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

#include <Tempus_StepperDIRK_decl.hpp>

Inheritance diagram for Tempus::StepperDIRK< Scalar >:

Public Member Functions
	StepperDIRK ()
	Default constructor. 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="SDIRK 2 Stage 2nd order")
	Constructor to use default Stepper parameters. More...

	StepperDIRK (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel, std::string stepperType, Teuchos::RCP< Teuchos::ParameterList > pList)
	Constructor for StepperFactory. More...

virtual Scalar	getAlpha (const Scalar dt) const
	Return alpha = d(xDot)/dx. More...

virtual Scalar	getBeta (const Scalar) const
	Return beta = d(x)/dx. 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 > > DIRK_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 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 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::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 Teuchos::RCP< const WrapperModelEvaluator< Scalar > >	getWrapperModel ()

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. (Needs to be deprecated!) More...

const Thyra::SolveStatus< Scalar >	solveImplicitODE (const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &xDot, const Scalar time, const Teuchos::RCP< ImplicitODEParameters< Scalar > > &p)
	Solve implicit ODE, f(x, xDot, t, p) = 0. More...

void	evaluateImplicitODE (Teuchos::RCP< Thyra::VectorBase< Scalar > > &f, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &xDot, const Scalar time, const Teuchos::RCP< ImplicitODEParameters< Scalar > > &p)
	Evaluate implicit ODE, f(x, xDot, t, p), residual. More...

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

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	setStepperXDot (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDot)
	Set xDot for 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...

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 > >	DIRK_ButcherTableau_

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

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

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

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

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_

Teuchos::RCP< StepperObserver < Scalar > >	stepperObserver_

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

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

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 do
- if
  - $X_i \leftarrow x_{n-1} + \Delta t\,\sum_{j=1}^{i-1} a_{ij}\,\dot{X}_j$
  - 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
  - $\dot{X}_i \leftarrow \frac{X_{i} - \tilde{X}}{a_{ii} \Delta t}$
end for
$x_n \leftarrow x_{n-1} + \Delta t\,\sum_{i=1}^{s}b_i\,\dot{X}_i$

The First-Step-As-Last (FSAL) principle is not needed with DIRK, but maybe useful if the first stage is explicit (i.e, EDIRK). The default is to set useFSAL=false.

Definition at line 87 of file Tempus_StepperDIRK_decl.hpp.

Constructor & Destructor Documentation

template<class Scalar >

Tempus::StepperDIRK< Scalar >::StepperDIRK ( )

Default constructor.

Constructs with a default ParameterList.
Can reset ParameterList with setParameterList().
Requires subsequent setModel() and initialize() calls before calling takeStep().

Definition at line 27 of file Tempus_StepperDIRK_impl.hpp.

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 35 of file Tempus_StepperDIRK_impl.hpp.

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 52 of file Tempus_StepperDIRK_impl.hpp.

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 68 of file Tempus_StepperDIRK_impl.hpp.

Member Function Documentation

template<class Scalar >

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

virtual

Definition at line 386 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

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

virtual

Definition at line 379 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperDIRK< Scalar >::getAlpha ( const Scalar dt ) const

inlinevirtual

Return alpha = d(xDot)/dx.

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 163 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperDIRK< Scalar >::getBeta ( const Scalar ) const

inlinevirtual

Return beta = d(x)/dx.

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 169 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

virtual

Implements Tempus::Stepper< Scalar >.

Definition at line 431 of file Tempus_StepperDIRK_impl.hpp.

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 370 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

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

Definition at line 449 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperDIRK< Scalar >::getOrder ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 141 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperDIRK< Scalar >::getOrderMax ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 143 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperDIRK< Scalar >::getOrderMin ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 142 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 159 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

Definition at line 412 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

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

virtual

Initialize during construction and after changing input parameters.

Implements Tempus::Stepper< Scalar >.

Definition at line 154 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 145 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 154 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 153 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 157 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 156 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

virtual

Set the initial conditions and make them consistent.

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 187 of file Tempus_StepperDIRK_impl.hpp.

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 133 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

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

Definition at line 396 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

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

virtual

Definition at line 87 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

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

virtual

Definition at line 100 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

void Tempus::StepperDIRK< Scalar >::setTableau ( Teuchos::RCP< const RKButcherTableau< Scalar > > DIRK_ButcherTableau )

virtual

Definition at line 120 of file Tempus_StepperDIRK_impl.hpp.

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 203 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

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

Definition at line 457 of file Tempus_StepperDIRK_impl.hpp.

Member Data Documentation

template<class Scalar >

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

protected

Definition at line 201 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

protected

Definition at line 200 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

Teuchos::RCP<const RKButcherTableau<Scalar> > Tempus::StepperDIRK< Scalar >::DIRK_ButcherTableau_

protected

Definition at line 189 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

protected

Definition at line 197 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

protected

Definition at line 202 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperDIRK< Scalar >::stageX_

protected

Definition at line 192 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

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

protected

Definition at line 191 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

Teuchos::RCP<StepperDIRKObserver<Scalar> > Tempus::StepperDIRK< Scalar >::stepperDIRKObserver_

protected

Definition at line 195 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

Teuchos::RCP<Thyra::VectorBase<Scalar> > Tempus::StepperDIRK< Scalar >::xTilde_

protected

Definition at line 193 of file Tempus_StepperDIRK_decl.hpp.

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

http://docs.trilinos.org/r12.16/packages/tempus/src/Tempus_StepperDIRK_decl.hpp
http://docs.trilinos.org/r12.16/packages/tempus/src/Tempus_StepperDIRK_impl.hpp

Public Member Functions

Protected Attributes

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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