Date: 2026-03-31T05:46:36+00:00

Actual source code: ex3.c

      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:   -use_ifunc          : Use IFunction/IJacobian interface\n\
      6:   -debug              : Activate debugging printouts\n\
      7:   -nox                : Deactivate x-window graphics\n\n";

      9: /* ------------------------------------------------------------------------

     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.

     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:        ex3 -ts_type <timestepping solver>

     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)

     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)

     37:     The parallel version of this code is ts/tutorials/ex4.c

     39:   ------------------------------------------------------------------------- */

     41: /*
     42:    Include "petscts.h" so that we can use TS solvers.  Note that this file
     43:    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: */

     51: #include <petscts.h>
     52: #include <petscdraw.h>

     54: /*
     55:    User-defined application context - contains data needed by the
     56:    application-provided call-back routines.
     57: */
     58: typedef struct {
     59:   Vec         solution;         /* global exact solution vector */
     60:   PetscInt    m;                /* total number of grid points */
     61:   PetscReal   h;                /* mesh width h = 1/(m-1) */
     62:   PetscBool   debug;            /* flag (1 indicates activation of debugging printouts) */
     63:   PetscViewer viewer1, viewer2; /* viewers for the solution and error */
     64:   PetscReal   norm_2, norm_max; /* error norms */
     65:   Mat         A;                /* RHS mat, used with IFunction interface */
     66:   PetscReal   oshift;           /* old shift applied, prevent to recompute the IJacobian */
     67: } AppCtx;

     69: /*
     70:    User-defined routines
     71: */
     72: extern PetscErrorCode InitialConditions(Vec, AppCtx *);
     73: extern PetscErrorCode RHSMatrixHeat(TS, PetscReal, Vec, Mat, Mat, void *);
     74: extern PetscErrorCode IFunctionHeat(TS, PetscReal, Vec, Vec, Vec, void *);
     75: extern PetscErrorCode IJacobianHeat(TS, PetscReal, Vec, Vec, PetscReal, Mat, Mat, void *);
     76: extern PetscErrorCode Monitor(TS, PetscInt, PetscReal, Vec, void *);
     77: extern PetscErrorCode ExactSolution(PetscReal, Vec, AppCtx *);

     79: int main(int argc, char **argv)
     80: {
     81:   AppCtx      appctx;                 /* user-defined application context */
     82:   TS          ts;                     /* timestepping context */
     83:   Mat         A;                      /* matrix data structure */
     84:   Vec         u;                      /* approximate solution vector */
     85:   PetscReal   time_total_max = 100.0; /* default max total time */
     86:   PetscInt    time_steps_max = 100;   /* default max timesteps */
     87:   PetscDraw   draw;                   /* drawing context */
     88:   PetscInt    steps, m;
     89:   PetscMPIInt size;
     90:   PetscReal   dt;
     91:   PetscBool   flg, flg_string;

     93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     94:      Initialize program and set problem parameters
     95:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     97:   PetscFunctionBeginUser;
     98:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
     99:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
    100:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");

    102:   m = 60;
    103:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
    104:   PetscCall(PetscOptionsHasName(NULL, NULL, "-debug", &appctx.debug));
    105:   flg_string = PETSC_FALSE;
    106:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_string_viewer", &flg_string, NULL));

    108:   appctx.m        = m;
    109:   appctx.h        = 1.0 / (m - 1.0);
    110:   appctx.norm_2   = 0.0;
    111:   appctx.norm_max = 0.0;

    113:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "Solving a linear TS problem on 1 processor\n"));

    115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    116:      Create vector data structures
    117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    119:   /*
    120:      Create vector data structures for approximate and exact solutions
    121:   */
    122:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &u));
    123:   PetscCall(VecDuplicate(u, &appctx.solution));

    125:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    126:      Set up displays to show graphs of the solution and error
    127:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    129:   PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, "", 80, 380, 400, 160, &appctx.viewer1));
    130:   PetscCall(PetscViewerDrawGetDraw(appctx.viewer1, 0, &draw));
    131:   PetscCall(PetscDrawSetDoubleBuffer(draw));
    132:   PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, "", 80, 0, 400, 160, &appctx.viewer2));
    133:   PetscCall(PetscViewerDrawGetDraw(appctx.viewer2, 0, &draw));
    134:   PetscCall(PetscDrawSetDoubleBuffer(draw));

    136:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    137:      Create timestepping solver context
    138:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    140:   PetscCall(TSCreate(PETSC_COMM_SELF, &ts));
    141:   PetscCall(TSSetProblemType(ts, TS_LINEAR));

    143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    144:      Set optional user-defined monitoring routine
    145:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    147:   if (!flg_string) PetscCall(TSMonitorSet(ts, Monitor, &appctx, NULL));

    149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    151:      Create matrix data structure; set matrix evaluation routine.
    152:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    154:   PetscCall(MatCreate(PETSC_COMM_SELF, &A));
    155:   PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, m, m));
    156:   PetscCall(MatSetFromOptions(A));
    157:   PetscCall(MatSetUp(A));

    159:   flg = PETSC_FALSE;
    160:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_ifunc", &flg, NULL));
    161:   if (!flg) {
    162:     appctx.A = NULL;
    163:     PetscCall(PetscOptionsGetBool(NULL, NULL, "-time_dependent_rhs", &flg, NULL));
    164:     if (flg) {
    165:       /*
    166:          For linear problems with a time-dependent f(u,t) in the equation
    167:          u_t = f(u,t), the user provides the discretized right-hand side
    168:          as a time-dependent matrix.
    169:       */
    170:       PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx));
    171:       PetscCall(TSSetRHSJacobian(ts, A, A, RHSMatrixHeat, &appctx));
    172:     } else {
    173:       /*
    174:          For linear problems with a time-independent f(u) in the equation
    175:          u_t = f(u), the user provides the discretized right-hand side
    176:          as a matrix only once, and then sets the special Jacobian evaluation
    177:          routine TSComputeRHSJacobianConstant() which will NOT recompute the Jacobian.
    178:       */
    179:       PetscCall(RHSMatrixHeat(ts, 0.0, u, A, A, &appctx));
    180:       PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx));
    181:       PetscCall(TSSetRHSJacobian(ts, A, A, TSComputeRHSJacobianConstant, &appctx));
    182:     }
    183:   } else {
    184:     Mat J;

    186:     PetscCall(RHSMatrixHeat(ts, 0.0, u, A, A, &appctx));
    187:     PetscCall(MatDuplicate(A, MAT_DO_NOT_COPY_VALUES, &J));
    188:     PetscCall(TSSetIFunction(ts, NULL, IFunctionHeat, &appctx));
    189:     PetscCall(TSSetIJacobian(ts, J, J, IJacobianHeat, &appctx));
    190:     PetscCall(MatDestroy(&J));

    192:     PetscCall(PetscObjectReference((PetscObject)A));
    193:     appctx.A      = A;
    194:     appctx.oshift = PETSC_MIN_REAL;
    195:   }
    196:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    197:      Set solution vector and initial timestep
    198:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    200:   dt = appctx.h * appctx.h / 2.0;
    201:   PetscCall(TSSetTimeStep(ts, dt));

    203:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    204:      Customize timestepping solver:
    205:        - Set the solution method to be the Backward Euler method.
    206:        - Set timestepping duration info
    207:      Then set runtime options, which can override these defaults.
    208:      For example,
    209:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
    210:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
    211:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    213:   PetscCall(TSSetMaxSteps(ts, time_steps_max));
    214:   PetscCall(TSSetMaxTime(ts, time_total_max));
    215:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
    216:   PetscCall(TSSetFromOptions(ts));

    218:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    219:      Solve the problem
    220:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    222:   /*
    223:      Evaluate initial conditions
    224:   */
    225:   PetscCall(InitialConditions(u, &appctx));

    227:   /*
    228:      Run the timestepping solver
    229:   */
    230:   PetscCall(TSSolve(ts, u));
    231:   PetscCall(TSGetStepNumber(ts, &steps));

    233:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    234:      View timestepping solver info
    235:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    237:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "avg. error (2 norm) = %g, avg. error (max norm) = %g\n", (double)(appctx.norm_2 / steps), (double)(appctx.norm_max / steps)));
    238:   if (!flg_string) {
    239:     PetscCall(TSView(ts, PETSC_VIEWER_STDOUT_SELF));
    240:   } else {
    241:     PetscViewer stringviewer;
    242:     char        string[512];
    243:     const char *outstring;

    245:     PetscCall(PetscViewerStringOpen(PETSC_COMM_WORLD, string, sizeof(string), &stringviewer));
    246:     PetscCall(TSView(ts, stringviewer));
    247:     PetscCall(PetscViewerStringGetStringRead(stringviewer, &outstring, NULL));
    248:     PetscCheck((char *)outstring == (char *)string, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "String returned from viewer does not equal original string");
    249:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Output from string viewer:%s\n", outstring));
    250:     PetscCall(PetscViewerDestroy(&stringviewer));
    251:   }

    253:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    254:      Free work space.  All PETSc objects should be destroyed when they
    255:      are no longer needed.
    256:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    258:   PetscCall(TSDestroy(&ts));
    259:   PetscCall(MatDestroy(&A));
    260:   PetscCall(VecDestroy(&u));
    261:   PetscCall(PetscViewerDestroy(&appctx.viewer1));
    262:   PetscCall(PetscViewerDestroy(&appctx.viewer2));
    263:   PetscCall(VecDestroy(&appctx.solution));
    264:   PetscCall(MatDestroy(&appctx.A));

    266:   /*
    267:      Always call PetscFinalize() before exiting a program.  This routine
    268:        - finalizes the PETSc libraries as well as MPI
    269:        - provides summary and diagnostic information if certain runtime
    270:          options are chosen (e.g., -log_view).
    271:   */
    272:   PetscCall(PetscFinalize());
    273:   return 0;
    274: }
    275: /* --------------------------------------------------------------------- */
    276: /*
    277:    InitialConditions - Computes the solution at the initial time.

    279:    Input Parameter:
    280:    u - uninitialized solution vector (global)
    281:    appctx - user-defined application context

    283:    Output Parameter:
    284:    u - vector with solution at initial time (global)
    285: */
    286: PetscErrorCode InitialConditions(Vec u, AppCtx *appctx)
    287: {
    288:   PetscScalar *u_localptr, h = appctx->h;
    289:   PetscInt     i;

    291:   PetscFunctionBeginUser;
    292:   /*
    293:     Get a pointer to vector data.
    294:     - For default PETSc vectors, VecGetArray() returns a pointer to
    295:       the data array.  Otherwise, the routine is implementation dependent.
    296:     - You MUST call VecRestoreArray() when you no longer need access to
    297:       the array.
    298:     - Note that the Fortran interface to VecGetArray() differs from the
    299:       C version.  See the users manual for details.
    300:   */
    301:   PetscCall(VecGetArrayWrite(u, &u_localptr));

    303:   /*
    304:      We initialize the solution array by simply writing the solution
    305:      directly into the array locations.  Alternatively, we could use
    306:      VecSetValues() or VecSetValuesLocal().
    307:   */
    308:   for (i = 0; i < appctx->m; i++) u_localptr[i] = PetscSinScalar(PETSC_PI * i * 6. * h) + 3. * PetscSinScalar(PETSC_PI * i * 2. * h);

    310:   /*
    311:      Restore vector
    312:   */
    313:   PetscCall(VecRestoreArrayWrite(u, &u_localptr));

    315:   /*
    316:      Print debugging information if desired
    317:   */
    318:   if (appctx->debug) {
    319:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Initial guess vector\n"));
    320:     PetscCall(VecView(u, PETSC_VIEWER_STDOUT_SELF));
    321:   }
    322:   PetscFunctionReturn(PETSC_SUCCESS);
    323: }
    324: /* --------------------------------------------------------------------- */
    325: /*
    326:    ExactSolution - Computes the exact solution at a given time.

    328:    Input Parameters:
    329:    t - current time
    330:    solution - vector in which exact solution will be computed
    331:    appctx - user-defined application context

    333:    Output Parameter:
    334:    solution - vector with the newly computed exact solution
    335: */
    336: PetscErrorCode ExactSolution(PetscReal t, Vec solution, AppCtx *appctx)
    337: {
    338:   PetscScalar *s_localptr, h = appctx->h, ex1, ex2, sc1, sc2, tc = t;
    339:   PetscInt     i;

    341:   PetscFunctionBeginUser;
    342:   /*
    343:      Get a pointer to vector data.
    344:   */
    345:   PetscCall(VecGetArrayWrite(solution, &s_localptr));

    347:   /*
    348:      Simply write the solution directly into the array locations.
    349:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
    350:   */
    351:   ex1 = PetscExpScalar(-36. * PETSC_PI * PETSC_PI * tc);
    352:   ex2 = PetscExpScalar(-4. * PETSC_PI * PETSC_PI * tc);
    353:   sc1 = PETSC_PI * 6. * h;
    354:   sc2 = PETSC_PI * 2. * h;
    355:   for (i = 0; i < appctx->m; i++) s_localptr[i] = PetscSinScalar(sc1 * (PetscReal)i) * ex1 + 3. * PetscSinScalar(sc2 * (PetscReal)i) * ex2;

    357:   /*
    358:      Restore vector
    359:   */
    360:   PetscCall(VecRestoreArrayWrite(solution, &s_localptr));
    361:   PetscFunctionReturn(PETSC_SUCCESS);
    362: }
    363: /* --------------------------------------------------------------------- */
    364: /*
    365:    Monitor - User-provided routine to monitor the solution computed at
    366:    each timestep.  This example plots the solution and computes the
    367:    error in two different norms.

    369:    This example also demonstrates changing the timestep via TSSetTimeStep().

    371:    Input Parameters:
    372:    ts     - the timestep context
    373:    step   - the count of the current step (with 0 meaning the
    374:              initial condition)
    375:    time   - the current time
    376:    u      - the solution at this timestep
    377:    ctx    - the user-provided context for this monitoring routine.
    378:             In this case we use the application context which contains
    379:             information about the problem size, workspace and the exact
    380:             solution.
    381: */
    382: PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal time, Vec u, PetscCtx ctx)
    383: {
    384:   AppCtx   *appctx = (AppCtx *)ctx; /* user-defined application context */
    385:   PetscReal norm_2, norm_max, dt, dttol;

    387:   PetscFunctionBeginUser;
    388:   /*
    389:      View a graph of the current iterate
    390:   */
    391:   PetscCall(VecView(u, appctx->viewer2));

    393:   /*
    394:      Compute the exact solution
    395:   */
    396:   PetscCall(ExactSolution(time, appctx->solution, appctx));

    398:   /*
    399:      Print debugging information if desired
    400:   */
    401:   if (appctx->debug) {
    402:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Computed solution vector\n"));
    403:     PetscCall(VecView(u, PETSC_VIEWER_STDOUT_SELF));
    404:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Exact solution vector\n"));
    405:     PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_SELF));
    406:   }

    408:   /*
    409:      Compute the 2-norm and max-norm of the error
    410:   */
    411:   PetscCall(VecAXPY(appctx->solution, -1.0, u));
    412:   PetscCall(VecNorm(appctx->solution, NORM_2, &norm_2));
    413:   norm_2 = PetscSqrtReal(appctx->h) * norm_2;
    414:   PetscCall(VecNorm(appctx->solution, NORM_MAX, &norm_max));

    416:   PetscCall(TSGetTimeStep(ts, &dt));
    417:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Timestep %3" PetscInt_FMT ": step size = %g, time = %g, 2-norm error = %g, max norm error = %g\n", step, (double)dt, (double)time, (double)norm_2, (double)norm_max));

    419:   appctx->norm_2 += norm_2;
    420:   appctx->norm_max += norm_max;

    422:   dttol = .0001;
    423:   PetscCall(PetscOptionsGetReal(NULL, NULL, "-dttol", &dttol, NULL));
    424:   if (dt < dttol) {
    425:     dt *= .999;
    426:     PetscCall(TSSetTimeStep(ts, dt));
    427:   }

    429:   /*
    430:      View a graph of the error
    431:   */
    432:   PetscCall(VecView(appctx->solution, appctx->viewer1));

    434:   /*
    435:      Print debugging information if desired
    436:   */
    437:   if (appctx->debug) {
    438:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error vector\n"));
    439:     PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_SELF));
    440:   }
    441:   PetscFunctionReturn(PETSC_SUCCESS);
    442: }
    443: /* --------------------------------------------------------------------- */
    444: /*
    445:    RHSMatrixHeat - User-provided routine to compute the right-hand-side
    446:    matrix for the heat equation.

    448:    Input Parameters:
    449:    ts - the TS context
    450:    t - current time
    451:    global_in - global input vector
    452:    dummy - optional user-defined context, as set by TSetRHSJacobian()

    454:    Output Parameters:
    455:    AA - Jacobian matrix
    456:    BB - optionally different matrix used to construct the preconditioner

    458:    Notes:
    459:    Recall that MatSetValues() uses 0-based row and column numbers
    460:    in Fortran as well as in C.
    461: */
    462: PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec X, Mat AA, Mat BB, PetscCtx ctx)
    463: {
    464:   Mat         A      = AA;            /* Jacobian matrix */
    465:   AppCtx     *appctx = (AppCtx *)ctx; /* user-defined application context */
    466:   PetscInt    mstart = 0;
    467:   PetscInt    mend   = appctx->m;
    468:   PetscInt    i, idx[3];
    469:   PetscScalar v[3], stwo = -2. / (appctx->h * appctx->h), sone = -.5 * stwo;

    471:   PetscFunctionBeginUser;
    472:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    473:      Compute entries for the locally owned part of the matrix
    474:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    475:   /*
    476:      Set matrix rows corresponding to boundary data
    477:   */

    479:   mstart = 0;
    480:   v[0]   = 1.0;
    481:   PetscCall(MatSetValues(A, 1, &mstart, 1, &mstart, v, INSERT_VALUES));
    482:   mstart++;

    484:   mend--;
    485:   v[0] = 1.0;
    486:   PetscCall(MatSetValues(A, 1, &mend, 1, &mend, v, INSERT_VALUES));

    488:   /*
    489:      Set matrix rows corresponding to interior data.  We construct the
    490:      matrix one row at a time.
    491:   */
    492:   v[0] = sone;
    493:   v[1] = stwo;
    494:   v[2] = sone;
    495:   for (i = mstart; i < mend; i++) {
    496:     idx[0] = i - 1;
    497:     idx[1] = i;
    498:     idx[2] = i + 1;
    499:     PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES));
    500:   }

    502:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    503:      Complete the matrix assembly process and set some options
    504:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    505:   /*
    506:      Assemble matrix, using the 2-step process:
    507:        MatAssemblyBegin(), MatAssemblyEnd()
    508:      Computations can be done while messages are in transition
    509:      by placing code between these two statements.
    510:   */
    511:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    512:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

    514:   /*
    515:      Set and option to indicate that we will never add a new nonzero location
    516:      to the matrix. If we do, it will generate an error.
    517:   */
    518:   PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    519:   PetscFunctionReturn(PETSC_SUCCESS);
    520: }

    522: PetscErrorCode IFunctionHeat(TS ts, PetscReal t, Vec X, Vec Xdot, Vec r, PetscCtx ctx)
    523: {
    524:   AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */

    526:   PetscFunctionBeginUser;
    527:   PetscCall(MatMult(appctx->A, X, r));
    528:   PetscCall(VecAYPX(r, -1.0, Xdot));
    529:   PetscFunctionReturn(PETSC_SUCCESS);
    530: }

    532: PetscErrorCode IJacobianHeat(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal s, Mat A, Mat B, PetscCtx ctx)
    533: {
    534:   AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */

    536:   PetscFunctionBeginUser;
    537:   if (appctx->oshift == s) PetscFunctionReturn(PETSC_SUCCESS);
    538:   PetscCall(MatCopy(appctx->A, A, SAME_NONZERO_PATTERN));
    539:   PetscCall(MatScale(A, -1));
    540:   PetscCall(MatShift(A, s));
    541:   PetscCall(MatCopy(A, B, SAME_NONZERO_PATTERN));
    542:   appctx->oshift = s;
    543:   PetscFunctionReturn(PETSC_SUCCESS);
    544: }

    546: /*TEST

    548:     test:
    549:       args: -nox -ts_type ssp -ts_time_step 0.0005

    551:     test:
    552:       suffix: 2
    553:       args: -nox -ts_type ssp -ts_time_step 0.0005 -time_dependent_rhs 1

    555:     test:
    556:       suffix: 3
    557:       args: -nox -ts_type rosw -ts_max_steps 3 -ksp_converged_reason
    558:       filter: sed "s/ATOL/RTOL/g"
    559:       requires: !single

    561:     test:
    562:       suffix: 4
    563:       args: -nox -ts_type beuler -ts_max_steps 3 -ksp_converged_reason
    564:       filter: sed "s/ATOL/RTOL/g"

    566:     test:
    567:       suffix: 5
    568:       args: -nox -ts_type beuler -ts_max_steps 3 -ksp_converged_reason -time_dependent_rhs
    569:       filter: sed "s/ATOL/RTOL/g"

    571:     test:
    572:       requires: !single
    573:       suffix: pod_guess
    574:       args: -nox -ts_type beuler -use_ifunc -ts_time_step 0.0005 -ksp_guess_type pod -pc_type none -ksp_converged_reason

    576:     test:
    577:       requires: !single
    578:       suffix: pod_guess_Ainner
    579:       args: -nox -ts_type beuler -use_ifunc -ts_time_step 0.0005 -ksp_guess_type pod -ksp_guess_pod_Ainner -pc_type none -ksp_converged_reason

    581:     test:
    582:       requires: !single
    583:       suffix: fischer_guess
    584:       args: -nox -ts_type beuler -use_ifunc -ts_time_step 0.0005 -ksp_guess_type fischer -pc_type none -ksp_converged_reason

    586:     test:
    587:       requires: !single
    588:       suffix: fischer_guess_2
    589:       args: -nox -ts_type beuler -use_ifunc -ts_time_step 0.0005 -ksp_guess_type fischer -ksp_guess_fischer_model 2,10 -pc_type none -ksp_converged_reason

    591:     test:
    592:       requires: !single
    593:       suffix: fischer_guess_3
    594:       args: -nox -ts_type beuler -use_ifunc -ts_time_step 0.0005 -ksp_guess_type fischer -ksp_guess_fischer_model 3,10 -pc_type none -ksp_converged_reason

    596:     test:
    597:       requires: !single
    598:       suffix: stringview
    599:       args: -nox -ts_type rosw -test_string_viewer

    601:     test:
    602:       requires: !single
    603:       suffix: stringview_euler
    604:       args: -nox -ts_type euler -test_string_viewer

    606: TEST*/