Actual source code: ex4.c

      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";

      9: /*
     10:    Concepts: TS^time-dependent linear problems
     11:    Concepts: TS^heat equation
     12:    Concepts: TS^diffusion equation
     13:    Processors: n
     14: */

     16: /* ------------------------------------------------------------------------

     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.

     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>

     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)

     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)

     44:     The uniprocessor version of this code is ts/tutorials/ex3.c

     46:   ------------------------------------------------------------------------- */

     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: */

     59: #include <petscdm.h>
     60: #include <petscdmda.h>
     61: #include <petscts.h>
     62: #include <petscdraw.h>

     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;

     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*);

     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 */
    100:   PetscInt       steps,m;
    101:   PetscMPIInt    size;
    102:   PetscReal      dt,ftime;
    103:   PetscBool      flg;
    104:   TSProblemType  tsproblem = TS_LINEAR;

    106:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    107:      Initialize program and set problem parameters
    108:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    110:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
    111:   appctx.comm = PETSC_COMM_WORLD;

    113:   m               = 60;
    114:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
    115:   PetscOptionsHasName(NULL,NULL,"-debug",&appctx.debug);
    116:   appctx.m        = m;
    117:   appctx.h        = 1.0/(m-1.0);
    118:   appctx.norm_2   = 0.0;
    119:   appctx.norm_max = 0.0;

    121:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
    122:   PetscPrintf(PETSC_COMM_WORLD,"Solving a linear TS problem, number of processors = %d\n",size);

    124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    125:      Create vector data structures
    126:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    127:   /*
    128:      Create distributed array (DMDA) to manage parallel grid and vectors
    129:      and to set up the ghost point communication pattern.  There are M
    130:      total grid values spread equally among all the processors.
    131:   */

    133:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,m,1,1,NULL,&appctx.da);
    134:   DMSetFromOptions(appctx.da);
    135:   DMSetUp(appctx.da);

    137:   /*
    138:      Extract global and local vectors from DMDA; we use these to store the
    139:      approximate solution.  Then duplicate these for remaining vectors that
    140:      have the same types.
    141:   */
    142:   DMCreateGlobalVector(appctx.da,&u);
    143:   DMCreateLocalVector(appctx.da,&appctx.u_local);

    145:   /*
    146:      Create local work vector for use in evaluating right-hand-side function;
    147:      create global work vector for storing exact solution.
    148:   */
    149:   VecDuplicate(appctx.u_local,&appctx.localwork);
    150:   VecDuplicate(u,&appctx.solution);

    152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    153:      Set up displays to show graphs of the solution and error
    154:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    156:   PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"",80,380,400,160,&appctx.viewer1);
    157:   PetscViewerDrawGetDraw(appctx.viewer1,0,&draw);
    158:   PetscDrawSetDoubleBuffer(draw);
    159:   PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"",80,0,400,160,&appctx.viewer2);
    160:   PetscViewerDrawGetDraw(appctx.viewer2,0,&draw);
    161:   PetscDrawSetDoubleBuffer(draw);

    163:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    164:      Create timestepping solver context
    165:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    167:   TSCreate(PETSC_COMM_WORLD,&ts);

    169:   flg  = PETSC_FALSE;
    170:   PetscOptionsGetBool(NULL,NULL,"-nonlinear",&flg,NULL);
    171:   TSSetProblemType(ts,flg ? TS_NONLINEAR : TS_LINEAR);

    173:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    174:      Set optional user-defined monitoring routine
    175:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    176:   TSMonitorSet(ts,Monitor,&appctx,NULL);

    178:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    180:      Create matrix data structure; set matrix evaluation routine.
    181:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    183:   MatCreate(PETSC_COMM_WORLD,&A);
    184:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,m);
    185:   MatSetFromOptions(A);
    186:   MatSetUp(A);

    188:   flg  = PETSC_FALSE;
    189:   PetscOptionsGetBool(NULL,NULL,"-time_dependent_rhs",&flg,NULL);
    190:   if (flg) {
    191:     /*
    192:        For linear problems with a time-dependent f(u,t) in the equation
    193:        u_t = f(u,t), the user provides the discretized right-hand-side
    194:        as a time-dependent matrix.
    195:     */
    196:     TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx);
    197:     TSSetRHSJacobian(ts,A,A,RHSMatrixHeat,&appctx);
    198:   } else {
    199:     /*
    200:        For linear problems with a time-independent f(u) in the equation
    201:        u_t = f(u), the user provides the discretized right-hand-side
    202:        as a matrix only once, and then sets a null matrix evaluation
    203:        routine.
    204:     */
    205:     RHSMatrixHeat(ts,0.0,u,A,A,&appctx);
    206:     TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx);
    207:     TSSetRHSJacobian(ts,A,A,TSComputeRHSJacobianConstant,&appctx);
    208:   }

    210:   if (tsproblem == TS_NONLINEAR) {
    211:     SNES snes;
    212:     TSSetRHSFunction(ts,NULL,RHSFunctionHeat,&appctx);
    213:     TSGetSNES(ts,&snes);
    214:     SNESSetJacobian(snes,NULL,NULL,SNESComputeJacobianDefault,NULL);
    215:   }

    217:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    218:      Set solution vector and initial timestep
    219:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    221:   dt   = appctx.h*appctx.h/2.0;
    222:   TSSetTimeStep(ts,dt);
    223:   TSSetSolution(ts,u);

    225:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    226:      Customize timestepping solver:
    227:        - Set the solution method to be the Backward Euler method.
    228:        - Set timestepping duration info
    229:      Then set runtime options, which can override these defaults.
    230:      For example,
    231:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
    232:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
    233:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    235:   TSSetMaxSteps(ts,time_steps_max);
    236:   TSSetMaxTime(ts,time_total_max);
    237:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
    238:   TSSetFromOptions(ts);

    240:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    241:      Solve the problem
    242:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    244:   /*
    245:      Evaluate initial conditions
    246:   */
    247:   InitialConditions(u,&appctx);

    249:   /*
    250:      Run the timestepping solver
    251:   */
    252:   TSSolve(ts,u);
    253:   TSGetSolveTime(ts,&ftime);
    254:   TSGetStepNumber(ts,&steps);

    256:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    257:      View timestepping solver info
    258:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    259:   PetscPrintf(PETSC_COMM_WORLD,"Total timesteps %D, Final time %g\n",steps,(double)ftime);
    260:   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));

    262:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    263:      Free work space.  All PETSc objects should be destroyed when they
    264:      are no longer needed.
    265:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    267:   TSDestroy(&ts);
    268:   MatDestroy(&A);
    269:   VecDestroy(&u);
    270:   PetscViewerDestroy(&appctx.viewer1);
    271:   PetscViewerDestroy(&appctx.viewer2);
    272:   VecDestroy(&appctx.localwork);
    273:   VecDestroy(&appctx.solution);
    274:   VecDestroy(&appctx.u_local);
    275:   DMDestroy(&appctx.da);

    277:   /*
    278:      Always call PetscFinalize() before exiting a program.  This routine
    279:        - finalizes the PETSc libraries as well as MPI
    280:        - provides summary and diagnostic information if certain runtime
    281:          options are chosen (e.g., -log_view).
    282:   */
    283:   PetscFinalize();
    284:   return ierr;
    285: }
    286: /* --------------------------------------------------------------------- */
    287: /*
    288:    InitialConditions - Computes the solution at the initial time.

    290:    Input Parameter:
    291:    u - uninitialized solution vector (global)
    292:    appctx - user-defined application context

    294:    Output Parameter:
    295:    u - vector with solution at initial time (global)
    296: */
    297: PetscErrorCode InitialConditions(Vec u,AppCtx *appctx)
    298: {
    299:   PetscScalar    *u_localptr,h = appctx->h;
    300:   PetscInt       i,mybase,myend;

    303:   /*
    304:      Determine starting point of each processor's range of
    305:      grid values.
    306:   */
    307:   VecGetOwnershipRange(u,&mybase,&myend);

    309:   /*
    310:     Get a pointer to vector data.
    311:     - For default PETSc vectors, VecGetArray() returns a pointer to
    312:       the data array.  Otherwise, the routine is implementation dependent.
    313:     - You MUST call VecRestoreArray() when you no longer need access to
    314:       the array.
    315:     - Note that the Fortran interface to VecGetArray() differs from the
    316:       C version.  See the users manual for details.
    317:   */
    318:   VecGetArray(u,&u_localptr);

    320:   /*
    321:      We initialize the solution array by simply writing the solution
    322:      directly into the array locations.  Alternatively, we could use
    323:      VecSetValues() or VecSetValuesLocal().
    324:   */
    325:   for (i=mybase; i<myend; i++) u_localptr[i-mybase] = PetscSinScalar(PETSC_PI*i*6.*h) + 3.*PetscSinScalar(PETSC_PI*i*2.*h);

    327:   /*
    328:      Restore vector
    329:   */
    330:   VecRestoreArray(u,&u_localptr);

    332:   /*
    333:      Print debugging information if desired
    334:   */
    335:   if (appctx->debug) {
    336:     PetscPrintf(appctx->comm,"initial guess vector\n");
    337:     VecView(u,PETSC_VIEWER_STDOUT_WORLD);
    338:   }

    340:   return 0;
    341: }
    342: /* --------------------------------------------------------------------- */
    343: /*
    344:    ExactSolution - Computes the exact solution at a given time.

    346:    Input Parameters:
    347:    t - current time
    348:    solution - vector in which exact solution will be computed
    349:    appctx - user-defined application context

    351:    Output Parameter:
    352:    solution - vector with the newly computed exact solution
    353: */
    354: PetscErrorCode ExactSolution(PetscReal t,Vec solution,AppCtx *appctx)
    355: {
    356:   PetscScalar    *s_localptr,h = appctx->h,ex1,ex2,sc1,sc2;
    357:   PetscInt       i,mybase,myend;

    360:   /*
    361:      Determine starting and ending points of each processor's
    362:      range of grid values
    363:   */
    364:   VecGetOwnershipRange(solution,&mybase,&myend);

    366:   /*
    367:      Get a pointer to vector data.
    368:   */
    369:   VecGetArray(solution,&s_localptr);

    371:   /*
    372:      Simply write the solution directly into the array locations.
    373:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
    374:   */
    375:   ex1 = PetscExpReal(-36.*PETSC_PI*PETSC_PI*t); ex2 = PetscExpReal(-4.*PETSC_PI*PETSC_PI*t);
    376:   sc1 = PETSC_PI*6.*h;                 sc2 = PETSC_PI*2.*h;
    377:   for (i=mybase; i<myend; i++) s_localptr[i-mybase] = PetscSinScalar(sc1*(PetscReal)i)*ex1 + 3.*PetscSinScalar(sc2*(PetscReal)i)*ex2;

    379:   /*
    380:      Restore vector
    381:   */
    382:   VecRestoreArray(solution,&s_localptr);
    383:   return 0;
    384: }
    385: /* --------------------------------------------------------------------- */
    386: /*
    387:    Monitor - User-provided routine to monitor the solution computed at
    388:    each timestep.  This example plots the solution and computes the
    389:    error in two different norms.

    391:    Input Parameters:
    392:    ts     - the timestep context
    393:    step   - the count of the current step (with 0 meaning the
    394:              initial condition)
    395:    time   - the current time
    396:    u      - the solution at this timestep
    397:    ctx    - the user-provided context for this monitoring routine.
    398:             In this case we use the application context which contains
    399:             information about the problem size, workspace and the exact
    400:             solution.
    401: */
    402: PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec u,void *ctx)
    403: {
    404:   AppCtx         *appctx = (AppCtx*) ctx;   /* user-defined application context */
    406:   PetscReal      norm_2,norm_max;

    408:   /*
    409:      View a graph of the current iterate
    410:   */
    411:   VecView(u,appctx->viewer2);

    413:   /*
    414:      Compute the exact solution
    415:   */
    416:   ExactSolution(time,appctx->solution,appctx);

    418:   /*
    419:      Print debugging information if desired
    420:   */
    421:   if (appctx->debug) {
    422:     PetscPrintf(appctx->comm,"Computed solution vector\n");
    423:     VecView(u,PETSC_VIEWER_STDOUT_WORLD);
    424:     PetscPrintf(appctx->comm,"Exact solution vector\n");
    425:     VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD);
    426:   }

    428:   /*
    429:      Compute the 2-norm and max-norm of the error
    430:   */
    431:   VecAXPY(appctx->solution,-1.0,u);
    432:   VecNorm(appctx->solution,NORM_2,&norm_2);
    433:   norm_2 = PetscSqrtReal(appctx->h)*norm_2;
    434:   VecNorm(appctx->solution,NORM_MAX,&norm_max);
    435:   if (norm_2   < 1e-14) norm_2   = 0;
    436:   if (norm_max < 1e-14) norm_max = 0;

    438:   /*
    439:      PetscPrintf() causes only the first processor in this
    440:      communicator to print the timestep information.
    441:   */
    442:   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);
    443:   appctx->norm_2   += norm_2;
    444:   appctx->norm_max += norm_max;

    446:   /*
    447:      View a graph of the error
    448:   */
    449:   VecView(appctx->solution,appctx->viewer1);

    451:   /*
    452:      Print debugging information if desired
    453:   */
    454:   if (appctx->debug) {
    455:     PetscPrintf(appctx->comm,"Error vector\n");
    456:     VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD);
    457:   }

    459:   return 0;
    460: }

    462: /* --------------------------------------------------------------------- */
    463: /*
    464:    RHSMatrixHeat - User-provided routine to compute the right-hand-side
    465:    matrix for the heat equation.

    467:    Input Parameters:
    468:    ts - the TS context
    469:    t - current time
    470:    global_in - global input vector
    471:    dummy - optional user-defined context, as set by TSetRHSJacobian()

    473:    Output Parameters:
    474:    AA - Jacobian matrix
    475:    BB - optionally different preconditioning matrix
    476:    str - flag indicating matrix structure

    478:   Notes:
    479:   RHSMatrixHeat computes entries for the locally owned part of the system.
    480:    - Currently, all PETSc parallel matrix formats are partitioned by
    481:      contiguous chunks of rows across the processors.
    482:    - Each processor needs to insert only elements that it owns
    483:      locally (but any non-local elements will be sent to the
    484:      appropriate processor during matrix assembly).
    485:    - Always specify global row and columns of matrix entries when
    486:      using MatSetValues(); we could alternatively use MatSetValuesLocal().
    487:    - Here, we set all entries for a particular row at once.
    488:    - Note that MatSetValues() uses 0-based row and column numbers
    489:      in Fortran as well as in C.
    490: */
    491: PetscErrorCode RHSMatrixHeat(TS ts,PetscReal t,Vec X,Mat AA,Mat BB,void *ctx)
    492: {
    493:   Mat            A       = AA;              /* Jacobian matrix */
    494:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */
    496:   PetscInt       i,mstart,mend,idx[3];
    497:   PetscScalar    v[3],stwo = -2./(appctx->h*appctx->h),sone = -.5*stwo;

    499:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    500:      Compute entries for the locally owned part of the matrix
    501:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    503:   MatGetOwnershipRange(A,&mstart,&mend);

    505:   /*
    506:      Set matrix rows corresponding to boundary data
    507:   */

    509:   if (mstart == 0) {  /* first processor only */
    510:     v[0] = 1.0;
    511:     MatSetValues(A,1,&mstart,1,&mstart,v,INSERT_VALUES);
    512:     mstart++;
    513:   }

    515:   if (mend == appctx->m) { /* last processor only */
    516:     mend--;
    517:     v[0] = 1.0;
    518:     MatSetValues(A,1,&mend,1,&mend,v,INSERT_VALUES);
    519:   }

    521:   /*
    522:      Set matrix rows corresponding to interior data.  We construct the
    523:      matrix one row at a time.
    524:   */
    525:   v[0] = sone; v[1] = stwo; v[2] = sone;
    526:   for (i=mstart; i<mend; i++) {
    527:     idx[0] = i-1; idx[1] = i; idx[2] = i+1;
    528:     MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
    529:   }

    531:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    532:      Complete the matrix assembly process and set some options
    533:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    534:   /*
    535:      Assemble matrix, using the 2-step process:
    536:        MatAssemblyBegin(), MatAssemblyEnd()
    537:      Computations can be done while messages are in transition
    538:      by placing code between these two statements.
    539:   */
    540:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    541:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    543:   /*
    544:      Set and option to indicate that we will never add a new nonzero location
    545:      to the matrix. If we do, it will generate an error.
    546:   */
    547:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    549:   return 0;
    550: }

    552: PetscErrorCode RHSFunctionHeat(TS ts,PetscReal t,Vec globalin,Vec globalout,void *ctx)
    553: {
    555:   Mat            A;

    558:   TSGetRHSJacobian(ts,&A,NULL,NULL,&ctx);
    559:   RHSMatrixHeat(ts,t,globalin,A,NULL,ctx);
    560:   /* MatView(A,PETSC_VIEWER_STDOUT_WORLD); */
    561:   MatMult(A,globalin,globalout);
    562:   return(0);
    563: }

    565: /*TEST

    567:     test:
    568:       args: -ts_view -nox

    570:     test:
    571:       suffix: 2
    572:       args: -ts_view -nox
    573:       nsize: 3

    575:     test:
    576:       suffix: 3
    577:       args: -ts_view -nox -nonlinear

    579:     test:
    580:       suffix: 4
    581:       args: -ts_view -nox -nonlinear
    582:       nsize: 3
    583:       timeoutfactor: 3

    585:     test:
    586:       suffix: sundials
    587:       requires: sundials2
    588:       args: -nox -ts_type sundials -ts_max_steps 5 -nonlinear
    589:       nsize: 4

    591: TEST*/