Explicit Runge-Kutta time stepper. More...

#include <Tempus_StepperExplicitRK_decl.hpp>

Inheritance diagram for Tempus::StepperExplicitRK< Scalar >:

Public Member Functions
virtual Teuchos::RCP< const Teuchos::ParameterList >	getValidParameters () const

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

virtual bool	isValidSetup (Teuchos::FancyOStream &out) const

Public Member Functions inherited from Tempus::StepperExplicit< Scalar >
void	setStepperExplicitValues (Teuchos::RCP< Teuchos::ParameterList > pl)
	Set StepperExplicit member data from the ParameterList. More...

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

virtual Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > >	getModel ()

virtual void	setSolver (Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > solver)
	Set solver. More...

virtual Teuchos::RCP < Thyra::NonlinearSolverBase < Scalar > >	getSolver () const
	Get solver. More...

virtual void	setInitialGuess (Teuchos::RCP< const Thyra::VectorBase< Scalar > >)
	Pass initial guess to Newton solver (only relevant for implicit solvers) More...

virtual void	evaluateExplicitODE (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDot, Teuchos::RCP< const Thyra::VectorBase< Scalar > > x, const Scalar time, const Teuchos::RCP< ExplicitODEParameters< Scalar > > &p)
	Evaluate xDot = f(x,t). More...

virtual void	evaluateExplicitODE (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDotDot, Teuchos::RCP< const Thyra::VectorBase< Scalar > > x, Teuchos::RCP< const Thyra::VectorBase< Scalar > > xDot, const Scalar time, const Teuchos::RCP< ExplicitODEParameters< Scalar > > &p)
	Evaluate xDotDot = f(x, xDot, t). More...

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 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

Public Member Functions inherited from Tempus::StepperRKBase< Scalar >
virtual Teuchos::RCP< const RKButcherTableau< Scalar > >	getTableau () const

virtual Scalar	getOrder () const

virtual Scalar	getOrderMin () const

virtual Scalar	getOrderMax () const

virtual int	getNumberOfStages () const

virtual int	getStageNumber () const

virtual void	setStageNumber (int s)

virtual void	setUseEmbedded (bool a)

virtual bool	getUseEmbedded () const

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

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

virtual void	setStepperRKValues (Teuchos::RCP< Teuchos::ParameterList > pl)
	Set StepperRK member data from the ParameterList. More...

virtual Teuchos::RCP < RKButcherTableau< Scalar > >	createTableau (Teuchos::RCP< Teuchos::ParameterList > pl)

Protected Member Functions
virtual void	setupDefault ()
	Default setup for constructor. More...

virtual void	setup (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, bool useFSAL, std::string ICConsistency, bool ICConsistencyCheck, bool useEmbedded, const Teuchos::RCP< StepperRKAppAction< Scalar > > &stepperRKAppAction)
	Setup for constructor. More...

virtual void	setupTableau ()=0

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
std::vector< Teuchos::RCP < Thyra::VectorBase< Scalar > > >	stageXDot_

Protected Attributes inherited from Tempus::StepperExplicit< Scalar >
Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > >	appModel_
	Explicit ODE ModelEvaluator. More...

Thyra::ModelEvaluatorBase::InArgs < Scalar >	inArgs_

Thyra::ModelEvaluatorBase::OutArgs < Scalar >	outArgs_

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...

Protected Attributes inherited from Tempus::StepperRKBase< Scalar >
Teuchos::RCP< RKButcherTableau < Scalar > >	tableau_

bool	useEmbedded_

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

Teuchos::RCP < Thyra::VectorBase< Scalar > >	abs_u0

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

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

int	stageNumber_
	The current Runge-Kutta stage number, {0,...,s-1}. -1 indicates outside stage loop. More...

Teuchos::RCP < StepperRKAppAction< Scalar > >	stepperRKAppAction_

Basic stepper methods
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	getInitTimeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory) 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

virtual std::string	getDescription () const =0

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

Detailed Description

template<class Scalar>
class Tempus::StepperExplicitRK< Scalar >

Explicit Runge-Kutta time stepper.

For the explicit ODE system,

$\dot{x} = \bar{f}(x,t),$

the general explicit Runge-Kutta method for $s$ -stages can be written as

$X_{i} = x_{n-1} + \Delta t\,\sum_{j=1}^{i-1} a_{ij}\,\bar{f}(X_{j},t_{n-1}+c_{j}\Delta t)$

$x_{n} = x_{n-1} + \Delta t\,\sum_{i=1}^{s}b_{i}\,\bar{f}(X_{i},t_{n-1}+c_{i}\Delta t)$

where $X_{i}$ are intermediate approximations to the solution at times, $t_{n-1}+c_{i}\Delta t$ , (stage solutions) which may be correct to a lower order of accuracy than the solution, $x_{n}$ . We should note that these lower-order approximations are combined through $b_{i}$ so that error terms cancel out and produce a more accurate solution. Note for explicit RK that $a_{ij}=0$ for $j \leq i$ and does not require any solves. Note that the stage time derivatives are

$\dot{X}_{i} = \bar{f}(X_{i},t_{n-1}+c_{i}\Delta t),$

and the time derivative by definition is

$\dot{x}_{n} = \bar{f}(x_{n},t_{n}),$

Algorithm The single-timestep algorithm for Explicit RK is

$\begin{center} \parbox{5in}{ \rule{5in}{0.4pt} \\ {\bf Algorithm} Explicit RK \\ \rule{5in}{0.4pt} \vspace{-15pt} \begin{enumerate} \setlength{\itemsep}{0pt} \setlength{\parskip}{0pt} \setlength{\parsep}{0pt} \item $X \leftarrow x_{n-1}$ \item {\it appAction.execute(solutionHistory, stepper, BEGIN\_STEP)} \item {\bf for {$i = 0 \ldots s-1$}} \item \quad $X \leftarrow x_{n-1} + \Delta t\,\sum_{j=1}^{i-1} a_{ij}\,\dot{X}_j$ \item \quad {\it appAction.execute(solutionHistory, stepper, BEGIN\_STAGE)} \item \quad {\it appAction.execute(solutionHistory, stepper, BEFORE\_SOLVE)} \item \quad {\it appAction.execute(solutionHistory, stepper, AFTER\_SOLVE)} \item \quad {\it appAction.execute(solutionHistory, stepper, BEFORE\_EXPLICIT\_EVAL)} \item \quad {\bf if (i=0 and useFSAL and (previous step not failed)) then} \item \qquad tmp = $\dot{X}_0$ \item \qquad $\dot{X}_0 = \dot{X}_s$ \item \qquad $\dot{X}_s$ = tmp \item \qquad {\bf continue} \item \quad {\bf else} \item \qquad $\dot{X}_i \leftarrow \bar{f}(X_i,t_{n-1}+c_i\Delta t)$ \item \quad {\bf endif} \item \quad {\it appAction.execute(solutionHistory, stepper, END\_STAGE)} \item {\bf end for} \item $x_n \leftarrow x_{n-1} + \Delta t\,\sum_{i=1}^{s}b_i\,\dot{X}_i$ \item {\it appAction.execute(solutionHistory, stepper, END\_STEP)} \end{enumerate} \vspace{-10pt} \rule{5in}{0.4pt} } \end{center}$

For Explicit RK, FSAL requires $c_1 = 0$ , $c_s = 1$ , and be stiffly accurate ( $a_{sj} = b_j$ ). An example of this is the Bogacki-Shampine 3(2) method.

$\begin{array}{c|cccc} 0 & 0 & & & \\ 1/2 & 1/2 & 0 & & \\ 3/4 & 0 & 3/4 & 0 & \\ 1 & 2/9 & 1/3 & 4/9 & 0 \\ \hline & 2/9 & 1/3 & 4/9 & 0 \\ & 7/24 & 1/4 & 1/3 & 1/8 \end{array}$

Definition at line 100 of file Tempus_StepperExplicitRK_decl.hpp.

Member Function Documentation

template<class Scalar >

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

virtual

Initialize during construction and after changing input parameters.

Reimplemented from Tempus::Stepper< Scalar >.

Definition at line 160 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >

void Tempus::StepperExplicitRK< Scalar >::setInitialConditions ( const Teuchos::RCP< SolutionHistory< Scalar > > & solutionHistory )

virtual

Set the initial conditions and make them consistent.

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 190 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >

void Tempus::StepperExplicitRK< 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 207 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >

Teuchos::RCP< Tempus::StepperState< Scalar > > Tempus::StepperExplicitRK< 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 361 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >

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

virtual

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 54 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >

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

inlinevirtual

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 124 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >

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

inlinevirtual

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 125 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >

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

inlinevirtual

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 126 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >

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

inlinevirtual

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 128 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >

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

inlinevirtual

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 129 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 131 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >

virtual std::string Tempus::StepperExplicitRK< Scalar >::getDescription ( ) const

pure virtual

template<class Scalar >

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

virtual

Reimplemented from Tempus::Stepper< Scalar >.

Reimplemented in Tempus::StepperERK_General< Scalar >.

Definition at line 138 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >

Teuchos::RCP< Teuchos::ParameterList > Tempus::StepperExplicitRK< Scalar >::getValidParametersBasicERK ( ) const

Definition at line 146 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >

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

virtual

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 370 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >

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

virtual

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 397 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >

void Tempus::StepperExplicitRK< Scalar >::setupDefault ( )

protectedvirtual

Default setup for constructor.

Definition at line 21 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >

void Tempus::StepperExplicitRK< Scalar >::setup	(	const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &	appModel,
		bool	useFSAL,
		std::string	ICConsistency,
		bool	ICConsistencyCheck,
		bool	useEmbedded,
		const Teuchos::RCP< StepperRKAppAction< Scalar > > &	stepperRKAppAction
	)