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Reference documentation for deal.II version 9.1.1
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Reference documentation for deal.II version 9.1.1
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#include <deal.II/base/quadrature_lib.h>
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 |
| 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 |
| 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 |
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
Definition at line 499 of file quadrature_lib.h.
1.8.14