Dune::Fem::LumpingQuadrature< FieldImp, geometryId > Class Template Reference

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

Public Types
enum
	to be revised, look at caching quad

Public Member Functions
	LumpingQuadrature (const GeometryType &gt, int order, int id)
	constructor filling the list of points and weights. More...
virtual GeometryType	geometryType () const
virtual int	order () const
	obtain order of the integration point list More...
const FieldType &	weight (size_t i) const
	obtain weight of i-th integration point More...
const CoordinateType &	point (size_t i) const
	obtain coordinates of i-th integration point More...
size_t	nop () const
	obtain the number of integration points More...
size_t	id () const
	obtain the identifier of the integration point list More...
virtual std::vector< ElementCoordinateType >	interpolationPoints (const int reqDim) const
	returns list of element interpolation points for a given face quadrature
virtual bool	isFaceInterpolationQuadrature (const size_t numShapeFunctions) const
	return true if quadrature is also a set of interpolation points for a given number of shape functions

Static Public Member Functions
static std::size_t	maxOrder ()
	maximal order of available quadratures

Protected Member Functions
void	addQuadraturePoint (const CoordinateType &point, const FieldType weight)
	Adds a point-weight pair to the quadrature. More...
void	setIntegrationPoints (std::vector< CoordinateType > &&points)
	Overwrites integration point list

Detailed Description

template<class FieldImp, Dune::GeometryType::Id geometryId>
class Dune::Fem::LumpingQuadrature< FieldImp, geometryId >

Define a lumping quadrature for all geometries. Note, however, that this may not make sense for anything else than simplices or maybe hexagonal grids. For simplicial meshes the quadrature formula is exact on linear polynomials and hence the quadrature error is quadratic in the mesh-size. A mass-matrix assembled with the caching quadrature will be diagonal in the context of Lagrange spaces. Generally, it is a bad idea to use mass-lumping for anything else than linear (or maybe bilinear) finite elements.

There are probably much more efficient ways to perform mass-lumping. This "quadrature" approach is convenient, however, as it can simply be plugged into existing code by replacing the quadrature rules.

Constructor & Destructor Documentation

LumpingQuadrature()

template<class FieldImp , Dune::GeometryType::Id geometryId>

Dune::Fem::LumpingQuadrature< FieldImp, geometryId >::LumpingQuadrature ( const GeometryType &  gt, int  order, int  id  )

inline

constructor filling the list of points and weights.

Parameters

[in]	gt	geometry type for which a quadrature is desired
[in]	order	order (between 1 and 6)
[in]	id	unique identifier, ignored

References Dune::Fem::QuadratureImp< FieldImp, Dune::GeometryType(geometryId).dim()>::addQuadraturePoint(), Dune::Geo::ReferenceElements< ctype_, dim >::general(), Dune::FloatCmp::gt(), Dune::GeometryType::id(), and Dune::Fem::QuadratureImp< FieldImp, Dune::GeometryType(geometryId).dim()>::weight().

Member Function Documentation

addQuadraturePoint()

void Dune::Fem::QuadratureImp< FieldImp, dim >::addQuadraturePoint ( const CoordinateType &  point, const FieldType  weight  )

inlineprotectedinherited

Adds a point-weight pair to the quadrature.

This method allows derived classes to add quadrature points (and their respective weights) to the list. This mehtod should only be used within the constructor of the derived class.

geometryType()

template<class FieldImp , Dune::GeometryType::Id geometryId>

virtual GeometryType Dune::Fem::LumpingQuadrature< FieldImp, geometryId >::geometryType ( ) const

inlinevirtual

Implements Dune::Fem::IntegrationPointListImp< FieldImp, dim >.

id()

template<typename FieldImp , int dim>

size_t Dune::Fem::IntegrationPointListImp< FieldImp, dim >::id ( ) const

inlineinherited

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

Referenced by Dune::Fem::TwistProvider< ct, dim >::getTwistStorage().

nop()

template<typename FieldImp , int dim>

size_t Dune::Fem::IntegrationPointListImp< FieldImp, dim >::nop ( ) const

inlineinherited

obtain the number of integration points

Returns

number of integration points within this list

Referenced by Dune::Fem::IntegrationPointListImp< FieldImp, dim >::point().

order()

template<class FieldImp , Dune::GeometryType::Id geometryId>

virtual int Dune::Fem::LumpingQuadrature< FieldImp, geometryId >::order ( ) const

inlinevirtual

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.

Returns

the order of the integration point list

Implements Dune::Fem::IntegrationPointListImp< FieldImp, dim >.

point()

template<typename FieldImp , int dim>

const CoordinateType & Dune::Fem::IntegrationPointListImp< FieldImp, dim >::point ( size_t  i ) const

inlineinherited

obtain coordinates of i-th integration point

This method returns a reference to the coordinates of the i-th integration point for 0 <= i < nop(). The integration point is given in local coordinates, i.e., coordinates with respect to the reference element.

Parameters

[in]

i

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

Returns

reference to i-th integration point

References Dune::Fem::IntegrationPointListImp< FieldImp, dim >::nop().

Referenced by Dune::Fem::IntegrationPointListImp< FieldImp, dim >::addIntegrationPoint(), and Dune::Fem::QuadratureImp< FieldImp, dim >::addQuadraturePoint().

weight()

const FieldType & Dune::Fem::QuadratureImp< FieldImp, dim >::weight ( size_t  i ) const

inlineinherited

obtain weight of i-th integration point

This method returns the weight of the i-th integration point for 0 <= i < nop() within the quadrature.

Note

The integration point can be obtained via the point() method.

The quadrature weights sum up to the volume of the reference element.

Parameters

[in]

i

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

Returns

weight of the i-th integration point

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

• dune/fem/quadrature/lumpingquadrature.hh