1 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 -debug : Activate debugging printouts\n\ 7 -nox : Deactivate x-window graphics\n\n"; 8 9 /* ------------------------------------------------------------------------ 10 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. 19 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 mpiexec -n <procs> ex3 -ts_type <timestepping solver> 26 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) 30 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) 36 37 The uniprocessor version of this code is ts/tutorials/ex3.c 38 39 ------------------------------------------------------------------------- */ 40 41 /* 42 Include "petscdmda.h" so that we can use distributed arrays (DMDAs) to manage 43 the parallel grid. Include "petscts.h" so that we can use TS solvers. 44 Note that this file 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 */ 51 52 #include <petscdm.h> 53 #include <petscdmda.h> 54 #include <petscts.h> 55 #include <petscdraw.h> 56 57 /* 58 User-defined application context - contains data needed by the 59 application-provided call-back routines. 60 */ 61 typedef struct { 62 MPI_Comm comm; /* communicator */ 63 DM da; /* distributed array data structure */ 64 Vec localwork; /* local ghosted work vector */ 65 Vec u_local; /* local ghosted approximate solution vector */ 66 Vec solution; /* global exact solution vector */ 67 PetscInt m; /* total number of grid points */ 68 PetscReal h; /* mesh width h = 1/(m-1) */ 69 PetscBool debug; /* flag (1 indicates activation of debugging printouts) */ 70 PetscViewer viewer1, viewer2; /* viewers for the solution and error */ 71 PetscReal norm_2, norm_max; /* error norms */ 72 } AppCtx; 73 74 /* 75 User-defined routines 76 */ 77 extern PetscErrorCode InitialConditions(Vec, AppCtx *); 78 extern PetscErrorCode RHSMatrixHeat(TS, PetscReal, Vec, Mat, Mat, void *); 79 extern PetscErrorCode RHSFunctionHeat(TS, PetscReal, Vec, Vec, void *); 80 extern PetscErrorCode Monitor(TS, PetscInt, PetscReal, Vec, void *); 81 extern PetscErrorCode ExactSolution(PetscReal, Vec, AppCtx *); 82 83 int main(int argc, char **argv) { 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 PetscScalar *u_localptr, h = appctx->h; 291 PetscInt i, mybase, myend; 292 293 /* 294 Determine starting point of each processor's range of 295 grid values. 296 */ 297 PetscCall(VecGetOwnershipRange(u, &mybase, &myend)); 298 299 /* 300 Get a pointer to vector data. 301 - For default PETSc vectors, VecGetArray() returns a pointer to 302 the data array. Otherwise, the routine is implementation dependent. 303 - You MUST call VecRestoreArray() when you no longer need access to 304 the array. 305 - Note that the Fortran interface to VecGetArray() differs from the 306 C version. See the users manual for details. 307 */ 308 PetscCall(VecGetArray(u, &u_localptr)); 309 310 /* 311 We initialize the solution array by simply writing the solution 312 directly into the array locations. Alternatively, we could use 313 VecSetValues() or VecSetValuesLocal(). 314 */ 315 for (i = mybase; i < myend; i++) u_localptr[i - mybase] = PetscSinScalar(PETSC_PI * i * 6. * h) + 3. * PetscSinScalar(PETSC_PI * i * 2. * h); 316 317 /* 318 Restore vector 319 */ 320 PetscCall(VecRestoreArray(u, &u_localptr)); 321 322 /* 323 Print debugging information if desired 324 */ 325 if (appctx->debug) { 326 PetscCall(PetscPrintf(appctx->comm, "initial guess vector\n")); 327 PetscCall(VecView(u, PETSC_VIEWER_STDOUT_WORLD)); 328 } 329 330 return 0; 331 } 332 /* --------------------------------------------------------------------- */ 333 /* 334 ExactSolution - Computes the exact solution at a given time. 335 336 Input Parameters: 337 t - current time 338 solution - vector in which exact solution will be computed 339 appctx - user-defined application context 340 341 Output Parameter: 342 solution - vector with the newly computed exact solution 343 */ 344 PetscErrorCode ExactSolution(PetscReal t, Vec solution, AppCtx *appctx) { 345 PetscScalar *s_localptr, h = appctx->h, ex1, ex2, sc1, sc2; 346 PetscInt i, mybase, myend; 347 348 /* 349 Determine starting and ending points of each processor's 350 range of grid values 351 */ 352 PetscCall(VecGetOwnershipRange(solution, &mybase, &myend)); 353 354 /* 355 Get a pointer to vector data. 356 */ 357 PetscCall(VecGetArray(solution, &s_localptr)); 358 359 /* 360 Simply write the solution directly into the array locations. 361 Alternatively, we culd use VecSetValues() or VecSetValuesLocal(). 362 */ 363 ex1 = PetscExpReal(-36. * PETSC_PI * PETSC_PI * t); 364 ex2 = PetscExpReal(-4. * PETSC_PI * PETSC_PI * t); 365 sc1 = PETSC_PI * 6. * h; 366 sc2 = PETSC_PI * 2. * h; 367 for (i = mybase; i < myend; i++) s_localptr[i - mybase] = PetscSinScalar(sc1 * (PetscReal)i) * ex1 + 3. * PetscSinScalar(sc2 * (PetscReal)i) * ex2; 368 369 /* 370 Restore vector 371 */ 372 PetscCall(VecRestoreArray(solution, &s_localptr)); 373 return 0; 374 } 375 /* --------------------------------------------------------------------- */ 376 /* 377 Monitor - User-provided routine to monitor the solution computed at 378 each timestep. This example plots the solution and computes the 379 error in two different norms. 380 381 Input Parameters: 382 ts - the timestep context 383 step - the count of the current step (with 0 meaning the 384 initial condition) 385 time - the current time 386 u - the solution at this timestep 387 ctx - the user-provided context for this monitoring routine. 388 In this case we use the application context which contains 389 information about the problem size, workspace and the exact 390 solution. 391 */ 392 PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal time, Vec u, void *ctx) { 393 AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */ 394 PetscReal norm_2, norm_max; 395 396 /* 397 View a graph of the current iterate 398 */ 399 PetscCall(VecView(u, appctx->viewer2)); 400 401 /* 402 Compute the exact solution 403 */ 404 PetscCall(ExactSolution(time, appctx->solution, appctx)); 405 406 /* 407 Print debugging information if desired 408 */ 409 if (appctx->debug) { 410 PetscCall(PetscPrintf(appctx->comm, "Computed solution vector\n")); 411 PetscCall(VecView(u, PETSC_VIEWER_STDOUT_WORLD)); 412 PetscCall(PetscPrintf(appctx->comm, "Exact solution vector\n")); 413 PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_WORLD)); 414 } 415 416 /* 417 Compute the 2-norm and max-norm of the error 418 */ 419 PetscCall(VecAXPY(appctx->solution, -1.0, u)); 420 PetscCall(VecNorm(appctx->solution, NORM_2, &norm_2)); 421 norm_2 = PetscSqrtReal(appctx->h) * norm_2; 422 PetscCall(VecNorm(appctx->solution, NORM_MAX, &norm_max)); 423 if (norm_2 < 1e-14) norm_2 = 0; 424 if (norm_max < 1e-14) norm_max = 0; 425 426 /* 427 PetscPrintf() causes only the first processor in this 428 communicator to print the timestep information. 429 */ 430 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)); 431 appctx->norm_2 += norm_2; 432 appctx->norm_max += norm_max; 433 434 /* 435 View a graph of the error 436 */ 437 PetscCall(VecView(appctx->solution, appctx->viewer1)); 438 439 /* 440 Print debugging information if desired 441 */ 442 if (appctx->debug) { 443 PetscCall(PetscPrintf(appctx->comm, "Error vector\n")); 444 PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_WORLD)); 445 } 446 447 return 0; 448 } 449 450 /* --------------------------------------------------------------------- */ 451 /* 452 RHSMatrixHeat - User-provided routine to compute the right-hand-side 453 matrix for the heat equation. 454 455 Input Parameters: 456 ts - the TS context 457 t - current time 458 global_in - global input vector 459 dummy - optional user-defined context, as set by TSetRHSJacobian() 460 461 Output Parameters: 462 AA - Jacobian matrix 463 BB - optionally different preconditioning matrix 464 str - flag indicating matrix structure 465 466 Notes: 467 RHSMatrixHeat computes entries for the locally owned part of the system. 468 - Currently, all PETSc parallel matrix formats are partitioned by 469 contiguous chunks of rows across the processors. 470 - Each processor needs to insert only elements that it owns 471 locally (but any non-local elements will be sent to the 472 appropriate processor during matrix assembly). 473 - Always specify global row and columns of matrix entries when 474 using MatSetValues(); we could alternatively use MatSetValuesLocal(). 475 - Here, we set all entries for a particular row at once. 476 - Note that MatSetValues() uses 0-based row and column numbers 477 in Fortran as well as in C. 478 */ 479 PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec X, Mat AA, Mat BB, void *ctx) { 480 Mat A = AA; /* Jacobian matrix */ 481 AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */ 482 PetscInt i, mstart, mend, idx[3]; 483 PetscScalar v[3], stwo = -2. / (appctx->h * appctx->h), sone = -.5 * stwo; 484 485 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 486 Compute entries for the locally owned part of the matrix 487 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 488 489 PetscCall(MatGetOwnershipRange(A, &mstart, &mend)); 490 491 /* 492 Set matrix rows corresponding to boundary data 493 */ 494 495 if (mstart == 0) { /* first processor only */ 496 v[0] = 1.0; 497 PetscCall(MatSetValues(A, 1, &mstart, 1, &mstart, v, INSERT_VALUES)); 498 mstart++; 499 } 500 501 if (mend == appctx->m) { /* last processor only */ 502 mend--; 503 v[0] = 1.0; 504 PetscCall(MatSetValues(A, 1, &mend, 1, &mend, v, INSERT_VALUES)); 505 } 506 507 /* 508 Set matrix rows corresponding to interior data. We construct the 509 matrix one row at a time. 510 */ 511 v[0] = sone; 512 v[1] = stwo; 513 v[2] = sone; 514 for (i = mstart; i < mend; i++) { 515 idx[0] = i - 1; 516 idx[1] = i; 517 idx[2] = i + 1; 518 PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES)); 519 } 520 521 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 522 Complete the matrix assembly process and set some options 523 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 524 /* 525 Assemble matrix, using the 2-step process: 526 MatAssemblyBegin(), MatAssemblyEnd() 527 Computations can be done while messages are in transition 528 by placing code between these two statements. 529 */ 530 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 531 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 532 533 /* 534 Set and option to indicate that we will never add a new nonzero location 535 to the matrix. If we do, it will generate an error. 536 */ 537 PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE)); 538 539 return 0; 540 } 541 542 PetscErrorCode RHSFunctionHeat(TS ts, PetscReal t, Vec globalin, Vec globalout, void *ctx) { 543 Mat A; 544 545 PetscFunctionBeginUser; 546 PetscCall(TSGetRHSJacobian(ts, &A, NULL, NULL, &ctx)); 547 PetscCall(RHSMatrixHeat(ts, t, globalin, A, NULL, ctx)); 548 /* PetscCall(MatView(A,PETSC_VIEWER_STDOUT_WORLD)); */ 549 PetscCall(MatMult(A, globalin, globalout)); 550 PetscFunctionReturn(0); 551 } 552 553 /*TEST 554 555 test: 556 args: -ts_view -nox 557 558 test: 559 suffix: 2 560 args: -ts_view -nox 561 nsize: 3 562 563 test: 564 suffix: 3 565 args: -ts_view -nox -nonlinear 566 567 test: 568 suffix: 4 569 args: -ts_view -nox -nonlinear 570 nsize: 3 571 timeoutfactor: 3 572 573 test: 574 suffix: sundials 575 requires: sundials2 576 args: -nox -ts_type sundials -ts_max_steps 5 -nonlinear 577 nsize: 4 578 579 test: 580 suffix: sundials_dense 581 requires: sundials2 582 args: -nox -ts_type sundials -ts_sundials_use_dense -ts_max_steps 5 -nonlinear 583 nsize: 1 584 585 TEST*/ 586