Consider the ODE:

$m\ddot{x} + c\dot{x} + kx=f$

where $k \geq 0$ is a constant, $c$ is a constant damping parameter, $f$ is a constant forcing parameter, and $m>0$ is a constant mass parameter, with initial conditions are:

$\begin{eqnarray*} x(0) & = & 0\\ \dot{x}(0) & = & 1 \end{eqnarray*}$

It is straight-forward to show that the exact solution to this ODE is:

$\begin{eqnarray*} x(t) & = & t(1+0.5\tilde{f}t), \hspace{3.6cm} if \hspace{0.2cm} k = c = 0 \\ & = & \frac{(\tilde{c}-\tilde{f})}{\tilde{c}^2}(1-e^{-\tilde{c}t}) + \frac{f}{c}t, \hspace{1.9cm} if \hspace{0.2cm} k = 0, c\neq 0 \\ & = & \frac{1}{\sqrt{\tilde{k}}}\sin(\sqrt{\tilde{k}}t) + \frac{f}{k}\left(1-\cos(\sqrt{\tilde{k}}t) \right), \hspace{0.2cm} if \hspace{0.2cm} k > 0, c = 0 \end{eqnarray*}$

where $\tilde{c}\equiv c/m$ , $\tilde{k}\equiv k/m$ and $\tilde{f}\equiv f/m$ . While it is possible to derive the solution to this ODE for the case when $k > 0$ and $c \neq 0$ , we do not consider that case here. When $c = k = 0$ , $m=1$ , and $f=-1$ , our ODE simplies to a canonical differential equation model of a ball thrown up in the air, with a parabolic trajectory solution, namely

$x(t) = t(1-0.5t)$

where $t\in [0,2]$ . An EpetraExt version of this simplified version of the test is implemented in Piro::MockModelEval_B (see Trilinos/packages/piro/test), where it is used to test the Piro (EpetraExt) Newmark-Beta scheme (see input_Solver_NB.xml input file). When $c = f = 0$ and $m=k = 1$ , this test is equivalent to the SinCos model.. More...

#include <HarmonicOscillatorModel_decl.hpp>

Inheritance diagram for Tempus_Test::HarmonicOscillatorModel< Scalar >:

Public Member Functions
	HarmonicOscillatorModel (Teuchos::RCP< Teuchos::ParameterList > pList=Teuchos::null, const bool use_accel_IC=false)

Thyra::ModelEvaluatorBase::InArgs < Scalar >	getExactSolution (double t) const

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

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

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

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

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

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

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

int	vecLength_

int	numResponses_

Thyra::ModelEvaluatorBase::InArgs < Scalar >	inArgs_

Thyra::ModelEvaluatorBase::OutArgs < Scalar >	outArgs_

Thyra::ModelEvaluatorBase::InArgs < Scalar >	nominalValues_

bool	isInitialized_

double	c_

double	f_

double	k_

double	m_

Teuchos::RCP < Teuchos::FancyOStream >	out_

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::HarmonicOscillatorModel< Scalar >

Consider the ODE:

$m\ddot{x} + c\dot{x} + kx=f$

where $k \geq 0$ is a constant, $c$ is a constant damping parameter, $f$ is a constant forcing parameter, and $m>0$ is a constant mass parameter, with initial conditions are:

$\begin{eqnarray*} x(0) & = & 0\\ \dot{x}(0) & = & 1 \end{eqnarray*}$

It is straight-forward to show that the exact solution to this ODE is:

$\begin{eqnarray*} x(t) & = & t(1+0.5\tilde{f}t), \hspace{3.6cm} if \hspace{0.2cm} k = c = 0 \\ & = & \frac{(\tilde{c}-\tilde{f})}{\tilde{c}^2}(1-e^{-\tilde{c}t}) + \frac{f}{c}t, \hspace{1.9cm} if \hspace{0.2cm} k = 0, c\neq 0 \\ & = & \frac{1}{\sqrt{\tilde{k}}}\sin(\sqrt{\tilde{k}}t) + \frac{f}{k}\left(1-\cos(\sqrt{\tilde{k}}t) \right), \hspace{0.2cm} if \hspace{0.2cm} k > 0, c = 0 \end{eqnarray*}$

where $\tilde{c}\equiv c/m$ , $\tilde{k}\equiv k/m$ and $\tilde{f}\equiv f/m$ . While it is possible to derive the solution to this ODE for the case when $k > 0$ and $c \neq 0$ , we do not consider that case here. When $c = k = 0$ , $m=1$ , and $f=-1$ , our ODE simplies to a canonical differential equation model of a ball thrown up in the air, with a parabolic trajectory solution, namely

$x(t) = t(1-0.5t)$

where $t\in [0,2]$ . An EpetraExt version of this simplified version of the test is implemented in Piro::MockModelEval_B (see Trilinos/packages/piro/test), where it is used to test the Piro (EpetraExt) Newmark-Beta scheme (see input_Solver_NB.xml input file). When $c = f = 0$ and $m=k = 1$ , this test is equivalent to the SinCos model..

Definition at line 55 of file HarmonicOscillatorModel_decl.hpp.

Constructor & Destructor Documentation

template<class Scalar >

Tempus_Test::HarmonicOscillatorModel< Scalar >::HarmonicOscillatorModel	(	Teuchos::RCP< Teuchos::ParameterList >	pList = `Teuchos::null`,
		const bool	use_accel_IC = `false`
	)

Definition at line 27 of file HarmonicOscillatorModel_impl.hpp.

Member Function Documentation

template<class Scalar >

Thyra::ModelEvaluatorBase::InArgs< Scalar > Tempus_Test::HarmonicOscillatorModel< Scalar >::getExactSolution ( double t ) const

Definition at line 73 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 132 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 139 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 146 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 155 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 172 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 181 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 190 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 297 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 307 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Implements Thyra::ModelEvaluator< class >.

Definition at line 317 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Implements Teuchos::ParameterListAcceptor.

Definition at line 370 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

virtual

Reimplemented from Teuchos::ParameterListAcceptor.

Definition at line 408 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

private

Definition at line 329 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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

private

Definition at line 200 of file HarmonicOscillatorModel_impl.hpp.

template<class Scalar >

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