a local operator for solving the Poisson equation in instationary problems More...

#include <dune/pdelab/localoperator/poisson.hh>

Inheritance diagram for Dune::PDELab::InstationaryPoisson< Time, F, B, J >:

Public Types
enum	{ doPatternVolume = true }

enum	{ doAlphaVolume = true }

enum	{ doLambdaVolume = true }

enum	{ doLambdaBoundary = true }

typedef Time	RealType

Flags for the sparsity pattern
enum	{ doPatternVolume }
	Whether to assemble the pattern on the elements, i.e. whether or not pattern_volume() should be called. More...

enum	{ doPatternVolumePostSkeleton }
	Whether to assemble the pattern on the elements after the skeleton has been handled, i.e. whether or not pattern_volume_post_skeleton() should be called. More...

enum	{ doPatternSkeleton }
	Whether to assemble the pattern on the interior intersections, i.e. whether or not pattern_skeleton() should be called. More...

enum	{ doPatternBoundary }
	Whether to assemble the pattern on the boundary intersections, i.e. whether or not pattern_boundary() should be called. More...

Flags for the non-constant part of the residual and the jacobian
enum	{ doAlphaVolume }
	Whether to call the local operator's alpha_volume(), jacobian_apply_volume() and jacobian_volume(). More...

enum	{ doAlphaVolumePostSkeleton }
	Whether to call the local operator's alpha_volume_post_skeleton(), jacobian_apply_volume_post_skeleton() and jacobian_volume_post_skeleton(). More...

enum	{ doAlphaSkeleton }
	Whether to call the local operator's alpha_skeleton(), jacobian_apply_skeleton() and jacobian_skeleton(). More...

enum	{ doAlphaBoundary }
	Whether to call the local operator's alpha_boundary(), jacobian_apply_boundary() and jacobian_boundary(). More...

Flags for the constant part of the residual
enum	{ doLambdaVolume }
	Whether to call the local operator's lambda_volume(). More...

enum	{ doLambdaVolumePostSkeleton }
	Whether to call the local operator's lambda_volume_post_skeleton(). More...

enum	{ doLambdaSkeleton }
	Whether to call the local operator's lambda_skeleton(). More...

enum	{ doLambdaBoundary }
	Whether to call the local operator's lambda_boundary(). More...

Special flags
enum	{ doSkeletonTwoSided }
	Whether to visit the skeleton methods from both sides. More...

Public Member Functions
	InstationaryPoisson (F &f_, B &bctype_, J &j_, unsigned int quadOrder)
	construct InstationaryPoisson More...

void	setTime (Time t)
	set the time for subsequent evaluation on the parameter functions More...

template<typename EG , typename LFSU , typename X , typename LFSV , typename R >
void	alpha_volume (const EG &eg, const LFSU &lfsu, const X &x, const LFSV &lfsv, R &r) const

template<typename EG , typename LFSU , typename X , typename LFSV , typename M >
void	jacobian_volume (const EG &eg, const LFSU &lfsu, const X &x, const LFSV &lfsv, M &matrix) const
	Compute the Laplace stiffness matrix for the element given in 'eg'. More...

template<typename EG , typename LFSV , typename R >
void	lambda_volume (const EG &eg, const LFSV &lfsv, R &r) const

template<typename IG , typename LFSV , typename R >
void	lambda_boundary (const IG &ig, const LFSV &lfsv, R &r) const

void	jacobian_apply_volume (const EG &eg, const LFSU &lfsu, const X &x, const LFSV &lfsv, Y &y) const
	apply local jacobian of the volume term More...

template<typename LFSU , typename LFSV , typename LocalPattern >
void	pattern_volume (const LFSU &lfsu, const LFSV &lfsv, LocalPattern &pattern) const

Time	getTime () const
	get current time More...

void	preStep (RealType time, RealType dt, int stages)
	to be called once before each time step More...

void	postStep ()
	to be called once at the end of each time step More...

void	preStage (RealType time, int r)
	to be called once before each stage More...

int	getStage () const
	get current stage More...

void	postStage ()
	to be called once at the end of each stage More...

RealType	suggestTimestep (RealType dt) const
	to be called after stage 1 More...

Protected Attributes
F &	f

B &	bctype

J &	j

Laplace	laplace_

unsigned int	quadOrder_

Detailed Description

template<typename Time, typename F, typename B, typename J>
class Dune::PDELab::InstationaryPoisson< Time, F, B, J >

a local operator for solving the Poisson equation in instationary problems

$\begin{align*} - \Delta u &=& f \mbox{ in } \Omega, \\ u &=& g \mbox{ on } \partial\Omega_D \\ -\nabla u \cdot \nu &=& j \mbox{ on } \partial\Omega_N \\ \end{align*}$

with conforming finite elements on all types of grids in any dimension

Template Parameters

F	Grid function type giving f
B	Grid function type selecting boundary condition
J	Grid function type giving j

Note: The grid functions need to support the member function setTime().

Member Typedef Documentation

typedef Time Dune::PDELab::InstationaryLocalOperatorDefaultMethods< Time >::RealType

inherited

Member Enumeration Documentation

anonymous enum

inherited

Whether to assemble the pattern on the elements, i.e. whether or not pattern_volume() should be called.

Enumerator
doPatternVolume

anonymous enum

inherited

Whether to assemble the pattern on the elements after the skeleton has been handled, i.e. whether or not pattern_volume_post_skeleton() should be called.

Enumerator
doPatternVolumePostSkeleton

anonymous enum

inherited

Whether to assemble the pattern on the interior intersections, i.e. whether or not pattern_skeleton() should be called.

Enumerator
doPatternSkeleton

anonymous enum

inherited

Whether to assemble the pattern on the boundary intersections, i.e. whether or not pattern_boundary() should be called.

Enumerator
doPatternBoundary

anonymous enum

inherited

Whether to call the local operator's alpha_volume(), jacobian_apply_volume() and jacobian_volume().

Enumerator
doAlphaVolume

anonymous enum

inherited

Whether to call the local operator's alpha_volume_post_skeleton(), jacobian_apply_volume_post_skeleton() and jacobian_volume_post_skeleton().

Enumerator
doAlphaVolumePostSkeleton

anonymous enum

inherited

Whether to call the local operator's alpha_skeleton(), jacobian_apply_skeleton() and jacobian_skeleton().

Enumerator
doAlphaSkeleton

anonymous enum

inherited

Whether to call the local operator's alpha_boundary(), jacobian_apply_boundary() and jacobian_boundary().

Enumerator
doAlphaBoundary

anonymous enum

inherited

Whether to call the local operator's lambda_volume().

Enumerator
doLambdaVolume

anonymous enum

inherited

Whether to call the local operator's lambda_volume_post_skeleton().

Enumerator
doLambdaVolumePostSkeleton

anonymous enum

inherited

Whether to call the local operator's lambda_skeleton().

Enumerator
doLambdaSkeleton

anonymous enum

inherited

Whether to call the local operator's lambda_boundary().

Enumerator
doLambdaBoundary

anonymous enum

inherited

Whether to visit the skeleton methods from both sides.

Enumerator
doSkeletonTwoSided

template<typename F , typename B , typename J >

anonymous enum

inherited

Enumerator
doPatternVolume

template<typename F , typename B , typename J >

anonymous enum

inherited

Enumerator
doAlphaVolume

template<typename F , typename B , typename J >

anonymous enum

inherited

Enumerator
doLambdaVolume

template<typename F , typename B , typename J >

anonymous enum

inherited

Enumerator
doLambdaBoundary

Constructor & Destructor Documentation

template<typename Time , typename F , typename B , typename J >

Dune::PDELab::InstationaryPoisson< Time, F, B, J >::InstationaryPoisson	(	F &	f_,
		B &	bctype_,
		J &	j_,
		unsigned int	quadOrder
	)

inline

construct InstationaryPoisson

Member Function Documentation

template<typename F , typename B , typename J >

template<typename EG , typename LFSU , typename X , typename LFSV , typename R >

void Dune::PDELab::Poisson< F, B, J >::alpha_volume	(	const EG &	eg,
		const LFSU &	lfsu,
		const X &	x,
		const LFSV &	lfsv,
		R &	r
	)		const

inlineinherited

References Dune::PDELab::Laplace::alpha_volume(), and Dune::PDELab::Poisson< F, B, J >::laplace_.

int Dune::PDELab::InstationaryLocalOperatorDefaultMethods< Time >::getStage ( ) const

inlineinherited

get current stage

Returns: The current stage number previously set by preStage().

Time Dune::PDELab::InstationaryLocalOperatorDefaultMethods< Time >::getTime ( ) const

inlineinherited

get current time

Returns: The time previously set by setTime().

void Dune::PDELab::NumericalJacobianApplyVolume< Poisson< F, B, J > >::jacobian_apply_volume	(	const EG &	eg,
		const LFSU &	lfsu,
		const X &	x,
		const LFSV &	lfsv,
		Y &	y
	)		const

inlineinherited

apply local jacobian of the volume term

template<typename F , typename B , typename J >

template<typename EG , typename LFSU , typename X , typename LFSV , typename M >

void Dune::PDELab::Poisson< F, B, J >::jacobian_volume	(	const EG &	eg,
		const LFSU &	lfsu,
		const X &	x,
		const LFSV &	lfsv,
		M &	matrix
	)		const

inlineinherited

Compute the Laplace stiffness matrix for the element given in 'eg'.

Template Parameters

M	Type of the element stiffness matrix

Parameters

[in]	eg	The grid element we are assembling on
[in]	lfsu	Local ansatz function space basis
[in]	lfsv	Local test function space basis
[in]	x	Current configuration; gets ignored for linear problems like this one
[out]	matrix	Element stiffness matrix

References Dune::PDELab::Laplace::jacobian_volume(), and Dune::PDELab::Poisson< F, B, J >::laplace_.

template<typename F , typename B , typename J >

template<typename IG , typename LFSV , typename R >

void Dune::PDELab::Poisson< F, B, J >::lambda_boundary	(	const IG &	ig,
		const LFSV &	lfsv,
		R &	r
	)		const

inlineinherited

References Dune::PDELab::Poisson< F, B, J >::bctype, Dune::PDELab::Poisson< F, B, J >::j, and Dune::PDELab::Poisson< F, B, J >::quadOrder_.

template<typename F , typename B , typename J >

template<typename EG , typename LFSV , typename R >

void Dune::PDELab::Poisson< F, B, J >::lambda_volume	(	const EG &	eg,
		const LFSV &	lfsv,
		R &	r
	)		const

inlineinherited

References Dune::PDELab::Poisson< F, B, J >::f, and Dune::PDELab::Poisson< F, B, J >::quadOrder_.

template<typename LFSU , typename LFSV , typename LocalPattern >

void Dune::PDELab::FullVolumePattern::pattern_volume	(	const LFSU &	lfsu,
		const LFSV &	lfsv,
		LocalPattern &	pattern
	)		const

inlineinherited

void Dune::PDELab::InstationaryLocalOperatorDefaultMethods< Time >::postStage ( )

inlineinherited

to be called once at the end of each stage

void Dune::PDELab::InstationaryLocalOperatorDefaultMethods< Time >::postStep ( )

inlineinherited

to be called once at the end of each time step

Note: With the OneStepMethod and the ExplicitOneStepMetod, for reasons unknown this is only called for temporal but not for spatial local operators. With the MultiStepMethod this is called for all local operators.

void Dune::PDELab::InstationaryLocalOperatorDefaultMethods< Time >::preStage	(	RealType	time,
		int	r
	)

inlineinherited

to be called once before each stage

Parameters

time	Time of the stage
r	Number of the stage, r ∈ [1, nstages] inclusive, where nstages is the number of stage in the step given in the previous call to preStep()

Note: For ExplicitOneStepMethod the time given here for stage 1 may be incorrect, since the time step size is only finally determined after the first stage has been assembled.; For the MultiStepMethod, this is called once after preStep() with r=1.

void Dune::PDELab::InstationaryLocalOperatorDefaultMethods< Time >::preStep	(	RealType	time,
		RealType	dt,
		int	stages
	)

inlineinherited

to be called once before each time step

Parameters

time	Time at beginning of the step.
dt	Size of time step.
stages	Number of stages to do in the step. For the MultiStepMethod this is always 1.

Note

For ExplicitOneStepMethod the dt given here may be incorrect, since the time step size is only finally determined after the first stage has been assembled.

For the MultiStepMethod the number of stages is given as

Since there are no times of evaluation in the middle of the step, a multi-step method is similar to a one step method with one stage.

template<typename Time , typename F , typename B , typename J >

void Dune::PDELab::InstationaryPoisson< Time, F, B, J >::setTime ( Time t )

inline

set the time for subsequent evaluation on the parameter functions

References Dune::PDELab::InstationaryPoisson< Time, F, B, J >::bctype, Dune::PDELab::InstationaryPoisson< Time, F, B, J >::f, Dune::PDELab::InstationaryPoisson< Time, F, B, J >::j, and Dune::PDELab::InstationaryLocalOperatorDefaultMethods< Time >::setTime().

RealType Dune::PDELab::InstationaryLocalOperatorDefaultMethods< Time >::suggestTimestep ( RealType dt ) const

inlineinherited

to be called after stage 1

Note: Only used by the ExplicitOneStepMethod.

This may be called on the spatial local operator in the case of an explicit one step scheme. It is called after stage 1 has been assembled (so the time given to preStep() may not apply anymore in this case). All the alpha_*() and lambda_*() methods should have been called, so they are a good place to generate the information returned here.