Leapfrog time stepper. More...

#include <Tempus_StepperLeapfrog_decl.hpp>

Inheritance diagram for Tempus::StepperLeapfrog< Scalar >:

Public Member Functions
	StepperLeapfrog (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, Teuchos::RCP< Teuchos::ParameterList > pList=Teuchos::null)
	Constructor. More...

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

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

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

virtual void	setSolver (std::string solverName)
	Set solver via ParameterList solver name. More...

virtual void	setSolver (Teuchos::RCP< Teuchos::ParameterList > solverPL=Teuchos::null)
	Set solver via solver ParameterList. More...

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	setObserver (Teuchos::RCP< StepperObserver< Scalar > > obs=Teuchos::null)
	Set Observer. More...

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

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

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

virtual std::string	getStepperType () const

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 > > &solutionHistory) const

virtual bool	isExplicit () const

virtual bool	isImplicit () const

virtual bool	isExplicitImplicit () const

virtual bool	isOneStepMethod () const

virtual bool	isMultiStepMethod () const

virtual void	setIsXDotXDotInitialized (bool tf)

virtual bool	getIsXDotXDotInitialized () const

ParameterList methods
void	setParameterList (const Teuchos::RCP< Teuchos::ParameterList > &pl)

Teuchos::RCP< Teuchos::ParameterList >	getNonconstParameterList ()

Teuchos::RCP< Teuchos::ParameterList >	unsetParameterList ()

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

Teuchos::RCP< Teuchos::ParameterList >	getDefaultParameters () const

Public Member Functions inherited from Tempus::Stepper< Scalar >
virtual void	createSubSteppers (std::vector< Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > > models)

void	validExplicitODE (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &model) const
	Validate that the model supports explicit ODE evaluation, f(x,t) [=xdot]. More...

void	validSecondOrderExplicitODE (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &model) const
	Validate that the model supports explicit second order ODE evaluation, f(x,xdot,t) [=xdotdot]. More...

void	validImplicitODE_DAE (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &model) const
	Validate ME supports implicit ODE/DAE evaluation, f(xdot,x,t) [= 0]. More...

void	validSecondOrderODE_DAE (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &model) const
	Validate ME supports 2nd order implicit ODE/DAE evaluation, f(xdotdot,xdot,x,t) [= 0]. More...

Teuchos::RCP< Teuchos::ParameterList >	defaultSolverParameters () const

Overridden from Teuchos::Describable
Teuchos::RCP< Teuchos::ParameterList >	stepperPL_

Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > >	appModel_
	Explicit ODE ModelEvaluator. More...

Thyra::ModelEvaluatorBase::InArgs< Scalar >	inArgs_

Thyra::ModelEvaluatorBase::OutArgs< Scalar >	outArgs_

Teuchos::RCP< StepperObserver< Scalar > >	stepperObserver_

Teuchos::RCP< StepperLeapfrogObserver< Scalar > >	stepperLFObserver_

Teuchos::RCP< const Thyra::VectorBase< Scalar > >	initial_guess_

virtual std::string	description () const

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

	StepperLeapfrog ()
	Default Constructor – not allowed. More...

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

Beginning with $(x_n,\dot{x}_{n+1/2})$ or $(x_n,\dot{x}_{n})$ and/or ending with $(x_{n+1},\dot{x}_{n+3/2})$ or $(x_{n+1},\dot{x}_{n+1})$ , the algorithm for Leapfrog is

if "startup"
- $\ddot{x}_{n} \leftarrow f(x_{n},t_{n})$
- $\dot{x}_{n+1/2} \leftarrow \dot{x}_{n} + \frac{1}{2} \Delta t\, \ddot{x}_{n}$
$x_{n+1} \leftarrow x_{n} + \Delta t\, \dot{x}_{n+1/2}$
$\ddot{x}_{n+1} \leftarrow f(x_{n+1},t_{n+1})$
if "ending"
- $\dot{x}_{n+1} \leftarrow \dot{x}_{n+1/2} +\frac{1}{2} \Delta t\, \ddot{x}_{n+1}$
else
- $\dot{x}_{n+3/2} \leftarrow \dot{x}_{n+1/2} + \Delta t\, \ddot{x}_{n+1}$

Definition at line 71 of file Tempus_StepperLeapfrog_decl.hpp.

Constructor & Destructor Documentation

◆ StepperLeapfrog() [1/2]

template<class Scalar >

Tempus::StepperLeapfrog< Scalar >::StepperLeapfrog	(	const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &	appModel,
		Teuchos::RCP< Teuchos::ParameterList >	pList = `Teuchos::null`
	)

Constructor.

Definition at line 20 of file Tempus_StepperLeapfrog_impl.hpp.

◆ StepperLeapfrog() [2/2]

template<class Scalar>

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

private

Default Constructor – not allowed.

Member Function Documentation

◆ describe()

template<class Scalar >

void Tempus::StepperLeapfrog< Scalar >::describe	(	Teuchos::FancyOStream &	out,
		const Teuchos::EVerbosityLevel	verbLevel
	)		const

virtual

Definition at line 238 of file Tempus_StepperLeapfrog_impl.hpp.

◆ description()

template<class Scalar >

std::string Tempus::StepperLeapfrog< Scalar >::description ( ) const

virtual

Definition at line 230 of file Tempus_StepperLeapfrog_impl.hpp.

◆ getDefaultParameters()

template<class Scalar >

Teuchos::RCP< Teuchos::ParameterList > Tempus::StepperLeapfrog< Scalar >::getDefaultParameters ( ) const

virtual

Public Member Functions

Overridden from Teuchos::Describable

Detailed Description

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

Constructor & Destructor Documentation

◆ StepperLeapfrog() [1/2]

◆ StepperLeapfrog() [2/2]

Member Function Documentation

◆ describe()

◆ description()

◆ getDefaultParameters()

◆ getDefaultStepperState()

◆ getInitTimeStep()

◆ getIsXDotXDotInitialized()

◆ getModel()

◆ getNonconstParameterList()

◆ getOrder()

◆ getOrderMax()

◆ getOrderMin()

◆ getSolver()

◆ getStepperType()

◆ getValidParameters()

◆ initialize()

◆ isExplicit()

◆ isExplicitImplicit()

◆ isImplicit()

◆ isMultiStepMethod()

◆ isOneStepMethod()

◆ setInitialGuess()

◆ setIsXDotXDotInitialized()

◆ setModel()

◆ setNonConstModel()

◆ setObserver()

◆ setParameterList()

◆ setSolver() [1/3]

◆ setSolver() [2/3]

◆ setSolver() [3/3]

◆ takeStep()

◆ unsetParameterList()

Member Data Documentation

◆ appModel_

◆ inArgs_

◆ initial_guess_

◆ outArgs_

◆ stepperLFObserver_

◆ stepperObserver_

◆ stepperPL_

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