A 2D element map for a quadrilateral given by a formula. More...

#include <elementMaps.hh>

Inheritance diagram for concepts::MapQuad2d:

Collaboration diagram for concepts::MapQuad2d:

Public Member Functions
virtual MapQuad2d *	clone () const
	Returns a copy of the map.
virtual MappingEdge2d *	edge (const uint edge) const
	Returns a copy of the edge mapping of one edge.
virtual MapReal2d	hessian (uint i, const Real x, const Real y) const
	Returns the Hessian in a 2D linear map.
virtual MapReal2d	jacobian (const Real x, const Real y) const
	Returns the Jacobian in a 2D linear 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 Real	lineElement (const Real x, const uint edge) const
	Returns factor of differential element integrating over an edge.
	MapQuad2d (const char *map, Real scX, Real scY, Real2d org, Real2d scaling)
	MapQuad2d (const char *map, Real scX, Real scY, Real2d org=Real2d(0.0, 0.0), Real stretch=1.0)
	Constructor.
	MapQuad2d (const MapQuad2d &map)
	Copy constructor.
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.
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.
virtual bool	straight () const
virtual	~MapQuad2d ()
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Private Member Functions
void	operator= (const MapQuad2d &)
	Private assignement operator.
Private Attributes
uchar *	map_
	Parsed formula for the map.
Real2d	org_
Real2d	scaling_
Real	scx_
	Right border of the x parameter domain.
Real	scy_
	Right border of the y parameter domain.
uint	sz_
	Length of the parsed formula.

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 736 of file elementMaps.hh.

Constructor & Destructor Documentation

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

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

concepts::MapQuad2d::MapQuad2d ( const MapQuad2d & map )

Copy constructor.

virtual concepts::MapQuad2d::~MapQuad2d ( ) [virtual]

Member Function Documentation

virtual MapQuad2d* concepts::MapQuad2d::clone ( ) const [inline, virtual]

Returns a copy of the map.

Implements concepts::MappingQuad2d.

Definition at line 768 of file elementMaps.hh.

Here is the call graph for this function:

virtual MappingEdge2d* concepts::MappingQuad2d::edge ( const uint edge ) const [inline, virtual, inherited]

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 711 of file elementMaps.hh.

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.

virtual std::ostream& concepts::MapQuad2d::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::MappingQuad2d.

virtual MapReal2d concepts::MapQuad2d::jacobian	(	const Real	x,
		const Real	y
	)		const `[virtual]`

Returns the Jacobian in a 2D linear map.

Implements concepts::MappingQuad2d.

virtual Real concepts::MappingQuad2d::jacobianDeterminant	(	const Real	x,
		const Real	y
	)		const `[virtual, inherited]`

Returns determinant of the Jacobian.

virtual MapReal2d concepts::MappingQuad2d::jacobianInverse	(	const Real	x,
		const Real	y
	)		const `[virtual, inherited]`

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

virtual Real concepts::MappingQuad2d::lineElement	(	const Real	x,
		const uint	edge
	)		const `[virtual, inherited]`

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: $\xi_1 = 0$