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

#include <elementMaps.hh>

Inheritance diagram for concepts::MapQuad2d:

Public Member Functions
virtual MapQuad2d *	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...

	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. More...

	MapQuad2d (const MapQuad2d &map)
	Copy constructor. 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

virtual	~MapQuad2d ()

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

Private Member Functions
void	operator= (const MapQuad2d &)
	Private assignement operator. More...

Private Attributes
uchar *	map_
	Parsed formula for the map. More...

Real2d	org_

Real2d	scaling_

Real	scx_
	Right border of the x parameter domain. More...

Real	scy_
	Right border of the y parameter domain. More...

uint	sz_
	Length of the parsed formula. More...

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() [1/3]

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

◆ MapQuad2d() [2/3]

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

◆ MapQuad2d() [3/3]

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

Copy constructor.

◆ ~MapQuad2d()

virtual concepts::MapQuad2d::~MapQuad2d ( )

virtual

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

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.

◆ 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: $\xi_1 = 0$

Reimplemented in concepts::BlendingQuad2d, and concepts::VertexQuad2d.

◆ operator()()

virtual Real2d concepts::MapQuad2d::operator()	(	Real	x,
		Real	y
	)		const

inlinevirtual

Returns a point in 2D mapped from the unit square [0,1]² onto the element in the original mesh.

Returns

Implements concepts::MappingQuad2d.

Definition at line 779 of file elementMaps.hh.

◆ operator=()

void concepts::MapQuad2d::operator= ( const MapQuad2d & )

private

Private assignement operator.

◆ part()

virtual MappingQuad2d* concepts::MappingQuad2d::part	(	const Real2d	x0,
		const Real2d	y0
	)		const

virtualinherited

Returns a new object of an element map for a rectangular part of the reference cell defined by the two points.

Reimplemented in concepts::VertexQuad2d.

◆ straight()

virtual bool concepts::Map2d::straight ( ) const

inlinevirtualinherited

Reimplemented in concepts::VertexQuad2d, and concepts::VertexTriangle2d.

Definition at line 37 of file elementMaps.hh.

Member Data Documentation

◆ map_

uchar* concepts::MapQuad2d::map_

private

Parsed formula for the map.

Definition at line 793 of file elementMaps.hh.

◆ org_

Real2d concepts::MapQuad2d::org_

private

Definition at line 804 of file elementMaps.hh.

◆ scaling_

Real2d concepts::MapQuad2d::scaling_

private

Definition at line 805 of file elementMaps.hh.

◆ scx_

Real concepts::MapQuad2d::scx_

private

Right border of the x parameter domain.

Definition at line 799 of file elementMaps.hh.

◆ scy_

Real concepts::MapQuad2d::scy_

private

Right border of the y parameter domain.

Definition at line 802 of file elementMaps.hh.

◆ sz_

uint concepts::MapQuad2d::sz_

private

Length of the parsed formula.

Definition at line 796 of file elementMaps.hh.

The documentation for this class was generated from the following file:

geometry/elementMaps.hh

concepts::MapQuad2d Class Reference

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MapQuad2d() [1/3]

◆ MapQuad2d() [2/3]

◆ MapQuad2d() [3/3]

◆ ~MapQuad2d()

Member Function Documentation

◆ clone()

◆ edge()

◆ hessian()

◆ info()

◆ inverseLaplace()

◆ jacobian()

◆ jacobianDeterminant()

◆ jacobianInverse()

◆ lineElement()

◆ operator()()

◆ operator=()

◆ part()

◆ straight()

Member Data Documentation

◆ map_

◆ org_

◆ scaling_

◆ scx_

◆ scy_

◆ sz_