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Tempus::StepperBDF2< Scalar > Class Template Reference

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

#include <Tempus_StepperBDF2_decl.hpp>

Inheritance diagram for Tempus::StepperBDF2< Scalar >:
Tempus::StepperImplicit< Scalar > Tempus::Stepper< Scalar > Teuchos::Describable Teuchos::VerboseObject< Stepper< Scalar > > Teuchos::LabeledObject Teuchos::VerboseObjectBase

Public Member Functions

 StepperBDF2 ()
 Default constructor. More...
 
 StepperBDF2 (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &solver, const Teuchos::RCP< Stepper< Scalar > > &startUpStepper, bool useFSAL, std::string ICConsistency, bool ICConsistencyCheck, bool zeroInitialGuess, const Teuchos::RCP< StepperBDF2AppAction< Scalar > > &stepperBDF2AppAction)
 
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...
 
Teuchos::RCP< const
Teuchos::ParameterList
getValidParameters () const
 
virtual bool isValidSetup (Teuchos::FancyOStream &out) const
 
- 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 () const override
 
virtual Teuchos::RCP< const
WrapperModelEvaluator< Scalar > > 
getWrapperModel ()
 
virtual void setDefaultSolver ()
 
virtual void setSolver (Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > solver) override
 Set solver. More...
 
virtual Teuchos::RCP
< Thyra::NonlinearSolverBase
< Scalar > > 
getSolver () const override
 Get solver. 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, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &y=Teuchos::null, const int index=-1)
 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) override
 Pass initial guess to Newton solver (only relevant for implicit solvers) More...
 
virtual void setZeroInitialGuess (bool zIG)
 
virtual bool getZeroInitialGuess () const
 
virtual Scalar getInitTimeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &) const override
 
- 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 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 VerboseObjectsetVerbLevel (const EVerbosityLevel verbLevel) const
 
virtual const VerboseObjectsetOverridingVerbLevel (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 VerboseObjectBasesetOStream (const RCP< FancyOStream > &oStream) const
 
virtual const VerboseObjectBasesetOverridingOStream (const RCP< FancyOStream > &oStream) const
 
virtual VerboseObjectBasesetLinePrefix (const std::string &linePrefix)
 
virtual RCP< FancyOStreamgetOStream () const
 
virtual RCP< FancyOStreamgetOverridingOStream () const
 
virtual std::string getLinePrefix () const
 
virtual OSTab getOSTab (const int tabs=1, const std::string &linePrefix="") const
 

Private Attributes

Teuchos::RCP< Stepper< Scalar > > startUpStepper_
 
Teuchos::RCP
< StepperBDF2AppAction< Scalar > > 
stepperBDF2AppAction_
 
Scalar order_ = Scalar(2.0)
 

Basic stepper methods

virtual void setModel (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel)
 Set the model. More...
 
virtual void setAppAction (Teuchos::RCP< StepperBDF2AppAction< Scalar > > appAction)
 
virtual Teuchos::RCP
< StepperBDF2AppAction< Scalar > > 
getAppAction () const
 
void setStartUpStepper (std::string startupStepperType)
 Set the stepper to use in first step. More...
 
void setStartUpStepper (Teuchos::RCP< Stepper< Scalar > > startupStepper)
 
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
 

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< FancyOStreamgetDefaultOStream ()
 
- 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_
 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 The single-timestep algorithm for BDF2 is

\begin{center} \parbox{5in}{ \rule{5in}{0.4pt} \\ {\bf Algorithm} BDF2 \\ \rule{5in}{0.4pt} \vspace{-15pt} \begin{enumerate} \setlength{\itemsep}{0pt} \setlength{\parskip}{0pt} \setlength{\parsep}{0pt} \item {\bf if ( "Startup", i.e., number of states $<$ 3) then} \item \quad {\bf Take timestep with startup Stepper.} \item \quad {\bf return} \item {\bf endif} \item {\it appAction.execute(solutionHistory, stepper, BEGIN\_STEP)} \item {\bf Get old states $x_{n-1}$ and $x_{n-2}$.} \item {\bf Set ODE parameters.} \item \quad {\bf Time derivative: } $\dot{x}_{n} = \frac{2\tau_n + \tau_{n-1}}{\tau_n + \tau_{n-1}} \left[ \frac{x_n-x_{n-1}}{\tau_n}\right] - \frac{\tau_n}{\tau_n + \tau_{n-1}} \left[ \frac{x_{n-1}-x_{n-2}}{\tau_{n-1}}\right]$ \item \quad {\bf Alpha: $\alpha = \frac{2\tau_n + \tau_{n-1}}{(\tau_n + \tau_{n-1})\tau_n}$} \item \quad {\bf Beta: $\beta = 1$} \item {\it appAction.execute(solutionHistory, stepper, BEFORE\_SOLVE)} \item {\bf Solve $\mathcal{F}(\dot{x}_n,x_n,t_n) = 0$ for $x_n$.} \item {\it appAction.execute(solutionHistory, stepper, AFTER\_SOLVE)} \item {\bf Update} $\dot{x}_{n} = \frac{2\tau_n + \tau_{n-1}}{\tau_n + \tau_{n-1}} \left[ \frac{x_n-x_{n-1}}{\tau_n}\right] - \frac{\tau_n}{\tau_n + \tau_{n-1}} \left[ \frac{x_{n-1}-x_{n-2}}{\tau_{n-1}}\right]$ \item {\it appAction.execute(solutionHistory, stepper, END\_STEP)} \end{enumerate} \vspace{-10pt} \rule{5in}{0.4pt} } \end{center}

The startup stepper allows BDF2 to use user-specified Stepper for the first timestep in order to populate the SolutionHistory with past states. A one-step startup stepper is perfect for this situation, e.g., Backward Euler or RK4. The default startup stepper is 'DIRK 1 Stage Theta Method', which is second order accurate and allows an overall second-order solution.

The First-Same-As-Last (FSAL) principle is not needed for BDF2. The default is to set useFSAL=false, however useFSAL=true will also work but have no affect (i.e., no-op).

Iteration Matrix, $W$. 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 103 of file Tempus_StepperBDF2_decl.hpp.

Constructor & Destructor Documentation

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

Default constructor.

Definition at line 20 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >
Tempus::StepperBDF2< Scalar >::StepperBDF2 ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  appModel,
const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &  solver,
const Teuchos::RCP< Stepper< Scalar > > &  startUpStepper,
bool  useFSAL,
std::string  ICConsistency,
bool  ICConsistencyCheck,
bool  zeroInitialGuess,
const Teuchos::RCP< StepperBDF2AppAction< Scalar > > &  stepperBDF2AppAction 
)

Definition at line 35 of file Tempus_StepperBDF2_impl.hpp.

Member Function Documentation

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

Set the model.

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 60 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >
void Tempus::StepperBDF2< Scalar >::setAppAction ( Teuchos::RCP< StepperBDF2AppAction< Scalar > >  appAction)
virtual

Definition at line 111 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >
virtual Teuchos::RCP<StepperBDF2AppAction<Scalar> > Tempus::StepperBDF2< Scalar >::getAppAction ( ) const
inlinevirtual

Definition at line 127 of file Tempus_StepperBDF2_decl.hpp.

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

Set the stepper to use in first step.

Definition at line 74 of file Tempus_StepperBDF2_impl.hpp.

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

Definition at line 90 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 125 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 131 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 148 of file Tempus_StepperBDF2_impl.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 259 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >
virtual Scalar Tempus::StepperBDF2< Scalar >::getOrder ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 149 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >
virtual Scalar Tempus::StepperBDF2< Scalar >::getOrderMin ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 150 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >
virtual Scalar Tempus::StepperBDF2< Scalar >::getOrderMax ( ) const
inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 151 of file Tempus_StepperBDF2_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 153 of file Tempus_StepperBDF2_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 154 of file Tempus_StepperBDF2_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 155 of file Tempus_StepperBDF2_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 159 of file Tempus_StepperBDF2_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 160 of file Tempus_StepperBDF2_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 161 of file Tempus_StepperBDF2_decl.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 165 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 166 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 171 of file Tempus_StepperBDF2_decl.hpp.

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 236 of file Tempus_StepperBDF2_impl.hpp.

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

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 316 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 267 of file Tempus_StepperBDF2_impl.hpp.

template<class Scalar >
bool Tempus::StepperBDF2< Scalar >::isValidSetup ( Teuchos::FancyOStream out) const
virtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 294 of file Tempus_StepperBDF2_impl.hpp.

Member Data Documentation

template<class Scalar >
Teuchos::RCP<Stepper<Scalar> > Tempus::StepperBDF2< Scalar >::startUpStepper_
private

Definition at line 188 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >
Teuchos::RCP<StepperBDF2AppAction<Scalar> > Tempus::StepperBDF2< Scalar >::stepperBDF2AppAction_
private

Definition at line 189 of file Tempus_StepperBDF2_decl.hpp.

template<class Scalar >
Scalar Tempus::StepperBDF2< Scalar >::order_ = Scalar(2.0)
private

Definition at line 190 of file Tempus_StepperBDF2_decl.hpp.


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