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, 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 */ 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 */ 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 */ 395 PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal time, Vec u, void *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 preconditioning matrix 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 */ 482 PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec X, Mat AA, Mat BB, void *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 } 545 546 PetscErrorCode RHSFunctionHeat(TS ts, PetscReal t, Vec globalin, Vec globalout, void *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