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

#include <neumannTrace.hh>

Inheritance diagram for hp2D::NTElement_BA< 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 Real	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. More...

void	appendT (concepts::TColumn< F > *T)
	Appends the T columns to the T matrix. More...

virtual const concepts::Edge2d &	cell () const

virtual const Cell &	cell () const=0
	Returns the cell on which the element is built. More...

const concepts::Real3d	chi (const Real x) const
	Computes the element map. More...

Real3d	elemMap (const Real coord_local) const

Real3d	elemMap (const Real2d &coord_local) const

Real3d	elemMap (const Real3d &coord_local) const

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

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

const concepts::Z2	mapRho () const
	Returns the orientation of the MappingEdge2d corresponding to the quad. More...

	NTElement_BA (const concepts::Edge2d &cell)
	Constructor. More...

ushort	p () const

virtual bool	quadraturePoint (uint i, intPoint &p, intFormType form=ZERO, bool localCoord=false) const
	Delivers a quadrature point. More...

void	recomputeShapefunctions ()
	Recompute shape functions, e.g. More...

const concepts::ShapeFunction1D< Real > *	shpfct () const
	Returns the shape functions. More...

const concepts::ShapeFunction1D< Real > *	shpfctD () const
	Returns the derivatives of the shape functions. More...

virtual const concepts::Edge &	support () const

virtual const concepts::TMatrix< F > &	T () const

virtual const TMatrixBase< Real > &	T () const=0
	Returns the T matrix of the element. More...

const concepts::Sequence< UnderlyingElement > &	uelm () const
	Returns the Underlying Element(s) More...

virtual concepts::Real3d	vertex (uint i) const

virtual	~NTElement_BA ()

Static Public Member Functions
static concepts::QuadRuleFactory &	rule ()
	Access to the quadrature rule, which is valid for all elements of this type (hp1D::IntegrableElm). More...

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

Protected Attributes
std::unique_ptr< concepts::QuadratureRule1d >	int_
	The integration rule. More...

concepts::TMatrix< Real >	T_
	T matrix of the element. More...

Static Protected Attributes
static concepts::QuadRuleFactory	rule_

Private Attributes
const concepts::Edge2d &	cell_
	The cell. More...

concepts::Sequence< uint >	dim_
	Local number of shape functions coming from one side. More...

concepts::Z2	mapRho_

concepts::Sequence< uint >	p_
	Polynomial degree along the edge for each side. More...

std::unique_ptr< concepts::ShapeFunction1D< Real > >	shpfct_
	The shape functions, precomputed on quadrature points. More...

std::unique_ptr< concepts::ShapeFunction1D< Real > >	shpfctD_
	The derivatives of the shape functions. More...

concepts::Sequence< UnderlyingElement >	uelm_

concepts::Array< Real >	values_
	The actual storage of the values of the shape functions and their derivatives along the edge. More...

concepts::Array< Real >	valuesD_

concepts::Sequence< Real >	weights_
	Weight for each side. More...

Detailed Description

template<class F = Real>
class hp2D::NTElement_BA< 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, Robert Gruhlke 2012

Definition at line 39 of file neumannTrace.hh.

Member Typedef Documentation

◆ type

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

inherited

Definition at line 81 of file element.hh.

◆ UnderlyingElement

template<class F = Real>

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

Definition at line 42 of file neumannTrace.hh.

Member Enumeration Documentation

◆ intFormType

enum concepts::IntegrationCell::intFormType

inherited

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

Enumerator
ZERO
ONE
TWO
THREE

Definition at line 29 of file integral.hh.

Constructor & Destructor Documentation

◆ NTElement_BA()

template<class F = Real>

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

Constructor.

Creates the Neumann trace from the element on one side.

◆ ~NTElement_BA()

template<class F = Real>

virtual hp2D::NTElement_BA< F >::~NTElement_BA ( )

virtual

Member Function Documentation

◆ addElement()

template<class F = Real>

void hp2D::NTElement_BA< 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.

◆ appendT()

template<class F = Real>

void hp2D::NTElement_BA< F >::appendT ( concepts::TColumn< F > * T )

inline

Appends the T columns to the T matrix.

Definition at line 123 of file neumannTrace.hh.

◆ cell() [1/2]

template<class F = Real>

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

inlinevirtual

Definition at line 76 of file neumannTrace.hh.

◆ cell() [2/2]

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

pure virtualinherited

Returns the cell on which the element is built.

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

◆ chi()

const concepts::Real3d hp1D::IntegrableElm::chi ( const Real x ) const

inlineinherited

Computes the element map.

The reference element is [0,1].

Definition at line 40 of file element.hh.

◆ 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.

◆ info()

template<class F = Real>

virtual std::ostream& hp2D::NTElement_BA< F >::info ( std::ostream & os ) const

protectedvirtual

◆ integration()

const concepts::QuadratureRule1d* hp1D::IntegrableElm::integration ( ) const

inlineinherited

Returns the integration rule.

Definition at line 51 of file element.hh.

◆ jacobianDeterminant()

Real hp1D::IntegrableElm::jacobianDeterminant ( const Real x ) const

inlineinherited

Computes the determinant of the Jacobian.

Definition at line 45 of file element.hh.

◆ mapRho()

template<class F = Real>

const concepts::Z2 hp2D::NTElement_BA< F >::mapRho ( ) const

inline

Returns the orientation of the MappingEdge2d corresponding to the quad.

Analogue to understand like topological orientations. I.e. this method just makes sense after adding a quad TODO: For 2 Quads make sequence<concepts::Z2> datatype returns : 0 if mapping is counter-clockwise 1 if mapping is clock-wise

Definition at line 113 of file neumannTrace.hh.

◆ p()

template<class F = Real>

ushort hp2D::NTElement_BA< F >::p ( ) const

inline

Definition at line 127 of file neumannTrace.hh.

◆ quadraturePoint()

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

virtualinherited

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.

◆ recomputeShapefunctions()

template<class F = Real>

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

Recompute shape functions, e.g.

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

◆ rule()

static concepts::QuadRuleFactory& hp1D::IntegrableElm::rule ( )

inlinestaticinherited

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 62 of file element.hh.

◆ shpfct()

template<class F = Real>

const concepts::ShapeFunction1D<Real>* hp2D::NTElement_BA< F >::shpfct ( ) const

inline

Returns the shape functions.

Definition at line 86 of file neumannTrace.hh.

◆ shpfctD()

template<class F = Real>

const concepts::ShapeFunction1D<Real>* hp2D::NTElement_BA< F >::shpfctD ( ) const

inline

Returns the derivatives of the shape functions.

TODO: implementation.

Definition at line 92 of file neumannTrace.hh.

◆ support()

template<class F = Real>

virtual const concepts::Edge& hp2D::NTElement_BA< F >::support ( ) const

inlinevirtual

Definition at line 73 of file neumannTrace.hh.

◆ T() [1/2]

template<class F = Real>

virtual const concepts::TMatrix<F>& hp2D::NTElement_BA< F >::T ( ) const

inlinevirtual

Definition at line 78 of file neumannTrace.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 >.

◆ uelm()

template<class F = Real>

const concepts::Sequence<UnderlyingElement>& hp2D::NTElement_BA< F >::uelm ( ) const

inline

Returns the Underlying Element(s)

Definition at line 101 of file neumannTrace.hh.

◆ vertex()

template<class F = Real>

virtual concepts::Real3d hp2D::NTElement_BA< F >::vertex ( uint i ) const

virtual

Member Data Documentation

◆ cell_

template<class F = Real>

const concepts::Edge2d& hp2D::NTElement_BA< F >::cell_

private

The cell.

Definition at line 142 of file neumannTrace.hh.

◆ dim_

template<class F = Real>

concepts::Sequence<uint> hp2D::NTElement_BA< F >::dim_

private

Local number of shape functions coming from one side.

Definition at line 155 of file neumannTrace.hh.

◆ int_

std::unique_ptr<concepts::QuadratureRule1d> hp1D::IntegrableElm::int_

protectedinherited

The integration rule.

Definition at line 72 of file element.hh.

◆ mapRho_

template<class F = Real>

concepts::Z2 hp2D::NTElement_BA< F >::mapRho_

private

Definition at line 162 of file neumannTrace.hh.

◆ p_

template<class F = Real>

concepts::Sequence<uint> hp2D::NTElement_BA< F >::p_

private

Polynomial degree along the edge for each side.

Definition at line 157 of file neumannTrace.hh.

◆ rule_

concepts::QuadRuleFactory hp1D::IntegrableElm::rule_

staticprotectedinherited

Definition at line 74 of file element.hh.

◆ shpfct_

template<class F = Real>

std::unique_ptr<concepts::ShapeFunction1D<Real> > hp2D::NTElement_BA< F >::shpfct_

private

The shape functions, precomputed on quadrature points.

Definition at line 147 of file neumannTrace.hh.

◆ shpfctD_

template<class F = Real>

std::unique_ptr<concepts::ShapeFunction1D<Real> > hp2D::NTElement_BA< F >::shpfctD_

private

The derivatives of the shape functions.

Definition at line 149 of file neumannTrace.hh.

◆ T_

template<class F = Real>

concepts::TMatrix<Real> hp2D::NTElement_BA< F >::T_

protected

T matrix of the element.

Definition at line 139 of file neumannTrace.hh.

◆ uelm_

template<class F = Real>

concepts::Sequence<UnderlyingElement> hp2D::NTElement_BA< F >::uelm_

private

Definition at line 144 of file neumannTrace.hh.

◆ values_

template<class F = Real>

concepts::Array<Real> hp2D::NTElement_BA< F >::values_

private

The actual storage of the values of the shape functions and their derivatives along the edge.

Definition at line 153 of file neumannTrace.hh.

◆ valuesD_

template<class F = Real>

concepts::Array<Real> hp2D::NTElement_BA< F >::valuesD_

private

Definition at line 153 of file neumannTrace.hh.

◆ weights_

template<class F = Real>

concepts::Sequence<Real> hp2D::NTElement_BA< F >::weights_

private

Weight for each side.

Definition at line 159 of file neumannTrace.hh.

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

hp2D/neumannTrace.hh

hp2D::NTElement_BA< F > Class Template Referenceabstract

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Private Attributes

Detailed Description

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

Member Typedef Documentation

◆ type

◆ UnderlyingElement

Member Enumeration Documentation

◆ intFormType

Constructor & Destructor Documentation

◆ NTElement_BA()

◆ ~NTElement_BA()

Member Function Documentation

◆ addElement()

◆ appendT()

◆ cell() [1/2]

◆ cell() [2/2]

◆ chi()

◆ elemMap() [1/3]

◆ elemMap() [2/3]

◆ elemMap() [3/3]

◆ info()

◆ integration()

◆ jacobianDeterminant()

◆ mapRho()

◆ p()

◆ quadraturePoint()

◆ recomputeShapefunctions()

◆ rule()

◆ shpfct()

◆ shpfctD()

◆ support()

◆ T() [1/2]

◆ T() [2/2]

◆ uelm()

◆ vertex()

Member Data Documentation

◆ cell_

◆ dim_

◆ int_

◆ mapRho_

◆ p_

◆ rule_

◆ shpfct_

◆ shpfctD_

◆ T_

◆ uelm_

◆ values_

◆ valuesD_

◆ weights_

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