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Tempus::TimeStepControlStrategyBasicVS< Scalar > Class Template Reference

StepControlStrategy class for TimeStepControl. More...

#include <Tempus_TimeStepControlStrategyBasicVS.hpp>

Inheritance diagram for Tempus::TimeStepControlStrategyBasicVS< Scalar >:
Tempus::TimeStepControlStrategy< Scalar >

Public Member Functions

 TimeStepControlStrategyBasicVS (Teuchos::RCP< Teuchos::ParameterList > pList=Teuchos::null)
 Constructor. More...
 
virtual ~TimeStepControlStrategyBasicVS ()
 Destructor. More...
 
virtual void getNextTimeStep (const TimeStepControl< Scalar > tsc, Teuchos::RCP< SolutionHistory< Scalar > > solutionHistory, Status &integratorStatus) override
 Determine the time step size. More...
 
- Public Member Functions inherited from Tempus::TimeStepControlStrategy< Scalar >
 TimeStepControlStrategy ()
 Constructor. More...
 
virtual ~TimeStepControlStrategy ()
 Destructor. More...
 
void setParameterList (const Teuchos::RCP< Teuchos::ParameterList > &pl)
 
Teuchos::RCP< const Teuchos::ParameterList > getValidParameters () const
 
Teuchos::RCP< Teuchos::ParameterList > getNonconstParameterList ()
 
Teuchos::RCP< Teuchos::ParameterList > unsetParameterList ()
 

Overridden from Teuchos::ParameterListAcceptor

Teuchos::RCP< Teuchos::ParameterList > tscsPL_
 
void setParameterList (const Teuchos::RCP< Teuchos::ParameterList > &pList) override
 
Teuchos::RCP< const Teuchos::ParameterList > getValidParameters () const override
 
Teuchos::RCP< Teuchos::ParameterList > getNonconstParameterList () override
 
Teuchos::RCP< Teuchos::ParameterList > unsetParameterList () override
 
virtual Scalar getAmplFactor () const
 
virtual Scalar getReductFactor () const
 
virtual Scalar getMinEta () const
 
virtual Scalar getMaxEta () const
 
Scalar computeEta (const TimeStepControl< Scalar > tsc, const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
 

Detailed Description

template<class Scalar>
class Tempus::TimeStepControlStrategyBasicVS< Scalar >

StepControlStrategy class for TimeStepControl.

This TimeStepControlStrategy primarily tries to maintain a certain level of change in the solution ill-respective of the error involved, e.g., the solution should change by 1% every time step. The relative solution change is measured by

\[ \eta_{n-1} = \frac{|| x_{n-1} - x_{n-2} ||}{ || x_{n-2} || + \epsilon } \]

where $\epsilon$ is a small constant to ensure that $\eta_n$ remains finite. The user can select the desired relative change in the solution by choosing a range for $\eta_n$

\[ \eta_{min} < \eta_n < \eta_{max} \]

If the solution change is outside this range, an amplification ( $\rho$) or reduction factor ( $\sigma$) is applied to the timestep to bring the solution change back into the desired range. This can be written as

\[ \Delta t_n = \left\{ \begin{array}{rll} \sigma \Delta t_{n-1} & \mbox{if $\eta_{n-1} > \eta_{max}$} & \mbox{where $0 < \sigma < 1$} \\ \rho \Delta t_{n-1} & \mbox{else if $\eta_{n-1} < \eta_{min}$} & \mbox{where $\rho > 1$} \\ \Delta t_{n-1} & \mbox{else if $\eta_{min}<\eta_{n-1}<\eta_{max}$} \\ \end{array} \right. \]

In the full implementation, several other mechanisms can amplify or reduce the timestep.

  • Stepper fails
  • Maximum Absolute error, $e_{abs}^{max}$
  • Maximum Relative error, $e_{rel}^{max}$
  • Order, $p$

    \[ \Delta t_n = \left\{ \begin{array}{rll} \sigma \Delta t_{n-1} & \mbox{if Stepper fails} & \mbox{where $0 < \sigma < 1$} \\ \rho \Delta t_{n-1} & \mbox{else if $\eta_{n-1} < \eta_{min}$} & \mbox{where $\rho > 1$} \\ \sigma \Delta t_{n-1} & \mbox{else if $\eta_{n-1} > \eta_{max}$} & \mbox{where $0 < \sigma < 1$} \\ \sigma \Delta t_{n-1} & \mbox{else if $e_{abs} > e_{abs}^{max}$} & \mbox{where $0 < \sigma < 1$} \\ \sigma \Delta t_{n-1} & \mbox{else if $e_{rel} > e_{rel}^{max}$} & \mbox{where $0 < \sigma < 1$} \\ \rho \Delta t_{n-1} & \mbox{else if $p < p_{min}$} & \mbox{where $\rho > 1$} \\ \sigma \Delta t_{n-1} & \mbox{else if $p > p_{max}$} & \mbox{where $0 < \sigma < 1$} \\ \Delta t_{n-1} & \mbox{else} & \\ \end{array} \right. \]

Note

  • Only one amplification or reduction is applied each timestep.
  • The priority is specified by the order of list.
  • The timestep, $\Delta t_n$, is still constrained to the maximum and minimum timestep size. $\Delta t_{min} < \Delta t_n < \Delta t_{max}$
  • If $ \eta_{min} < \eta_n < \eta_{max}$, the timestep is unchanged, i.e., constant timestep size.
  • To have constant timesteps, set $\eta_{min}=0$ and $\eta_{max}=10^{16}$. These are the defaults.
  • From (Denner, 2014), amplification factor, $\rho$, is required to be less than 1.91 for stability ( $\rho < 1.91$).
  • Denner (2014) suggests that $\eta_{min} = 0.1*\eta_{max}$ and the numerical tests confirm this for their problems.

References

Section 2.2.1 / Algorithm 2.4 of A. Denner, "Experiments on Temporal Variable Step BDF2 Algorithms", Masters Thesis, U Wisconsin-Madison, 2014.

Definition at line 105 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

Constructor & Destructor Documentation

◆ TimeStepControlStrategyBasicVS()

template<class Scalar >
Tempus::TimeStepControlStrategyBasicVS< Scalar >::TimeStepControlStrategyBasicVS ( Teuchos::RCP< Teuchos::ParameterList >  pList = Teuchos::null)
inline

Constructor.

Definition at line 111 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ ~TimeStepControlStrategyBasicVS()

template<class Scalar >
virtual Tempus::TimeStepControlStrategyBasicVS< Scalar >::~TimeStepControlStrategyBasicVS ( )
inlinevirtual

Destructor.

Definition at line 117 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

Member Function Documentation

◆ computeEta()

template<class Scalar >
Scalar Tempus::TimeStepControlStrategyBasicVS< Scalar >::computeEta ( const TimeStepControl< Scalar >  tsc,
const Teuchos::RCP< SolutionHistory< Scalar > > &  solutionHistory 
)
inline

Definition at line 284 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ getAmplFactor()

template<class Scalar >
virtual Scalar Tempus::TimeStepControlStrategyBasicVS< Scalar >::getAmplFactor ( ) const
inlinevirtual

Definition at line 275 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ getMaxEta()

template<class Scalar >
virtual Scalar Tempus::TimeStepControlStrategyBasicVS< Scalar >::getMaxEta ( ) const
inlinevirtual

Definition at line 281 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ getMinEta()

template<class Scalar >
virtual Scalar Tempus::TimeStepControlStrategyBasicVS< Scalar >::getMinEta ( ) const
inlinevirtual

Definition at line 279 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ getNextTimeStep()

template<class Scalar >
virtual void Tempus::TimeStepControlStrategyBasicVS< Scalar >::getNextTimeStep ( const TimeStepControl< Scalar >  tsc,
Teuchos::RCP< SolutionHistory< Scalar > >  solutionHistory,
Status &  integratorStatus 
)
inlineoverridevirtual

Determine the time step size.

Reimplemented from Tempus::TimeStepControlStrategy< Scalar >.

Definition at line 120 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ getNonconstParameterList()

template<class Scalar >
Teuchos::RCP<Teuchos::ParameterList> Tempus::TimeStepControlStrategyBasicVS< Scalar >::getNonconstParameterList ( )
inlineoverride

Definition at line 264 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ getReductFactor()

template<class Scalar >
virtual Scalar Tempus::TimeStepControlStrategyBasicVS< Scalar >::getReductFactor ( ) const
inlinevirtual

Definition at line 277 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ getValidParameters()

template<class Scalar >
Teuchos::RCP<const Teuchos::ParameterList> Tempus::TimeStepControlStrategyBasicVS< Scalar >::getValidParameters ( ) const
inlineoverride

Definition at line 249 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ setParameterList()

template<class Scalar >
void Tempus::TimeStepControlStrategyBasicVS< Scalar >::setParameterList ( const Teuchos::RCP< Teuchos::ParameterList > &  pList)
inlineoverride

Definition at line 219 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ unsetParameterList()

template<class Scalar >
Teuchos::RCP<Teuchos::ParameterList> Tempus::TimeStepControlStrategyBasicVS< Scalar >::unsetParameterList ( )
inlineoverride

Definition at line 268 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

Member Data Documentation

◆ tscsPL_

template<class Scalar >
Teuchos::RCP<Teuchos::ParameterList> Tempus::TimeStepControlStrategyBasicVS< Scalar >::tscsPL_
private

Definition at line 331 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

The documentation for this class was generated from the following file: