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 Concepts: TS^time-dependent linear problems 11 Concepts: TS^heat equation 12 Concepts: TS^diffusion equation 13 Processors: n 14 */ 15 16 /* ------------------------------------------------------------------------ 17 18 This program solves the one-dimensional heat equation (also called the 19 diffusion equation), 20 u_t = u_xx, 21 on the domain 0 <= x <= 1, with the boundary conditions 22 u(t,0) = 0, u(t,1) = 0, 23 and the initial condition 24 u(0,x) = sin(6*pi*x) + 3*sin(2*pi*x). 25 This is a linear, second-order, parabolic equation. 26 27 We discretize the right-hand side using finite differences with 28 uniform grid spacing h: 29 u_xx = (u_{i+1} - 2u_{i} + u_{i-1})/(h^2) 30 We then demonstrate time evolution using the various TS methods by 31 running the program via 32 mpiexec -n <procs> ex3 -ts_type <timestepping solver> 33 34 We compare the approximate solution with the exact solution, given by 35 u_exact(x,t) = exp(-36*pi*pi*t) * sin(6*pi*x) + 36 3*exp(-4*pi*pi*t) * sin(2*pi*x) 37 38 Notes: 39 This code demonstrates the TS solver interface to two variants of 40 linear problems, u_t = f(u,t), namely 41 - time-dependent f: f(u,t) is a function of t 42 - time-independent f: f(u,t) is simply f(u) 43 44 The uniprocessor version of this code is ts/tutorials/ex3.c 45 46 ------------------------------------------------------------------------- */ 47 48 /* 49 Include "petscdmda.h" so that we can use distributed arrays (DMDAs) to manage 50 the parallel grid. Include "petscts.h" so that we can use TS solvers. 51 Note that this file automatically includes: 52 petscsys.h - base PETSc routines petscvec.h - vectors 53 petscmat.h - matrices 54 petscis.h - index sets petscksp.h - Krylov subspace methods 55 petscviewer.h - viewers petscpc.h - preconditioners 56 petscksp.h - linear solvers petscsnes.h - nonlinear solvers 57 */ 58 59 #include <petscdm.h> 60 #include <petscdmda.h> 61 #include <petscts.h> 62 #include <petscdraw.h> 63 64 /* 65 User-defined application context - contains data needed by the 66 application-provided call-back routines. 67 */ 68 typedef struct { 69 MPI_Comm comm; /* communicator */ 70 DM da; /* distributed array data structure */ 71 Vec localwork; /* local ghosted work vector */ 72 Vec u_local; /* local ghosted approximate solution vector */ 73 Vec solution; /* global exact solution vector */ 74 PetscInt m; /* total number of grid points */ 75 PetscReal h; /* mesh width h = 1/(m-1) */ 76 PetscBool debug; /* flag (1 indicates activation of debugging printouts) */ 77 PetscViewer viewer1,viewer2; /* viewers for the solution and error */ 78 PetscReal norm_2,norm_max; /* error norms */ 79 } AppCtx; 80 81 /* 82 User-defined routines 83 */ 84 extern PetscErrorCode InitialConditions(Vec,AppCtx*); 85 extern PetscErrorCode RHSMatrixHeat(TS,PetscReal,Vec,Mat,Mat,void*); 86 extern PetscErrorCode RHSFunctionHeat(TS,PetscReal,Vec,Vec,void*); 87 extern PetscErrorCode Monitor(TS,PetscInt,PetscReal,Vec,void*); 88 extern PetscErrorCode ExactSolution(PetscReal,Vec,AppCtx*); 89 90 int main(int argc,char **argv) 91 { 92 AppCtx appctx; /* user-defined application context */ 93 TS ts; /* timestepping context */ 94 Mat A; /* matrix data structure */ 95 Vec u; /* approximate solution vector */ 96 PetscReal time_total_max = 1.0; /* default max total time */ 97 PetscInt time_steps_max = 100; /* default max timesteps */ 98 PetscDraw draw; /* drawing context */ 99 PetscInt steps,m; 100 PetscMPIInt size; 101 PetscReal dt,ftime; 102 PetscBool flg; 103 TSProblemType tsproblem = TS_LINEAR; 104 105 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 106 Initialize program and set problem parameters 107 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 108 109 CHKERRQ(PetscInitialize(&argc,&argv,(char*)0,help)); 110 appctx.comm = PETSC_COMM_WORLD; 111 112 m = 60; 113 CHKERRQ(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL)); 114 CHKERRQ(PetscOptionsHasName(NULL,NULL,"-debug",&appctx.debug)); 115 appctx.m = m; 116 appctx.h = 1.0/(m-1.0); 117 appctx.norm_2 = 0.0; 118 appctx.norm_max = 0.0; 119 120 CHKERRMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 121 CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"Solving a linear TS problem, number of processors = %d\n",size)); 122 123 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 124 Create vector data structures 125 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 126 /* 127 Create distributed array (DMDA) to manage parallel grid and vectors 128 and to set up the ghost point communication pattern. There are M 129 total grid values spread equally among all the processors. 130 */ 131 132 CHKERRQ(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,m,1,1,NULL,&appctx.da)); 133 CHKERRQ(DMSetFromOptions(appctx.da)); 134 CHKERRQ(DMSetUp(appctx.da)); 135 136 /* 137 Extract global and local vectors from DMDA; we use these to store the 138 approximate solution. Then duplicate these for remaining vectors that 139 have the same types. 140 */ 141 CHKERRQ(DMCreateGlobalVector(appctx.da,&u)); 142 CHKERRQ(DMCreateLocalVector(appctx.da,&appctx.u_local)); 143 144 /* 145 Create local work vector for use in evaluating right-hand-side function; 146 create global work vector for storing exact solution. 147 */ 148 CHKERRQ(VecDuplicate(appctx.u_local,&appctx.localwork)); 149 CHKERRQ(VecDuplicate(u,&appctx.solution)); 150 151 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 152 Set up displays to show graphs of the solution and error 153 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 154 155 CHKERRQ(PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"",80,380,400,160,&appctx.viewer1)); 156 CHKERRQ(PetscViewerDrawGetDraw(appctx.viewer1,0,&draw)); 157 CHKERRQ(PetscDrawSetDoubleBuffer(draw)); 158 CHKERRQ(PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"",80,0,400,160,&appctx.viewer2)); 159 CHKERRQ(PetscViewerDrawGetDraw(appctx.viewer2,0,&draw)); 160 CHKERRQ(PetscDrawSetDoubleBuffer(draw)); 161 162 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 163 Create timestepping solver context 164 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 165 166 CHKERRQ(TSCreate(PETSC_COMM_WORLD,&ts)); 167 168 flg = PETSC_FALSE; 169 CHKERRQ(PetscOptionsGetBool(NULL,NULL,"-nonlinear",&flg,NULL)); 170 CHKERRQ(TSSetProblemType(ts,flg ? TS_NONLINEAR : TS_LINEAR)); 171 172 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 173 Set optional user-defined monitoring routine 174 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 175 CHKERRQ(TSMonitorSet(ts,Monitor,&appctx,NULL)); 176 177 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 178 179 Create matrix data structure; set matrix evaluation routine. 180 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 181 182 CHKERRQ(MatCreate(PETSC_COMM_WORLD,&A)); 183 CHKERRQ(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,m)); 184 CHKERRQ(MatSetFromOptions(A)); 185 CHKERRQ(MatSetUp(A)); 186 187 flg = PETSC_FALSE; 188 CHKERRQ(PetscOptionsGetBool(NULL,NULL,"-time_dependent_rhs",&flg,NULL)); 189 if (flg) { 190 /* 191 For linear problems with a time-dependent f(u,t) in the equation 192 u_t = f(u,t), the user provides the discretized right-hand-side 193 as a time-dependent matrix. 194 */ 195 CHKERRQ(TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx)); 196 CHKERRQ(TSSetRHSJacobian(ts,A,A,RHSMatrixHeat,&appctx)); 197 } else { 198 /* 199 For linear problems with a time-independent f(u) in the equation 200 u_t = f(u), the user provides the discretized right-hand-side 201 as a matrix only once, and then sets a null matrix evaluation 202 routine. 203 */ 204 CHKERRQ(RHSMatrixHeat(ts,0.0,u,A,A,&appctx)); 205 CHKERRQ(TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx)); 206 CHKERRQ(TSSetRHSJacobian(ts,A,A,TSComputeRHSJacobianConstant,&appctx)); 207 } 208 209 if (tsproblem == TS_NONLINEAR) { 210 SNES snes; 211 CHKERRQ(TSSetRHSFunction(ts,NULL,RHSFunctionHeat,&appctx)); 212 CHKERRQ(TSGetSNES(ts,&snes)); 213 CHKERRQ(SNESSetJacobian(snes,NULL,NULL,SNESComputeJacobianDefault,NULL)); 214 } 215 216 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 217 Set solution vector and initial timestep 218 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 219 220 dt = appctx.h*appctx.h/2.0; 221 CHKERRQ(TSSetTimeStep(ts,dt)); 222 CHKERRQ(TSSetSolution(ts,u)); 223 224 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 225 Customize timestepping solver: 226 - Set the solution method to be the Backward Euler method. 227 - Set timestepping duration info 228 Then set runtime options, which can override these defaults. 229 For example, 230 -ts_max_steps <maxsteps> -ts_max_time <maxtime> 231 to override the defaults set by TSSetMaxSteps()/TSSetMaxTime(). 232 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 233 234 CHKERRQ(TSSetMaxSteps(ts,time_steps_max)); 235 CHKERRQ(TSSetMaxTime(ts,time_total_max)); 236 CHKERRQ(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); 237 CHKERRQ(TSSetFromOptions(ts)); 238 239 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 240 Solve the problem 241 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 242 243 /* 244 Evaluate initial conditions 245 */ 246 CHKERRQ(InitialConditions(u,&appctx)); 247 248 /* 249 Run the timestepping solver 250 */ 251 CHKERRQ(TSSolve(ts,u)); 252 CHKERRQ(TSGetSolveTime(ts,&ftime)); 253 CHKERRQ(TSGetStepNumber(ts,&steps)); 254 255 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 256 View timestepping solver info 257 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 258 CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"Total timesteps %D, Final time %g\n",steps,(double)ftime)); 259 CHKERRQ(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))); 260 261 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 262 Free work space. All PETSc objects should be destroyed when they 263 are no longer needed. 264 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 265 266 CHKERRQ(TSDestroy(&ts)); 267 CHKERRQ(MatDestroy(&A)); 268 CHKERRQ(VecDestroy(&u)); 269 CHKERRQ(PetscViewerDestroy(&appctx.viewer1)); 270 CHKERRQ(PetscViewerDestroy(&appctx.viewer2)); 271 CHKERRQ(VecDestroy(&appctx.localwork)); 272 CHKERRQ(VecDestroy(&appctx.solution)); 273 CHKERRQ(VecDestroy(&appctx.u_local)); 274 CHKERRQ(DMDestroy(&appctx.da)); 275 276 /* 277 Always call PetscFinalize() before exiting a program. This routine 278 - finalizes the PETSc libraries as well as MPI 279 - provides summary and diagnostic information if certain runtime 280 options are chosen (e.g., -log_view). 281 */ 282 CHKERRQ(PetscFinalize()); 283 return 0; 284 } 285 /* --------------------------------------------------------------------- */ 286 /* 287 InitialConditions - Computes the solution at the initial time. 288 289 Input Parameter: 290 u - uninitialized solution vector (global) 291 appctx - user-defined application context 292 293 Output Parameter: 294 u - vector with solution at initial time (global) 295 */ 296 PetscErrorCode InitialConditions(Vec u,AppCtx *appctx) 297 { 298 PetscScalar *u_localptr,h = appctx->h; 299 PetscInt i,mybase,myend; 300 301 /* 302 Determine starting point of each processor's range of 303 grid values. 304 */ 305 CHKERRQ(VecGetOwnershipRange(u,&mybase,&myend)); 306 307 /* 308 Get a pointer to vector data. 309 - For default PETSc vectors, VecGetArray() returns a pointer to 310 the data array. Otherwise, the routine is implementation dependent. 311 - You MUST call VecRestoreArray() when you no longer need access to 312 the array. 313 - Note that the Fortran interface to VecGetArray() differs from the 314 C version. See the users manual for details. 315 */ 316 CHKERRQ(VecGetArray(u,&u_localptr)); 317 318 /* 319 We initialize the solution array by simply writing the solution 320 directly into the array locations. Alternatively, we could use 321 VecSetValues() or VecSetValuesLocal(). 322 */ 323 for (i=mybase; i<myend; i++) u_localptr[i-mybase] = PetscSinScalar(PETSC_PI*i*6.*h) + 3.*PetscSinScalar(PETSC_PI*i*2.*h); 324 325 /* 326 Restore vector 327 */ 328 CHKERRQ(VecRestoreArray(u,&u_localptr)); 329 330 /* 331 Print debugging information if desired 332 */ 333 if (appctx->debug) { 334 CHKERRQ(PetscPrintf(appctx->comm,"initial guess vector\n")); 335 CHKERRQ(VecView(u,PETSC_VIEWER_STDOUT_WORLD)); 336 } 337 338 return 0; 339 } 340 /* --------------------------------------------------------------------- */ 341 /* 342 ExactSolution - Computes the exact solution at a given time. 343 344 Input Parameters: 345 t - current time 346 solution - vector in which exact solution will be computed 347 appctx - user-defined application context 348 349 Output Parameter: 350 solution - vector with the newly computed exact solution 351 */ 352 PetscErrorCode ExactSolution(PetscReal t,Vec solution,AppCtx *appctx) 353 { 354 PetscScalar *s_localptr,h = appctx->h,ex1,ex2,sc1,sc2; 355 PetscInt i,mybase,myend; 356 357 /* 358 Determine starting and ending points of each processor's 359 range of grid values 360 */ 361 CHKERRQ(VecGetOwnershipRange(solution,&mybase,&myend)); 362 363 /* 364 Get a pointer to vector data. 365 */ 366 CHKERRQ(VecGetArray(solution,&s_localptr)); 367 368 /* 369 Simply write the solution directly into the array locations. 370 Alternatively, we culd use VecSetValues() or VecSetValuesLocal(). 371 */ 372 ex1 = PetscExpReal(-36.*PETSC_PI*PETSC_PI*t); ex2 = PetscExpReal(-4.*PETSC_PI*PETSC_PI*t); 373 sc1 = PETSC_PI*6.*h; sc2 = PETSC_PI*2.*h; 374 for (i=mybase; i<myend; i++) s_localptr[i-mybase] = PetscSinScalar(sc1*(PetscReal)i)*ex1 + 3.*PetscSinScalar(sc2*(PetscReal)i)*ex2; 375 376 /* 377 Restore vector 378 */ 379 CHKERRQ(VecRestoreArray(solution,&s_localptr)); 380 return 0; 381 } 382 /* --------------------------------------------------------------------- */ 383 /* 384 Monitor - User-provided routine to monitor the solution computed at 385 each timestep. This example plots the solution and computes the 386 error in two different norms. 387 388 Input Parameters: 389 ts - the timestep context 390 step - the count of the current step (with 0 meaning the 391 initial condition) 392 time - the current time 393 u - the solution at this timestep 394 ctx - the user-provided context for this monitoring routine. 395 In this case we use the application context which contains 396 information about the problem size, workspace and the exact 397 solution. 398 */ 399 PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec u,void *ctx) 400 { 401 AppCtx *appctx = (AppCtx*) ctx; /* user-defined application context */ 402 PetscReal norm_2,norm_max; 403 404 /* 405 View a graph of the current iterate 406 */ 407 CHKERRQ(VecView(u,appctx->viewer2)); 408 409 /* 410 Compute the exact solution 411 */ 412 CHKERRQ(ExactSolution(time,appctx->solution,appctx)); 413 414 /* 415 Print debugging information if desired 416 */ 417 if (appctx->debug) { 418 CHKERRQ(PetscPrintf(appctx->comm,"Computed solution vector\n")); 419 CHKERRQ(VecView(u,PETSC_VIEWER_STDOUT_WORLD)); 420 CHKERRQ(PetscPrintf(appctx->comm,"Exact solution vector\n")); 421 CHKERRQ(VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD)); 422 } 423 424 /* 425 Compute the 2-norm and max-norm of the error 426 */ 427 CHKERRQ(VecAXPY(appctx->solution,-1.0,u)); 428 CHKERRQ(VecNorm(appctx->solution,NORM_2,&norm_2)); 429 norm_2 = PetscSqrtReal(appctx->h)*norm_2; 430 CHKERRQ(VecNorm(appctx->solution,NORM_MAX,&norm_max)); 431 if (norm_2 < 1e-14) norm_2 = 0; 432 if (norm_max < 1e-14) norm_max = 0; 433 434 /* 435 PetscPrintf() causes only the first processor in this 436 communicator to print the timestep information. 437 */ 438 CHKERRQ(PetscPrintf(appctx->comm,"Timestep %D: time = %g 2-norm error = %g max norm error = %g\n",step,(double)time,(double)norm_2,(double)norm_max)); 439 appctx->norm_2 += norm_2; 440 appctx->norm_max += norm_max; 441 442 /* 443 View a graph of the error 444 */ 445 CHKERRQ(VecView(appctx->solution,appctx->viewer1)); 446 447 /* 448 Print debugging information if desired 449 */ 450 if (appctx->debug) { 451 CHKERRQ(PetscPrintf(appctx->comm,"Error vector\n")); 452 CHKERRQ(VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD)); 453 } 454 455 return 0; 456 } 457 458 /* --------------------------------------------------------------------- */ 459 /* 460 RHSMatrixHeat - User-provided routine to compute the right-hand-side 461 matrix for the heat equation. 462 463 Input Parameters: 464 ts - the TS context 465 t - current time 466 global_in - global input vector 467 dummy - optional user-defined context, as set by TSetRHSJacobian() 468 469 Output Parameters: 470 AA - Jacobian matrix 471 BB - optionally different preconditioning matrix 472 str - flag indicating matrix structure 473 474 Notes: 475 RHSMatrixHeat computes entries for the locally owned part of the system. 476 - Currently, all PETSc parallel matrix formats are partitioned by 477 contiguous chunks of rows across the processors. 478 - Each processor needs to insert only elements that it owns 479 locally (but any non-local elements will be sent to the 480 appropriate processor during matrix assembly). 481 - Always specify global row and columns of matrix entries when 482 using MatSetValues(); we could alternatively use MatSetValuesLocal(). 483 - Here, we set all entries for a particular row at once. 484 - Note that MatSetValues() uses 0-based row and column numbers 485 in Fortran as well as in C. 486 */ 487 PetscErrorCode RHSMatrixHeat(TS ts,PetscReal t,Vec X,Mat AA,Mat BB,void *ctx) 488 { 489 Mat A = AA; /* Jacobian matrix */ 490 AppCtx *appctx = (AppCtx*)ctx; /* user-defined application context */ 491 PetscInt i,mstart,mend,idx[3]; 492 PetscScalar v[3],stwo = -2./(appctx->h*appctx->h),sone = -.5*stwo; 493 494 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 495 Compute entries for the locally owned part of the matrix 496 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 497 498 CHKERRQ(MatGetOwnershipRange(A,&mstart,&mend)); 499 500 /* 501 Set matrix rows corresponding to boundary data 502 */ 503 504 if (mstart == 0) { /* first processor only */ 505 v[0] = 1.0; 506 CHKERRQ(MatSetValues(A,1,&mstart,1,&mstart,v,INSERT_VALUES)); 507 mstart++; 508 } 509 510 if (mend == appctx->m) { /* last processor only */ 511 mend--; 512 v[0] = 1.0; 513 CHKERRQ(MatSetValues(A,1,&mend,1,&mend,v,INSERT_VALUES)); 514 } 515 516 /* 517 Set matrix rows corresponding to interior data. We construct the 518 matrix one row at a time. 519 */ 520 v[0] = sone; v[1] = stwo; v[2] = sone; 521 for (i=mstart; i<mend; i++) { 522 idx[0] = i-1; idx[1] = i; idx[2] = i+1; 523 CHKERRQ(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 CHKERRQ(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); 536 CHKERRQ(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 CHKERRQ(MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE)); 543 544 return 0; 545 } 546 547 PetscErrorCode RHSFunctionHeat(TS ts,PetscReal t,Vec globalin,Vec globalout,void *ctx) 548 { 549 Mat A; 550 551 PetscFunctionBeginUser; 552 CHKERRQ(TSGetRHSJacobian(ts,&A,NULL,NULL,&ctx)); 553 CHKERRQ(RHSMatrixHeat(ts,t,globalin,A,NULL,ctx)); 554 /* CHKERRQ(MatView(A,PETSC_VIEWER_STDOUT_WORLD)); */ 555 CHKERRQ(MatMult(A,globalin,globalout)); 556 PetscFunctionReturn(0); 557 } 558 559 /*TEST 560 561 test: 562 args: -ts_view -nox 563 564 test: 565 suffix: 2 566 args: -ts_view -nox 567 nsize: 3 568 569 test: 570 suffix: 3 571 args: -ts_view -nox -nonlinear 572 573 test: 574 suffix: 4 575 args: -ts_view -nox -nonlinear 576 nsize: 3 577 timeoutfactor: 3 578 579 test: 580 suffix: sundials 581 requires: sundials2 582 args: -nox -ts_type sundials -ts_max_steps 5 -nonlinear 583 nsize: 4 584 585 test: 586 suffix: sundials_dense 587 requires: sundials2 588 args: -nox -ts_type sundials -ts_sundials_use_dense -ts_max_steps 5 -nonlinear 589 nsize: 1 590 591 TEST*/ 592