#include <neumannTraceElement.hh>

Inheritance diagram for hp2D::NeumannTraceElement< F >:

Classes
struct	mapPart

class	NTShapeFunction

Public Types
typedef concepts::ElementAndFacette< hp2D::Element< F > >	UnderlyingElement

typedef F	FieldT

typedef F	type

enum	intFormType { ZERO , ONE , TWO , THREE }

Public Member Functions
	NeumannTraceElement (const concepts::EdgeNd &cell, uint p, const mapPart *coarseCell=0)

virtual const concepts::TMatrix< F > &	T () const
	Returns the T matrix of the element.

void	computeShpfctVals (const concepts::Array< Real > &xP, concepts::Array< Real > &val) const

virtual void	recomputeShapefunctions ()

void	buildT ()

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

const concepts::Sequence< UnderlyingElement > &	uelm () const

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

void	addIrrElement (const hp2D::Quad< Real > &coarseQuad, uint k_coarse, Real weight)

virtual const concepts::Edge &	support () const

virtual concepts::Real3d	vertex (uint i) const

virtual const concepts::EdgeNd &	cell () const
	Returns the cell on which the element is built.

ushort	p () const

virtual const concepts::ElementGraphics< Real > *	graphics () const
	Returns element graphics class.

Real3d	elemMap (const Real coord_local) const

Real3d	elemMap (const Real2d &coord_local) const

Real3d	elemMap (const Real3d &coord_local) const

uint &	tag ()
	Returns the tag.

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

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

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

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

Static Public Member Functions
static concepts::QuadRuleFactory &	rule ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.

Protected Attributes
ushort	p_
	T matrix of the element.

const concepts::EdgeNd &	cell_
	The cell.

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

Static Protected Attributes
static std::unique_ptr< LineGraphics >	graphics_

static concepts::QuadRuleFactory	rule_

Detailed Description

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

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

Also a PLUS and MINUS setting is involded, that is a FIRST trace kind, with respect to the K+ and K- introduced elements via the setted Normalvector.

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

Author: Robert Gruhlke 2013, 2016

Definition at line 42 of file neumannTraceElement.hh.

Member Typedef Documentation

◆ FieldT

template<class F >

typedef F hp1D::BaseElement< F >::FieldT

inherited

Definition at line 82 of file element.hh.

◆ type

template<typename F >

typedef F concepts::ElementWithCell< F >::type

inherited

Definition at line 81 of file element.hh.

◆ UnderlyingElement

template<class F = Real>

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

Definition at line 44 of file neumannTraceElement.hh.

Member Enumeration Documentation

◆ intFormType

enum concepts::IntegrationCell::intFormType

inherited

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

Definition at line 29 of file integral.hh.

Constructor & Destructor Documentation

◆ NeumannTraceElement()

template<class F = Real>

hp2D::NeumannTraceElement< F >::NeumannTraceElement	(	const concepts::EdgeNd &	cell,
		uint	p,
		const mapPart *	coarseCell = `0`
	)

Constructor

For irregular meshes the underlying elements of a neumanntraceelement is a fine Quad and a neighboured coarse Quad. The coarseCell describes the edgemapping of the coarseedge of which the cell is a subset (part). The coarseCellpart also marks if a neumanntraceElement is build upon regular or irregular mesh

Parameters

cell	geometric cell of this element
p	highest Polynomial degree of underlying Elements
coarseCell	for irregular meshes where cell's underlying

Member Function Documentation

◆ addElement()

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. Basis functions between quads do not have to be continous. In this case the highest polynomial degree along edge is set, i.e. for integration rule

Parameters

quad	Quad with k-th edge is NeumannTraceElement's topological cell.

◆ addIrrElement()

template<class F = Real>

void hp2D::NeumannTraceElement< F >::addIrrElement	(	const hp2D::Quad< Real > &	coarseQuad,
		uint	k_coarse,
		Real	weight
	)

Basically the same as addElement, but with the difference in the meaning. In this case the general ancestor edge of this finer Edge is the k-th edge of the coarseQuad.

Parameters

coarseQuad Quad with k-th edge is general ancestor of NeumannTraceElement's topological cell.

◆ buildT()

template<class F = Real>

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

After adding the Elements this routine builds the TMatrix and polynomial informations on the element.

◆ cell()

template<class F >

virtual const concepts::EdgeNd & hp1D::BaseElement< F >::cell ( ) const

inlinevirtualinherited

Returns the cell on which the element is built.

Implements concepts::ElementWithCell< F >.

Definition at line 99 of file element.hh.

◆ 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.

◆ computeShpfctVals()

template<class F = Real>

void hp2D::NeumannTraceElement< F >::computeShpfctVals	(	const concepts::Array< Real > &	xP,
		concepts::Array< Real > &	val
	)		const

Evaluation method to get basisfunctions evaluated on requested points this should be used for functions, i.e. hp2D::Value

Parameters

xP	requested Points to evaluate on
val	evaluated shpfct, method resizes array.

◆ elemMap() [1/3]

template<typename F >

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

inlineinherited

Definition at line 86 of file element.hh.

◆ elemMap() [2/3]

template<typename F >

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

inlineinherited

Definition at line 90 of file element.hh.

◆ elemMap() [3/3]

template<typename F >

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

inlineinherited

Definition at line 94 of file element.hh.

◆ graphics()

template<class F >

virtual const concepts::ElementGraphics< Real > * hp1D::BaseElement< F >::graphics ( ) const

virtualinherited

Returns element graphics class.

Reimplemented from concepts::Element< F >.

◆ info()

template<class F = Real>

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

protectedvirtual

Returns information in an output stream.

Reimplemented from hp1D::BaseElement< F >.

◆ 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.

◆ p()

template<class F >

ushort hp1D::BaseElement< F >::p ( ) const

inlineinherited

Definition at line 103 of file element.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>

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

virtual

Recompute shape functions, e.g. for other abscissas redefined through IntegrableElm::rule().set(...)

Implements hp1D::BaseElement< F >.

◆ 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>

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

virtual

Returns the shape functions.

Implements hp1D::BaseElement< F >.

◆ support()

template<class F >

virtual const concepts::Edge & hp1D::BaseElement< F >::support ( ) const

inlinevirtualinherited

Definition at line 91 of file element.hh.

◆ T()

template<class F = Real>

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

inlinevirtual

Returns the T matrix of the element.

Implements concepts::ElementWithCell< F >.

Definition at line 121 of file neumannTraceElement.hh.

◆ tag()

template<class F >

uint & concepts::Element< F >::tag ( )

inlineinherited

Returns the tag.

Definition at line 66 of file element.hh.

◆ uelm()

template<class F = Real>

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

inline

Returns the Underlying Element(s)

Definition at line 151 of file neumannTraceElement.hh.

◆ vertex()

template<class F >

virtual concepts::Real3d hp1D::BaseElement< F >::vertex ( uint i ) const

inlinevirtualinherited

Definition at line 95 of file element.hh.

Member Data Documentation

◆ cell_

const concepts::EdgeNd& hp1D::IntegrableElm::cell_

protectedinherited

The cell.

Definition at line 70 of file element.hh.

◆ graphics_

template<class F >

std::unique_ptr<LineGraphics> hp1D::BaseElement< F >::graphics_

staticprotectedinherited

Definition at line 126 of file element.hh.

◆ int_

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

protectedinherited

The integration rule.

Definition at line 72 of file element.hh.

◆ p_

template<class F >

ushort hp1D::BaseElement< F >::p_

protectedinherited

T matrix of the element.

Definition at line 124 of file element.hh.

◆ rule_

concepts::QuadRuleFactory hp1D::IntegrableElm::rule_

staticprotectedinherited

Definition at line 74 of file element.hh.

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

hp2D/neumannTraceElement.hh

Class documentation of Concepts

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Member Typedef Documentation

◆ FieldT

◆ type

◆ UnderlyingElement

Member Enumeration Documentation

◆ intFormType

Constructor & Destructor Documentation

◆ NeumannTraceElement()

Member Function Documentation

◆ addElement()

◆ addIrrElement()

◆ buildT()

◆ cell()

◆ chi()

◆ computeShpfctVals()

◆ elemMap() [1/3]

◆ elemMap() [2/3]

◆ elemMap() [3/3]

◆ graphics()

◆ info()

◆ integration()

◆ jacobianDeterminant()

◆ p()

◆ quadraturePoint()

◆ recomputeShapefunctions()

◆ rule()

◆ shpfct()

◆ support()

◆ T()

◆ tag()

◆ uelm()

◆ vertex()

Member Data Documentation

◆ cell_

◆ graphics_

◆ int_

◆ p_

◆ rule_