A 2D element map for a quadrilateral given by a the four vertices. More...

#include <elementMaps.hh>

Inheritance diagram for concepts::VertexQuad2d:

Collaboration diagram for concepts::VertexQuad2d:

Public Member Functions
virtual VertexQuad2d *	clone () const
	Returns a copy of the map.
virtual MappingStraightEdge2d *	edge (const uint edge) const
	Returns a copy of the edge mapping of one edge.
virtual MapReal2d	hessian (uint i, const Real x, const Real y) const
	Returns the Hessian in a 2D linear map.
virtual MapReal2d	jacobian (const Real x, const Real y) const
	Returns the jacobian of the element map $\left(\frac{\partial F_K}{\partial\vec\xi}\right) = \left\{\frac{\partial x^i}{\partial \xi_j}\right\}_{i,j=1}^2$ .
virtual Real	jacobianDeterminant (const Real x, const Real y) const
	Returns determinant of the Jacobian.
virtual MapReal2d	jacobianInverse (const Real x, const Real y) const
	Returns the inverse of the Jacobian in a 2D linear map.
virtual Real	lineElement (const Real x, const uint edge) const
	Returns factor of differential element integrating over an edge.
virtual Real	lineElement (const Real x, const uint edge)
	Returns factor of differential element integrating over an edge.
virtual Real2d	operator() (Real x, Real y) const
	Returns a point in 2D mapped from the unit square [0,1]² onto the element in the original mesh.
virtual VertexQuad2d *	part (const Real2d x0, const Real2d y0) const
	Returns a new object of an element map for a rectangular part of the reference cell defined by the two points.
virtual bool	straight () const
	VertexQuad2d (const VertexQuad2d &v)
	Copy constructor.
	VertexQuad2d (Real2d vtx0, Real2d vtx1, Real2d vtx2, Real2d vtx3)
	Constructor.
virtual	~VertexQuad2d ()
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Private Attributes
bool	hasLength_
	Length computed?
Real	len_ [4]
	Length of Edges, used for.
Real2d	vtx_ [4]
	Vertices.

Detailed Description

A 2D element map for a quadrilateral given by a the four vertices.

Author:: Philipp Frauenfelder, 2002.

Test:

test::TestJacobian2D

test::TestMatrices2D

Definition at line 798 of file elementMaps.hh.

Constructor & Destructor Documentation

concepts::VertexQuad2d::VertexQuad2d	(	Real2d	vtx0,
		Real2d	vtx1,
		Real2d	vtx2,
		Real2d	vtx3
	)

Constructor.

The four vertices have to be given counter clockwise.

concepts::VertexQuad2d::VertexQuad2d ( const VertexQuad2d & v )

Copy constructor.

virtual concepts::VertexQuad2d::~VertexQuad2d ( ) [virtual]

Member Function Documentation

virtual VertexQuad2d* concepts::VertexQuad2d::clone ( ) const [virtual]

Returns a copy of the map.

Implements concepts::MappingQuad2d.

virtual MappingStraightEdge2d* concepts::VertexQuad2d::edge ( const uint edge ) const [virtual]

Returns a copy of the edge mapping of one edge.

The edge mappings are directed counter-clockwise, i.e. for the lower edge from the left lower vertex to the right lower one.

Parameters:

edge	number of edge, i.e. 0 - lower, 1 - right, 2 - upper, 3 - left

Reimplemented from concepts::MappingQuad2d.

virtual MapReal2d concepts::VertexQuad2d::hessian	(	uint	i,
		const Real	x,
		const Real	y
	)		const `[virtual]`

Returns the Hessian in a 2D linear map.

Parameters:

i	coordinate (0 = x, 1 = y)

Implements concepts::MappingQuad2d.

virtual std::ostream& concepts::VertexQuad2d::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::MappingQuad2d.

virtual MapReal2d concepts::VertexQuad2d::jacobian	(	const Real	x,
		const Real	y
	)		const `[virtual]`

Returns the jacobian of the element map

$\left(\frac{\partial F_K}{\partial\vec\xi}\right) = \left\{\frac{\partial x^i}{\partial \xi_j}\right\}_{i,j=1}^2$

.

Implements concepts::MappingQuad2d.

virtual Real concepts::MappingQuad2d::jacobianDeterminant	(	const Real	x,
		const Real	y
	)		const `[virtual, inherited]`

Returns determinant of the Jacobian.

virtual MapReal2d concepts::MappingQuad2d::jacobianInverse	(	const Real	x,
		const Real	y
	)		const `[virtual, inherited]`

Returns the inverse of the Jacobian in a 2D linear map.

virtual Real concepts::VertexQuad2d::lineElement	(	const Real	x,
		const uint	edge
	)		`[virtual]`

Returns factor of differential element integrating over an edge.

See also:: MappingQuad2d

virtual Real concepts::MappingQuad2d::lineElement	(	const Real	x,
		const uint	edge
	)		const `[virtual, inherited]`

Returns factor of differential element integrating over an edge.

The factor is either $\sqrt{J_{11}^2+J_{21}^2}$ or $\sqrt{J_{12}^2+J_{22}^2}$ .

The routine exists explicitly because it is more efficient to implement it than to use jacobian itself, i.e. for affine elements the line element is constant.

Parameters:

x	local variable on edge (in [0,1]), stands for $\xi_1$ or $\xi_2$
edge	number of edge, i.e. 0: $\xi_2 = 0$ , 1: $\xi_1 = 1$ , 2: $\xi_2 = 1$ , 3: $\xi_1 = 0$