Definition of a 2D finite element. More...

#include <ptems/finiteelement.hpp>

Inheritance diagram for ptems::FiniteElement< 2 >:

Collaboration diagram for ptems::FiniteElement< 2 >:

Public Types
typedef LegacyRandomAccessIterator< const Vector< 2 > >	iterator
	Type for an iterator over the list of vertices for the element. More...

typedef iterator	const_iterator
	Type for a const iterator over the list of vertices for the element. More...

typedef std::reverse_iterator< iterator >	reverse_iterator
	Type for an iterator over the list of vertices for the element, iterating in reverse. More...

typedef std::reverse_iterator< reverse_iterator >	const_reverse_iterator
	Type for a const iterator over the list of vertices for the element, iterating in reverse. More...

typedef LegacyRandomAccessIterator< const PFEFace< 2 > >	faceiterator
	Type for an iterator over the list of faces for the element. More...

typedef faceiterator	const_faceiterator
	Type for a const iterator over the list of faces for the element. More...

typedef std::reverse_iterator< faceiterator >	reverse_faceiterator
	Type for an iterator over the list of faces for the element, iterating in reverse. More...

typedef std::reverse_iterator< const_faceiterator >	const_reverse_faceiterator
	Type for a const iterator over the list of faces for the element, iterating in reverse. More...

Public Member Functions
std::size_t	Index () const
	The index of the finite element within the mesh,. More...

const Vector< 2 > &	operator[] (std::size_t i) const
	Returns the ith vertex of the finite element. More...

const Vector< 2 > &	Vertex (std::size_t i) const
	Returns the ith vertex of the finite element. More...

std::size_t	VertexIndex (std::size_t i) const
	Returns the index in the mesh of ith vertex of the finite element. More...

Vector< 2 >	VertexLocal (std::size_t i) const
	Returns the ith vertex of the finite element in local coordinates. More...

iterator	begin () const
	Gets the begin iterator for iterating over the vertices of the element. More...

iterator	end () const
	Gets the end iterator for iterating over the vertices of the element. More...

const_iterator	cbegin () const
	Gets the const begin iterator for iterating over the vertices of the element. More...

const_iterator	cend () const
	Gets the const end iterator for iterating over the vertices of the element. More...

reverse_iterator	rbegin () const
	Gets the begin iterator for iterating over the vertices of the element in reverse. More...

reverse_iterator	rend () const
	Gets the end iterator for iterating over the vertices of the element in reverse. More...

const_reverse_iterator	crbegin () const
	Gets the const begin iterator for iterating over the vertices of the element in reverse. More...

const_reverse_iterator	crend () const
	Gets the const end iterator for iterating over the vertices of the element in reverse. More...

const PFEFace< 2 > &	Face (std::size_t i) const
	Returns the ith face of the finite element. More...

faceiterator	begin_faces () const
	Gets the begin iterator for iterating over the faces of the element. More...

faceiterator	end_faces () const
	Gets the end iterator for iterating over the faces of the element. More...

const_faceiterator	cbegin_faces () const
	Gets the const begin iterator for iterating over the faces of the element. More...

const_faceiterator	cend_faces () const
	Gets the const end iterator for iterating over the faces of the element. More...

reverse_faceiterator	rbegin_faces () const
	Gets the begin iterator for iterating over the faces of the element in reverse. More...

reverse_faceiterator	rend_faces () const
	Gets the end iterator for iterating over the faces of the element in reverse. More...

const_reverse_faceiterator	crbegin_faces () const
	Gets the const begin iterator for iterating over the faces of the element in reverse. More...

const_reverse_faceiterator	crend_faces () const
	Gets the const end iterator for iterating over the faces of the element in reverse. More...

std::size_t	VertexCount () const
	Gets the number of vertices in the element. More...

std::size_t	FaceCount () const
	Gets the number of faces in the element. More...

double	Diameter () const
	Gets the diameter of the element. More...

double	Volume () const
	Gets the volume of the element. More...

Vector< 2 >	Barycentre () const
	Gets the barycentre of the element. More...

const std::vector< std::shared_ptr< FiniteElement< 2 > > > &	Agglomerates () const
	Gets the list of base mesh elements if this element is an agglomerated element. More...

BBox< 2 >	BoundingBox () const
	Computes the bounding box for the element. More...

bool	SetNeighbour (const std::shared_ptr< FiniteElement< 2 >> &element)
	Specify that the specified element is a neighbour of this element. More...

std::shared_ptr< FEMesh< 2 > >	Mesh () const
	Gets a reference to the underlying mesh for the element. More...

const std::vector< ReferenceMapping< 2 > > &	ReferenceMappings () const
	Gets set of mappings from the element to standard reference elements. More...

Vector< 2 >	LocalToGlobal (const Vector< 2 > &pt)
	Converts a local point on the element (local to the reference element if only one reference element, otherwise the bounding box) into a global point. More...

Vector< 2 >	GlobalToLocal (const Vector< 2 > &pt)
	Converts a global point into a local point on the element (local to the reference element if only one reference element, otherwise the bounding box) More...

template<typename ALGO >
QuadraturePoints< 2 >	ComputeQuadraturePoints (ALGO algorithm, std::size_t order)
	Computes the quadrature points for the element. More...

T	shared_from_this (T... args)

T	weak_from_this (T... args)

Friends
class	FEMesh< 2 >

Detailed Description

Definition of a 2D finite element.

Warning: Object of this type MUST be constructed and stored in a shared_ptr.

Member Typedef Documentation

◆ const_faceiterator

typedef faceiterator ptems::FiniteElement< 2 >::const_faceiterator

Type for a const iterator over the list of faces for the element.

◆ const_iterator

typedef iterator ptems::FiniteElement< 2 >::const_iterator

Type for a const iterator over the list of vertices for the element.

◆ const_reverse_faceiterator

typedef std::reverse_iterator<const_faceiterator> ptems::FiniteElement< 2 >::const_reverse_faceiterator

Type for a const iterator over the list of faces for the element, iterating in reverse.

◆ const_reverse_iterator

typedef std::reverse_iterator<reverse_iterator> ptems::FiniteElement< 2 >::const_reverse_iterator

Type for a const iterator over the list of vertices for the element, iterating in reverse.

◆ faceiterator

typedef LegacyRandomAccessIterator< const PFEFace<2> > ptems::FiniteElement< 2 >::faceiterator

Type for an iterator over the list of faces for the element.

◆ iterator

typedef LegacyRandomAccessIterator< const Vector<2> > ptems::FiniteElement< 2 >::iterator

Type for an iterator over the list of vertices for the element.

◆ reverse_faceiterator

typedef std::reverse_iterator<faceiterator> ptems::FiniteElement< 2 >::reverse_faceiterator

Type for an iterator over the list of faces for the element, iterating in reverse.

◆ reverse_iterator

typedef std::reverse_iterator<iterator> ptems::FiniteElement< 2 >::reverse_iterator

Type for an iterator over the list of vertices for the element, iterating in reverse.

Member Function Documentation

◆ Agglomerates()

const std::vector<std::shared_ptr<FiniteElement<2> > >& ptems::FiniteElement< 2 >::Agglomerates ( ) const

inline

Gets the list of base mesh elements if this element is an agglomerated element.

Parameters

List	of base mesh elements, or empty vector if not an agglomerated element

◆ Barycentre()

Vector<2> ptems::FiniteElement< 2 >::Barycentre ( ) const

inline

Gets the barycentre of the element.

Returns: Element barycentre

◆ begin()

iterator ptems::FiniteElement< 2 >::begin ( ) const

inline

Gets the begin iterator for iterating over the vertices of the element.

◆ begin_faces()

faceiterator ptems::FiniteElement< 2 >::begin_faces ( ) const

inline

Gets the begin iterator for iterating over the faces of the element.

◆ BoundingBox()

BBox<2> ptems::FiniteElement< 2 >::BoundingBox ( ) const

inline

Computes the bounding box for the element.

Returns: The minimum and maximum point of the bounding box for the element

◆ cbegin()

const_iterator ptems::FiniteElement< 2 >::cbegin ( ) const

inline

Gets the const begin iterator for iterating over the vertices of the element.

◆ cbegin_faces()

const_faceiterator ptems::FiniteElement< 2 >::cbegin_faces ( ) const

inline

Gets the const begin iterator for iterating over the faces of the element.

◆ cend()

const_iterator ptems::FiniteElement< 2 >::cend ( ) const

inline

Gets the const end iterator for iterating over the vertices of the element.

◆ cend_faces()

const_faceiterator ptems::FiniteElement< 2 >::cend_faces ( ) const

inline

Gets the const end iterator for iterating over the faces of the element.

◆ ComputeQuadraturePoints()

template<typename ALGO >

QuadraturePoints<2> ptems::FiniteElement< 2 >::ComputeQuadraturePoints	(	ALGO	algorithm,
		std::size_t	order
	)

inline

Computes the quadrature points for the element.

The points are in local element coordinates, and weights are for the global integration.

Template Parameters

ALGO	Type of an algorithm for generating quadrature points on a reference element

Parameters

algorithm	An algorithm for generating quadrature points on a reference element
order	The order of the quadrature

Returns: The set of quadrature points to use in local element coordinates (local to reference element if only one reference element, otherwise to bounding box)

◆ crbegin()

const_reverse_iterator ptems::FiniteElement< 2 >::crbegin ( ) const

inline

Gets the const begin iterator for iterating over the vertices of the element in reverse.

◆ crbegin_faces()

const_reverse_faceiterator ptems::FiniteElement< 2 >::crbegin_faces ( ) const

inline

Gets the const begin iterator for iterating over the faces of the element in reverse.

◆ crend()

const_reverse_iterator ptems::FiniteElement< 2 >::crend ( ) const

inline

Gets the const end iterator for iterating over the vertices of the element in reverse.

◆ crend_faces()

const_reverse_faceiterator ptems::FiniteElement< 2 >::crend_faces ( ) const

inline

Gets the const end iterator for iterating over the faces of the element in reverse.

◆ Diameter()

double ptems::FiniteElement< 2 >::Diameter ( ) const

inline

Gets the diameter of the element.

Returns: The element diameter.

◆ end()

iterator ptems::FiniteElement< 2 >::end ( ) const

inline

Gets the end iterator for iterating over the vertices of the element.

◆ end_faces()

faceiterator ptems::FiniteElement< 2 >::end_faces ( ) const

inline

Gets the end iterator for iterating over the faces of the element.

◆ Face()

const PFEFace<2>& ptems::FiniteElement< 2 >::Face ( std::size_t i ) const

inline

Returns the ith face of the finite element.

Parameters

i	The index of the face to get.

Exceptions

std::out_of_range If i is not less than FaceCount()

Returns: Immutable reference to the specified face.

◆ FaceCount()

std::size_t ptems::FiniteElement< 2 >::FaceCount ( ) const

inline

Gets the number of faces in the element.

Returns: Number of faces in the element.

◆ GlobalToLocal()

Vector<2> ptems::FiniteElement< 2 >::GlobalToLocal ( const Vector< 2 > & pt )

inline

Converts a global point into a local point on the element (local to the reference element if only one reference element, otherwise the bounding box)

Parameters

pt	The global point to map

Returns: The local point

◆ Index()

std::size_t ptems::FiniteElement< 2 >::Index ( ) const

inline

The index of the finite element within the mesh,.

Returns: The index of the finite element

◆ LocalToGlobal()

Vector<2> ptems::FiniteElement< 2 >::LocalToGlobal ( const Vector< 2 > & pt )

inline

Converts a local point on the element (local to the reference element if only one reference element, otherwise the bounding box) into a global point.

Parameters

pt	The local point to map

Returns: The global point

◆ Mesh()

std::shared_ptr<FEMesh<2> > ptems::FiniteElement< 2 >::Mesh ( ) const

inline

Gets a reference to the underlying mesh for the element.

Returns: The underlying mesh

◆ operator[]()

const Vector<2>& ptems::FiniteElement< 2 >::operator[] ( std::size_t i ) const

inline

Returns the ith vertex of the finite element.

Parameters

i	The index of the vertex to get.

Exceptions

std::out_of_range If i is not less than VertexCount()

Returns: Immutable reference to the specified vertex.

◆ rbegin()

reverse_iterator ptems::FiniteElement< 2 >::rbegin ( ) const

inline

Gets the begin iterator for iterating over the vertices of the element in reverse.

◆ rbegin_faces()

reverse_faceiterator ptems::FiniteElement< 2 >::rbegin_faces ( ) const

inline

Gets the begin iterator for iterating over the faces of the element in reverse.

◆ ReferenceMappings()

const std::vector<ReferenceMapping<2> >& ptems::FiniteElement< 2 >::ReferenceMappings ( ) const

inline

Gets set of mappings from the element to standard reference elements.

If the element is a "basic" element a single reference element (reference triangle or reference cube) will be returned; otherwise, if a polygon, the element will be decomposed into sub-triangles and multiple reference triangles will be returned.

Returns: Mappings to reference elements

◆ rend()

reverse_iterator ptems::FiniteElement< 2 >::rend ( ) const

inline

Gets the end iterator for iterating over the vertices of the element in reverse.

◆ rend_faces()

reverse_faceiterator ptems::FiniteElement< 2 >::rend_faces ( ) const

inline

Gets the end iterator for iterating over the faces of the element in reverse.

◆ SetNeighbour()

bool ptems::FiniteElement< 2 >::SetNeighbour ( const std::shared_ptr< FiniteElement< 2 >> & element )

inline

Specify that the specified element is a neighbour of this element.

Parameters

element The neighbour

Returns: true If the element was added as neighbour; false otherwise (error)

◆ Vertex()

const Vector<2>& ptems::FiniteElement< 2 >::Vertex ( std::size_t i ) const

inline

Returns the ith vertex of the finite element.

Parameters

i	The index of the vertex to get.

Exceptions

std::out_of_range If i is not less than VertexCount()

Returns: Immutable reference to the specified vertex.

◆ VertexCount()

std::size_t ptems::FiniteElement< 2 >::VertexCount ( ) const

inline

Gets the number of vertices in the element.

Returns: Number of vertices in the element.

◆ VertexIndex()

std::size_t ptems::FiniteElement< 2 >::VertexIndex ( std::size_t i ) const

inline

Returns the index in the mesh of ith vertex of the finite element.

Parameters

i	The index of the vertex to get.

Exceptions

std::out_of_range If i is not less than VertexCount()

Returns: Mesh index of the vertex at the specified element vertex index

◆ VertexLocal()

Vector<2> ptems::FiniteElement< 2 >::VertexLocal ( std::size_t i ) const

inline

Returns the ith vertex of the finite element in local coordinates.

Parameters

i	The index of the vertex to get.

Exceptions

std::out_of_range If i is not less than VertexCount()

Returns: The local coordinates of the specified vertex (local to the reference element if only one reference element, otherwise the bounding box)

◆ Volume()

double ptems::FiniteElement< 2 >::Volume ( ) const

inline

Gets the volume of the element.

Returns: Element volume

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

ptems/finiteelement.hpp

Public Types

Public Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ const_faceiterator

◆ const_iterator

◆ const_reverse_faceiterator

◆ const_reverse_iterator

◆ faceiterator

◆ iterator

◆ reverse_faceiterator

◆ reverse_iterator

Member Function Documentation

◆ Agglomerates()

◆ Barycentre()

◆ begin()

◆ begin_faces()

◆ BoundingBox()

◆ cbegin()

◆ cbegin_faces()

◆ cend()

◆ cend_faces()

◆ ComputeQuadraturePoints()

◆ crbegin()

◆ crbegin_faces()

◆ crend()

◆ crend_faces()

◆ Diameter()

◆ end()

◆ end_faces()

◆ Face()

◆ FaceCount()

◆ GlobalToLocal()

◆ Index()

◆ LocalToGlobal()

◆ Mesh()

◆ operator[]()

◆ rbegin()

◆ rbegin_faces()

◆ ReferenceMappings()

◆ rend()

◆ rend_faces()

◆ SetNeighbour()

◆ Vertex()

◆ VertexCount()

◆ VertexIndex()

◆ VertexLocal()

◆ Volume()