Tetra4 Class Reference

Defines a three-dimensional 4-node tetrahedral finite element using P1 interpolation. More...

#include <Tetra4.h>

Inheritance diagram for Tetra4:

Public Member Functions
	Tetra4 ()
	Default Constructor.
	Tetra4 (const Element *el)
	Constructor when data of Element el are given.
	~Tetra4 ()
	Destructor.
void	set (const Element *el)
	Choose element by giving its pointer.
real_t	Sh (size_t i, Point< real_t > s) const
	Calculate shape function of node i at a given point s.
real_t	getVolume () const
	Return volume of element.
Point< real_t >	getRefCoord (const Point< real_t > &x) const
	Return reference coordinates of a point x in element.
bool	isIn (const Point< real_t > &x)
	Check whether point x is in current tetrahedron or not.
real_t	getInterpolate (const Point< real_t > &x, const LocalVect< real_t, 4 > &v)
	Return interpolated value at point of coordinate x
Point< real_t >	EdgeSh (size_t k, Point< real_t > s)
	Return edge shape function.
Point< real_t >	CurlEdgeSh (size_t k)
	Return curl of edge shape function.
real_t	getMaxEdgeLength () const
	Return maximal edge length of tetrahedron.
real_t	getMinEdgeLength () const
	Return minimal edge length of tetrahedron.
std::vector< Point< real_t > >	DSh () const
	Calculate partial derivatives of shape functions at element nodes.
Public Member Functions inherited from FEShape
	FEShape ()
	Default Constructor.
	FEShape (const Element *el)
	Constructor for an element.
	FEShape (const Side *sd)
	Constructor for a side.
virtual	~FEShape ()
	Destructor.
real_t	Sh (size_t i) const
	Return shape function of node i at given point.
real_t	Sh (size_t i, Point< real_t > s) const
	Calculate shape function of node i at a given point s.
real_t	getDet () const
	Return determinant of jacobian.
Point< real_t >	getCenter () const
	Return coordinates of center of element.
Point< real_t >	getLocalPoint () const
	Localize a point in the element.
Point< real_t >	getLocalPoint (const Point< real_t > &s) const
	Localize a point in the element.

Detailed Description

Defines a three-dimensional 4-node tetrahedral finite element using P1 interpolation.

The reference element is the right tetrahedron with four unit edges interpolation.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Member Function Documentation

CurlEdgeSh()

Point< real_t > CurlEdgeSh

(

size_t

k

)

Return curl of edge shape function.

Parameters

[in]

k

Local edge number for which the curl of the edge shape function is computed

Remarks

Element edges are ordered as follows: Edge k has end vertices k and k+1

DSh()

std::vector< Point< real_t > > DSh

(

)

const

Calculate partial derivatives of shape functions at element nodes.

Returns

Vector of partial derivatives of shape functions e.g. dsh[i-1].x, dsh[i-1].y, are partial derivatives of the i-th shape function

EdgeSh()

Point< real_t > EdgeSh	(	size_t	k,
		Point< real_t >	s
	)

Return edge shape function.

Parameters

[in]	k	Local edge number for which the edge shape function is computed
[in]	s	Local coordinates in element

Remarks

Element edges are ordered as follows: Edge k has end vertices k and k+1

Sh()

real_t Sh	(	size_t	i,
		Point< real_t >	s
	)		const

Calculate shape function of node i at a given point s.

s is a point in the reference tetrahedron.