An edge of a 2D FEM edge element quad. More...

#include <bf_graduv.hh>

Public Member Functions
concepts::Real2d	chi (const Real t) const
	Computes the element map. More...

Real	diffElement (const Real t) const
	Computes the differential element for integration over [-1,1]. More...

const ushort	direction () const
	Returns direction of edge on reference quad [0,1]^2, 0 - x, 1 - y. More...

const ushort	edge () const
	Returns number of the edge. More...

	Edge (const Quad< F > &elm, const ushort k)
	Constructor. More...

const Quad< F > &	elm () const
	Returns element. More...

const concepts::QuadratureRule1d *	integration () const
	Returns the integration rule. More...

concepts::MapReal2d	jacobian (const Real t) const
	Computes the Jacobian matrix of element transformation on the edge. More...

Real	jacobianDeterminant (const Real t) const
	Computes the determinant of the Jacobian. More...

concepts::MapReal2d	jacobianInverse (const Real t) const
	Computes the inverse of the Jacobian. More...

concepts::Real2d	localCoords (const Real t) const
	coordinate of point on the edge inside reference element [0,1]^2 More...

const hp2D::KarniadakisDeriv2 *	shpfct () const

const Real	sign () const
	Returns sign of outer normal vector, e.g. left edge -1, right edge +1. More...

virtual const concepts::Edge &	support () const

virtual const concepts::TMatrixBase< F > &	T () const
	T-Matrix of the appropiate Quad, not used. More...

concepts::Real2d	vertex (uint i) const

virtual	~Edge ()

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

Private Attributes
const Quad< F > &	elm_
	The element. More...

const concepts::QuadratureRule1d *	int_
	The integration rule. More...

const ushort	k_
	The number of the edge. More...

const ushort	l_
	Direction of edge on reference element, 0 - x, 1 - y. More...

const hp2D::KarniadakisDeriv2 *	shpfct_
	The shape functions. More...

const concepts::TMatrixBase< F > *	T_
	T matrix from edge dof to element dof. More...

concepts::Real	x_
	Local coordinate on the element, perpendicular to edge, e.g. More...

Detailed Description

template<class F = Real>
class hp2Dedge::Edge< F >

An edge of a 2D FEM edge element quad.

Useful for integration over the edge, in a bilinearform or linearform. E.g. hp2Dedge::Dirichlet need it to calculate the local coefficients.

Definition at line 47 of file bf_graduv.hh.

Constructor & Destructor Documentation

◆ Edge()

template<class F = Real>

hp2Dedge::Edge< F >::Edge	(	const Quad< F > &	elm,
		const ushort	k
	)

Constructor.

Parameters

elm	element, on which the edge lies
k	number of edge, 0 - left, 1 - upper, 2 - right, 3 - bottom

◆ ~Edge()

template<class F = Real>

virtual hp2Dedge::Edge< F >::~Edge ( )

virtual

Member Function Documentation

◆ chi()

template<class F = Real>

concepts::Real2d hp2Dedge::Edge< F >::chi ( const Real t ) const

inline

Computes the element map.

The reference element is [0,1]

Definition at line 232 of file quad.hh.

◆ diffElement()

template<class F = Real>

Real hp2Dedge::Edge< F >::diffElement ( const Real t ) const

inline

Computes the differential element for integration over [-1,1].

Definition at line 260 of file quad.hh.

◆ direction()

template<class F = Real>

const ushort hp2Dedge::Edge< F >::direction ( ) const

inline

Returns direction of edge on reference quad [0,1]^2, 0 - x, 1 - y.

Definition at line 197 of file quad.hh.

◆ edge()

template<class F = Real>

const ushort hp2Dedge::Edge< F >::edge ( ) const

inline

Returns number of the edge.

Definition at line 185 of file quad.hh.

◆ elm()

template<class F = Real>

const Quad<F>& hp2Dedge::Edge< F >::elm ( ) const

inline

Returns element.

Definition at line 191 of file quad.hh.

◆ info()

template<class F = Real>

virtual std::ostream& hp2Dedge::Edge< F >::info ( std::ostream & os ) const

protectedvirtual

◆ integration()

template<class F = Real>

const concepts::QuadratureRule1d* hp2Dedge::Edge< F >::integration ( ) const

inline

Returns the integration rule.

Definition at line 216 of file quad.hh.

◆ jacobian()

template<class F = Real>

concepts::MapReal2d hp2Dedge::Edge< F >::jacobian ( const Real t ) const

inline

Computes the Jacobian matrix of element transformation on the edge.

Definition at line 241 of file quad.hh.

◆ jacobianDeterminant()

template<class F = Real>

Real hp2Dedge::Edge< F >::jacobianDeterminant ( const Real t ) const

inline

Computes the determinant of the Jacobian.

Definition at line 254 of file quad.hh.

◆ jacobianInverse()

template<class F = Real>

concepts::MapReal2d hp2Dedge::Edge< F >::jacobianInverse ( const Real t ) const

inline

Computes the inverse of the Jacobian.

Definition at line 248 of file quad.hh.

◆ localCoords()

template<class F = Real>

concepts::Real2d hp2Dedge::Edge< F >::localCoords ( const Real t ) const

inline

coordinate of point on the edge inside reference element [0,1]^2

Definition at line 222 of file quad.hh.

◆ shpfct()

template<class F = Real>

const hp2D::KarniadakisDeriv2* hp2Dedge::Edge< F >::shpfct ( ) const

inline

Definition at line 211 of file quad.hh.

◆ sign()

template<class F = Real>

const Real hp2Dedge::Edge< F >::sign ( ) const

inline

Returns sign of outer normal vector, e.g. left edge -1, right edge +1.

Definition at line 203 of file quad.hh.

◆ support()

template<class F = Real>

virtual const concepts::Edge& hp2Dedge::Edge< F >::support ( ) const

inlinevirtual

Definition at line 179 of file quad.hh.

◆ T()

template<class F = Real>

virtual const concepts::TMatrixBase<F>& hp2Dedge::Edge< F >::T ( ) const

inlinevirtual

T-Matrix of the appropiate Quad, not used.

Definition at line 268 of file quad.hh.

◆ vertex()

template<class F = Real>

concepts::Real2d hp2Dedge::Edge< F >::vertex ( uint i ) const

inline

Definition at line 173 of file quad.hh.

Member Data Documentation

◆ elm_

template<class F = Real>

const Quad<F>& hp2Dedge::Edge< F >::elm_

private

The element.

Definition at line 276 of file quad.hh.

◆ int_

template<class F = Real>

const concepts::QuadratureRule1d* hp2Dedge::Edge< F >::int_

private

The integration rule.

Definition at line 288 of file quad.hh.

◆ k_

template<class F = Real>

const ushort hp2Dedge::Edge< F >::k_

private

The number of the edge.

Definition at line 278 of file quad.hh.

◆ l_

template<class F = Real>

const ushort hp2Dedge::Edge< F >::l_

private

Direction of edge on reference element, 0 - x, 1 - y.

Definition at line 280 of file quad.hh.

◆ shpfct_

template<class F = Real>

const hp2D::KarniadakisDeriv2* hp2Dedge::Edge< F >::shpfct_

private

The shape functions.

Definition at line 286 of file quad.hh.

◆ T_

template<class F = Real>

const concepts::TMatrixBase<F>* hp2Dedge::Edge< F >::T_

private

T matrix from edge dof to element dof.

Definition at line 290 of file quad.hh.

◆ x_

template<class F = Real>

concepts::Real hp2Dedge::Edge< F >::x_

private

Local coordinate on the element, perpendicular to edge, e.g.

on left x_ = 0

Definition at line 284 of file quad.hh.

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

hp2Dedge/bf_graduv.hh
hp2Dedge/quad.hh

hp2Dedge::Edge< F > Class Template Reference

Public Member Functions

Protected Member Functions

Private Attributes

Detailed Description

template<class F = Real> class hp2Dedge::Edge< F >

Constructor & Destructor Documentation

◆ Edge()

◆ ~Edge()

Member Function Documentation

◆ chi()

◆ diffElement()

◆ direction()

◆ edge()

◆ elm()

◆ info()

◆ integration()

◆ jacobian()

◆ jacobianDeterminant()

◆ jacobianInverse()

◆ localCoords()

◆ shpfct()

◆ sign()

◆ support()

◆ T()

◆ vertex()

Member Data Documentation

◆ elm_

◆ int_

◆ k_

◆ l_

◆ shpfct_

◆ T_

◆ x_

template<class F = Real>
class hp2Dedge::Edge< F >