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

Inheritance diagram for QGaussRadauChebyshev< dim >:

Public Types
enum	EndPoint { left, right }

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

Public Member Functions
	QGaussRadauChebyshev (const unsigned int n, EndPoint ep=QGaussRadauChebyshev::left)
	Generate a formula with `n` quadrature points.

	QGaussRadauChebyshev (QGaussRadauChebyshev< dim > &&) noexcept=default

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 > &&) noexcept=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 ()=default

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

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

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)

bool	is_tensor_product () const

std::conditional< dim==1, std::array< Quadrature< 1 >, dim >, const std::array< Quadrature< 1 >, dim > & >::type	get_tensor_basis () const

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

void	subscribe (const char *identifier=nullptr) const

void	unsubscribe (const char *identifier=nullptr) const

unsigned int	n_subscriptions () const

void	list_subscribers () const

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

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

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

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

std::vector< double >	weights

bool	is_tensor_product_flag

std::unique_ptr< std::array< Quadrature< 1 >, dim > >	tensor_basis

Detailed Description

template<int dim>
class QGaussRadauChebyshev< dim >

Gauss-Radau-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 a quadrature point lies at one of the two extrema of the interval. The nodes and weights are known analytically, and are exact for monomials up to the order \(2n-2\), 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: \(w(x) = 1/\sqrt{x(1-x)}\). By default the quadrature is constructed with the left endpoint as quadrature node, but the quadrature node can be imposed at the right endpoint through the variable ep that can assume the values left or right.

Author: Giuseppe Pitton, Luca Heltai 2015

Definition at line 526 of file quadrature_lib.h.

Member Enumeration Documentation

◆ EndPoint

template<int dim>

enum QGaussRadauChebyshev::EndPoint

Enumerator
left	Left end point.
right	Right end point.

Definition at line 532 of file quadrature_lib.h.

Constructor & Destructor Documentation

◆ QGaussRadauChebyshev()

template<int dim>

QGaussRadauChebyshev< dim >::QGaussRadauChebyshev ( QGaussRadauChebyshev< dim > && )

defaultnoexcept

Move constructor. We cannot rely on the move constructor for Quadrature, since it does not know about the additional member ep of this class.

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

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

Public Types

Public Member Functions