Actual source code: ex3.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:   -use_ifunc          : Use IFunction/IJacobian interface\n\
      7:   -debug              : Activate debugging printouts\n\
      8:   -nox                : Deactivate x-window graphics\n\n";

     10: /* ------------------------------------------------------------------------

     12:    This program solves the one-dimensional heat equation (also called the
     13:    diffusion equation),
     14:        u_t = u_xx,
     15:    on the domain 0 <= x <= 1, with the boundary conditions
     16:        u(t,0) = 0, u(t,1) = 0,
     17:    and the initial condition
     18:        u(0,x) = sin(6*pi*x) + 3*sin(2*pi*x).
     19:    This is a linear, second-order, parabolic equation.

     21:    We discretize the right-hand side using finite differences with
     22:    uniform grid spacing h:
     23:        u_xx = (u_{i+1} - 2u_{i} + u_{i-1})/(h^2)
     24:    We then demonstrate time evolution using the various TS methods by
     25:    running the program via
     26:        ex3 -ts_type <timestepping solver>

     28:    We compare the approximate solution with the exact solution, given by
     29:        u_exact(x,t) = exp(-36*pi*pi*t) * sin(6*pi*x) +
     30:                       3*exp(-4*pi*pi*t) * sin(2*pi*x)

     32:    Notes:
     33:    This code demonstrates the TS solver interface to two variants of
     34:    linear problems, u_t = f(u,t), namely
     35:      - time-dependent f:   f(u,t) is a function of t
     36:      - time-independent f: f(u,t) is simply f(u)

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

     40:   ------------------------------------------------------------------------- */

     42: /*
     43:    Include "petscts.h" so that we can use TS solvers.  Note that this file
     44:    automatically includes:
     45:      petscsys.h       - base PETSc routines   petscvec.h  - vectors
     46:      petscmat.h  - matrices
     47:      petscis.h     - index sets            petscksp.h  - Krylov subspace methods
     48:      petscviewer.h - viewers               petscpc.h   - preconditioners
     49:      petscksp.h   - linear solvers        petscsnes.h - nonlinear solvers
     50: */

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

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

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

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

     94:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     95:      Initialize program and set problem parameters
     96:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     98:   PetscInitialize(&argc,&argv,(char*)0,help);
     99:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

    102:   m    = 60;
    103:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
    104:   PetscOptionsHasName(NULL,NULL,"-debug",&appctx.debug);
    105:   flg_string = PETSC_FALSE;
    106:   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:   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:   VecCreateSeq(PETSC_COMM_SELF,m,&u);
    123:   VecDuplicate(u,&appctx.solution);

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

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

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

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

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

    147:   if (!flg_string) {
    148:     TSMonitorSet(ts,Monitor,&appctx,NULL);
    149:   }

    151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    153:      Create matrix data structure; set matrix evaluation routine.
    154:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    156:   MatCreate(PETSC_COMM_SELF,&A);
    157:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,m);
    158:   MatSetFromOptions(A);
    159:   MatSetUp(A);

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

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

    194:     PetscObjectReference((PetscObject)A);
    195:     appctx.A = A;
    196:     appctx.oshift = PETSC_MIN_REAL;
    197:   }
    198:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    199:      Set solution vector and initial timestep
    200:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    202:   dt   = appctx.h*appctx.h/2.0;
    203:   TSSetTimeStep(ts,dt);

    205:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    206:      Customize timestepping solver:
    207:        - Set the solution method to be the Backward Euler method.
    208:        - Set timestepping duration info
    209:      Then set runtime options, which can override these defaults.
    210:      For example,
    211:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
    212:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
    213:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    215:   TSSetMaxSteps(ts,time_steps_max);
    216:   TSSetMaxTime(ts,time_total_max);
    217:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
    218:   TSSetFromOptions(ts);

    220:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    221:      Solve the problem
    222:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    224:   /*
    225:      Evaluate initial conditions
    226:   */
    227:   InitialConditions(u,&appctx);

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

    235:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    236:      View timestepping solver info
    237:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    239:   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));
    240:   if (!flg_string) {
    241:     TSView(ts,PETSC_VIEWER_STDOUT_SELF);
    242:   } else {
    243:     PetscViewer stringviewer;
    244:     char        string[512];
    245:     const char  *outstring;

    247:     PetscViewerStringOpen(PETSC_COMM_WORLD,string,sizeof(string),&stringviewer);
    248:     TSView(ts,stringviewer);
    249:     PetscViewerStringGetStringRead(stringviewer,&outstring,NULL);
    251:     PetscPrintf(PETSC_COMM_WORLD,"Output from string viewer:%s\n",outstring);
    252:     PetscViewerDestroy(&stringviewer);
    253:   }

    255:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    256:      Free work space.  All PETSc objects should be destroyed when they
    257:      are no longer needed.
    258:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    268:   /*
    269:      Always call PetscFinalize() before exiting a program.  This routine
    270:        - finalizes the PETSc libraries as well as MPI
    271:        - provides summary and diagnostic information if certain runtime
    272:          options are chosen (e.g., -log_view).
    273:   */
    274:   PetscFinalize();
    275:   return 0;
    276: }
    277: /* --------------------------------------------------------------------- */
    278: /*
    279:    InitialConditions - Computes the solution at the initial time.

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

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

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

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

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

    316:   /*
    317:      Print debugging information if desired
    318:   */
    319:   if (appctx->debug) {
    320:     PetscPrintf(PETSC_COMM_WORLD,"Initial guess vector\n");
    321:     VecView(u,PETSC_VIEWER_STDOUT_SELF);
    322:   }

    324:   return 0;
    325: }
    326: /* --------------------------------------------------------------------- */
    327: /*
    328:    ExactSolution - Computes the exact solution at a given time.

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

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

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

    348:   /*
    349:      Simply write the solution directly into the array locations.
    350:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
    351:   */
    352:   ex1 = PetscExpScalar(-36.*PETSC_PI*PETSC_PI*tc);
    353:   ex2 = PetscExpScalar(-4.*PETSC_PI*PETSC_PI*tc);
    354:   sc1 = PETSC_PI*6.*h;                 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:   VecRestoreArrayWrite(solution,&s_localptr);
    361:   return 0;
    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,void *ctx)
    383: {
    384:   AppCtx         *appctx = (AppCtx*) ctx;   /* user-defined application context */
    385:   PetscReal      norm_2,norm_max,dt,dttol;

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

    392:   /*
    393:      Compute the exact solution
    394:   */
    395:   ExactSolution(time,appctx->solution,appctx);

    397:   /*
    398:      Print debugging information if desired
    399:   */
    400:   if (appctx->debug) {
    401:     PetscPrintf(PETSC_COMM_SELF,"Computed solution vector\n");
    402:     VecView(u,PETSC_VIEWER_STDOUT_SELF);
    403:     PetscPrintf(PETSC_COMM_SELF,"Exact solution vector\n");
    404:     VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF);
    405:   }

    407:   /*
    408:      Compute the 2-norm and max-norm of the error
    409:   */
    410:   VecAXPY(appctx->solution,-1.0,u);
    411:   VecNorm(appctx->solution,NORM_2,&norm_2);
    412:   norm_2 = PetscSqrtReal(appctx->h)*norm_2;
    413:   VecNorm(appctx->solution,NORM_MAX,&norm_max);

    415:   TSGetTimeStep(ts,&dt);
    416:   PetscPrintf(PETSC_COMM_WORLD,"Timestep %3D: 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);

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

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

    428:   /*
    429:      View a graph of the error
    430:   */
    431:   VecView(appctx->solution,appctx->viewer1);

    433:   /*
    434:      Print debugging information if desired
    435:   */
    436:   if (appctx->debug) {
    437:     PetscPrintf(PETSC_COMM_SELF,"Error vector\n");
    438:     VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF);
    439:   }

    441:   return 0;
    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 preconditioning matrix
    457:    str - flag indicating matrix structure

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

    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:   MatSetValues(A,1,&mstart,1,&mstart,v,INSERT_VALUES);
    482:   mstart++;

    484:   mend--;
    485:   v[0] = 1.0;
    486:   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; v[1] = stwo; v[2] = sone;
    493:   for (i=mstart; i<mend; i++) {
    494:     idx[0] = i-1; idx[1] = i; idx[2] = i+1;
    495:     MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
    496:   }

    498:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    499:      Complete the matrix assembly process and set some options
    500:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    501:   /*
    502:      Assemble matrix, using the 2-step process:
    503:        MatAssemblyBegin(), MatAssemblyEnd()
    504:      Computations can be done while messages are in transition
    505:      by placing code between these two statements.
    506:   */
    507:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    508:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    510:   /*
    511:      Set and option to indicate that we will never add a new nonzero location
    512:      to the matrix. If we do, it will generate an error.
    513:   */
    514:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    516:   return 0;
    517: }

    519: PetscErrorCode IFunctionHeat(TS ts,PetscReal t,Vec X,Vec Xdot,Vec r,void *ctx)
    520: {
    521:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */

    523:   MatMult(appctx->A,X,r);
    524:   VecAYPX(r,-1.0,Xdot);
    525:   return 0;
    526: }

    528: PetscErrorCode IJacobianHeat(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal s,Mat A,Mat B,void *ctx)
    529: {
    530:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */

    532:   if (appctx->oshift == s) return 0;
    533:   MatCopy(appctx->A,A,SAME_NONZERO_PATTERN);
    534:   MatScale(A,-1);
    535:   MatShift(A,s);
    536:   MatCopy(A,B,SAME_NONZERO_PATTERN);
    537:   appctx->oshift = s;
    538:   return 0;
    539: }

    541: /*TEST

    543:     test:
    544:       args: -nox -ts_type ssp -ts_dt 0.0005

    546:     test:
    547:       suffix: 2
    548:       args: -nox -ts_type ssp -ts_dt 0.0005 -time_dependent_rhs 1

    550:     test:
    551:       suffix: 3
    552:       args:  -nox -ts_type rosw -ts_max_steps 3 -ksp_converged_reason
    553:       filter: sed "s/ATOL/RTOL/g"
    554:       requires: !single

    556:     test:
    557:       suffix: 4
    558:       args: -nox -ts_type beuler -ts_max_steps 3 -ksp_converged_reason
    559:       filter: sed "s/ATOL/RTOL/g"

    561:     test:
    562:       suffix: 5
    563:       args: -nox -ts_type beuler -ts_max_steps 3 -ksp_converged_reason -time_dependent_rhs
    564:       filter: sed "s/ATOL/RTOL/g"

    566:     test:
    567:       requires: !single
    568:       suffix: pod_guess
    569:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type pod -pc_type none -ksp_converged_reason

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

    576:     test:
    577:       requires: !single
    578:       suffix: fischer_guess
    579:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type fischer -pc_type none -ksp_converged_reason

    581:     test:
    582:       requires: !single
    583:       suffix: fischer_guess_2
    584:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type fischer -ksp_guess_fischer_model 2,10 -pc_type none -ksp_converged_reason

    586:     test:
    587:       requires: !single
    588:       suffix: fischer_guess_3
    589:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type fischer -ksp_guess_fischer_model 3,10 -pc_type none -ksp_converged_reason

    591:     test:
    592:       requires: !single
    593:       suffix: stringview
    594:       args: -nox -ts_type rosw -test_string_viewer

    596:     test:
    597:       requires: !single
    598:       suffix: stringview_euler
    599:       args: -nox -ts_type euler -test_string_viewer

    601: TEST*/