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Tempus::StepperExplicitRK< Scalar > Class Template Referenceabstract

Explicit Runge-Kutta time stepper. More...

#include <Tempus_StepperExplicitRK_decl.hpp>

Inheritance diagram for Tempus::StepperExplicitRK< Scalar >:
Tempus::StepperExplicit< Scalar > Tempus::Stepper< Scalar > Tempus::StepperERK_3_8Rule< Scalar > Tempus::StepperERK_3Stage3rdOrder< Scalar > Tempus::StepperERK_3Stage3rdOrderHeun< Scalar > Tempus::StepperERK_3Stage3rdOrderTVD< Scalar > Tempus::StepperERK_4Stage3rdOrderRunge< Scalar > Tempus::StepperERK_4Stage4thOrder< Scalar > Tempus::StepperERK_5Stage3rdOrderKandG< Scalar > Tempus::StepperERK_BogackiShampine32< Scalar > Tempus::StepperERK_ForwardEuler< Scalar > Tempus::StepperERK_General< Scalar > Tempus::StepperERK_Merson45< Scalar > Tempus::StepperERK_Midpoint< Scalar > Tempus::StepperERK_Trapezoidal< Scalar >

Public Member Functions

Teuchos::RCP< const
Teuchos::ParameterList > 		getValidParameters () const
 
Basic stepper methods
virtual void setObserver (Teuchos::RCP< StepperObserver< Scalar > > obs=Teuchos::null)
 Set Observer. More...
 
virtual Teuchos::RCP< const
RKButcherTableau< Scalar > > 		getTableau ()
 
virtual Teuchos::RCP
< StepperObserver< Scalar > > 		getObserver () const
 Get 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 Scalar getInitTimeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory) const
 
virtual Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		getStageX ()
 
virtual bool isExplicit () const
 
virtual bool isImplicit () const
 
virtual bool isExplicitImplicit () const
 
virtual bool isOneStepMethod () const
 
virtual bool isMultiStepMethod () const
 
virtual OrderODE getOrderODE () const
 
void getValidParametersBasicERK (Teuchos::RCP< Teuchos::ParameterList > pl) const
 
virtual std::string getDescription () const =0
 
Overridden from Teuchos::Describable
virtual void describe (Teuchos::FancyOStream &out, const Teuchos::EVerbosityLevel verbLevel) const
 
Accessors methods
virtual void setUseEmbedded (bool a)
 Use embedded if avialable. More...
 
virtual bool getUseEmbedded () const
 
virtual bool getUseEmbeddedDefault () const
 
- Public Member Functions inherited from Tempus::StepperExplicit< 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 (Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > solver=Teuchos::null)
 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 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...
 
virtual Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		getStepperX (Teuchos::RCP< SolutionState< Scalar > > state)
 Get x from SolutionState or 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...
 
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 setStepperType (std::string s)
 
std::string getStepperType () const
 
void setUseFSAL (bool a)
 
bool getUseFSAL () const
 
virtual bool getUseFSALDefault () const
 
void setICConsistency (std::string s)
 
std::string getICConsistency () const
 
virtual std::string getICConsistencyDefault () const
 
void setICConsistencyCheck (bool c)
 
bool getICConsistencyCheck () const
 
virtual bool getICConsistencyCheckDefault () const
 
virtual std::string description () const
 
virtual void createSubSteppers (std::vector< Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > >)
 

Protected Member Functions

virtual void setupDefault ()
 Default setup for constructor. More...
 
virtual void setup (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, const Teuchos::RCP< StepperRKObserverComposite< Scalar > > &obs, bool useFSAL, std::string ICConsistency, bool ICConsistencyCheck, bool useEmbedded)
 Setup for constructor. More...
 
virtual void setupTableau ()=0
 

Protected Attributes

Teuchos::RCP< RKButcherTableau
< Scalar > > 		tableau_
 
std::vector< Teuchos::RCP
< Thyra::VectorBase< Scalar > > > 		stageXDot_
 
Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		stageX_
 
Teuchos::RCP
< StepperRKObserverComposite
< Scalar > > 		stepperObserver_
 
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
 
- 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_
 
Teuchos::RCP< StepperObserver
< Scalar > > 		stepperObserver_
 
Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		stepperX_
 
Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		stepperXDot_
 
Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		stepperXDotDot_
 

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 simply,

  • for $i = 1 \ldots s$ do
    • $X_i \leftarrow x_{n-1} + \Delta t\,\sum_{j=1}^{i-1} a_{ij}\,\dot{X}_j$
    • Evaluate $\bar{f}(X_{i},t_{n-1}+c_{i}\Delta t)$
    • $\dot{X}_i \leftarrow \bar{f}(X_i,t_{n-1}+c_i\Delta t)$
  • end for
  • $x_n \leftarrow x_{n-1} + \Delta t\,\sum_{i=1}^{s}b_i\,\dot{X}_i$

When using the First-Step-As-Last (FSAL) priniciple, where one can reuse the last function evaulation as the first evaluation of the next time step, the algorithm is only slightly more complicated.

  • for $i = 1 \ldots s$ do
    • if ( i==1 && useFSAL && (previous step not failed) )
      • tmp = $\dot{X}_1$
      • $\dot{X}_1 = \dot{X}_s$
      • $\dot{X}_s$ = tmp
    • else
      • $X_i \leftarrow x_{n-1} + \Delta t\,\sum_{j=1}^{i-1} a_{ij}\,\dot{X}_j$
      • Evaluate $\bar{f}(X_{i},t_{n-1}+c_{i}\Delta t)$
      • $\dot{X}_i \leftarrow \bar{f}(X_i,t_{n-1}+c_i\Delta t)$
  • end for
  • $x_n \leftarrow x_{n-1} + \Delta t\,\sum_{i=1}^{s}b_i\,\dot{X}_i$

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.

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

Definition at line 91 of file Tempus_StepperExplicitRK_decl.hpp.

Member Function Documentation

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

Definition at line 379 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 370 of file Tempus_StepperExplicitRK_impl.hpp.

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

Implemented in Tempus::StepperERK_General< Scalar >, Tempus::StepperERK_Trapezoidal< Scalar >, Tempus::StepperERK_Midpoint< Scalar >, Tempus::StepperERK_3Stage3rdOrderHeun< Scalar >, Tempus::StepperERK_3Stage3rdOrderTVD< Scalar >, Tempus::StepperERK_3Stage3rdOrder< Scalar >, Tempus::StepperERK_5Stage3rdOrderKandG< Scalar >, Tempus::StepperERK_4Stage3rdOrderRunge< Scalar >, Tempus::StepperERK_3_8Rule< Scalar >, Tempus::StepperERK_Merson45< Scalar >, Tempus::StepperERK_BogackiShampine32< Scalar >, Tempus::StepperERK_4Stage4thOrder< Scalar >, and Tempus::StepperERK_ForwardEuler< Scalar >.

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

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 59 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
virtual Teuchos::RCP<StepperObserver<Scalar> > Tempus::StepperExplicitRK< Scalar >::getObserver ( ) const
inlinevirtual

Get Observer.

Implements Tempus::Stepper< Scalar >.

Definition at line 104 of file Tempus_StepperExplicitRK_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 120 of file Tempus_StepperExplicitRK_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 122 of file Tempus_StepperExplicitRK_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 121 of file Tempus_StepperExplicitRK_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 135 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
virtual Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperExplicitRK< Scalar >::getStageX ( )
inlinevirtual

Definition at line 126 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
virtual Teuchos::RCP<const RKButcherTableau<Scalar> > Tempus::StepperExplicitRK< Scalar >::getTableau ( )
inlinevirtual

Definition at line 101 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
virtual bool Tempus::StepperExplicitRK< Scalar >::getUseEmbedded ( ) const
inlinevirtual

Definition at line 153 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
virtual bool Tempus::StepperExplicitRK< Scalar >::getUseEmbeddedDefault ( ) const
inlinevirtual

Definition at line 154 of file Tempus_StepperExplicitRK_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Reimplemented in Tempus::StepperERK_General< Scalar >.

Definition at line 390 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
void Tempus::StepperExplicitRK< Scalar >::getValidParametersBasicERK ( Teuchos::RCP< Teuchos::ParameterList >  pl) const

Definition at line 143 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
void Tempus::StepperExplicitRK< Scalar >::initialize ( )
virtual

Initialize during construction and after changing input parameters.

Implements Tempus::Stepper< Scalar >.

Definition at line 186 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 128 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 130 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 129 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 133 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 132 of file Tempus_StepperExplicitRK_decl.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 221 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
void Tempus::StepperExplicitRK< Scalar >::setObserver ( Teuchos::RCP< StepperObserver< Scalar > >  obs = Teuchos::null)
virtual

Set Observer.

Implements Tempus::Stepper< Scalar >.

Definition at line 156 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
void Tempus::StepperExplicitRK< Scalar >::setup ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  appModel,
const Teuchos::RCP< StepperRKObserverComposite< Scalar > > &  obs,
bool  useFSAL,
std::string  ICConsistency,
bool  ICConsistencyCheck,
bool  useEmbedded 
)
protectedvirtual

Setup for constructor.

Definition at line 34 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 >
virtual void Tempus::StepperExplicitRK< Scalar >::setupTableau ( )
protectedpure virtual

Implemented in Tempus::StepperERK_General< Scalar >, Tempus::StepperERK_Trapezoidal< Scalar >, Tempus::StepperERK_Midpoint< Scalar >, Tempus::StepperERK_3Stage3rdOrderHeun< Scalar >, Tempus::StepperERK_3Stage3rdOrderTVD< Scalar >, Tempus::StepperERK_3Stage3rdOrder< Scalar >, Tempus::StepperERK_5Stage3rdOrderKandG< Scalar >, Tempus::StepperERK_4Stage3rdOrderRunge< Scalar >, Tempus::StepperERK_3_8Rule< Scalar >, Tempus::StepperERK_Merson45< Scalar >, Tempus::StepperERK_BogackiShampine32< Scalar >, Tempus::StepperERK_4Stage4thOrder< Scalar >, and Tempus::StepperERK_ForwardEuler< Scalar >.

template<class Scalar >
virtual void Tempus::StepperExplicitRK< Scalar >::setUseEmbedded ( bool  a)
inlinevirtual

Use embedded if avialable.

Definition at line 152 of file Tempus_StepperExplicitRK_decl.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 237 of file Tempus_StepperExplicitRK_impl.hpp.

Member Data Documentation

template<class Scalar >
Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperExplicitRK< Scalar >::abs_u
protected

Definition at line 186 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperExplicitRK< Scalar >::abs_u0
protected

Definition at line 185 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperExplicitRK< Scalar >::ee_
protected

Definition at line 184 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperExplicitRK< Scalar >::sc
protected

Definition at line 187 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperExplicitRK< Scalar >::stageX_
protected

Definition at line 178 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
std::vector<Teuchos::RCP<Thyra::VectorBase<Scalar> > > Tempus::StepperExplicitRK< Scalar >::stageXDot_
protected

Definition at line 177 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
Teuchos::RCP<StepperRKObserverComposite<Scalar> > Tempus::StepperExplicitRK< Scalar >::stepperObserver_
protected

Definition at line 180 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
Teuchos::RCP<RKButcherTableau<Scalar> > Tempus::StepperExplicitRK< Scalar >::tableau_
protected

Definition at line 175 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
bool Tempus::StepperExplicitRK< Scalar >::useEmbedded_
protected

Definition at line 183 of file Tempus_StepperExplicitRK_decl.hpp.

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