Newmark time stepper in acceleration form (a-form). More...

#include <Tempus_StepperNewmarkImplicitAForm_decl.hpp>

Inheritance diagram for Tempus::StepperNewmarkImplicitAForm< Scalar >:

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

	StepperNewmarkImplicitAForm (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, const Teuchos::RCP< StepperObserver< Scalar > > &obs, const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &solver, bool useFSAL, std::string ICConsistency, bool ICConsistencyCheck, bool zeroInitialGuess, std::string schemeName, Scalar beta, Scalar gamma)
	Constructor. More...

virtual Scalar	getW_xDotDot_coeff (const Scalar) const
	Return W_xDotxDot_coeff = d(xDotDot)/d(xDotDot). More...

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

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

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

void	predictVelocity (Thyra::VectorBase< Scalar > &vPred, const Thyra::VectorBase< Scalar > &v, const Thyra::VectorBase< Scalar > &a, const Scalar dt) const

void	predictDisplacement (Thyra::VectorBase< Scalar > &dPred, const Thyra::VectorBase< Scalar > &d, const Thyra::VectorBase< Scalar > &v, const Thyra::VectorBase< Scalar > &a, const Scalar dt) const

void	correctVelocity (Thyra::VectorBase< Scalar > &v, const Thyra::VectorBase< Scalar > &vPred, const Thyra::VectorBase< Scalar > &a, const Scalar dt) const

void	correctDisplacement (Thyra::VectorBase< Scalar > &d, const Thyra::VectorBase< Scalar > &dPred, const Thyra::VectorBase< Scalar > &a, const Scalar dt) const

void	setSchemeName (std::string schemeName)

void	setBeta (Scalar beta)

void	setGamma (Scalar gamma)

virtual bool	getUseFSALDefault () const

virtual std::string	getICConsistencyDefault () const

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

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

virtual Teuchos::RCP < StepperObserver< Scalar > >	getObserver () const
	Get Observer. 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 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 (Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > solver=Teuchos::null)
	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 > > 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 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 >
void	setStepperType (std::string s)

std::string	getStepperType () const

void	setUseFSAL (bool a)

bool	getUseFSAL () const

void	setICConsistency (std::string s)

std::string	getICConsistency () const

void	setICConsistencyCheck (bool c)

bool	getICConsistencyCheck () const

virtual bool	getICConsistencyCheckDefault () const

virtual std::string	description () const

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

Private Attributes
std::string	schemeName_

Scalar	beta_

Scalar	gamma_

Teuchos::RCP < Teuchos::FancyOStream >	out_

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

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

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

bool	zeroInitialGuess_

Teuchos::RCP< StepperObserver < Scalar > >	stepperObserver_

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

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

Detailed Description

template<class Scalar>
class Tempus::StepperNewmarkImplicitAForm< Scalar >

Newmark time stepper in acceleration form (a-form).

Here, we implement the Newmark scheme in predictor/corrector form; see equations (34)-(35) in: A. Mota, W. Klug, M. Ortiz, "Finite element simulation of firearm injury to the human cranium", Computational Mechanics 31(1) 115-121 (2003).

Newmark has two parameters: $\beta$ and $\gamma$ , both of which need to be in the range $[0,1]$ . Newmark can be an explicit or implicit method, depending on the value of the $\beta$ parameter. If $\beta = 0$ , the method is explicit. Regardless of whether the method is implicit or explicit, a linear solve is required. This linear solve can be optimized, however, for the explicit case by lumping the mass matrix. This optimization can be invoked by running "Newmark Explicit d-Form" Stepper through the Piro::TempusSolver class.

Newmark is second order accurate if $\gamma = 0.5$ ; otherwise it is first order accurate. Some additional properties about the Newmark scheme can be found here.

The governing equation solved by this stepper is

$\mathbf{M}\, \ddot{\mathbf{x}} + \mathbf{C}\, \dot{\mathbf{x}} + \mathbf{K}\, \mathbf{x} + \mathbf{F}(t) = 0$

For the A-form (i.e., solving for the acceleration, $\mathbf{a} = \ddot{\mathbf{x}}$ ), we have the following implicit ODE

$\mathbf{M}\, \mathbf{a} + \mathbf{C}\, \mathbf{v} + \mathbf{K}\, \mathbf{d} + \mathbf{F}(t) = \mathbf{f}(\mathbf{d}, \mathbf{v}, \mathbf{a}, t) = 0$

where $\mathbf{v} = \dot{\mathbf{x}}$ and $\mathbf{d} = \mathbf{x}$ .

Algorithm The algorithm for the Newmark implicit A-form with predictors and correctors is

$\mathbf{d}^{\ast} = \mathbf{d}^{n-1} + \Delta t \mathbf{v}^{n-1} + \Delta t^2 (1-2 \beta) \mathbf{a}^{n-1} / 2$
$\mathbf{v}^{\ast} = \mathbf{v}^{n-1} + \Delta t (1-\gamma) \mathbf{a}^{n-1}$
Solve for where
- $\mathbf{d}^n = \mathbf{d}^{\ast} + \beta \Delta t^2 \mathbf{a}^n$
- $\mathbf{v}^n = \mathbf{v}^{\ast} + \gamma \Delta t \mathbf{a}^n$

The First-Step-As-Last (FSAL) principle is part of the Newmark implicit A-Form as the acceleration from the previous time step is used for the predictors. The default is to set useFSAL=true, and useFSAL=false will be ignored.

Definition at line 73 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

Constructor & Destructor Documentation

template<class Scalar >

Tempus::StepperNewmarkImplicitAForm< Scalar >::StepperNewmarkImplicitAForm ( )

Default constructor.

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

Definition at line 167 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

template<class Scalar >

Tempus::StepperNewmarkImplicitAForm< Scalar >::StepperNewmarkImplicitAForm	(	const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &	appModel,
		const Teuchos::RCP< StepperObserver< Scalar > > &	obs,
		const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &	solver,
		bool	useFSAL,
		std::string	ICConsistency,
		bool	ICConsistencyCheck,
		bool	zeroInitialGuess,
		std::string	schemeName,
		Scalar	beta,
		Scalar	gamma
	)

Constructor.

Definition at line 186 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

Member Function Documentation

template<class Scalar >

void Tempus::StepperNewmarkImplicitAForm< Scalar >::correctDisplacement	(	Thyra::VectorBase< Scalar > &	d,
		const Thyra::VectorBase< Scalar > &	dPred,
		const Thyra::VectorBase< Scalar > &	a,
		const Scalar	dt
	)		const

Definition at line 76 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

template<class Scalar >

void Tempus::StepperNewmarkImplicitAForm< Scalar >::correctVelocity	(	Thyra::VectorBase< Scalar > &	v,
		const Thyra::VectorBase< Scalar > &	vPred,
		const Thyra::VectorBase< Scalar > &	a,
		const Scalar	dt
	)		const

Definition at line 62 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

template<class Scalar >

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

virtual

Definition at line 510 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

template<class Scalar >

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

inlinevirtual

Return alpha = d(xDot)/d(xDotDot).

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 143 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperNewmarkImplicitAForm< Scalar >::getBeta ( const Scalar dt ) const

inlinevirtual

Return beta = d(x)/d(xDotDot).

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 145 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

Teuchos::RCP< Tempus::StepperState< Scalar > > Tempus::StepperNewmarkImplicitAForm< 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.

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<class Scalar> class Tempus::StepperNewmarkImplicitAForm< Scalar >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class Scalar>
class Tempus::StepperNewmarkImplicitAForm< Scalar >