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Tempus_Test::VanDerPolModel< Scalar > Class Template Reference

van der Pol model problem for nonlinear electrical circuit. More...

#include <VanDerPolModel_decl.hpp>

Inheritance diagram for Tempus_Test::VanDerPolModel< Scalar >:

Public Member Functions

 VanDerPolModel (Teuchos::RCP< Teuchos::ParameterList > pList=Teuchos::null)
 
Thyra::ModelEvaluatorBase::InArgs< Scalar > getExactSolution (double t) const
 
Thyra::ModelEvaluatorBase::InArgs< Scalar > getExactSensSolution (int j, double t) const
 

Private functions overridden from ModelEvaluatorDefaultBase.

int dim_
 Number of state unknowns (2)
 
int Np_
 Number of parameter vectors (1)
 
int np_
 Number of parameters in this vector (1)
 
int Ng_
 Number of observation functions (0)
 
int ng_
 Number of elements in this observation function (0)
 
bool haveIC_
 false => no nominal values are provided (default=true)
 
bool acceptModelParams_
 Changes inArgs to require parameters.
 
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 > > g_space_
 
Scalar epsilon_
 This is a model parameter.
 
Scalar t0_ic_
 initial time
 
Scalar x0_ic_
 initial condition for x0
 
Scalar x1_ic_
 initial condition for x1
 
Thyra::ModelEvaluatorBase::OutArgs< Scalar > createOutArgsImpl () const
 
void evalModelImpl (const Thyra::ModelEvaluatorBase::InArgs< Scalar > &inArgs_bar, const Thyra::ModelEvaluatorBase::OutArgs< Scalar > &outArgs_bar) const
 

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
 
void setupInOutArgs_ () const
 

Detailed Description

template<class Scalar>
class Tempus_Test::VanDerPolModel< Scalar >

van der Pol model problem for nonlinear electrical circuit.

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*}
  \mathcal{F}_0 & = & \dot{x}_0(t) - x_1(t) = 0 \\
  \mathcal{F}_1 & = & \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*}

Hairer and Wanner suggest the output times of $t = 1,2,3,4,...,11$, and $\epsilon = 10^{-6}$ to make the problem very stiff. For $\epsilon = 0$, the solution becomes

\begin{eqnarray*}
  \ln \left|x_0\right| - \frac{x_0^2}{2} & = & t + C \\
  x_1 & = & \frac{x_0}{1-x_0^2}
\end{eqnarray*}

where $C =\ln \left|x_0(t=0)\right| - \frac{x_0^2(t=0)}{2} =-1.306853.$

The components of iteration matrix, $W$, are defined to be

\[
  W_{ij} \equiv \frac{d\mathcal{F}_i}{dx_j} = \frac{d}{dx_j}
         \mathcal{F}_i (\dot{x}_i, x_0, \ldots, x_k, \ldots, x_K, t)
\]

(not using Einstein summation). Using the chain rule, we can write

\[
  \frac{d\mathcal{F}_i}{dx_j} =
   \frac{\partial\dot{x}_i}{\partial x_j}
   \frac{\partial\mathcal{F}_i}{\partial \dot{x}_i}
   + \sum_{k=0}^K \frac{\partial x_k}{\partial x_j}
     \frac{\partial\mathcal{F}_i}{\partial x_k}
   + \frac{\partial t}{\partial x_j}
   \frac{\partial\mathcal{F}_i}{\partial t}
\]

but noting that $\partial t/\partial x_j = 0$ and

\[
   \frac{\partial x_k}{\partial x_j} = \left\{
     \begin{array}{c}
       1 \mbox{ if } j = k \\
       0 \mbox{ if } j \neq k
     \end{array}
   \right.
\]

we can write

\[
  \frac{d\mathcal{F}_i}{dx_j} =
    \alpha \frac{\partial\mathcal{F}_i}{\partial \dot{x}_j}
  + \beta \frac{\partial\mathcal{F}_i}{\partial x_j}
\]

where

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

Thus for the van der Pol problem, we have

\begin{eqnarray*}
  W_{00} = \alpha \frac{\partial\mathcal{F}_0}{\partial \dot{x}_0}
          + \beta \frac{\partial\mathcal{F}_0}{\partial x_0}
       & = & \alpha \\
  W_{01} = \alpha \frac{\partial\mathcal{F}_0}{\partial \dot{x}_1}
          + \beta \frac{\partial\mathcal{F}_0}{\partial x_1}
       & = & -\beta \\
  W_{10} = \alpha \frac{\partial\mathcal{F}_1}{\partial \dot{x}_0}
          + \beta \frac{\partial\mathcal{F}_1}{\partial x_0}
       & = & \beta (2 x_0 x_1 + 1)/\epsilon \\
  W_{11} = \alpha \frac{\partial\mathcal{F}_1}{\partial \dot{x}_1}
          + \beta \frac{\partial\mathcal{F}_1}{\partial x_1}
       & = & \alpha + \beta (x^2_0 - 1)/\epsilon \\
\end{eqnarray*}

Definition at line 111 of file VanDerPolModel_decl.hpp.

Constructor & Destructor Documentation

◆ VanDerPolModel()

template<class Scalar >
Tempus_Test::VanDerPolModel< Scalar >::VanDerPolModel ( Teuchos::RCP< Teuchos::ParameterList > pList = Teuchos::null)

Definition at line 28 of file VanDerPolModel_impl.hpp.

Member Function Documentation

◆ getExactSolution()

template<class Scalar >
Thyra::ModelEvaluatorBase::InArgs< Scalar > Tempus_Test::VanDerPolModel< Scalar >::getExactSolution ( double t) const

Definition at line 56 of file VanDerPolModel_impl.hpp.

◆ getExactSensSolution()

template<class Scalar >
Thyra::ModelEvaluatorBase::InArgs< Scalar > Tempus_Test::VanDerPolModel< Scalar >::getExactSensSolution ( int j,
double t ) const

Definition at line 66 of file VanDerPolModel_impl.hpp.

◆ get_x_space()

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

Definition at line 76 of file VanDerPolModel_impl.hpp.

◆ get_f_space()

template<class Scalar >
Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > > Tempus_Test::VanDerPolModel< Scalar >::get_f_space ( ) const

Definition at line 85 of file VanDerPolModel_impl.hpp.

◆ getNominalValues()

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

Definition at line 94 of file VanDerPolModel_impl.hpp.

◆ create_W()

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

Definition at line 105 of file VanDerPolModel_impl.hpp.

◆ create_W_op()

template<class Scalar >
Teuchos::RCP< Thyra::LinearOpBase< Scalar > > Tempus_Test::VanDerPolModel< Scalar >::create_W_op ( ) const

Definition at line 143 of file VanDerPolModel_impl.hpp.

◆ get_W_factory()

template<class Scalar >
Teuchos::RCP< const Thyra::LinearOpWithSolveFactoryBase< Scalar > > Tempus_Test::VanDerPolModel< Scalar >::get_W_factory ( ) const

Definition at line 153 of file VanDerPolModel_impl.hpp.

◆ createInArgs()

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

Definition at line 164 of file VanDerPolModel_impl.hpp.

◆ get_p_space()

template<class Scalar >
Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > > Tempus_Test::VanDerPolModel< Scalar >::get_p_space ( int l) const

Definition at line 285 of file VanDerPolModel_impl.hpp.

◆ get_p_names()

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

Definition at line 297 of file VanDerPolModel_impl.hpp.

◆ get_g_space()

template<class Scalar >
Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > > Tempus_Test::VanDerPolModel< Scalar >::get_g_space ( int j) const

Definition at line 312 of file VanDerPolModel_impl.hpp.

◆ setParameterList()

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

Definition at line 395 of file VanDerPolModel_impl.hpp.

◆ getValidParameters()

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

Definition at line 423 of file VanDerPolModel_impl.hpp.

◆ setupInOutArgs_()

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

Definition at line 323 of file VanDerPolModel_impl.hpp.

◆ createOutArgsImpl()

template<class Scalar >
Thyra::ModelEvaluatorBase::OutArgs< Scalar > Tempus_Test::VanDerPolModel< Scalar >::createOutArgsImpl ( ) const
private

Definition at line 177 of file VanDerPolModel_impl.hpp.

◆ evalModelImpl()

template<class Scalar >
void Tempus_Test::VanDerPolModel< Scalar >::evalModelImpl ( const Thyra::ModelEvaluatorBase::InArgs< Scalar > & inArgs_bar,
const Thyra::ModelEvaluatorBase::OutArgs< Scalar > & outArgs_bar ) const
private

Definition at line 187 of file VanDerPolModel_impl.hpp.

Member Data Documentation

◆ dim_

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

Number of state unknowns (2)

Definition at line 162 of file VanDerPolModel_decl.hpp.

◆ Np_

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

Number of parameter vectors (1)

Definition at line 163 of file VanDerPolModel_decl.hpp.

◆ np_

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

Number of parameters in this vector (1)

Definition at line 164 of file VanDerPolModel_decl.hpp.

◆ Ng_

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

Number of observation functions (0)

Definition at line 165 of file VanDerPolModel_decl.hpp.

◆ ng_

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

Number of elements in this observation function (0)

Definition at line 166 of file VanDerPolModel_decl.hpp.

◆ haveIC_

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

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

Definition at line 167 of file VanDerPolModel_decl.hpp.

◆ acceptModelParams_

template<class Scalar >
bool Tempus_Test::VanDerPolModel< Scalar >::acceptModelParams_
private

Changes inArgs to require parameters.

Definition at line 168 of file VanDerPolModel_decl.hpp.

◆ isInitialized_

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

Definition at line 169 of file VanDerPolModel_decl.hpp.

◆ inArgs_

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

Definition at line 170 of file VanDerPolModel_decl.hpp.

◆ outArgs_

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

Definition at line 171 of file VanDerPolModel_decl.hpp.

◆ nominalValues_

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

Definition at line 172 of file VanDerPolModel_decl.hpp.

◆ x_space_

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

Definition at line 173 of file VanDerPolModel_decl.hpp.

◆ f_space_

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

Definition at line 174 of file VanDerPolModel_decl.hpp.

◆ p_space_

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

Definition at line 175 of file VanDerPolModel_decl.hpp.

◆ g_space_

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

Definition at line 176 of file VanDerPolModel_decl.hpp.

◆ epsilon_

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

This is a model parameter.

Definition at line 179 of file VanDerPolModel_decl.hpp.

◆ t0_ic_

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

initial time

Definition at line 180 of file VanDerPolModel_decl.hpp.

◆ x0_ic_

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

initial condition for x0

Definition at line 181 of file VanDerPolModel_decl.hpp.

◆ x1_ic_

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

initial condition for x1

Definition at line 182 of file VanDerPolModel_decl.hpp.


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