Part of a map of a quadrilateral. More...

#include <elementMaps.hh>

Inheritance diagram for concepts::PartMappingQuad2d:

Public Member Functions
virtual PartMappingQuad2d *	clone () const
	Virtual copy constructor. 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
	Application operator. 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...

	PartMappingQuad2d (const MappingQuad2d &map, const Real2d xi0, const Real2d xi1)
	Constructor. More...

	PartMappingQuad2d (const PartMappingQuad2d &map)
	Copy Constructor. More...

virtual bool	straight () const

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

Private Member Functions
const Real2d	xi_ (const Real x, const Real y) const
	Returns the parameter in the original mapping. More...

Private Attributes
const Real2d	d_
	Vector from the lower left to the upper right vertex in the reference cell of original map. More...

std::unique_ptr< const MappingQuad2d >	map_
	Original edge map. More...

const Real2d	x0_
	Parameter of the lower left vertex in the reference cell of the original map. More...

Detailed Description

Part of a map of a quadrilateral.

Author: , Kersten Schmidt, 2009

Definition at line 938 of file elementMaps.hh.

Constructor & Destructor Documentation

◆ PartMappingQuad2d() [1/2]

concepts::PartMappingQuad2d::PartMappingQuad2d	(	const MappingQuad2d &	map,
		const Real2d	xi0,
		const Real2d	xi1
	)

Constructor.

Parameters

map	original element map
x0,x1	lower left and upper right point in the rectangle in the reference cell

◆ PartMappingQuad2d() [2/2]

concepts::PartMappingQuad2d::PartMappingQuad2d ( const PartMappingQuad2d & map )

Copy Constructor.

Member Function Documentation

◆ clone()

virtual PartMappingQuad2d* concepts::PartMappingQuad2d::clone ( ) const

virtual

Virtual copy constructor.

Implements concepts::MappingQuad2d.

◆ edge()

virtual MappingEdge2d* concepts::PartMappingQuad2d::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::PartMappingQuad2d::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::PartMappingQuad2d::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::PartMappingQuad2d::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::MappingQuad2d::lineElement	(	const Real	x,
		const uint	edge
	)		const

virtualinherited

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: $\xi_1 = 0$