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

Inheritance diagram for QGaussLobattoChebyshev< dim >:

Public Member Functions
	QGaussLobattoChebyshev (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 QGaussLobattoChebyshev< dim >

Gauss-Lobatto-Chebyshev quadrature rules integrate the weighted product \(\int_{-1}^1 f(x) w(x) dx\) with weight given by: \(w(x) = 1/\sqrt{1-x^2}\), with the additional constraint that two of the quadrature points are located at the endpoints of the quadrature interval. The nodes and weights are known analytically, and are exact for monomials up to the order \(2n-3\), 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. 25.4.40

Author: Giuseppe Pitton, Luca Heltai 2015

Definition at line 639 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 QGaussLobattoChebyshev< dim >

template<int dim>
class QGaussLobattoChebyshev< dim >