Element on an edge representing the normal derivative of neighbouring elements, especially their mean or jump. More...

#include <neumannTrace.hh>

Inheritance diagram for hp2D::NeumannTraceElement< F >:

Collaboration diagram for hp2D::NeumannTraceElement< F >:

Classes
class	ShapeFunction
Public Types
enum	intFormType { ZERO, ONE, TWO, THREE }
	Integration form, which determines terms coming from integration over reference element. More...
typedef F	type
typedef concepts::ElementAndFacette < hp2D::Element< F > >	UnderlyingElement
Public Member Functions
void	addElement (const hp2D::Quad< Real > &quad, uint k, Real weight=1.0)
	Adds the contribution to the Neumann trace from the element on one of the (at most two) sides.
virtual const concepts::EdgeNd &	cell () const
	Returns the cell on which the element is built.
const concepts::Real3d	chi (const Real x) const
	Computes the element map.
Real3d	elemMap (const Real coord_local) const
Real3d	elemMap (const Real2d &coord_local) const
Real3d	elemMap (const Real3d &coord_local) const
virtual const ElementGraphics < F > *	graphics () const
const concepts::QuadratureRule *	integration () const
	Returns the integration rule.
Real	jacobianDeterminant (const Real x) const
	Computes the determinant of the Jacobian.
	NeumannTraceElement (const concepts::Edge2d &cell)
	Constructor.
virtual bool	quadraturePoint (uint i, intPoint &p, intFormType form=ZERO, bool localCoord=false) const
	Delivers a quadrature point.
void	recomputeShapefunctions ()
	Recompute shape functions, e.g.
const concepts::ShapeFunction1D < Real > *	shpfct () const
	Returns the shape functions.
const concepts::ShapeFunction1D < Real > *	shpfctD () const
	Returns the derivatives of the shape functions.
virtual const concepts::Edge &	support () const
virtual const vectorial::TMatrix< F > &	T () const
	Returns the T matrix of the element.
uint &	tag ()
	Returns the tag.
virtual concepts::Real3d	vertex (uint i) const
virtual	~NeumannTraceElement ()
Static Public Member Functions
static concepts::QuadRuleFactory &	rule ()
	Access to the quadrature rule, which is valid for all elements of this type (hp1D::IntegrableElm).
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Protected Attributes
std::auto_ptr < concepts::QuadratureRule >	int_
	The integration rule.
vectorial::TMatrix< Real >	T_
	T matrix of the element.
Static Protected Attributes
static concepts::QuadRuleFactory	rule_
Private Attributes
const concepts::Edge2d &	cell_
	The cell.
concepts::Sequence< uint >	dim_
	Local number of shape functions coming from one side.
concepts::Sequence< uint >	p_
	Polynomial degree along the edge for each side.
std::auto_ptr < concepts::ShapeFunction1D < Real > >	shpfct_
	The shape functions, precomputed on quadrature points.
std::auto_ptr < concepts::ShapeFunction1D < Real > >	shpfctD_
	The derivatives of the shape functions.
concepts::Sequence < UnderlyingElement >	uelm_
concepts::Array< Real >	values_
	The actual storage of the values of the shape functions and their derivatives along the edge.
concepts::Array< Real >	valuesD_
concepts::Sequence< Real >	weights_
	Weight for each side.

Detailed Description

template<class F = Real>
class hp2D::NeumannTraceElement< F >

Element on an edge representing the normal derivative of neighbouring elements, especially their mean or jump.

The number of shape functions are the sum of the number of shape functions of the two neighbouring 2D elements.

Author:: Kersten Schmidt, 2010

Definition at line 38 of file neumannTrace.hh.

Member Typedef Documentation

template<class F>

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

Definition at line 53 of file element.hh.

template<class F = Real>

typedef concepts::ElementAndFacette<hp2D::Element<F> > hp2D::NeumannTraceElement< F >::UnderlyingElement

Definition at line 41 of file neumannTrace.hh.

Member Enumeration Documentation

enum concepts::IntegrationCell::intFormType [inherited]

Integration form, which determines terms coming from integration over reference element.

Enumerator:

ZERO
ONE
TWO
THREE

Definition at line 27 of file integral.hh.

Constructor & Destructor Documentation

template<class F = Real>

hp2D::NeumannTraceElement< F >::NeumannTraceElement ( const concepts::Edge2d & cell )

Constructor.

Creates the Neumann trace from the element on one side.

template<class F = Real>

virtual hp2D::NeumannTraceElement< F >::~NeumannTraceElement ( ) [virtual]

Member Function Documentation

template<class F = Real>

void hp2D::NeumannTraceElement< F >::addElement	(	const hp2D::Quad< Real > &	quad,
		uint	k,
		Real	weight = `1.0`
	)

Adds the contribution to the Neumann trace from the element on one of the (at most two) sides.

template<class F = Real>

virtual const concepts::EdgeNd& hp2D::NeumannTraceElement< F >::cell ( ) const [inline, virtual]

Returns the cell on which the element is built.

Implements concepts::ElementWithCell< F >.

Definition at line 73 of file neumannTrace.hh.

const concepts::Real3d hp1D::IntegrableElm::chi ( const Real x ) const [inline, inherited]

Computes the element map.

The reference element is [0,1].

Definition at line 32 of file element.hh.

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template<typename F>

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

Definition at line 83 of file element.hh.

template<typename F>

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

Definition at line 87 of file element.hh.

template<typename F>

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

Definition at line 91 of file element.hh.

template<class F>

virtual const ElementGraphics<F>* concepts::Element< F >::graphics ( ) const [inline, virtual, inherited]

template<class F = Real>

virtual std::ostream& hp2D::NeumannTraceElement< F >::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

const concepts::QuadratureRule* hp1D::IntegrableElm::integration ( ) const [inline, inherited]

Returns the integration rule.

Definition at line 41 of file element.hh.

Real hp1D::IntegrableElm::jacobianDeterminant ( const Real x ) const [inline, inherited]

Computes the determinant of the Jacobian.

Definition at line 35 of file element.hh.

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virtual bool hp1D::IntegrableElm::quadraturePoint	(	uint	i,
		intPoint &	p,
		intFormType	form = `ZERO`,
		bool	localCoord = `false`
	)		const `[virtual, inherited]`

Delivers a quadrature point.

Quadrature point consists of coordinates (for evaluation of formulas) and intermediate data, consisting of the weight and term coming from mapping.

Returns false, if the number of quadrature points is overstepped.

Parameters:

i	number of quadrature point
intPoint	data given back
form	Integration form
localCoord	If true, local coordinates are returned. Else physical coordinates.

Implements concepts::IntegrationCell.

template<class F = Real>

void hp2D::NeumannTraceElement< F >::recomputeShapefunctions ( )

Recompute shape functions, e.g.

for other abscissas redefined through IntegrableElm::rule().set(...)

static concepts::QuadRuleFactory& hp1D::IntegrableElm::rule ( ) [inline, static, inherited]

Access to the quadrature rule, which is valid for all elements of this type (hp1D::IntegrableElm).

Change of the quadrature rule is put into practice for newly created elements and for already created elements by precomputing the integration points and shape functions on them.

Definition at line 52 of file element.hh.

template<class F = Real>

const concepts::ShapeFunction1D<Real>* hp2D::NeumannTraceElement< F >::shpfct ( ) const [inline]

Returns the shape functions.

Definition at line 83 of file neumannTrace.hh.

template<class F = Real>

const concepts::ShapeFunction1D<Real>* hp2D::NeumannTraceElement< F >::shpfctD ( ) const [inline]

Returns the derivatives of the shape functions.

TODO: implementation.

Definition at line 89 of file neumannTrace.hh.

template<class F = Real>

virtual const concepts::Edge& hp2D::NeumannTraceElement< F >::support ( ) const [inline, virtual]