A the NeumannTrace space of a given 2D - Finite Element space. More...

#include <neumannTraceSpace.hh>

Inheritance diagram for hp2D::NeumannTraceSpace:

Public Types
typedef concepts::Scan< hp1D::BaseElement< Real > >	Scan

typedef Scan< ElementWithCell< Real > >	Scanner

typedef ElementWithCell< Real >	type

typedef concepts::ElementAndFacette< concepts::Edge >	UnderlyingEdge

typedef concepts::ElementAndFacette< hp2D::Element< Real > >	UnderlyingElement

Public Member Functions
virtual uint	dim () const
	Returns the dimension of the underlying Finite Element Space. More...

virtual uint	dim () const=0
	Returns the dimension of the space. More...

virtual uint	getOutputDimension () const
	Returns the default output dimension, when we consider plotting a real-valued operator on this space. More...

virtual uint	nelm () const
	Returns the number of NeumannTraceElements in the Space. More...

virtual uint	nelm () const=0
	Returns the number of elements in the space. More...

	NeumannTraceSpace (concepts::SpaceOnCells< Real > &spc, const concepts::EdgeTraceTypes &ettypes, bool emptyElm=true)
	Constructor. More...

	NeumannTraceSpace (const concepts::SpaceOnCells< Real > &spc, const concepts::Set< uint > edgeAttr, enum concepts::EdgeTraceType::traceTypes type=concepts::EdgeTraceType::FIRST, const concepts::EdgeNormalVectorRule &normalVectorRule=concepts::EdgeNormalVectorRule(), bool emptyElm=true)
	Constructor. More...

	NeumannTraceSpace (const GridInfo< Real > &gInfo, uint sDim, enum concepts::EdgeTraceType::traceTypes type=concepts::EdgeTraceType::FIRST, const concepts::EdgeNormalVectorRule &normalVectorRule=concepts::EdgeNormalVectorRule(), bool emptyElm=true)
	Constructor. More...

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

virtual Scan *	scan () const
	Returns a scanner to iterate over the elements of the space. More...

virtual Scanner *	scan () const=0
	Returns a scanner to iterate over the elements of the space. More...

const concepts::Sequence< UnderlyingElement >	uelm (const concepts::Edge edge) const
	Returns the underlying 2D elements of the given edge if existing. More...

virtual	~NeumannTraceSpace ()
	Deconstructor. More...

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

Private Member Functions
void	build_irregular_ (const hp2D::GridInfo< Real > &gInfo)

void	build_regular_ (const hp2D::GridInfo< Real > &gInfo)

Real	weight_ (bool first, const Z2 dir, const uint nUelm, const concepts::Attribute attrb) const
	Consider the outwards pointing normalvector evaluations of a neumantrace basis function u. More...

Private Attributes
concepts::Sequence< concepts::Edge2d * >	coarseCells_
	Collection of coarse edges, i.e. More...

const uint	dim_
	Dimension of the FE space. More...

concepts::HashMap< hp2D::NeumannTraceElement< Real > * >	edges_
	Map from key of (topological) edge to the element. More...

concepts::Joiner< hp1D::BaseElement< Real > , 1 >	elm_
	Linked list of the elements. More...

bool	emptyElements_

GridInfo< Real >::CoarseToSuccessor	mapCtS_
	Map from coarse cells by key to its successors that are in space. More...

uint	nelm_
	Number of elements currently active in the mesh. More...

uint	nIrrelm_

concepts::EdgeTraceTypes	trTypes_
	Mapping from Attributes to a given EdgeTracetype. More...

Detailed Description

A the NeumannTrace space of a given 2D - Finite Element space.

The elements are from type hp2D::Edge. One can restrict the trace operation by EdgeTraceTypes or via Attributes and a EdgeNormalVectorRule. If the FE space is rebuild, one has to construct the NeumannTraceSpace again. Additonally a map from the topological edge to the set of the underlying elements is stored.

Space can be builded on irregular spaces, i.e. with k-irregular mesh with hanging nodes.

Caution: Coarse irregular elements are currently not space members, that must be taken into account when using the space in ElementFormulaVector, Linearforms, Bilinearforms or integration

Author: Gruhlke, Robert, 2013, 2016

Definition at line 51 of file neumannTraceSpace.hh.

Member Typedef Documentation

◆ Scan

typedef concepts::Scan<hp1D::BaseElement<Real> > hp2D::NeumannTraceSpace::Scan

Definition at line 53 of file neumannTraceSpace.hh.

◆ Scanner

typedef Scan<ElementWithCell<Real > > concepts::SpaceOnCells< Real >::Scanner

inherited

Definition at line 84 of file space.hh.

◆ type

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

inherited

Definition at line 83 of file space.hh.

◆ UnderlyingEdge

typedef concepts::ElementAndFacette<concepts::Edge> hp2D::NeumannTraceSpace::UnderlyingEdge

Definition at line 55 of file neumannTraceSpace.hh.

◆ UnderlyingElement

typedef concepts::ElementAndFacette<hp2D::Element<Real> > hp2D::NeumannTraceSpace::UnderlyingElement

Definition at line 54 of file neumannTraceSpace.hh.

Constructor & Destructor Documentation

◆ NeumannTraceSpace() [1/3]

hp2D::NeumannTraceSpace::NeumannTraceSpace	(	const concepts::SpaceOnCells< Real > &	spc,
		const concepts::Set< uint >	edgeAttr,
		enum concepts::EdgeTraceType::traceTypes	type = `concepts::EdgeTraceType::FIRST`,
		const concepts::EdgeNormalVectorRule &	normalVectorRule = `concepts::EdgeNormalVectorRule()`,
		bool	emptyElm = `true`
	)

Constructor.

This builds a NeumannTraceSpace only for edges with attributes that are requested.

The EdgeTraceType can be FIRST, MEAN, JUMP or PLUS and MINUS. Since the EdgeNormalVectorRule in a sense is constant for all requested edges, you have to think about the Meaning of these Traces then, since they are also defined with the help of the first underlying Element. Alternativly one uses the second Constructor.

This Constructor may easy applicate for Boundary Elements with a FIRST neumanntrace, since these elements only have up to one underlying Element.

Additional a Flag for empty Elements is given, that controls the build up of Elements with no degrees of freedoms on it. This might be used for graphical Output.

Parameters

spc	underlying Finite Element Space
edgeAttr	set of requested edge attributes
traceTypes	the type of NeumannTrace, i.e. FIRST,MEAN,JUMP,PLUS,MINUS
normalVectorRule	Given rule for the Normalvector behaviour
emptyElm	Flag to control build of empty Elements

◆ NeumannTraceSpace() [2/3]

hp2D::NeumannTraceSpace::NeumannTraceSpace	(	const GridInfo< Real > &	gInfo,
		uint	sDim,
		enum concepts::EdgeTraceType::traceTypes	type = `concepts::EdgeTraceType::FIRST`,
		const concepts::EdgeNormalVectorRule &	normalVectorRule = `concepts::EdgeNormalVectorRule()`,
		bool	emptyElm = `true`
	)

Constructor.

Parameters

gInfo	External build grid Info, contains attribute data
sDim	space dimension of space on which `gInfo` is built
traceTypes	the type of NeumannTrace, i.e. FIRST,MEAN,JUMP,PLUS,MINUS
normalVectorRule	Given rule for the Normalvector behaviour

◆ NeumannTraceSpace() [3/3]

hp2D::NeumannTraceSpace::NeumannTraceSpace	(	concepts::SpaceOnCells< Real > &	spc,
		const concepts::EdgeTraceTypes &	ettypes,
		bool	emptyElm = `true`
	)

Constructor.

This builds a NeumannTraceSpace for edges that are requested in the EdgeTraceTypes semantic.

The EdgeTraceType can be FIRST, MEAN, JUMP or PLUS and MINUS for different edges with different attributes. In opposite to the first constructor the EdgeNormalVectorRule is not constant, since they can vary for each Attribute. This is controlled with the EdgeTraceTypes variable.

This constructor may is the choice when building a NeumannTraceSpace on a Finite Element Space with different material attributes.

Additional a Flag for empty Elements is given, that controls the build up of Elements with no degrees of freedoms on it. This might be used for graphical Output.

Parameters

spc	underlying Finite Element Space
edgeAttr	set of requested edge attributes
traceTypes	the type of NeumannTrace, i.e. FIRST,MEAN,JUMP,PLUS,MINUS
normalVectorRule	Given rule for the Normalvector behaviour
emptyElm	Flag to control build of empty Elements

◆ ~NeumannTraceSpace()

virtual hp2D::NeumannTraceSpace::~NeumannTraceSpace ( )

virtual

Deconstructor.

Member Function Documentation

◆ build_irregular_()

void hp2D::NeumannTraceSpace::build_irregular_ ( const hp2D::GridInfo< Real > & gInfo )

private

◆ build_regular_()

void hp2D::NeumannTraceSpace::build_regular_ ( const hp2D::GridInfo< Real > & gInfo )

private

◆ dim() [1/2]

virtual uint hp2D::NeumannTraceSpace::dim ( ) const

inlinevirtual

Returns the dimension of the underlying Finite Element Space.

Definition at line 129 of file neumannTraceSpace.hh.

◆ dim() [2/2]

virtual uint concepts::SpaceOnCells< Real >::dim ( ) const

pure virtualinherited

Returns the dimension of the space.

Implements concepts::Space< Real >.

Implemented in hp2D::hpAdaptiveSpace< Real >, hp3D::Space, hp2Dedge::Space, hp2D::Space, hp2D::hpAdaptiveSpace< Real >, and hp1D::Space.

◆ getOutputDimension()

virtual uint concepts::Space< Real >::getOutputDimension ( ) const

inlinevirtualinherited

Returns the default output dimension, when we consider plotting a real-valued operator on this space.

Definition at line 50 of file space.hh.

◆ info()

virtual std::ostream& hp2D::NeumannTraceSpace::info ( std::ostream & os ) const

protectedvirtual

Reimplemented from concepts::SpaceOnCells< Real >.

◆ nelm() [1/2]

virtual uint hp2D::NeumannTraceSpace::nelm ( ) const

inlinevirtual

Returns the number of NeumannTraceElements in the Space.

Definition at line 136 of file neumannTraceSpace.hh.

◆ nelm() [2/2]

virtual uint concepts::SpaceOnCells< Real >::nelm ( ) const

pure virtualinherited

Returns the number of elements in the space.

Implements concepts::Space< Real >.

Implemented in hp2D::hpAdaptiveSpace< Real >, hp3D::Space, hp2Dedge::Space, hp2D::Space, hp2D::hpAdaptiveSpace< Real >, and hp1D::Space.

◆ recomputeShapefunctions()

virtual void hp2D::NeumannTraceSpace::recomputeShapefunctions ( )

virtual

Recompute shape functions, e.g.

for other abscissas redefined through setIntegrationRule

◆ scan() [1/2]

virtual Scan* hp2D::NeumannTraceSpace::scan ( ) const

inlinevirtual

Returns a scanner to iterate over the elements of the space.

Definition at line 143 of file neumannTraceSpace.hh.

◆ scan() [2/2]

virtual Scanner* concepts::SpaceOnCells< Real >::scan ( ) const

pure virtualinherited

Returns a scanner to iterate over the elements of the space.

Implements concepts::Space< Real >.

Implemented in hp2D::hpAdaptiveSpace< Real >, hp3D::Space, hp2Dedge::Space, hp2D::Space, hp2D::hpAdaptiveSpace< Real >, and hp1D::Space.

◆ uelm()

const concepts::Sequence<UnderlyingElement> hp2D::NeumannTraceSpace::uelm ( const concepts::Edge edge ) const

inline

Returns the underlying 2D elements of the given edge if existing.

Definition at line 150 of file neumannTraceSpace.hh.

◆ weight_()

Real hp2D::NeumannTraceSpace::weight_	(	bool	first,
		const Z2	dir,
		const uint	nUelm,
		const concepts::Attribute	attrb
	)		const

private

Consider the outwards pointing normalvector evaluations of a neumantrace basis function u.

The defintion of the normalvector n above, introduce K+ and K- and therefore normal traces: n * grad(u+) and n * grad(u-)

Parameters

pos	0 if first underlying element, 1 if second
dir	0 if underlying element is K-, 1 if K+
nUelm

Precondition: nUelm is either 1 or 2. number of underlying elements

Parameters

attrb Attribute of the current cell, to access EdgeTraceType information.

Member Data Documentation

◆ coarseCells_

concepts::Sequence<concepts::Edge2d*> hp2D::NeumannTraceSpace::coarseCells_

private

Collection of coarse edges, i.e.

having successors that are element edges in the space

Definition at line 193 of file neumannTraceSpace.hh.

◆ dim_

const uint hp2D::NeumannTraceSpace::dim_

private

Dimension of the FE space.

Definition at line 168 of file neumannTraceSpace.hh.

◆ edges_

concepts::HashMap<hp2D::NeumannTraceElement<Real>*> hp2D::NeumannTraceSpace::edges_

private

Map from key of (topological) edge to the element.

Definition at line 201 of file neumannTraceSpace.hh.

◆ elm_

concepts::Joiner<hp1D::BaseElement<Real>*, 1>* hp2D::NeumannTraceSpace::elm_

private

Linked list of the elements.

Definition at line 174 of file neumannTraceSpace.hh.

◆ emptyElements_

bool hp2D::NeumannTraceSpace::emptyElements_

private

Definition at line 180 of file neumannTraceSpace.hh.

◆ mapCtS_

GridInfo<Real>::CoarseToSuccessor hp2D::NeumannTraceSpace::mapCtS_

private

Map from coarse cells by key to its successors that are in space.

Definition at line 198 of file neumannTraceSpace.hh.

◆ nelm_

uint hp2D::NeumannTraceSpace::nelm_

private

Number of elements currently active in the mesh.

Definition at line 171 of file neumannTraceSpace.hh.

◆ nIrrelm_

uint hp2D::NeumannTraceSpace::nIrrelm_

private

Definition at line 177 of file neumannTraceSpace.hh.

◆ trTypes_

concepts::EdgeTraceTypes hp2D::NeumannTraceSpace::trTypes_

private

Mapping from Attributes to a given EdgeTracetype.

This controlls the NeumannTraces indeed.

Definition at line 187 of file neumannTraceSpace.hh.

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

hp2D/neumannTraceSpace.hh

hp2D::NeumannTraceSpace Class Referenceabstract

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ Scan

◆ Scanner

◆ type

◆ UnderlyingEdge

◆ UnderlyingElement

Constructor & Destructor Documentation

◆ NeumannTraceSpace() [1/3]

◆ NeumannTraceSpace() [2/3]

◆ NeumannTraceSpace() [3/3]

◆ ~NeumannTraceSpace()

Member Function Documentation

◆ build_irregular_()

◆ build_regular_()

◆ dim() [1/2]

◆ dim() [2/2]

◆ getOutputDimension()

◆ info()

◆ nelm() [1/2]

◆ nelm() [2/2]

◆ recomputeShapefunctions()

◆ scan() [1/2]

◆ scan() [2/2]

◆ uelm()

◆ weight_()

Member Data Documentation

◆ coarseCells_

◆ dim_

◆ edges_

◆ elm_

◆ emptyElements_

◆ mapCtS_

◆ nelm_

◆ nIrrelm_

◆ trTypes_