#include <elementMaps.hh>

Inheritance diagram for concepts::MappingQuad2d:

Public Member Functions
virtual Real2d	operator() (Real x, Real y) const =0

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

virtual MapReal2d	jacobian (const Real x, const Real y) const =0
	Returns the Jacobian in a 2D linear map.

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

virtual MapReal2d	hessian (uint i, const Real x, const Real y) const =0

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

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

virtual MappingEdge2d *	edge (const uint edge) const

virtual MappingQuad2d *	part (const Real2d x0, const Real2d y0) const

virtual MappingQuad2d *	clone () const =0
	Returns a copy of the map.

virtual bool	straight () 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. The reference element is the unit square.

Author: Philipp Frauenfelder, 2002.

Definition at line 667 of file elementMaps.hh.

Member Function Documentation

◆ clone()

virtual MappingQuad2d * concepts::MappingQuad2d::clone ( ) const

pure virtual

Returns a copy of the map.

Implemented in concepts::MapQuad2d, concepts::VertexQuad2d, concepts::BlendingQuad2d, and concepts::PartMappingQuad2d.

◆ edge()

virtual MappingEdge2d * concepts::MappingQuad2d::edge ( const uint edge ) const

inlinevirtual

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 in concepts::VertexQuad2d, concepts::BlendingQuad2d, and concepts::PartMappingQuad2d.

Definition at line 731 of file elementMaps.hh.

◆ hessian()

virtual MapReal2d concepts::MappingQuad2d::hessian	(	uint	i,
		const Real	x,
		const Real	y
	)		const

pure virtual

Returns the Hessian in a 2D linear map

Parameters

i	coordinate (0 = x, 1 = y)

Implemented in concepts::MapQuad2d, concepts::VertexQuad2d, concepts::BlendingQuad2d, and concepts::PartMappingQuad2d.

◆ info()

virtual std::ostream & concepts::MappingQuad2d::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::Map2d.

Reimplemented in concepts::MapQuad2d, concepts::VertexQuad2d, concepts::BlendingQuad2d, and concepts::PartMappingQuad2d.

◆ inverseLaplace()

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

virtual

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::MappingQuad2d::jacobian	(	const Real	x,
		const Real	y
	)		const

pure virtual

Returns the Jacobian in a 2D linear map.

Implemented in concepts::MapQuad2d, concepts::VertexQuad2d, concepts::BlendingQuad2d, and concepts::PartMappingQuad2d.

◆ lineElement()

virtual Real concepts::MappingQuad2d::lineElement	(	const Real	x,
		const uint	edge
	)		const

virtual

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: $\xi_1 = 0$