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";
7
8 /* ------------------------------------------------------------------------
9
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.
18
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> ./ex4 -ts_type <timestepping solver>
25
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)
29
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)
35
36 The uniprocessor version of this code is ts/tutorials/ex3.c
37
38 ------------------------------------------------------------------------- */
39
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 */
50
51 #include <petscdm.h>
52 #include <petscdmda.h>
53 #include <petscts.h>
54 #include <petscdraw.h>
55
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;
72
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 *);
81
main(int argc,char ** argv)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;
96
97 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
98 Initialize program and set problem parameters
99 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
100
101 PetscFunctionBeginUser;
102 PetscCall(PetscInitialize(&argc, &argv, NULL, help));
103 appctx.comm = PETSC_COMM_WORLD;
104
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;
112
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));
115
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 */
124
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));
128
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));
136
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));
143
144 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145 Set up displays to show graphs of the solution and error
146 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147
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));
154
155 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156 Create timestepping solver context
157 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158
159 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
160
161 flg = PETSC_FALSE;
162 PetscCall(PetscOptionsGetBool(NULL, NULL, "-nonlinear", &flg, NULL));
163 PetscCall(TSSetProblemType(ts, flg ? TS_NONLINEAR : TS_LINEAR));
164
165 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166 Set optional user-defined monitoring routine
167 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
168 PetscCall(TSMonitorSet(ts, Monitor, &appctx, NULL));
169
170 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171
172 Create matrix data structure; set matrix evaluation routine.
173 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
174
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));
179
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 }
201
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 }
208
209 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
210 Set solution vector and initial timestep
211 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
212
213 dt = appctx.h * appctx.h / 2.0;
214 PetscCall(TSSetTimeStep(ts, dt));
215 PetscCall(TSSetSolution(ts, u));
216
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 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
226
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));
231
232 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
233 Solve the problem
234 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
235
236 /*
237 Evaluate initial conditions
238 */
239 PetscCall(InitialConditions(u, &appctx));
240
241 /*
242 Run the timestepping solver
243 */
244 PetscCall(TSSolve(ts, u));
245 PetscCall(TSGetSolveTime(ts, &ftime));
246 PetscCall(TSGetStepNumber(ts, &steps));
247
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)));
253
254 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
255 Free work space. All PETSc objects should be destroyed when they
256 are no longer needed.
257 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
258
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));
268
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.
281
282 Input Parameter:
283 u - uninitialized solution vector (global)
284 appctx - user-defined application context
285
286 Output Parameter:
287 u - vector with solution at initial time (global)
288 */
InitialConditions(Vec u,AppCtx * appctx)289 PetscErrorCode InitialConditions(Vec u, AppCtx *appctx)
290 {
291 PetscScalar *u_localptr, h = appctx->h;
292 PetscInt i, mybase, myend;
293
294 PetscFunctionBeginUser;
295 /*
296 Determine starting point of each processor's range of
297 grid values.
298 */
299 PetscCall(VecGetOwnershipRange(u, &mybase, &myend));
300
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));
311
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);
318
319 /*
320 Restore vector
321 */
322 PetscCall(VecRestoreArray(u, &u_localptr));
323
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.
336
337 Input Parameters:
338 t - current time
339 solution - vector in which exact solution will be computed
340 appctx - user-defined application context
341
342 Output Parameter:
343 solution - vector with the newly computed exact solution
344 */
ExactSolution(PetscReal t,Vec solution,AppCtx * appctx)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;
349
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));
356
357 /*
358 Get a pointer to vector data.
359 */
360 PetscCall(VecGetArray(solution, &s_localptr));
361
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;
371
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.
383
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 */
Monitor(TS ts,PetscInt step,PetscReal time,Vec u,PetscCtx ctx)395 PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal time, Vec u, PetscCtx ctx)
396 {
397 AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */
398 PetscReal norm_2, norm_max;
399
400 PetscFunctionBeginUser;
401 /*
402 View a graph of the current iterate
403 */
404 PetscCall(VecView(u, appctx->viewer2));
405
406 /*
407 Compute the exact solution
408 */
409 PetscCall(ExactSolution(time, appctx->solution, appctx));
410
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 }
420
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;
430
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;
438
439 /*
440 View a graph of the error
441 */
442 PetscCall(VecView(appctx->solution, appctx->viewer1));
443
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 }
453
454 /* --------------------------------------------------------------------- */
455 /*
456 RHSMatrixHeat - User-provided routine to compute the right-hand-side
457 matrix for the heat equation.
458
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()
464
465 Output Parameters:
466 AA - Jacobian matrix
467 BB - optionally different matrix used to construct the preconditioner
468
469 Notes:
470 RHSMatrixHeat computes entries for the locally owned part of the system.
471 - Currently, all PETSc parallel matrix formats are partitioned by
472 contiguous chunks of rows across the processors.
473 - Each processor needs to insert only elements that it owns
474 locally (but any non-local elements will be sent to the
475 appropriate processor during matrix assembly).
476 - Always specify global row and columns of matrix entries when
477 using MatSetValues(); we could alternatively use MatSetValuesLocal().
478 - Here, we set all entries for a particular row at once.
479 - Note that MatSetValues() uses 0-based row and column numbers
480 in Fortran as well as in C.
481 */
RHSMatrixHeat(TS ts,PetscReal t,Vec X,Mat AA,Mat BB,PetscCtx ctx)482 PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec X, Mat AA, Mat BB, PetscCtx ctx)
483 {
484 Mat A = AA; /* Jacobian matrix */
485 AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */
486 PetscInt i, mstart, mend, idx[3];
487 PetscScalar v[3], stwo = -2. / (appctx->h * appctx->h), sone = -.5 * stwo;
488
489 PetscFunctionBeginUser;
490 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
491 Compute entries for the locally owned part of the matrix
492 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
493
494 PetscCall(MatGetOwnershipRange(A, &mstart, &mend));
495
496 /*
497 Set matrix rows corresponding to boundary data
498 */
499
500 if (mstart == 0) { /* first processor only */
501 v[0] = 1.0;
502 PetscCall(MatSetValues(A, 1, &mstart, 1, &mstart, v, INSERT_VALUES));
503 mstart++;
504 }
505
506 if (mend == appctx->m) { /* last processor only */
507 mend--;
508 v[0] = 1.0;
509 PetscCall(MatSetValues(A, 1, &mend, 1, &mend, v, INSERT_VALUES));
510 }
511
512 /*
513 Set matrix rows corresponding to interior data. We construct the
514 matrix one row at a time.
515 */
516 v[0] = sone;
517 v[1] = stwo;
518 v[2] = sone;
519 for (i = mstart; i < mend; i++) {
520 idx[0] = i - 1;
521 idx[1] = i;
522 idx[2] = i + 1;
523 PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES));
524 }
525
526 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
527 Complete the matrix assembly process and set some options
528 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
529 /*
530 Assemble matrix, using the 2-step process:
531 MatAssemblyBegin(), MatAssemblyEnd()
532 Computations can be done while messages are in transition
533 by placing code between these two statements.
534 */
535 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
536 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
537
538 /*
539 Set and option to indicate that we will never add a new nonzero location
540 to the matrix. If we do, it will generate an error.
541 */
542 PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
543 PetscFunctionReturn(PETSC_SUCCESS);
544 }
545
RHSFunctionHeat(TS ts,PetscReal t,Vec globalin,Vec globalout,PetscCtx ctx)546 PetscErrorCode RHSFunctionHeat(TS ts, PetscReal t, Vec globalin, Vec globalout, PetscCtx ctx)
547 {
548 Mat A;
549
550 PetscFunctionBeginUser;
551 PetscCall(TSGetRHSJacobian(ts, &A, NULL, NULL, &ctx));
552 PetscCall(RHSMatrixHeat(ts, t, globalin, A, NULL, ctx));
553 /* PetscCall(MatView(A,PETSC_VIEWER_STDOUT_WORLD)); */
554 PetscCall(MatMult(A, globalin, globalout));
555 PetscFunctionReturn(PETSC_SUCCESS);
556 }
557
558 /*TEST
559
560 test:
561 args: -ts_view -nox
562
563 test:
564 suffix: 2
565 args: -ts_view -nox
566 nsize: 3
567
568 test:
569 suffix: 3
570 args: -ts_view -nox -nonlinear
571
572 test:
573 suffix: 4
574 args: -ts_view -nox -nonlinear
575 nsize: 3
576 timeoutfactor: 3
577
578 test:
579 suffix: sundials
580 requires: sundials2
581 args: -nox -ts_type sundials -ts_max_steps 5 -nonlinear
582 nsize: 4
583
584 test:
585 suffix: sundials_dense
586 requires: sundials2
587 args: -nox -ts_type sundials -ts_sundials_use_dense -ts_max_steps 5 -nonlinear
588 nsize: 1
589
590 TEST*/
591