The class for a reference Lagrangian finite element. More...

#include <ReferenceFE.hpp>

Inheritance diagram for ReferenceFE:

Collaboration diagram for ReferenceFE:

Private Attributes
const ReferenceFE *	M_boundaryFE
	Reference to the boundary finite element. More...

const FE_TYPE	M_type
	Type of finite element (FE_P1_2D, ..., see the #define at the beginning of refFE.h. More...

Public Types
typedef ReferenceElement::function_Type	function_Type

Constructor & Destructor
	ReferenceFE (std::string name, FE_TYPE type, ReferenceShapes shape, Int nbDofPerVertex, Int nbDofPerEdge, Int nbDofPerFace, Int nbDofPerVolume, Int nbDof, Int nbLocalCoor, Int FEDim, const function_Type phi, const function_Type dPhi, const function_Type d2Phi, const function_Type divPhi, const Real refCoor, DofPatternType patternType, const ReferenceFE bdRefFE)
	Constructor of a reference Lagrangian finite element. More...

virtual	~ReferenceFE ()
	Destructor. More...

Get Methods
bool	hasBoundaryFE () const
	Check if the reference element has boundary elements. More...

const ReferenceFE &	boundaryFE () const
	Getter for the boundary finite element. More...

const FE_TYPE &	type () const
	Getter for the type of the finite element. More...

Private Methods
	ReferenceFE ()
	No empty constructor. More...

	ReferenceFE (const ReferenceFE &)
	No copy constructor. More...

Additional Inherited Members
Public Types inherited from ReferenceElement
typedef Real(*	function_Type) (const GeoVector &)

Public Member Functions inherited from ReferenceElement
	ReferenceElement (std::string name, ReferenceShapes shape, UInt nbDof, UInt nbLocalCoor, UInt feDim, const function_Type phi, const function_Type dPhi, const function_Type d2Phi, const function_Type divPhi, const Real *refCoor)
	Full constructor. More...

virtual	~ReferenceElement ()
	Destructor. More...

Real	xi (UInt i) const
	return the first local coordinate of the i-th node of the reference element More...

Real	eta (UInt i) const
	return the second local coordinate of the i-th node of the reference element More...

Real	zeta (UInt i) const
	return the third local coordinate of the i-th node of the reference element More...

Real	refCoor (UInt i, UInt icoor) const
	return the icoor-th local coordinate of the i-th node of the reference element More...

std::vector< GeoVector >	refCoor () const
	return the coordinates of the reference element More...

Real	phi (UInt i, const GeoVector &v) const
	Return the value of the i-th basis function in the point v. More...

Real	phi (UInt i, UInt icoor, const GeoVector &v) const
	return the value of the component icoor-th of the i-th basis function on point v. More...

Real	dPhi (UInt i, UInt icoor, const GeoVector &v) const
	return the value of the icoor-th derivative of the i-th basis function on point v More...

Real	d2Phi (UInt i, UInt icoor, UInt jcoor, const GeoVector &v) const
	return the value of the (icoor,jcoor)-th second derivative of the i-th basis function on point v More...

Real	divPhi (UInt i, const GeoVector &v) const
	return the value of the divergence of the i-th basis function on point v. More...

bool	hasPhi () const
	Check if the refEle has phi functions. More...

bool	hasDPhi () const
	Check if the refEle has dPhi functions. More...

bool	hasD2Phi () const
	Check if the refEle has d2Phi functions. More...

bool	hasDivPhi () const
	Check if the refEle has divPhi functions. More...

virtual std::vector< Real >	nodalToFEValues (const std::vector< Real > &) const
	Method for transforming nodal values into FE values. More...

const std::string &	name () const
	Return the name of the reference element. More...

const UInt &	nbDof () const
	Return the number of degrees of freedom for this reference element. More...

const	LIFEV_DEPRECATED (UInt &) nbCoor() const
	OLD: Return the number of local coordinates. More...

const UInt &	nbLocalCoor () const
	Return the number of local coordinates. More...

const UInt &	feDim () const
	Return the dimension of the FE (scalar vs vectorial FE) More...

const ReferenceShapes &	shape () const
	Return the shape of the element. More...

Real	phi (UInt i, const Real &x, const Real &y, const Real &z) const
	return the value of the i-th basis function on point (x,y,z) More...

Real	phi (UInt i, UInt icoor, const Real &x, const Real &y, const Real &z) const
	return the value of the component icoor-th of the i-th basis function on point (x,y,z). More...

Real	dPhi (UInt i, UInt icoor, const Real &x, const Real &y, const Real &z) const
	return the value of the icoor-th derivative of the i-th basis function on point (x,y,z) More...

Real	d2Phi (UInt i, UInt icoor, UInt jcoor, const Real &x, const Real &y, const Real &z) const
	return the value of the (icoor,jcoor)-th second derivative of the i-th basis function on point (x,y,z) More...

Real	divPhi (UInt i, const Real &x, const Real &y, const Real &z) const
	return the value of the divergence of the i-th basis function on point (x,y,z). More...

Public Member Functions inherited from DOFLocalPattern
	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...

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...

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...

Detailed Description

The class for a reference Lagrangian finite element.

Author: J.-F. Gerbeau

Date: 04/2002

How to add a new finite element ?

(1) in refEle.h : you declare the functions you need (fct1_Pipo_2D, derfct1_1_Pipo_2D, etc...), the static arrays containing these functions and the coordinates of the nodes on the reference element.

: (2) in defQuadRuleFE.cc : you define these functions (fct1_Pipo_2D, etc...)

: (3) in refFE.h, you declare your finite element:
extern const ReferenceFE fePipo;

: (4) in defQuadRuleFE.cc: you define your new element with a command like:
const ReferenceFE feTriaPipo("Pipo element on a triangle",TRIANGLE,1,0,0,0,3,2,
fct_Pipo_2D,derfct_Pipo_2D,der2fct_Pipo_2D,refcoor_Pipo_2D,allQuadRuleTria,STANDARD_PATTERN,&feSegP1);
See documentation of ReferenceFE::ReferenceFE(...) for a precise description of all arguments

Definition at line 115 of file ReferenceFE.hpp.

Member Typedef Documentation

◆ function_Type

typedef ReferenceElement::function_Type function_Type

Definition at line 125 of file ReferenceFE.hpp.

Constructor & Destructor Documentation

◆ ReferenceFE() [1/3]

ReferenceFE	(	std::string	name,
		FE_TYPE	type,
		ReferenceShapes	shape,
		Int	nbDofPerVertex,
		Int	nbDofPerEdge,
		Int	nbDofPerFace,
		Int	nbDofPerVolume,
		Int	nbDof,
		Int	nbLocalCoor,
		Int	FEDim,
		const function_Type *	phi,
		const function_Type *	dPhi,
		const function_Type *	d2Phi,
		const function_Type *	divPhi,
		const Real *	refCoor,
		DofPatternType	patternType,
		const ReferenceFE *	bdRefFE
	)

Constructor of a reference Lagrangian finite element.

Constructor of a reference finite element. The arguments are:

Parameters

name	the name of the f.e.
type	the type of the f.e. (FE_P1_2D,... see the #define at the begining of refFE.h)
shape	the geometry belongs to enum ReferenceShapes {NONE, POINT, LINE, TRIANGLE, QUAD, HEXA, PRISM, TETRA}; (see ElementShapes.h)
nbDofPerVertex	the number of degrees of freedom per vertex
nbDofPerEdge	the number of degrees of freedom per edge
nbDofPerFace	the number of degrees of freedom per face
nbDofPerVolume	the number of degrees of freedom per volume
nbDof	the total number of d.o.f ( = nbDofPerVertex * nb vertex + nbDofPerEdge * nb edges + etc...)
nbLocalCoor	number of local coordinates
phi	the static array containing the basis functions (defined in refEle.h)
dPhi	the static array containing the derivatives of the basis functions (defined in refEle.h)
d2Phi	the static array containing the second derivatives of the basis functions (defined in refEle.h)
divPhi	the static array containing the divergence of the basis function
refCoor	the static array containing the coordinates of the nodes on the reference element (defined in refEle.h)
patternType	in most of cases STANDARD_PATTERN, except for elements like P1isoP2 (to define a new pattern, add a new #define in refFE.h and code it in refFE.cc following the example of P1ISOP2_TRIA_PATTERN)
bdRefFE	a pointer on the associated reference finite element on the boundary

Definition at line 47 of file ReferenceFE.cpp.

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◆ ~ReferenceFE()

~ReferenceFE ( )

virtual

Destructor.

Definition at line 58 of file ReferenceFE.cpp.

◆ ReferenceFE() [2/3]

ReferenceFE ( )

private

No empty constructor.

◆ ReferenceFE() [3/3]

ReferenceFE ( const ReferenceFE & )

private

No copy constructor.

Member Function Documentation

◆ hasBoundaryFE()

bool hasBoundaryFE ( ) const

inline

Check if the reference element has boundary elements.

Definition at line 190 of file ReferenceFE.hpp.

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◆ boundaryFE()

const ReferenceFE& boundaryFE ( ) const

inline

Getter for the boundary finite element.

Definition at line 199 of file ReferenceFE.hpp.

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◆ type()

const FE_TYPE& type ( ) const

inline

Getter for the type of the finite element.

Definition at line 206 of file ReferenceFE.hpp.

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Field Documentation

◆ M_boundaryFE

const ReferenceFE* M_boundaryFE

private

Reference to the boundary finite element.

Definition at line 228 of file ReferenceFE.hpp.

◆ M_type

const FE_TYPE M_type

private

Type of finite element (FE_P1_2D, ..., see the #define at the beginning of refFE.h.

Definition at line 231 of file ReferenceFE.hpp.

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

Private Attributes

Public Types

Constructor & Destructor

Get Methods

Private Methods

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ function_Type

Constructor & Destructor Documentation

◆ ReferenceFE() [1/3]

◆ ~ReferenceFE()

◆ ReferenceFE() [2/3]

◆ ReferenceFE() [3/3]

Member Function Documentation

◆ hasBoundaryFE()

◆ boundaryFE()

◆ type()

Field Documentation

◆ M_boundaryFE

◆ M_type