Reference documentation for deal.II version Git 35565f205e 2019-09-24 08:33:37 +0200
Public Types | Public Member Functions | List of all members
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.
 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 () override=default
Quadratureoperator= (const Quadrature< dim > &)
Quadratureoperator= (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
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 Subscriptor (const Subscriptor &)
 Subscriptor (Subscriptor &&) noexcept
virtual ~Subscriptor ()
Subscriptoroperator= (const Subscriptor &)
Subscriptoroperator= (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

- Static Public Member Functions inherited from Subscriptor
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
static ::ExceptionBaseExcNoSubscriber (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.

Giuseppe Pitton, Luca Heltai 2015

Definition at line 524 of file quadrature_lib.h.

Member Enumeration Documentation

◆ EndPoint

template<int dim>
enum QGaussRadauChebyshev::EndPoint

Left end point.


Right end point.

Definition at line 530 of file quadrature_lib.h.

Constructor & Destructor Documentation

◆ QGaussRadauChebyshev()

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

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: