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, const Teuchos::RCP< StepperObserver< Scalar > > &obs, const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &solver, const Teuchos::RCP< Stepper< Scalar > > &startUpStepper, bool useFSAL, std::string ICConsistency, bool ICConsistencyCheck, bool zeroInitialGuess)
	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...

virtual bool	getICConsistencyCheckDefault () const

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

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

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

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

virtual Teuchos::RCP < StepperObserver< Scalar > >	getObserver () const
	Get Observer. More...

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

void	setStartUpStepper (Teuchos::RCP< Stepper< Scalar > > startupStepper)
	Set the start up stepper. 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

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

Public Member Functions inherited from Tempus::StepperImplicit< Scalar >
virtual Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > >	getModel ()

virtual Teuchos::RCP< const WrapperModelEvaluator< Scalar > >	getWrapperModel ()

virtual void	setDefaultSolver ()

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

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

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 residual, f(x, xDot, t, p). More...

virtual void	setInitialGuess (Teuchos::RCP< const Thyra::VectorBase< Scalar > > initialGuess)
	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

Public Member Functions inherited from Tempus::Stepper< Scalar >
virtual void	setNonConstModel (const Teuchos::RCP< Thyra::ModelEvaluator< Scalar > > &)

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

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

void	setStepperType (std::string s)

std::string	getStepperType () const

void	setUseFSAL (bool a)

bool	getUseFSAL () const

virtual bool	getUseFSALDefault () const

void	setICConsistency (std::string s)

std::string	getICConsistency () const

virtual std::string	getICConsistencyDefault () const

void	setICConsistencyCheck (bool c)

bool	getICConsistencyCheck () const

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStepperX (Teuchos::RCP< SolutionState< Scalar > > state)
	Get x from SolutionState or 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...

virtual std::string	description () const

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

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

Teuchos::RCP < StepperObserverComposite < Scalar > >	stepperObserver_

Teuchos::RCP < StepperBDF2Observer< Scalar > >	stepperBDF2Observer_

Scalar	order_ = Scalar(2.0)

Additional Inherited Members
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...

Protected Attributes inherited from Tempus::StepperImplicit< Scalar >
Teuchos::RCP < WrapperModelEvaluator < Scalar > >	wrapperModel_

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

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

bool	zeroInitialGuess_

Teuchos::RCP< StepperObserver < Scalar > >	stepperObserver_

Protected Attributes inherited from Tempus::Stepper< Scalar >
bool	isInitialized_ = false
	True if stepper's member data is initialized. More...

Detailed Description

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

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

For the implicit ODE system, $\mathcal{F}(\dot{x},x,t) = 0$ , 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).

Iteration Matrix, . Recalling that the definition of the iteration matrix, $W$ , is

$W = \alpha \frac{\partial \mathcal{F}_n}{\partial \dot{x}_n} + \beta \frac{\partial \mathcal{F}_n}{\partial x_n},$

where $\alpha \equiv \frac{\partial \dot{x}_n(x_n) }{\partial x_n},$ and $\beta \equiv \frac{\partial x_n}{\partial x_n} = 1$ , and the time derivative for BDF2 is

$\dot{x}_n(x_n) = \frac{2\tau_n + \tau_{n-1}}{\tau_n + \tau_{n-1}} \left[ \frac{x_n-x_{n-1}}{\tau_n}\right] - \frac{\tau_n}{\tau_n + \tau_{n-1}} \left[ \frac{x_{n-1}-x_{n-2}}{\tau_{n-1}}\right],$

where $\Delta t_n = \tau_n = t_n - t_{n-1}$ , we can determine that $\alpha = \frac{2\tau_n + \tau_{n-1}}{(\tau_n + \tau_{n-1})\tau_n}$ and $\beta = 1$ , and therefore write

$W = \frac{2\tau_n + \tau_{n-1}}{(\tau_n + \tau_{n-1})\tau_n} \frac{\partial \mathcal{F}_n}{\partial \dot{x}_n} + \frac{\partial \mathcal{F}_n}{\partial x_n}.$

Definition at line 76 of file Tempus_StepperBDF2_decl.hpp.

Constructor & Destructor Documentation

template<class Scalar >

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

Default constructor.

Requires the following calls before takeStep(): setModel() and initialize().

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,
		const Teuchos::RCP< StepperObserver< Scalar > > &	obs,
		const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &	solver,
		const Teuchos::RCP< Stepper< Scalar > > &	startUpStepper,
		bool	useFSAL,
		std::string	ICConsistency,
		bool	ICConsistencyCheck,
		bool	zeroInitialGuess
	)

Constructor.

Constructs a fully initialized stepper.

Definition at line 41 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 248 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

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

virtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 280 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 144 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 145 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 148 of file Tempus_StepperBDF2_decl.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 271 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

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

inlinevirtual

Reimplemented from Tempus::Stepper< Scalar >.

Definition at line 154 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

virtual Teuchos::RCP<StepperObserver<Scalar> > Tempus::StepperBDF2< Scalar >::getObserver ( ) const

inlinevirtual

Get Observer.

Reimplemented from Tempus::Stepper< Scalar >.

Definition at line 109 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 129 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 131 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 130 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 140 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

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

virtual

Implements Tempus::Stepper< Scalar >.

Definition at line 328 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

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

virtual

Initialize during construction and after changing input parameters.

Reimplemented from Tempus::Stepper< Scalar >.

Definition at line 148 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 133 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 135 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 134 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 138 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 137 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

bool Tempus::StepperBDF2< Scalar >::isValidSetup ( Teuchos::FancyOStream & out ) const

virtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 305 of file Tempus_StepperBDF2_impl.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 155 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

void Tempus::StepperBDF2< Scalar >::setModel ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > & appModel )

virtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 70 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

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

virtual

Set Observer.

Reimplemented from Tempus::Stepper< Scalar >.

Definition at line 125 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

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

Set the stepper to use in first step.

Set the startup stepper to a default stepper.

Definition at line 85 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >

void Tempus::StepperBDF2< Scalar >::setStartUpStepper ( Teuchos::RCP< Stepper< Scalar > > startupStepper )

Set the start up stepper.

Definition at line 103 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 171 of file Tempus_StepperBDF2_impl.hpp.

Member Data Documentation

template<class Scalar >

Scalar Tempus::StepperBDF2< Scalar >::order_ = Scalar(2.0)

private

Definition at line 170 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

Teuchos::RCP<Stepper<Scalar> > Tempus::StepperBDF2< Scalar >::startUpStepper_

private

Definition at line 167 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

Teuchos::RCP<StepperBDF2Observer<Scalar> > Tempus::StepperBDF2< Scalar >::stepperBDF2Observer_

private

Definition at line 169 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >

Teuchos::RCP<StepperObserverComposite<Scalar> > Tempus::StepperBDF2< Scalar >::stepperObserver_

private

Definition at line 168 of file Tempus_StepperBDF2_decl.hpp.

The documentation for this class was generated from the following files:

http://docs.trilinos.org/r13.0/packages/tempus/src/Tempus_StepperBDF2_decl.hpp
http://docs.trilinos.org/r13.0/packages/tempus/src/Tempus_StepperBDF2_impl.hpp

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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