dune-fem  2.4.1-rc
Public Types | Public Member Functions | Static Public Member Functions | Protected Types | Protected Member Functions | Static Protected Attributes | List of all members
Dune::Fem::LumpingQuadrature< FieldImp, Topology > Class Template Reference

#include </local/tomalk/somewhere/tmp/dune-fem/dune/fem/quadrature/lumpingquadrature.hh>

Inheritance diagram for Dune::Fem::LumpingQuadrature< FieldImp, Topology >:
Inheritance graph

Public Types

enum  { dimension = TopologyType::dimension }
 
typedef FieldImp FieldType
 
typedef Topology TopologyType
 
typedef BaseType::CoordinateType CoordinateType
 
enum  { codimension = 0 }
 to be revised, look at caching quad More...
 

Public Member Functions

 LumpingQuadrature (const GeometryType &geometry, int ignored, 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 FieldTypeweight (size_t i) const
 obtain weight of i-th integration point More...
 
const CoordinateTypepoint (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...
 

Static Public Member Functions

static size_t maxOrder ()
 maximal order of available quadratures More...
 

Protected Types

typedef Dune::GenericGeometry::ReferenceDomain< TopologyTypeReferenceDomain
 

Protected Member Functions

void addQuadraturePoint (const CoordinateType &point, const FieldType weight)
 Adds a point-weight pair to the quadrature. More...
 

Static Protected Attributes

static const unsigned int topologyId = TopologyType::id
 

Detailed Description

template<class FieldImp, class Topology>
class Dune::Fem::LumpingQuadrature< FieldImp, Topology >

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.

Member Typedef Documentation

template<class FieldImp , class Topology >
typedef BaseType::CoordinateType Dune::Fem::LumpingQuadrature< FieldImp, Topology >::CoordinateType
template<class FieldImp , class Topology >
typedef FieldImp Dune::Fem::LumpingQuadrature< FieldImp, Topology >::FieldType
template<class FieldImp , class Topology >
typedef Dune::GenericGeometry::ReferenceDomain<TopologyType> Dune::Fem::LumpingQuadrature< FieldImp, Topology >::ReferenceDomain
protected
template<class FieldImp , class Topology >
typedef Topology Dune::Fem::LumpingQuadrature< FieldImp, Topology >::TopologyType

Member Enumeration Documentation

template<class FieldImp , class Topology >
anonymous enum
Enumerator
dimension 
template<typename FieldImp, int dim>
anonymous enum
inherited

to be revised, look at caching quad

Enumerator
codimension 

Constructor & Destructor Documentation

template<class FieldImp , class Topology >
Dune::Fem::LumpingQuadrature< FieldImp, Topology >::LumpingQuadrature ( const GeometryType &  geometry,
int  ignored,
int  id 
)
inline

constructor filling the list of points and weights.

Parameters
[in]gemoetrygeometry type for which a quadrature is desired
[in]ignoredorder is ignored
[in]idunique identifier, ignored

References Dune::Fem::QuadratureImp< FieldImp, Topology::dimension >::addQuadraturePoint().

Member Function Documentation

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.

Referenced by Dune::Fem::LumpingQuadrature< FieldImp, Topology >::LumpingQuadrature().

template<class FieldImp , class Topology >
virtual GeometryType Dune::Fem::LumpingQuadrature< FieldImp, Topology >::geometryType ( ) const
inlinevirtual
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::CacheProvider< GridPart, 1 >::getMapper(), Dune::Fem::PointProvider< ct, dim, 1 >::getMappers(), Dune::Fem::PointProvider< ct, dim, 1 >::getPoints(), Dune::Fem::TwistProvider< ct, dim >::getTwistStorage(), and Dune::Fem::PointProvider< ct, dim, 0 >::registerQuadrature().

template<class FieldImp , class Topology >
static size_t Dune::Fem::LumpingQuadrature< FieldImp, Topology >::maxOrder ( )
inlinestatic

maximal order of available quadratures

template<typename FieldImp, int dim>
size_t Dune::Fem::IntegrationPointListImp< FieldImp, dim >::nop ( ) const
inlineinherited
template<class FieldImp , class Topology >
virtual int Dune::Fem::LumpingQuadrature< FieldImp, Topology >::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 >.

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]inumber of the integration point, 0 <= i < nop()
Returns
reference to i-th integration point

Referenced by Dune::Fem::TwistMapperCreator< ct, dim >::createStorage(), Dune::Fem::PointProvider< ct, dim, 1 >::getMappers(), Dune::Fem::PointProvider< ct, dim, 0 >::registerQuadrature(), and Dune::Fem::QuadratureImp< FieldImp, 1 >::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]inumber of the integration point, 0 <= i < nop()
Returns
weight of the i-th integration point

Member Data Documentation

template<class FieldImp , class Topology >
const unsigned int Dune::Fem::LumpingQuadrature< FieldImp, Topology >::topologyId = TopologyType::id
staticprotected

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