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> ex3 -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 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, (char *)0, 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 */ 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 } 331 332 PetscFunctionReturn(PETSC_SUCCESS); 333 } 334 /* --------------------------------------------------------------------- */ 335 /* 336 ExactSolution - Computes the exact solution at a given time. 337 338 Input Parameters: 339 t - current time 340 solution - vector in which exact solution will be computed 341 appctx - user-defined application context 342 343 Output Parameter: 344 solution - vector with the newly computed exact solution 345 */ 346 PetscErrorCode ExactSolution(PetscReal t, Vec solution, AppCtx *appctx) 347 { 348 PetscScalar *s_localptr, h = appctx->h, ex1, ex2, sc1, sc2; 349 PetscInt i, mybase, myend; 350 351 PetscFunctionBeginUser; 352 /* 353 Determine starting and ending points of each processor's 354 range of grid values 355 */ 356 PetscCall(VecGetOwnershipRange(solution, &mybase, &myend)); 357 358 /* 359 Get a pointer to vector data. 360 */ 361 PetscCall(VecGetArray(solution, &s_localptr)); 362 363 /* 364 Simply write the solution directly into the array locations. 365 Alternatively, we culd use VecSetValues() or VecSetValuesLocal(). 366 */ 367 ex1 = PetscExpReal(-36. * PETSC_PI * PETSC_PI * t); 368 ex2 = PetscExpReal(-4. * PETSC_PI * PETSC_PI * t); 369 sc1 = PETSC_PI * 6. * h; 370 sc2 = PETSC_PI * 2. * h; 371 for (i = mybase; i < myend; i++) s_localptr[i - mybase] = PetscSinScalar(sc1 * (PetscReal)i) * ex1 + 3. * PetscSinScalar(sc2 * (PetscReal)i) * ex2; 372 373 /* 374 Restore vector 375 */ 376 PetscCall(VecRestoreArray(solution, &s_localptr)); 377 PetscFunctionReturn(PETSC_SUCCESS); 378 } 379 /* --------------------------------------------------------------------- */ 380 /* 381 Monitor - User-provided routine to monitor the solution computed at 382 each timestep. This example plots the solution and computes the 383 error in two different norms. 384 385 Input Parameters: 386 ts - the timestep context 387 step - the count of the current step (with 0 meaning the 388 initial condition) 389 time - the current time 390 u - the solution at this timestep 391 ctx - the user-provided context for this monitoring routine. 392 In this case we use the application context which contains 393 information about the problem size, workspace and the exact 394 solution. 395 */ 396 PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal time, Vec u, void *ctx) 397 { 398 AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */ 399 PetscReal norm_2, norm_max; 400 401 PetscFunctionBeginUser; 402 /* 403 View a graph of the current iterate 404 */ 405 PetscCall(VecView(u, appctx->viewer2)); 406 407 /* 408 Compute the exact solution 409 */ 410 PetscCall(ExactSolution(time, appctx->solution, appctx)); 411 412 /* 413 Print debugging information if desired 414 */ 415 if (appctx->debug) { 416 PetscCall(PetscPrintf(appctx->comm, "Computed solution vector\n")); 417 PetscCall(VecView(u, PETSC_VIEWER_STDOUT_WORLD)); 418 PetscCall(PetscPrintf(appctx->comm, "Exact solution vector\n")); 419 PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_WORLD)); 420 } 421 422 /* 423 Compute the 2-norm and max-norm of the error 424 */ 425 PetscCall(VecAXPY(appctx->solution, -1.0, u)); 426 PetscCall(VecNorm(appctx->solution, NORM_2, &norm_2)); 427 norm_2 = PetscSqrtReal(appctx->h) * norm_2; 428 PetscCall(VecNorm(appctx->solution, NORM_MAX, &norm_max)); 429 if (norm_2 < 1e-14) norm_2 = 0; 430 if (norm_max < 1e-14) norm_max = 0; 431 432 /* 433 PetscPrintf() causes only the first processor in this 434 communicator to print the timestep information. 435 */ 436 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)); 437 appctx->norm_2 += norm_2; 438 appctx->norm_max += norm_max; 439 440 /* 441 View a graph of the error 442 */ 443 PetscCall(VecView(appctx->solution, appctx->viewer1)); 444 445 /* 446 Print debugging information if desired 447 */ 448 if (appctx->debug) { 449 PetscCall(PetscPrintf(appctx->comm, "Error vector\n")); 450 PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_WORLD)); 451 } 452 453 PetscFunctionReturn(PETSC_SUCCESS); 454 } 455 456 /* --------------------------------------------------------------------- */ 457 /* 458 RHSMatrixHeat - User-provided routine to compute the right-hand-side 459 matrix for the heat equation. 460 461 Input Parameters: 462 ts - the TS context 463 t - current time 464 global_in - global input vector 465 dummy - optional user-defined context, as set by TSetRHSJacobian() 466 467 Output Parameters: 468 AA - Jacobian matrix 469 BB - optionally different preconditioning matrix 470 str - flag indicating matrix structure 471 472 Notes: 473 RHSMatrixHeat computes entries for the locally owned part of the system. 474 - Currently, all PETSc parallel matrix formats are partitioned by 475 contiguous chunks of rows across the processors. 476 - Each processor needs to insert only elements that it owns 477 locally (but any non-local elements will be sent to the 478 appropriate processor during matrix assembly). 479 - Always specify global row and columns of matrix entries when 480 using MatSetValues(); we could alternatively use MatSetValuesLocal(). 481 - Here, we set all entries for a particular row at once. 482 - Note that MatSetValues() uses 0-based row and column numbers 483 in Fortran as well as in C. 484 */ 485 PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec X, Mat AA, Mat BB, void *ctx) 486 { 487 Mat A = AA; /* Jacobian matrix */ 488 AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */ 489 PetscInt i, mstart, mend, idx[3]; 490 PetscScalar v[3], stwo = -2. / (appctx->h * appctx->h), sone = -.5 * stwo; 491 492 PetscFunctionBeginUser; 493 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 494 Compute entries for the locally owned part of the matrix 495 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 496 497 PetscCall(MatGetOwnershipRange(A, &mstart, &mend)); 498 499 /* 500 Set matrix rows corresponding to boundary data 501 */ 502 503 if (mstart == 0) { /* first processor only */ 504 v[0] = 1.0; 505 PetscCall(MatSetValues(A, 1, &mstart, 1, &mstart, v, INSERT_VALUES)); 506 mstart++; 507 } 508 509 if (mend == appctx->m) { /* last processor only */ 510 mend--; 511 v[0] = 1.0; 512 PetscCall(MatSetValues(A, 1, &mend, 1, &mend, v, INSERT_VALUES)); 513 } 514 515 /* 516 Set matrix rows corresponding to interior data. We construct the 517 matrix one row at a time. 518 */ 519 v[0] = sone; 520 v[1] = stwo; 521 v[2] = sone; 522 for (i = mstart; i < mend; i++) { 523 idx[0] = i - 1; 524 idx[1] = i; 525 idx[2] = i + 1; 526 PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES)); 527 } 528 529 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 530 Complete the matrix assembly process and set some options 531 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 532 /* 533 Assemble matrix, using the 2-step process: 534 MatAssemblyBegin(), MatAssemblyEnd() 535 Computations can be done while messages are in transition 536 by placing code between these two statements. 537 */ 538 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 539 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 540 541 /* 542 Set and option to indicate that we will never add a new nonzero location 543 to the matrix. If we do, it will generate an error. 544 */ 545 PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE)); 546 547 PetscFunctionReturn(PETSC_SUCCESS); 548 } 549 550 PetscErrorCode RHSFunctionHeat(TS ts, PetscReal t, Vec globalin, Vec globalout, void *ctx) 551 { 552 Mat A; 553 554 PetscFunctionBeginUser; 555 PetscCall(TSGetRHSJacobian(ts, &A, NULL, NULL, &ctx)); 556 PetscCall(RHSMatrixHeat(ts, t, globalin, A, NULL, ctx)); 557 /* PetscCall(MatView(A,PETSC_VIEWER_STDOUT_WORLD)); */ 558 PetscCall(MatMult(A, globalin, globalout)); 559 PetscFunctionReturn(PETSC_SUCCESS); 560 } 561 562 /*TEST 563 564 test: 565 args: -ts_view -nox 566 567 test: 568 suffix: 2 569 args: -ts_view -nox 570 nsize: 3 571 572 test: 573 suffix: 3 574 args: -ts_view -nox -nonlinear 575 576 test: 577 suffix: 4 578 args: -ts_view -nox -nonlinear 579 nsize: 3 580 timeoutfactor: 3 581 582 test: 583 suffix: sundials 584 requires: sundials2 585 args: -nox -ts_type sundials -ts_max_steps 5 -nonlinear 586 nsize: 4 587 588 test: 589 suffix: sundials_dense 590 requires: sundials2 591 args: -nox -ts_type sundials -ts_sundials_use_dense -ts_max_steps 5 -nonlinear 592 nsize: 1 593 594 TEST*/ 595