Actual source code: ex3.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:   -use_ifunc          : Use IFunction/IJacobian interface\n\
6:   -debug              : Activate debugging printouts\n\
7:   -nox                : Deactivate x-window graphics\n\n";

9: /* ------------------------------------------------------------------------

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

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

27:    We compare the approximate solution with the exact solution, given by
28:        u_exact(x,t) = exp(-36*pi*pi*t) * sin(6*pi*x) +
29:                       3*exp(-4*pi*pi*t) * sin(2*pi*x)

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

37:     The parallel version of this code is ts/tutorials/ex4.c

39:   ------------------------------------------------------------------------- */

41: /*
42:    Include "petscts.h" so that we can use TS solvers.  Note that this file
43:    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 <petscts.h>
52: #include <petscdraw.h>

54: /*
55:    User-defined application context - contains data needed by the
56:    application-provided call-back routines.
57: */
58: typedef struct {
59:   Vec         solution;         /* global exact solution vector */
60:   PetscInt    m;                /* total number of grid points */
61:   PetscReal   h;                /* mesh width h = 1/(m-1) */
62:   PetscBool   debug;            /* flag (1 indicates activation of debugging printouts) */
63:   PetscViewer viewer1, viewer2; /* viewers for the solution and error */
64:   PetscReal   norm_2, norm_max; /* error norms */
65:   Mat         A;                /* RHS mat, used with IFunction interface */
66:   PetscReal   oshift;           /* old shift applied, prevent to recompute the IJacobian */
67: } AppCtx;

69: /*
70:    User-defined routines
71: */
72: extern PetscErrorCode InitialConditions(Vec, AppCtx *);
73: extern PetscErrorCode RHSMatrixHeat(TS, PetscReal, Vec, Mat, Mat, void *);
74: extern PetscErrorCode IFunctionHeat(TS, PetscReal, Vec, Vec, Vec, void *);
75: extern PetscErrorCode IJacobianHeat(TS, PetscReal, Vec, Vec, PetscReal, Mat, Mat, void *);
76: extern PetscErrorCode Monitor(TS, PetscInt, PetscReal, Vec, void *);
77: extern PetscErrorCode ExactSolution(PetscReal, Vec, AppCtx *);

79: int main(int argc, char **argv)
80: {
81:   AppCtx      appctx;                 /* user-defined application context */
82:   TS          ts;                     /* timestepping context */
83:   Mat         A;                      /* matrix data structure */
84:   Vec         u;                      /* approximate solution vector */
85:   PetscReal   time_total_max = 100.0; /* default max total time */
86:   PetscInt    time_steps_max = 100;   /* default max timesteps */
87:   PetscDraw   draw;                   /* drawing context */
88:   PetscInt    steps, m;
89:   PetscMPIInt size;
90:   PetscReal   dt;
91:   PetscBool   flg, flg_string;

93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
94:      Initialize program and set problem parameters
95:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

97:   PetscFunctionBeginUser;
98:   PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
99:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
100:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");

102:   m = 60;
103:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
104:   PetscCall(PetscOptionsHasName(NULL, NULL, "-debug", &appctx.debug));
105:   flg_string = PETSC_FALSE;
106:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_string_viewer", &flg_string, NULL));

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:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "Solving a linear TS problem on 1 processor\n"));

115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116:      Create vector data structures
117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

119:   /*
120:      Create vector data structures for approximate and exact solutions
121:   */
122:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &u));
123:   PetscCall(VecDuplicate(u, &appctx.solution));

125:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126:      Set up displays to show graphs of the solution and error
127:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

129:   PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, "", 80, 380, 400, 160, &appctx.viewer1));
130:   PetscCall(PetscViewerDrawGetDraw(appctx.viewer1, 0, &draw));
131:   PetscCall(PetscDrawSetDoubleBuffer(draw));
132:   PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, "", 80, 0, 400, 160, &appctx.viewer2));
133:   PetscCall(PetscViewerDrawGetDraw(appctx.viewer2, 0, &draw));
134:   PetscCall(PetscDrawSetDoubleBuffer(draw));

136:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137:      Create timestepping solver context
138:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

140:   PetscCall(TSCreate(PETSC_COMM_SELF, &ts));
141:   PetscCall(TSSetProblemType(ts, TS_LINEAR));

143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144:      Set optional user-defined monitoring routine
145:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

147:   if (!flg_string) PetscCall(TSMonitorSet(ts, Monitor, &appctx, NULL));

149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

154:   PetscCall(MatCreate(PETSC_COMM_SELF, &A));
155:   PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, m, m));
156:   PetscCall(MatSetFromOptions(A));
157:   PetscCall(MatSetUp(A));

159:   flg = PETSC_FALSE;
160:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_ifunc", &flg, NULL));
161:   if (!flg) {
162:     appctx.A = NULL;
163:     PetscCall(PetscOptionsGetBool(NULL, NULL, "-time_dependent_rhs", &flg, NULL));
164:     if (flg) {
165:       /*
166:          For linear problems with a time-dependent f(u,t) in the equation
167:          u_t = f(u,t), the user provides the discretized right-hand side
168:          as a time-dependent matrix.
169:       */
170:       PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx));
171:       PetscCall(TSSetRHSJacobian(ts, A, A, RHSMatrixHeat, &appctx));
172:     } else {
173:       /*
174:          For linear problems with a time-independent f(u) in the equation
175:          u_t = f(u), the user provides the discretized right-hand side
176:          as a matrix only once, and then sets the special Jacobian evaluation
177:          routine TSComputeRHSJacobianConstant() which will NOT recompute the Jacobian.
178:       */
179:       PetscCall(RHSMatrixHeat(ts, 0.0, u, A, A, &appctx));
180:       PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx));
181:       PetscCall(TSSetRHSJacobian(ts, A, A, TSComputeRHSJacobianConstant, &appctx));
182:     }
183:   } else {
184:     Mat J;

186:     PetscCall(RHSMatrixHeat(ts, 0.0, u, A, A, &appctx));
187:     PetscCall(MatDuplicate(A, MAT_DO_NOT_COPY_VALUES, &J));
188:     PetscCall(TSSetIFunction(ts, NULL, IFunctionHeat, &appctx));
189:     PetscCall(TSSetIJacobian(ts, J, J, IJacobianHeat, &appctx));
190:     PetscCall(MatDestroy(&J));

192:     PetscCall(PetscObjectReference((PetscObject)A));
193:     appctx.A      = A;
194:     appctx.oshift = PETSC_MIN_REAL;
195:   }
196:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
197:      Set solution vector and initial timestep
198:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

200:   dt = appctx.h * appctx.h / 2.0;
201:   PetscCall(TSSetTimeStep(ts, dt));

203:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204:      Customize timestepping solver:
205:        - Set the solution method to be the Backward Euler method.
206:        - Set timestepping duration info
207:      Then set runtime options, which can override these defaults.
208:      For example,
209:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
210:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
211:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

213:   PetscCall(TSSetMaxSteps(ts, time_steps_max));
214:   PetscCall(TSSetMaxTime(ts, time_total_max));
215:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
216:   PetscCall(TSSetFromOptions(ts));

218:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
219:      Solve the problem
220:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

222:   /*
223:      Evaluate initial conditions
224:   */
225:   PetscCall(InitialConditions(u, &appctx));

227:   /*
228:      Run the timestepping solver
229:   */
230:   PetscCall(TSSolve(ts, u));
231:   PetscCall(TSGetStepNumber(ts, &steps));

233:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
234:      View timestepping solver info
235:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

237:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "avg. error (2 norm) = %g, avg. error (max norm) = %g\n", (double)(appctx.norm_2 / steps), (double)(appctx.norm_max / steps)));
238:   if (!flg_string) {
239:     PetscCall(TSView(ts, PETSC_VIEWER_STDOUT_SELF));
240:   } else {
241:     PetscViewer stringviewer;
242:     char        string[512];
243:     const char *outstring;

245:     PetscCall(PetscViewerStringOpen(PETSC_COMM_WORLD, string, sizeof(string), &stringviewer));
246:     PetscCall(TSView(ts, stringviewer));
248:     PetscCheck((char *)outstring == (char *)string, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "String returned from viewer does not equal original string");
249:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Output from string viewer:%s\n", outstring));
250:     PetscCall(PetscViewerDestroy(&stringviewer));
251:   }

253:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
254:      Free work space.  All PETSc objects should be destroyed when they
255:      are no longer needed.
256:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

258:   PetscCall(TSDestroy(&ts));
259:   PetscCall(MatDestroy(&A));
260:   PetscCall(VecDestroy(&u));
261:   PetscCall(PetscViewerDestroy(&appctx.viewer1));
262:   PetscCall(PetscViewerDestroy(&appctx.viewer2));
263:   PetscCall(VecDestroy(&appctx.solution));
264:   PetscCall(MatDestroy(&appctx.A));

266:   /*
267:      Always call PetscFinalize() before exiting a program.  This routine
268:        - finalizes the PETSc libraries as well as MPI
269:        - provides summary and diagnostic information if certain runtime
270:          options are chosen (e.g., -log_view).
271:   */
272:   PetscCall(PetscFinalize());
273:   return 0;
274: }
275: /* --------------------------------------------------------------------- */
276: /*
277:    InitialConditions - Computes the solution at the initial time.

279:    Input Parameter:
280:    u - uninitialized solution vector (global)
281:    appctx - user-defined application context

283:    Output Parameter:
284:    u - vector with solution at initial time (global)
285: */
286: PetscErrorCode InitialConditions(Vec u, AppCtx *appctx)
287: {
288:   PetscScalar *u_localptr, h = appctx->h;
289:   PetscInt     i;

291:   PetscFunctionBeginUser;
292:   /*
293:     Get a pointer to vector data.
294:     - For default PETSc vectors, VecGetArray() returns a pointer to
295:       the data array.  Otherwise, the routine is implementation dependent.
296:     - You MUST call VecRestoreArray() when you no longer need access to
297:       the array.
298:     - Note that the Fortran interface to VecGetArray() differs from the
299:       C version.  See the users manual for details.
300:   */
301:   PetscCall(VecGetArrayWrite(u, &u_localptr));

303:   /*
304:      We initialize the solution array by simply writing the solution
305:      directly into the array locations.  Alternatively, we could use
306:      VecSetValues() or VecSetValuesLocal().
307:   */
308:   for (i = 0; i < appctx->m; i++) u_localptr[i] = PetscSinScalar(PETSC_PI * i * 6. * h) + 3. * PetscSinScalar(PETSC_PI * i * 2. * h);

310:   /*
311:      Restore vector
312:   */
313:   PetscCall(VecRestoreArrayWrite(u, &u_localptr));

315:   /*
316:      Print debugging information if desired
317:   */
318:   if (appctx->debug) {
319:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Initial guess vector\n"));
320:     PetscCall(VecView(u, PETSC_VIEWER_STDOUT_SELF));
321:   }
322:   PetscFunctionReturn(PETSC_SUCCESS);
323: }
324: /* --------------------------------------------------------------------- */
325: /*
326:    ExactSolution - Computes the exact solution at a given time.

328:    Input Parameters:
329:    t - current time
330:    solution - vector in which exact solution will be computed
331:    appctx - user-defined application context

333:    Output Parameter:
334:    solution - vector with the newly computed exact solution
335: */
336: PetscErrorCode ExactSolution(PetscReal t, Vec solution, AppCtx *appctx)
337: {
338:   PetscScalar *s_localptr, h = appctx->h, ex1, ex2, sc1, sc2, tc = t;
339:   PetscInt     i;

341:   PetscFunctionBeginUser;
342:   /*
343:      Get a pointer to vector data.
344:   */
345:   PetscCall(VecGetArrayWrite(solution, &s_localptr));

347:   /*
348:      Simply write the solution directly into the array locations.
349:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
350:   */
351:   ex1 = PetscExpScalar(-36. * PETSC_PI * PETSC_PI * tc);
352:   ex2 = PetscExpScalar(-4. * PETSC_PI * PETSC_PI * tc);
353:   sc1 = PETSC_PI * 6. * h;
354:   sc2 = PETSC_PI * 2. * h;
355:   for (i = 0; i < appctx->m; i++) s_localptr[i] = PetscSinScalar(sc1 * (PetscReal)i) * ex1 + 3. * PetscSinScalar(sc2 * (PetscReal)i) * ex2;

357:   /*
358:      Restore vector
359:   */
360:   PetscCall(VecRestoreArrayWrite(solution, &s_localptr));
361:   PetscFunctionReturn(PETSC_SUCCESS);
362: }
363: /* --------------------------------------------------------------------- */
364: /*
365:    Monitor - User-provided routine to monitor the solution computed at
366:    each timestep.  This example plots the solution and computes the
367:    error in two different norms.

369:    This example also demonstrates changing the timestep via TSSetTimeStep().

371:    Input Parameters:
372:    ts     - the timestep context
373:    step   - the count of the current step (with 0 meaning the
374:              initial condition)
375:    time   - the current time
376:    u      - the solution at this timestep
377:    ctx    - the user-provided context for this monitoring routine.
378:             In this case we use the application context which contains
379:             information about the problem size, workspace and the exact
380:             solution.
381: */
382: PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal time, Vec u, void *ctx)
383: {
384:   AppCtx   *appctx = (AppCtx *)ctx; /* user-defined application context */
385:   PetscReal norm_2, norm_max, dt, dttol;

387:   PetscFunctionBeginUser;
388:   /*
389:      View a graph of the current iterate
390:   */
391:   PetscCall(VecView(u, appctx->viewer2));

393:   /*
394:      Compute the exact solution
395:   */
396:   PetscCall(ExactSolution(time, appctx->solution, appctx));

398:   /*
399:      Print debugging information if desired
400:   */
401:   if (appctx->debug) {
402:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Computed solution vector\n"));
403:     PetscCall(VecView(u, PETSC_VIEWER_STDOUT_SELF));
404:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Exact solution vector\n"));
405:     PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_SELF));
406:   }

408:   /*
409:      Compute the 2-norm and max-norm of the error
410:   */
411:   PetscCall(VecAXPY(appctx->solution, -1.0, u));
412:   PetscCall(VecNorm(appctx->solution, NORM_2, &norm_2));
413:   norm_2 = PetscSqrtReal(appctx->h) * norm_2;
414:   PetscCall(VecNorm(appctx->solution, NORM_MAX, &norm_max));

416:   PetscCall(TSGetTimeStep(ts, &dt));
417:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Timestep %3" PetscInt_FMT ": step size = %g, time = %g, 2-norm error = %g, max norm error = %g\n", step, (double)dt, (double)time, (double)norm_2, (double)norm_max));

419:   appctx->norm_2 += norm_2;
420:   appctx->norm_max += norm_max;

422:   dttol = .0001;
423:   PetscCall(PetscOptionsGetReal(NULL, NULL, "-dttol", &dttol, NULL));
424:   if (dt < dttol) {
425:     dt *= .999;
426:     PetscCall(TSSetTimeStep(ts, dt));
427:   }

429:   /*
430:      View a graph of the error
431:   */
432:   PetscCall(VecView(appctx->solution, appctx->viewer1));

434:   /*
435:      Print debugging information if desired
436:   */
437:   if (appctx->debug) {
438:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error vector\n"));
439:     PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_SELF));
440:   }
441:   PetscFunctionReturn(PETSC_SUCCESS);
442: }
443: /* --------------------------------------------------------------------- */
444: /*
445:    RHSMatrixHeat - User-provided routine to compute the right-hand-side
446:    matrix for the heat equation.

448:    Input Parameters:
449:    ts - the TS context
450:    t - current time
451:    global_in - global input vector
452:    dummy - optional user-defined context, as set by TSetRHSJacobian()

454:    Output Parameters:
455:    AA - Jacobian matrix
456:    BB - optionally different preconditioning matrix
457:    str - flag indicating matrix structure

459:    Notes:
460:    Recall that MatSetValues() uses 0-based row and column numbers
461:    in Fortran as well as in C.
462: */
463: PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec X, Mat AA, Mat BB, void *ctx)
464: {
465:   Mat         A      = AA;            /* Jacobian matrix */
466:   AppCtx     *appctx = (AppCtx *)ctx; /* user-defined application context */
467:   PetscInt    mstart = 0;
468:   PetscInt    mend   = appctx->m;
469:   PetscInt    i, idx[3];
470:   PetscScalar v[3], stwo = -2. / (appctx->h * appctx->h), sone = -.5 * stwo;

472:   PetscFunctionBeginUser;
473:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
474:      Compute entries for the locally owned part of the matrix
475:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
476:   /*
477:      Set matrix rows corresponding to boundary data
478:   */

480:   mstart = 0;
481:   v[0]   = 1.0;
482:   PetscCall(MatSetValues(A, 1, &mstart, 1, &mstart, v, INSERT_VALUES));
483:   mstart++;

485:   mend--;
486:   v[0] = 1.0;
487:   PetscCall(MatSetValues(A, 1, &mend, 1, &mend, v, INSERT_VALUES));

489:   /*
490:      Set matrix rows corresponding to interior data.  We construct the
491:      matrix one row at a time.
492:   */
493:   v[0] = sone;
494:   v[1] = stwo;
495:   v[2] = sone;
496:   for (i = mstart; i < mend; i++) {
497:     idx[0] = i - 1;
498:     idx[1] = i;
499:     idx[2] = i + 1;
500:     PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES));
501:   }

503:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
504:      Complete the matrix assembly process and set some options
505:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
506:   /*
507:      Assemble matrix, using the 2-step process:
508:        MatAssemblyBegin(), MatAssemblyEnd()
509:      Computations can be done while messages are in transition
510:      by placing code between these two statements.
511:   */
512:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
513:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

515:   /*
516:      Set and option to indicate that we will never add a new nonzero location
517:      to the matrix. If we do, it will generate an error.
518:   */
519:   PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
520:   PetscFunctionReturn(PETSC_SUCCESS);
521: }

523: PetscErrorCode IFunctionHeat(TS ts, PetscReal t, Vec X, Vec Xdot, Vec r, void *ctx)
524: {
525:   AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */

527:   PetscFunctionBeginUser;
528:   PetscCall(MatMult(appctx->A, X, r));
529:   PetscCall(VecAYPX(r, -1.0, Xdot));
530:   PetscFunctionReturn(PETSC_SUCCESS);
531: }

533: PetscErrorCode IJacobianHeat(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal s, Mat A, Mat B, void *ctx)
534: {
535:   AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */

537:   PetscFunctionBeginUser;
538:   if (appctx->oshift == s) PetscFunctionReturn(PETSC_SUCCESS);
539:   PetscCall(MatCopy(appctx->A, A, SAME_NONZERO_PATTERN));
540:   PetscCall(MatScale(A, -1));
541:   PetscCall(MatShift(A, s));
542:   PetscCall(MatCopy(A, B, SAME_NONZERO_PATTERN));
543:   appctx->oshift = s;
544:   PetscFunctionReturn(PETSC_SUCCESS);
545: }

547: /*TEST

549:     test:
550:       args: -nox -ts_type ssp -ts_dt 0.0005

552:     test:
553:       suffix: 2
554:       args: -nox -ts_type ssp -ts_dt 0.0005 -time_dependent_rhs 1

556:     test:
557:       suffix: 3
558:       args: -nox -ts_type rosw -ts_max_steps 3 -ksp_converged_reason
559:       filter: sed "s/ATOL/RTOL/g"
560:       requires: !single

562:     test:
563:       suffix: 4
564:       args: -nox -ts_type beuler -ts_max_steps 3 -ksp_converged_reason
565:       filter: sed "s/ATOL/RTOL/g"

567:     test:
568:       suffix: 5
569:       args: -nox -ts_type beuler -ts_max_steps 3 -ksp_converged_reason -time_dependent_rhs
570:       filter: sed "s/ATOL/RTOL/g"

572:     test:
573:       requires: !single
574:       suffix: pod_guess
575:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type pod -pc_type none -ksp_converged_reason

577:     test:
578:       requires: !single
579:       suffix: pod_guess_Ainner
580:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type pod -ksp_guess_pod_Ainner -pc_type none -ksp_converged_reason

582:     test:
583:       requires: !single
584:       suffix: fischer_guess
585:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type fischer -pc_type none -ksp_converged_reason

587:     test:
588:       requires: !single
589:       suffix: fischer_guess_2
590:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type fischer -ksp_guess_fischer_model 2,10 -pc_type none -ksp_converged_reason

592:     test:
593:       requires: !single
594:       suffix: fischer_guess_3
595:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type fischer -ksp_guess_fischer_model 3,10 -pc_type none -ksp_converged_reason

597:     test:
598:       requires: !single
599:       suffix: stringview
600:       args: -nox -ts_type rosw -test_string_viewer

602:     test:
603:       requires: !single
604:       suffix: stringview_euler
605:       args: -nox -ts_type euler -test_string_viewer

607: TEST*/
```