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Tempus::StepperDIRK< Scalar > Class Template Reference

Diagonally Implicit Runge-Kutta (DIRK) time stepper. More...

#include <Tempus_StepperDIRK_decl.hpp>

Inheritance diagram for Tempus::StepperDIRK< Scalar >:
Tempus::StepperImplicit< Scalar > Tempus::Stepper< Scalar >

Public Member Functions

 StepperDIRK (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, std::string stepperType="SDIRK 2 Stage 2nd order")
 Constructor to use default Stepper parameters. More...
 
 StepperDIRK (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, Teuchos::RCP< Teuchos::ParameterList > pList)
 Constructor to specialize Stepper parameters. More...
 
 StepperDIRK (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 initialize ()
 Initialize during construction and after changing input parameters. 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 void setInitialGuess (Teuchos::RCP< const Thyra::VectorBase< Scalar > > initial_guess)
 Pass initial guess to Newton solver. More...
 
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
 
- Public Member Functions inherited from Tempus::StepperImplicit< 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 std::string getStepperType () const
 
const Thyra::SolveStatus< Scalar > solveImplicitODE (const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x)
 Solve problem using x in-place. More...
 
virtual void setZeroInitialGuess (bool zIG)
 Set parameter so that the initial guess is set to zero (=True) or use last timestep (=False). More...
 
virtual bool getZeroInitialGuess () const
 
virtual bool getEmbedded () const
 
virtual Scalar getInitTimeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory) const
 
- Public Member Functions inherited from Tempus::Stepper< Scalar >
virtual void createSubSteppers (std::vector< Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > > models)
 
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
 

Overridden from Teuchos::Describable

std::string description_
 
Teuchos::RCP< const RKButcherTableau< Scalar > > DIRK_ButcherTableau_
 
std::vector< Teuchos::RCP< Thyra::VectorBase< Scalar > > > stageXDot_
 
Teuchos::RCP< Thyra::VectorBase< Scalar > > stageX_
 
Teuchos::RCP< Thyra::VectorBase< Scalar > > xTilde_
 
Teuchos::RCP< StepperObserver< Scalar > > stepperObserver_
 
Teuchos::RCP< StepperDIRKObserver< Scalar > > stepperDIRKObserver_
 
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< const Thyra::VectorBase< Scalar > > initial_guess_
 
virtual std::string description () const
 
virtual void describe (Teuchos::FancyOStream &out, const Teuchos::EVerbosityLevel verbLevel) const
 
 StepperDIRK ()
 Default Constructor – not allowed. More...
 

Additional Inherited Members

- Protected Attributes inherited from Tempus::StepperImplicit< Scalar >
Teuchos::RCP< Teuchos::ParameterList > stepperPL_
 
Teuchos::RCP< WrapperModelEvaluator< Scalar > > wrapperModel_
 
Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > solver_
 
Teuchos::RCP< const Thyra::VectorBase< Scalar > > initial_guess_
 

Detailed Description

template<class Scalar>
class Tempus::StepperDIRK< Scalar >

Diagonally Implicit Runge-Kutta (DIRK) time stepper.

For the implicit ODE system, $\mathcal{F}(\dot{x},x,t) = 0$, the general DIRK method for $s$-stages, can be written as

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

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

where $\dot{x}=\bar{f}(x,t)$ is the explicit form of the ODE, $X_{i}$ 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 DIRK methods that $a_{ii}=a$ for all the diagonal components is referred to as Singly Diagonal Implicit Runge-Kutta (SDIRK) methods.

Note that the stage time derivatives,

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

can be found via

\begin{eqnarray*} \dot{X}_{i} & = & \frac{1}{a_{ii} \Delta t} [ X_{i} - x_{n-1} - \Delta t\,\sum_{j=1}^{i-1} a_{ij}\,\dot{X}_{j} ] \\ \dot{X}_{i} & = & \frac{X_{i} - \tilde{X}}{a_{ii} \Delta t} \end{eqnarray*}

where

\[ \tilde{X} = x_{n-1} + \Delta t \sum_{j=1}^{i-1} a_{ij}\, \dot{X}_{j} \]

Recalling that the definition for a DIRK is that for $j>i$, $a_{ij} = 0$ and $a_{ii} \neq 0$ for at least one $i$. Thus for stages where $a_{ii} = 0$, we can use the explicit RK methods (see StepperExplicitRK for additional details).

Algorithm The single-timestep algorithm for DIRK is,

  • for $i = 1 \ldots s$ do
    • if $a_{ii} = 0$
      • $X_i \leftarrow x_{n-1} + \Delta t\,\sum_{j=1}^{i-1} a_{ij}\,\dot{X}_j$
      • Evaluate $\bar{f}(X_{i},t_{n-1}+c_{i}\Delta t)$
      • $\dot{X}_i \leftarrow \bar{f}(X_i,t_{n-1}+c_i\Delta t)$
    • else
      • $\tilde{X} = x_{n-1} +\Delta t \sum_{j=1}^{i-1} a_{ij}\,\dot{X}_{j}$
      • Define $\dot{X}_i \leftarrow \frac{X_{i} - \tilde{X}}{a_{ii} \Delta t}$
      • Solve $f(\dot{x} = \dot{X}_i,X_i,t_{n-1}+c_{i}\Delta t)=0$ for $X_i$
      • $\dot{X}_i \leftarrow \frac{X_{i} - \tilde{X}}{a_{ii} \Delta t}$
  • end for
  • $x_n \leftarrow x_{n-1} + \Delta t\,\sum_{i=1}^{s}b_i\,\dot{X}_i$
  • Solve $f(\dot{x}_n,x_n,t_n)=0$ for $\dot{x}_n$ [Optional]

Definition at line 84 of file Tempus_StepperDIRK_decl.hpp.

Constructor & Destructor Documentation

◆ StepperDIRK() [1/4]

template<class Scalar >
Tempus::StepperDIRK< Scalar >::StepperDIRK ( const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &  appModel,
std::string  stepperType = "SDIRK 2 Stage 2nd order" 
)

Constructor to use default Stepper parameters.

Definition at line 27 of file Tempus_StepperDIRK_impl.hpp.

◆ StepperDIRK() [2/4]

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

Constructor to specialize Stepper parameters.

Definition at line 37 of file Tempus_StepperDIRK_impl.hpp.

◆ StepperDIRK() [3/4]

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

Constructor for StepperFactory.

Definition at line 48 of file Tempus_StepperDIRK_impl.hpp.

◆ StepperDIRK() [4/4]

template<class Scalar>
Tempus::StepperDIRK< Scalar >::StepperDIRK ( )
private

Default Constructor – not allowed.

Member Function Documentation

◆ describe()

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

Definition at line 331 of file Tempus_StepperDIRK_impl.hpp.

◆ description()

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

Definition at line 324 of file Tempus_StepperDIRK_impl.hpp.

◆ getDefaultParameters()

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

Implements Tempus::Stepper< Scalar >.

Definition at line 367 of file Tempus_StepperDIRK_impl.hpp.

◆ getDefaultStepperState()

template<class Scalar >
Teuchos::RCP< Tempus::StepperState< Scalar > > Tempus::StepperDIRK< 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 315 of file Tempus_StepperDIRK_impl.hpp.

◆ getNonconstParameterList()

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

Definition at line 387 of file Tempus_StepperDIRK_impl.hpp.

◆ getOrder()

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

Implements Tempus::Stepper< Scalar >.

Definition at line 121 of file Tempus_StepperDIRK_decl.hpp.

◆ getOrderMax()

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

Implements Tempus::Stepper< Scalar >.

Definition at line 123 of file Tempus_StepperDIRK_decl.hpp.

◆ getOrderMin()

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

Implements Tempus::Stepper< Scalar >.

Definition at line 122 of file Tempus_StepperDIRK_decl.hpp.

◆ getValidParameters()

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

Definition at line 357 of file Tempus_StepperDIRK_impl.hpp.

◆ initialize()

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

Initialize during construction and after changing input parameters.

Implements Tempus::Stepper< Scalar >.

Definition at line 123 of file Tempus_StepperDIRK_impl.hpp.

◆ isExplicit()

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

Implements Tempus::Stepper< Scalar >.

Definition at line 125 of file Tempus_StepperDIRK_decl.hpp.

◆ isExplicitImplicit()

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

Implements Tempus::Stepper< Scalar >.

Definition at line 134 of file Tempus_StepperDIRK_decl.hpp.

◆ isImplicit()

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

Implements Tempus::Stepper< Scalar >.

Definition at line 133 of file Tempus_StepperDIRK_decl.hpp.

◆ isMultiStepMethod()

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

Implements Tempus::Stepper< Scalar >.

Definition at line 137 of file Tempus_StepperDIRK_decl.hpp.

◆ isOneStepMethod()

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

Implements Tempus::Stepper< Scalar >.

Definition at line 136 of file Tempus_StepperDIRK_decl.hpp.

◆ setInitialGuess()

template<class Scalar>
virtual void Tempus::StepperDIRK< Scalar >::setInitialGuess ( Teuchos::RCP< const Thyra::VectorBase< Scalar > >  initial_guess)
inlinevirtual

Pass initial guess to Newton solver.

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 141 of file Tempus_StepperDIRK_decl.hpp.

◆ setObserver()

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

Set Observer.

Implements Tempus::Stepper< Scalar >.

Definition at line 102 of file Tempus_StepperDIRK_impl.hpp.

◆ setParameterList()

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

Definition at line 341 of file Tempus_StepperDIRK_impl.hpp.

◆ setTableau() [1/2]

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

Definition at line 61 of file Tempus_StepperDIRK_impl.hpp.

◆ setTableau() [2/2]

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

Definition at line 78 of file Tempus_StepperDIRK_impl.hpp.

◆ takeStep()

template<class Scalar >
void Tempus::StepperDIRK< 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 155 of file Tempus_StepperDIRK_impl.hpp.

◆ unsetParameterList()

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

Definition at line 395 of file Tempus_StepperDIRK_impl.hpp.

Member Data Documentation

◆ abs_u

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

Definition at line 183 of file Tempus_StepperDIRK_decl.hpp.

◆ abs_u0

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

Definition at line 182 of file Tempus_StepperDIRK_decl.hpp.

◆ description_

template<class Scalar>
std::string Tempus::StepperDIRK< Scalar >::description_
protected

Definition at line 168 of file Tempus_StepperDIRK_decl.hpp.

◆ DIRK_ButcherTableau_

template<class Scalar>
Teuchos::RCP<const RKButcherTableau<Scalar> > Tempus::StepperDIRK< Scalar >::DIRK_ButcherTableau_
protected

Definition at line 170 of file Tempus_StepperDIRK_decl.hpp.

◆ ee_

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

Definition at line 179 of file Tempus_StepperDIRK_decl.hpp.

◆ initial_guess_

template<class Scalar>
Teuchos::RCP<const Thyra::VectorBase<Scalar> > Tempus::StepperDIRK< Scalar >::initial_guess_
protected

Definition at line 186 of file Tempus_StepperDIRK_decl.hpp.

◆ sc

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

Definition at line 184 of file Tempus_StepperDIRK_decl.hpp.

◆ stageX_

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

Definition at line 173 of file Tempus_StepperDIRK_decl.hpp.

◆ stageXDot_

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

Definition at line 172 of file Tempus_StepperDIRK_decl.hpp.

◆ stepperDIRKObserver_

template<class Scalar>
Teuchos::RCP<StepperDIRKObserver<Scalar> > Tempus::StepperDIRK< Scalar >::stepperDIRKObserver_
protected

Definition at line 177 of file Tempus_StepperDIRK_decl.hpp.

◆ stepperObserver_

template<class Scalar>
Teuchos::RCP<StepperObserver<Scalar> > Tempus::StepperDIRK< Scalar >::stepperObserver_
protected

Definition at line 176 of file Tempus_StepperDIRK_decl.hpp.

◆ xTilde_

template<class Scalar>
Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperDIRK< Scalar >::xTilde_
protected

Definition at line 174 of file Tempus_StepperDIRK_decl.hpp.

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