Reference documentation for deal.II version Git 57495fa5ad 2019-09-23 17:04:23 +0200
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Public Member Functions | List of all members
QGaussChebyshev< dim > Class Template Reference

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

Inheritance diagram for QGaussChebyshev< dim >:
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Public Member Functions

 QGaussChebyshev (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 > &&) 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

- Public Types inherited from Quadrature< dim >
using SubQuadrature = Quadrature< dim - 1 >
 
- 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 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.


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