complete the matrix assembly process and set some options
682: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
683: /*
684: Assemble matrix, using the 2-step process:
685: MatAssemblyBegin(), MatAssemblyEnd()
686: Computations can be done while messages are in transition
687: by placing code between these two statements.
688: */
689: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
690: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
692: /*
693: Set and option to indicate that we will never add a new nonzero location
694: to the matrix. If we do, it will generate an error.
695: */
696: MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
698: return 0;
699: }