#include <elementMaps.hh>

Inheritance diagram for concepts::MapQuad2d:

Public Member Functions
	MapQuad2d (const char *map, Real scX, Real scY, Real2d org=Real2d(0.0, 0.0), Real stretch=1.0)

	MapQuad2d (const char *map, Real scX, Real scY, Real2d org, Real2d scaling)

	MapQuad2d (const MapQuad2d &map)
	Copy constructor.

virtual Real2d	operator() (Real x, Real y) const

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

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

virtual MapQuad2d *	clone () const
	Returns a copy of the map.

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

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

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 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 given by a formula. The reference element is the unit square. For easier construction of the element map, a rectangle square $[0,a] \times [0,b]$ can be given as the parameter domain.

If the map gives curved boundaries, they are approxmated better with more refined elements.

Examples: meshes.cc.

Definition at line 756 of file elementMaps.hh.

Constructor & Destructor Documentation

◆ MapQuad2d()

concepts::MapQuad2d::MapQuad2d	(	const char *	map,
		Real	scX,
		Real	scY,
		Real2d	org = `Real2d(0.0, 0.0)`,
		Real	stretch = `1.0`
	)

Constructor. The values of scX and scY are only for the map, they are not needed by the user for mapping a point from the reference element onto the Real element.

Parameters

map	The element map for this quadrilateral as a string, x and y are the variables, the first and the second component are separated by a comma.
scX	The range of x is [0, scX]
scY	The range of y is [0, scY]
org	The origin of the element
stretch	Scaling factor of the element

Member Function Documentation

◆ clone()

virtual MapQuad2d * concepts::MapQuad2d::clone ( ) const

inlinevirtual

Returns a copy of the map.

Implements concepts::MappingQuad2d.

Definition at line 788 of file elementMaps.hh.

◆ edge()

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

inlinevirtualinherited

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::MapQuad2d::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::MapQuad2d::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::MapQuad2d::jacobian	(	const Real	x,
		const Real	y
	)		const

virtual

Returns the Jacobian in a 2D linear map.

Implements concepts::MappingQuad2d.

◆ 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: $\xi_1 = 0$