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

#include <elementMaps.hh>

Inheritance diagram for concepts::BlendingQuad2d:

Public Member Functions
	BlendingQuad2d (const BlendingQuad2d &v)
	Copy constructor. More...

	BlendingQuad2d (const MappingEdge2d edgemap0, const MappingEdge2d edgemap1, const MappingEdge2d edgemap2, const MappingEdge2d edgemap3=0, const Real2d vtx0=0, const Real2d vtx1=0, const Real2d vtx2=0, const Real2d vtx3=0)
	Constructor. More...

virtual BlendingQuad2d *	clone () const
	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
	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 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
	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

	~BlendingQuad2d ()

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

Private Member Functions
void	testJacobian_ () const
	Tests if the jacobian is positive. More...

Private Attributes
const MappingEdge2d *	edgemap_ [4]
	Map of the edges. More...

Real2d	vtx_ [4]
	Vector that contains the vertices. More...

Detailed Description

A 2D element map for a curved quadrilateral.

The mapping is defined by the Linear Blending Function Method (proposed by Gordon and Hall, 1971). Therefor the mapping of the edges has to be given.

Test:: test::TestBlending2D

Author: , Kersten Schmidt, 2004

Definition at line 872 of file elementMaps.hh.

Constructor & Destructor Documentation

◆ BlendingQuad2d() [1/2]

concepts::BlendingQuad2d::BlendingQuad2d	(	const MappingEdge2d *	edgemap0,
		const MappingEdge2d *	edgemap1,
		const MappingEdge2d *	edgemap2,
		const MappingEdge2d *	edgemap3 = `0`,
		const Real2d *	vtx0 = `0`,
		const Real2d *	vtx1 = `0`,
		const Real2d *	vtx2 = `0`,
		const Real2d *	vtx3 = `0`
	)

Constructor.

Pointers to edge mappings and vertex coordinates can be given. There has to be given at least

two opposite edges
two adjacent edges and a the other vertex
an edge and the two other vertices
four vertices

If more edges or vertices are given, the particular coordinates of the vertices has to match.

The edges or vertices have to be given counter clockwise. The first vertex of the edgemap0 is the first vertex of the quad, the second in the edge map the second ...

The direction of an edge has to be changed by its method inverse(), e.g.

std::unique_ptr<MappingEdge2d> invEdge = edge.inverse();
BlendingQuad2d quad(invEdge, ...);

The class holds own copies of the given edge mappings and coordinates of the vertices.

First edge is $\xi_2=0$ , where $\xi_2$ is the second local coordinate.

◆ BlendingQuad2d() [2/2]

concepts::BlendingQuad2d::BlendingQuad2d ( const BlendingQuad2d & v )

Copy constructor.

◆ ~BlendingQuad2d()

concepts::BlendingQuad2d::~BlendingQuad2d ( )

Member Function Documentation

◆ clone()

virtual BlendingQuad2d* concepts::BlendingQuad2d::clone ( ) const

inlinevirtual

Returns a copy of the map.

Implements concepts::MappingQuad2d.

Definition at line 920 of file elementMaps.hh.

◆ edge()

virtual MappingEdge2d* concepts::BlendingQuad2d::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 from concepts::MappingQuad2d.

Definition at line 916 of file elementMaps.hh.

◆ hessian()

virtual MapReal2d concepts::BlendingQuad2d::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::BlendingQuad2d::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::BlendingQuad2d::jacobian	(	const Real	x,
		const Real	y
	)		const

virtual

Returns the Jacobian in a 2D linear map.

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::BlendingQuad2d::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: $\xi_1 = 0$