linearFEM::Triangle Class Referenceabstract

Triangular element with linear shape functions in 2D. More...

#include <element2D.hh>

Inheritance diagram for linearFEM::Triangle:

Public Types
typedef Real	type

Public Member Functions
virtual const concepts::Triangle2d &	cell () const
	Returns the cell of this element. More...
virtual const Cell &	cell () const=0
	Returns the cell on which the element is built. More...
Real3d	elemMap (const Real coord_local) const
Real3d	elemMap (const Real2d &coord_local) const
Real3d	elemMap (const Real3d &coord_local) const
virtual const concepts::ElementGraphics< Real > *	graphics () const
Real	shapefct (const uint i, const Real xi1, const Real xi2) const
	Computes the value of the ith shape function in the point (xi1, xi2). More...
concepts::Real2d	shapefctD (const uint i) const
	Returns the gradient of the ith shape function. More...
virtual const concepts::Triangle &	support () const
	Returns the support of this element. More...
virtual const concepts::TMatrixBase< Real > &	T () const
	Returns the T matrix of this element. More...
virtual const TMatrixBase< Real > &	T () const=0
	Returns the T matrix of the element. More...
	Triangle (const concepts::Triangle2d &cell, concepts::TColumn< Real > *T0, concepts::TColumn< Real > *T1=0)
	Constructor. More...
	Triangle (const concepts::Triangle2d &cell, uint idx[])
	Constructor. More...

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const

Protected Attributes
std::unique_ptr< concepts::TMatrixBase< Real > >	T_
	T matrix of this element. More...

Private Attributes
const concepts::Triangle2d &	cell_
	Cell of the element. More...

Static Private Attributes
static std::unique_ptr< TriangleGraphics >	graphics_

Detailed Description

Triangular element with linear shape functions in 2D.

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

Author

Philipp Frauenfelder, 2002

Definition at line 29 of file element2D.hh.

Member Typedef Documentation

type

typedef Real concepts::ElementWithCell< Real >::type

inherited

Definition at line 81 of file element.hh.

Constructor & Destructor Documentation

Triangle() [1/2]

linearFEM::Triangle::Triangle ( const concepts::Triangle2d &  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 36 of file element2D.hh.

Triangle() [2/2]

linearFEM::Triangle::Triangle ( const concepts::Triangle2d &  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 44 of file element2D.hh.

Member Function Documentation

cell() [1/2]

virtual const concepts::Triangle2d& linearFEM::Triangle::cell ( ) const

inlinevirtual

Returns the cell of this element.

Implements linearFEM::Element.

Definition at line 49 of file element2D.hh.

cell() [2/2]

virtual const Cell& concepts::ElementWithCell< Real >::cell ( ) const

pure virtualinherited

Returns the cell on which the element is built.

Implemented in hp3D::Element< Real >, hp2D::Element< Real >, and hp1D::BaseElement< Real >.

elemMap() [1/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real  coord_local ) const

inlineinherited

Definition at line 86 of file element.hh.

elemMap() [2/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real2d &  coord_local ) const

inlineinherited

Definition at line 90 of file element.hh.

elemMap() [3/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real3d &  coord_local ) const

inlineinherited

Definition at line 94 of file element.hh.

graphics()

virtual const concepts::ElementGraphics<Real>* linearFEM::Triangle::graphics ( ) const

virtual

info()

virtual std::ostream& linearFEM::Triangle::info ( std::ostream &  os ) const

protectedvirtual

shapefct()

Real linearFEM::Triangle::shapefct	(	const uint	i,
		const Real	xi1,
		const Real	xi2
	)		const

Computes the value of the ith shape function in the point (xi1, xi2).

Precondition

xi1, xi2 >= 0 and xi2 <= xi1 <= 1

Parameters

i	Index of the shape fct. (0, 1, 2)
xi1	First coordinate
xi2	Second coordinate

shapefctD()

concepts::Real2d linearFEM::Triangle::shapefctD

(

const uint

i

)

const

Returns the gradient of the ith shape function.

The shape functions are linear and the gradient is constant. Therefore, no coordinates are necessary.

Parameters

i	Index of the shape fct. (0, 1, 2)

support()

virtual const concepts::Triangle& linearFEM::Triangle::support ( ) const

inlinevirtual

Returns the support of this element.

Implements linearFEM::Element.

Definition at line 47 of file element2D.hh.

T() [1/2]

virtual const concepts::TMatrixBase<Real>& linearFEM::Element::T ( ) const

inlinevirtualinherited

Returns the T matrix of this element.

Definition at line 47 of file element.hh.

T() [2/2]

virtual const TMatrixBase<Real >& concepts::ElementWithCell< Real >::T ( ) const

pure virtualinherited

Returns the T matrix of the element.

Implemented in hp3D::Element< Real >, and hp2D::Element< Real >.

Member Data Documentation

cell_

const concepts::Triangle2d& linearFEM::Triangle::cell_

private

Cell of the element.

Definition at line 69 of file element2D.hh.

graphics_

std::unique_ptr<TriangleGraphics> linearFEM::Triangle::graphics_

staticprivate

Definition at line 70 of file element2D.hh.

T_

std::unique_ptr<concepts::TMatrixBase<Real> > linearFEM::Element::T_

protectedinherited

T matrix of this element.

Definition at line 50 of file element.hh.

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

• linearFEM/element2D.hh