DOFLocalPattern - A class to store the "couplings" between the basis functions. More...

#include <DOFLocalPattern.hpp>

Inheritance diagram for DOFLocalPattern:

Collaboration diagram for DOFLocalPattern:

Private Attributes
UInt	M_dim
	dimension of the element (3 for a tetrahedra for example). More...

UInt	M_nbLocalDof
	Total number of degrees of freedom (equal to refEle::nbDof) More...

std::vector< UInt >	M_nbDofPerDimEntity
	Number of degrees of freedom per geometric entity. More...

DofPatternType	M_patternType
	Type of the pattern stored. More...

std::vector< std::pair< UInt, UInt > >	M_pattern
	Pairs of couplings to appear in the pattern. More...

UInt	M_nbPattern
	Number of non-zero terms in the element matrix. More...

UInt	M_nbDiag
	Number of diagonal terms in the element matrix. More...

UInt	M_nbUpper
	Number of upper terms in the element matrix. More...

Constructor & Destructor
	DOFLocalPattern (const UInt &nbLocalDof, const UInt &nbDofPerVertex, const UInt &nbDofPerEdge, const UInt &nbDofPerFace, const UInt &nbDofPerVolume, const DofPatternType &patternType, UInt nbLocalCoor)
	Full constructor. More...

	DOFLocalPattern (const DOFLocalPattern &localDofPattern)
	Simple copy constructor. More...

virtual	~DOFLocalPattern ()
	Empty destructor. More...

Methods
const UInt &	patternFirst (const UInt &i) const
	patternFirst(i): row index in the element matrix of the i-th term of the pattern (the index starts from 0, not from 1 !). More...

const UInt &	patternSecond (const UInt &i) const
	patternSecond(i): column index in the element matrix of the i-th term of the pattern (the index starts from 0, not from 1 !). More...

void	showMe (std::ostream &output=std::cout) const
	The showMe method for the pattern. More...

Get Methods
const UInt &	nbPattern () const
	Number of non-zero terms in the element matrix. More...

const UInt &	nbDiag () const
	Number of diagonal terms in the element matrix. More...

const UInt &	nbUpper () const
	Number of upper terms in the element matrix. More...

const UInt &	nbLocalDof () const
	Return the number of local degrees of freedom. More...

const UInt &	nbDofPerVertex () const
	Return the number of degrees of freedom located on the vertices (0D structures) More...

const UInt &	nbDofPerEdge () const
	Return the number of degrees of freedom located on the edges (1D structures) More...

UInt	nbDofPerPeak () const
	Return the number of degrees of freedom located on the peak (vertex in 3D). More...

UInt	nbDofPerRidge () const
	Return the number of degrees of freedom located on the ridge. (edge in 3D) More...

UInt	nbDofPerFacet () const
	Return the number of degrees of freedom located on the facet. (face in 3D) More...

const UInt &	nbDofPerElement () const
	Return the number of degrees of freedom located on the element. (volume in 3D) More...

const UInt &	nbDofPerFace () const
	Return the number of degrees of freedom located on the faces (2D structures). More...

const UInt &	nbDofPerVolume () const
	Return the number of degrees of freedom located in the volume (3D structures). More...

const UInt &	nbDofPerDimStrut (const UInt &structDim) const
	Return the number of degrees of freedom located per structDim object. More...

const UInt &	nbDofPerCodimStrut (const UInt &structCodim) const
	Return the number of degrees of freedom located per structCodim object. More...

Private Methods
	DOFLocalPattern ()
	Default constructor disabled (because there is no setup/set method) More...

void	setupStandardPattern ()
	Method to setup the standard pattern, i.e. with all degrees of freedom coupled. More...

void	setupP1isoP2SegPattern ()
	Method for the P1isoP2 pattern for the segments (1D) More...

void	setupP1isoP2TriaPattern ()
	Method for the P1isoP2 pattern for the triangles (2D) More...

Detailed Description

DOFLocalPattern - A class to store the "couplings" between the basis functions.

The aim of this class is to store the way the basis functions couple one with each other. This might seem useless, however, some "advanced" finite elements require this structure.

For example, consider the P1-iso-P2 element in 2D. This finite element is composed of 6 basis functions, based on the nodes with the same numbering as the P2 element. The reference triangle is split into 4 subtriangles using the nodes on the faces. Each basis function is build such that it is 1 on its node, 0 on all the other nodes and such that it is linear in each subtriangle.

See also: in "Numerical Approximation of Partial Differential Equations" by A. Quarteroni and A. Valli, p.311, for an illustration and further informations.

With this definition of the P1-iso-P2 finite element, we see that the basis functions 1 and 2 have no common support. So, they are not directly coupled.

In order to represent the couplings between the basis functions, we can use a matrix $ C $ such that $C_{ij} = 1$ if the basis functions $ i $ and $ j $ have a common support, otherwise it is $ 0 $ . This matrix is symmetric.

For the P1-iso-P2 element, this matrix would be:

$\begin{array}{|c||cccccc|} \hline & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \hline 1 & 1 & 0 & 0 & 1 & 0 & 1 \\ 2 & 0 & 1 & 0 & 1 & 1 & 0 \\ 3 & 0 & 0 & 1 & 0 & 1 & 1 \\ 4 & 1 & 1 & 0 & 1 & 1 & 1 \\ 5 & 0 & 1 & 1 & 1 & 1 & 1 \\ 6 & 1 & 0 & 1 & 1 & 1 & 1 \\ \hline \end{array}$

When references to diagonal or upper part are made, it is with respect to this matrix. For most of the finite elements, this matrix is full (lagrangian FE, lagrangian FE with bubbles,...).

Instead of this representation with a matrix, we usually prefer to get the DoFs that are coupled in a list. This is the implemented in this class and the list of pairs (patternFirst(i),patternSecond(i)) represents all the DoFs that are coupled.

Note: The documentation of this class (and some improvements) has been done by Samuel Quinodoz (15.01.2010), but its original implementation was prior the documentation and no name of author or date was available.

Definition at line 106 of file DOFLocalPattern.hpp.

Constructor & Destructor Documentation

◆ DOFLocalPattern() [1/3]

DOFLocalPattern	(	const UInt &	nbLocalDof,
		const UInt &	nbDofPerVertex,
		const UInt &	nbDofPerEdge,
		const UInt &	nbDofPerFace,
		const UInt &	nbDofPerVolume,
		const DofPatternType &	patternType,
		UInt	nbLocalCoor
	)

Full constructor.

Definition at line 45 of file DOFLocalPattern.cpp.

Here is the caller graph for this function:

◆ DOFLocalPattern() [2/3]

DOFLocalPattern ( const DOFLocalPattern & localDofPattern )

Simple copy constructor.

Definition at line 78 of file DOFLocalPattern.cpp.

Here is the caller graph for this function:

◆ ~DOFLocalPattern()

virtual ~DOFLocalPattern ( )

inlinevirtual

Empty destructor.

Definition at line 122 of file DOFLocalPattern.hpp.

◆ DOFLocalPattern() [3/3]

DOFLocalPattern ( )

private

Default constructor disabled (because there is no setup/set method)

Member Function Documentation

◆ patternFirst()

const UInt& patternFirst ( const UInt & i ) const

inline

patternFirst(i): row index in the element matrix of the i-th term of the pattern (the index starts from 0, not from 1 !).

Definition at line 132 of file DOFLocalPattern.hpp.

◆ patternSecond()

const UInt& patternSecond ( const UInt & i ) const

inline

patternSecond(i): column index in the element matrix of the i-th term of the pattern (the index starts from 0, not from 1 !).

Definition at line 139 of file DOFLocalPattern.hpp.

◆ showMe()

void showMe ( std::ostream & output = std::cout ) const

The showMe method for the pattern.

Definition at line 93 of file DOFLocalPattern.cpp.

◆ nbPattern()

const UInt& nbPattern ( ) const

inline

Number of non-zero terms in the element matrix.

Definition at line 155 of file DOFLocalPattern.hpp.

◆ nbDiag()

const UInt& nbDiag ( ) const

inline

Number of diagonal terms in the element matrix.

Definition at line 161 of file DOFLocalPattern.hpp.

◆ nbUpper()

const UInt& nbUpper ( ) const

inline

Number of upper terms in the element matrix.

Definition at line 167 of file DOFLocalPattern.hpp.

◆ nbLocalDof()

const UInt& nbLocalDof ( ) const

inline

Return the number of local degrees of freedom.

Definition at line 173 of file DOFLocalPattern.hpp.

Here is the caller graph for this function:

◆ nbDofPerVertex()

const UInt& nbDofPerVertex ( ) const

inline

Return the number of degrees of freedom located on the vertices (0D structures)

Definition at line 179 of file DOFLocalPattern.hpp.

Here is the caller graph for this function:

◆ nbDofPerEdge()

const UInt& nbDofPerEdge ( ) const

inline

Return the number of degrees of freedom located on the edges (1D structures)

Definition at line 185 of file DOFLocalPattern.hpp.

Here is the caller graph for this function:

◆ nbDofPerPeak()

UInt nbDofPerPeak ( ) const

inline

Return the number of degrees of freedom located on the peak (vertex in 3D).

Definition at line 191 of file DOFLocalPattern.hpp.

Here is the caller graph for this function:

◆ nbDofPerRidge()

UInt nbDofPerRidge ( ) const

inline

Return the number of degrees of freedom located on the ridge. (edge in 3D)

Definition at line 197 of file DOFLocalPattern.hpp.

Here is the caller graph for this function:

◆ nbDofPerFacet()

UInt nbDofPerFacet ( ) const

inline

Return the number of degrees of freedom located on the facet. (face in 3D)

Definition at line 203 of file DOFLocalPattern.hpp.

Here is the caller graph for this function:

◆ nbDofPerElement()

const UInt& nbDofPerElement ( ) const

inline

Return the number of degrees of freedom located on the element. (volume in 3D)

Definition at line 209 of file DOFLocalPattern.hpp.

Here is the caller graph for this function:

◆ nbDofPerFace()

const UInt& nbDofPerFace ( ) const

inline

Return the number of degrees of freedom located on the faces (2D structures).

Beware that in the 2D case, the face of a triangle is the triangle itself (use edges or vertices if you want to access substructures).

Definition at line 218 of file DOFLocalPattern.hpp.

Here is the caller graph for this function:

◆ nbDofPerVolume()

const UInt& nbDofPerVolume ( ) const

inline

Return the number of degrees of freedom located in the volume (3D structures).

Definition at line 224 of file DOFLocalPattern.hpp.

◆ nbDofPerDimStrut()

const UInt& nbDofPerDimStrut ( const UInt & structDim ) const

inline

Return the number of degrees of freedom located per structDim object.

For example, if we want to access the vertices, structDim should be 0, if we want the edges, then it should be 1,...

Definition at line 233 of file DOFLocalPattern.hpp.

◆ nbDofPerCodimStrut()

const UInt& nbDofPerCodimStrut ( const UInt & structCodim ) const

inline

Return the number of degrees of freedom located per structCodim object.

The codimension of a structure is the full dimension of the element minus the dimension of the structure. For example, in 3D, faces have codimension 1, edges 2 and vertices 3. This method could be useful to code "dimension-free" code. (for example, IP is built on edges in 2D, faces in 3D, so on objects with codimension 1).

Definition at line 245 of file DOFLocalPattern.hpp.

◆ setupStandardPattern()

void setupStandardPattern ( )

private

Method to setup the standard pattern, i.e. with all degrees of freedom coupled.

Definition at line 109 of file DOFLocalPattern.cpp.

Here is the caller graph for this function:

◆ setupP1isoP2SegPattern()

void setupP1isoP2SegPattern ( )

private

Method for the P1isoP2 pattern for the segments (1D)

Definition at line 152 of file DOFLocalPattern.cpp.

◆ setupP1isoP2TriaPattern()

void setupP1isoP2TriaPattern ( )

private

Method for the P1isoP2 pattern for the triangles (2D)

Definition at line 180 of file DOFLocalPattern.cpp.

Field Documentation

◆ M_dim

UInt M_dim

private

dimension of the element (3 for a tetrahedra for example).

Definition at line 276 of file DOFLocalPattern.hpp.

◆ M_nbLocalDof

UInt M_nbLocalDof

private

Total number of degrees of freedom (equal to refEle::nbDof)

Definition at line 279 of file DOFLocalPattern.hpp.

◆ M_nbDofPerDimEntity

std::vector< UInt> M_nbDofPerDimEntity

private

Number of degrees of freedom per geometric entity.

In this vector, we store all the number of degrees of freedom sorted by the dimension of the object where they lie. For example, the number of DoF per vertex (dimension 0) is stored as the 0th element. Then, for edges (dimension 1), it is stored in the 1st element of the vector,... This enables a n-dimensional implementation (not only 3D)

Definition at line 289 of file DOFLocalPattern.hpp.

◆ M_patternType

DofPatternType M_patternType

private

Type of the pattern stored.

Definition at line 293 of file DOFLocalPattern.hpp.

◆ M_pattern

std::vector< std::pair< UInt, UInt > > M_pattern

private

Pairs of couplings to appear in the pattern.

Definition at line 296 of file DOFLocalPattern.hpp.

◆ M_nbPattern

UInt M_nbPattern

private

Number of non-zero terms in the element matrix.

Definition at line 299 of file DOFLocalPattern.hpp.

◆ M_nbDiag

UInt M_nbDiag

private

Number of diagonal terms in the element matrix.

Definition at line 302 of file DOFLocalPattern.hpp.

◆ M_nbUpper

UInt M_nbUpper

private

Number of upper terms in the element matrix.

Definition at line 305 of file DOFLocalPattern.hpp.

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

Private Attributes

Constructor & Destructor

Methods

Get Methods

Private Methods

Detailed Description

Constructor & Destructor Documentation

◆ DOFLocalPattern() [1/3]

◆ DOFLocalPattern() [2/3]

◆ ~DOFLocalPattern()

◆ DOFLocalPattern() [3/3]

Member Function Documentation

◆ patternFirst()

◆ patternSecond()

◆ showMe()

◆ nbPattern()

◆ nbDiag()

◆ nbUpper()

◆ nbLocalDof()

◆ nbDofPerVertex()

◆ nbDofPerEdge()

◆ nbDofPerPeak()

◆ nbDofPerRidge()

◆ nbDofPerFacet()

◆ nbDofPerElement()

◆ nbDofPerFace()

◆ nbDofPerVolume()

◆ nbDofPerDimStrut()

◆ nbDofPerCodimStrut()

◆ setupStandardPattern()

◆ setupP1isoP2SegPattern()

◆ setupP1isoP2TriaPattern()

Field Documentation

◆ M_dim

◆ M_nbLocalDof

◆ M_nbDofPerDimEntity

◆ M_patternType

◆ M_pattern

◆ M_nbPattern

◆ M_nbDiag

◆ M_nbUpper