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

#include <neumannTraceElement.hh>

Inheritance diagram for hp2D::NeumannTraceElement< F >:

Classes
struct	mapPart

class	NTShapeFunction

Public Types
typedef Real	FieldT

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	addIrrElement (const hp2D::Quad< Real > &coarseQuad, uint k_coarse, Real weight)
	Basically the same as addElement, but with the difference in the meaning. More...

void	buildT ()
	After adding the Elements this routine builds the TMatrix and polynomial informations on the element. More...

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

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

void	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. 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
	Returns element graphics class. More...

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

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

	NeumannTraceElement (const concepts::EdgeNd &cell, uint p, const mapPart *coarseCell=0)
	Constructor. More...

ushort	p () const

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

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

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

virtual const concepts::ShapeFunction1D< Real > *	shpfct () const=0
	Returns 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	~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). More...

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

Protected Attributes
const concepts::EdgeNd &	cell_
	The cell. More...

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

ushort	p_
	T matrix of the element. More...

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

static concepts::QuadRuleFactory	rule_

Private Member Functions
void	compute_ (const concepts::Array< Real > &q, concepts::Array< Real > &val) const
	Routine calculating the normal derivative of the basis functions (of underlying quads), with normalvector pointing outwards the respective underlying Quad on a given Set of Points. More...

void	irregularCompute_ (const concepts::Array< Real > &q, concepts::Array< Real > &val) const
	Routine calculating the normal derivative of the basis functions (of underlying quads), with normalvector pointing outwards the respective underlying Quad on a given Set of Points. More...

Private Attributes
mapPart	coarseCell_

bool	irregular_

std::unique_ptr< concepts::ShapeFunction1D< Real > >	shpfct_

concepts::TMatrix< Real >	T_

concepts::Sequence< UnderlyingElement >	uelm_

concepts::Array< Real >	values_
	The actual storage of the values of the shape functions along the edge on integration points. More...

concepts::Sequence< Real >	weights_
	Weight for each side. This defines the TraceType on the Element. More...

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

typedef Real hp1D::BaseElement< Real >::FieldT

inherited

Definition at line 82 of file element.hh.

◆ 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::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.

Enumerator
ZERO
ONE
TWO
THREE

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

◆ ~NeumannTraceElement()

template<class F = Real>

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

virtual

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()

virtual const concepts::EdgeNd& hp1D::BaseElement< Real >::cell

inlinevirtualinherited

Returns the cell on which the element is built.

Implements concepts::ElementWithCell< Real >.

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.

◆ compute_()

template<class F = Real>

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

private

Routine calculating the normal derivative of the basis functions (of underlying quads), with normalvector pointing outwards the respective underlying Quad on a given Set of Points.

Parameters

q	evaluation domain points
val	of evaluations of shapefunctions on q values

◆ 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]

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>* hp1D::BaseElement< Real >::graphics

virtualinherited

Returns element graphics class.

◆ info()

template<class F = Real>

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

protectedvirtual

Reimplemented from hp1D::BaseElement< Real >.

◆ integration()

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

inlineinherited

Returns the integration rule.

Definition at line 51 of file element.hh.

◆ irregularCompute_()

template<class F = Real>

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

private

Routine calculating the normal derivative of the basis functions (of underlying quads), with normalvector pointing outwards the respective underlying Quad on a given Set of Points.

This is for irregular underlying elements

Parameters

q	evaluation domain points
val	of evaluations of shapefunctions on q values

◆ 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()

ushort hp1D::BaseElement< Real >::p

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< Real >.

◆ 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() [1/2]

template<class F = Real>

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

virtual

Returns the shape functions.

◆ shpfct() [2/2]

virtual const concepts::ShapeFunction1D<Real>* hp1D::BaseElement< Real >::shpfct

pure virtualinherited

Returns the shape functions.

◆ support()

virtual const concepts::Edge& hp1D::BaseElement< Real >::support

inlinevirtualinherited

Definition at line 91 of file element.hh.

◆ T() [1/2]

template<class F = Real>

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

inlinevirtual

Definition at line 121 of file neumannTraceElement.hh.

◆ T() [2/2]

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

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::NeumannTraceElement< F >::uelm ( ) const

inline

Returns the Underlying Element(s)

Definition at line 151 of file neumannTraceElement.hh.

◆ vertex()

virtual concepts::Real3d hp1D::BaseElement< Real >::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.

◆ coarseCell_

template<class F = Real>

mapPart hp2D::NeumannTraceElement< F >::coarseCell_

private

Definition at line 190 of file neumannTraceElement.hh.

◆ graphics_

std::unique_ptr<LineGraphics> hp1D::BaseElement< Real >::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.

◆ irregular_

template<class F = Real>

bool hp2D::NeumannTraceElement< F >::irregular_

private

Definition at line 188 of file neumannTraceElement.hh.

◆ p_

ushort hp1D::BaseElement< Real >::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.

◆ shpfct_

template<class F = Real>

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

mutableprivate

Definition at line 179 of file neumannTraceElement.hh.

◆ T_

template<class F = Real>

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

private

Definition at line 182 of file neumannTraceElement.hh.

◆ uelm_

template<class F = Real>

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

private

Definition at line 192 of file neumannTraceElement.hh.

◆ values_

template<class F = Real>

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

mutableprivate

The actual storage of the values of the shape functions along the edge on integration points.

The values corresponding to the local shapefunctions of its underlying quad(s) are computed with the normalvector pointing outwards the quad respectivly.

This have to be noticed for defining the weights for trace types. mutable to work with const compute_ as needed for const

Definition at line 201 of file neumannTraceElement.hh.

◆ weights_

template<class F = Real>

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

private

Weight for each side. This defines the TraceType on the Element.

Definition at line 204 of file neumannTraceElement.hh.

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

hp2D/neumannTraceElement.hh

hp2D::NeumannTraceElement< F > Class Template Referenceabstract

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

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

Member Typedef Documentation

◆ FieldT

◆ type

◆ UnderlyingElement

Member Enumeration Documentation

◆ intFormType

Constructor & Destructor Documentation

◆ NeumannTraceElement()

◆ ~NeumannTraceElement()

Member Function Documentation

◆ addElement()

◆ addIrrElement()

◆ buildT()

◆ cell()

◆ chi()

◆ compute_()

◆ computeShpfctVals()

◆ elemMap() [1/3]

◆ elemMap() [2/3]

◆ elemMap() [3/3]

◆ graphics()

◆ info()

◆ integration()

◆ irregularCompute_()

◆ jacobianDeterminant()

◆ p()

◆ quadraturePoint()

◆ recomputeShapefunctions()

◆ rule()

◆ shpfct() [1/2]

◆ shpfct() [2/2]

◆ support()

◆ T() [1/2]

◆ T() [2/2]

◆ uelm()

◆ vertex()

Member Data Documentation

◆ cell_

◆ coarseCell_

◆ graphics_

◆ int_

◆ irregular_

◆ p_

◆ rule_

◆ shpfct_

◆ T_

◆ uelm_

◆ values_

◆ weights_

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