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

#include <elementMaps.hh>

Inheritance diagram for concepts::VertexQuad2d:

Public Member Functions
virtual VertexQuad2d *	clone () const
	Returns a copy of the map. More...

virtual MappingStraightEdge2d *	edge (const uint edge) const
	Returns a copy of the edge mapping of one edge. More...

virtual MapReal2d	hessian (uint i, const Real x, const Real y) const
	Returns the Hessian in a 2D linear map. More...

virtual MapReal2d	inverseLaplace (const Real x, const Real y) const
	NEW: More...

virtual MapReal2d	jacobian (const Real x, const Real y) const
	Returns the jacobian of the element map. More...

virtual Real	jacobianDeterminant (const Real x, const Real y) const
	Returns determinant of the Jacobian. More...

virtual MapReal2d	jacobianInverse (const Real x, const Real y) const
	Returns the inverse of the Jacobian in a 2D linear map. More...

virtual Real	lineElement (const Real x, const uint edge) const
	Returns factor of differential element integrating over an edge. More...

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. More...

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. More...

virtual bool	straight () const

	VertexQuad2d (const VertexQuad2d &v)
	Copy constructor. More...

	VertexQuad2d (Real2d vtx0, Real2d vtx1, Real2d vtx2, Real2d vtx3)
	Constructor. More...

virtual	~VertexQuad2d ()

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

Private Attributes
bool	hasLength_
	Length computed? More...

Real	len_ [4]
	Length of Edges, used for computation of the line elements. More...

Real2d	vtx_ [4]
	Vertices. More...

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() [1/2]

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

Constructor.

The four vertices have to be given counter clockwise.

◆ VertexQuad2d() [2/2]

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

Copy constructor.

◆ ~VertexQuad2d()

virtual concepts::VertexQuad2d::~VertexQuad2d ( )

virtual

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:

dxdx phi_1^{-1} dydy phi_1^{-1}

dxdx phi_2^{-1} dydy phi_2^{-1}

◆ jacobian()

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.

◆ jacobianDeterminant()

virtual Real concepts::MappingQuad2d::jacobianDeterminant	(	const Real	x,
		const Real	y
	)		const

virtualinherited

Returns determinant of the Jacobian.

◆ jacobianInverse()

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

virtualinherited

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

◆ lineElement()

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

virtual

Returns factor of differential element integrating over an edge.

See also: MappingQuad2d

Reimplemented from concepts::MappingQuad2d.

◆ operator()()

virtual Real2d concepts::VertexQuad2d::operator()	(	Real	x,
		Real	y
	)		const

virtual

Returns a point in 2D mapped from the unit square [0,1]² onto the element in the original mesh.

Returns

Implements concepts::MappingQuad2d.

◆ part()

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

virtual

Returns a new object of an element map for a rectangular part of the reference cell defined by the two points.

Reimplemented from concepts::MappingQuad2d.

◆ straight()

virtual bool concepts::VertexQuad2d::straight ( ) const

inlinevirtual

Reimplemented from concepts::Map2d.

Definition at line 848 of file elementMaps.hh.

Member Data Documentation

◆ hasLength_

bool concepts::VertexQuad2d::hasLength_

private

Length computed?

Definition at line 857 of file elementMaps.hh.

◆ len_

Real concepts::VertexQuad2d::len_[4]

mutableprivate

Length of Edges, used for computation of the line elements.

Definition at line 855 of file elementMaps.hh.

◆ vtx_

Real2d concepts::VertexQuad2d::vtx_[4]

private

Vertices.

Definition at line 853 of file elementMaps.hh.

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

geometry/elementMaps.hh

concepts::VertexQuad2d Class Reference

Public Member Functions

Protected Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ VertexQuad2d() [1/2]

◆ VertexQuad2d() [2/2]

◆ ~VertexQuad2d()

Member Function Documentation

◆ clone()

◆ edge()

◆ hessian()

◆ info()

◆ inverseLaplace()

◆ jacobian()

◆ jacobianDeterminant()

◆ jacobianInverse()

◆ lineElement()

◆ operator()()

◆ part()

◆ straight()

Member Data Documentation

◆ hasLength_

◆ len_

◆ vtx_