Base class for all unstructured element types. More...

#include <element.h>

Inheritance diagram for Element_Unstructured:

Public Member Functions
	Element_Unstructured (const Element_Unstructured &el)

virtual void	Initialise (const NodeList &nlist)
	Element initialisation. More...

virtual void	PostInitialisation (const NodeList &nlist)
	Element setup after mesh initialisation. More...

double	Size () const
	Returns the element size. More...

void	operator= (const Element_Unstructured &el)

virtual bool	GContains (const Point &glob, const NodeList &nlist) const
	Checks if a global point coordinate is inside the element. More...

RSymMatrix	IntDD () const
	Integrals of all products of two shape function derivatives over the element. More...

double	IntDD (int i, int j) const
	Integral of a product of two shape function derivatives over the element. More...

RSymMatrix	BndIntFF () const
	Boundary integral of all products of two shape functions over all boundary sides of the element. More...

double	BndIntFF (int i, int j)
	Boundary integral of a product of two shape functions over all boundary sides of the element. More...

Public Member Functions inherited from Element
	Element ()
	Creates a new element with no nodes.

	Element (const Element &el)
	Creates a new element as a copy of 'el'.

virtual	~Element ()
	Destroys the element.

virtual Element *	Copy ()=0
	Create a copy of the element and return a pointer to it.

void	operator= (const Element &el)
	Element assignment. More...

virtual BYTE	Type () const =0
	Returns an element type identifier. More...

virtual BYTE	VtkType () const
	Returns the VTK element type identifier, or 0 if the element doesn't have a VTK representation.

virtual unsigned long	GetCaps () const =0
	Returns element capability flags. More...

virtual int	Dimension () const =0
	Returns the spatial dimension of the element. More...

virtual int	nNode () const =0
	Returns the number of nodes associated with the element. More...

virtual int	nSide () const =0
	Returns the number of element sides. More...

virtual int	nSideNode (int side) const =0
	Returns the number of vertices associated with a side. More...

virtual int	SideNode (int side, int node) const =0
	Returns relative node index for a side vertex. More...

virtual bool	IsNode (int node)
	Checks if a node is part of the element. More...

int	IsSide (int nn, int *nd)
	Checks if a face defined by vertex nodes is part of the element. More...

virtual bool	IsSideNode (int side, int node)
	Checks if a node is associated with a specific side. More...

bool	IsBoundarySide (int side)
	Checks if a side is on the mesh surface. More...

bool	HasBoundarySide ()
	Checks if the element contains any surface sides. More...

bool	HasInterfaceSide ()
	Checks if the element contains any internal interface sides. More...

virtual Point	Local (const NodeList &nlist, const Point &glob) const =0
	Maps a point from global to local element coordinates. More...

virtual Point	NodeLocal (int node) const =0
	Returns the local coordinates of an element node. More...

virtual Point	SurfToLocal (int side, const Point &p) const
	Maps a point from surface coordinates to local element coordinates. More...

virtual void	MapToSide (int side, Point &loc) const
	Translates a point to an element surface. More...

virtual Point	SideCentre (int side) const
	Returns the centre point of a side. More...

Element *	SideNeighbour (int side) const
	returns a pointer to the element connected at 'side', or NULL if this is a boundary side. More...

int	SideNeighbourIndex (int side) const
	Returns the list index of the element connected at 'side', or -1 if this is a boundary side. More...

Point	Global (const NodeList &nlist, const Point &loc) const
	Maps a point from local element coordinates to global coordinates. More...

virtual RDenseMatrix	Elgeom (const NodeList &nlist) const
	Returns the element's global node coordinates. More...

virtual RVector	DirectionCosine (int side, RDenseMatrix &jacin)=0
	Returns the direction cosines of a side normal. More...

virtual const RVector &	LNormal (int side) const =0
	Returns a side normal in local coordinates. More...

virtual double	SideSize (int side, const NodeList &nlist) const
	Returns the size of an element side. More...

virtual double	DetJ (const Point &loc, const NodeList *nlist=0) const
	Returns determinant of Jacobian at a given point inside the element in the local frame. More...

virtual bool	LContains (const Point &loc, bool pad=true) const =0
	Checks if a local point coordinate is inside the element. More...

virtual int	BndSideList (const NodeList &nlist, int *list)
	Returns a list of boundary sides. More...

void	InitNeighbourSupport ()

void	InitSubdivisionSupport ()

int	SubdivisionLevel () const
	Returns the element's subdivison level. More...

virtual void	Subdivide (Mesh *mesh)

virtual RVector	LocalShapeF (const Point &loc) const =0
	Returns the values of the shape functions at a local point. More...

virtual RDenseMatrix	LocalShapeD (const Point &loc) const =0
	Returns the values of the shape function derivatives at a local point. More...

virtual RVector	GlobalShapeF (const NodeList &nlist, const Point &glob) const
	Returns the values of the shape functions at a global point. More...

virtual RDenseMatrix	GlobalShapeD (const NodeList &nlist, const Point &glob) const
	Returns the values of the shape function derivatives at a global point. More...

virtual int	QuadRule (int order, const double wght, const Point absc) const
	Returns the weights and abscissae of quadrature rules over the element. More...

virtual double	IntF (int i) const =0
	Integral of a shape function over the element. More...

virtual RSymMatrix	IntFF () const =0
	Integrals of all products of two shape functions over the element. More...

virtual double	IntFF (int i, int j) const =0
	Integral of a product of two shape functions over the element. More...

virtual double	IntFFF (int i, int j, int k) const =0
	Integral of a product of three shape functions over the element. More...

virtual RSymMatrix	IntPFF (const RVector &P) const =0
	Integrals of all products of two shape functions and a nodal function over the element. More...

virtual double	IntPFF (int i, int j, const RVector &P) const =0
	Integral of a product of two shape functions and a nodal function over the element. More...

virtual RVector	IntFD (int i, int j) const
	Integral of a product of a shape function and a shape function derivative over the element. More...

virtual double	IntFDD (int i, int j, int k) const =0
	Integral of a product of a shape function and two shape function derivatives over the element. More...

virtual RSymMatrix	IntPDD (const RVector &P) const =0
	All integrals of products of a nodal function and two shape function derivatives over the element. More...

virtual double	IntPDD (int i, int j, const RVector &P) const =0
	Integrals of a product of a nodal function and two shape function derivatives over the element. More...

virtual RVector	BndIntF () const
	Boundary integral of all shape functions over all boundary sides of the element. More...

virtual double	BndIntFSide (int i, int sd)
	Surface integral of a shape function over one of the sides of the element. More...

virtual double	BndIntFFSide (int i, int j, int sd)=0
	Surface integral of a product of two shape functions over one of the sides of the element. More...

virtual RSymMatrix	BndIntPFF (const RVector &P) const =0
	Surface integrals of all products of a nodal function and two shape functions over all boundary sides of the element. More...

virtual double	BndIntPFF (int i, int j, const RVector &P) const =0
	Surface integrals of a product of a nodal function and two shape functions over all boundary sides of the element. More...

virtual double	Intd (int i, int k) const
	Integral of partial shape function derivative over the element. More...

virtual double	IntFd (int i, int j, int k) const
	Integral of the product of a shape function and a partial shape function derivative over the element. More...

virtual double	IntPd (const RVector &P, int j, int k) const
	Integral of the product of a nodal function and a partial shape function derivative over the element. More...

virtual RSymMatrix	Intdd () const
	Integral of the product of two partial shape function derivatives over the element. More...

virtual double	IntFdd (int i, int j, int k, int l, int m) const
	Integral of the product of a shape function and two partial shape function derivatives over the element. More...

virtual double	IntPdd (const RVector &p, int j, int k, int l, int m) const

virtual double	IntFfd (int i, int j, int k, int l) const

virtual double	IntPfd (const RVector &p, int j, int k, int l) const

virtual double	IntUnitSphereP (const NodeList &nlist, const RVector &P) const

virtual double	IntUnitSphereFF (const NodeList &nlist, const int i, const int j) const

virtual double	IntUnitSpherePFF (const NodeList &nlist, const int i, const int j, const RVector &P) const

virtual RVector	BndIntFX (int side, double(*func)(const Point &), const NodeList &nlist) const

virtual RVector	BndIntFCos (int side, const Surface *surf, const RVector &cntcos, double sigma, double sup, const NodeList &nlist) const

virtual RVector	BndIntFCos (int side, const RVector &cntcos, double a, const NodeList &nlist) const

virtual RVector	BndIntFDelta (int side, const Surface *surf, const RVector &pos, const NodeList &nlist) const

int	GetSubsampleFD (int &n, double &wght, Point &absc, RVector &F, RDenseMatrix &D, const NodeList &nlist) const

int	GetBndSubsampleFD (int side, int &n, double &wght, Point &absc, RVector &F, RDenseMatrix &D, const NodeList &nlist) const

virtual int	GetLocalSubsampleAbsc (const Point *&absc) const

virtual int	GetBndSubsampleAbsc (int side, const Point *&absc) const

virtual RDenseMatrix	StrainDisplacementMatrix (const Point &glob) const

virtual RDenseMatrix	ElasticityStiffnessMatrix (const RDenseMatrix &D) const

virtual RDenseMatrix	ElasticityStiffnessMatrix (double E, double nu) const

RDenseMatrix	ElasticStrainDisplacement (const RVector &loc, const RDenseMatrix &gder) const

virtual RDenseMatrix	IsotropicElasticityMatrix (double E, double nu) const

virtual RVector	InitialStrainVector (double E, double nu, const RVector &e0)

virtual RVector	ThermalExpansionVector (double E, double nu, double alpha, double dT)

virtual RVector	DThermalExpansionVector (double E, double nu)

virtual int	GlobalIntersection (const NodeList &nlist, const Point &p1, const Point &p2, Point **list)=0

virtual int	Intersection (const Point &, const Point &, Point **)=0

virtual RDenseMatrix	LocaltoGlobalMat () const

virtual RDenseMatrix	GlobaltoLocalMat () const

virtual RDenseMatrix	FTAMat () const

int	Region () const

void	SetRegion (int nr)

virtual void	SplitSide (Mesh mesh, int side, int newnode, Element nbr1, Element nbr2, Element el1, Element *el2)

virtual void	Bisect (Mesh mesh, int side, int newnode, Element nbr1, Element nbr2, Element el1, Element *el2)

virtual void	MergeAndResplit (Mesh mesh, int side, int newnode, Element nbr1, Element nbr2, Element el1, Element *el2)

Protected Member Functions
virtual double	ComputeSize (const NodeList &) const =0

virtual RSymMatrix	ComputeIntDD (const NodeList &nlist) const =0

virtual RSymMatrix	ComputeBndIntFF (const NodeList &nlist) const =0

Protected Attributes
double	size

RSymMatrix	intdd

RSymMatrix	intbff

Point	bbmin

Point	bbmax

Protected Attributes inherited from Element
bool *	bndside

bool	bndel

bool	interfaceel

int	region

Additional Inherited Members
Public Attributes inherited from Element
int *	Node

ElementSubdivisionData *	subdivdata

Element **	sdnbhr

int *	sdnbhridx

Detailed Description

Base class for all unstructured element types.

Unstructured elements within a mesh differ in shape and size. Therefore they must store shape parameters on an individual element basis.

Member Function Documentation

RSymMatrix Element_Unstructured::BndIntFF ( ) const

inlinevirtual

Boundary integral of all products of two shape functions over all boundary sides of the element.

Returns: Matrix of size nNode x nNode, containing the integrals
$\int_{\partial\Omega} u_i(\vec{r}) u_j(\vec{r}) d\vec{r}$
where the integration is performed over all sides of the element that are part of the mesh surface.

Note: The returned matrix contains nonzero entries at (i,j) only if nodes i and j are both boundary nodes.; If the element does not contain boundary sides, the returned matrix is zero.

See Also: BndIntFF(int,int), BndIntFFSide

Implements Element.

double Element_Unstructured::BndIntFF	(	int	i,
		int	j
	)

inlinevirtual

Boundary integral of a product of two shape functions over all boundary sides of the element.

Parameters

i	first node index (range 0 .. nNode-1)
j	second node index (range 0 .. nNode-1)

Returns: Value of the integral
$\int_{\partial\Omega} u_i(\vec{r}) u_j(\vec{r}) d\vec{r}$
where the integration is performed over all sides of the element that are part of the mesh surface.

Note: The return value is nonzero only if both nodes i and j are boundary nodes.

See Also: BndIntFF()const, BndIntFFSide

Implements Element.

virtual bool Element_Unstructured::GContains	(	const Point &	glob,
		const NodeList &	nlist
	)		const

virtual

Checks if a global point coordinate is inside the element.

Parameters

glob	point in global coordinates
nlist	mesh node list

Returns: true if the point is inside the element, false otherwise.

See Also: LContains

Reimplemented from Element.

Reimplemented in Triangle3, Triangle3D6, Line2D2, Triangle3D3, Triangle10, Triangle3old, Triangle6, Triangle10_ip, Triangle6_ip, and Quad4.

virtual void Element_Unstructured::Initialise ( const NodeList & nlist )

virtual

Element initialisation.

Calculation of geometric element parameters, including element size and pre-calculation of geometry dependent element matrices.

Parameters

nlist Node list, containing node geometry

Note: Should be called after the node list has been generated, and whenever the node list changes.

Reimplemented from Element.

Reimplemented in Triangle3, Tetrahedron4, Triangle10, Triangle6, Triangle3D6, Tetrahedron10_ip, Tetrahedron10, Triangle10_ip, Triangle6_ip, Line2D2, Triangle3D3, Quad4, Triangle3old, Wedge6, and Wedge18inf.

RSymMatrix Element_Unstructured::IntDD ( ) const

inlinevirtual

Integrals of all products of two shape function derivatives over the element.

Returns: Matrix of size nNode x nNode, containing the integrals
$\int_\Omega \nabla u_i(\vec{r}) \nabla u_j(\vec{r}) d\vec{r}$

See Also: IntDD(int,int)const,
IntF, IntFF, IntFFF, IntFD, IntDD, IntPFF, IntPDD

Implements Element.

double Element_Unstructured::IntDD	(	int	i,
		int	j
	)		const

inlinevirtual

Integral of a product of two shape function derivatives over the element.

Parameters

i	first node index (range 0 .. nNode-1)
j	second node index (range 0 .. nNode-1)

Returns: Value of the integral
$\int_\Omega \nabla u_i(\vec{r}) \nabla u_j(\vec{r}) d\vec{r}$

See Also: IntDD()const,
IntF, IntFF, IntFFF, IntFD, IntDD, IntPFF, IntPDD

Implements Element.

virtual void Element_Unstructured::PostInitialisation ( const NodeList & nlist )

virtual

Element setup after mesh initialisation.

This method is called after all mesh elements have been initialised. It can be used to perform any element initialisation steps that require the rest of the mesh to be initialised.

Reimplemented from Element.

double Element_Unstructured::Size ( ) const

inlinevirtual

Returns the element size.

Returns: Area (for 2-D elements) or volume (for 3-D elements) of the element.

See Also: SideSize

Implements Element.

Referenced by Tetrahedron4::DetJ(), and Triangle3::DetJ().

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

/home/ucacmas/src/toast/toast_sf/toastpp-code/toast/trunk/src/libfe/element.h

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation