Mesh Class Reference
[Finite Element Mesh]

#include <Mesh.h>

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.

Although each instance of classes Element, Node and Side can be accessed individually, it is highly recommended for a developer to modify any information about these classes only by using the Mesh members. Otherwise, the modifications would have no effect on the global mesh.

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 (called an MDF file). Of course, a developer can write his own function to read his finite element mesh file using the methods in Mesh.


Public Types
enum	ElementShape { LINE, TRIANGLE, QUADRILATERAL, TETRAHEDRON, HEXAHEDRON, PENTAHEDRON }
Public Member Functions
void	Add (size_t num, double *x)
	Add a node by giving its label and an array containing its coordinates.
void	Add (Edge *ed)
	Add an edge to mesh.
void	Add (Side *sd)
	Add a side to mesh.
void	Add (Element *el)
	Add an element to mesh.
void	Add (Node *nd)
	Add a node to mesh.
void	AddMidNodes (int g=0)
	Add mid-side nodes.
void	Bput (const string &mesh_file) const
	Write mesh data on a binary file.
int	createBoundarySideList ()
	Create list of boundary sides.
int	createInternalSideList ()
	Create list of internal sides (not on the boundary).
void	Delete (Edge *ed)
	Remove an edge given by its pointer.
void	Delete (Side *sd)
	Remove a side given by its pointer.
void	Delete (Element *el)
	Remove a node given by its pointer.
void	Delete (Node *nd)
	Remove a node given by its pointer.
void	DeleteElement (size_t label)
	Remove an element given by its label.
void	DeleteNode (size_t label)
	Remove a node given by its label.
void	DeleteSide (size_t label)
	Remove a side given by its label.
bool	EdgesAreDOF () const
	Return information about DOF type.
bool	ElementsAreDOF () const
	Return information about DOF type.
void	EliminateImposedDOF ()
	Eliminate equations corresponding to imposed DOF.
void	get (const string &mesh_file)
	Read mesh data in file written in MDF Format.
int	getAllEdges ()
	Determine all edges.
int	getAllSides (int opt=1)
	Determine all mesh sides.
Edge *	getBoundaryEdge ()
	Return pointer to current boundary edge and move to next one (Non constant version).
const Edge *	getBoundaryEdge () const
	Return pointer to current boundary edge and move to next one (Constant version).
Side *	getBoundarySide ()
	Return pointer to current boundary side and move to next one (Non constant version).
const Side *	getBoundarySide () const
	Return pointer to current boundary side and move to next one (Constant version).
int	getBoundarySides (int opt=1)
	Determine all boundary sides.
size_t	getDim () const
	Return space dimension.
Edge *	getEdge ()
	Return pointer to current edge and move to next one (Non constant version).
const Edge *	getEdge () const
	Return pointer to current edge and move to next one (Constant version).
Edge &	getEdge (size_t i) const
	Return reference to edge with label i.
size_t	getEdgeLabel (size_t i) const
	Return label of i-th edge.
Element *	getElement ()
	Return pointer to current element and move to next one (Non constant version).
const Element *	getElement () const
	Return pointer to current element and move to next one (Constant version).
Element &	getElement (size_t i) const
	Return reference to element with label i.
size_t	getElementLabel (size_t i) const
	Return label of i-th element.
void	getElementNeighborElements ()
	Create element neighboring elements.
Side *	getInternalSide ()
	Return pointer to current internal side and move to next one (Non constant version).
const Side *	getInternalSide () const
	Return pointer to current internal side and move to next one (Constant version).
Node *	getMarkedNode ()
	Return pointer to current marked node and move to next one (Non constant version).
const Node *	getMarkedNode () const
	Return pointer to current marked node and move to next one (Constant version).
Point< double >	getMaxCoord () const
	Return maximum coordinates of nodes.
Point< double >	getMinCoord () const
	Return minimum coordinates of nodes.
size_t	getNbBoundarySides () const
	Return number of boundary sides.
size_t	getNbDOF () const
	Return total number of degrees of freedom (DOF).
size_t	getNbEdges () const
	Return number of sides.
size_t	getNbElements () const
	Return number of elements.
size_t	getNbEq () const
	Return number of equations.
size_t	getNbInternalSides () const
	Return number of internal sides.
size_t	getNbMarkedNodes () const
	Return number of marked nodes.
size_t	getNbMat () const
	Return number of materials.
size_t	getNbNodes () const
	Return number of nodes.
size_t	getNbSides () const
	Return number of sides.
size_t	getNbVertices () const
	Return number of vertices.
Node *	getNode ()
	Return pointer to current node and move to next one (Non constant version).
const Node *	getNode () const
	Return pointer to current node and move to next one (Constant version).
Node &	getNode (size_t i) const
	Return refenrece to node with label i.
size_t	getNodeLabel (size_t i) const
	Return label of i-th node.
void	getNodeNeighborElements ()
	Create node neighboring elements.
size_t	getNodeNewLabel (size_t n) const
	Return new label of node of a renumbered node.
Edge *	getPtrEdge (size_t i) const
	Return pointer to edge with label i.
Element *	getPtrElement (size_t i) const
	Return pointer to element with label i.
Node *	getPtrNode (size_t i) const
	Return pointer to node with label i.
Side *	getPtrSide (size_t i) const
	Return pointer to side with label i.
int	getShape () const
	Determine shape of elements Returns Shape index (see enum ElementShape) if all elements have the same shape, 0 if not.
Side *	getSide ()
	Return pointer to current side and move to next one (Non constant version).
const Side *	getSide () const
	Return pointer to current side and move to next one (Constant version).
Side &	getSide (size_t i) const
	Return reference to side with label i.
size_t	getSideLabel (size_t i) const
	Return label of i-th side.
int	getVerbose () const
	Return Verbose Parameter.
bool	isStructured () const
	Return true is mesh is structured, false if not.
	Mesh (const Mesh &ms)
	Copy Constructor.
	Mesh (const Mesh &m, const Point< double > &x_bl, const Point< double > &x_tr)
	Constructor that extracts the mesh of a rectangular region from an initial mesh.
	Mesh (double x_min, double x_max, double y_min, double y_max, size_t nx, size_t ny, int c1, int c2, int c3, int c4, int with_elements=0)
	Constructor for a uniform finite difference grid.
	Mesh (const Grid &g, int opt=QUADRILATERAL)
	Constructor for a uniform finite difference grid given by and instance of class Grid.
	Mesh (double Lmin, double Lmax, size_t nb_el, size_t p=1, size_t nb_dof=1)
	Constructor for a 1-D mesh.
	Mesh (const string &file, bool bc=false, int opt=NODE_DOF)
	Constructor using a mesh file (MDF format).
	Mesh ()
	Default constructor (Empty mesh).
bool	NodesAreDOF () const
	Return information about DOF type.
size_t	NumberEquations (size_t dof=0)
	Renumber Equations.
size_t	operator() (size_t i, size_t n)
	Operator () : Returns pointer to i-th node of n-th element.
Element *	operator() (size_t i)
	Operator () : Returns pointer to i-th element.
Mesh &	operator= (Mesh &ms)
	Operator = : Assign a Mesh instance.
Node *	operator[] (size_t i)
	Operator [] : Returns pointer to i-th node.
void	put (const string &mesh_file) const
	Write mesh data on an MDF file.
void	Refresh ()
	Refresh mesh after deletions.
void	removeImposedDOF ()
	Eliminate equations corresponding to imposed DOF.
void	RenumberEdge (size_t n1, size_t n2)
	Renumber an edge.
void	RenumberElement (size_t n1, size_t n2)
	Renumber an element.
void	RenumberNode (size_t n1, size_t n2)
	Renumber a node.
void	RenumberSide (size_t n1, size_t n2)
	Renumber a side.
void	Reorder (size_t m=GRAPH_MEMORY)
	Renumber mesh nodes according to reverse Cuthill Mc Kee algorithm.
void	setBoundaryOrientation ()
	Orient boundary sides in the direct sense.
void	setDim (size_t dim)
	Define space dimension.
void	setDOFSupport (int opt)
	Define supports of degrees of freedom.
void	setElementView (size_t n1, size_t n2)
	Set viewing window for elements.
void	setMaterial (int code, const string &mname)
	Associate material to code of element.
void	setNodeView (size_t n1, size_t n2)
	Set viewing window for nodes.
void	setPointInDomain (Point< double > x)
	Define a point in the domain.
void	setSideView (size_t n1, size_t n2)
	Set viewing window for sides.
void	setVerbose (int verb)
	Define Verbose Parameter.
bool	SidesAreDOF () const
	Return information about DOF type.
void	topBoundaryEdge () const
	Reset list of boundary edges at its top position (Constant version).
void	topBoundaryEdge ()
	Reset list of boundary edges at its top position (Non constant version).
void	topBoundarySide () const
	Reset list of boundary sides at its top position (Constant version).
void	topBoundarySide ()
	Reset list of boundary sides at its top position (Non constant version).
void	topEdge () const
	Reset list of edges at its top position (Constant version).
void	topEdge ()
	Reset list of edges at its top position (Non constant version).
void	topElement () const
	Reset list of elements at its top position (Constant version).
void	topElement ()
	Reset list of elements at its top position (Non constant version).
void	topInternalSide () const
	Reset list of internal sides at its top position (Constant version).
void	topInternalSide ()
	Reset list of intrenal sides at its top position (Non constant version).
void	topMarkedNode () const
	Reset list of marked nodes at its top position (Constant version).
void	topMarkedNode ()
	Reset list of marked nodes at its top position (Non constant version).
void	topNode () const
	Reset list of nodes at its top position (Constant version).
void	topNode ()
	Reset list of nodes at its top position (Non constant version).
void	topSide () const
	Reset list of sides at its top position (Constant version).
void	topSide ()
	Reset list of sides at its top position (Non constant version).
bool	withImposedDOF () const
	Return true if imposed DOF count in equations, false if not.
	~Mesh ()
	Destructor.
Friends
void	Refine (Mesh &in_mesh, Mesh &out_mesh)
	Refine mesh.

Member Enumeration Documentation

enum ElementShape

Enumerate list for element shapes

Enumerator:

LINE	Elements are segment lines
TRIANGLE	Elements are triangles
QUADRILATERAL	Elements are quadrilaterals
TETRAHEDRON	Elements are tetrahedra
HEXAHEDRON	Elements are hexahedra (bricks)
PENTAHEDRON	Elements are pentahedra (prisms)

Constructor & Destructor Documentation

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

Constructor using a mesh file (MDF format).

Parameters:

`[in]`	file	File containing mesh data in MDF format
`[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.

Mesh	(	double	Lmin,
		double	Lmax,
		size_t	nb_el,
		size_t	p = `1`,
		size_t	nb_dof = `1`
	)

Constructor for a 1-D mesh.

The domain is the interval [Lmin,Lmax]

Parameters:

`[in]`	Lmin	First end of the interval
`[in]`	Lmax	Second end of the interval
`[in]`	nb_el	Number of elements to generate
`[in]`	p	Degree of finite element polynomial (Default = 1)
`[in]`	nb_dof	Number of degrees of freedom for each node (Default = 1)

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	(	double	x_min,
		double	x_max,
		double	y_min,
		double	y_max,
		size_t	nx,
		size_t	ny,
		int	c1,
		int	c2,
		int	c3,
		int	c4,
		int	with_elements = `0`
	)

Constructor for a uniform finite difference grid.

The domain is the rectangle (x_min,x_max)x(y_min,y_max)

Parameters:

`[in]`	x_min	Min. value for x coordinate
`[in]`	x_max	Max. value for y coordinate
`[in]`	y_min	Min. value for x coordinate
`[in]`	y_max	Max. value for y coordinate
`[in]`	nx	Number of subintervals on the x-axis
`[in]`	ny	Number of subintervals on the y-axis
`[in]`	c1	Code for nodes generated on the line y=y_min
`[in]`	c2	Code for nodes generated on the line x=x_max
`[in]`	c3	Code for nodes generated on the line y=y_max
`[in]`	c4	Code for nodes generated on the line x=x_min
`[in]`	with_elements	Flag to generate elements as well (if not zero) ( Default = 0).

Mesh	(	const Mesh &	m,
		const Point< double > &	x_bl,
		const Point< double > &	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 ( const Mesh & ms )

Copy Constructor.

Parameters:

[in] ms Mesh instance to copy

Member Function Documentation

void Add	(	size_t	num,
		double *	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

void Add ( Edge * ed )

Add an edge to mesh.

Parameters:

[in] ed Pointer to Edge to add

void Add ( Side * sd )

Add a side to mesh.

Parameters:

[in] sd Pointer to Side to add

void Add ( Element * el )

Add an element to mesh.

Parameters:

[in] el Pointer to Element to add

void Add ( Node * nd )

Add a node to mesh.

Parameters:

[in] nd Pointer to Node to add

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)

void Bput ( const string & mesh_file ) const

Write mesh data on a binary file.

Parameters:

[in] mesh_file Mesh file name

int createBoundarySideList ( )

Create list of boundary sides.

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

Return values:

n

Number of boundary sides.

int createInternalSideList ( )

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

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

Return values:

n

Number of internal sides.

void Delete ( Edge * ed )

Remove an edge given by its pointer.