#include <deal.II/base/quadrature_lib.h>

Inheritance diagram for QGaussChebyshev< dim >:

Public Member Functions
	QGaussChebyshev (const unsigned int n)
	Generate a formula with `n` quadrature points.

Public Member Functions inherited from Quadrature< dim >
	Quadrature (const unsigned int n_quadrature_points=0)

	Quadrature (const SubQuadrature &, const Quadrature< 1 > &)

	Quadrature (const Quadrature< dim !=1 ? 1 :0 > &quadrature_1d)

	Quadrature (const Quadrature< dim > &q)

	Quadrature (Quadrature< dim > &&)=default

	Quadrature (const std::vector< Point< dim > > &points, const std::vector< double > &weights)

	Quadrature (const std::vector< Point< dim > > &points)

	Quadrature (const Point< dim > &point)

virtual	~Quadrature ()

Quadrature &	operator= (const Quadrature< dim > &)

bool	operator== (const Quadrature< dim > &p) const

void	initialize (const std::vector< Point< dim > > &points, const std::vector< double > &weights)

unsigned int	size () const

const Point< dim > &	point (const unsigned int i) const

const std::vector< Point< dim > > &	get_points () const

double	weight (const unsigned int i) const

const std::vector< double > &	get_weights () const

std::size_t	memory_consumption () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&)

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&)

void	subscribe (const char *identifier=0) const

void	unsubscribe (const char *identifier=0) const

unsigned int	n_subscriptions () const

void	list_subscribers () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Static Private Member Functions
static std::vector< double >	get_quadrature_points (const unsigned int n)
	Computes the points of the quadrature formula.

static std::vector< double >	get_quadrature_weights (const unsigned int n)
	Computes the weights of the quadrature formula.

Additional Inherited Members
Public Types inherited from Quadrature< dim >
typedef Quadrature< dim-1 >	SubQuadrature

Static Public Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, char *arg2, std::string &arg3)

static ::ExceptionBase &	ExcNoSubscriber (char arg1, char arg2)

Protected Attributes inherited from Quadrature< dim >
std::vector< Point< dim > >	quadrature_points

std::vector< double >	weights

Detailed Description

template<int dim>
class QGaussChebyshev< dim >

Gauss-Chebyshev quadrature rules integrate the weighted product \(\int_{-1}^1 f(x) w(x) dx\) with weight given by: \(w(x) = 1/\sqrt{1-x^2}\). The nodes and weights are known analytically, and are exact for monomials up to the order \(2n-1\), where \(n\) is the number of quadrature points. Here we rescale the quadrature formula so that it is defined on the interval \([0,1]\) instead of \([-1,1]\). So the quadrature formulas integrate exactly the integral \(\int_0^1 f(x) w(x) dx\) with the weight: \(w(x) = 1/sqrt{x(1-x)}\). For details see: M. Abramowitz & I.A. Stegun: Handbook of Mathematical Functions, par. 25.4.38

Author: Giuseppe Pitton, Luca Heltai 2015

Definition at line 547 of file quadrature_lib.h.

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

deal.II/base/quadrature_lib.h
source/base/quadrature_lib.cc

Public Member Functions

Static Private Member Functions

Additional Inherited Members

Detailed Description

template<int dim> class QGaussChebyshev< dim >

template<int dim>
class QGaussChebyshev< dim >