HHT-Alpha time stepper. More...

#include <Tempus_StepperHHTAlpha_decl.hpp>

Inheritance diagram for Tempus::StepperHHTAlpha< Scalar >:

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

	StepperHHTAlpha (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &solver, bool useFSAL, std::string ICConsistency, bool ICConsistencyCheck, bool zeroInitialGuess, std::string schemeName, Scalar beta, Scalar gamma, Scalar alpha_f_, Scalar alpha_m_, const Teuchos::RCP< StepperHHTAlphaAppAction< Scalar > > &stepperHHTAlphaAppAction)
	Constructor. More...

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

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

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

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

virtual bool	isValidSetup (Teuchos::FancyOStream &out) 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	predictVelocity_alpha_f (Thyra::VectorBase< Scalar > &vPred, const Thyra::VectorBase< Scalar > &v) const

void	predictDisplacement_alpha_f (Thyra::VectorBase< Scalar > &dPred, const Thyra::VectorBase< Scalar > &d) const

void	correctAcceleration (Thyra::VectorBase< Scalar > &a_n_plus1, const Thyra::VectorBase< Scalar > &a_n) 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)

void	setAlphaF (Scalar alpha_f)

void	setAlphaM (Scalar alpha_m)

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

void	setStepperImplicitValues (Teuchos::RCP< Teuchos::ParameterList > pl)
	Set StepperImplicit member data from the ParameterList. More...

void	setStepperSolverValues (Teuchos::RCP< Teuchos::ParameterList > pl)
	Set solver from ParameterList. More...

void	setSolverName (std::string i)
	Set the Solver Name. More...

std::string	getSolverName () const
	Get the Solver Name. More...

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 >
void	setStepperValues (const Teuchos::RCP< Teuchos::ParameterList > pl)
	Set Stepper member data from ParameterList. More...

Teuchos::RCP < Teuchos::ParameterList >	getValidParametersBasic () const
	Add basic parameters to Steppers ParameterList. More...

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

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

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

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

void	setStepperName (std::string s)
	Set the stepper name. More...

std::string	getStepperName () const
	Get the stepper name. More...

std::string	getStepperType () const
	Get the stepper type. The stepper type is used as an identifier for the stepper, and can only be set by the derived Stepper class. More...

virtual void	setUseFSAL (bool a)

void	setUseFSALTrueOnly (bool a)

void	setUseFSALFalseOnly (bool a)

bool	getUseFSAL () const

void	setICConsistency (std::string s)

std::string	getICConsistency () const

void	setICConsistencyCheck (bool c)

bool	getICConsistencyCheck () const

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStepperX ()
	Get Stepper x. More...

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStepperXDot ()
	Get Stepper xDot. More...

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStepperXDotDot ()
	Get Stepper xDotDot. 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

Public Member Functions inherited from Teuchos::Describable
void	describe (std::ostream &out, const EVerbosityLevel verbLevel=verbLevel_default) const

virtual	~Describable ()

	LabeledObject ()

virtual	~LabeledObject ()

virtual void	setObjectLabel (const std::string &objectLabel)

virtual std::string	getObjectLabel () const

DescribableStreamManipulatorState	describe (const Describable &describable, const EVerbosityLevel verbLevel=Describable::verbLevel_default)

std::ostream &	operator<< (std::ostream &os, const DescribableStreamManipulatorState &d)

Public Member Functions inherited from Teuchos::VerboseObject< Stepper< Scalar > >
	VerboseObject (const EVerbosityLevel verbLevel=VERB_DEFAULT, const RCP< FancyOStream > &oStream=Teuchos::null)

virtual const VerboseObject &	setVerbLevel (const EVerbosityLevel verbLevel) const

virtual const VerboseObject &	setOverridingVerbLevel (const EVerbosityLevel verbLevel) const

virtual EVerbosityLevel	getVerbLevel () const

TEUCHOSPARAMETERLIST_LIB_DLL_EXPORT RCP< const ParameterList >	getValidVerboseObjectSublist ()

TEUCHOSPARAMETERLIST_LIB_DLL_EXPORT void	setupVerboseObjectSublist (ParameterList *paramList)

TEUCHOSPARAMETERLIST_LIB_DLL_EXPORT void	readVerboseObjectSublist (ParameterList paramList, RCP< FancyOStream > oStream, EVerbosityLevel *verbLevel)

void	readVerboseObjectSublist (ParameterList paramList, VerboseObject< ObjectType > verboseObject)

Public Member Functions inherited from Teuchos::VerboseObjectBase
virtual	~VerboseObjectBase ()

	VerboseObjectBase (const RCP< FancyOStream > &oStream=Teuchos::null)

virtual const VerboseObjectBase &	setOStream (const RCP< FancyOStream > &oStream) const

virtual const VerboseObjectBase &	setOverridingOStream (const RCP< FancyOStream > &oStream) const

virtual VerboseObjectBase &	setLinePrefix (const std::string &linePrefix)

virtual RCP< FancyOStream >	getOStream () const

virtual RCP< FancyOStream >	getOverridingOStream () const

virtual std::string	getLinePrefix () const

virtual OSTab	getOSTab (const int tabs=1, const std::string &linePrefix="") const

Private Attributes
Teuchos::RCP < StepperHHTAlphaAppAction < Scalar > >	stepperHHTAlphaAppAction_

std::string	schemeName_

Scalar	beta_

Scalar	gamma_

Scalar	alpha_f_

Scalar	alpha_m_

Teuchos::RCP < Teuchos::FancyOStream >	out_

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

virtual void	setAppAction (Teuchos::RCP< StepperHHTAlphaAppAction< Scalar > > appAction)

virtual Teuchos::RCP < StepperHHTAlphaAppAction < Scalar > >	getAppAction () const

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

Additional Inherited Members
Static Public Member Functions inherited from Teuchos::VerboseObject< Stepper< Scalar > >
static void	setDefaultVerbLevel (const EVerbosityLevel defaultVerbLevel)

static EVerbosityLevel	getDefaultVerbLevel ()

Static Public Member Functions inherited from Teuchos::VerboseObjectBase
static void	setDefaultOStream (const RCP< FancyOStream > &defaultOStream)

static RCP< FancyOStream >	getDefaultOStream ()

Static Public Attributes inherited from Teuchos::Describable
static const EVerbosityLevel	verbLevel_default

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...

void	setStepperType (std::string s)
	Set the stepper type. More...

Protected Member Functions inherited from Teuchos::VerboseObject< Stepper< Scalar > >
void	initializeVerboseObject (const EVerbosityLevel verbLevel=VERB_DEFAULT, const RCP< FancyOStream > &oStream=Teuchos::null)

Protected Member Functions inherited from Teuchos::VerboseObjectBase
void	initializeVerboseObjectBase (const RCP< FancyOStream > &oStream=Teuchos::null)

virtual void	informUpdatedVerbosityState () const

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_

std::string	solverName_

Protected Attributes inherited from Tempus::Stepper< Scalar >
bool	useFSAL_ = false
	Use First-Same-As-Last (FSAL) principle. More...

bool	isInitialized_ = false
	True if stepper's member data is initialized. More...

Detailed Description

template<class Scalar>
class Tempus::StepperHHTAlpha< Scalar >

HHT-Alpha time stepper.

Here, we implement the HHT-Alpha scheme in predictor/corrector form; see equations (10) and (13)-(19) in: G.M. Hulbert, J. Chung, "Explicit time integration algorithms for structural dynamics with optimal numerical dissipation", Comput. Methods Appl. Mech. Engrg. 137 175-188 (1996).

There are four parameters in the scheme: $\alpha_m$ , $\alpha_f$ , $\beta$ and $\gamma$ , all of which must be in the range $[0,1]$ . When $\alpha_m=\alpha_f = 0$ , the scheme reduces to the Newmark Beta scheme (see Tempus::StepperNewmark for details). Like the Newmark Beta scheme, the HHT-Alpha scheme can be either first or second order accurate, and either explicit or implicit.

Although the general form of the scheme has been implemented in Tempus, it has only been verified for the case when $\alpha_m=\alpha_f = 0$ (corresponding to the Newmark Beta) scheme, so other values for these parameters are not allowed at the present time. Also, note that, like the Newmark Beta stepper, the linear solve for the explicit version of this scheme has not been optimized (the mass matrix is not lumped).

The First-Same-As-Last (FSAL) principle is not used with the HHT-Alpha method.

Definition at line 46 of file Tempus_StepperHHTAlpha_decl.hpp.

Constructor & Destructor Documentation

template<class Scalar >

Tempus::StepperHHTAlpha< Scalar >::StepperHHTAlpha ( )

Default constructor.

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

Definition at line 241 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

Tempus::StepperHHTAlpha< Scalar >::StepperHHTAlpha	(	const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &	appModel,
		const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &	solver,
		bool	useFSAL,
		std::string	ICConsistency,
		bool	ICConsistencyCheck,
		bool	zeroInitialGuess,
		std::string	schemeName,
		Scalar	beta,
		Scalar	gamma,
		Scalar	alpha_f_,
		Scalar	alpha_m_,
		const Teuchos::RCP< StepperHHTAlphaAppAction< Scalar > > &	stepperHHTAlphaAppAction
	)

Constructor.

Definition at line 262 of file Tempus_StepperHHTAlpha_impl.hpp.

Member Function Documentation

template<class Scalar >

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

virtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 314 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

void Tempus::StepperHHTAlpha< Scalar >::setAppAction ( Teuchos::RCP< StepperHHTAlphaAppAction< Scalar > > appAction )

virtual

Definition at line 300 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

virtual Teuchos::RCP<StepperHHTAlphaAppAction<Scalar> > Tempus::StepperHHTAlpha< Scalar >::getAppAction ( ) const

inlinevirtual

Definition at line 80 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

virtual void Tempus::StepperHHTAlpha< Scalar >::setInitialConditions ( const Teuchos::RCP< SolutionHistory< Scalar > > & )

inlinevirtual

Set the initial conditions and make them consistent.

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 84 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

void Tempus::StepperHHTAlpha< 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 336 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

Teuchos::RCP< Tempus::StepperState< Scalar > > Tempus::StepperHHTAlpha< 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 475 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 93 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 97 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 98 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 100 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 101 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 102 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 104 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 105 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 106 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperHHTAlpha< Scalar >::getW_xDotDot_coeff ( const Scalar dt ) const

inlinevirtual

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

Definition at line 110 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

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

inlinevirtual

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

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 113 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

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

inlinevirtual

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

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 115 of file Tempus_StepperHHTAlpha_decl.hpp.

template<class Scalar >

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

virtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 541 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

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

virtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 487 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

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

virtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 513 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

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

Definition at line 24 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

void Tempus::StepperHHTAlpha< 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 38 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

void Tempus::StepperHHTAlpha< Scalar >::predictVelocity_alpha_f	(	Thyra::VectorBase< Scalar > &	vPred,
		const Thyra::VectorBase< Scalar > &	v
	)		const

Definition at line 57 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

void Tempus::StepperHHTAlpha< Scalar >::predictDisplacement_alpha_f	(	Thyra::VectorBase< Scalar > &	dPred,
		const Thyra::VectorBase< Scalar > &	d
	)		const

Definition at line 70 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

void Tempus::StepperHHTAlpha< Scalar >::correctAcceleration	(	Thyra::VectorBase< Scalar > &	a_n_plus1,
		const Thyra::VectorBase< Scalar > &	a_n
	)		const

Definition at line 82 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

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

Definition at line 97 of file Tempus_StepperHHTAlpha_impl.hpp.

template<class Scalar >

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