Utilities

---

Detailed Description

A module that groups utility functions and classes.

Files
file	OFELI.h
	Header file that includes all kernel classes of the library.
file	OFELI_Config.h
	File that contains some macros.
file	OFELI_Const.h
	File that contains some widely used constants.
Classes
class	Gauss
	Calculate data for Gauss integration. More...
class	Point
	Defines a point with arbitrary type coordinates. More...
class	Point2D
	Defines a 2-D point with arbitrary type coordinates. More...
class	Timer
	To set time counting. More...
class	UserData
	Abstract class to define by user various problem data. More...
Defines
#define	OFELI_E   2.71828182845904523536028747135
#define	OFELI_EPSMCH   DBL_EPSILON
#define	OFELI_GAUSS2   0.57735026918962576450914878050196
#define	OFELI_IMAG   std::complex<double>(0.,1.);
#define	OFELI_ONEOVERPI   0.31830988618379067153776752675
#define	OFELI_PI   3.14159265358979323846264338328
#define	OFELI_SIXTH   0.16666666666666666666666666667
#define	OFELI_SQRT2   1.41421356237309504880168872421
#define	OFELI_SQRT3   1.73205080756887729352744634151
#define	OFELI_THIRD   0.33333333333333333333333333333
#define	OFELI_TOLERANCE   OFELI_EPSMCH*10000
#define	OFELI_TWELVETH   0.08333333333333333333333333333
Typedefs
typedef std::complex< double >	complex_t
typedef unsigned long	lsize_t
typedef double	real_t
Functions
double	Abs (const Point< double > &p)
	Return Norm of vector a.
double	Abs (complex_t a)
	Return modulus of complex number a.
double	Abs (double a)
	Return absolute value of a.
double	Abs2 (double a)
	Return square of real number a.
double	Abs2 (complex_t a)
	Return square of modulus of complex number a.
bool	areClose (const Point2D< double > &a, const Point2D< double > &b, double toler=OFELI_TOLERANCE)
	Return true if both instances of class Point2D<double> are distant with less then toler.
bool	areClose (const Point< double > &a, const Point< double > &b, double toler=OFELI_TOLERANCE)
	Return true if both instances of class Point<double> are distant with less then toler.
double	Arg (complex_t x)
	Return argument of complex number x.
template<class T_>
void	Axpy (T_ a, const valarray< T_ > &x, valarray< T_ > &y)
	Multiply vector x by a and add result to y.
template<class T_>
void	Axpy (T_ a, const vector< T_ > &x, vector< T_ > &y)
	Multiply vector x by a and add result to y.
template<class T_>
void	Axpy (size_t n, T_ a, T_ *x, T_ *y)
	Multiply array x by a and add result to y.
void	banner (const string &prog=" ")
	Outputs a banner as header of any developed program.
void	BSpline (size_t n, size_t t, Vect< Point< double > > &control, Vect< Point< double > > &output, size_t num_output)
	Function to perform a B-spline interpolation.
complex_t	CDot (const valarray< complex_t > &x, valarray< complex_t > &y)
	Return dot product of complex vectors x and y.
complex_t	CDot (size_t n, const complex_t *x, const complex_t *y)
	Return dot product of complex arrays x and y.
template<class T_>
void	Clear (vector< T_ > &v)
	Clear (set entries to zero) vector v.
template<class T_>
void	Clear (valarray< T_ > &v)
	Clear (set entries to zero) vector v.
complex_t	Conjg (complex_t a)
	Return complex conjugate of complex number a.
double	Conjg (double a)
	Return complex conjugate of real number a.
template<class T_>
void	Copy (const valarray< T_ > &x, valarray< T_ > &y)
	Copy vector x to y.
template<class T_>
void	Copy (size_t n, T_ *x, T_ *y)
	Copy array x to y.
double	Distance (const Point2D< double > &a, const Point2D< double > &b)
	Return euclidean distance between points a and b.
double	Distance (const Point< double > &a, const Point< double > &b)
	Return euclidean distance between points a and b.
template<class T_>
T_	Dot (const Point< T_ > &x, const Point< T_ > &y)
	Return dot product of x and y.
complex_t	Dot (const valarray< complex_t > &x, const valarray< complex_t > &y)
	Return dot product of vectors x and y.
real_t	Dot (const valarray< real_t > &x, const valarray< real_t > &y)
	Return dot product of vectors x and y.
template<class T_>
T_	Dot (const vector< T_ > &x, const vector< T_ > &y)
	Return dot product of vectors x and y.
template<class T_>
T_	Dot (size_t n, T_ *x, T_ *y)
	Return dot product of arrays x and y.
std::string	dtos (double d)
	Function to convert a double real to a string.
void	FDF2Gmsh (const string &file, const Mesh &mesh, FDF &fdf, NodeVect< double > &v)
	Convert an FDF file to a Gmsh file.
void	FDF2Gnuplot (const string &file, const Mesh &mesh, FDF &fdf, NodeVect< double > &v)
	Convert an FDF file to an input Gnuplot file.
void	FDF2Tecplot (const string &file, const Mesh &mesh, FDF &fdf, NodeVect< double > &v, int opt)
	Convert an FDF file to an input Tecplot file.
void	FDF2Vigie (const string &file, const Mesh &mesh, FDF &fdf, NodeVect< double > &v, int option, int wm)
	Convert an FDF file to an input Vigie file.
void	FDF2VTK (const string &file, const Mesh &mesh, FDF &fdf, NodeVect< double > &v, int opt=0)
	Convert an FDF file to a VTK file.
std::string	ftos (float f)
	Function to convert a float real to a string.
void	getBamg (const string &file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Bamg format.
void	getEasymesh (const string &file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Easymesh format.
void	getEMC2 (const string &file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in EMC2 format.
void	getGambit (const string &file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Gambit neutral format.
void	getGmsh (const string &file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Gmsh format.
void	getMatlab (const string &file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a Matlab mesh data.
void	getNetgen (const string &file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Netgen format.
void	getTetgen (const string &file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Tetgen format.
void	getTriangle (const string &file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Triangle format.
char	itoc (int i)
	Function to convert an integer to a character.
std::string	itos (int i)
	Function to convert an integer to a string.
complex_t	Log (complex_t x)
	Return principal determination of logarithm of complex number x.
void	LTrim (char *s)
	Function to remove blanks at the beginning of a string.
int	Max (int a, int b, int c, int d)
	Return maximum value of integer numbers a, b, c and d.
double	Max (double a, double b, double c, double d)
	Return maximum value of integer numbers a, b, c and d.
int	Max (int a, int b, int c)
	Return maximum value of integer numbers a, b and c.
double	Max (double a, double b, double c)
	Return maximum value of real numbers a, b and c.
int	Min (int a, int b, int c, int d)
	Return minimum value of integer numbers a, b, c and d.
double	Min (double a, double b, double c, double d)
	Return minimum value of real numbers a, b, c and d.
int	Min (int a, int b, int c)
	Return minimum value of integer numbers a, b and c.
double	Min (double a, double b, double c)
	Return minimum value of real numbers a, b and c.
template<class T_>
double	Nrm2 (const Point< T_ > &a)
	Return 2-norm of a.
double	Nrm2 (const valarray< double > &x)
	Return 2-norm of vector x.
double	Nrm2 (size_t n, double *x)
	Return 2-norm of array x.
template<class T_>
T_	operator* (const Point2D< T_ > &b, const Point2D< T_ > &a)
	Operator *.
template<class T_>
Point2D< T_ >	operator* (const Point2D< T_ > &b, const int &a)
	Operator *.
template<class T_>
Point2D< T_ >	operator* (const Point2D< T_ > &b, const T_ &a)
	Operator /.
template<class T_>
Point2D< T_ >	operator* (const int &a, const Point2D< T_ > &b)
	Operator *.
template<class T_>
Point2D< T_ >	operator* (const T_ &a, const Point2D< T_ > &b)
	Operator *.
template<class T_>
T_	operator* (const Point< T_ > &b, const Point< T_ > &a)
	Operator *.
template<class T_>
Point< T_ >	operator* (const Point< T_ > &b, const int &a)
	Operator *.
template<class T_>
Point< T_ >	operator* (const Point< T_ > &b, const T_ &a)
	Operator /.
template<class T_>
Point< T_ >	operator* (const int &a, const Point< T_ > &b)
	Operator *.
template<class T_>
Point< T_ >	operator* (const T_ &a, const Point< T_ > &b)
	Operator *.
template<class T_>
Point2D< T_ >	operator+ (const Point2D< T_ > &a, const T_ &x)
	Operator +.
template<class T_>
Point2D< T_ >	operator+ (const Point2D< T_ > &a, const Point2D< T_ > &b)
	Operator +.
template<class T_>
Point< T_ >	operator+ (const Point< T_ > &a, const T_ &x)
	Operator +.
template<class T_>
Point< T_ >	operator+ (const Point< T_ > &a, const Point< T_ > &b)
	Operator +.
template<class T_>
Point2D< T_ >	operator- (const Point2D< T_ > &a, const T_ &x)
	Operator -.
template<class T_>
Point2D< T_ >	operator- (const Point2D< T_ > &a, const Point2D< T_ > &b)
	Operator -.
template<class T_>
Point2D< T_ >	operator- (const Point2D< T_ > &a)
	Unary Operator -.
template<class T_>
Point< T_ >	operator- (const Point< T_ > &a, const T_ &x)
	Operator -.
template<class T_>
Point< T_ >	operator- (const Point< T_ > &a, const Point< T_ > &b)
	Operator -.
template<class T_>
Point< T_ >	operator- (const Point< T_ > &a)
	Unary Operator -.
template<class T_>
Point2D< T_ >	operator/ (const Point2D< T_ > &b, const T_ &a)
	Operator /.
template<class T_>
Point< T_ >	operator/ (const Point< T_ > &b, const T_ &a)
	Operator /.
template<class T_>
std::ostream &	operator<< (std::ostream &s, const Point2D< T_ > &a)
	Output point coordinates.
template<class T_>
std::ostream &	operator<< (std::ostream &s, const Point< T_ > &a)
	Output point coordinates.
template<class T_>
ostream &	operator<< (ostream &s, const std::pair< T_, T_ > &a)
	Output a pair instance.
template<class T_>
ostream &	operator<< (ostream &s, const valarray< T_ > &v)
	Output a valarray instance.
template<class T_>
ostream &	operator<< (ostream &s, const vector< T_ > &v)
	Output a vector instance.
ostream &	operator<< (ostream &s, const std::string &c)
	Output a string.
ostream &	operator<< (ostream &s, const std::complex< double > &x)
	Output a complex number.
template<class T_>
bool	operator== (const Point2D< T_ > &a, const Point2D< T_ > &b)
	Operator ==.
template<class T_>
bool	operator== (const Point< T_ > &a, const Point< T_ > &b)
	Operator ==.
template<class T_, class C_>
void	qksort (std::valarray< T_ > &a, int begin, int end, C_ compare)
	Function to sort a vector according to a key function.
template<class T_>
void	qksort (std::valarray< T_ > &a, int begin, int end)
	Function to sort a vector.
template<class T_, class C_>
void	qksort (std::vector< T_ > &a, int begin, int end, C_ compare)
	Function to sort a vector according to a key function.
template<class T_>
void	qksort (std::vector< T_ > &a, int begin, int end)
	Function to sort a vector according to a key function.
template<class T_>
void	QuickSort (std::vector< T_ > &a, int begin, int end)
	Function to sort a vector.
void	RTrim (char *s)
	Function to remove blanks at the end of a string.
void	saveGmsh (const string &gp_file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in Gmsh format.
void	saveGnuplot (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in Gmsh format.
void	saveGnuplot (const string &input_file, const string &output_file, const string &mesh_file, Mesh &mesh)
	Convert an OFELI field file to an input Gnuplot file.
void	saveMatlab (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in Matlab format.
void	saveTecplot (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in Tecplot format.
void	saveVTK (const string &file, const Mesh &mesh, int format=0)
	This function outputs a Mesh instance in a file in VTK format.
template<class T_>
void	Scale (T_ a, valarray< T_ > &x)
	Mutiply vector x by a.
template<class T_>
void	Scale (T_ a, vector< T_ > &x)
	Mutiply vector x by a.
template<class T_>
void	Scale (T_ a, const valarray< T_ > &x, valarray< T_ > &y)
	Mutiply vector x by a and save result in vector y.
template<class T_>
void	Scale (T_ a, const vector< T_ > &x, vector< T_ > &y)
	Mutiply vector x by a and save result in vector y.
int	Sgn (double a)
	Return sign of a.
template<class T_>
T_	Sqr (T_ &x)
	Return square of value x.
double	SqrDistance (const Point2D< double > &a, const Point2D< double > &b)
	Return squared euclidean distance between points a and b.
double	SqrDistance (const Point< double > &a, const Point< double > &b)
	Return squared euclidean distance between points a and b.
template<class T_>
void	Swap (T_ &a, T_ &b)
	Swap elements a and b.
void	Trim (char *s)
	Function to remove blanks at the beginning and end of a string.
template<class T_>
void	Xpy (const valarray< T_ > &x, valarray< T_ > &y)
	Add vector x to y.
template<class T_>
void	Xpy (const vector< T_ > &x, vector< T_ > &y)
	Add vector x to y.
template<class T_>
void	Xpy (size_t n, T_ *x, T_ *y)
	Add array x to y.

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Define Documentation

#define OFELI_E   2.71828182845904523536028747135

Value of e or exp (with 28 digits)

#define OFELI_EPSMCH   DBL_EPSILON

Value of Machine Epsilon

Referenced by LocalMatrix::Factor(), OFELI::GS(), OFELI::Jacobi(), LocalMatrix::Solve(), and OFELI::SSOR().

#define OFELI_GAUSS2   0.57735026918962576450914878050196

Value of 1/sqrt(3) (with 32 digits)

#define OFELI_IMAG   std::complex<double>(0.,1.);

= Unit imaginary number (i)

#define OFELI_ONEOVERPI   0.31830988618379067153776752675

Value of 1/Pi (with 28 digits)

#define OFELI_PI   3.14159265358979323846264338328

Value of Pi (with 28 digits)

Referenced by OFELI::Arg().

#define OFELI_SIXTH   0.16666666666666666666666666667

Value of 1/6 (with 28 digits)

Referenced by Tetra4::getVolume().

#define OFELI_SQRT2   1.41421356237309504880168872421

Value of sqrt(2) (with 28 digits)

#define OFELI_SQRT3   1.73205080756887729352744634151

Value of sqrt(3) (with 28 digits)

#define OFELI_THIRD   0.33333333333333333333333333333

Value of 1/3 (with 28 digits)

#define OFELI_TOLERANCE   OFELI_EPSMCH*10000

Default tolerance for an iterative process = OFELI_EPSMCH * 10000

Referenced by SkSMatrix::Factor(), SkMatrix::Factor(), DSMatrix::Factor(), DMatrix::Factor(), TrMatrix::Solve(), SkMatrix::Solve(), and DMatrix::Solve().

#define OFELI_TWELVETH   0.08333333333333333333333333333

Value of 1/12 (with 28 digits)

---

Typedef Documentation

complex_t

This type stands for type std::complex<double>

lsize_t

This type stands for type unsigned long

real_t

This type stands for type double

---

Function Documentation

double Abs

(

const Point< double > &

p

)

Return Norm of vector a.

References Point::Norm().

Referenced by SpMatrix::DiagPrescribe(), SkSMatrix::Factor(), SkMatrix::Factor(), LocalMatrix::Factor(), DSMatrix::Factor(), DMatrix::Factor(), Vect::getNorm1(), Vect::getNormMax(), AbsVect::getNormMax(), OFELI::GMRes(), OFELI::GS(), OFELI::Log(), TrMatrix::Solve(), SkMatrix::Solve(), LocalMatrix::Solve(), and DMatrix::Solve().

double Abs

(

complex_t

a

)

Return modulus of complex number a.

References OFELI::Abs2().

double Abs

(

double

a

)

Return absolute value of a.

double Abs2

(

double

a

)

Return square of real number a.

Referenced by OFELI::Abs(), and Vect::getNorm2().

double Abs2

(

complex_t

a

)

Return square of modulus of complex number a.

double Arg

(

complex_t

x

)

Return argument of complex number x.

References OFELI_PI.

Referenced by OFELI::Log().

void Axpy	(	T_	a,
		const valarray< T_ > &	x,
		valarray< T_ > &	y
	)

Multiply vector x by a and add result to y.

x and y are instances of class valarray<T_>

Referenced by OFELI::BiCG(), and OFELI::CGS().

void Axpy	(	T_	a,
		const vector< T_ > &	x,
		vector< T_ > &	y
	)

Multiply vector x by a and add result to y.

x and y are instances of class vector<T_>

void Axpy	(	size_t	n,
		T_	a,
		T_ *	x,
		T_ *	y
	)

Multiply array x by a and add result to y.

n is the arrays length.

void banner

(

const string &

prog = " "

)

Outputs a banner as header of any developed program.

Parameters:

[in]

prog

Calling program name. Enables writing a copyright notice accompanying the program.

References OFELI_RELEASE_DATE, and OFELI_VERSION.

BSpline	(	size_t	n,
		size_t	t,
		Vect< Point< double > > &	control,
		Vect< Point< double > > &	output,
		size_t	num_output
	)

Function to perform a B-spline interpolation.

This program is adapted from a free program ditributed by Keith Vertanen (vertankd@cda.mrs.umn.edu) in 1994.

Parameters:

[in]	n	Number of control points minus 1.
[in]	t	Degree of the polynomial plus 1.
[in]	control	Control point array made up of Point stucture.
[out]	output	Vector in which the calculated spline points are to be put.
[in]	num_output	How many points on the spline are to be calculated.

Note:

Condition: n+2>t (No curve results if n+2<=t) Control vector contains the number of points specified by n Output array is the proper size to hold num_output point structures

complex_t CDot	(	const valarray< complex_t > &	x,
		valarray< complex_t > &	y
	)

Return dot product of complex vectors x and y.

References OFELI::Conjg().

complex_t CDot	(	size_t	n,
		const complex_t *	x,
		const complex_t *	y
	)

Return dot product of complex arrays x and y.

n is the arrays length.

References OFELI::Conjg().

void Clear

(

valarray< T_ > &

v

)

Clear (set entries to zero) vector v.

complex_t Conjg

(

complex_t

x

)

Return complex conjugate of complex number a.

Referenced by OFELI::CDot(), and OFELI::Dot().

double Conjg

(

double

x

)

Return complex conjugate of real number a.

void Copy	(	const valarray< T_ > &	x,
		valarray< T_ > &	y
	)

Copy vector x to y.

void Copy	(	size_t	n,
		T_ *	x,
		T_ *	y
	)

Copy array x to y.

n is the arrays length.

T_ Dot	(	const Point< T_ > &	x,
		const Point< T_ > &	y
	)

Return dot product of x and y.

References Point::x, Point::y, and Point::z.

complex_t Dot	(	const valarray< complex_t > &	x,
		const valarray< complex_t > &	y
	)

Return dot product of vectors x and y.

x and y are instances of class valarray<T_>

real_t Dot	(	const valarray< real_t > &	x,
		const valarray< real_t > &	y
	)

Return dot product of vectors x and y.

x and y are instances of class valarray<T_>

T_ Dot	(	const vector< T_ > &	x,
		const vector< T_ > &	y
	)

Return dot product of vectors x and y.

x and y are instances of class vector<T_>

T_ Dot	(	size_t	n,
		T_ *	x,
		T_ *	y
	)

Return dot product of arrays x and y.

n is the arrays length.

References OFELI::Conjg().

void FDF2Gmsh	(	const string &	file,
		const Mesh &	mesh,
		FDF &	fdf,
		NodeVect< double > &	v
	)

Convert an FDF file to a Gmsh file.

Gmsh is a free mesh generator and postprocessor that can be downloaded from the site:
http://www.geuz.org/gmsh/

Parameters:

[out]	file	Output file.
[in]	mesh	Mesh instance associated to field
[out]	fdf	FDF instance associated to input field
[out]	v	NodeVect instance used as work variable

void FDF2Gnuplot	(	const string &	file,
		const Mesh &	mesh,
		FDF &	fdf,
		NodeVect< double > &	v
	)

Convert an FDF file to an input Gnuplot file.

Gnuplot is a command-line driven program for producing 2D and 3D plots. It is under the GNU General Public License. Available information can be found in the site:
http://www.gnuplot.info/

Parameters:

[out]	file	Output file.
[in]	mesh	Mesh instance associated to field
[out]	fdf	FDF instance associated to input field
[out]	v	NodeVect instance used as work variable

void FDF2Tecplot	(	const string &	file,
		const Mesh &	mesh,
		FDF &	fdf,
		NodeVect< double > &	v,
		int	option
	)

Convert an FDF file to an input Tecplot file.

Tecplot is high quality post graphical commercial processing program developed by Amtec. Available information can be found in the site: http://www.tecplot.com

Parameters:

[out]	file	Output file.
[in]	mesh	Mesh instance associated to field
[out]	fdf	FDF instance associated to input field
[out]	v	NodeVect instance used as work variable
[in]	option	Store (1) or not (0) the mesh with data

void FDF2Vigie	(	const string &	file,
		const Mesh &	mesh,
		FDF &	fdf,
		NodeVect< double > &	v,
		int	option,
		int	wm
	)

Convert an FDF file to an input Vigie file.

Vigie is a free interactive visualization software developed ar INTIA. Available information can be found in the site:
http://www-sop.inria.fr/sinus/Softs/Vigie/

Parameters:

[out]	file	Output file.
[in]	mesh	Mesh instance associated to field
[out]	fdf	FDF instance associated to input field
[out]	v	NodeVect instance used as work variable
[in]	option	Unused
[in]	wm	Unused

void FDF2VTK	(	const string &	file,
		const Mesh &	mesh,
		FDF &	fdf,
		NodeVect< double > &	v,
		int	opt = 0
	)

Convert an FDF file to a VTK file.

The Visualization ToolKit (VTK) is an open source, freely available software system for 3D computer graphics. Available information can be found in the site:
http://public.kitware.com/VTK/

Parameters:

[out]	file	Output file.
[in]	mesh	Mesh instance associated to field
[out]	fdf	FDF instance associated to input field
[out]	v	NodeVect instance used as work variable
[in]	opt	Store all fields in one fdf file (0) or one file per field (1)

void getBamg	(	const string &	file,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)

Construct an instance of class Mesh from a mesh file stored in Bamg format.

Parameters:

[out]

file

Name of a file written in the Bamg format.

Note:

Bamg is a 2-D mesh generator. It allows to construct adapted meshes from a given metric. It was developed at INRIA, France. Available information can be found in the site:
www-rocq1.inria.fr/gamma/cdrom/www/bamg/eng.htm

Parameters:

[out]	mesh	Mesh instance created by the function.
[in]	nb_dof	Number of degrees of freedom for each node. This information is not provided, in general, by mesh generators. Its default value here is 1.

void getEasymesh	(	const string &	file,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)

Construct an instance of class Mesh from a mesh file stored in Easymesh format.

Parameters:

[in]

file

Name of a file (without extension) written in Easymesh format. Actually, the function Easymesh2MDF attempts to read mesh data from files file.e, file.n and file.s produced by Easymesh.

Note:

Easymesh is a free program that generates 2-D, unstructured, Delaunay and constrained Delaunay triangulations in general domains. It can be downloaded from the site:
http://www-dinma.univ.trieste.it/nirftc/research/easymesh/Default.htm

Parameters:

[in]	mesh	Mesh instance created by the function.
[in]	nb_dof	Number of degrees of freedom for each node. This information is not provided, in general, by mesh generators. Its default value here is 1.

void getEMC2	(	const string &	file,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)