Backward Euler time stepper. More...

#include <Tempus_StepperBackwardEuler_decl.hpp>

Inheritance diagram for Tempus::StepperBackwardEuler< Scalar >:

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

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

void	setPredictor (std::string predictorName)
	Set the predictor. More...

void	setPredictor (Teuchos::RCP< Teuchos::ParameterList >predPL=Teuchos::null)
	Set the predictor to the supplied Parameter sublist. This adds a new predictor Parameter sublist to the Stepper's ParameterList. If the predictor sublist is null, it tests if the predictor is set in the Stepper's ParameterList. More...

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

virtual void	takeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
	Take the specified timestep, dt, and return true if successful. More...

virtual void	setInitialGuess (Teuchos::RCP< const Thyra::VectorBase< Scalar > > initial_guess)
	Pass initial guess to Newton solver. 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 void	computePredictor (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
	Compute predictor given the supplied stepper. More...

virtual Teuchos::RCP< Thyra::VectorBase< Scalar > >	getXDotTemp (Teuchos::RCP< const Thyra::VectorBase< Scalar > > x) const
	Provide temporary xDot memory for Stepper if SolutionState doesn't. More...

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 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. 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 bool	getEmbedded () const

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

Public Member Functions inherited from Tempus::Stepper< Scalar >
virtual void	createSubSteppers (std::vector< Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > > models)

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

Public Member Functions inherited from Tempus::StepperOptimizationInterface< Scalar >
	StepperOptimizationInterface ()

virtual	~StepperOptimizationInterface ()

Implementation of StepperOptimizationInterface
Teuchos::RCP< Stepper< Scalar > >	predictorStepper_

Teuchos::RCP< StepperObserver< Scalar > >	stepperObserver_

Teuchos::RCP< StepperBackwardEulerObserver< Scalar > >	stepperBEObserver_

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

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

virtual int	stencilLength () const
	Return the number of solution vectors in the time step stencil. More...

virtual void	computeStepResidual (Thyra::VectorBase< Scalar > &residual, const Teuchos::Array< Teuchos::RCP< const Thyra::VectorBase< Scalar > > > &x, const Teuchos::Array< Scalar > &t, const Thyra::VectorBase< Scalar > &p, const int param_index) const
	Compute time step residual. More...

virtual void	computeStepJacobian (Thyra::LinearOpBase< Scalar > &jacobian, const Teuchos::Array< Teuchos::RCP< const Thyra::VectorBase< Scalar > > > &x, const Teuchos::Array< Scalar > &t, const Thyra::VectorBase< Scalar > &p, const int param_index, const int deriv_index) const
	Compute time step Jacobian. More...

virtual void	computeStepParamDeriv (Thyra::LinearOpBase< Scalar > &deriv, const Teuchos::Array< Teuchos::RCP< const Thyra::VectorBase< Scalar > > > &x, const Teuchos::Array< Scalar > &t, const Thyra::VectorBase< Scalar > &p, const int param_index) const
	Compute time step derivative w.r.t. model parameters. More...

virtual void	computeStepSolver (Thyra::LinearOpWithSolveBase< Scalar > &jacobian_solver, const Teuchos::Array< Teuchos::RCP< const Thyra::VectorBase< Scalar > > > &x, const Teuchos::Array< Scalar > &t, const Thyra::VectorBase< Scalar > &p, const int param_index) const
	Compute time step Jacobian solver. More...

	StepperBackwardEuler ()
	Default Constructor – not allowed. More...

void	computeStepResidDerivImpl (const Thyra::ModelEvaluatorBase::OutArgs< Scalar > &outArgs, const Teuchos::Array< Teuchos::RCP< const Thyra::VectorBase< Scalar > > > &x, const Teuchos::Array< Scalar > &t, const Thyra::VectorBase< Scalar > &p, const int param_index, const int deriv_index=0) const
	Implementation of computeStep*() methods. More...

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_

Detailed Description

template<class Scalar>
class Tempus::StepperBackwardEuler< Scalar >

Backward Euler 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).

Algorithm The single-timestep algorithm for Backward Euler is simply,

Solve $f(\dot{x}=(x_n-x_{n-1})/\Delta t_n, x_n, t_n)=0$ for
$\dot{x}_n \leftarrow (x_n-x_{n-1})/\Delta t_n$ [Optional]
Solve $f(\dot{x}_n,x_n,t_n)=0$ for $\dot{x}_n$ [Optional]

Definition at line 33 of file Tempus_StepperBackwardEuler_decl.hpp.

Constructor & Destructor Documentation

◆ StepperBackwardEuler() [1/2]

template<class Scalar >

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

Constructor.

Definition at line 27 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ StepperBackwardEuler() [2/2]

template<class Scalar>

Tempus::StepperBackwardEuler< Scalar >::StepperBackwardEuler ( )

private

Default Constructor – not allowed.

Member Function Documentation

◆ computePredictor()

template<class Scalar >

void Tempus::StepperBackwardEuler< Scalar >::computePredictor ( const Teuchos::RCP< SolutionHistory< Scalar > > & solutionHistory )

virtual

Compute predictor given the supplied stepper.

Definition at line 221 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ computeStepJacobian()

template<class Scalar >

void Tempus::StepperBackwardEuler< Scalar >::computeStepJacobian	(	Thyra::LinearOpBase< Scalar > &	jacobian,
		const Teuchos::Array< Teuchos::RCP< const Thyra::VectorBase< Scalar > > > &	x,
		const Teuchos::Array< Scalar > &	t,
		const Thyra::VectorBase< Scalar > &	p,
		const int	param_index,
		const int	deriv_index
	)		const

virtual

Compute time step Jacobian.

deriv_index determines which component of x the derivative should be computed with respect to.

Implements Tempus::StepperOptimizationInterface< Scalar >.

Definition at line 381 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ computeStepParamDeriv()

template<class Scalar >

void Tempus::StepperBackwardEuler< Scalar >::computeStepParamDeriv	(	Thyra::LinearOpBase< Scalar > &	deriv,
		const Teuchos::Array< Teuchos::RCP< const Thyra::VectorBase< Scalar > > > &	x,
		const Teuchos::Array< Scalar > &	t,
		const Thyra::VectorBase< Scalar > &	p,
		const int	param_index
	)		const

virtual

Compute time step derivative w.r.t. model parameters.

Implements Tempus::StepperOptimizationInterface< Scalar >.

Definition at line 398 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ computeStepResidDerivImpl()

template<class Scalar >

void Tempus::StepperBackwardEuler< Scalar >::computeStepResidDerivImpl	(	const Thyra::ModelEvaluatorBase::OutArgs< Scalar > &	outArgs,
		const Teuchos::Array< Teuchos::RCP< const Thyra::VectorBase< Scalar > > > &	x,
		const Teuchos::Array< Scalar > &	t,
		const Thyra::VectorBase< Scalar > &	p,
		const int	param_index,
		const int	deriv_index = `0`
	)		const

private

Implementation of computeStep*() methods.

Definition at line 431 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ computeStepResidual()

template<class Scalar >

void Tempus::StepperBackwardEuler< Scalar >::computeStepResidual	(	Thyra::VectorBase< Scalar > &	residual,
		const Teuchos::Array< Teuchos::RCP< const Thyra::VectorBase< Scalar > > > &	x,
		const Teuchos::Array< Scalar > &	t,
		const Thyra::VectorBase< Scalar > &	p,
		const int	param_index
	)		const

virtual

Compute time step residual.

Implements Tempus::StepperOptimizationInterface< Scalar >.

Definition at line 366 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ computeStepSolver()

template<class Scalar >

void Tempus::StepperBackwardEuler< Scalar >::computeStepSolver	(	Thyra::LinearOpWithSolveBase< Scalar > &	jacobian_solver,
		const Teuchos::Array< Teuchos::RCP< const Thyra::VectorBase< Scalar > > > &	x,
		const Teuchos::Array< Scalar > &	t,
		const Thyra::VectorBase< Scalar > &	p,
		const int	param_index
	)		const

virtual

Compute time step Jacobian solver.

Derivative is always w.r.t. the most current solution vector

Implements Tempus::StepperOptimizationInterface< Scalar >.

Definition at line 415 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ describe()

template<class Scalar >

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

virtual

Definition at line 264 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ description()

template<class Scalar >

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

virtual

Definition at line 256 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ getDefaultParameters()

template<class Scalar >

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

virtual

Implements Tempus::Stepper< Scalar >.

Definition at line 320 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ getDefaultStepperState()

template<class Scalar >

Teuchos::RCP< Tempus::StepperState< Scalar > > Tempus::StepperBackwardEuler< 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 247 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ getNonconstParameterList()

template<class Scalar >

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

Definition at line 340 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ getOrder()

template<class Scalar>

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 66 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ getOrderMax()

template<class Scalar>

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 68 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ getOrderMin()

template<class Scalar>

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 67 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ getValidParameters()

template<class Scalar >

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

Definition at line 305 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ getXDotTemp()

template<class Scalar >

Teuchos::RCP< Thyra::VectorBase< Scalar > > Tempus::StepperBackwardEuler< Scalar >::getXDotTemp ( Teuchos::RCP< const Thyra::VectorBase< Scalar > > x ) const

virtual

Provide temporary xDot memory for Stepper if SolutionState doesn't.

Definition at line 211 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ initialize()

template<class Scalar >

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

virtual

Initialize during construction and after changing input parameters.

Implements Tempus::Stepper< Scalar >.

Definition at line 124 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ isExplicit()

template<class Scalar>

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 70 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ isExplicitImplicit()

template<class Scalar>

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 72 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ isImplicit()

template<class Scalar>

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 71 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ isMultiStepMethod()

template<class Scalar>

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 75 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ isOneStepMethod()

template<class Scalar>

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 74 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ setInitialGuess()

template<class Scalar>

virtual void Tempus::StepperBackwardEuler< Scalar >::setInitialGuess ( Teuchos::RCP< const Thyra::VectorBase< Scalar > > initial_guess )

inlinevirtual

Pass initial guess to Newton solver.

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 61 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ setObserver()

template<class Scalar >

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

virtual

Set Observer.

Implements Tempus::Stepper< Scalar >.

Definition at line 103 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ setParameterList()

template<class Scalar >

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

Definition at line 274 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ setPredictor() [1/2]

template<class Scalar >

void Tempus::StepperBackwardEuler< Scalar >::setPredictor ( std::string predictorName )

Set the predictor.

Set the predictor to a pre-defined predictor in the ParameterList. The predictor is set to predictorName sublist in the Stepper's ParameterList. The predictorName sublist should already be defined in the Stepper's ParameterList. Otherwise it will fail.

Definition at line 47 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ setPredictor() [2/2]

template<class Scalar >

void Tempus::StepperBackwardEuler< Scalar >::setPredictor ( Teuchos::RCP< Teuchos::ParameterList > predPL = Teuchos::null )

Set the predictor to the supplied Parameter sublist. This adds a new predictor Parameter sublist to the Stepper's ParameterList. If the predictor sublist is null, it tests if the predictor is set in the Stepper's ParameterList.

Definition at line 66 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ stencilLength()

template<class Scalar >

int Tempus::StepperBackwardEuler< Scalar >::stencilLength ( ) const

virtual

Return the number of solution vectors in the time step stencil.

Implements Tempus::StepperOptimizationInterface< Scalar >.

Definition at line 358 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ takeStep()

template<class Scalar >

void Tempus::StepperBackwardEuler< 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 139 of file Tempus_StepperBackwardEuler_impl.hpp.

◆ unsetParameterList()

template<class Scalar >

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

Definition at line 348 of file Tempus_StepperBackwardEuler_impl.hpp.

Member Data Documentation

◆ initial_guess_

template<class Scalar>

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

private

Definition at line 153 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ predictorStepper_

template<class Scalar>

Teuchos::RCP<Stepper<Scalar> > Tempus::StepperBackwardEuler< Scalar >::predictorStepper_

private

Definition at line 148 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ stepperBEObserver_

template<class Scalar>

Teuchos::RCP<StepperBackwardEulerObserver<Scalar> > Tempus::StepperBackwardEuler< Scalar >::stepperBEObserver_

private

Definition at line 150 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ stepperObserver_

template<class Scalar>

Teuchos::RCP<StepperObserver<Scalar> > Tempus::StepperBackwardEuler< Scalar >::stepperObserver_

private

Definition at line 149 of file Tempus_StepperBackwardEuler_decl.hpp.

◆ xDotTemp_

template<class Scalar>

Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperBackwardEuler< Scalar >::xDotTemp_

mutableprivate

Definition at line 152 of file Tempus_StepperBackwardEuler_decl.hpp.

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

/home/abuild/rpmbuild/BUILD/Trilinos-trilinos-release-12-14-1/packages/tempus/src/Tempus_StepperBackwardEuler_decl.hpp
/home/abuild/rpmbuild/BUILD/Trilinos-trilinos-release-12-14-1/packages/tempus/src/Tempus_StepperBackwardEuler_impl.hpp

Public Member Functions

Implementation of StepperOptimizationInterface

Additional Inherited Members

Detailed Description

template<class Scalar> class Tempus::StepperBackwardEuler< Scalar >

Constructor & Destructor Documentation

◆ StepperBackwardEuler() [1/2]

◆ StepperBackwardEuler() [2/2]

Member Function Documentation

◆ computePredictor()

◆ computeStepJacobian()

◆ computeStepParamDeriv()

◆ computeStepResidDerivImpl()

◆ computeStepResidual()

◆ computeStepSolver()

◆ describe()

◆ description()

◆ getDefaultParameters()

◆ getDefaultStepperState()

◆ getNonconstParameterList()

◆ getOrder()

◆ getOrderMax()

◆ getOrderMin()

◆ getValidParameters()

◆ getXDotTemp()

◆ initialize()

◆ isExplicit()

◆ isExplicitImplicit()

◆ isImplicit()

◆ isMultiStepMethod()

◆ isOneStepMethod()

◆ setInitialGuess()

◆ setObserver()

◆ setParameterList()

◆ setPredictor() [1/2]

◆ setPredictor() [2/2]

◆ stencilLength()

◆ takeStep()

◆ unsetParameterList()

Member Data Documentation

◆ initial_guess_

◆ predictorStepper_

◆ stepperBEObserver_

◆ stepperObserver_

◆ xDotTemp_

template<class Scalar>
class Tempus::StepperBackwardEuler< Scalar >