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| QGaussLobatto (const unsigned int n) |
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template<> |
| QGaussLobatto (const unsigned int n) |
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| Quadrature (const unsigned int n_quadrature_points=0) |
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| Quadrature (const SubQuadrature &, const Quadrature< 1 > &) |
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| Quadrature (const Quadrature< dim!=1?1:0 > &quadrature_1d) |
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| Quadrature (const Quadrature< dim > &q) |
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| Quadrature (const std::vector< Point< dim > > &points, const std::vector< double > &weights) |
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| Quadrature (const std::vector< Point< dim > > &points) |
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| Quadrature (const Point< dim > &point) |
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virtual | ~Quadrature () |
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Quadrature & | operator= (const Quadrature< dim > &) |
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bool | operator== (const Quadrature< dim > &p) const |
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void | initialize (const std::vector< Point< dim > > &points, const std::vector< double > &weights) |
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unsigned int | size () const |
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const Point< dim > & | point (const unsigned int i) const |
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const std::vector< Point< dim > > & | get_points () const |
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double | weight (const unsigned int i) const |
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const std::vector< double > & | get_weights () const |
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std::size_t | memory_consumption () const |
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void | serialize (Archive &ar, const unsigned int version) |
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| Subscriptor () |
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| Subscriptor (const Subscriptor &) |
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virtual | ~Subscriptor () |
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Subscriptor & | operator= (const Subscriptor &) |
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void | subscribe (const char *identifier=0) const |
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void | unsubscribe (const char *identifier=0) const |
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unsigned int | n_subscriptions () const |
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void | list_subscribers () const |
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| DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.") |
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| DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1) |
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template<class Archive > |
void | serialize (Archive &ar, const unsigned int version) |
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std::vector< long double > | compute_quadrature_points (const unsigned int q, const int alpha, const int beta) const |
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std::vector< long double > | compute_quadrature_weights (const std::vector< long double > &x, const int alpha, const int beta) const |
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long double | JacobiP (const long double x, const int alpha, const int beta, const unsigned int n) const |
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long double | gamma (const unsigned int n) const |
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template<> |
std::vector< long double > | compute_quadrature_points (const unsigned int, const int, const int) const |
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template<> |
std::vector< long double > | compute_quadrature_weights (const std::vector< long double > &, const int, const int) const |
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template<> |
long double | JacobiP (const long double, const int, const int, const unsigned int) const |
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template<> |
long double | gamma (const unsigned int n) const |
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template<int dim>
class QGaussLobatto< dim >
The Gauss-Lobatto quadrature rule.
This modification of the Gauss quadrature uses the two interval end points as well. Being exact for polynomials of degree 2n-3, this formula is suboptimal by two degrees.
The quadrature points are interval end points plus the roots of the derivative of the Legendre polynomial Pn-1 of degree n-1. The quadrature weights are 2/(n(n-1)(Pn-1(xi)2).
Note: This implementation has not yet been optimized concerning numerical stability and efficiency. It can be easily adapted to the general case of Gauss-Lobatto-Jacobi-Bouzitat quadrature with arbitrary parameters alpha, beta, of which the Gauss-Lobatto-Legendre quadrature (alpha = beta = 0) is a special case.
- See Also
- http://en.wikipedia.org/wiki/Handbook_of_Mathematical_Functions
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Karniadakis, G.E. and Sherwin, S.J.: Spectral/hp element methods for computational fluid dynamics. Oxford: Oxford University Press, 2005
- Author
- Guido Kanschat, 2005, 2006; F. Prill, 2006
Definition at line 79 of file quadrature_lib.h.