RefinedSimplexGeometry< ct, 2, 3 > Class Template Reference

Mimics a once refined simplex surface element geometry for parametric surfaces, i.e. the vertices of the "refined" triangles are in general not complanar. More...

#include <dune/fufem/geometry/refinedsimplexgeometry.hh>

Classes
class	JacobianInverseTransposed

Public Types
typedef ct	ctype
typedef Dune::FieldVector< ctype, 2 >	LocalCoordinate
typedef Dune::FieldVector< ctype, 3 >	GlobalCoordinate
typedef Dune::FieldMatrix< ctype, 2, 3 >	JacobianTransposed

Public Member Functions
template<class VertexContainerType >
	RefinedSimplexGeometry (const VertexContainerType &vertices)
	constructor taking the global coordinates of the "refined" vertices
GlobalCoordinate	global (const LocalCoordinate &local) const
bool	affine () const
Dune::GeometryType	type () const
int	corners () const
GlobalCoordinate	corner (int i) const
LocalCoordinate	local (const GlobalCoordinate &) const
GlobalCoordinate	center () const
ctype	volume () const
ctype	integrationElement (const LocalCoordinate &local) const
JacobianTransposed	jacobianTransposed (const LocalCoordinate &local) const
JacobianInverseTransposed	jacobianInverseTransposed (const LocalCoordinate &local) const

Detailed Description

template<class ct>
class RefinedSimplexGeometry< ct, 2, 3 >

Mimics a once refined simplex surface element geometry for parametric surfaces, i.e. the vertices of the "refined" triangles are in general not complanar.

The geometry mapping from the (pseudorefined) reference element to the pseudorefined simplicial complex is here done in two steps. First a mapping from the reference element to local coordinates in the corresponding subElement resulting from virtual refinement. This mapping is effected in the subElement(local,subElt,subEltLocal)-method which computes the index of the subElement and the local coordinates in that subElement for local coordinates in the reference element. The mapping from local subElement coordinates to world coordinates is effected in the method global.

Such a geometry is needed for hierarchical error estimators with RefinedP1 elements for surface meshes.

Template Parameters

ct	the scalar type of the coordinates e.g. double

Member Typedef Documentation

ctype

template<class ct >

typedef ct RefinedSimplexGeometry< ct, 2, 3 >::ctype

GlobalCoordinate

template<class ct >

typedef Dune::FieldVector<ctype,3> RefinedSimplexGeometry< ct, 2, 3 >::GlobalCoordinate

JacobianTransposed

template<class ct >

typedef Dune::FieldMatrix<ctype,2,3> RefinedSimplexGeometry< ct, 2, 3 >::JacobianTransposed

LocalCoordinate

template<class ct >

typedef Dune::FieldVector<ctype,2> RefinedSimplexGeometry< ct, 2, 3 >::LocalCoordinate

Constructor & Destructor Documentation

RefinedSimplexGeometry()

template<class ct >

template<class VertexContainerType >

RefinedSimplexGeometry< ct, 2, 3 >::RefinedSimplexGeometry ( const VertexContainerType &  vertices )

inline

constructor taking the global coordinates of the "refined" vertices

Constructor builds the geometry mapping from the supplied vertices

Template Parameters

VertexContainerType

the type of the container for the vertices; std::array<GlobalCoordinate,6> must be constructible from it

Parameters

vertices

a container of 6 GlobalCoordinates corresponding to the 6 vertices of the "refined" simplicial complex. The order of the vertices must be as follows 2 |\ | \ 4|--\5 |\ |\ | \| \ ------- 0 3 1

Member Function Documentation

affine()

template<class ct >

bool RefinedSimplexGeometry< ct, 2, 3 >::affine ( ) const

inline

center()

template<class ct >

GlobalCoordinate RefinedSimplexGeometry< ct, 2, 3 >::center ( ) const

inline

corner()

template<class ct >

GlobalCoordinate RefinedSimplexGeometry< ct, 2, 3 >::corner ( int  i ) const

inline

corners()

template<class ct >

int RefinedSimplexGeometry< ct, 2, 3 >::corners ( ) const

inline

global()

template<class ct >

GlobalCoordinate RefinedSimplexGeometry< ct, 2, 3 >::global ( const LocalCoordinate &  local ) const

inline

integrationElement()

template<class ct >

ctype RefinedSimplexGeometry< ct, 2, 3 >::integrationElement ( const LocalCoordinate &  local ) const

inline

jacobianInverseTransposed()

template<class ct >

JacobianInverseTransposed RefinedSimplexGeometry< ct, 2, 3 >::jacobianInverseTransposed ( const LocalCoordinate &  local ) const

inline

jacobianTransposed()

template<class ct >

JacobianTransposed RefinedSimplexGeometry< ct, 2, 3 >::jacobianTransposed ( const LocalCoordinate &  local ) const

inline

local()

template<class ct >

LocalCoordinate RefinedSimplexGeometry< ct, 2, 3 >::local ( const GlobalCoordinate &  ) const

inline

type()

template<class ct >

Dune::GeometryType RefinedSimplexGeometry< ct, 2, 3 >::type ( ) const

inline

volume()

template<class ct >

ctype RefinedSimplexGeometry< ct, 2, 3 >::volume ( ) const

inline

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

• refinedsimplexgeometry.hh