#include <elementMaps.hh>

Inheritance diagram for concepts::VertexQuad2d:

Public Member Functions
	VertexQuad2d (Real2d vtx0, Real2d vtx1, Real2d vtx2, Real2d vtx3)

	VertexQuad2d (const VertexQuad2d &v)
	Copy constructor.

virtual Real2d	operator() (Real x, Real y) const

virtual MapReal2d	jacobian (const Real x, const Real y) const

virtual MapReal2d	hessian (uint i, const Real x, const Real y) const

virtual Real	lineElement (const Real x, const uint edge) const

virtual MappingStraightEdge2d *	edge (const uint edge) const

virtual VertexQuad2d *	part (const Real2d x0, const Real2d y0) const

virtual VertexQuad2d *	clone () const
	Returns a copy of the map.

virtual bool	straight () const

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 MapReal2d	inverseLaplace (const Real x, const Real y) const

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.

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 818 of file elementMaps.hh.

Constructor & Destructor Documentation

◆ VertexQuad2d()

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

Constructor. The four vertices have to be given counter clockwise.

Member Function Documentation

◆ clone()

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

virtual

Returns a copy of the map.

Implements concepts::MappingQuad2d.

◆ edge()

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.

◆ hessian()

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.

◆ info()

virtual std::ostream & concepts::VertexQuad2d::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::MappingQuad2d.

◆ inverseLaplace()

virtual MapReal2d concepts::MappingQuad2d::inverseLaplace	(	const Real	x,
		const Real	y
	)		const

virtualinherited

NEW:

Returns the 2nd partial derivatives of the inverse Mapping that maps from a mappingQuad2D to the reference Quad. This inverse is called $\phi^{-1}=(\phi_1^{-1} , \phi_2^{-1})$ . The function returns a 2x2 matrix of the following form: