Quadrilateral element with bilinear shape functions in 2D. More...

#include <element2D.hh>

Inheritance diagram for linearFEM::Quad:

Collaboration diagram for linearFEM::Quad:

Public Types
typedef Real	type
Public Member Functions
virtual const concepts::Quad2d &	cell () const
	Returns the cell of this element.
Real3d	elemMap (const Real coord_local) const
Real3d	elemMap (const Real2d &coord_local) const
Real3d	elemMap (const Real3d &coord_local) const
void	evaluate (Real res, const Real x, const uint n) const
	Evaluates the shape functions in the given one dimensional points.
void	evaluateD (concepts::Real2d res, const Real x, const uint n) const
	Evaluates the derivatives of the shape functions in the given one dimensional points.
virtual const concepts::ElementGraphics < Real > *	graphics () const
	Quad (const concepts::Quad2d &cell, concepts::TColumn< Real > T0, concepts::TColumn< Real > T1=0)
	Constructor.
	Quad (const concepts::Quad2d &cell, uint idx[])
	Constructor.
virtual const concepts::Quad &	support () const
	Returns the support of this element.
virtual const concepts::TMatrixBase< Real > &	T () const
	Returns the T matrix of this element.
uint &	tag ()
	Returns the tag.
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Protected Attributes
std::auto_ptr < concepts::TMatrixBase< Real > >	T_
	T matrix of this element.
Private Attributes
const concepts::Quad2d &	cell_
	Cell of the element.
Static Private Attributes
static std::auto_ptr < QuadGraphics >	graphics_

Detailed Description

Quadrilateral element with bilinear shape functions in 2D.

In 2D, two different elements are possible: triangles and quadrilaterals.

Author:: Philipp Frauenfelder, 2002

Definition at line 76 of file element2D.hh.

Member Typedef Documentation

typedef Real concepts::Element< Real >::type [inherited]

Definition at line 53 of file element.hh.

Constructor & Destructor Documentation

linearFEM::Quad::Quad	(	const concepts::Quad2d &	cell,
		uint	idx[]
	)		`[inline]`

Constructor.

Creates a T matrix out of idx.

See also:: concepts::TIndex

Parameters:

cell	Cell of the element
idx	Describes the map local / global dof

Definition at line 83 of file element2D.hh.

linearFEM::Quad::Quad	(	const concepts::Quad2d &	cell,
		concepts::TColumn< Real > *	T0,
		concepts::TColumn< Real > *	T1 = `0`
	)		`[inline]`

Constructor.

Creates a T matrix out of T0 and T1

See also:: concepts::TMatrix

Parameters:

cell	Cell of the element
T0	Contains T columns
T1	Contains T columns

Definition at line 91 of file element2D.hh.

Member Function Documentation

virtual const concepts::Quad2d& linearFEM::Quad::cell ( ) const [inline, virtual]

Returns the cell of this element.

Implements linearFEM::Element.

Definition at line 94 of file element2D.hh.

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real coord_local ) const [inline, inherited]

Definition at line 83 of file element.hh.

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Real3d concepts::ElementWithCell< Real >::elemMap ( const Real2d & coord_local ) const [inline, inherited]

Definition at line 87 of file element.hh.

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Real3d concepts::ElementWithCell< Real >::elemMap ( const Real3d & coord_local ) const [inline, inherited]

Definition at line 91 of file element.hh.

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void linearFEM::Quad::evaluate	(	Real *	res,
		const Real *	x,
		const uint	n
	)		const

Evaluates the shape functions in the given one dimensional points.

The points in x have to be between -1 and 1 and are tensorised to get two dimensional points.

Precondition:: res has to allocated, size: 4*n*n

Parameters:

res	Values of the shapefunctions with index k in the points (x_i, x_j) with j running fastest and k running slowest
x	Points in 1D where the shape functions have to be evaluated. Size: `n`
n	Number of points in `x`

void linearFEM::Quad::evaluateD	(	concepts::Real2d *	res,
		const Real *	x,
		const uint	n
	)		const

Evaluates the derivatives of the shape functions in the given one dimensional points.

The points in x have to be between -1 and 1 and are tensorised to get two dimensional points.

Precondition:: res has to allocated, size: 4*n*n

Parameters:

res	Values of the shapefunctions with index k in the points (x_i, x_j) with j running fastest and k running slowest
x	Points in 1D where the shape functions have to be evaluated. Size: `n`
n	Number of points in `x`