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, Teuchos::RCP< Teuchos::ParameterList > pList=Teuchos::null)
	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...

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

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 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	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
Scalar	beta_

Scalar	gamma_

Teuchos::RCP < Teuchos::FancyOStream >	out_

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::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.

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

Definition at line 90 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

template<class Scalar >

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

Constructor.

Definition at line 103 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 428 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

template<class Scalar >

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

virtual

Definition at line 417 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 134 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 136 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

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

virtual

Implements Tempus::Stepper< Scalar >.

Definition at line 551 of file Tempus_StepperNewmarkImplicitAForm_impl.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.

Implements Tempus::Stepper< Scalar >.

Definition at line 405 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

template<class Scalar >

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

Definition at line 573 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 114 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 119 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 118 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 128 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

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

Definition at line 532 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperNewmarkImplicitAForm< Scalar >::getW_xDotDot_coeff ( const Scalar ) const

inlinevirtual

Return W_xDotxDot_coeff = d(xDotDot)/d(xDotDot).

Definition at line 132 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

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

virtual

Initialize during construction and after changing input parameters.

Implements Tempus::Stepper< Scalar >.

Definition at line 140 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 121 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 123 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 122 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 126 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 125 of file Tempus_StepperNewmarkImplicitAForm_decl.hpp.

template<class Scalar >

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

Definition at line 42 of file Tempus_StepperNewmarkImplicitAForm_impl.hpp.

template<class Scalar >

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