StepControlStrategy class for TimeStepControl. More...

#include <Tempus_TimeStepControlStrategyBasicVS.hpp>

Inheritance diagram for Tempus::TimeStepControlStrategyBasicVS< Scalar >:

Public Member Functions
	TimeStepControlStrategyBasicVS ()
	Default Constructor.

	TimeStepControlStrategyBasicVS (Scalar rho, Scalar sigma, Scalar minEta, Scalar maxEta, std::string name="Basic VS")
	Full Constructor.

virtual	~TimeStepControlStrategyBasicVS ()
	Destructor.

virtual void	setNextTimeStep (const TimeStepControl< Scalar > &tsc, Teuchos::RCP< SolutionHistory< Scalar > > solutionHistory, Status &) override
	Set the time step size.

Public Member Functions inherited from Tempus::TimeStepControlStrategy< Scalar >
	TimeStepControlStrategy ()
	Constructor.

virtual	~TimeStepControlStrategy ()
	Destructor.

virtual bool	isInitialized ()

virtual void	checkInitialized ()

virtual void	setName (std::string s)

virtual std::string	getStrategyType () const

virtual std::string	getStepType () const

virtual std::string	getName () const

Overridden from Teuchos::Describable
Scalar	rho_
	Amplification Factor.

Scalar	sigma_
	Reduction Factor.

Scalar	minEta_
	Minimum Value Monitoring Function.

Scalar	maxEta_
	Maximum Value Monitoring Function.

std::string	description () const override

void	describe (Teuchos::FancyOStream &out, const Teuchos::EVerbosityLevel verbLevel) const override

virtual Teuchos::RCP< const Teuchos::ParameterList >	getValidParameters () const override
	Return ParameterList with current values.

virtual void	initialize () const override

virtual Scalar	getAmplFactor () const

virtual Scalar	getReductFactor () const

virtual Scalar	getMinEta () const

virtual Scalar	getMaxEta () const

virtual void	setAmplFactor (Scalar rho)

virtual void	setReductFactor (Scalar sigma)

virtual void	setMinEta (Scalar minEta)

virtual void	setMaxEta (Scalar maxEta)

Additional Inherited Members
Protected Member Functions inherited from Tempus::TimeStepControlStrategy< Scalar >
virtual void	setStrategyType (std::string s)

virtual void	setStepType (std::string s)

Protected Attributes inherited from Tempus::TimeStepControlStrategy< Scalar >
std::string	strategyType_
	Strategy type.

std::string	stepType_
	Step Type - "Constant" or "Variable".

std::string	name_
	Name of strategy.

bool	isInitialized_
	Bool if strategy is initialized.

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 between 1% and 3% ( $\eta_{min}=0.01$ and $\eta_{max}=0.03$ ) 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 $\eta_{n-1}$ remains finite. The user can select the desired relative change in the solution by choosing a range for $\eta_{n-1}$

$\eta_{min} < \eta_{n-1} < \eta_{max}$

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, $e_{rel}^{max}$
$\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 104 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

Constructor & Destructor Documentation

◆ TimeStepControlStrategyBasicVS() [1/2]

template<class Scalar >

Tempus::TimeStepControlStrategyBasicVS< Scalar >::TimeStepControlStrategyBasicVS ( )

inline

Default Constructor.

Definition at line 108 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ TimeStepControlStrategyBasicVS() [2/2]

template<class Scalar >

Tempus::TimeStepControlStrategyBasicVS< Scalar >::TimeStepControlStrategyBasicVS	(	Scalar	rho,
		Scalar	sigma,
		Scalar	minEta,
		Scalar	maxEta,
		std::string	name = `"Basic VS"`
	)

inline

Full Constructor.

Definition at line 118 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

◆ ~TimeStepControlStrategyBasicVS()

template<class Scalar >

virtual Tempus::TimeStepControlStrategyBasicVS< Scalar >::~TimeStepControlStrategyBasicVS ( )

inlinevirtual

Destructor.

Definition at line 129 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

Member Function Documentation

◆ setNextTimeStep()

template<class Scalar >

virtual void Tempus::TimeStepControlStrategyBasicVS< Scalar >::setNextTimeStep	(	const TimeStepControl< Scalar > &	tsc,
		Teuchos::RCP< SolutionHistory< Scalar > >	solutionHistory,
		Status &
	)