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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::StepperRKBase< Scalar > Tempus::Stepper< Scalar > Tempus::Stepper< Scalar > Tempus::StepperERK_3Stage3rdOrder< Scalar > Tempus::StepperERK_3Stage3rdOrderHeun< Scalar > Tempus::StepperERK_3Stage3rdOrderTVD< Scalar > Tempus::StepperERK_3_8Rule< 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_Ralston< Scalar > Tempus::StepperERK_SSPERK54< Scalar > Tempus::StepperERK_Trapezoidal< Scalar >

Overridden from Teuchos::Describable

std::vector< Teuchos::RCP< Thyra::VectorBase< Scalar > > > stageXDot_
 
virtual void describe (Teuchos::FancyOStream &out, const Teuchos::EVerbosityLevel verbLevel) const
 
virtual bool isValidSetup (Teuchos::FancyOStream &out) const
 
virtual void setupDefault ()
 Default setup for constructor.
 
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.
 
virtual void setupTableau ()=0
 
virtual void setEmbeddedMemory ()
 

Basic stepper methods

virtual void initialize ()
 Initialize during construction and after changing input parameters.
 
virtual void setModel (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel)
 Set model.
 
virtual void setInitialConditions (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
 Set the initial conditions and make them consistent.
 
virtual void takeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
 Take the specified timestep, dt, and return true if successful.
 
virtual Teuchos::RCP< Tempus::StepperState< Scalar > > getDefaultStepperState ()
 Get a default (initial) StepperState.
 
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
 
virtual Teuchos::RCP< const Teuchos::ParameterList > getValidParameters () const
 
Teuchos::RCP< Teuchos::ParameterList > getValidParametersBasicERK () const
 

Additional Inherited Members

- Public Member Functions inherited from Tempus::StepperExplicit< Scalar >
void setStepperExplicitValues (Teuchos::RCP< Teuchos::ParameterList > pl)
 Set StepperExplicit member data from the ParameterList.
 
virtual Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > getModel () const
 Return the application ModelEvaluator.
 
virtual void setSolver (Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > solver)
 Set solver.
 
virtual Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > getSolver () const
 Get solver.
 
virtual void setInitialGuess (Teuchos::RCP< const Thyra::VectorBase< Scalar > >)
 Pass initial guess to Newton solver (only relevant for implicit solvers)
 
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).
 
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).
 
- Public Member Functions inherited from Tempus::Stepper< Scalar >
virtual std::string description () const
 
void setStepperValues (const Teuchos::RCP< Teuchos::ParameterList > pl)
 Set Stepper member data from ParameterList.
 
Teuchos::RCP< Teuchos::ParameterList > getValidParametersBasic () const
 Add basic parameters to Steppers ParameterList.
 
virtual bool isInitialized ()
 True if stepper's member data is initialized.
 
virtual void checkInitialized ()
 Check initialization, and error out on failure.
 
void setStepperName (std::string s)
 Set the stepper name.
 
std::string getStepperName () const
 Get the stepper name.
 
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.
 
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.
 
virtual Teuchos::RCP< Thyra::VectorBase< Scalar > > getStepperXDot ()
 Get Stepper xDot.
 
virtual Teuchos::RCP< Thyra::VectorBase< Scalar > > getStepperXDotDot ()
 Get Stepper xDotDot.
 
virtual Teuchos::RCP< Thyra::VectorBase< Scalar > > getStepperXDotDot (Teuchos::RCP< SolutionState< Scalar > > state)
 Get xDotDot from SolutionState or Stepper storage.
 
- 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 setErrorNorm (const Teuchos::RCP< Stepper_ErrorNorm< Scalar > > &errCalculator=Teuchos::null)
 
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.
 
virtual Teuchos::RCP< RKButcherTableau< Scalar > > createTableau (Teuchos::RCP< Teuchos::ParameterList > pl)
 
- Protected Member Functions inherited from Tempus::Stepper< Scalar >
virtual void setStepperX (Teuchos::RCP< Thyra::VectorBase< Scalar > > x)
 Set x for Stepper storage.
 
virtual void setStepperXDot (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDot)
 Set xDot for Stepper storage.
 
virtual void setStepperXDotDot (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDotDot)
 Set x for Stepper storage.
 
void setStepperType (std::string s)
 Set the stepper type.
 
virtual void setEmbeddedMemory ()
 
- Protected Attributes inherited from Tempus::StepperExplicit< Scalar >
Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > appModel_
 Explicit ODE ModelEvaluator.
 
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.
 
bool isInitialized_ = false
 True if stepper's member data is initialized.
 
- 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
 
Teuchos::RCP< Stepper_ErrorNorm< Scalar > > stepperErrorNormCalculator_
 
int stageNumber_
 The current Runge-Kutta stage number, {0,...,s-1}. -1 indicates outside stage loop.
 
Teuchos::RCP< StepperRKAppAction< Scalar > > stepperRKAppAction_
 

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

◆ initialize()

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 151 of file Tempus_StepperExplicitRK_impl.hpp.

◆ setModel()

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

Set model.

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 166 of file Tempus_StepperExplicitRK_impl.hpp.

◆ setInitialConditions()

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 207 of file Tempus_StepperExplicitRK_impl.hpp.

◆ takeStep()

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 224 of file Tempus_StepperExplicitRK_impl.hpp.

◆ getDefaultStepperState()

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 371 of file Tempus_StepperExplicitRK_impl.hpp.

◆ getInitTimeStep()

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

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 56 of file Tempus_StepperExplicitRK_impl.hpp.

◆ isExplicit()

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.

◆ isImplicit()

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.

◆ isExplicitImplicit()

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.

◆ isOneStepMethod()

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.

◆ isMultiStepMethod()

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.

◆ getOrderODE()

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.

◆ getDescription()

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

◆ getValidParameters()

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

Reimplemented from Tempus::Stepper< Scalar >.

Reimplemented in Tempus::StepperERK_General< Scalar >.

Definition at line 129 of file Tempus_StepperExplicitRK_impl.hpp.

◆ getValidParametersBasicERK()

template<class Scalar >
Teuchos::RCP< Teuchos::ParameterList > Tempus::StepperExplicitRK< Scalar >::getValidParametersBasicERK

Definition at line 137 of file Tempus_StepperExplicitRK_impl.hpp.

◆ describe()

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 381 of file Tempus_StepperExplicitRK_impl.hpp.

◆ isValidSetup()

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

Reimplemented from Tempus::StepperExplicit< Scalar >.

Definition at line 409 of file Tempus_StepperExplicitRK_impl.hpp.

◆ setupDefault()

template<class Scalar >
void Tempus::StepperExplicitRK< Scalar >::setupDefault
protectedvirtual

Default setup for constructor.

Definition at line 22 of file Tempus_StepperExplicitRK_impl.hpp.

◆ setup()

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 
)
protectedvirtual

Setup for constructor.

Definition at line 31 of file Tempus_StepperExplicitRK_impl.hpp.

◆ setupTableau()

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

◆ setEmbeddedMemory()

template<class Scalar >
void Tempus::StepperExplicitRK< Scalar >::setEmbeddedMemory
protectedvirtual

Reimplemented from Tempus::StepperRKBase< Scalar >.

Definition at line 187 of file Tempus_StepperExplicitRK_impl.hpp.

Member Data Documentation

◆ stageXDot_

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

Definition at line 172 of file Tempus_StepperExplicitRK_decl.hpp.


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