Date: 2022-03-31T04:48:45+00:00

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: /*
     11:    Concepts: TS^time-dependent linear problems
     12:    Concepts: TS^heat equation
     13:    Concepts: TS^diffusion equation
     14:    Processors: 1
     15: */

     17: /* ------------------------------------------------------------------------

     19:    This program solves the one-dimensional heat equation (also called the
     20:    diffusion equation),
     21:        u_t = u_xx,
     22:    on the domain 0 <= x <= 1, with the boundary conditions
     23:        u(t,0) = 0, u(t,1) = 0,
     24:    and the initial condition
     25:        u(0,x) = sin(6*pi*x) + 3*sin(2*pi*x).
     26:    This is a linear, second-order, parabolic equation.

     28:    We discretize the right-hand side using finite differences with
     29:    uniform grid spacing h:
     30:        u_xx = (u_{i+1} - 2u_{i} + u_{i-1})/(h^2)
     31:    We then demonstrate time evolution using the various TS methods by
     32:    running the program via
     33:        ex3 -ts_type <timestepping solver>

     35:    We compare the approximate solution with the exact solution, given by
     36:        u_exact(x,t) = exp(-36*pi*pi*t) * sin(6*pi*x) +
     37:                       3*exp(-4*pi*pi*t) * sin(2*pi*x)

     39:    Notes:
     40:    This code demonstrates the TS solver interface to two variants of
     41:    linear problems, u_t = f(u,t), namely
     42:      - time-dependent f:   f(u,t) is a function of t
     43:      - time-independent f: f(u,t) is simply f(u)

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

     47:   ------------------------------------------------------------------------- */

     49: /*
     50:    Include "petscts.h" so that we can use TS solvers.  Note that this file
     51:    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 <petscts.h>
     60: #include <petscdraw.h>

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

     77: /*
     78:    User-defined routines
     79: */
     80: extern PetscErrorCode InitialConditions(Vec,AppCtx*);
     81: extern PetscErrorCode RHSMatrixHeat(TS,PetscReal,Vec,Mat,Mat,void*);
     82: extern PetscErrorCode IFunctionHeat(TS,PetscReal,Vec,Vec,Vec,void*);
     83: extern PetscErrorCode IJacobianHeat(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);
     84: extern PetscErrorCode Monitor(TS,PetscInt,PetscReal,Vec,void*);
     85: extern PetscErrorCode ExactSolution(PetscReal,Vec,AppCtx*);

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

    101:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    102:      Initialize program and set problem parameters
    103:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    109:   m    = 60;
    110:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
    111:   PetscOptionsHasName(NULL,NULL,"-debug",&appctx.debug);
    112:   flg_string = PETSC_FALSE;
    113:   PetscOptionsGetBool(NULL,NULL,"-test_string_viewer",&flg_string,NULL);

    115:   appctx.m        = m;
    116:   appctx.h        = 1.0/(m-1.0);
    117:   appctx.norm_2   = 0.0;
    118:   appctx.norm_max = 0.0;

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

    122:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    123:      Create vector data structures
    124:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    126:   /*
    127:      Create vector data structures for approximate and exact solutions
    128:   */
    129:   VecCreateSeq(PETSC_COMM_SELF,m,&u);
    130:   VecDuplicate(u,&appctx.solution);

    132:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    133:      Set up displays to show graphs of the solution and error
    134:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    136:   PetscViewerDrawOpen(PETSC_COMM_SELF,0,"",80,380,400,160,&appctx.viewer1);
    137:   PetscViewerDrawGetDraw(appctx.viewer1,0,&draw);
    138:   PetscDrawSetDoubleBuffer(draw);
    139:   PetscViewerDrawOpen(PETSC_COMM_SELF,0,"",80,0,400,160,&appctx.viewer2);
    140:   PetscViewerDrawGetDraw(appctx.viewer2,0,&draw);
    141:   PetscDrawSetDoubleBuffer(draw);

    143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    144:      Create timestepping solver context
    145:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    147:   TSCreate(PETSC_COMM_SELF,&ts);
    148:   TSSetProblemType(ts,TS_LINEAR);

    150:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    151:      Set optional user-defined monitoring routine
    152:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    154:   if (!flg_string) {
    155:     TSMonitorSet(ts,Monitor,&appctx,NULL);
    156:   }

    158:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    160:      Create matrix data structure; set matrix evaluation routine.
    161:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    163:   MatCreate(PETSC_COMM_SELF,&A);
    164:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,m);
    165:   MatSetFromOptions(A);
    166:   MatSetUp(A);

    168:   flg  = PETSC_FALSE;
    169:   PetscOptionsGetBool(NULL,NULL,"-use_ifunc",&flg,NULL);
    170:   if (!flg) {
    171:     appctx.A = NULL;
    172:     PetscOptionsGetBool(NULL,NULL,"-time_dependent_rhs",&flg,NULL);
    173:     if (flg) {
    174:       /*
    175:          For linear problems with a time-dependent f(u,t) in the equation
    176:          u_t = f(u,t), the user provides the discretized right-hand-side
    177:          as a time-dependent matrix.
    178:       */
    179:       TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx);
    180:       TSSetRHSJacobian(ts,A,A,RHSMatrixHeat,&appctx);
    181:     } else {
    182:       /*
    183:          For linear problems with a time-independent f(u) in the equation
    184:          u_t = f(u), the user provides the discretized right-hand-side
    185:          as a matrix only once, and then sets the special Jacobian evaluation
    186:          routine TSComputeRHSJacobianConstant() which will NOT recompute the Jacobian.
    187:       */
    188:       RHSMatrixHeat(ts,0.0,u,A,A,&appctx);
    189:       TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx);
    190:       TSSetRHSJacobian(ts,A,A,TSComputeRHSJacobianConstant,&appctx);
    191:     }
    192:   } else {
    193:     Mat J;

    195:     RHSMatrixHeat(ts,0.0,u,A,A,&appctx);
    196:     MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&J);
    197:     TSSetIFunction(ts,NULL,IFunctionHeat,&appctx);
    198:     TSSetIJacobian(ts,J,J,IJacobianHeat,&appctx);
    199:     MatDestroy(&J);

    201:     PetscObjectReference((PetscObject)A);
    202:     appctx.A = A;
    203:     appctx.oshift = PETSC_MIN_REAL;
    204:   }
    205:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    206:      Set solution vector and initial timestep
    207:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    209:   dt   = appctx.h*appctx.h/2.0;
    210:   TSSetTimeStep(ts,dt);

    212:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    213:      Customize timestepping solver:
    214:        - Set the solution method to be the Backward Euler method.
    215:        - Set timestepping duration info
    216:      Then set runtime options, which can override these defaults.
    217:      For example,
    218:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
    219:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
    220:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    222:   TSSetMaxSteps(ts,time_steps_max);
    223:   TSSetMaxTime(ts,time_total_max);
    224:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
    225:   TSSetFromOptions(ts);

    227:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    228:      Solve the problem
    229:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    231:   /*
    232:      Evaluate initial conditions
    233:   */
    234:   InitialConditions(u,&appctx);

    236:   /*
    237:      Run the timestepping solver
    238:   */
    239:   TSSolve(ts,u);
    240:   TSGetStepNumber(ts,&steps);

    242:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    243:      View timestepping solver info
    244:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    246:   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));
    247:   if (!flg_string) {
    248:     TSView(ts,PETSC_VIEWER_STDOUT_SELF);
    249:   } else {
    250:     PetscViewer stringviewer;
    251:     char        string[512];
    252:     const char  *outstring;

    254:     PetscViewerStringOpen(PETSC_COMM_WORLD,string,sizeof(string),&stringviewer);
    255:     TSView(ts,stringviewer);
    256:     PetscViewerStringGetStringRead(stringviewer,&outstring,NULL);
    258:     PetscPrintf(PETSC_COMM_WORLD,"Output from string viewer:%s\n",outstring);
    259:     PetscViewerDestroy(&stringviewer);
    260:   }

    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.solution);
    273:   MatDestroy(&appctx.A);

    275:   /*
    276:      Always call PetscFinalize() before exiting a program.  This routine
    277:        - finalizes the PETSc libraries as well as MPI
    278:        - provides summary and diagnostic information if certain runtime
    279:          options are chosen (e.g., -log_view).
    280:   */
    281:   PetscFinalize();
    282:   return 0;
    283: }
    284: /* --------------------------------------------------------------------- */
    285: /*
    286:    InitialConditions - Computes the solution at the initial time.

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

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

    300:   /*
    301:     Get a pointer to vector data.
    302:     - For default PETSc vectors, VecGetArray() returns a pointer to
    303:       the data array.  Otherwise, the routine is implementation dependent.
    304:     - You MUST call VecRestoreArray() when you no longer need access to
    305:       the array.
    306:     - Note that the Fortran interface to VecGetArray() differs from the
    307:       C version.  See the users manual for details.
    308:   */
    309:   VecGetArrayWrite(u,&u_localptr);

    311:   /*
    312:      We initialize the solution array by simply writing the solution
    313:      directly into the array locations.  Alternatively, we could use
    314:      VecSetValues() or VecSetValuesLocal().
    315:   */
    316:   for (i=0; i<appctx->m; i++) u_localptr[i] = PetscSinScalar(PETSC_PI*i*6.*h) + 3.*PetscSinScalar(PETSC_PI*i*2.*h);

    318:   /*
    319:      Restore vector
    320:   */
    321:   VecRestoreArrayWrite(u,&u_localptr);

    323:   /*
    324:      Print debugging information if desired
    325:   */
    326:   if (appctx->debug) {
    327:     PetscPrintf(PETSC_COMM_WORLD,"Initial guess vector\n");
    328:     VecView(u,PETSC_VIEWER_STDOUT_SELF);
    329:   }

    331:   return 0;
    332: }
    333: /* --------------------------------------------------------------------- */
    334: /*
    335:    ExactSolution - Computes the exact solution at a given time.

    337:    Input Parameters:
    338:    t - current time
    339:    solution - vector in which exact solution will be computed
    340:    appctx - user-defined application context

    342:    Output Parameter:
    343:    solution - vector with the newly computed exact solution
    344: */
    345: PetscErrorCode ExactSolution(PetscReal t,Vec solution,AppCtx *appctx)
    346: {
    347:   PetscScalar    *s_localptr,h = appctx->h,ex1,ex2,sc1,sc2,tc = t;
    348:   PetscInt       i;

    350:   /*
    351:      Get a pointer to vector data.
    352:   */
    353:   VecGetArrayWrite(solution,&s_localptr);

    355:   /*
    356:      Simply write the solution directly into the array locations.
    357:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
    358:   */
    359:   ex1 = PetscExpScalar(-36.*PETSC_PI*PETSC_PI*tc);
    360:   ex2 = PetscExpScalar(-4.*PETSC_PI*PETSC_PI*tc);
    361:   sc1 = PETSC_PI*6.*h;                 sc2 = PETSC_PI*2.*h;
    362:   for (i=0; i<appctx->m; i++) s_localptr[i] = PetscSinScalar(sc1*(PetscReal)i)*ex1 + 3.*PetscSinScalar(sc2*(PetscReal)i)*ex2;

    364:   /*
    365:      Restore vector
    366:   */
    367:   VecRestoreArrayWrite(solution,&s_localptr);
    368:   return 0;
    369: }
    370: /* --------------------------------------------------------------------- */
    371: /*
    372:    Monitor - User-provided routine to monitor the solution computed at
    373:    each timestep.  This example plots the solution and computes the
    374:    error in two different norms.

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

    378:    Input Parameters:
    379:    ts     - the timestep context
    380:    step   - the count of the current step (with 0 meaning the
    381:              initial condition)
    382:    time   - the current time
    383:    u      - the solution at this timestep
    384:    ctx    - the user-provided context for this monitoring routine.
    385:             In this case we use the application context which contains
    386:             information about the problem size, workspace and the exact
    387:             solution.
    388: */
    389: PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec u,void *ctx)
    390: {
    391:   AppCtx         *appctx = (AppCtx*) ctx;   /* user-defined application context */
    392:   PetscReal      norm_2,norm_max,dt,dttol;

    394:   /*
    395:      View a graph of the current iterate
    396:   */
    397:   VecView(u,appctx->viewer2);

    399:   /*
    400:      Compute the exact solution
    401:   */
    402:   ExactSolution(time,appctx->solution,appctx);

    404:   /*
    405:      Print debugging information if desired
    406:   */
    407:   if (appctx->debug) {
    408:     PetscPrintf(PETSC_COMM_SELF,"Computed solution vector\n");
    409:     VecView(u,PETSC_VIEWER_STDOUT_SELF);
    410:     PetscPrintf(PETSC_COMM_SELF,"Exact solution vector\n");
    411:     VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF);
    412:   }

    414:   /*
    415:      Compute the 2-norm and max-norm of the error
    416:   */
    417:   VecAXPY(appctx->solution,-1.0,u);
    418:   VecNorm(appctx->solution,NORM_2,&norm_2);
    419:   norm_2 = PetscSqrtReal(appctx->h)*norm_2;
    420:   VecNorm(appctx->solution,NORM_MAX,&norm_max);

    422:   TSGetTimeStep(ts,&dt);
    423:   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);

    425:   appctx->norm_2   += norm_2;
    426:   appctx->norm_max += norm_max;

    428:   dttol = .0001;
    429:   PetscOptionsGetReal(NULL,NULL,"-dttol",&dttol,NULL);
    430:   if (dt < dttol) {
    431:     dt  *= .999;
    432:     TSSetTimeStep(ts,dt);
    433:   }

    435:   /*
    436:      View a graph of the error
    437:   */
    438:   VecView(appctx->solution,appctx->viewer1);

    440:   /*
    441:      Print debugging information if desired
    442:   */
    443:   if (appctx->debug) {
    444:     PetscPrintf(PETSC_COMM_SELF,"Error vector\n");
    445:     VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF);
    446:   }

    448:   return 0;
    449: }
    450: /* --------------------------------------------------------------------- */
    451: /*
    452:    RHSMatrixHeat - User-provided routine to compute the right-hand-side
    453:    matrix for the heat equation.

    455:    Input Parameters:
    456:    ts - the TS context
    457:    t - current time
    458:    global_in - global input vector
    459:    dummy - optional user-defined context, as set by TSetRHSJacobian()

    461:    Output Parameters:
    462:    AA - Jacobian matrix
    463:    BB - optionally different preconditioning matrix
    464:    str - flag indicating matrix structure

    466:    Notes:
    467:    Recall that MatSetValues() uses 0-based row and column numbers
    468:    in Fortran as well as in C.
    469: */
    470: PetscErrorCode RHSMatrixHeat(TS ts,PetscReal t,Vec X,Mat AA,Mat BB,void *ctx)
    471: {
    472:   Mat            A       = AA;                /* Jacobian matrix */
    473:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */
    474:   PetscInt       mstart  = 0;
    475:   PetscInt       mend    = appctx->m;
    476:   PetscInt       i,idx[3];
    477:   PetscScalar    v[3],stwo = -2./(appctx->h*appctx->h),sone = -.5*stwo;

    479:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    480:      Compute entries for the locally owned part of the matrix
    481:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    482:   /*
    483:      Set matrix rows corresponding to boundary data
    484:   */

    486:   mstart = 0;
    487:   v[0]   = 1.0;
    488:   MatSetValues(A,1,&mstart,1,&mstart,v,INSERT_VALUES);
    489:   mstart++;

    491:   mend--;
    492:   v[0] = 1.0;
    493:   MatSetValues(A,1,&mend,1,&mend,v,INSERT_VALUES);

    495:   /*
    496:      Set matrix rows corresponding to interior data.  We construct the
    497:      matrix one row at a time.
    498:   */
    499:   v[0] = sone; v[1] = stwo; v[2] = sone;
    500:   for (i=mstart; i<mend; i++) {
    501:     idx[0] = i-1; idx[1] = i; idx[2] = i+1;
    502:     MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
    503:   }

    505:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    506:      Complete the matrix assembly process and set some options
    507:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    508:   /*
    509:      Assemble matrix, using the 2-step process:
    510:        MatAssemblyBegin(), MatAssemblyEnd()
    511:      Computations can be done while messages are in transition
    512:      by placing code between these two statements.
    513:   */
    514:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    515:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

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

    523:   return 0;
    524: }

    526: PetscErrorCode IFunctionHeat(TS ts,PetscReal t,Vec X,Vec Xdot,Vec r,void *ctx)
    527: {
    528:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */

    530:   MatMult(appctx->A,X,r);
    531:   VecAYPX(r,-1.0,Xdot);
    532:   return 0;
    533: }

    535: PetscErrorCode IJacobianHeat(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal s,Mat A,Mat B,void *ctx)
    536: {
    537:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */

    539:   if (appctx->oshift == s) return 0;
    540:   MatCopy(appctx->A,A,SAME_NONZERO_PATTERN);
    541:   MatScale(A,-1);
    542:   MatShift(A,s);
    543:   MatCopy(A,B,SAME_NONZERO_PATTERN);
    544:   appctx->oshift = s;
    545:   return 0;
    546: }

    548: /*TEST

    550:     test:
    551:       args: -nox -ts_type ssp -ts_dt 0.0005

    553:     test:
    554:       suffix: 2
    555:       args: -nox -ts_type ssp -ts_dt 0.0005 -time_dependent_rhs 1

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

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

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

    573:     test:
    574:       requires: !single
    575:       suffix: pod_guess
    576:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type pod -pc_type none -ksp_converged_reason

    578:     test:
    579:       requires: !single
    580:       suffix: pod_guess_Ainner
    581:       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

    583:     test:
    584:       requires: !single
    585:       suffix: fischer_guess
    586:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type fischer -pc_type none -ksp_converged_reason

    588:     test:
    589:       requires: !single
    590:       suffix: fischer_guess_2
    591:       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

    593:     test:
    594:       requires: !single
    595:       suffix: fischer_guess_3
    596:       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

    598:     test:
    599:       requires: !single
    600:       suffix: stringview
    601:       args: -nox -ts_type rosw -test_string_viewer

    603:     test:
    604:       requires: !single
    605:       suffix: stringview_euler
    606:       args: -nox -ts_type euler -test_string_viewer

    608: TEST*/