BDF2 (Backward-Difference-Formula-2) time stepper. More...

#include <Tempus_StepperBDF2_decl.hpp>

Inheritance diagram for Tempus::StepperBDF2< Scalar >:

Public Member Functions
	StepperBDF2 ()
	Default constructor. More...

	StepperBDF2 (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, Teuchos::RCP< Teuchos::ParameterList > pList=Teuchos::null)
	Constructor. More...

virtual Scalar	getAlpha (const Scalar dt) const
	Return alpha = d(xDot)/dx. More...

virtual Scalar	getAlpha (const Scalar dt, const Scalar dtOld) const

virtual Scalar	getBeta (const Scalar) const
	Return beta = d(x)/dx. More...

virtual void	computeStartUp (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
	Compute the first time step given the supplied startup stepper. More...

Basic stepper methods
virtual void	setObserver (Teuchos::RCP< StepperObserver< Scalar > > obs=Teuchos::null)
	Set Observer. More...

void	setStartUpStepper (std::string startupStepperName)
	Set the stepper to use in first step. More...

void	setStartUpStepper (Teuchos::RCP< Teuchos::ParameterList >startUpStepperPL=Teuchos::null)
	Set the start up stepper to the supplied Parameter sublist. More...

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

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 bool	isExplicit () const

virtual bool	isImplicit () const

virtual bool	isExplicitImplicit () const

virtual bool	isOneStepMethod () const

virtual bool	isMultiStepMethod () const

virtual OrderODE	getOrderODE () 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

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

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

Public Member Functions inherited from Tempus::StepperImplicit< Scalar >
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 Teuchos::RCP< const WrapperModelEvaluator< Scalar > >	getWrapperModel ()

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 std::string	getStepperType () const

const Thyra::SolveStatus< Scalar >	solveImplicitODE (const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x)
	Solve problem using x in-place. (Needs to be deprecated!) More...

const Thyra::SolveStatus< Scalar >	solveImplicitODE (const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &xDot, const Scalar time, const Teuchos::RCP< ImplicitODEParameters< Scalar > > &p)
	Solve implicit ODE, f(x, xDot, t, p) = 0. More...

void	evaluateImplicitODE (Teuchos::RCP< Thyra::VectorBase< Scalar > > &f, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &xDot, const Scalar time, const Teuchos::RCP< ImplicitODEParameters< Scalar > > &p)
	Evaluate implicit ODE, f(x, xDot, t, p), residual. 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 void	setZeroInitialGuess (bool zIG)
	Set parameter so that the initial guess is set to zero (=True) or use last timestep (=False). More...

virtual bool	getZeroInitialGuess () const

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

virtual bool	getEmbedded () const

virtual void	setUseFSAL (bool a)

virtual bool	getUseFSAL () const

virtual void	setICConsistency (std::string s)

virtual std::string	getICConsistency () const

virtual void	setICConsistencyCheck (bool c)

virtual bool	getICConsistencyCheck () const

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

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

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

Public Member Functions inherited from Tempus::Stepper< Scalar >
virtual void	modelWarning () const

void	getValidParametersBasic (Teuchos::RCP< Teuchos::ParameterList > pl) const

virtual void	createSubSteppers (std::vector< Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > >)

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

Private Attributes
Teuchos::RCP< Stepper< Scalar > >	startUpStepper_

Teuchos::RCP < StepperBDF2Observer< Scalar > >	stepperBDF2Observer_

Scalar	order_

Additional Inherited Members
Protected Attributes inherited from Tempus::StepperImplicit< Scalar >
Teuchos::RCP < Teuchos::ParameterList >	stepperPL_

Teuchos::RCP < WrapperModelEvaluator < Scalar > >	wrapperModel_

Teuchos::RCP < Thyra::NonlinearSolverBase < Scalar > >	solver_

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

Teuchos::RCP< StepperObserver < Scalar > >	stepperObserver_

Teuchos::RCP < Thyra::VectorBase< Scalar > >	stepperXDot_

Teuchos::RCP < Thyra::VectorBase< Scalar > >	stepperXDotDot_

Detailed Description

template<class Scalar>
class Tempus::StepperBDF2< Scalar >

BDF2 (Backward-Difference-Formula-2) time stepper.

For the implicit ODE system, $f(\dot{x},x,t) = 0$ , the solution, $\dot{x}$ and $x$ , is determined using a solver (e.g., a non-linear solver, like NOX). This stepper allows for a variable time-step, $\Delta t$ . It is a 2-step method.

Algorithm

For , set the initial condition, .
For , use a one-step startup stepper, e.g., Backward Euler or RK4. The default startup stepper is 'IRK 1 Stage Theta Method' which second order.
For , solve for via $f\left(x_n, \dot{x}_n, t_n\right) = 0$ where $\dot{x}_{n} = \frac{2\tau_n + \tau_{n-1}}{\tau_n + \tau_{n-1}} \left[ \frac{x_n-x_{n-1}}{\tau_n}\right] - \frac{\tau_n}{\tau_n + \tau_{n-1}} \left[ \frac{x_{n-1}-x_{n-2}}{\tau_{n-1}}\right],$ and $\Delta t_n = \tau_n = t_n - t_{n-1}$ .
$\dot{x}_n \leftarrow \dot{x}_{n} = \frac{2\tau_n + \tau_{n-1}}{\tau_n + \tau_{n-1}} \left[ \frac{x_n-x_{n-1}}{\tau_n}\right] - \frac{\tau_n}{\tau_n + \tau_{n-1}} \left[ \frac{x_{n-1}-x_{n-2}}{\tau_{n-1}}\right],$

The First-Step-As-Last (FSAL) principle is not needed BDF2. The default is to set useFSAL=false, however useFSAL=true will also work but have no affect (i.e., no-op).

Definition at line 50 of file Tempus_StepperBDF2_decl.hpp.

Constructor & Destructor Documentation

template<class Scalar >

Tempus::StepperBDF2< Scalar >::StepperBDF2 ( )

Default constructor.

Constructs with a default ParameterList.
Can reset ParameterList with setParameterList().
Requires subsequent setModel() and initialize() calls before calling takeStep().

Definition at line 26 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

Tempus::StepperBDF2< Scalar >::StepperBDF2	(	const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &	appModel,
		Teuchos::RCP< Teuchos::ParameterList >	pList = `Teuchos::null`
	)

Constructor.

Definition at line 34 of file Tempus_StepperBDF2_impl.hpp.

Member Function Documentation

template<class Scalar >

void Tempus::StepperBDF2< Scalar >::computeStartUp ( const Teuchos::RCP< SolutionHistory< Scalar > > & solutionHistory )

virtual

Compute the first time step given the supplied startup stepper.

Definition at line 265 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

void Tempus::StepperBDF2< Scalar >::describe	(	Teuchos::FancyOStream &	out,
		const Teuchos::EVerbosityLevel	verbLevel
	)		const

virtual

Definition at line 305 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

std::string Tempus::StepperBDF2< Scalar >::description ( ) const

virtual

Definition at line 297 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperBDF2< Scalar >::getAlpha ( const Scalar dt ) const

inlinevirtual

Return alpha = d(xDot)/dx.

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 105 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperBDF2< Scalar >::getAlpha	(	const Scalar	dt,
		const Scalar	dtOld
	)		const

inlinevirtual

Definition at line 106 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperBDF2< Scalar >::getBeta ( const Scalar ) const

inlinevirtual

Return beta = d(x)/dx.

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 109 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

Teuchos::RCP< Teuchos::ParameterList > Tempus::StepperBDF2< Scalar >::getDefaultParameters ( ) const

virtual

Implements Tempus::Stepper< Scalar >.

Definition at line 362 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

Teuchos::RCP< Tempus::StepperState< Scalar > > Tempus::StepperBDF2< 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 288 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

Teuchos::RCP< Teuchos::ParameterList > Tempus::StepperBDF2< Scalar >::getNonconstParameterList ( )

Definition at line 381 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperBDF2< Scalar >::getOrder ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 90 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperBDF2< Scalar >::getOrderMax ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 92 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperBDF2< Scalar >::getOrderMin ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 91 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

virtual OrderODE Tempus::StepperBDF2< Scalar >::getOrderODE ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 101 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

Teuchos::RCP< const Teuchos::ParameterList > Tempus::StepperBDF2< Scalar >::getValidParameters ( ) const

Definition at line 345 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

void Tempus::StepperBDF2< Scalar >::initialize ( )

virtual

Initialize during construction and after changing input parameters.

Implements Tempus::Stepper< Scalar >.

Definition at line 152 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

virtual bool Tempus::StepperBDF2< Scalar >::isExplicit ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 94 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

virtual bool Tempus::StepperBDF2< Scalar >::isExplicitImplicit ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 96 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

virtual bool Tempus::StepperBDF2< Scalar >::isImplicit ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 95 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

virtual bool Tempus::StepperBDF2< Scalar >::isMultiStepMethod ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 99 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

virtual bool Tempus::StepperBDF2< Scalar >::isOneStepMethod ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 98 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

void Tempus::StepperBDF2< Scalar >::setInitialConditions ( const Teuchos::RCP< SolutionHistory< Scalar > > & solutionHistory )

virtual

Set the initial conditions and make them consistent.

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 168 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

void Tempus::StepperBDF2< Scalar >::setObserver ( Teuchos::RCP< StepperObserver< Scalar > > obs = Teuchos::null )

virtual

Set Observer.

Implements Tempus::Stepper< Scalar >.

Definition at line 131 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

void Tempus::StepperBDF2< Scalar >::setParameterList ( const Teuchos::RCP< Teuchos::ParameterList > & pl )

Definition at line 315 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

void Tempus::StepperBDF2< Scalar >::setStartUpStepper ( std::string startupStepperName )

Set the stepper to use in first step.

Set the startup stepper to a pre-defined stepper in the ParameterList.

The startup stepper is set to stepperName sublist in the Stepper's ParameterList. The stepperName sublist should already be defined in the Stepper's ParameterList. Otherwise it will fail.

Definition at line 57 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

void Tempus::StepperBDF2< Scalar >::setStartUpStepper ( Teuchos::RCP< Teuchos::ParameterList > startupStepperPL = Teuchos::null )

Set the start up stepper to the supplied Parameter sublist.

This adds a new start up stepper Parameter sublist to the Stepper's ParameterList. If the start up stepper sublist is null, it tests if the stepper sublist is set in the Stepper's ParameterList.

Definition at line 78 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

void Tempus::StepperBDF2< 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 193 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

Teuchos::RCP< Teuchos::ParameterList > Tempus::StepperBDF2< Scalar >::unsetParameterList ( )

Definition at line 389 of file Tempus_StepperBDF2_impl.hpp.