van der Pol model formulated for the partitioned IMEX-RK. More...

#include <VanDerPol_IMEXPart_ImplicitModel_decl.hpp>

Inheritance diagram for Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >:

Public Member Functions
	VanDerPol_IMEXPart_ImplicitModel (Teuchos::RCP< Teuchos::ParameterList > pList=Teuchos::null)

Public Member Functions inherited from Thyra::StateFuncModelEvaluatorBase< Scalar >
RCP< const VectorSpaceBase < Scalar > >	get_p_space (int l) const

RCP< const Teuchos::Array < std::string > >	get_p_names (int l) const

RCP< const VectorSpaceBase < Scalar > >	get_g_space (int j) const

Teuchos::ArrayView< const std::string >	get_g_names (int j) const

ModelEvaluatorBase::InArgs < Scalar >	getNominalValues () const

ModelEvaluatorBase::InArgs < Scalar >	getLowerBounds () const

ModelEvaluatorBase::InArgs < Scalar >	getUpperBounds () const

RCP< LinearOpBase< Scalar > >	create_W_op () const

RCP< PreconditionerBase< Scalar > >	create_W_prec () const

RCP< const LinearOpWithSolveFactoryBase < Scalar > >	get_W_factory () const

void	reportFinalPoint (const ModelEvaluatorBase::InArgs< Scalar > &finalPoint, const bool wasSolved)

Public Member Functions inherited from Thyra::ModelEvaluator< class >
virtual int	Np () const =0

virtual int	Ng () const =0

virtual RCP< const VectorSpaceBase< Scalar > >	get_f_multiplier_space () const =0

virtual RCP< const VectorSpaceBase< Scalar > >	get_g_multiplier_space (int j) const =0

virtual RCP< LinearOpBase < Scalar > >	create_DfDp_op (int l) const =0

virtual RCP< LinearOpBase < Scalar > >	create_DgDx_dot_op (int j) const =0

virtual RCP< LinearOpBase < Scalar > >	create_DgDx_op (int j) const =0

virtual RCP< LinearOpBase < Scalar > >	create_DgDp_op (int j, int l) const =0

virtual ModelEvaluatorBase::OutArgs < Scalar >	createOutArgs () const =0

virtual void	evalModel (const ModelEvaluatorBase::InArgs< Scalar > &inArgs, const ModelEvaluatorBase::OutArgs< Scalar > &outArgs) const =0

	ModelEvaluatorBase ()

std::string	toString (ModelEvaluatorBase::EInArgsMembers)

std::string	toString (ModelEvaluatorBase::EOutArgsMembers)

std::string	toString (ModelEvaluatorBase::EDerivativeMultiVectorOrientation orientation)

ModelEvaluatorBase::EDerivativeMultiVectorOrientation	getOtherDerivativeMultiVectorOrientation (ModelEvaluatorBase::EDerivativeMultiVectorOrientation orientation)

Public Member Functions inherited from Teuchos::Describable
virtual std::string	description () const

virtual void	describe (FancyOStream &out, const EVerbosityLevel verbLevel=verbLevel_default) const

void	describe (std::ostream &out, const EVerbosityLevel verbLevel=verbLevel_default) const

virtual	~Describable ()

	LabeledObject ()

virtual	~LabeledObject ()

virtual void	setObjectLabel (const std::string &objectLabel)

virtual std::string	getObjectLabel () const

DescribableStreamManipulatorState	describe (const Describable &describable, const EVerbosityLevel verbLevel=Describable::verbLevel_default)

std::ostream &	operator<< (std::ostream &os, const DescribableStreamManipulatorState &d)

Public Member Functions inherited from Teuchos::ParameterListAcceptorDefaultBase
RCP< ParameterList >	getNonconstParameterList ()

RCP< ParameterList >	unsetParameterList ()

RCP< const ParameterList >	getParameterList () const

Private Member Functions
void	setupInOutArgs_ () const

Private Attributes
int	dim_
	Number of state unknowns (1) More...

int	Np_
	Number of parameter vectors (1) More...

int	np_
	Number of parameters in this vector (1) More...

int	Ng_
	Number of observation functions (0) More...

int	ng_
	Number of elements in this observation function (0) More...

bool	haveIC_
	false => no nominal values are provided (default=true) More...

bool	useDfDpAsTangent_
	Treat DfDp OutArg as tangent (df/dx*dx/dp+df/dp) More...

bool	isInitialized_

Thyra::ModelEvaluatorBase::InArgs < Scalar >	inArgs_

Thyra::ModelEvaluatorBase::OutArgs < Scalar >	outArgs_

Thyra::ModelEvaluatorBase::InArgs < Scalar >	nominalValues_

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	x_space_

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	f_space_

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	p_space_

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	y_space_

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	dxdp_space_

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	dydp_space_

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	g_space_

Scalar	epsilon_
	This is a model parameter. More...

Scalar	t0_ic_
	initial time More...

Scalar	x0_ic_
	initial condition for x0 More...

Scalar	x1_ic_
	initial condition for x1 More...

Public functions overridden from ModelEvaluator.
Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	get_x_space () const

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	get_f_space () const

Thyra::ModelEvaluatorBase::InArgs < Scalar >	getNominalValues () const

Teuchos::RCP < Thyra::LinearOpWithSolveBase < Scalar > >	create_W () const

Teuchos::RCP < Thyra::LinearOpBase< Scalar > >	create_W_op () const

Teuchos::RCP< const Thyra::LinearOpWithSolveFactoryBase < Scalar > >	get_W_factory () const

Thyra::ModelEvaluatorBase::InArgs < Scalar >	createInArgs () const

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	get_p_space (int l) const

Teuchos::RCP< const Teuchos::Array< std::string > >	get_p_names (int l) const

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	get_g_space (int j) const

Public functions overridden from ParameterListAcceptor.
void	setParameterList (Teuchos::RCP< Teuchos::ParameterList > const &paramList)

Teuchos::RCP< const Teuchos::ParameterList >	getValidParameters () const

Private functions overridden from ModelEvaluatorDefaultBase.
Thyra::ModelEvaluatorBase::OutArgs < Scalar >	createOutArgsImpl () const

void	evalModelImpl (const Thyra::ModelEvaluatorBase::InArgs< Scalar > &inArgs_bar, const Thyra::ModelEvaluatorBase::OutArgs< Scalar > &outArgs_bar) const

Additional Inherited Members
Public Types inherited from Thyra::ModelEvaluator< class >
enum	EInArgsMembers

enum	EInArgs_p_mp

enum	EEvalType

enum	EDerivativeMultiVectorOrientation

enum	EDerivativeLinearOp

enum	EDerivativeLinearity

enum	ERankStatus

enum	EOutArgsMembers

enum	EOutArgsDfDp

enum	EOutArgsDgDx_dot

enum	EOutArgsDgDx

enum	EOutArgsDgDp

enum	EOutArgsDfDp_mp

enum	EOutArgs_g_mp

enum	EOutArgsDgDx_dot_mp

enum	EOutArgsDgDx_mp

enum	EOutArgsDgDp_mp

typedef Teuchos::ScalarTraits < Scalar >::magnitudeType	ScalarMag

Static Public Attributes inherited from Thyra::ModelEvaluator< class >
static const int	NUM_E_IN_ARGS_MEMBERS

static const int	NUM_E_OUT_ARGS_MEMBERS

Static Public Attributes inherited from Teuchos::Describable
static const EVerbosityLevel	verbLevel_default

Protected Member Functions inherited from Teuchos::ParameterListAcceptorDefaultBase
void	setMyParamList (const RCP< ParameterList > &paramList)

RCP< ParameterList >	getMyNonconstParamList ()

RCP< const ParameterList >	getMyParamList () const

Detailed Description

template<class Scalar>
class Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >

van der Pol model formulated for the partitioned IMEX-RK.

This is a canonical equation of a nonlinear oscillator (Hairer, Norsett, and Wanner, pp. 111-115, and Hairer and Wanner, pp. 4-5) for an electrical circuit. In implicit ODE form, $\mathcal{F}(\dot{x},x,t) = 0$ , the scaled problem can be written as

$\begin{eqnarray*} \dot{x}_0(t) - x_1(t) & = & 0 \\ \dot{x}_1(t) - [(1-x_0^2)x_1-x_0]/\epsilon & = & 0 \end{eqnarray*}$

where the initial conditions are

$\begin{eqnarray*} x_0(t_0=0) & = & 2 \\ x_1(t_0=0) & = & 0 \end{eqnarray*}$

and the initial time derivatives are

$\begin{eqnarray*} \dot{x}_0(t_0=0) & = & x_1(t_0=0) = 0 \\ \dot{x}_1(t_0=0) & = & [(1-x_0^2)x_1-x_0]/\epsilon = -2/\epsilon \end{eqnarray*}$

For a partitioned IMEX-RK time stepper, we need to rewrite this in the following form

$\begin{eqnarray*} M(z,t)\, \dot{z} + G(z,t) + F(z,t) & = & 0, \\ \mathcal{G}(\dot{z},z,t) + F(z,t) & = & 0, \end{eqnarray*}$

where $\mathcal{G}(\dot{z},z,t) = M(z,t)\, \dot{z} + G(z,t)$ , $M(z,t)$ is the mass matrix, $F(z,t)$ is the operator representing the "slow" physics (and evolved explicitly), and $G(z,t)$ is the operator representing the "fast" physics. For the van der Pol problem, we can separate the terms as follows

$z = \left\{\begin{array}{c} y \\ x \end{array}\right\} = \left\{\begin{array}{c} x_0 \\ x_1 \end{array}\right\},\;\;\; F(z,t) = \left\{\begin{array}{c} F^y(x,y,t)\\F^x(x,y,t)\end{array}\right\} = \left\{\begin{array}{c} -x_1 \\ x_0/\epsilon\end{array}\right\}, \mbox{ and } G(z,t) = \left\{\begin{array}{c} 0 \\ G^x(x,y,t)\end{array}\right\} = \left\{\begin{array}{c} 0 \\ -(1-x_0^2)x_1/\epsilon \end{array}\right\}$

where $M(z,t)=I$ is the identity matrix.

Thus the explicit van der Pol model (VanDerPol_IMEX_ExplicitModel) formulated for the partitioned IMEX-RK is

$\begin{eqnarray*} F^y(x,y,t) & = & \dot{x}_0(t) - x_1(t) = 0 \\ F^x(x,y,t) & = & \dot{x}_1(t) + x_0/\epsilon = 0 \end{eqnarray*}$

and the implicit van der Pol model (VanDerPol_IMEXPart_ImplicitModel) formulated for the partitioned IMEX-RK is

$G^x(x,y,t) = \dot{x}_1(t) - (1-x_0^2)x_1/\epsilon = 0$

Noting that $G^y(x,y,t) = \dot{x}_0(t) = 0$ is not needed.

Recalling the defintion of the iteration matrix, $W$ ,

$W_{ij} \equiv \frac{d\mathcal{G}^x_i}{dx_j} = \alpha \frac{\partial\mathcal{G}^x_i}{\partial \dot{x}_j} + \beta \frac{\partial\mathcal{G}^x_i}{\partial x_j}$

where

$\alpha = \left\{ \begin{array}{cl} \frac{\partial\dot{x}_i}{\partial x_j} & \mbox{ if } i = j \\ 0 & \mbox{ if } i \neq j \end{array} \right. \;\;\;\; \mbox{ and } \;\;\;\; \beta = 1$

we can write for the implicit van der Pol model (VanDerPol_IMEXPart_ImplicitModel)

$\begin{eqnarray*} W_{00} = \alpha \frac{\partial\mathcal{G}^x_0}{\partial \dot{x}_1} + \beta \frac{\partial\mathcal{G}^x_0}{\partial x_1} & = & \alpha + \beta (x^2_0 - 1)/\epsilon \\ \end{eqnarray*}$

Definition at line 103 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

Constructor & Destructor Documentation

template<class Scalar >

Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::VanDerPol_IMEXPart_ImplicitModel ( Teuchos::RCP< Teuchos::ParameterList > pList = Teuchos::null )

Definition at line 30 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

Member Function Documentation

template<class Scalar >

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::get_x_space ( ) const

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 64 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::get_f_space ( ) const

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 71 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

Thyra::ModelEvaluatorBase::InArgs< Scalar > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::getNominalValues ( ) const

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 78 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

Teuchos::RCP< Thyra::LinearOpWithSolveBase< Scalar > > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::create_W ( ) const

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 87 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

Teuchos::RCP< Thyra::LinearOpBase< Scalar > > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::create_W_op ( ) const

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 119 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

Teuchos::RCP< const Thyra::LinearOpWithSolveFactoryBase< Scalar > > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::get_W_factory ( ) const

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 128 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

Thyra::ModelEvaluatorBase::InArgs< Scalar > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::createInArgs ( ) const

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 137 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::get_p_space ( int l ) const

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 284 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

Teuchos::RCP< const Teuchos::Array< std::string > > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::get_p_names ( int l ) const

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 300 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::get_g_space ( int j ) const

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 320 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

void Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::setParameterList ( Teuchos::RCP< Teuchos::ParameterList > const & paramList )

virtual

Implements Teuchos::ParameterListAcceptor.

Definition at line 393 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

Teuchos::RCP< const Teuchos::ParameterList > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::getValidParameters ( ) const

virtual

Reimplemented from Teuchos::ParameterListAcceptor.

Definition at line 418 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

void Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::setupInOutArgs_ ( ) const

private

Definition at line 327 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

Thyra::ModelEvaluatorBase::OutArgs< Scalar > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::createOutArgsImpl ( ) const

private

Definition at line 147 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >

void Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::evalModelImpl	(	const Thyra::ModelEvaluatorBase::InArgs< Scalar > &	inArgs_bar,
		const Thyra::ModelEvaluatorBase::OutArgs< Scalar > &	outArgs_bar
	)		const