Actual source code: ex3.c


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

 10: /* ------------------------------------------------------------------------

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

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

 28:    We compare the approximate solution with the exact solution, given by
 29:        u_exact(x,t) = exp(-36*pi*pi*t) * sin(6*pi*x) +
 30:                       3*exp(-4*pi*pi*t) * sin(2*pi*x)

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

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

 40:   ------------------------------------------------------------------------- */

 42: /*
 43:    Include "petscts.h" so that we can use TS solvers.  Note that this file
 44:    automatically includes:
 45:      petscsys.h       - base PETSc routines   petscvec.h  - vectors
 46:      petscmat.h  - matrices
 47:      petscis.h     - index sets            petscksp.h  - Krylov subspace methods
 48:      petscviewer.h - viewers               petscpc.h   - preconditioners
 49:      petscksp.h   - linear solvers        petscsnes.h - nonlinear solvers
 50: */

 52: #include <petscts.h>
 53: #include <petscdraw.h>

 55: /*
 56:    User-defined application context - contains data needed by the
 57:    application-provided call-back routines.
 58: */
 59: typedef struct {
 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:   PetscViewer viewer1, viewer2; /* viewers for the solution and error */
 65:   PetscReal   norm_2, norm_max; /* error norms */
 66:   Mat         A;                /* RHS mat, used with IFunction interface */
 67:   PetscReal   oshift;           /* old shift applied, prevent to recompute the IJacobian */
 68: } AppCtx;

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

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

 94:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 95:      Initialize program and set problem parameters
 96:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

109:   appctx.m        = m;
110:   appctx.h        = 1.0 / (m - 1.0);
111:   appctx.norm_2   = 0.0;
112:   appctx.norm_max = 0.0;

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

116:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117:      Create vector data structures
118:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127:      Set up displays to show graphs of the solution and error
128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

137:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
138:      Create timestepping solver context
139:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

144:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145:      Set optional user-defined monitoring routine
146:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

150:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

152:      Create matrix data structure; set matrix evaluation routine.
153:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

193:     PetscCall(PetscObjectReference((PetscObject)A));
194:     appctx.A      = A;
195:     appctx.oshift = PETSC_MIN_REAL;
196:   }
197:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198:      Set solution vector and initial timestep
199:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

204:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205:      Customize timestepping solver:
206:        - Set the solution method to be the Backward Euler method.
207:        - Set timestepping duration info
208:      Then set runtime options, which can override these defaults.
209:      For example,
210:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
211:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
212:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

219:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
220:      Solve the problem
221:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

234:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
235:      View timestepping solver info
236:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

238:   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)));
239:   if (!flg_string) {
240:     PetscCall(TSView(ts, PETSC_VIEWER_STDOUT_SELF));
241:   } else {
242:     PetscViewer stringviewer;
243:     char        string[512];
244:     const char *outstring;

246:     PetscCall(PetscViewerStringOpen(PETSC_COMM_WORLD, string, sizeof(string), &stringviewer));
247:     PetscCall(TSView(ts, stringviewer));
248:     PetscCall(PetscViewerStringGetStringRead(stringviewer, &outstring, NULL));
249:     PetscCheck((char *)outstring == (char *)string, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "String returned from viewer does not equal original string");
250:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Output from string viewer:%s\n", outstring));
251:     PetscCall(PetscViewerDestroy(&stringviewer));
252:   }

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.solution));
265:   PetscCall(MatDestroy(&appctx.A));

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

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

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

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

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

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

316:   /*
317:      Print debugging information if desired
318:   */
319:   if (appctx->debug) {
320:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Initial guess vector\n"));
321:     PetscCall(VecView(u, PETSC_VIEWER_STDOUT_SELF));
322:   }

324:   PetscFunctionReturn(PETSC_SUCCESS);
325: }
326: /* --------------------------------------------------------------------- */
327: /*
328:    ExactSolution - Computes the exact solution at a given time.

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

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

343:   PetscFunctionBeginUser;
344:   /*
345:      Get a pointer to vector data.
346:   */
347:   PetscCall(VecGetArrayWrite(solution, &s_localptr));

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

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

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

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

389:   PetscFunctionBeginUser;
390:   /*
391:      View a graph of the current iterate
392:   */
393:   PetscCall(VecView(u, appctx->viewer2));

395:   /*
396:      Compute the exact solution
397:   */
398:   PetscCall(ExactSolution(time, appctx->solution, appctx));

400:   /*
401:      Print debugging information if desired
402:   */
403:   if (appctx->debug) {
404:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Computed solution vector\n"));
405:     PetscCall(VecView(u, PETSC_VIEWER_STDOUT_SELF));
406:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Exact solution vector\n"));
407:     PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_SELF));
408:   }

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

418:   PetscCall(TSGetTimeStep(ts, &dt));
419:   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));

421:   appctx->norm_2 += norm_2;
422:   appctx->norm_max += norm_max;

424:   dttol = .0001;
425:   PetscCall(PetscOptionsGetReal(NULL, NULL, "-dttol", &dttol, NULL));
426:   if (dt < dttol) {
427:     dt *= .999;
428:     PetscCall(TSSetTimeStep(ts, dt));
429:   }

431:   /*
432:      View a graph of the error
433:   */
434:   PetscCall(VecView(appctx->solution, appctx->viewer1));

436:   /*
437:      Print debugging information if desired
438:   */
439:   if (appctx->debug) {
440:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error vector\n"));
441:     PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_SELF));
442:   }

444:   PetscFunctionReturn(PETSC_SUCCESS);
445: }
446: /* --------------------------------------------------------------------- */
447: /*
448:    RHSMatrixHeat - User-provided routine to compute the right-hand-side
449:    matrix for the heat equation.

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

457:    Output Parameters:
458:    AA - Jacobian matrix
459:    BB - optionally different preconditioning matrix
460:    str - flag indicating matrix structure

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

475:   PetscFunctionBeginUser;
476:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
477:      Compute entries for the locally owned part of the matrix
478:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
479:   /*
480:      Set matrix rows corresponding to boundary data
481:   */

483:   mstart = 0;
484:   v[0]   = 1.0;
485:   PetscCall(MatSetValues(A, 1, &mstart, 1, &mstart, v, INSERT_VALUES));
486:   mstart++;

488:   mend--;
489:   v[0] = 1.0;
490:   PetscCall(MatSetValues(A, 1, &mend, 1, &mend, v, INSERT_VALUES));

492:   /*
493:      Set matrix rows corresponding to interior data.  We construct the
494:      matrix one row at a time.
495:   */
496:   v[0] = sone;
497:   v[1] = stwo;
498:   v[2] = sone;
499:   for (i = mstart; i < mend; i++) {
500:     idx[0] = i - 1;
501:     idx[1] = i;
502:     idx[2] = i + 1;
503:     PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES));
504:   }

506:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
507:      Complete the matrix assembly process and set some options
508:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
509:   /*
510:      Assemble matrix, using the 2-step process:
511:        MatAssemblyBegin(), MatAssemblyEnd()
512:      Computations can be done while messages are in transition
513:      by placing code between these two statements.
514:   */
515:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
516:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

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

524:   PetscFunctionReturn(PETSC_SUCCESS);
525: }

527: PetscErrorCode IFunctionHeat(TS ts, PetscReal t, Vec X, Vec Xdot, Vec r, void *ctx)
528: {
529:   AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */

531:   PetscFunctionBeginUser;
532:   PetscCall(MatMult(appctx->A, X, r));
533:   PetscCall(VecAYPX(r, -1.0, Xdot));
534:   PetscFunctionReturn(PETSC_SUCCESS);
535: }

537: PetscErrorCode IJacobianHeat(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal s, Mat A, Mat B, void *ctx)
538: {
539:   AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */

541:   PetscFunctionBeginUser;
542:   if (appctx->oshift == s) PetscFunctionReturn(PETSC_SUCCESS);
543:   PetscCall(MatCopy(appctx->A, A, SAME_NONZERO_PATTERN));
544:   PetscCall(MatScale(A, -1));
545:   PetscCall(MatShift(A, s));
546:   PetscCall(MatCopy(A, B, SAME_NONZERO_PATTERN));
547:   appctx->oshift = s;
548:   PetscFunctionReturn(PETSC_SUCCESS);
549: }

551: /*TEST

553:     test:
554:       args: -nox -ts_type ssp -ts_dt 0.0005

556:     test:
557:       suffix: 2
558:       args: -nox -ts_type ssp -ts_dt 0.0005 -time_dependent_rhs 1

560:     test:
561:       suffix: 3
562:       args:  -nox -ts_type rosw -ts_max_steps 3 -ksp_converged_reason
563:       filter: sed "s/ATOL/RTOL/g"
564:       requires: !single

566:     test:
567:       suffix: 4
568:       args: -nox -ts_type beuler -ts_max_steps 3 -ksp_converged_reason
569:       filter: sed "s/ATOL/RTOL/g"

571:     test:
572:       suffix: 5
573:       args: -nox -ts_type beuler -ts_max_steps 3 -ksp_converged_reason -time_dependent_rhs
574:       filter: sed "s/ATOL/RTOL/g"

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

581:     test:
582:       requires: !single
583:       suffix: pod_guess_Ainner
584:       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

586:     test:
587:       requires: !single
588:       suffix: fischer_guess
589:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type fischer -pc_type none -ksp_converged_reason

591:     test:
592:       requires: !single
593:       suffix: fischer_guess_2
594:       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

596:     test:
597:       requires: !single
598:       suffix: fischer_guess_3
599:       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

601:     test:
602:       requires: !single
603:       suffix: stringview
604:       args: -nox -ts_type rosw -test_string_viewer

606:     test:
607:       requires: !single
608:       suffix: stringview_euler
609:       args: -nox -ts_type euler -test_string_viewer

611: TEST*/