Leapfrog time stepper. More...

#include <Tempus_StepperLeapfrog_decl.hpp>

Inheritance diagram for Tempus::StepperLeapfrog< Scalar >:

Public Member Functions
	StepperLeapfrog ()
	Default constructor. More...

	StepperLeapfrog (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, bool useFSAL, std::string ICConsistency, bool ICConsistencyCheck, const Teuchos::RCP< StepperLeapfrogAppAction< Scalar > > &stepperLFAppAction)
	Constructor. More...

virtual bool	isValidSetup (Teuchos::FancyOStream &out) const

Public Member Functions inherited from Tempus::StepperExplicit< Scalar >
void	setStepperExplicitValues (Teuchos::RCP< Teuchos::ParameterList > pl)
	Set StepperExplicit member data from the ParameterList. More...

virtual void	setModel (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel)

virtual Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > >	getModel ()

virtual void	setSolver (Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > solver)
	Set solver. More...

virtual Teuchos::RCP < Thyra::NonlinearSolverBase < Scalar > >	getSolver () const
	Get solver. More...

virtual void	setInitialGuess (Teuchos::RCP< const Thyra::VectorBase< Scalar > >)
	Pass initial guess to Newton solver (only relevant for implicit solvers) More...

virtual void	evaluateExplicitODE (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDot, Teuchos::RCP< const Thyra::VectorBase< Scalar > > x, const Scalar time, const Teuchos::RCP< ExplicitODEParameters< Scalar > > &p)
	Evaluate xDot = f(x,t). More...

virtual void	evaluateExplicitODE (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDotDot, Teuchos::RCP< const Thyra::VectorBase< Scalar > > x, Teuchos::RCP< const Thyra::VectorBase< Scalar > > xDot, const Scalar time, const Teuchos::RCP< ExplicitODEParameters< Scalar > > &p)
	Evaluate xDotDot = f(x, xDot, t). More...

Public Member Functions inherited from Tempus::Stepper< Scalar >
void	setStepperValues (const Teuchos::RCP< Teuchos::ParameterList > pl)
	Set Stepper member data from ParameterList. More...

virtual Teuchos::RCP< const Teuchos::ParameterList >	getValidParameters () const

Teuchos::RCP < Teuchos::ParameterList >	getValidParametersBasic () const
	Add basic parameters to Steppers ParameterList. More...

virtual void	setNonConstModel (const Teuchos::RCP< Thyra::ModelEvaluator< Scalar > > &)

virtual void	initialize ()
	Initialize after construction and changing input parameters. More...

virtual bool	isInitialized ()
	True if stepper's member data is initialized. More...

virtual void	checkInitialized ()
	Check initialization, and error out on failure. More...

void	setStepperName (std::string s)
	Set the stepper name. More...

std::string	getStepperName () const
	Get the stepper name. More...

std::string	getStepperType () const
	Get the stepper type. The stepper type is used as an identifier for the stepper, and can only be set by the derived Stepper class. More...

virtual void	setUseFSAL (bool a)

void	setUseFSALTrueOnly (bool a)

void	setUseFSALFalseOnly (bool a)

bool	getUseFSAL () const

void	setICConsistency (std::string s)

std::string	getICConsistency () const

void	setICConsistencyCheck (bool c)

bool	getICConsistencyCheck () const

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStepperX ()
	Get Stepper x. More...

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStepperXDot ()
	Get Stepper xDot. More...

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStepperXDotDot ()
	Get Stepper xDotDot. More...

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStepperXDotDot (Teuchos::RCP< SolutionState< Scalar > > state)
	Get xDotDot from SolutionState or Stepper storage. More...

virtual std::string	description () 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< Stepper< 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

Protected Attributes
Teuchos::RCP < StepperLeapfrogAppAction < Scalar > >	stepperLFAppAction_

Protected Attributes inherited from Tempus::StepperExplicit< Scalar >
Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > >	appModel_
	Explicit ODE ModelEvaluator. More...

Thyra::ModelEvaluatorBase::InArgs < Scalar >	inArgs_

Thyra::ModelEvaluatorBase::OutArgs < Scalar >	outArgs_

Protected Attributes inherited from Tempus::Stepper< Scalar >
bool	useFSAL_ = false
	Use First-Same-As-Last (FSAL) principle. More...

bool	isInitialized_ = false
	True if stepper's member data is initialized. More...

Basic stepper methods
virtual void	setAppAction (Teuchos::RCP< StepperLeapfrogAppAction< Scalar > > appAction)

virtual Teuchos::RCP < StepperLeapfrogAppAction < Scalar > >	getAppAction () const

virtual void	setInitialConditions (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
	Set the initial conditions and make them consistent. More...

virtual void	takeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
	Take the specified timestep, dt, and return true if successful. More...

virtual Teuchos::RCP < Tempus::StepperState< Scalar > >	getDefaultStepperState ()
	Get a default (initial) StepperState. More...

virtual Scalar	getOrder () const

virtual Scalar	getOrderMin () const

virtual Scalar	getOrderMax () const

virtual Scalar	getInitTimeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &) const

virtual bool	isExplicit () const

virtual bool	isImplicit () const

virtual bool	isExplicitImplicit () const

virtual bool	isOneStepMethod () const

virtual bool	isMultiStepMethod () const

virtual OrderODE	getOrderODE () const

Overridden from Teuchos::Describable
virtual void	describe (Teuchos::FancyOStream &out, const Teuchos::EVerbosityLevel verbLevel) const

Additional Inherited Members
Static Public Member Functions inherited from Teuchos::VerboseObject< Stepper< 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::Stepper< Scalar >
virtual void	setStepperX (Teuchos::RCP< Thyra::VectorBase< Scalar > > x)
	Set x for Stepper storage. More...

virtual void	setStepperXDot (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDot)
	Set xDot for Stepper storage. More...

virtual void	setStepperXDotDot (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDotDot)
	Set x for Stepper storage. More...

void	setStepperType (std::string s)
	Set the stepper type. More...

Protected Member Functions inherited from Teuchos::VerboseObject< Stepper< 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

Detailed Description

template<class Scalar>
class Tempus::StepperLeapfrog< Scalar >

Leapfrog time stepper.

For the governing equation,

$M(t) \ddot{x} + K(t) x = F(t),$

one can write the explicit ODE system,

$\ddot{x} = f(x,t),$

where

$f(x,t) = \left(M(t)\right)^{-1} \left( F(t) - K(t) x \right).$

The Leapfrog stepper can be written as

$\begin{eqnarray*} x_{n+1} & = & x_{n} + \Delta t\, \dot{x}_{n+1/2} \\ \ddot{x}_{n+1} & = & f(x_{n+1},t_{n+1}) \\ \dot{x}_{n+3/2} & = & \dot{x}_{n+1/2} + \Delta t\, \ddot{x}_{n+1} \end{eqnarray*}$

where the position and velocity are leapfrogged over each other. On startup the velocity half-step can be obtained with

$\begin{eqnarray*} \dot{x}_{n+1/2} & = & \dot{x}_{n} + \frac{1}{2} \Delta t\, \ddot{x}_{n} \\ \dot{x}_{n+1/2} & = & \dot{x}_{n} + \frac{1}{2} \Delta t\, f(x_{n},t_{n}) \end{eqnarray*}$

and to complete the time step, the final velocity half-step is obtained with

$\begin{eqnarray*} \dot{x}_{n+1}&=&\dot{x}_{n+1/2} +\frac{1}{2} \Delta t\, \ddot{x}_{n+1} \\ \dot{x}_{n+1}&=&\dot{x}_{n+1/2} +\frac{1}{2} \Delta t\, f(x_{n+1},t_{n+1}) \end{eqnarray*}$

Algorithm The single-timestep algorithm for Leapfrog is

$\begin{center} \parbox{5in}{ \rule{5in}{0.4pt} \\ {\bf Algorithm} Leapfrog \\ \rule{5in}{0.4pt} \vspace{-15pt} \begin{enumerate} \setlength{\itemsep}{0pt} \setlength{\parskip}{0pt} \setlength{\parsep}{0pt} \item {\it appAction.execute(solutionHistory, stepper, BEGIN\_STEP)} \item {\bf if (``Startup") then} \hfill {\it * Take half-step startup.} \item \quad $\dot{x}_{n+1/2} = \dot{x}_n + \frac{1}{2}\Delta t \ddot{x}_n$ \item {\bf endif} \item {\it appAction.execute(solutionHistory, stepper, BEFORE\_X\_UPDATE)} \item $x_{n+1} = x_n + \Delta t \dot{x}_{n+1/2}$ \item {\it appAction.execute(solutionHistory, stepper, BEFORE\_EXPLICIT\_EVAL)} \item $\ddot{x}_{n+1} = f(x_{n+1},t_{n+1})$ \item {\it appAction.execute(solutionHistory, stepper, BEFORE\_XDOT\_UPDATE)} \item {\bf if (``Ending") then} \hfill {\it * Take half-step to get solution at the same time level.} \item \quad $\dot{x}_{n+1} \leftarrow \dot{x}_{n+1/2} +\frac{1}{2} \Delta t\, \ddot{x}_{n+1}$ \item {\bf else} \item \quad $\dot{x}_{n+3/2} \leftarrow \dot{x}_{n+1/2} + \Delta t\, \ddot{x}_{n+1}$ \item {\bf endif} \item {\it appAction.execute(solutionHistory, stepper, END\_STEP)} \end{enumerate} \vspace{-10pt} \rule{5in}{0.4pt} } \end{center}$

where one can begin with $(x_n,\dot{x}_{n+1/2})$ or $(x_n,\dot{x}_{n})$ and/or end with $(x_{n+1},\dot{x}_{n+3/2})$ or $(x_{n+1},\dot{x}_{n+1})$ .

The First-Same-As-Last (FSAL) principle is not used with Leapfrog because of the algorithm's prescribed order of solution update. The default is to set useFSAL=false, and useFSAL=true will issue a warning that it will have no affect.

Definition at line 96 of file Tempus_StepperLeapfrog_decl.hpp.

Constructor & Destructor Documentation

template<class Scalar >

Tempus::StepperLeapfrog< Scalar >::StepperLeapfrog ( )

Default constructor.

Requires subsequent setModel() and initialize() calls before calling takeStep().

Definition at line 21 of file Tempus_StepperLeapfrog_impl.hpp.

template<class Scalar >

Tempus::StepperLeapfrog< Scalar >::StepperLeapfrog	(	const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &	appModel,
		bool	useFSAL,
		std::string	ICConsistency,
		bool	ICConsistencyCheck,
		const Teuchos::RCP< StepperLeapfrogAppAction< Scalar > > &	stepperLFAppAction
	)

Constructor.

Definition at line 33 of file Tempus_StepperLeapfrog_impl.hpp.

Member Function Documentation

template<class Scalar >

void Tempus::StepperLeapfrog< Scalar >::setAppAction ( Teuchos::RCP< StepperLeapfrogAppAction< Scalar > > appAction )

virtual

Definition at line 55 of file Tempus_StepperLeapfrog_impl.hpp.

template<class Scalar >

virtual Teuchos::RCP<StepperLeapfrogAppAction<Scalar> > Tempus::StepperLeapfrog< Scalar >::getAppAction ( ) const

inlinevirtual

Definition at line 120 of file Tempus_StepperLeapfrog_decl.hpp.

template<class Scalar >

void Tempus::StepperLeapfrog< Scalar >::setInitialConditions ( const Teuchos::RCP< SolutionHistory< Scalar > > & solutionHistory )

virtual

Set the initial conditions and make them consistent.

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 70 of file Tempus_StepperLeapfrog_impl.hpp.

template<class Scalar >

void Tempus::StepperLeapfrog< Scalar >::takeStep ( const Teuchos::RCP< SolutionHistory< Scalar > > & solutionHistory )

virtual

Take the specified timestep, dt, and return true if successful.

Implements Tempus::Stepper< Scalar >.

Definition at line 97 of file Tempus_StepperLeapfrog_impl.hpp.

template<class Scalar >

Teuchos::RCP< Tempus::StepperState< Scalar > > Tempus::StepperLeapfrog< Scalar >::getDefaultStepperState ( )

virtual

Get a default (initial) StepperState.

Provide a StepperState to the SolutionState. This Stepper does not have any special state data, so just provide the base class StepperState with the Stepper description. This can be checked to ensure that the input StepperState can be used by this Stepper.

Implements Tempus::Stepper< Scalar >.

Definition at line 179 of file Tempus_StepperLeapfrog_impl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperLeapfrog< Scalar >::getOrder ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 133 of file Tempus_StepperLeapfrog_decl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperLeapfrog< Scalar >::getOrderMin ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 134 of file Tempus_StepperLeapfrog_decl.hpp.