Extrapolated linearly implicit Euler method. More...

#include <limex.hh>

Detailed Description

template<class Eq>
class Kaskade::Limex< Eq >

Extrapolated linearly implicit Euler method.

This class implements the extrapolated linearly implicit Euler method for integrating time-dependent evolution problems. The implementation follows Deuflhard/Bornemann Chapter 6.4.3.

Todo:: Currently the matrix \( B \) has to be constant.

This class implements the extrapolated linearly implicit Euler method for integrating time-dependent evolution problems. The implementation follows Deuflhard/Bornemann Chapter 6.4.3.

Template Parameters

Eq	a parabolic equation, a model of the ParabolicEquation interface.

This class implements the extrapolated linearly implicit Euler method for integrating time-dependent evolution problems. The implementation follows Deuflhard/Bornemann Chapter 6.4.3.

Definition at line 32 of file limex.hh.

Public Types
typedef Eq	EvolutionEquation

typedef EvolutionEquation::AnsatzVars::VariableSet	State

typedef Eq	EvolutionEquation

typedef EvolutionEquation::AnsatzVars::VariableSet	State

typedef Eq	EvolutionEquation

typedef EvolutionEquation::AnsatzVars::VariableSet	State

Public Member Functions
	Limex (GridManager< typename EvolutionEquation::AnsatzVars::Grid > &gridManager, EvolutionEquation &eq_, typename EvolutionEquation::AnsatzVars const &ansatzVars_, std::vector< std::pair< double, double > > const &tolX)

State const &	step (State const &x, double dt, int order)

double	estimateError (State const &x, int i, int j) const

template<class OutStream >
void	reportTime (OutStream &out) const

void	advanceTime (double dt)

	Limex (GridManager< typename EvolutionEquation::AnsatzVars::Grid > &gridManager_, EvolutionEquation &eq_, typename EvolutionEquation::AnsatzVars const &ansatzVars_, DirectType st=DirectType::MUMPS, PrecondType precondType_=PrecondType::ILUK, int verbosity_=1)

State const &	step (State const &x, double dt, int order, std::vector< std::pair< double, double > > const &tolX)
	Computes a state increment that advances the given state in time. The time in the given evolution equation is increased by dt. More...

std::vector< std::pair< double, double > >	estimateError (State const &x, int i, int j) const

template<class OutStream >
void	reportTime (OutStream &out) const

void	advanceTime (double dt)

	Limex (GridManager< typename EvolutionEquation::AnsatzVars::Grid > &gridManager_, EvolutionEquation &eq_, typename EvolutionEquation::AnsatzVars const &ansatzVars_, DirectType st=DirectType::UMFPACK)

State const &	step (State const &x, double dt, int order, std::vector< std::pair< double, double > > const &tolX)

State const &	step (State const &x, double dt, int order, std::vector< std::pair< double, double > > const &tolX, std::vector< std::vector< bool > > &refinements)

std::vector< std::pair< double, double > >	estimateError (State const &x, int i, int j) const

template<class OutStream >
void	reportTime (OutStream &out) const

void	advanceTime (double dt)

Public Attributes
ExtrapolationTableau< State >	extrap

double	rhsAssemblyTime

double	matrixAssemblyTime

double	factorizationTime

double	solutionTime

double	precAssemblyTime

double	elapsedTimeSinceReset

double	initSolutionTime

double	estimateTime

DirectType	directType

PrecondType	precondType

int	verbosity

double	adaptivityTime

DirectType	solverType

Member Typedef Documentation

◆ EvolutionEquation [1/3]

template<class Eq >

typedef Eq Kaskade::Limex< Eq >::EvolutionEquation

Definition at line 35 of file limex.hh.

◆ EvolutionEquation [2/3]

template<class Eq >

typedef Eq Kaskade::Limex< Eq >::EvolutionEquation

Definition at line 58 of file limexWithoutJens.hh.

◆ EvolutionEquation [3/3]

template<class Eq >

typedef Eq Kaskade::Limex< Eq >::EvolutionEquation

Definition at line 73 of file limexWithoutJensHierarchicEst.hh.

◆ State [1/3]

template<class Eq >

typedef EvolutionEquation::AnsatzVars::VariableSet Kaskade::Limex< Eq >::State

Definition at line 36 of file limex.hh.

◆ State [2/3]

template<class Eq >

typedef EvolutionEquation::AnsatzVars::VariableSet Kaskade::Limex< Eq >::State

Definition at line 59 of file limexWithoutJens.hh.

◆ State [3/3]

template<class Eq >

typedef EvolutionEquation::AnsatzVars::VariableSet Kaskade::Limex< Eq >::State

Definition at line 74 of file limexWithoutJensHierarchicEst.hh.

Constructor & Destructor Documentation

◆ Limex() [1/3]

template<class Eq >

Kaskade::Limex< Eq >::Limex	(	GridManager< typename EvolutionEquation::AnsatzVars::Grid > &	gridManager,
		EvolutionEquation &	eq_,
		typename EvolutionEquation::AnsatzVars const &	ansatzVars_,
		std::vector< std::pair< double, double > > const &	tolX
	)

inline

Constructs an ODE integrator. The arguments eq and ansatzVars have to exist during the lifetime of the integrator.

Definition at line 47 of file limex.hh.

◆ Limex() [2/3]

template<class Eq >

Kaskade::Limex< Eq >::Limex	(	GridManager< typename EvolutionEquation::AnsatzVars::Grid > &	gridManager_,
		EvolutionEquation &	eq_,
		typename EvolutionEquation::AnsatzVars const &	ansatzVars_,
		DirectType	st = `DirectType::MUMPS`,
		PrecondType	precondType_ = `PrecondType::ILUK`,
		int	verbosity_ = `1`
	)

inline

Constructs an ODE integrator. The arguments eq and ansatzVars have to exist during the lifetime of the integrator.

Definition at line 70 of file limexWithoutJens.hh.

◆ Limex() [3/3]

template<class Eq >

Kaskade::Limex< Eq >::Limex	(	GridManager< typename EvolutionEquation::AnsatzVars::Grid > &	gridManager_,
		EvolutionEquation &	eq_,
		typename EvolutionEquation::AnsatzVars const &	ansatzVars_,
		DirectType	st = `DirectType::UMFPACK`
	)

inline

Constructs an ODE integrator. The arguments eq and ansatzVars have to exist during the lifetime of the integrator.

Definition at line 106 of file limexWithoutJensHierarchicEst.hh.

Member Function Documentation

◆ advanceTime() [1/3]

template<class Eq >

void Kaskade::Limex< Eq >::advanceTime ( double dt )

inline

Definition at line 162 of file limex.hh.

◆ advanceTime() [2/3]

template<class Eq >

void Kaskade::Limex< Eq >::advanceTime ( double dt )

inline

Definition at line 424 of file limexWithoutJens.hh.

◆ advanceTime() [3/3]

template<class Eq >

void Kaskade::Limex< Eq >::advanceTime ( double dt )

inline

Definition at line 705 of file limexWithoutJensHierarchicEst.hh.

◆ estimateError() [1/3]

template<class Eq >

double Kaskade::Limex< Eq >::estimateError	(	State const &	x,
		int	i,
		int	j
	)		const

inline

Definition at line 141 of file limex.hh.

◆ estimateError() [2/3]

template<class Eq >

std::vector< std::pair< double, double > > Kaskade::Limex< Eq >::estimateError	(	State const &	x,
		int	i,
		int	j
	)		const

inline

Estimates the time discretization error of the previously computed step by taking the difference between the diagonal and subdiagonal extrapolation values of maximal order. This requires that order>1 has been given for the last step.

Definition at line 399 of file limexWithoutJens.hh.

◆ estimateError() [3/3]

template<class Eq >

std::vector< std::pair< double, double > > Kaskade::Limex< Eq >::estimateError	(	State const &	x,
		int	i,
		int	j
	)		const

inline

Estimates the time discretization error of the previously computed step by taking the difference between the diagonal and subdiagonal extrapolation values of maximal order. This requires that order>1 has been given for the last step.

Definition at line 683 of file limexWithoutJensHierarchicEst.hh.

◆ reportTime() [1/3]

template<class Eq >

template<class OutStream >

void Kaskade::Limex< Eq >::reportTime ( OutStream & out ) const

inline

Definition at line 155 of file limex.hh.

◆ reportTime() [2/3]

template<class Eq >

template<class OutStream >

void Kaskade::Limex< Eq >::reportTime ( OutStream & out ) const

inline

Definition at line 413 of file limexWithoutJens.hh.

◆ reportTime() [3/3]

template<class Eq >

template<class OutStream >

void Kaskade::Limex< Eq >::reportTime ( OutStream & out ) const

inline

Definition at line 697 of file limexWithoutJensHierarchicEst.hh.

◆ step() [1/4]

template<class Eq >

State const & Kaskade::Limex< Eq >::step	(	State const &	x,
		double	dt,
		int	order
	)

inline

Computes a state increment that advances the given state in time. The time in the given evolution equation is increased by dt.

Parameters

x	the initial state to be evolved
dt	the time step
order	the extrapolation order

Returns: the state increment (references an internal variable that will be invalidated by a subsequent call of step)

Todo:: (i) check for B constant, do not reassemble matrix in this case (ii) implement fixed point iteration instead of new factorization in case B is not constant

Definition at line 66 of file limex.hh.

Referenced by Kaskade::Limex< Eq >::step().

◆ step() [2/4]

template<class Eq >

State const & Kaskade::Limex< Eq >::step	(	State const &	x,
		double	dt,
		int	order,
		std::vector< std::pair< double, double > > const &	tolX
	)

inline

Computes a state increment that advances the given state in time. The time in the given evolution equation is increased by dt.

Parameters

x	the initial state to be evolved
dt	the time step
order	the extrapolation order >= 0 (0 corresponds to the linearly implicit Euler)
tolX

Returns: the state increment (references an internal variable that will be invalidated by a subsequent call of step)

Todo:: (i) check for B constant, do not reassemble matrix in this case (ii) implement fixed point iteration instead of new factorization in case B is not constant

Definition at line 98 of file limexWithoutJens.hh.

◆ step() [3/4]

template<class Eq >

State const & Kaskade::Limex< Eq >::step	(	State const &	x,
		double	dt,
		int	order,
		std::vector< std::pair< double, double > > const &	tolX
	)

inline

In order to maintain compatibility with existing code, this overload is needed, as non const reference parameters (refinements) can not have default values. All ist does is call the original method with a temporary parameter.

Definition at line 122 of file limexWithoutJensHierarchicEst.hh.

◆ step() [4/4]

template<class Eq >

State const & Kaskade::Limex< Eq >::step	(	State const &	x,
		double	dt,
		int	order,
		std::vector< std::pair< double, double > > const &	tolX,
		std::vector< std::vector< bool > > &	refinements
	)

inline

Computes a state increment that advances the given state in time. The time in the given evolution equation is increased by dt.

Parameters

x	the initial state to be evolved
dt	the time step
order	the extrapolation order >= 0 (0 corresponds to the linearly implicit Euler)
tolX
refinements	keep track of the cells marked for refinement

Returns: the state increment (references an internal variable that will be invalidated by a subsequent call of step)

Todo:: (i) check for B constant, do not reassemble matrix in this case (ii) implement fixed point iteration instead of new factorization in case B is not constant

Definition at line 146 of file limexWithoutJensHierarchicEst.hh.