A 2D element map for a quadrilateral. More...

#include <elementMaps.hh>

Inheritance diagram for concepts::MappingQuad2d:

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

virtual MappingEdge2d *	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 =0
	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 =0
	Returns the Jacobian in a 2D linear 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 =0
	Returns a point in 2D mapped from the unit square [0,1]² onto the element in the original mesh. More...

virtual MappingQuad2d *	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

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

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

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

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

◆ 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::PartMappingQuad2d, concepts::BlendingQuad2d, concepts::VertexQuad2d, and concepts::MapQuad2d.

◆ 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::PartMappingQuad2d, concepts::BlendingQuad2d, concepts::VertexQuad2d, and concepts::MapQuad2d.

◆ jacobianDeterminant()

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

virtual

Returns determinant of the Jacobian.

◆ jacobianInverse()

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

virtual

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

◆ 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: $\xi_1 = 0$