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Tempus::StepperExplicitRK< Scalar > Class Template Reference

Explicit Runge-Kutta time stepper. More...

#include <Tempus_StepperExplicitRK_decl.hpp>

Inheritance diagram for Tempus::StepperExplicitRK< Scalar >:
Tempus::StepperExplicit< Scalar > Tempus::Stepper< Scalar >

Public Member Functions

 StepperExplicitRK ()
 Default constructor. More...
 
 StepperExplicitRK (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, Teuchos::RCP< Teuchos::ParameterList > pList)
 Constructor to specialize Stepper parameters. More...
 
 StepperExplicitRK (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, std::string stepperType="RK Explicit 4 Stage")
 Constructor to use default Stepper parameters. More...
 
 StepperExplicitRK (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, std::string stepperType, Teuchos::RCP< Teuchos::ParameterList > pList)
 Constructor for StepperFactory. More...
 
Basic stepper methods
virtual void setObserver (Teuchos::RCP< StepperObserver< Scalar > > obs=Teuchos::null)
 Set Observer. More...
 
virtual void setTableau (std::string stepperType)
 
virtual void setTableau (Teuchos::RCP< Teuchos::ParameterList > pList=Teuchos::null)
 
virtual void setTableau (Teuchos::RCP< const RKButcherTableau< Scalar > > ERK_ButcherTableau)
 
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 std::string getStepperType () const
 
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 bool isExplicit () const
 
virtual bool isImplicit () const
 
virtual bool isExplicitImplicit () const
 
virtual bool isOneStepMethod () const
 
virtual bool isMultiStepMethod () const
 
virtual OrderODE getOrderODE () const
 
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::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 (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 void setInitialGuess (Teuchos::RCP< const Thyra::VectorBase< Scalar > >)
 Pass initial guess to Newton solver (only relevant for implicit solvers) More...
 
virtual bool getEmbedded () const
 
virtual void setUseFSAL (bool a)
 
virtual bool getUseFSAL () const
 
virtual void setICConsistency (std::string s)
 
virtual std::string getICConsistency () const
 
virtual void setICConsistencyCheck (bool c)
 
virtual bool getICConsistencyCheck () const
 
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)
 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)
 Evaluate xDotDot = f(x, xDot, t). More...
 
- Public Member Functions inherited from Tempus::Stepper< Scalar >
virtual void modelWarning () const
 
void getValidParametersBasic (Teuchos::RCP< Teuchos::ParameterList > pl) const
 
virtual void createSubSteppers (std::vector< Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > >)
 
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
 

Protected Attributes

Teuchos::RCP< const
RKButcherTableau< Scalar > > 		ERK_ButcherTableau_
 
std::vector< Teuchos::RCP
< Thyra::VectorBase< Scalar > > > 		stageXDot_
 
Teuchos::RCP
< Thyra::VectorBase< Scalar > > 		stageX_
 
Teuchos::RCP
< StepperExplicitRKObserver
< Scalar > > 		stepperExplicitRKObserver_
 
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
< Teuchos::ParameterList > 		stepperPL_
 
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.

Constructor & Destructor Documentation

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

Default constructor.

Definition at line 21 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
Tempus::StepperExplicitRK< Scalar >::StepperExplicitRK ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  appModel,
Teuchos::RCP< Teuchos::ParameterList >  pList 
)

Constructor to specialize Stepper parameters.

Definition at line 29 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
Tempus::StepperExplicitRK< Scalar >::StepperExplicitRK ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  appModel,
std::string  stepperType = "RK Explicit 4 Stage" 
)

Constructor to use default Stepper parameters.

Definition at line 46 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
Tempus::StepperExplicitRK< Scalar >::StepperExplicitRK ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  appModel,
std::string  stepperType,
Teuchos::RCP< Teuchos::ParameterList >  pList 
)

Constructor for StepperFactory.

Definition at line 62 of file Tempus_StepperExplicitRK_impl.hpp.

Member Function Documentation

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

Definition at line 422 of file Tempus_StepperExplicitRK_impl.hpp.

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

Definition at line 415 of file Tempus_StepperExplicitRK_impl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 472 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 406 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 80 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
Teuchos::RCP< Teuchos::ParameterList > Tempus::StepperExplicitRK< Scalar >::getNonconstParameterList ( )

Definition at line 487 of file Tempus_StepperExplicitRK_impl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 148 of file Tempus_StepperExplicitRK_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 150 of file Tempus_StepperExplicitRK_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 149 of file Tempus_StepperExplicitRK_decl.hpp.

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

Implements Tempus::Stepper< Scalar >.

Definition at line 161 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
virtual std::string Tempus::StepperExplicitRK< Scalar >::getStepperType ( ) const
inlinevirtual

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 143 of file Tempus_StepperExplicitRK_decl.hpp.

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

Definition at line 449 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 230 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 154 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 156 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 155 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 159 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 158 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 265 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 208 of file Tempus_StepperExplicitRK_impl.hpp.

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

Definition at line 432 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
void Tempus::StepperExplicitRK< Scalar >::setTableau ( std::string  stepperType)
virtual

Definition at line 163 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
void Tempus::StepperExplicitRK< Scalar >::setTableau ( Teuchos::RCP< Teuchos::ParameterList >  pList = Teuchos::null)
virtual

Definition at line 175 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
void Tempus::StepperExplicitRK< Scalar >::setTableau ( Teuchos::RCP< const RKButcherTableau< Scalar > >  ERK_ButcherTableau)
virtual

Definition at line 195 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 281 of file Tempus_StepperExplicitRK_impl.hpp.

template<class Scalar >
Teuchos::RCP< Teuchos::ParameterList > Tempus::StepperExplicitRK< Scalar >::unsetParameterList ( )

Definition at line 495 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 192 of file Tempus_StepperExplicitRK_decl.hpp.

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

Definition at line 191 of file Tempus_StepperExplicitRK_decl.hpp.

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

Definition at line 190 of file Tempus_StepperExplicitRK_decl.hpp.

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

Definition at line 182 of file Tempus_StepperExplicitRK_decl.hpp.

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

Definition at line 193 of file Tempus_StepperExplicitRK_decl.hpp.

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

Definition at line 185 of file Tempus_StepperExplicitRK_decl.hpp.

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

Definition at line 184 of file Tempus_StepperExplicitRK_decl.hpp.

template<class Scalar >
Teuchos::RCP<StepperExplicitRKObserver<Scalar> > Tempus::StepperExplicitRK< Scalar >::stepperExplicitRKObserver_
protected

Definition at line 187 of file Tempus_StepperExplicitRK_decl.hpp.

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