Reference documentation for deal.II version Git d9b14c2d54 2019-09-14 18:13:29 -0600
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Public Member Functions | List of all members
QGaussLobattoChebyshev< dim > Class Template Reference

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

Inheritance diagram for QGaussLobattoChebyshev< dim >:
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Public Member Functions

 QGaussLobattoChebyshev (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 QGaussLobattoChebyshev< dim >

Gauss-Lobatto-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 two of the quadrature points are located at the endpoints of the quadrature interval. The nodes and weights are known analytically, and are exact for monomials up to the order \(2n-3\), 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. 25.4.40

Author
Giuseppe Pitton, Luca Heltai 2015

Definition at line 571 of file quadrature_lib.h.


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