QGaussChebyshev< dim > Class Template Reference

#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. More...
	QGaussChebyshev (const unsigned int n)
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)

Additional Inherited Members
Public Types inherited from Quadrature< dim >
using	SubQuadrature = Quadrature< dim - 1 >
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 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 499 of file quadrature_lib.h.

Constructor & Destructor Documentation

QGaussChebyshev() [1/2]

template<int dim>

QGaussChebyshev< dim >::QGaussChebyshev

(

const unsigned int

n

)

Generate a formula with n quadrature points.

Definition at line 1019 of file quadrature_lib.cc.

QGaussChebyshev() [2/2]

QGaussChebyshev< 1 >::QGaussChebyshev

(

const unsigned int

n

)

Definition at line 1003 of file quadrature_lib.cc.

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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