Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits > Class Template Reference

ElementPointListBase. More...

#include <dune/fem/quadrature/elementpointlistbase.hh>

Public Types
enum	Side
	inside and outside flags
typedef GridPartImp	GridPartType
	type of the grid partition
typedef GridPartType::ctype	RealType
	coordinate type
typedef IntegrationTraits::IntegrationPointListType	IntegrationPointListType
	type of the integration point list

Public Member Functions
	ElementPointListBase (const GeometryType &elementGeo, const GeometryType &faceGeo, const int localFaceIndex, const QuadratureKeyType &quadKey)
	constructor More...
	ElementPointListBase (const GeometryType &elementGeo, const int localFaceIndex, const QuadratureKeyType &quadKey)
	constructor More...
size_t	nop () const
	obtain the number of integration points More...
const LocalCoordinateType &	localPoint (size_t i) const
	obtain local coordinates of i-th integration point More...
size_t	id () const
	obtain the identifier of the integration point list More...
int	order () const
	obtain order of the integration point list More...
GeometryType	geometry () const
	obtain GeometryType for this integration point list
GeometryType	elementGeometry () const
	obtain GeometryType of the corresponding codim-0 the integration point list belongs to More...
int	twistId () const
	convenience implementation for Dune::Fem::CachingInterface

Static Public Member Functions
static constexpr bool	twisted ()
	convenience implementation for Dune::Fem::CachingInterface

Static Public Attributes
static const int	codimension = codim
	codimension of the element integration point list
static const int	dimension = GridPartType::dimension
	dimension of the grid

Protected Member Functions
const IntegrationPointListType &	quadImp () const
	obtain the actual implementation of the quadrature More...

Detailed Description

template<class GridPartImp, int codim, class IntegrationTraits>
class Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >

ElementPointListBase.

integration point list on the codim-0 reference element

DUNE quadratures are defined per geometry type, using local coordinates for the quadrature points. To evaluate a base function in some quadrature point, the quadrature must return points within the codim-0 reference element.

Now, assume you want to integrate over the face of a tetrahedron. This means you need a quadrature for a triangle, but the quadrature points should be specified with respect to the tetrahedron, since we want to evaluate our function in these points. This is where the ElementQuadrature comes into play.

The ElementIntegrationPointList takes a subentity and transforms the integration point list corresponding to the geometry to the codim-0 reference element.

To achieve this goal, an ElementIntegrationPointList depends stronger on the context in which it is used. For example, for each face within a tetrahedron (though they are all the same) we need a different ElementIntegrationPointList, since the coordinates of the quadrature points with respect to the codim-0 entity differ for each face.

Note

Actually, codim-1 element integration point lists depend on the intersection.

This integration point list does not support caching of base functions in integration points (see also CachingPointList).

For the actual implementations see

• ElementIntegrationPointList<GridPartImp,0,IntegrationTraits>
• ElementIntegrationPointList<GridPartImp,1,IntegrationTraits>

Constructor & Destructor Documentation

ElementPointListBase() [1/2]

template<class GridPartImp , int codim, class IntegrationTraits >

Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::ElementPointListBase ( const GeometryType &  elementGeo, const GeometryType &  faceGeo, const int  localFaceIndex, const QuadratureKeyType &  quadKey  )

inline

constructor

Parameters

[in]	elementGeo	geometry type of the element
[in]	faceGeo	geometry type of the subentity
[in]	localFaceIndex	index of the subentity
[in]	order	desired order of the quadrature

ElementPointListBase() [2/2]

template<class GridPartImp , int codim, class IntegrationTraits >

Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::ElementPointListBase ( const GeometryType &  elementGeo, const int  localFaceIndex, const QuadratureKeyType &  quadKey  )

inline

constructor

Parameters

[in]	elementGeo	geometry type of the element
[in]	localFaceIndex	index of the subentity
[in]	order	desired order of the quadrature

Member Function Documentation

elementGeometry()

template<class GridPartImp , int codim, class IntegrationTraits >

GeometryType Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::elementGeometry ( ) const

inline

obtain GeometryType of the corresponding codim-0 the integration point list belongs to

An element integration point list can return the coordinates of integration points with resepct to the codim-0 reference element and the reference element corresponding to the subentity the quadrature actually lives on. This method returns the geometry of the codim-0 entity.

Note

Calling this method yields a virtual function call, so do not call this method unnecessarily.

Returns

GeometryType for this integration point list

id()

template<class GridPartImp , int codim, class IntegrationTraits >

size_t Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::id ( ) const

inline

obtain the identifier of the integration point list

The identifier of an integration point list must be globally unique. Even integration point lists for different dimensions must have different identifiers.

Note

Quadratures are considered distinct if they differ in one of the following points: geometry type, order, dimension or implementation.

Returns

globally unique identifier of the integration point list

References Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::quadImp().

localPoint()

template<class GridPartImp , int codim, class IntegrationTraits >

const LocalCoordinateType & Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::localPoint ( size_t  i ) const

inline

obtain local coordinates of i-th integration point

This method returns a reference to the local coordinates of the i-th integration point for 0 <= i < nop(). Here, local coordinates means coordinates with respect to the reference element of the subentity.

Parameters

[in]

i

number of the integration point, 0 <= i < nop()

Returns

reference to i-th integration point

nop()

template<class GridPartImp , int codim, class IntegrationTraits >

size_t Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::nop ( ) const

inline

obtain the number of integration points

Returns

number of integration points within this list

References Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::quadImp().

order()

template<class GridPartImp , int codim, class IntegrationTraits >

int Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::order ( ) const

inline

obtain order of the integration point list

The order of a quadrature is the maximal polynomial degree that is guaranteed to be integrated exactly by the quadrature.

In case of an integration point list, the definition of this value is left to the implementor.

Note

Calling this method yields a virtual function call, so do not call this method unnecessarily.

Returns

the order of the integration point list

References Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::quadImp().

quadImp()

template<class GridPartImp , int codim, class IntegrationTraits >

const IntegrationPointListType & Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::quadImp ( ) const

inlineprotected

obtain the actual implementation of the quadrature

Note

This method may only be used in derived classes.

Returns

a reference to the actual implementation of the quadrature

Referenced by Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::geometry(), Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::id(), Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::nop(), and Dune::Fem::ElementPointListBase< GridPartImp, codim, IntegrationTraits >::order().

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

• dune/fem/quadrature/elementpointlistbase.hh