To store and manipulate finite element meshes. More...

Public Member Functions
	Mesh ()
	Default constructor (Empty mesh)

	Mesh (const string &file, bool bc=false, int opt=NODE_DOF, int nb_dof=1)
	Constructor using a mesh file. More...

	Mesh (real_t xmin, real_t xmax, size_t nb_el, bool bc=false, size_t p=1, size_t nb_dof=1, int c1=0, int c2=0)
	Constructor for a 1-D mesh. The domain is the interval [xmin,xmax]. More...

	Mesh (const Grid &g, int opt=QUADRILATERAL)
	Constructor for a uniform finite difference grid given by and instance of class Grid. More...

	Mesh (const Grid &g, int shape, int opt)
	Constructor of dual mesh for a uniform finite difference grid given by and instance of class Grid. More...

	Mesh (real_t xmin, real_t xmax, size_t ne, int c1, int c2, int p=1, size_t nb_dof=1)
	Constructor for a uniform 1-D finite element mesh. More...

	Mesh (real_t xmin, real_t xmax, real_t ymin, real_t ymax, size_t nx, size_t ny, int cx0, int cxN, int cy0, int cyN, int opt=0, size_t nb_dof=1)
	Constructor for a uniform 2-D structured finite element mesh. More...

	Mesh (real_t xmin, real_t xmax, real_t ymin, real_t ymax, real_t zmin, real_t zmax, size_t nx, size_t ny, size_t nz, int cx0, int cxN, int cy0, int cyN, int cz0, int czN, int opt=0, size_t nb_dof=1)
	Constructor for a uniform 3-D structured finite element mesh. More...

	Mesh (const Mesh &m, const Point< real_t > &x_bl, const Point< real_t > &x_tr)
	Constructor that extracts the mesh of a rectangular region from an initial mesh. More...

	Mesh (const Mesh &mesh, int opt, size_t dof1, size_t dof2, bool bc=false)
	Constructor that copies the input mesh and selects given degrees of freedom. More...

	Mesh (const Mesh &ms)
	Copy Constructor. More...

	~Mesh ()
	Destructor.

void	setDim (size_t dim)
	Define space dimension. Normally, between 1 and 3. More...

void	Add (Node *nd)
	Add a node to mesh. More...

void	Add (Element *el)
	Add an element to mesh. More...

void	Add (Side *sd)
	Add a side to mesh. More...

void	Add (Edge *ed)
	Add an edge to mesh. More...

Mesh &	operator*= (real_t a)
	Operator `*=` More...

void	get (const string &mesh_file)
	Read mesh data in file. More...

void	get (const string &mesh_file, int ff, int nb_dof=1)
	Read mesh data in file with giving its format. More...

void	setDOFSupport (int opt, int nb_nodes=1)
	Define supports of degrees of freedom. More...

void	setNbDOFPerNode (size_t nb_dof=1)
	Define number of degrees of freedom for each node. More...

void	setPointInDomain (Point< real_t > x)
	Define a point in the domain. This function makes sense only if boundary mesh is given without internal mesh (Case of Boundary Elements) More...

void	removeImposedDOF ()
	Eliminate equations corresponding to imposed DOF.

size_t	NumberEquations (size_t dof=0)
	Renumber Equations. More...

size_t	NumberEquations (size_t dof, int c)
	Renumber Equations. More...

int	getAllSides (int opt=0)
	Determine all mesh sides. More...

size_t	getNbSideNodes () const
	Return the number of nodes on each side.

size_t	getNbElementNodes () const
	Return the number of nodes in each element.

int	getBoundarySides ()
	Determine all boundary sides. More...

int	createBoundarySideList ()
	Create list of boundary sides. More...

int	getBoundaryNodes ()
	Determine all boundary nodes. More...

int	createInternalSideList ()
	Create list of internal sides (not on the boundary). More...

int	getAllEdges ()
	Determine all edges. More...

void	getNodeNeighborElements ()
	Create node neighboring elements. More...

void	getElementNeighborElements ()
	Create element neighboring elements. More...

void	setMaterial (int code, const string &mname)
	Associate material to code of element. More...

void	Reorder (size_t m=GRAPH_MEMORY)
	Renumber mesh nodes according to reverse Cuthill Mc Kee algorithm. More...

void	Add (size_t num, real_t *x)
	Add a node by giving its label and an array containing its coordinates. More...

void	DeleteNode (size_t label)
	Remove a node given by its label. More...

void	DeleteElement (size_t label)
	Remove an element given by its label. More...

void	DeleteSide (size_t label)
	Remove a side given by its label. More...

void	Delete (Node *nd)
	Remove a node given by its pointer. More...

void	Delete (Element *el)
	Remove a node given by its pointer. More...

void	Delete (Side *sd)
	Remove a side given by its pointer. More...

void	Delete (Edge *ed)
	Remove an edge given by its pointer. More...

void	RenumberNode (size_t n1, size_t n2)
	Renumber a node. More...

void	RenumberElement (size_t n1, size_t n2)
	Renumber an element. More...

void	RenumberSide (size_t n1, size_t n2)
	Renumber a side. More...

void	RenumberEdge (size_t n1, size_t n2)
	Renumber an edge. More...

void	setList (const vector< Node *> &nl)
	Initialize list of mesh nodes using the input vector. More...

void	setList (const vector< Element *> &el)
	Initialize list of mesh elements using the input vector. More...

void	setList (const vector< Side *> &sl)
	Initialize list of mesh sides using the input vector. More...

void	Rescale (real_t sx, real_t sy=0., real_t sz=0.)
	Rescale mesh by multiplying node coordinates by constants. More...

size_t	getDim () const
	Return space dimension.

size_t	getNbNodes () const
	Return number of nodes.

size_t	getNbMarkedNodes () const
	Return number of marked nodes.

size_t	getNbVertices () const
	Return number of vertices.

size_t	getNbDOF () const
	Return total number of degrees of freedom (DOF)

size_t	getNbEq () const
	Return number of equations.

size_t	getNbEq (int i) const
	Return number of equations for the i-th set of degrees of freedom.

size_t	getNbElements () const
	Return number of elements.

size_t	getNbSides () const
	Return number of sides.

size_t	getNbEdges () const
	Return number of sides.

size_t	getNbBoundarySides () const
	Return number of boundary sides. More...

size_t	getNbInternalSides () const
	Return number of internal sides. More...

size_t	getNbMat () const
	Return number of materials.

void	AddMidNodes (int g=0)
	Add mid-side nodes. More...

Point< real_t >	getMaxCoord () const
	Return maximum coordinates of nodes.

Point< real_t >	getMinCoord () const
	Return minimum coordinates of nodes.

void	set (Node *nd)
	Replace node in the mesh. More...

void	set (Element *el)
	Replace element in the mesh. More...

void	set (Side *sd)
	Choose side in the mesh. More...

bool	NodesAreDOF () const
	Return information about DOF type. More...

bool	SidesAreDOF () const
	Return information about DOF type. More...

bool	EdgesAreDOF () const
	Return information about DOF type. More...

bool	ElementsAreDOF () const
	Return information about DOF type. More...

int	getDOFSupport () const
	Return information on dof support Return an integer according to enumerated values: NODE_DOF, ELEMENT_DOF SIDE_DOF.

void	Deform (const Vect< real_t > &u, real_t rate=0.2)
	Deform mesh according to a displacement vector. More...

void	put (const string &mesh_file) const
	Write mesh data on file. More...

void	save (const string &mesh_file) const
	Write mesh data on file in various formats. More...

bool	withImposedDOF () const
	Return true if imposed DOF count in equations, false if not.

bool	isStructured () const
	Return true is mesh is structured, false if not.

size_t	getNodeNewLabel (size_t n) const
	Return new label of node of a renumbered node.

void	getList (vector< Node *> &nl) const
	Fill vector `nl` with list of pointers to nodes. More...

void	getList (vector< Element *> &el) const
	Fill vector `el` with list of pointers to elements. More...

void	getList (vector< Side *> &sl) const
	Fill vector `sl` with list of pointers to sides. More...

Node *	getPtrNode (size_t i) const
	Return pointer to node with label `i`.

Node &	getNode (size_t i) const
	Return refenrece to node with label `i`

Element *	getPtrElement (size_t i) const
	Return pointer to element with label `i`

Side *	getPtrSide (size_t i) const
	Return pointer to side with label `i`

Side &	getSide (size_t i) const
	Return reference to side with label `i`

Edge *	getPtrEdge (size_t i) const
	Return pointer to edge with label `i`

size_t	getNodeLabel (size_t i) const
	Return label of `i`-th node. More...

size_t	getElementLabel (size_t i) const
	Return label of `i`-th element. More...

size_t	getSideLabel (size_t i) const
	Return label of `i`-th side. More...

size_t	getEdgeLabel (size_t i) const
	Return label of `i`-th edge. More...

int	getShape () const
	Determine shape of elements Return Shape index (see enum ElementShape) if all elements have the same shape, 0 if not.

Element *	operator() (size_t i) const
	Operator () : Return pointer to i-th element.

Node *	operator[] (size_t i) const
	Operator [] : Return pointer to i-th node.

size_t	operator() (size_t i, size_t n) const
	Operator () : Return pointer to i-th node of n-th element.

Mesh &	operator= (Mesh &ms)
	Operator = : Assign a Mesh instance.

Friends
void	Refine (Mesh &in_mesh, Mesh &out_mesh)
	Refine mesh. Subdivide each triangle into 4 subtriangles. This member function is valid for 2-D triangular meshes only. More...

Detailed Description

To store and manipulate finite element meshes.

Class Mesh enables defining as an object a finite element mesh. A finite element mesh is characterized by its nodes, elements and sides. Each of these types of data constitutes a class in the OFELI library.

The standard procedure to introduce the finite element mesh is to provide an input file containing its data. For this, we have defined our own mesh data file (following the XML syntax). Of course, a developer can write his own function to read his finite element mesh file using the methods in Mesh.

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ Mesh() [1/10]

Mesh	(	const string &	file,
		bool	bc = `false`,
		int	opt = `NODE_DOF`,
		int	nb_dof = `1`
	)

Constructor using a mesh file.

Parameters

[in]	file	File containing mesh data. The extension of the file yields the file format: The extension .m implies OFELI file format and .msh implies GMSH msh file.
[in]	bc	Flag to remove (true) or not (false) imposed Degrees of Freedom [default: false]
[in]	opt	Type of DOF support: To choose among enumerated values `NODE_DOF`, `SIDE_DOF` or `ELEMENT_DOF`. Say if degrees of freedom (unknowns) are supported by nodes, sides or elements.
[in]	nb_dof	Number of degrees of freedom per node [Default: `1`].

◆ Mesh() [2/10]

Mesh	(	real_t	xmin,
		real_t	xmax,
		size_t	nb_el,
		bool	bc = `false`,
		size_t	p = `1`,
		size_t	nb_dof = `1`,
		int	c1 = `0`,
		int	c2 = `0`
	)

Constructor for a 1-D mesh. The domain is the interval [xmin,xmax].

Parameters

[in]	xmin	Value of xmin
[in]	xmax	Value of xmax
[in]	nb_el	Number of elements to generate
[in]	bc	Flag to remove (true) or not (false) imposed Degrees of Freedom [default: false]
[in]	p	Degree of finite element polynomial [default: 1]
[in]	nb_dof	Number of degrees of freedom for each node [default: 1]
[in]	c1	Code to assign to first node (at `x=xmin`) [default: 0]
[in]	c2	Code to assign to last node (at `x=xmax`) [default: 0]

◆ Mesh() [3/10]

Mesh	(	const Grid &	g,
		int	opt = `QUADRILATERAL`
	)

Constructor for a uniform finite difference grid given by and instance of class Grid.

Parameters

[in]	g	Grid instance
[in]	opt	Optional value to say which type of elements to generate TRIANGLE: Mesh elements are triangles QUADRILATERAL: Mesh elements are quadrilaterals [default]

◆ Mesh() [4/10]

Mesh	(	const Grid &	g,
		int	shape,
		int	opt
	)

Constructor of dual mesh for a uniform finite difference grid given by and instance of class Grid.

Parameters

[in]	g	Grid instance
[in]	shape	Value to say which type of elements to generate TRIANGLE: Mesh elements are triangles QUADRILATERAL: Mesh elements are quadrilaterals [default]
[in]	opt	This argument can take any value. It is here only to distinguish from the other constructor using Grid instance.

Remarks: This constructor is to be used to obtain a dual mesh from a structured grid. It is mainly useful if a cell centered finite volume method is used.

◆ Mesh() [5/10]

Mesh	(	real_t	xmin,
		real_t	xmax,
		size_t	ne,
		int	c1,
		int	c2,
		int	p = `1`,
		size_t	nb_dof = `1`
	)

Constructor for a uniform 1-D finite element mesh.

The domain is the line (xmin,xmax)

Parameters

[in]	xmin	Minimal coordinate
[in]	xmax	Maximal coordinate
[in]	ne	Number of elements
[in]	c1	Code for the first node (x=xmin)
[in]	c2	Code for the last node (x=xmax)
[in]	p	Degree of approximation polynomial [Default: `1`].
[in]	nb_dof	Number of degrees of freedom per node [Default: `1`].

Remarks: The option p can be set to 1 if the user intends to use finite differences.

◆ Mesh() [6/10]

Mesh	(	real_t	xmin,
		real_t	xmax,
		real_t	ymin,
		real_t	ymax,
		size_t	nx,
		size_t	ny,
		int	cx0,
		int	cxN,
		int	cy0,
		int	cyN,
		int	opt = `0`,
		size_t	nb_dof = `1`
	)

Constructor for a uniform 2-D structured finite element mesh.

The domain is the rectangle (xmin,xmax)x(ymin,ymax)

Parameters

[in]	xmin	Minimal x-coordinate
[in]	xmax	Maximal x-coordinate
[in]	ymin	Minimal y-coordinate
[in]	ymax	Maximal y-coordinate
[in]	nx	Number of subintervals on the x-axis
[in]	ny	Number of subintervals on the y-axis
[in]	cx0	Code for nodes generated on the line x=x0 if >0, for sides on this line if <0
[in]	cxN	Code for nodes generated on the line x=xN if >0, for sides on this line if <0
[in]	cy0	Code for nodes generated on the line y=y0 if >0, for sides on this line if <0
[in]	cyN	Code for nodes generated on the line y=yN if >0, for sides on this line if <0
[in]	opt	Flag to generate elements as well (if not zero) [Default: `0`]. If the flag is not 0, it can take one of the enumerated values: TRIANGLE or QUADRILATERAL, with obvious meaning.
[in]	nb_dof	Number of degrees of freedom per node [Default: `1`].

Remarks: The option opt can be set to 0 if the user intends to use finite differences.

◆ Mesh() [7/10]

Mesh	(	real_t	xmin,
		real_t	xmax,
		real_t	ymin,
		real_t	ymax,
		real_t	zmin,
		real_t	zmax,
		size_t	nx,
		size_t	ny,
		size_t	nz,
		int	cx0,
		int	cxN,
		int	cy0,
		int	cyN,
		int	cz0,
		int	czN,
		int	opt = `0`,
		size_t	nb_dof = `1`
	)

Constructor for a uniform 3-D structured finite element mesh.

The domain is the parallepiped (xmin,xmax)x(ymin,ymax)x(zmin,zmax)

Parameters

[in]	xmin	Minimal x-coordinate
[in]	xmax	Maximal x-coordinate
[in]	ymin	Minimal y-coordinate
[in]	ymax	Maximal y-coordinate
[in]	zmin	Minimal z-coordinate
[in]	zmax	Maximal z-coordinate
[in]	nx	Number of subintervals on the x-axis
[in]	ny	Number of subintervals on the y-axis
[in]	nz	Number of subintervals on the z-axis
[in]	cx0	Code for nodes generated on the line x=xmin if >0, for sides on this line if <0
[in]	cxN	Code for nodes generated on the line x=xmax if >0, for sides on this line if <0
[in]	cy0	Code for nodes generated on the line y=ymin if >0, for sides on this line if <0
[in]	cyN	Code for nodes generated on the line y=ymax if >0, for sides on this line if <0
[in]	cz0	Code for nodes generated on the line z=zmin if >0, for sides on this line if <0
[in]	czN	Code for nodes generated on the line z=zmax if >0, for sides on this line if <0
[in]	opt	Flag to generate elements as well (if not zero) [Default: 0]. If the flag is not 0, it can take one of the enumerated values: HEXAHEDRON or TETRAHEDRON, with obvious meaning.
[in]	nb_dof	Number of degrees of freedom per node [Default: `1`].

Remarks: The option opt can be set to 0 if the user intends to use finite differences.

◆ Mesh() [8/10]

Mesh	(	const Mesh &	m,
		const Point< real_t > &	x_bl,
		const Point< real_t > &	x_tr
	)

Constructor that extracts the mesh of a rectangular region from an initial mesh.

This constructor is useful for zooming purposes for instance.

Parameters

[in]	m	Initial mesh from which the submesh is extracted
[in]	x_bl	Coordinate of bottom left vertex of the rectangle
[in]	x_tr	Coordinate of top right vertex of the rectangle

◆ Mesh() [9/10]

Mesh	(	const Mesh &	mesh,
		int	opt,
		size_t	dof1,
		size_t	dof2,
		bool	bc = `false`
	)

Constructor that copies the input mesh and selects given degrees of freedom.

This constructor is to be used for coupled problems where each subproblem uses a choice of degrees of freedom.

Parameters

[in]	mesh	Initial mesh from which the submesh is extracted
[in]	opt	Type of DOF support: To choose among enumerated values `NODE_DOF`, `SIDE_DOF` or `ELEMENT_DOF`.
[in]	dof1	Label of first degree of freedom to select to the output mesh
[in]	dof2	Label of last degree of freedom to select to the output mesh
[in]	bc	Flag to remove (`true`) or not (`false`) imposed Degrees of Freedom [Default: `false`]

◆ Mesh() [10/10]

Mesh ( const Mesh & ms )

Copy Constructor.

Parameters

[in] ms Mesh instance to copy

Member Function Documentation

◆ Add() [1/5]

void Add ( Node * nd )

Add a node to mesh.

Parameters

[in] nd Pointer to Node to add

◆ Add() [2/5]

void Add ( Element * el )

Add an element to mesh.

Parameters

[in] el Pointer to Element to add

◆ Add() [3/5]

void Add ( Side * sd )

Add a side to mesh.

Parameters

[in] sd Pointer to Side to add

◆ Add() [4/5]

void Add ( Edge * ed )

Add an edge to mesh.

Parameters

[in] ed Pointer to Edge to add

◆ Add() [5/5]

void Add	(	size_t	num,
		real_t *	x
	)

Add a node by giving its label and an array containing its coordinates.

Parameters

[in]	num	Label of node to add
[in]	x	C-array of node coordinates

◆ AddMidNodes()

void AddMidNodes ( int g = 0 )

Add mid-side nodes.

This is function is valid for triangles only

Parameters

[in] g Option to say of barycentre node is to be added (>0) or not (=0)

◆ createBoundarySideList()

int createBoundarySideList ( )

Create list of boundary sides.

This function is useful to loop over boundary sides without testing Once this one is called, the function getNbBoundarySides() is available. Moreover, looping over boundary sides is available via the member functions topBoundarySide() and getBoundarySide()

Returns: Number of boundary sides.

◆ createInternalSideList()

int createInternalSideList ( )

Create list of internal sides (not on the boundary).

This function is useful to loop over internal sides without testing Once this one is called, the function getNbInternalSides() is available. Moreover, looping over internal sides is available via the member functions topInternalSide() and getInternalSide()

Returns: n Number of internal sides.

◆ Deform()

void Deform	(	const Vect< real_t > &	u,
		real_t	rate = `0.2`
	)

Deform mesh according to a displacement vector.

This function modifies node coordinates according to given displacement vector and given rate

Parameters

[in]	u	Displacement vector
[in]	rate	Maximal rate of deformation of resulting mesh. Its default value is 0.2, i.e. The resulting mesh has a maximum of deformation rate of 20%