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Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar > Class Template Reference

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 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 Member Functions

void setupInOutArgs_ () 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
 

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...
 

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 102 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 31 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

Member Function Documentation

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

Definition at line 91 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

Definition at line 124 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

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

Definition at line 146 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 159 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
private

Definition at line 169 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

Definition at line 73 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

Definition at line 337 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

Definition at line 316 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

Definition at line 299 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

Definition at line 135 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

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

Definition at line 65 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

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

Definition at line 81 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

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

Definition at line 441 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

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

Definition at line 416 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

template<class Scalar >
void Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::setupInOutArgs_ ( ) const
private

Definition at line 346 of file VanDerPol_IMEXPart_ImplicitModel_impl.hpp.

Member Data Documentation

template<class Scalar >
int Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::dim_
private

Number of state unknowns (1)

Definition at line 147 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::dxdp_space_
private

Definition at line 162 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::dydp_space_
private

Definition at line 163 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

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

This is a model parameter.

Definition at line 167 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::f_space_
private

Definition at line 159 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::g_space_
private

Definition at line 164 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
bool Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::haveIC_
private

false => no nominal values are provided (default=true)

Definition at line 152 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Thyra::ModelEvaluatorBase::InArgs<Scalar> Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::inArgs_
mutableprivate

Definition at line 155 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
bool Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::isInitialized_
mutableprivate

Definition at line 154 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
int Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::Ng_
private

Number of observation functions (0)

Definition at line 150 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
int Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::ng_
private

Number of elements in this observation function (0)

Definition at line 151 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Thyra::ModelEvaluatorBase::InArgs<Scalar> Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::nominalValues_
mutableprivate

Definition at line 157 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
int Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::Np_
private

Number of parameter vectors (1)

Definition at line 148 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
int Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::np_
private

Number of parameters in this vector (1)

Definition at line 149 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Thyra::ModelEvaluatorBase::OutArgs<Scalar> Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::outArgs_
mutableprivate

Definition at line 156 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::p_space_
private

Definition at line 160 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Scalar Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::t0_ic_
private

initial time

Definition at line 168 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
bool Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::useDfDpAsTangent_
private

Treat DfDp OutArg as tangent (df/dx*dx/dp+df/dp)

Definition at line 153 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Scalar Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::x0_ic_
private

initial condition for x0

Definition at line 169 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Scalar Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::x1_ic_
private

initial condition for x1

Definition at line 170 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::x_space_
private

Definition at line 158 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

template<class Scalar >
Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> > Tempus_Test::VanDerPol_IMEXPart_ImplicitModel< Scalar >::y_space_
private

Definition at line 161 of file VanDerPol_IMEXPart_ImplicitModel_decl.hpp.

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