Actual source code: ex4.c

1: static char help[] = "Solves a simple time-dependent linear PDE (the heat equation).\n\
2: Input parameters include:\n\
3:   -m <points>, where <points> = number of grid points\n\
4:   -time_dependent_rhs : Treat the problem as having a time-dependent right-hand side\n\
5:   -debug              : Activate debugging printouts\n\
6:   -nox                : Deactivate x-window graphics\n\n";

8: /* ------------------------------------------------------------------------

10:    This program solves the one-dimensional heat equation (also called the
11:    diffusion equation),
12:        u_t = u_xx,
13:    on the domain 0 <= x <= 1, with the boundary conditions
14:        u(t,0) = 0, u(t,1) = 0,
15:    and the initial condition
16:        u(0,x) = sin(6*pi*x) + 3*sin(2*pi*x).
17:    This is a linear, second-order, parabolic equation.

19:    We discretize the right-hand side using finite differences with
20:    uniform grid spacing h:
21:        u_xx = (u_{i+1} - 2u_{i} + u_{i-1})/(h^2)
22:    We then demonstrate time evolution using the various TS methods by
23:    running the program via
24:        mpiexec -n <procs> ex3 -ts_type <timestepping solver>

26:    We compare the approximate solution with the exact solution, given by
27:        u_exact(x,t) = exp(-36*pi*pi*t) * sin(6*pi*x) +
28:                       3*exp(-4*pi*pi*t) * sin(2*pi*x)

30:    Notes:
31:    This code demonstrates the TS solver interface to two variants of
32:    linear problems, u_t = f(u,t), namely
33:      - time-dependent f:   f(u,t) is a function of t
34:      - time-independent f: f(u,t) is simply f(u)

36:     The uniprocessor version of this code is ts/tutorials/ex3.c

38:   ------------------------------------------------------------------------- */

40: /*
41:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs) to manage
42:    the parallel grid.  Include "petscts.h" so that we can use TS solvers.
43:    Note that this file automatically includes:
44:      petscsys.h       - base PETSc routines   petscvec.h  - vectors
45:      petscmat.h  - matrices
46:      petscis.h     - index sets            petscksp.h  - Krylov subspace methods
47:      petscviewer.h - viewers               petscpc.h   - preconditioners
48:      petscksp.h   - linear solvers        petscsnes.h - nonlinear solvers
49: */

51: #include <petscdm.h>
52: #include <petscdmda.h>
53: #include <petscts.h>
54: #include <petscdraw.h>

56: /*
57:    User-defined application context - contains data needed by the
58:    application-provided call-back routines.
59: */
60: typedef struct {
61:   MPI_Comm    comm;             /* communicator */
62:   DM          da;               /* distributed array data structure */
63:   Vec         localwork;        /* local ghosted work vector */
64:   Vec         u_local;          /* local ghosted approximate solution vector */
65:   Vec         solution;         /* global exact solution vector */
66:   PetscInt    m;                /* total number of grid points */
67:   PetscReal   h;                /* mesh width h = 1/(m-1) */
68:   PetscBool   debug;            /* flag (1 indicates activation of debugging printouts) */
69:   PetscViewer viewer1, viewer2; /* viewers for the solution and error */
70:   PetscReal   norm_2, norm_max; /* error norms */
71: } AppCtx;

73: /*
74:    User-defined routines
75: */
76: extern PetscErrorCode InitialConditions(Vec, AppCtx *);
77: extern PetscErrorCode RHSMatrixHeat(TS, PetscReal, Vec, Mat, Mat, void *);
78: extern PetscErrorCode RHSFunctionHeat(TS, PetscReal, Vec, Vec, void *);
79: extern PetscErrorCode Monitor(TS, PetscInt, PetscReal, Vec, void *);
80: extern PetscErrorCode ExactSolution(PetscReal, Vec, AppCtx *);

82: int main(int argc, char **argv)
83: {
84:   AppCtx        appctx;               /* user-defined application context */
85:   TS            ts;                   /* timestepping context */
86:   Mat           A;                    /* matrix data structure */
87:   Vec           u;                    /* approximate solution vector */
88:   PetscReal     time_total_max = 1.0; /* default max total time */
89:   PetscInt      time_steps_max = 100; /* default max timesteps */
90:   PetscDraw     draw;                 /* drawing context */
91:   PetscInt      steps, m;
92:   PetscMPIInt   size;
93:   PetscReal     dt, ftime;
94:   PetscBool     flg;
95:   TSProblemType tsproblem = TS_LINEAR;

97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
98:      Initialize program and set problem parameters
99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

101:   PetscFunctionBeginUser;
102:   PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
103:   appctx.comm = PETSC_COMM_WORLD;

105:   m = 60;
106:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
107:   PetscCall(PetscOptionsHasName(NULL, NULL, "-debug", &appctx.debug));
108:   appctx.m        = m;
109:   appctx.h        = 1.0 / (m - 1.0);
110:   appctx.norm_2   = 0.0;
111:   appctx.norm_max = 0.0;

113:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
114:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Solving a linear TS problem, number of processors = %d\n", size));

116:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117:      Create vector data structures
118:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119:   /*
120:      Create distributed array (DMDA) to manage parallel grid and vectors
121:      and to set up the ghost point communication pattern.  There are M
122:      total grid values spread equally among all the processors.
123:   */

125:   PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, m, 1, 1, NULL, &appctx.da));
126:   PetscCall(DMSetFromOptions(appctx.da));
127:   PetscCall(DMSetUp(appctx.da));

129:   /*
130:      Extract global and local vectors from DMDA; we use these to store the
131:      approximate solution.  Then duplicate these for remaining vectors that
132:      have the same types.
133:   */
134:   PetscCall(DMCreateGlobalVector(appctx.da, &u));
135:   PetscCall(DMCreateLocalVector(appctx.da, &appctx.u_local));

137:   /*
138:      Create local work vector for use in evaluating right-hand-side function;
139:      create global work vector for storing exact solution.
140:   */
141:   PetscCall(VecDuplicate(appctx.u_local, &appctx.localwork));
142:   PetscCall(VecDuplicate(u, &appctx.solution));

144:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145:      Set up displays to show graphs of the solution and error
146:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

148:   PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD, 0, "", 80, 380, 400, 160, &appctx.viewer1));
149:   PetscCall(PetscViewerDrawGetDraw(appctx.viewer1, 0, &draw));
150:   PetscCall(PetscDrawSetDoubleBuffer(draw));
151:   PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD, 0, "", 80, 0, 400, 160, &appctx.viewer2));
152:   PetscCall(PetscViewerDrawGetDraw(appctx.viewer2, 0, &draw));
153:   PetscCall(PetscDrawSetDoubleBuffer(draw));

155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156:      Create timestepping solver context
157:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

159:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));

161:   flg = PETSC_FALSE;
162:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-nonlinear", &flg, NULL));
163:   PetscCall(TSSetProblemType(ts, flg ? TS_NONLINEAR : TS_LINEAR));

165:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166:      Set optional user-defined monitoring routine
167:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
168:   PetscCall(TSMonitorSet(ts, Monitor, &appctx, NULL));

170:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

172:      Create matrix data structure; set matrix evaluation routine.
173:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

175:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
176:   PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, m, m));
177:   PetscCall(MatSetFromOptions(A));
178:   PetscCall(MatSetUp(A));

180:   flg = PETSC_FALSE;
181:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-time_dependent_rhs", &flg, NULL));
182:   if (flg) {
183:     /*
184:        For linear problems with a time-dependent f(u,t) in the equation
185:        u_t = f(u,t), the user provides the discretized right-hand side
186:        as a time-dependent matrix.
187:     */
188:     PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx));
189:     PetscCall(TSSetRHSJacobian(ts, A, A, RHSMatrixHeat, &appctx));
190:   } else {
191:     /*
192:        For linear problems with a time-independent f(u) in the equation
193:        u_t = f(u), the user provides the discretized right-hand side
194:        as a matrix only once, and then sets a null matrix evaluation
195:        routine.
196:     */
197:     PetscCall(RHSMatrixHeat(ts, 0.0, u, A, A, &appctx));
198:     PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx));
199:     PetscCall(TSSetRHSJacobian(ts, A, A, TSComputeRHSJacobianConstant, &appctx));
200:   }

202:   if (tsproblem == TS_NONLINEAR) {
203:     SNES snes;
204:     PetscCall(TSSetRHSFunction(ts, NULL, RHSFunctionHeat, &appctx));
205:     PetscCall(TSGetSNES(ts, &snes));
206:     PetscCall(SNESSetJacobian(snes, NULL, NULL, SNESComputeJacobianDefault, NULL));
207:   }

209:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
210:      Set solution vector and initial timestep
211:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

213:   dt = appctx.h * appctx.h / 2.0;
214:   PetscCall(TSSetTimeStep(ts, dt));
215:   PetscCall(TSSetSolution(ts, u));

217:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
218:      Customize timestepping solver:
219:        - Set the solution method to be the Backward Euler method.
220:        - Set timestepping duration info
221:      Then set runtime options, which can override these defaults.
222:      For example,
223:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
224:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
225:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

227:   PetscCall(TSSetMaxSteps(ts, time_steps_max));
228:   PetscCall(TSSetMaxTime(ts, time_total_max));
229:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
230:   PetscCall(TSSetFromOptions(ts));

232:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
233:      Solve the problem
234:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

236:   /*
237:      Evaluate initial conditions
238:   */
239:   PetscCall(InitialConditions(u, &appctx));

241:   /*
242:      Run the timestepping solver
243:   */
244:   PetscCall(TSSolve(ts, u));
245:   PetscCall(TSGetSolveTime(ts, &ftime));
246:   PetscCall(TSGetStepNumber(ts, &steps));

248:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
249:      View timestepping solver info
250:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
251:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Total timesteps %" PetscInt_FMT ", Final time %g\n", steps, (double)ftime));
252:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Avg. error (2 norm) = %g Avg. error (max norm) = %g\n", (double)(appctx.norm_2 / steps), (double)(appctx.norm_max / steps)));

254:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
255:      Free work space.  All PETSc objects should be destroyed when they
256:      are no longer needed.
257:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

259:   PetscCall(TSDestroy(&ts));
260:   PetscCall(MatDestroy(&A));
261:   PetscCall(VecDestroy(&u));
262:   PetscCall(PetscViewerDestroy(&appctx.viewer1));
263:   PetscCall(PetscViewerDestroy(&appctx.viewer2));
264:   PetscCall(VecDestroy(&appctx.localwork));
265:   PetscCall(VecDestroy(&appctx.solution));
266:   PetscCall(VecDestroy(&appctx.u_local));
267:   PetscCall(DMDestroy(&appctx.da));

269:   /*
270:      Always call PetscFinalize() before exiting a program.  This routine
271:        - finalizes the PETSc libraries as well as MPI
272:        - provides summary and diagnostic information if certain runtime
273:          options are chosen (e.g., -log_view).
274:   */
275:   PetscCall(PetscFinalize());
276:   return 0;
277: }
278: /* --------------------------------------------------------------------- */
279: /*
280:    InitialConditions - Computes the solution at the initial time.

282:    Input Parameter:
283:    u - uninitialized solution vector (global)
284:    appctx - user-defined application context

286:    Output Parameter:
287:    u - vector with solution at initial time (global)
288: */
289: PetscErrorCode InitialConditions(Vec u, AppCtx *appctx)
290: {
291:   PetscScalar *u_localptr, h = appctx->h;
292:   PetscInt     i, mybase, myend;

294:   PetscFunctionBeginUser;
295:   /*
296:      Determine starting point of each processor's range of
297:      grid values.
298:   */
299:   PetscCall(VecGetOwnershipRange(u, &mybase, &myend));

301:   /*
302:     Get a pointer to vector data.
303:     - For default PETSc vectors, VecGetArray() returns a pointer to
304:       the data array.  Otherwise, the routine is implementation dependent.
305:     - You MUST call VecRestoreArray() when you no longer need access to
306:       the array.
307:     - Note that the Fortran interface to VecGetArray() differs from the
308:       C version.  See the users manual for details.
309:   */
310:   PetscCall(VecGetArray(u, &u_localptr));

312:   /*
313:      We initialize the solution array by simply writing the solution
314:      directly into the array locations.  Alternatively, we could use
315:      VecSetValues() or VecSetValuesLocal().
316:   */
317:   for (i = mybase; i < myend; i++) u_localptr[i - mybase] = PetscSinScalar(PETSC_PI * i * 6. * h) + 3. * PetscSinScalar(PETSC_PI * i * 2. * h);

319:   /*
320:      Restore vector
321:   */
322:   PetscCall(VecRestoreArray(u, &u_localptr));

324:   /*
325:      Print debugging information if desired
326:   */
327:   if (appctx->debug) {
328:     PetscCall(PetscPrintf(appctx->comm, "initial guess vector\n"));
329:     PetscCall(VecView(u, PETSC_VIEWER_STDOUT_WORLD));
330:   }
331:   PetscFunctionReturn(PETSC_SUCCESS);
332: }
333: /* --------------------------------------------------------------------- */
334: /*
335:    ExactSolution - Computes the exact solution at a given time.

337:    Input Parameters:
338:    t - current time
339:    solution - vector in which exact solution will be computed
340:    appctx - user-defined application context

342:    Output Parameter:
343:    solution - vector with the newly computed exact solution
344: */
345: PetscErrorCode ExactSolution(PetscReal t, Vec solution, AppCtx *appctx)
346: {
347:   PetscScalar *s_localptr, h = appctx->h, ex1, ex2, sc1, sc2;
348:   PetscInt     i, mybase, myend;

350:   PetscFunctionBeginUser;
351:   /*
352:      Determine starting and ending points of each processor's
353:      range of grid values
354:   */
355:   PetscCall(VecGetOwnershipRange(solution, &mybase, &myend));

357:   /*
358:      Get a pointer to vector data.
359:   */
360:   PetscCall(VecGetArray(solution, &s_localptr));

362:   /*
363:      Simply write the solution directly into the array locations.
364:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
365:   */
366:   ex1 = PetscExpReal(-36. * PETSC_PI * PETSC_PI * t);
367:   ex2 = PetscExpReal(-4. * PETSC_PI * PETSC_PI * t);
368:   sc1 = PETSC_PI * 6. * h;
369:   sc2 = PETSC_PI * 2. * h;
370:   for (i = mybase; i < myend; i++) s_localptr[i - mybase] = PetscSinScalar(sc1 * (PetscReal)i) * ex1 + 3. * PetscSinScalar(sc2 * (PetscReal)i) * ex2;

372:   /*
373:      Restore vector
374:   */
375:   PetscCall(VecRestoreArray(solution, &s_localptr));
376:   PetscFunctionReturn(PETSC_SUCCESS);
377: }
378: /* --------------------------------------------------------------------- */
379: /*
380:    Monitor - User-provided routine to monitor the solution computed at
381:    each timestep.  This example plots the solution and computes the
382:    error in two different norms.

384:    Input Parameters:
385:    ts     - the timestep context
386:    step   - the count of the current step (with 0 meaning the
387:              initial condition)
388:    time   - the current time
389:    u      - the solution at this timestep
390:    ctx    - the user-provided context for this monitoring routine.
391:             In this case we use the application context which contains
392:             information about the problem size, workspace and the exact
393:             solution.
394: */
395: PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal time, Vec u, void *ctx)
396: {
397:   AppCtx   *appctx = (AppCtx *)ctx; /* user-defined application context */
398:   PetscReal norm_2, norm_max;

400:   PetscFunctionBeginUser;
401:   /*
402:      View a graph of the current iterate
403:   */
404:   PetscCall(VecView(u, appctx->viewer2));

406:   /*
407:      Compute the exact solution
408:   */
409:   PetscCall(ExactSolution(time, appctx->solution, appctx));

411:   /*
412:      Print debugging information if desired
413:   */
414:   if (appctx->debug) {
415:     PetscCall(PetscPrintf(appctx->comm, "Computed solution vector\n"));
416:     PetscCall(VecView(u, PETSC_VIEWER_STDOUT_WORLD));
417:     PetscCall(PetscPrintf(appctx->comm, "Exact solution vector\n"));
418:     PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_WORLD));
419:   }

421:   /*
422:      Compute the 2-norm and max-norm of the error
423:   */
424:   PetscCall(VecAXPY(appctx->solution, -1.0, u));
425:   PetscCall(VecNorm(appctx->solution, NORM_2, &norm_2));
426:   norm_2 = PetscSqrtReal(appctx->h) * norm_2;
427:   PetscCall(VecNorm(appctx->solution, NORM_MAX, &norm_max));
428:   if (norm_2 < 1e-14) norm_2 = 0;
429:   if (norm_max < 1e-14) norm_max = 0;

431:   /*
432:      PetscPrintf() causes only the first processor in this
433:      communicator to print the timestep information.
434:   */
435:   PetscCall(PetscPrintf(appctx->comm, "Timestep %" PetscInt_FMT ": time = %g 2-norm error = %g max norm error = %g\n", step, (double)time, (double)norm_2, (double)norm_max));
436:   appctx->norm_2 += norm_2;
437:   appctx->norm_max += norm_max;

439:   /*
440:      View a graph of the error
441:   */
442:   PetscCall(VecView(appctx->solution, appctx->viewer1));

444:   /*
445:      Print debugging information if desired
446:   */
447:   if (appctx->debug) {
448:     PetscCall(PetscPrintf(appctx->comm, "Error vector\n"));
449:     PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_WORLD));
450:   }
451:   PetscFunctionReturn(PETSC_SUCCESS);
452: }

454: /* --------------------------------------------------------------------- */
455: /*
456:    RHSMatrixHeat - User-provided routine to compute the right-hand-side
457:    matrix for the heat equation.

459:    Input Parameters:
460:    ts - the TS context
461:    t - current time
462:    global_in - global input vector
463:    dummy - optional user-defined context, as set by TSetRHSJacobian()

465:    Output Parameters:
466:    AA - Jacobian matrix
467:    BB - optionally different preconditioning matrix
468:    str - flag indicating matrix structure

470:   Notes:
471:   RHSMatrixHeat computes entries for the locally owned part of the system.
472:    - Currently, all PETSc parallel matrix formats are partitioned by
473:      contiguous chunks of rows across the processors.
474:    - Each processor needs to insert only elements that it owns
475:      locally (but any non-local elements will be sent to the
476:      appropriate processor during matrix assembly).
477:    - Always specify global row and columns of matrix entries when
478:      using MatSetValues(); we could alternatively use MatSetValuesLocal().
479:    - Here, we set all entries for a particular row at once.
480:    - Note that MatSetValues() uses 0-based row and column numbers
481:      in Fortran as well as in C.
482: */
483: PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec X, Mat AA, Mat BB, void *ctx)
484: {
485:   Mat         A      = AA;            /* Jacobian matrix */
486:   AppCtx     *appctx = (AppCtx *)ctx; /* user-defined application context */
487:   PetscInt    i, mstart, mend, idx[3];
488:   PetscScalar v[3], stwo = -2. / (appctx->h * appctx->h), sone = -.5 * stwo;

490:   PetscFunctionBeginUser;
491:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
492:      Compute entries for the locally owned part of the matrix
493:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

495:   PetscCall(MatGetOwnershipRange(A, &mstart, &mend));

497:   /*
498:      Set matrix rows corresponding to boundary data
499:   */

501:   if (mstart == 0) { /* first processor only */
502:     v[0] = 1.0;
503:     PetscCall(MatSetValues(A, 1, &mstart, 1, &mstart, v, INSERT_VALUES));
504:     mstart++;
505:   }

507:   if (mend == appctx->m) { /* last processor only */
508:     mend--;
509:     v[0] = 1.0;
510:     PetscCall(MatSetValues(A, 1, &mend, 1, &mend, v, INSERT_VALUES));
511:   }

513:   /*
514:      Set matrix rows corresponding to interior data.  We construct the
515:      matrix one row at a time.
516:   */
517:   v[0] = sone;
518:   v[1] = stwo;
519:   v[2] = sone;
520:   for (i = mstart; i < mend; i++) {
521:     idx[0] = i - 1;
522:     idx[1] = i;
523:     idx[2] = i + 1;
524:     PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES));
525:   }

527:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
528:      Complete the matrix assembly process and set some options
529:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
530:   /*
531:      Assemble matrix, using the 2-step process:
532:        MatAssemblyBegin(), MatAssemblyEnd()
533:      Computations can be done while messages are in transition
534:      by placing code between these two statements.
535:   */
536:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
537:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

539:   /*
540:      Set and option to indicate that we will never add a new nonzero location
541:      to the matrix. If we do, it will generate an error.
542:   */
543:   PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
544:   PetscFunctionReturn(PETSC_SUCCESS);
545: }

547: PetscErrorCode RHSFunctionHeat(TS ts, PetscReal t, Vec globalin, Vec globalout, void *ctx)
548: {
549:   Mat A;

551:   PetscFunctionBeginUser;
552:   PetscCall(TSGetRHSJacobian(ts, &A, NULL, NULL, &ctx));
553:   PetscCall(RHSMatrixHeat(ts, t, globalin, A, NULL, ctx));
554:   /* PetscCall(MatView(A,PETSC_VIEWER_STDOUT_WORLD)); */
555:   PetscCall(MatMult(A, globalin, globalout));
556:   PetscFunctionReturn(PETSC_SUCCESS);
557: }

559: /*TEST

561:     test:
562:       args: -ts_view -nox

564:     test:
565:       suffix: 2
566:       args: -ts_view -nox
567:       nsize: 3

569:     test:
570:       suffix: 3
571:       args: -ts_view -nox -nonlinear

573:     test:
574:       suffix: 4
575:       args: -ts_view -nox -nonlinear
576:       nsize: 3
577:       timeoutfactor: 3

579:     test:
580:       suffix: sundials
581:       requires: sundials2
582:       args: -nox -ts_type sundials -ts_max_steps 5 -nonlinear
583:       nsize: 4

585:     test:
586:       suffix: sundials_dense
587:       requires: sundials2
588:       args: -nox -ts_type sundials -ts_sundials_use_dense -ts_max_steps 5 -nonlinear
589:       nsize: 1

591: TEST*/