StepControlStrategy class for TimeStepControl. More...

#include <Tempus_TimeStepControlStrategyBasicVS.hpp>

Inheritance diagram for Tempus::TimeStepControlStrategyBasicVS< Scalar >:

Public Member Functions
	TimeStepControlStrategyBasicVS ()
	Default Constructor. More...

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

virtual	~TimeStepControlStrategyBasicVS ()
	Destructor. More...

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

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

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)

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

virtual	~TimeStepControlStrategy ()
	Destructor. More...

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

Public Member Functions inherited from Teuchos::Describable
void	describe (std::ostream &out, const EVerbosityLevel verbLevel=verbLevel_default) const

virtual	~Describable ()

	LabeledObject ()

virtual	~LabeledObject ()

virtual void	setObjectLabel (const std::string &objectLabel)

virtual std::string	getObjectLabel () const

DescribableStreamManipulatorState	describe (const Describable &describable, const EVerbosityLevel verbLevel=Describable::verbLevel_default)

std::ostream &	operator<< (std::ostream &os, const DescribableStreamManipulatorState &d)

Public Member Functions inherited from Teuchos::VerboseObject< Tempus::TimeStepControlStrategy< Scalar > >
	VerboseObject (const EVerbosityLevel verbLevel=VERB_DEFAULT, const RCP< FancyOStream > &oStream=Teuchos::null)

virtual const VerboseObject &	setVerbLevel (const EVerbosityLevel verbLevel) const

virtual const VerboseObject &	setOverridingVerbLevel (const EVerbosityLevel verbLevel) const

virtual EVerbosityLevel	getVerbLevel () const

TEUCHOSPARAMETERLIST_LIB_DLL_EXPORT RCP< const ParameterList >	getValidVerboseObjectSublist ()

TEUCHOSPARAMETERLIST_LIB_DLL_EXPORT void	setupVerboseObjectSublist (ParameterList *paramList)

TEUCHOSPARAMETERLIST_LIB_DLL_EXPORT void	readVerboseObjectSublist (ParameterList paramList, RCP< FancyOStream > oStream, EVerbosityLevel *verbLevel)

void	readVerboseObjectSublist (ParameterList paramList, VerboseObject< ObjectType > verboseObject)

Public Member Functions inherited from Teuchos::VerboseObjectBase
virtual	~VerboseObjectBase ()

	VerboseObjectBase (const RCP< FancyOStream > &oStream=Teuchos::null)

virtual const VerboseObjectBase &	setOStream (const RCP< FancyOStream > &oStream) const

virtual const VerboseObjectBase &	setOverridingOStream (const RCP< FancyOStream > &oStream) const

virtual VerboseObjectBase &	setLinePrefix (const std::string &linePrefix)

virtual RCP< FancyOStream >	getOStream () const

virtual RCP< FancyOStream >	getOverridingOStream () const

virtual std::string	getLinePrefix () const

virtual OSTab	getOSTab (const int tabs=1, const std::string &linePrefix="") const

Private Attributes
Scalar	rho_
	Amplification Factor. More...

Scalar	sigma_
	Reduction Factor. More...

Scalar	minEta_
	Minimum Value Monitoring Function. More...

Scalar	maxEta_
	Maximum Value Monitoring Function. More...

Overridden from Teuchos::Describable
std::string	description () const override

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

Additional Inherited Members
Static Public Member Functions inherited from Teuchos::VerboseObject< Tempus::TimeStepControlStrategy< Scalar > >
static void	setDefaultVerbLevel (const EVerbosityLevel defaultVerbLevel)

static EVerbosityLevel	getDefaultVerbLevel ()

Static Public Member Functions inherited from Teuchos::VerboseObjectBase
static void	setDefaultOStream (const RCP< FancyOStream > &defaultOStream)

static RCP< FancyOStream >	getDefaultOStream ()

Static Public Attributes inherited from Teuchos::Describable
static const EVerbosityLevel	verbLevel_default

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

virtual void	setStepType (std::string s)

Protected Member Functions inherited from Teuchos::VerboseObject< Tempus::TimeStepControlStrategy< Scalar > >
void	initializeVerboseObject (const EVerbosityLevel verbLevel=VERB_DEFAULT, const RCP< FancyOStream > &oStream=Teuchos::null)

Protected Member Functions inherited from Teuchos::VerboseObjectBase
void	initializeVerboseObjectBase (const RCP< FancyOStream > &oStream=Teuchos::null)

virtual void	informUpdatedVerbosityState () const

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

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

std::string	name_
	Name of strategy. More...

bool	isInitialized_
	Bool if strategy is initialized. More...

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 103 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

Constructor & Destructor Documentation

template<class Scalar >

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

inline

Default Constructor.

Definition at line 107 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

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 117 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

template<class Scalar >

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

inlinevirtual

Destructor.

Definition at line 128 of file Tempus_TimeStepControlStrategyBasicVS.hpp.

Member Function Documentation

template<class Scalar >

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