A class for a finite element on a manifold. More...

#include <CurrentFEManifold.hpp>

Inheritance diagram for CurrentFEManifold:

Collaboration diagram for CurrentFEManifold:

Constructor(s) & Destructor
	CurrentFEManifold (const ReferenceFE &refFE, const GeometricMap &geoMap)
	Constructor without quadrature specification. More...

	CurrentFEManifold (const ReferenceFE &refFE, const GeometricMap &geoMap, const QuadratureRule &qr)
	Full constructor with default quadrature. More...

	CurrentFEManifold (const ReferenceFE &refFE, const GeometricMap &geoMap, const QuadratureRule &qr, const Real *refCoor, UInt currentId, Real invArea=1.)
	Constructor used to create a static reference FE for hybrid elements. More...

	CurrentFEManifold (const CurrentFEManifold &feManifold)
	Copy constructor. More...

virtual	~CurrentFEManifold ()

Methods
virtual void	update (const std::vector< std::vector< Real > > &pts, flag_Type upFlag)
	Update method using only point coordinates. More...

void	coorMap (Real &x, Real &y, Real &z, Real xi, Real eta) const
	Maps a point from the reference element to the current element. More...

Real	measure () const
	Compute the measure of the current element. More...

template<typename FunctorType >
Real	integral (const FunctorType &f) const
	Compute the integral of a function f over the current element. More...

template<typename FunctorType >
Real	normalIntegral (const FunctorType &f) const
	Compute the integral of the normal component of a vector function f over the current element. More...

Get Methods
boost::multi_array< Real, 2 >	M_phiGeo
	Geometric map in the geometric nodes (different from M_phi only for Hybrid elements) More...

boost::multi_array< Real, 3 >	M_tangents
	Normal and tangent vectors, metric tensor and weighted measure in the quadrature nodes. More...

boost::multi_array< Real, 2 >	M_normal

boost::multi_array< Real, 3 >	M_metric

boost::multi_array< Real, 1 >	M_detMetric

boost::multi_array< Real, 3 >	M_inverseMetric

boost::multi_array< Real, 1 >	M_wRootDetMetric

bool	M_tangentsUpdated
	Check variables. More...

bool	M_normalUpdated

bool	M_metricUpdated

bool	M_detMetricUpdated

bool	M_inverseMetricUpdated

bool	M_wRootDetMetricUpdated

Real	phiGeo (UInt iGeoNode, UInt quadNode) const
	Values of the geometric basis functions on quadrature points (different from M_phi(iGeoNode,quadNode) only for Hybrid elements) More...

Real	tangent (UInt tangent, UInt coordinate, UInt quadNode) const
	Values of the tangents on the quadrature points. More...

Real	normal (UInt coordinate, UInt quadNode) const
	Values of the normal on the quadrature points. More...

Real	metric (UInt iCoor, UInt jCoor, UInt quadNode) const
	Metric tensor on the quadrature points. More...

Real	detMetric (UInt quadNode)
	Determinant of the metric tensor on the quadrature points. More...

Real	inverseMetric (UInt iCoor, UInt jCoor, UInt quadNode) const
	Inverse of the metric tensor on the quadrature points. More...

Real	wRootDetMetric (UInt quadNode) const
	Square root of the determinant of the metric times the weight on the quadrature points. More...

void	computeTangents ()
	Computes the tangent vectors in the quadrature nodes. More...

void	computeNormal ()
	Computes the normal vectors in the quadrature nodes. More...

void	computeMetric ()
	Computes the metric in the quadrature nodes. More...

void	computeDetMetric ()
	Computes the determinant of the metric tensor in the quadrature nodes. More...

void	computeInverseMetric ()
	Computes the inverse of the metric tensor in the quadrature nodes. More...

void	computeWRootDetMetric ()
	Computes the square root of the determinant of the metric times the weight in the quadrature nodes. More...

Additional Inherited Members
Public Member Functions inherited from CurrentFE
template<typename MeshElementMarked >
void	update (const MeshElementMarked &geoele, flag_Type upFlag)

template<typename MeshElementMarked >
void	computeCellNodes (const MeshElementMarked &geoele)

	CurrentFE (const ReferenceFE &refFE, const GeometricMap &geoMap, const QuadratureRule &qr)
	Full constructor with default quadrature. More...

	CurrentFE (const ReferenceFE &refFE, const GeometricMap &geoMap)
	Constructor without quadrature specification. More...

virtual	~CurrentFE ()
	Destructor. More...

template<typename MeshElementMarkedType >
void	update (const MeshElementMarkedType &geoele, flag_Type upFlag)
	Update method using a given element. More...

void	update (const std::vector< GeoVector > &pts, flag_Type upFlag)
	Update method using only point coordinates. It used the flags, as defined in this page. More...

void	barycenter (Real &x, Real &y, Real &z) const
	return the barycenter of the element More...

Real	diameter () const
	return the diameter of the element in the 1-norm More...

Real	diameter2 () const
	return the diameter of the element in the 2-norm More...

void	coorMap (Real &x, Real &y, Real &z, Real xi, Real eta, Real zeta) const

GeoVector	coorMap (const GeoVector &P) const

void	quadRuleVTKexport (const std::string &filename) const
	Export the quadrature rule on the current FE. More...

void	setQuadRule (const QuadratureRule &newQuadRule)
	Setter for the quadrature rule. More...

UInt	currentId () const
	Getter for the ID of the current cell. More...

UInt	currentLocalId () const
	Getter for the local ID of the current cell. More...

UInt	nbQuadPt () const
	Getter for the number of quadrature nodes. More...

UInt	nbGeoNode () const
	Getter for the number of geometrical nodes. More...

UInt	nbFEDof () const
	Getter for the number of nodes. More...

const ReferenceFE &	refFE () const
	Getter for the reference FE. More...

const GeometricMap &	geoMap () const
	Getter for the GeometricMap reference. More...

const QuadratureRule &	quadRule () const
	Getter for the quadrature rule. More...

UInt	nbPattern () const
	Getter for the number of entries in the pattern. More...

UInt	nbDiag () const
	Getter for the diagonal entries in the pattern. More...

UInt	nbUpper () const
	Getter for the number of entries in the pattern. More...

	LIFEV_DEPRECATED (UInt) nbCoor() const
	Old getter for the number of local coordinates. More...

UInt	nbLocalCoor () const
	Getter for the number of local coordinates. More...

Real	cellNode (UInt node, UInt coordinate) const
	Getter for the nodes of the cell. More...

Real	quadNode (UInt node, UInt coordinate) const
	Getter for the quadrature nodes. More...

Real	detJacobian (UInt quadNode) const
	Getter for the determinant of the jacobian in a given quadrature node. More...

Real	wDetJacobian (UInt quadNode) const
	Getter for the weighted jacobian determinant. More...

Real	tInverseJacobian (UInt element1, UInt element2, UInt quadNode) const
	Getter for the inverse of the jacobian. More...

Real	phi (UInt node, UInt quadNode) const
	Getter for basis function values (scalar FE case) More...

Real	phi (UInt node, UInt component, UInt quadNode) const
	Getter for basis function values (vectorial FE case) More...

Real	dphi (UInt node, UInt derivative, UInt quadNode) const
	Getter for the derivatives of the basis functions. More...

Real	d2phi (UInt node, UInt derivative1, UInt derivative2, UInt quadNode) const
	Getter for the second derivatives of the basis functions. More...

Real	divPhiRef (UInt node, UInt quadNode) const
	Getter for the divergence of a vectorial FE in the reference frame. More...

Real	point (UInt node, UInt coordinate) const
	Old accessor, use cellNode instead. More...

Real	quadPt (UInt node, UInt coordinate) const
	Old accessor, use quadNode instead. More...

Real	weightDet (UInt quadNode) const
	Old accessor, use wDetJacobian instead. More...

Real	detJac (UInt quadNode) const
	Getter for the determinant of the jacobian in a given quadrature node. More...

Real	tInvJac (UInt element1, UInt element2, UInt quadNode) const
	Old accessor, use iInverseJacobian instead. More...

Real	phiDer (UInt node, UInt derivative, UInt quadNode) const
	Old accessor, use dphi instead. More...

Real	phiDer2 (UInt node, UInt derivative1, UInt derivative2, UInt quadNode) const
	Old accessor, use d2phi instead. More...

void	coorBackMap (Real x, Real y, Real z, Real &xi, Real &eta, Real &zeta) const

Real	pointJacobian (Real hat_x, Real hat_y, Real hat_z, int compx, int compzeta) const

Real	pointInverseJacobian (Real hat_x, Real hat_y, Real hat_z, int compx, int compzeta) const

Real	pointDetJacobian (Real hat_x, Real hat_y, Real hat_z) const

void	coorQuadPt (Real &x, Real &y, Real &z, int ig) const

int	patternFirst (int i) const
	patternFirst(i): row index in the element matrix of the i-th term of the pattern More...

int	patternSecond (int i) const
	patternSecond(i): column index in the element matrix of the i-th term of the pattern More...

template<class MeshElementMarkedType >
void	update (const MeshElementMarkedType &geoele)
	DECLARATION of the update methods. More...

template<class MeshElementMarkedType >
void	updateJac (const MeshElementMarkedType &geoele)

template<class MeshElementMarkedType >
void	updateJacQuadPt (const MeshElementMarkedType &geoele)

template<class MeshElementMarkedType >
void	updateFirstDeriv (const MeshElementMarkedType &geoele)

template<class MeshElementMarkedType >
void	updateFirstDerivQuadPt (const MeshElementMarkedType &geoele)

template<class MeshElementMarkedType >
void	updateSecondDeriv (const MeshElementMarkedType &geoele)

template<class MeshElementMarkedType >
void	updateSecondDerivQuadPt (const MeshElementMarkedType &geoele)

template<class MeshElementMarkedType >
void	updateFirstSecondDeriv (const MeshElementMarkedType &geoele)

template<class MeshElementMarkedType >
void	updateFirstSecondDerivQuadPt (const MeshElementMarkedType &geoele)

Protected Member Functions inherited from CurrentFE
	CurrentFE ()

	CurrentFE (const CurrentFE &)

template<typename MeshElementMarkedType >
void	computeCellNodes (const MeshElementMarkedType &geoele)
	Update the nodes of the cell to the current one. More...

void	computeCellNodes (const std::vector< std::vector< Real > > &pts)
	Update only the nodes of the cells to the current one. More...

void	computeQuadNodes ()
	Update the location of the quadrature in the current cell. More...

void	computeDphiGeometricMap ()
	Compute the values of the derivatives of the mapping in the quadrature nodes. More...

void	computeJacobian ()
	Compute the jacobian in the quadrature nodes. More...

void	computeTInverseJacobian ()
	Compute the transposed inverse of the jacobian in the quadrature nodes. More...

void	computeDetJacobian ()
	Compute the determinant of the jacobian. More...

void	computeWDetJacobian ()
	Compute the determinant of the jacobian in the quadrature nodes. More...

void	computeDphiRef ()
	Compute the value of the derivatives in the reference frame. More...

void	computeDphi ()
	Compute the value of the derivatives in the current element. More...

void	computeD2phiRef ()
	Compute the value of the second derivatives in the reference frame. More...

void	computeD2phi ()
	Compute the value of the derivatives in the current element. More...

void	computePhiVect ()
	Compute the value of the vectorial FE using Piola transform. More...

Protected Attributes inherited from CurrentFE
const UInt	M_nbNode

const UInt	M_nbLocalCoor

const UInt	M_nbDiag

const UInt	M_nbUpper

const UInt	M_nbPattern

UInt	M_currentId

UInt	M_currentLocalId

UInt	M_nbGeoNode

UInt	M_nbQuadPt

const ReferenceFE *	M_refFE

const GeometricMap *	M_geoMap

QuadratureRule *	M_quadRule

boost::multi_array< Real, 2 >	M_cellNodes

boost::multi_array< Real, 2 >	M_quadNodes

boost::multi_array< Real, 3 >	M_dphiGeometricMap

boost::multi_array< Real, 3 >	M_jacobian

boost::multi_array< Real, 1 >	M_detJacobian

boost::multi_array< Real, 1 >	M_wDetJacobian

boost::multi_array< Real, 3 >	M_tInverseJacobian

boost::multi_array< Real, 3 >	M_phi

boost::multi_array< Real, 3 >	M_dphi

boost::multi_array< Real, 4 >	M_d2phi

boost::multi_array< Real, 3 >	M_phiVect

boost::multi_array< Real, 3 >	M_dphiRef

boost::multi_array< Real, 4 >	M_d2phiRef

boost::multi_array< Real, 2 >	M_divPhiRef

bool	M_cellNodesUpdated

bool	M_quadNodesUpdated

bool	M_dphiGeometricMapUpdated

bool	M_jacobianUpdated

bool	M_detJacobianUpdated

bool	M_wDetJacobianUpdated

bool	M_tInverseJacobianUpdated

bool	M_phiUpdated

bool	M_dphiUpdated

bool	M_d2phiUpdated

bool	M_phiVectUpdated

bool	M_dphiRefUpdated

bool	M_d2phiRefUpdated

bool	M_divPhiRefUpdated

Detailed Description

A class for a finite element on a manifold.

This class inherits from CurrentFE and adds some functionality related to the manifold, like normals, tangents, etc.

Definition at line 86 of file CurrentFEManifold.hpp.

Constructor & Destructor Documentation

◆ CurrentFEManifold() [1/4]

CurrentFEManifold	(	const ReferenceFE &	refFE,
		const GeometricMap &	geoMap
	)

Constructor without quadrature specification.

If you use this constructor, you have to use the method CurrentFE::setQuadRule before using any update method!

Parameters

refFE	Reference finite element used
geoMap	Geometric mapping used

Definition at line 55 of file CurrentFEManifold.cpp.

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◆ CurrentFEManifold() [2/4]

CurrentFEManifold	(	const ReferenceFE &	refFE,
		const GeometricMap &	geoMap,
		const QuadratureRule &	qr
	)

Full constructor with default quadrature.

Parameters

refFE	Reference finite element used
geoMap	Geometric mapping used
qr	Quadrature rule for the computations

Definition at line 36 of file CurrentFEManifold.cpp.

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◆ CurrentFEManifold() [3/4]

CurrentFEManifold	(	const ReferenceFE &	refFE,
		const GeometricMap &	geoMap,
		const QuadratureRule &	qr,
		const Real *	refCoor,
		UInt	currentId,
		Real	invArea = `1.`
	)

Constructor used to create a static reference FE for hybrid elements.

Definition at line 74 of file CurrentFEManifold.cpp.

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◆ CurrentFEManifold() [4/4]

CurrentFEManifold ( const CurrentFEManifold & feManifold )

Copy constructor.

Definition at line 127 of file CurrentFEManifold.cpp.

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◆ ~CurrentFEManifold()

virtual ~CurrentFEManifold ( )

inlinevirtual

Definition at line 119 of file CurrentFEManifold.hpp.

Member Function Documentation

◆ update()

void update	(	const std::vector< std::vector< Real > > &	pts,
		flag_Type	upFlag
	)

virtual

Update method using only point coordinates.

Overrides the method of base class CurrentFE. Actually, it calls the method of the base class and then performs some extra updates if upFlag contains also some boundary updates

Parameters

pts	The coordinates of the points defining the current element
upFlag	The update flag which determines what kind of update has to be done (see top of the file)

Reimplemented from CurrentFE.

Definition at line 172 of file CurrentFEManifold.cpp.

◆ coorMap()

void coorMap	(	Real &	x,
		Real &	y,
		Real &	z,
		Real	xi,
		Real	eta
	)		const

Maps a point from the reference element to the current element.

return the coordinate (x,y,z)= F(xi,eta), (F: geo mappping) where (xi,eta) are the coordinates in the reference element and (x,y,z) are the coor in the current element (if the code is compiled in 2D mode then z=0 and eta is disgarded)

Definition at line 155 of file CurrentFEManifold.cpp.

◆ measure()

Real measure ( ) const

virtual

Compute the measure of the current element.

Overrides the corresponding method in the mother class

Reimplemented from CurrentFE.

Definition at line 160 of file CurrentFEManifold.cpp.

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◆ integral()

Real integral ( const FunctorType & f ) const

Compute the integral of a function f over the current element.

Parameters

f	The function to be integrated. It must have the signature Real f(Real x, Real y, Real z)

Definition at line 266 of file CurrentFEManifold.hpp.

◆ normalIntegral()

Real normalIntegral ( const FunctorType & f ) const

Compute the integral of the normal component of a vector function f over the current element.

Parameters

f The function to be integrated. It must have the signature void f(Real x, Real y, Real z, Real* result) where result is an array of size equal to the dimension of the ambient space. The function should NOT create the array, but instead should assume that the array is already created. The dimension of the ambient spase should be equal to M_nbLocalCoor+1

Definition at line 279 of file CurrentFEManifold.hpp.

◆ phiGeo()

Real phiGeo	(	UInt	iGeoNode,
		UInt	quadNode
	)		const

inline

Values of the geometric basis functions on quadrature points (different from M_phi(iGeoNode,quadNode) only for Hybrid elements)

Definition at line 178 of file CurrentFEManifold.hpp.

◆ tangent()

Real tangent	(	UInt	tangent,
		UInt	coordinate,
		UInt	quadNode
	)		const

inline

Values of the tangents on the quadrature points.

Definition at line 184 of file CurrentFEManifold.hpp.

◆ normal()

Real normal	(	UInt	coordinate,
		UInt	quadNode
	)		const

inline

Values of the normal on the quadrature points.

Definition at line 191 of file CurrentFEManifold.hpp.

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◆ metric()

Real metric	(	UInt	iCoor,
		UInt	jCoor,
		UInt	quadNode
	)		const

inline

Metric tensor on the quadrature points.

Definition at line 198 of file CurrentFEManifold.hpp.

◆ detMetric()

Real detMetric ( UInt quadNode )

inline

Determinant of the metric tensor on the quadrature points.

Definition at line 205 of file CurrentFEManifold.hpp.

◆ inverseMetric()

Real inverseMetric	(	UInt	iCoor,
		UInt	jCoor,
		UInt	quadNode
	)		const

inline

Inverse of the metric tensor on the quadrature points.

Definition at line 212 of file CurrentFEManifold.hpp.

◆ wRootDetMetric()

Real wRootDetMetric ( UInt quadNode ) const

inline

Square root of the determinant of the metric times the weight on the quadrature points.

Definition at line 219 of file CurrentFEManifold.hpp.

◆ computeTangents()

void computeTangents ( )

protected

Computes the tangent vectors in the quadrature nodes.

Definition at line 217 of file CurrentFEManifold.cpp.

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◆ computeNormal()

void computeNormal ( )

protected

Computes the normal vectors in the quadrature nodes.

Definition at line 236 of file CurrentFEManifold.cpp.

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◆ computeMetric()

void computeMetric ( )

protected

Computes the metric in the quadrature nodes.

Definition at line 281 of file CurrentFEManifold.cpp.

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◆ computeDetMetric()

void computeDetMetric ( )

protected

Computes the determinant of the metric tensor in the quadrature nodes.

Definition at line 310 of file CurrentFEManifold.cpp.

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◆ computeInverseMetric()

void computeInverseMetric ( )

protected

Computes the inverse of the metric tensor in the quadrature nodes.

Definition at line 331 of file CurrentFEManifold.cpp.

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◆ computeWRootDetMetric()

void computeWRootDetMetric ( )

protected

Computes the square root of the determinant of the metric times the weight in the quadrature nodes.

Definition at line 359 of file CurrentFEManifold.cpp.

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Field Documentation

◆ M_phiGeo

boost::multi_array<Real, 2> M_phiGeo

protected

Geometric map in the geometric nodes (different from M_phi only for Hybrid elements)

Definition at line 246 of file CurrentFEManifold.hpp.

◆ M_tangents

boost::multi_array<Real, 3> M_tangents

protected

Normal and tangent vectors, metric tensor and weighted measure in the quadrature nodes.

Definition at line 249 of file CurrentFEManifold.hpp.

◆ M_normal

boost::multi_array<Real, 2> M_normal

protected

Definition at line 250 of file CurrentFEManifold.hpp.

◆ M_metric

boost::multi_array<Real, 3> M_metric

protected

Definition at line 251 of file CurrentFEManifold.hpp.

◆ M_detMetric

boost::multi_array<Real, 1> M_detMetric

protected

Definition at line 252 of file CurrentFEManifold.hpp.

◆ M_inverseMetric

boost::multi_array<Real, 3> M_inverseMetric

protected

Definition at line 253 of file CurrentFEManifold.hpp.

◆ M_wRootDetMetric

boost::multi_array<Real, 1> M_wRootDetMetric

protected

Definition at line 254 of file CurrentFEManifold.hpp.

◆ M_tangentsUpdated

bool M_tangentsUpdated

protected

Check variables.

Definition at line 257 of file CurrentFEManifold.hpp.

◆ M_normalUpdated

bool M_normalUpdated

protected

Definition at line 258 of file CurrentFEManifold.hpp.

◆ M_metricUpdated

bool M_metricUpdated

protected

Definition at line 259 of file CurrentFEManifold.hpp.

◆ M_detMetricUpdated

bool M_detMetricUpdated

protected

Definition at line 260 of file CurrentFEManifold.hpp.

◆ M_inverseMetricUpdated

bool M_inverseMetricUpdated

protected

Definition at line 261 of file CurrentFEManifold.hpp.

◆ M_wRootDetMetricUpdated

bool M_wRootDetMetricUpdated

protected

Definition at line 262 of file CurrentFEManifold.hpp.

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

Constructor(s) & Destructor

Methods

Get Methods

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ CurrentFEManifold() [1/4]

◆ CurrentFEManifold() [2/4]

◆ CurrentFEManifold() [3/4]

◆ CurrentFEManifold() [4/4]

◆ ~CurrentFEManifold()

Member Function Documentation

◆ update()

◆ coorMap()

◆ measure()

◆ integral()

◆ normalIntegral()

◆ phiGeo()

◆ tangent()

◆ normal()

◆ metric()

◆ detMetric()

◆ inverseMetric()

◆ wRootDetMetric()

◆ computeTangents()

◆ computeNormal()

◆ computeMetric()

◆ computeDetMetric()

◆ computeInverseMetric()

◆ computeWRootDetMetric()

Field Documentation

◆ M_phiGeo

◆ M_tangents

◆ M_normal

◆ M_metric

◆ M_detMetric

◆ M_inverseMetric

◆ M_wRootDetMetric

◆ M_tangentsUpdated

◆ M_normalUpdated

◆ M_metricUpdated

◆ M_detMetricUpdated

◆ M_inverseMetricUpdated

◆ M_wRootDetMetricUpdated