QGaussRadauChebyshev< dim > Class Template Reference

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

Inheritance diagram for QGaussRadauChebyshev< dim >:

Public Types
enum	EndPoint { left, right }
Public Types inherited from Quadrature< dim >
using	SubQuadrature = Quadrature< dim - 1 >

Public Member Functions
	QGaussRadauChebyshev (const unsigned int n, EndPoint ep=QGaussRadauChebyshev::left)
	Generate a formula with n quadrature points. More...
	QGaussRadauChebyshev (QGaussRadauChebyshev< dim > &&) noexcept=default
	QGaussRadauChebyshev (const unsigned int n, EndPoint ep)
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 () override=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
const std::array< Quadrature< 1 >, dim > &	get_tensor_basis () const
	Quadrature (const unsigned int n_q)
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 (std::atomic< bool > *const validity, const std::string &identifier="") const
void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
unsigned int	n_subscriptions () const
template<typename StreamType >
void	list_subscribers (StreamType &stream) const
void	list_subscribers () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Private Attributes
const EndPoint	ep

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 524 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 530 of file quadrature_lib.h.

Constructor & Destructor Documentation

QGaussRadauChebyshev() [1/3]

template<int dim>

QGaussRadauChebyshev< dim >::QGaussRadauChebyshev	(	const unsigned int	n,
		EndPoint	ep = QGaussRadauChebyshev< dim >::left
	)

Generate a formula with n quadrature points.

Definition at line 1118 of file quadrature_lib.cc.

QGaussRadauChebyshev() [2/3]

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.

QGaussRadauChebyshev() [3/3]

QGaussRadauChebyshev< 1 >::QGaussRadauChebyshev	(	const unsigned int	n,
		EndPoint	ep
	)

Definition at line 1099 of file quadrature_lib.cc.

Member Data Documentation

ep

template<int dim>

const EndPoint QGaussRadauChebyshev< dim >::ep

private

Definition at line 552 of file quadrature_lib.h.

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

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