Mesh Class Reference

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

List of all members.

Public Member Functions
	Mesh ()
	Default constructor (Empty mesh)
	Mesh (const string &file, bool bc=false, int opt=NODE_DOF)
	Constructor using a mesh file.
	Mesh (double L, size_t nb_el, size_t p=1, size_t nb_dof=1)
	Constructor for a 1-D mesh. The domain is the interval [0,L].
	Mesh (const Grid &g, int opt=QUADRILATERAL)
	Constructor for a uniform finite difference grid given by and instance of class Grid.
	Mesh (double xL, double yL, size_t nx, size_t ny, int c1, int c2, int c3, int c4, int opt=0)
	Constructor for a uniform finite difference grid.
	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 (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.
	Mesh (const Mesh &ms)
	Copy Constructor.
	~Mesh ()
	Destructor.
void	setDim (size_t dim)
	Define space dimension. Normally, between 1 and 3.
void	setVerbose (int verb)
	Define Verbose Parameter. Controls output details.
void	Add (Node *nd)
	Add a node to mesh.
void	Add (Element *el)
	Add an element to mesh.
void	Add (Side *sd)
	Add a side to mesh.
void	Add (Edge *ed)
	Add an edge to mesh.
void	get (const string &mesh_file)
	Read mesh data in file.
void	setDOFSupport (int opt, int nb_nodes=1)
	Define supports of degrees of freedom.
void	setPointInDomain (Point< double > x)
	Define a point in the domain. This function makes sense only if boundary mesh is given without internal mesh (Case of Boundary Elements)
void	removeImposedDOF ()
	Eliminate equations corresponding to imposed DOF.
void	EliminateImposedDOF ()
	Eliminate equations corresponding to imposed DOF.
size_t	NumberEquations (size_t dof=0)
	Renumber Equations.
size_t	NumberEquations (size_t dof, int c)
	Renumber Equations.
int	getAllSides (int opt=0)
	Determine all mesh sides.
int	getNbSideNodes () const
	Return the number of nodes on each side.
int	getNbElementNodes () const
	Return the number of nodes in each element.
int	getBoundarySides ()
	Determine all boundary sides.
int	createBoundarySideList ()
	Create list of boundary sides.
int	getBoundaryNodes ()
	Determine all boundary nodes.
int	createInternalSideList ()
	Create list of internal sides (not on the boundary).
int	getAllEdges ()
	Determine all edges.
void	getNodeNeighborElements ()
	Create node neighboring elements.
void	getElementNeighborElements ()
	Create element neighboring elements.
void	setMaterial (int code, const string &mname)
	Associate material to code of element.
void	Reorder (size_t m=1000000)
	Renumber mesh nodes according to reverse Cuthill Mc Kee algorithm.
void	Add (size_t num, double *x)
	Add a node by giving its label and an array containing its coordinates.
void	DeleteNode (size_t label)
	Remove a node given by its label.
void	DeleteElement (size_t label)
	Remove an element given by its label.
void	DeleteSide (size_t label)
	Remove a side given by its label.
void	Delete (Node *nd)
	Remove a node given by its pointer.
void	Delete (Element *el)
	Remove a node given by its pointer.
void	Delete (Side *sd)
	Remove a side given by its pointer.
void	Delete (Edge *ed)
	Remove an edge given by its pointer.
void	RenumberNode (size_t n1, size_t n2)
	Renumber a node.
void	RenumberElement (size_t n1, size_t n2)
	Renumber an element.
void	RenumberSide (size_t n1, size_t n2)
	Renumber a side.
void	RenumberEdge (size_t n1, size_t n2)
	Renumber an edge.
void	setNodeView (size_t n1, size_t n2)
	Set viewing window for nodes.
void	setElementView (size_t n1, size_t n2)
	Set viewing window for elements.
void	setSideView (size_t n1, size_t n2)
	Set viewing window for sides.
void	setEdgeView (size_t n1, size_t n2)
	Set viewing window for edges.
void	setList (const std::vector< Node * > &nl)
void	setList (const std::vector< Element * > &el)
void	setList (const std::vector< Side * > &sl)
int	getVerbose () const
	Return Verbose Parameter.
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.
size_t	getNbInternalSides () const
	Return number of internal sides.
size_t	getNbMat () const
	Return number of materials.
void	AddMidNodes (int g=0)
	Add mid-side nodes.
Point< double >	getMaxCoord () const
	Return maximum coordinates of nodes.
Point< double >	getMinCoord () const
	Return minimum coordinates of nodes.
void	set (Node *nd)
	Replace node in the mesh.
void	set (Element *el)
	Replace element in the mesh.
void	set (Side *sd)
	Choose side in the mesh.
bool	NodesAreDOF () const
	Return information about DOF type.
bool	SidesAreDOF () const
	Return information about DOF type.
bool	EdgesAreDOF () const
	Return information about DOF type.
bool	ElementsAreDOF () const
	Return information about DOF type.
int	getDOFSupport () const
	Return information on dof support Return an integer according to enumerated values: NODE_DOF, ELEMENT_DOF SIDE_DOF.
void	put (const string &mesh_file) const
	Write mesh data on file.
void	save (const string &mesh_file) const
	Write mesh data on file in various formats.
void	Bput (const string &mesh_file) const
	Write mesh data on a binary file.
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
void	getList (vector< Element * > &el) const
void	getList (vector< Side * > &sl) const
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.
Element &	getElement (size_t i) const
	Return reference 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.
Edge &	getEdge (size_t i) const
	Return reference to edge with label i.
size_t	getNodeLabel (size_t i) const
	Return label of i-th node.
size_t	getElementLabel (size_t i) const
	Return label of i-th element.
size_t	getSideLabel (size_t i) const
	Return label of i-th side.
size_t	getEdgeLabel (size_t i) const
	Return label of i-th edge.
void	topNode () const
	Reset list of nodes at its top position (Non constant version)
void	topBoundaryNode () const
	Reset list of boundary nodes at its top position (Non constant version)
void	topMarkedNode () const
	Reset list of marked nodes at its top position (Non constant version)
void	topElement () const
	Reset list of elements at its top position (Non constant version)
void	topSide () const
	Reset list of sides at its top position (Non constant version)
void	topBoundarySide () const
	Reset list of boundary sides at its top position (Non constant version)
void	topInternalSide () const
	Reset list of intrenal sides at its top position (Non constant version)
void	topEdge () const
	Reset list of edges at its top position (Non constant version)
void	topBoundaryEdge () const
	Reset list of boundary edges at its top position (Non constant version)
Node *	getNode () const
	Return pointer to current node and move to next one (Non constant version)
Node *	getBoundaryNode () const
	Return pointer to current boundary node and move to next one (Non constant version)
Node *	getMarkedNode () const
	Return pointer to current marked node and move to next one (Non constant version)
Element *	getElement () const
	Return pointer to current element and move to next one (Non constant version)
Side *	getSide () const
	Return pointer to current side and move to next one (Non constant version)
Side *	getBoundarySide () const
	Return pointer to current boundary side and move to next one (Non constant version)
Side *	getInternalSide () const
	Return pointer to current internal side and move to next one (Non constant version)
Edge *	getEdge () const
	Return pointer to current edge and move to next one (Non constant version)
Edge *	getBoundaryEdge () const
	Return pointer to current boundary edge and move to next one (Non constant version)
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)
	Operator () : Return pointer to i-th element.
Node *	operator[] (size_t i)
	Operator [] : Return pointer to i-th node.
size_t	operator() (size_t i, size_t n)
	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.

---

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.

---

Constructor & Destructor Documentation

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

Constructor using a mesh file.

Parameters:

[in]	file	File containing mesh data
[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	L,
		size_t	nb_el,
		size_t	p = 1,
		size_t	nb_dof = 1
	)

Constructor for a 1-D mesh. The domain is the interval [0,L].

Parameters:

[in]	L	Length 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	xL,
		double	yL,
		size_t	nx,
		size_t	ny,
		int	c1,
		int	c2,
		int	c3,
		int	c4,
		int	opt = 0
	)

Constructor for a uniform finite difference grid.

The domain is the rectangle (0,Lx)x(0,Ly)

Parameters:

[in]	xL	Length in the x-direction
[in]	yL	Length in the y-direction
[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=0
[in]	c2	Code for nodes generated on the line x=Lx
[in]	c3	Code for nodes generated on the line y=Ly
[in]	c4	Code for nodes generated on the line x=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.

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 &	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

(

const Mesh &

ms

)

Copy Constructor.

Parameters:

[in]

ms

Mesh instance to copy

---

Member Function Documentation

void setDim

(

size_t

dim

)

Define space dimension. Normally, between 1 and 3.

Parameters:

[in]

dim

Space dimension to set (must be between 1 and 3)

void setVerbose

(

int

verb

)

Define Verbose Parameter. Controls output details.

Parameters:

[in]

verb

verbosity parameter (Must be between 0 and 10)

void Add

(

Node *

nd

)

Add a node to mesh.

Parameters:

[in]

nd

Pointer to Node to add

void Add

(

Element *

el

)

Add an element to mesh.

Parameters:

[in]

el

Pointer to Element to add

void Add

(

Side *

sd

)

Add a side to mesh.

Parameters:

[in]

sd

Pointer to Side to add

void Add

(

Edge *

ed

)

Add an edge to mesh.

Parameters:

[in]

ed

Pointer to Edge to add

void get

(

const string &

mesh_file

)

Read mesh data in file.

Parameters:

[in]

mesh_file

Mesh file name

void setDOFSupport	(	int	opt,
		int	nb_nodes = 1
	)

Define supports of degrees of freedom.

Parameters:

[in]	opt	DOF type = NODE_DOF, Degrees of freedom are supported by nodes SIDE_DOF, Degrees of freedom are supported by sides EDGE_DOF, Degrees of freedom are supported by edges ELEMENT_DOF, Degrees of freedom are supported by elements
[in]	nb_nodes	Number of nodes on sides or elements (default=1). This parameter is useful only if dofs are supported by sides or elements

Note:

This member function creates all mesh sides if the option ELEMENT_DOF or SIDE_DOF is selected. So it not necessary to call getAllSides() after

void setPointInDomain

(

Point< double >

x

)

Define a point in the domain. This function makes sense only if boundary mesh is given without internal mesh (Case of Boundary Elements)

Parameters:

[in]

x

Coordinates of point to define

size_t NumberEquations

(

size_t

dof = 0

)

Renumber Equations.

Parameters:

[in]

dof

Label of degree of freedom for which numbering is performed. Default value (0) means that all degrees of freedom are taken into account

size_t NumberEquations	(	size_t	dof,
		int	c
	)

Renumber Equations.

Parameters:

[in]	dof	Label of degree of freedom for which numbering is performed.
[in]	c	code for which degrees of freedom are enforced.

int getAllSides

(

int

opt = 0

)

Determine all mesh sides.

Returns:

Number of all sides.

int getBoundarySides

(

)

Determine all boundary sides.

Returns:

Number of boundary sides.

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.

int getBoundaryNodes

(

)

Determine all boundary nodes.

Returns:

n Number of boundary nodes.

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.

int getAllEdges

(

)

Determine all edges.

Returns:

Number of all edges.

void setMaterial	(	int	code,
		const string &	mname
	)

Associate material to code of element.

Parameters:

[in]	code	Element code for which material is assigned
[in]	mname	Name of material

void Reorder

(

size_t

m = 1000000

)

Renumber mesh nodes according to reverse Cuthill Mc Kee algorithm.

Parameters:

[in]

m

Memory size needed for matrix graph (default value is GRAPH_MEMORT, see OFELI_Config.h)

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 DeleteNode

(

size_t

label

)

Remove a node given by its label.

This function does not release the space previously occupied

Parameters:

[in]

label

Label of node to delete

void DeleteElement

(

size_t

label

)

Remove an element given by its label.

This function does not release the space previously occupied

Parameters:

[in]

label

Label of element to delete

void DeleteSide

(

size_t

label

)

Remove a side given by its label.

This function does not release the space previously occupied

Parameters:

[in]

label

Label of side to delete

void Delete

(

Node *

nd

)

Remove a node given by its pointer.

This function does not release the space previously occupied

Parameters:

[in]

nd

Pointer to node to delete

void Delete

(

Element *

el

)

Remove a node given by its pointer.

This function does not release the space previously occupied

Parameters:

[in]

el

Pointer to element to delete

void Delete

(

Side *

sd

)

Remove a side given by its pointer.

This function does not release the space previously occupied

Parameters:

[in]

sd

Pointer to side to delete

void Delete

(

Edge *

ed

)

Remove an edge given by its pointer.

This function does not release the space previously occupied

Parameters:

[in]

ed

Pointer to edge to delete

void RenumberNode	(	size_t	n1,
		size_t	n2
	)

Renumber a node.

Parameters:

[in]	n1	Old label
[in]	n2	New label

void RenumberElement	(	size_t	n1,
		size_t	n2
	)

Renumber an element.

Parameters:

[in]	n1	Old label
[in]	n2	New label

void RenumberSide	(	size_t	n1,
		size_t	n2
	)

Renumber a side.

Parameters:

[in]	n1	Old label
[in]	n2	New label

void RenumberEdge	(	size_t	n1,
		size_t	n2
	)

Renumber an edge.

Parameters:

[in]	n1	Old label
[in]	n2	New label

void setNodeView	(	size_t	n1,
		size_t	n2
	)

Set viewing window for nodes.

Parameters:

[in]	n1	First node to view
[in]	n2	last node to view

void setElementView	(	size_t	n1,
		size_t	n2
	)

Set viewing window for elements.

Parameters:

[in]	n1	First element to view
[in]	n2	last element to view

void setSideView	(	size_t	n1,
		size_t	n2
	)

Set viewing window for sides.

Parameters:

[in]	n1	First side to view
[in]	n2	last side to view

void setEdgeView	(	size_t	n1,
		size_t	n2
	)

Set viewing window for edges.

Parameters:

[in]	n1	First edge to view
[in]	n2	last edge to view

void setList

(

const std::vector< Node * > &

nl

)

Initialize list of mesh nodes using the input vector

Parameters:

[in]

nl

vector instance that contains the list of pointers to nodes

void setList

(

const std::vector< Element * > &

el

)

Initialize list of mesh elements using the input vector

Parameters:

[in]

sl

vector instance that contains the list of pointers to elements

void setList

(

const std::vector< Side * > &

sl

)

Initialize list of mesh sides using the input vector

Parameters:

[in]

sl

vector instance that contains the list of pointers to sides

size_t getNbBoundarySides

(

)

const

Return number of boundary sides.

This function is valid if member function getAllSides or getBoundarySides has been invoked before

size_t getNbInternalSides

(

)

const

Return number of internal sides.

This function is valid if member functions getAllSides and createInternalSideList have been invoked before

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 set

(

Node *

nd

)

Replace node in the mesh.

If the node label exists already, the existing node pointer will be replaced by the current one. If not, an error message is displayed.

Parameters:

[in]

nd

Pointer to node

void set

(

Element *

el

)

Replace element in the mesh.

If the element label exists already, the existing element pointer will be replaced by the current one. If not, an error message is displayed.

Parameters:

[in]

el

Pointer to element

void set

(

Side *

sd

)

Choose side in the mesh.

If the side label exists already, the existing side pointer will be replaced by the current one. If not, an error message is displayed.

Parameters:

[in]

sd

Pointer to side

bool NodesAreDOF

(

)

const

Return information about DOF type.

Returns:

true if DOF are supported by nodes, false otherwise

bool SidesAreDOF

(

)

const

Return information about DOF type.

Returns:

true if DOF are supported by sides, false otherwise

bool EdgesAreDOF

(

)

const

Return information about DOF type.

Returns:

true if DOF are supported by edges, false otherwise

bool ElementsAreDOF

(

)

const

Return information about DOF type.

Returns:

true if DOF are supported by elements, false otherwise

void put

(

const string &

mesh_file

)

const

Write mesh data on file.

Parameters:

[in]

mesh_file

Mesh file name

void save

(

const string &

mesh_file

)

const

Write mesh data on file in various formats.

File format depends on the extension in file name

Parameters:

[in]

mesh_file

Mesh file name If the extension is '.m', the output file is an OFELI file If the extension is '.gpl', the output file is a Gnuplot file If the extension is '.msh' or '.geo', the output file is a Gmsh file If the extension is '.vtk', the output file is a VTK file

void Bput

(

const string &

mesh_file

)

const

Write mesh data on a binary file.

Parameters:

[in]

mesh_file

Mesh file name

void getList

(

vector< Node * > &

nl

)

const

Fill vector nl with list of pointers to nodes

Parameters:

[out]

nl

Instance of class vector that contain on output the list

void getList

(

vector< Element * > &

el

)

const

Fill vector el with list of pointers to elements

Parameters:

[out]

el

Instance of class vector that contain on output the list

void getList

(

vector< Side * > &

sl

)

const

Fill vector sl with list of pointers to sides

Parameters:

[out]

sl

Instance of class vector that contain on output the list

size_t getNodeLabel

(

size_t

i

)

const

Return label of i-th node.

Parameters:

[in]

i

Node index

size_t getElementLabel

(

size_t

i

)

const

Return label of i-th element.

Parameters:

[in]

i

Element index

size_t getSideLabel

(

size_t

i

)

const

Return label of i-th side.

Parameters:

[in]

i

Side index

size_t getEdgeLabel

(

size_t

i

)

const

Return label of i-th edge.

Parameters:

[in]

i

Edge index

---

Friends And Related Function Documentation

void Refine	(	Mesh &	in_mesh,
		Mesh &	out_mesh
	)		[friend]

Refine mesh. Subdivide each triangle into 4 subtriangles. This member function is valid for 2-D triangular meshes only.

Parameters:

[in]	in_mesh	Input mesh
[out]	out_mesh	Output mesh