Пример #1
0
static PetscErrorCode TSSetUp_Theta(TS ts)
{
  TS_Theta       *th = (TS_Theta*)ts->data;
  PetscErrorCode ierr;
  SNES           snes;
  TSAdapt        adapt;
  DM             dm;

  PetscFunctionBegin;
  ierr = VecDuplicate(ts->vec_sol,&th->X);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&th->Xdot);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&th->X0);CHKERRQ(ierr);
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  if (dm) {
    ierr = DMCoarsenHookAdd(dm,DMCoarsenHook_TSTheta,DMRestrictHook_TSTheta,ts);CHKERRQ(ierr);
    ierr = DMSubDomainHookAdd(dm,DMSubDomainHook_TSTheta,DMSubDomainRestrictHook_TSTheta,ts);CHKERRQ(ierr);
  }
  if (th->Theta == 0.5 && th->endpoint) th->order = 2;
  else th->order = 1;

  ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr);
  if (!th->adapt) {
    ierr = TSAdaptSetType(adapt,TSADAPTNONE);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}
Пример #2
0
static PetscErrorCode TSSetUp_Alpha(TS ts)
{
  TS_Alpha       *th = (TS_Alpha*)ts->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = VecDuplicate(ts->vec_sol,&th->X0);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&th->Xa);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&th->X1);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&th->V0);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&th->Va);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&th->V1);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&th->A0);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&th->Aa);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&th->A1);CHKERRQ(ierr);

  ierr = TSGetAdapt(ts,&ts->adapt);CHKERRQ(ierr);
  ierr = TSAdaptCandidatesClear(ts->adapt);CHKERRQ(ierr);
  if (!th->adapt) {
    ierr = TSAdaptSetType(ts->adapt,TSADAPTNONE);CHKERRQ(ierr);
  } else {
    ierr = VecDuplicate(ts->vec_sol,&th->vec_sol_prev);CHKERRQ(ierr);
    ierr = VecDuplicate(ts->vec_sol,&th->vec_dot_prev);CHKERRQ(ierr);
    ierr = VecDuplicate(ts->vec_sol,&th->vec_lte_work[0]);CHKERRQ(ierr);
    ierr = VecDuplicate(ts->vec_sol,&th->vec_lte_work[1]);CHKERRQ(ierr);
    if (ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED)
      ts->exact_final_time = TS_EXACTFINALTIME_MATCHSTEP;
  }

  ierr = TSGetSNES(ts,&ts->snes);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
Пример #3
0
/*
   TSAdaptSetFromOptions - Sets various TSAdapt parameters from user options.

   Collective on TSAdapt

   Input Parameter:
.  adapt - the TSAdapt context

   Options Database Keys:
.  -ts_adapt_type <type> - basic

   Level: advanced

   Notes:
   This function is automatically called by TSSetFromOptions()

.keywords: TS, TSGetAdapt(), TSAdaptSetType()

.seealso: TSGetType()
*/
PetscErrorCode  TSAdaptSetFromOptions(PetscOptionItems *PetscOptionsObject,TSAdapt adapt)
{
  PetscErrorCode ierr;
  char           type[256] = TSADAPTBASIC;
  PetscBool      set,flg;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(adapt,TSADAPT_CLASSID,1);
  /* This should use PetscOptionsBegin() if/when this becomes an object used outside of TS, but currently this
   * function can only be called from inside TSSetFromOptions()  */
  ierr = PetscOptionsHead(PetscOptionsObject,"TS Adaptivity options");CHKERRQ(ierr);
  ierr = PetscOptionsFList("-ts_adapt_type","Algorithm to use for adaptivity","TSAdaptSetType",TSAdaptList,
                          ((PetscObject)adapt)->type_name ? ((PetscObject)adapt)->type_name : type,type,sizeof(type),&flg);CHKERRQ(ierr);
  if (flg || !((PetscObject)adapt)->type_name) {
    ierr = TSAdaptSetType(adapt,type);CHKERRQ(ierr);
  }
  ierr = PetscOptionsReal("-ts_adapt_dt_min","Minimum time step considered","TSAdaptSetStepLimits",adapt->dt_min,&adapt->dt_min,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsReal("-ts_adapt_dt_max","Maximum time step considered","TSAdaptSetStepLimits",adapt->dt_max,&adapt->dt_max,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsReal("-ts_adapt_scale_solve_failed","Scale step by this factor if solve fails","",adapt->scale_solve_failed,&adapt->scale_solve_failed,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-ts_adapt_monitor","Print choices made by adaptive controller","TSAdaptSetMonitor",adapt->monitor ? PETSC_TRUE : PETSC_FALSE,&flg,&set);CHKERRQ(ierr);
  ierr = PetscOptionsEnum("-ts_adapt_wnormtype","Type of norm computed for error estimation","",NormTypes,(PetscEnum)adapt->wnormtype,(PetscEnum*)&adapt->wnormtype,NULL);CHKERRQ(ierr);
  if (adapt->wnormtype != NORM_2 && adapt->wnormtype != NORM_INFINITY) SETERRQ(PetscObjectComm((PetscObject)adapt),PETSC_ERR_SUP,"Only 2-norm and infinite norm supported");
  if (set) {ierr = TSAdaptSetMonitor(adapt,flg);CHKERRQ(ierr);}
  if (adapt->ops->setfromoptions) {ierr = (*adapt->ops->setfromoptions)(PetscOptionsObject,adapt);CHKERRQ(ierr);}
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
Пример #4
0
/*
   TSAdaptSetFromOptions - Sets various TSAdapt parameters from user options.

   Collective on TSAdapt

   Input Parameter:
.  adapt - the TSAdapt context

   Options Database Keys:
+  -ts_adapt_type <type> - algorithm to use for adaptivity
.  -ts_adapt_always_accept - always accept steps regardless of error/stability goals
.  -ts_adapt_safety <safety> - safety factor relative to target error/stability goal
.  -ts_adapt_reject_safety <safety> - extra safety factor to apply if the last step was rejected
.  -ts_adapt_clip <low,high> - admissible time step decrease and increase factors
.  -ts_adapt_dt_min <min> - minimum timestep to use
.  -ts_adapt_dt_max <max> - maximum timestep to use
.  -ts_adapt_scale_solve_failed <scale> - scale timestep by this factor if a solve fails
.  -ts_adapt_wnormtype <2 or infinity> - type of norm for computing error estimates
-  -ts_adapt_time_step_increase_delay - number of timesteps to delay increasing the time step after it has been decreased due to failed solver

   Level: advanced

   Notes:
   This function is automatically called by TSSetFromOptions()

.keywords: TS, TSGetAdapt(), TSAdaptSetType(), TSAdaptSetStepLimits()

.seealso: TSGetAdapt(), TSAdaptSetType(), TSAdaptSetAlwaysAccept(), TSAdaptSetSafety(),
          TSAdaptSetClip(), TSAdaptSetStepLimits(), TSAdaptSetMonitor()
*/
PetscErrorCode  TSAdaptSetFromOptions(PetscOptionItems *PetscOptionsObject,TSAdapt adapt)
{
  PetscErrorCode ierr;
  char           type[256] = TSADAPTBASIC;
  PetscReal      safety,reject_safety,clip[2],hmin,hmax;
  PetscBool      set,flg;
  PetscInt       two;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(adapt,TSADAPT_CLASSID,1);
  /* This should use PetscOptionsBegin() if/when this becomes an object used outside of TS, but currently this
   * function can only be called from inside TSSetFromOptions()  */
  ierr = PetscOptionsHead(PetscOptionsObject,"TS Adaptivity options");CHKERRQ(ierr);
  ierr = PetscOptionsFList("-ts_adapt_type","Algorithm to use for adaptivity","TSAdaptSetType",TSAdaptList,((PetscObject)adapt)->type_name ? ((PetscObject)adapt)->type_name : type,type,sizeof(type),&flg);CHKERRQ(ierr);
  if (flg || !((PetscObject)adapt)->type_name) {
    ierr = TSAdaptSetType(adapt,type);CHKERRQ(ierr);
  }

  ierr = PetscOptionsBool("-ts_adapt_always_accept","Always accept the step","TSAdaptSetAlwaysAccept",adapt->always_accept,&flg,&set);CHKERRQ(ierr);
  if (set) {ierr = TSAdaptSetAlwaysAccept(adapt,flg);CHKERRQ(ierr);}

  safety = adapt->safety; reject_safety = adapt->reject_safety;
  ierr = PetscOptionsReal("-ts_adapt_safety","Safety factor relative to target error/stability goal","TSAdaptSetSafety",safety,&safety,&set);CHKERRQ(ierr);
  ierr = PetscOptionsReal("-ts_adapt_reject_safety","Extra safety factor to apply if the last step was rejected","TSAdaptSetSafety",reject_safety,&reject_safety,&flg);CHKERRQ(ierr);
  if (set || flg) {ierr = TSAdaptSetSafety(adapt,safety,reject_safety);CHKERRQ(ierr);}

  two = 2; clip[0] = adapt->clip[0]; clip[1] = adapt->clip[1];
  ierr = PetscOptionsRealArray("-ts_adapt_clip","Admissible decrease/increase factor in step size","TSAdaptSetClip",clip,&two,&set);CHKERRQ(ierr);
  if (set && (two != 2)) SETERRQ(PetscObjectComm((PetscObject)adapt),PETSC_ERR_ARG_OUTOFRANGE,"Must give exactly two values to -ts_adapt_clip");
  if (set) {ierr = TSAdaptSetClip(adapt,clip[0],clip[1]);CHKERRQ(ierr);}

  hmin = adapt->dt_min; hmax = adapt->dt_max;
  ierr = PetscOptionsReal("-ts_adapt_dt_min","Minimum time step considered","TSAdaptSetStepLimits",hmin,&hmin,&set);CHKERRQ(ierr);
  ierr = PetscOptionsReal("-ts_adapt_dt_max","Maximum time step considered","TSAdaptSetStepLimits",hmax,&hmax,&flg);CHKERRQ(ierr);
  if (set || flg) {ierr = TSAdaptSetStepLimits(adapt,hmin,hmax);CHKERRQ(ierr);}

  ierr = PetscOptionsReal("-ts_adapt_max_ignore","Adaptor ignores (absolute) solution values smaller than this value","",adapt->ignore_max,&adapt->ignore_max,&set);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-ts_adapt_glee_use_local","GLEE adaptor uses local error estimation for step control","",adapt->glee_use_local,&adapt->glee_use_local,&set);CHKERRQ(ierr);

  ierr = PetscOptionsReal("-ts_adapt_scale_solve_failed","Scale step by this factor if solve fails","",adapt->scale_solve_failed,&adapt->scale_solve_failed,NULL);CHKERRQ(ierr);

  ierr = PetscOptionsEnum("-ts_adapt_wnormtype","Type of norm computed for error estimation","",NormTypes,(PetscEnum)adapt->wnormtype,(PetscEnum*)&adapt->wnormtype,NULL);CHKERRQ(ierr);
  if (adapt->wnormtype != NORM_2 && adapt->wnormtype != NORM_INFINITY) SETERRQ(PetscObjectComm((PetscObject)adapt),PETSC_ERR_SUP,"Only 2-norm and infinite norm supported");

  ierr = PetscOptionsInt("-ts_adapt_time_step_increase_delay","Number of timesteps to delay increasing the time step after it has been decreased due to failed solver","TSAdaptSetTimeStepIncreaseDelay",adapt->timestepjustdecreased_delay,&adapt->timestepjustdecreased_delay,NULL);CHKERRQ(ierr);

  ierr = PetscOptionsBool("-ts_adapt_monitor","Print choices made by adaptive controller","TSAdaptSetMonitor",adapt->monitor ? PETSC_TRUE : PETSC_FALSE,&flg,&set);CHKERRQ(ierr);
  if (set) {ierr = TSAdaptSetMonitor(adapt,flg);CHKERRQ(ierr);}

  if (adapt->ops->setfromoptions) {ierr = (*adapt->ops->setfromoptions)(PetscOptionsObject,adapt);CHKERRQ(ierr);}
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
Пример #5
0
/*@C
  TSAdaptLoad - Loads a TSAdapt that has been stored in binary  with TSAdaptView().

  Collective on PetscViewer

  Input Parameters:
+ newdm - the newly loaded TSAdapt, this needs to have been created with TSAdaptCreate() or
           some related function before a call to TSAdaptLoad().
- viewer - binary file viewer, obtained from PetscViewerBinaryOpen() or
           HDF5 file viewer, obtained from PetscViewerHDF5Open()

   Level: intermediate

  Notes:
   The type is determined by the data in the file, any type set into the TSAdapt before this call is ignored.

  Notes for advanced users:
  Most users should not need to know the details of the binary storage
  format, since TSAdaptLoad() and TSAdaptView() completely hide these details.
  But for anyone who's interested, the standard binary matrix storage
  format is
.vb
     has not yet been determined
.ve

.seealso: PetscViewerBinaryOpen(), TSAdaptView(), MatLoad(), VecLoad()
@*/
PetscErrorCode  TSAdaptLoad(TSAdapt adapt,PetscViewer viewer)
{
  PetscErrorCode ierr;
  PetscBool      isbinary;
  char           type[256];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(adapt,TSADAPT_CLASSID,1);
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
  if (!isbinary) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid viewer; open viewer with PetscViewerBinaryOpen()");

  ierr = PetscViewerBinaryRead(viewer,type,256,NULL,PETSC_CHAR);CHKERRQ(ierr);
  ierr = TSAdaptSetType(adapt,type);CHKERRQ(ierr);
  if (adapt->ops->load) {
    ierr = (*adapt->ops->load)(adapt,viewer);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}
Пример #6
0
static PetscErrorCode TSSetUp_Theta(TS ts)
{
  TS_Theta       *th = (TS_Theta*)ts->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!th->VecCostIntegral0 && ts->vec_costintegral && ts->costintegralfwd) { /* back up cost integral */
    ierr = VecDuplicate(ts->vec_costintegral,&th->VecCostIntegral0);CHKERRQ(ierr);
  }
  if (!th->X) {
    ierr = VecDuplicate(ts->vec_sol,&th->X);CHKERRQ(ierr);
  }
  if (!th->Xdot) {
    ierr = VecDuplicate(ts->vec_sol,&th->Xdot);CHKERRQ(ierr);
  }
  if (!th->X0) {
    ierr = VecDuplicate(ts->vec_sol,&th->X0);CHKERRQ(ierr);
  }
  if (th->endpoint) {
    ierr = VecDuplicate(ts->vec_sol,&th->affine);CHKERRQ(ierr);
  }

  th->order = (th->Theta == 0.5) ? 2 : 1;

  ierr = TSGetDM(ts,&ts->dm);CHKERRQ(ierr);
  ierr = DMCoarsenHookAdd(ts->dm,DMCoarsenHook_TSTheta,DMRestrictHook_TSTheta,ts);CHKERRQ(ierr);
  ierr = DMSubDomainHookAdd(ts->dm,DMSubDomainHook_TSTheta,DMSubDomainRestrictHook_TSTheta,ts);CHKERRQ(ierr);

  ierr = TSGetAdapt(ts,&ts->adapt);CHKERRQ(ierr);
  ierr = TSAdaptCandidatesClear(ts->adapt);CHKERRQ(ierr);
  if (!th->adapt) {
    ierr = TSAdaptSetType(ts->adapt,TSADAPTNONE);CHKERRQ(ierr);
  } else {
    ierr = VecDuplicate(ts->vec_sol,&th->vec_sol_prev);CHKERRQ(ierr);
    ierr = VecDuplicate(ts->vec_sol,&th->vec_lte_work);CHKERRQ(ierr);
    if (ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED)
      ts->exact_final_time = TS_EXACTFINALTIME_MATCHSTEP;
  }

  ierr = TSGetSNES(ts,&ts->snes);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
Пример #7
0
/*@
  TSAdaptCreate - create an adaptive controller context for time stepping

  Collective on MPI_Comm

  Input Parameter:
. comm - The communicator

  Output Parameter:
. adapt - new TSAdapt object

  Level: developer

  Notes:
  TSAdapt creation is handled by TS, so users should not need to call this function.

.keywords: TSAdapt, create
.seealso: TSGetAdapt(), TSAdaptSetType(), TSAdaptDestroy()
@*/
PetscErrorCode  TSAdaptCreate(MPI_Comm comm,TSAdapt *inadapt)
{
  PetscErrorCode ierr;
  TSAdapt        adapt;

  PetscFunctionBegin;
  PetscValidPointer(inadapt,1);
  *inadapt = NULL;
  ierr = TSAdaptInitializePackage();CHKERRQ(ierr);

  ierr = PetscHeaderCreate(adapt,TSADAPT_CLASSID,"TSAdapt","Time stepping adaptivity","TS",comm,TSAdaptDestroy,TSAdaptView);CHKERRQ(ierr);

  adapt->dt_min             = 1e-20;
  adapt->dt_max             = 1e50;
  adapt->scale_solve_failed = 0.25;
  adapt->wnormtype          = NORM_2;
  ierr = TSAdaptSetType(adapt,TSADAPTBASIC);CHKERRQ(ierr);

  *inadapt = adapt;
  PetscFunctionReturn(0);
}
Пример #8
0
int main(int argc,char **argv)
{
  TS             ts;            /* ODE integrator */
  Vec            U;             /* solution will be stored here */
  PetscErrorCode ierr;
  PetscMPIInt    size;
  PetscInt       n = 2;
  PetscScalar    *u;
  AppCtx         app;
  PetscInt       direction[2];
  PetscBool      terminate[2];
  PetscBool      rhs_form=PETSC_FALSE,hist=PETSC_TRUE;
  TSAdapt        adapt;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
  if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

  app.nbounces = 0;
  app.maxbounces = 10;
  ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex40 options","");CHKERRQ(ierr);
  ierr = PetscOptionsInt("-maxbounces","","",app.maxbounces,&app.maxbounces,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-test_adapthistory","","",hist,&hist,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsEnd();CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
  ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set ODE routines
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
  /* Users are advised against the following branching and code duplication.
     For problems without a mass matrix like the one at hand, the RHSFunction
     (and companion RHSJacobian) interface is enough to support both explicit
     and implicit timesteppers. This tutorial example also deals with the
     IFunction/IJacobian interface for demonstration and testing purposes. */
  ierr = PetscOptionsGetBool(NULL,NULL,"-rhs-form",&rhs_form,NULL);CHKERRQ(ierr);
  if (rhs_form) {
    ierr = TSSetRHSFunction(ts,NULL,RHSFunction,NULL);CHKERRQ(ierr);
    ierr = TSSetRHSJacobian(ts,NULL,NULL,RHSJacobian,NULL);CHKERRQ(ierr);
  } else {
    Mat A; /* Jacobian matrix */
    ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
    ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr);
    ierr = MatSetFromOptions(A);CHKERRQ(ierr);
    ierr = MatSetUp(A);CHKERRQ(ierr);
    ierr = TSSetIFunction(ts,NULL,IFunction,NULL);CHKERRQ(ierr);
    ierr = TSSetIJacobian(ts,A,A,IJacobian,NULL);CHKERRQ(ierr);
    ierr = MatDestroy(&A);CHKERRQ(ierr);
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = VecCreate(PETSC_COMM_WORLD,&U);CHKERRQ(ierr);
  ierr = VecSetSizes(U,n,PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = VecSetUp(U);CHKERRQ(ierr);
  ierr = VecGetArray(U,&u);CHKERRQ(ierr);
  u[0] = 0.0;
  u[1] = 20.0;
  ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
  ierr = TSSetSolution(ts,U);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set solver options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
  ierr = TSSetMaxTime(ts,30.0);CHKERRQ(ierr);
  ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
  ierr = TSSetTimeStep(ts,0.1);CHKERRQ(ierr);
  /* The adapative time step controller could take very large timesteps resulting in
     the same event occuring multiple times in the same interval. A maximum step size
     limit is enforced here to avoid this issue. */
  ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr);
  ierr = TSAdaptSetStepLimits(adapt,0.0,0.5);CHKERRQ(ierr);

  /* Set directions and terminate flags for the two events */
  direction[0] = -1;            direction[1] = -1;
  terminate[0] = PETSC_FALSE;   terminate[1] = PETSC_TRUE;
  ierr = TSSetEventHandler(ts,2,direction,terminate,EventFunction,PostEventFunction,(void*)&app);CHKERRQ(ierr);

  ierr = TSSetFromOptions(ts);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Run timestepping solver
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSolve(ts,U);CHKERRQ(ierr);

  if (hist) { /* replay following history */
    TSTrajectory tj;
    PetscReal    tf,t0,dt;

    app.nbounces = 0;
    ierr = TSGetTime(ts,&tf);CHKERRQ(ierr);
    ierr = TSSetMaxTime(ts,tf);CHKERRQ(ierr);
    ierr = TSSetStepNumber(ts,0);CHKERRQ(ierr);
    ierr = TSRestartStep(ts);CHKERRQ(ierr);
    ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
    ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
    ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr);
    ierr = TSAdaptSetType(adapt,TSADAPTHISTORY);CHKERRQ(ierr);
    ierr = TSGetTrajectory(ts,&tj);CHKERRQ(ierr);
    ierr = TSAdaptHistorySetTrajectory(adapt,tj,PETSC_FALSE);CHKERRQ(ierr);
    ierr = TSAdaptHistoryGetStep(adapt,0,&t0,&dt);CHKERRQ(ierr);
    /* this example fails with single (or smaller) precision */
#if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL__FP16)
    ierr = TSAdaptSetType(adapt,TSADAPTBASIC);CHKERRQ(ierr);
    ierr = TSAdaptSetStepLimits(adapt,0.0,0.5);CHKERRQ(ierr);
    ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
#endif
    ierr = TSSetTime(ts,t0);CHKERRQ(ierr);
    ierr = TSSetTimeStep(ts,dt);CHKERRQ(ierr);
    ierr = TSResetTrajectory(ts);CHKERRQ(ierr);
    ierr = VecGetArray(U,&u);CHKERRQ(ierr);
    u[0] = 0.0;
    u[1] = 20.0;
    ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
    ierr = TSSolve(ts,U);CHKERRQ(ierr);
  }
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.  All PETSc objects should be destroyed when they are no longer needed.
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = VecDestroy(&U);CHKERRQ(ierr);
  ierr = TSDestroy(&ts);CHKERRQ(ierr);

  ierr = PetscFinalize();
  return ierr;
}