Inheritance diagram for Triangle10_ip:

Public Member Functions
	Triangle10_ip (const Triangle10_ip &el)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

int	Intersection (const Point &p1, const Point &p2, Point **pi)

Public Member Functions inherited from Element_Unstructured_2D
	Element_Unstructured_2D (const Element_Unstructured_2D &el)

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

Public Member Functions inherited from Element_Unstructured
	Element_Unstructured (const Element_Unstructured &el)

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)

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.

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

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

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	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 double	SideSize (int side, const NodeList &nlist) const
	Returns the size of an element side. 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	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 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 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	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 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
double	Jacobian (const Point &loc, RDenseMatrix &J) const

double	IJacobian (const Point &loc, RDenseMatrix &IJ) const

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...

double	ComputeSize (const NodeList &nlist) const

RSymMatrix	ComputeIntDD (const NodeList &nlist) const

RSymMatrix	ComputeBndIntFF (const NodeList &nlist) const

Protected Attributes
double	a0

double	b0

double	c0

double	a1

double	b1

double	c1

double	a2

double	b2

double	c2

Protected Attributes inherited from Element_Unstructured
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

Member Function Documentation

double Triangle10_ip::BndIntFFSide	(	int	i,
		int	j,
		int	sd
	)

inlinevirtual

Surface integral of a product of two shape functions over one of the sides of the element.

Parameters

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

Note: Nodes i and j must both belong to side sd.

See Also: BndIntFF()const, BndIntFF(int,int)

Implements Element.

RSymMatrix Triangle10_ip::BndIntPFF ( const RVector & P ) const

inlinevirtual

Surface integrals of all products of a nodal function and two shape functions over all boundary sides of the element.

Parameters

P	nodal function coefficients over the mesh

Returns: Matrix of size nNode x nNode, containing the integrals
$\int_{\partial\Omega} p(\vec{r}) u_i(\vec{r}) u_j(\vec{r}) d\vec{r} = \sum_k p_k \int_{\partial\Omega} u_i(\vec{r}) u_j(\vec{r}) u_k(\vec{r}) d\vec{r}$

Note: If the element does not contain boundary sides, the returned matrix is zero.

See Also: BndIntPFF(int,int,const RVector&)const, BndIntFF

Implements Element.

double Triangle10_ip::BndIntPFF	(	int	i,
		int	j,
		const RVector &	P
	)		const

virtual

Surface integrals of a product of a nodal function and 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)
P	nodal function coefficients over the mesh

Returns: Value of the integral
$\int_{\partial\Omega} p(\vec{r}) u_i(\vec{r}) u_j(\vec{r}) d\vec{r} = \sum_k p_k \int_{\partial\Omega} u_i(\vec{r}) u_j(\vec{r}) u_k(\vec{r}) d\vec{r}$

Note: If the element does not contain boundary sides, the returned matrix is zero.

See Also: BndIntPFF(const RVector&)const, BndIntFF

Implements Element.

double Triangle10_ip::DetJ	(	const Point &	loc,
		const NodeList *	nlist = `0`
	)		const

protectedvirtual

Returns determinant of Jacobian at a given point inside the element in the local frame.

Parameters

loc	evaluation point in local coordinates
nlist	node list of the associated mesh

Returns: det(J)

Reimplemented from Element.

RVector Triangle10_ip::DirectionCosine	(	int	side,
		RDenseMatrix &	jacin
	)

virtual

Returns the direction cosines of a side normal.

Parameters

side	side index (>= 0)
jacin	inverse of Jacobian

Returns: direction cosines of the normal to side in global coordinates.

See Also: LNormal

Implements Element.

bool Triangle10_ip::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_Unstructured.

unsigned long Triangle10_ip::GetCaps ( ) const

inlinevirtual

Returns element capability flags.

Returns: Bitflags for element caps. (see Element capability flags)

Implements Element.

References ELCAPS_CURVED_BOUNDARY.

void Triangle10_ip::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_Unstructured.

double Triangle10_ip::IntF ( int i ) const

inlinevirtual

Integral of a shape function over the element.

Parameters

i	node index (range: 0 .. nNode-1)

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

See Also: IntFF, IntFFF, IntDD, IntFD

Implements Element.

double Triangle10_ip::IntFDD	(	int	i,
		int	j,
		int	k
	)		const

virtual

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

Parameters

i	node index for shape function
j	first node index for shape function derivative
k	second node index for shape function derivative

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

See Also: IntDD, IntFD, IntPDD

Implements Element.

RSymMatrix Triangle10_ip::IntFF ( ) const

virtual

Integrals of all products of two shape functions over the element.

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

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

Implements Element.

double Triangle10_ip::IntFF	(	int	i,
		int	j
	)		const

virtual

Integral of a product of two shape functions 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
$\int_\Omega u_i(\vec{r}) u_j(\vec{r}) d\vec{r}$

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

Implements Element.

double Triangle10_ip::IntFFF	(	int	i,
		int	j,
		int	k
	)		const

virtual

Integral of a product of three shape functions over the element.

Parameters

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

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

See Also: IntF, IntFF, IntDD, IntFD

Implements Element.

RSymMatrix Triangle10_ip::IntPDD ( const RVector & P ) const

inlinevirtual

All integrals of products of a nodal function and two shape function derivatives over the element.

Parameters

P	nodal function coefficients over the mesh

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

See Also: IntPDD(int,int,const RVector&)const, IntFDD, IntFD, IntPFF

Implements Element.

double Triangle10_ip::IntPDD	(	int	i,
		int	j,
		const RVector &	P
	)		const

virtual

Integrals of a product of a nodal function and two shape function derivatives over the element.

Parameters

i	first node index
j	second node index
P	nodal function coefficients over the mesh

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

See Also: IntPDD(const RVector&)const, IntFDD, IntFD, IntPFF

Implements Element.

RSymMatrix Triangle10_ip::IntPFF ( const RVector & P ) const

virtual

Integrals of all products of two shape functions and a nodal function over the element.

Parameters

P	nodal basis coefficients of a function defined over the mesh

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

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

Implements Element.

double Triangle10_ip::IntPFF	(	int	i,
		int	j,
		const RVector &	P
	)		const

virtual

Integral of a product of two shape functions and a nodal function over the element.

Parameters

i	first node index (range 0 .. nNode-1)
j	second node index (range 0 .. nNode-1)
P	nodal basis coefficients of a function defined over the mesh

Returns: The value of the integral
$\int_\Omega p(\vec{r}) u_i(\vec{r}) u_j(\vec{r}) d\vec{r} = \sum_k p_k \int_\Omega u_i(\vec{r}) u_j(\vec{r}) u_k(\vec{r}) d\vec{r}$

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

Implements Element.

bool Triangle10_ip::LContains	(	const Point &	loc,
		bool	pad = `true`
	)		const

virtual

Checks if a local point coordinate is inside the element.

Parameters

loc	point in local coordinates
pad	Apply padding to the element to ensure that boundary points are considered inside.

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

Note: If pad == false, then the status of points exactly on the element boundary is undefined. They may or may not be considered inside. Use pad = true to ensure that they are regarded as inside.

See Also: GContains

Implements Element.

const RVector& Triangle10_ip::LNormal ( int side ) const

virtual

Returns a side normal in local coordinates.

Parameters

side	side index (>= 0)

Returns: Normal to side in local element coordinates.

See Also: DirectionCosine

Implements Element.

Point Triangle10_ip::Local	(	const NodeList &	nlist,
		const Point &	glob
	)		const

virtual

Maps a point from global to local element coordinates.

Parameters

nlist	mesh node list
glob	global point coordinates

Returns: Point coordinates in the element's local reference system.

Note: Point glob should have dimension Dimension(); glob does not have to be located inside the element.

See Also: NodeLocal, Global

Implements Element.

RDenseMatrix Triangle10_ip::LocalShapeD ( const Point & loc ) const

virtual

Returns the values of the shape function derivatives at a local point.

Parameters

loc	point coordinates in the local element system

Returns: Matrix (size nNode x Dimension) of shape function derivatives at the point for all shape functions associated with the element.

See Also: LocalShapeF, GlobalShapeF, GlobalShapeD

Implements Element.

RVector Triangle10_ip::LocalShapeF ( const Point & loc ) const

virtual

Returns the values of the shape functions at a local point.

Parameters

loc	point coordinates in the local element system

Returns: Vector (size nNode) of shape function values at the point for all shape functions associated with the element.

See Also: GlobalShapeF, LocalShapeD, GlobalShapeD

Implements Element.

int Triangle10_ip::nNode ( ) const

inlinevirtual

Returns the number of nodes associated with the element.

Returns: Number of nodes

Implements Element.

Point Triangle10_ip::NodeLocal ( int node ) const

virtual

Returns the local coordinates of an element node.

Parameters

node	node index (>= 0)

Returns: Node coordinates in the element's local reference system.

See Also: Local, Global

Implements Element.

int Triangle10_ip::nSide ( ) const

inlinevirtual

Returns the number of element sides.

Returns: Number of sides

Note: For 3-D elements, this returns the number of element faces (4 for tetrahedra, 6, for voxels, etc). For 2-D elements, it returns the number of boundary segments (3 for triangles, 4 for pixels, etc.)

Implements Element.

int Triangle10_ip::nSideNode ( int side ) const

inlinevirtual

Returns the number of vertices associated with a side.

Parameters

side	side index (>= 0)

Returns: Number of vertices connected to the side.

See Also: nSide, nNode, nSideNode

Implements Element.

int Triangle10_ip::SideNode	(	int	side,
		int	node
	)		const

virtual

Returns relative node index for a side vertex.

Parameters

side	side index (>= 0)
node	side node index (>= 0)

Returns: Relative node index

Note: Returns the node index for one of the vertices of a side.; side must be in the range 0 .. nSide()-1; node must be in the range 0 .. nSideNode (side); The return value is in the range 0 .. nNode()-1

See Also: nNode, nSide, nSideNode

Implements Element.

BYTE Triangle10_ip::Type ( ) const

inlinevirtual

Returns an element type identifier.

Returns: Element type identifier (see Element type identifiers).

Implements Element.

References ELID_TRI10_IP.

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

/home/ucacmas/src/toast/toast_sf/toastpp-code/toast/trunk/src/libfe/tri10_ip.h

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Member Function Documentation