NAME¶

quadrature - quadrature formulae on the reference lement

SYNOPSIS¶

The quadrature class defines a container for a quadrature formulae on the reference element (see reference_element(2)). This container stores the nodes coordinates and the weights.

THE CONSTRUCTOR TAKES TWO ARGUMENTS¶

the reference element K and the order r of the quadrature formulae. The formulae is exact when computing the integral of a polynom p that degree is less or equal to order r.

                  n


    /            ___


    | p(x) dx =      p(x_q) w_q


    / K          /__


                 q=1

LIMITATIONS¶

The formulae is optimal when it uses a minimal number of nodes n. Optimal quadrature formula are hard-coded in this class. Not all reference elements and orders are yet implemented. This class will be completed in the future.

IMPLEMENTATION¶

template<class T>
class quadrature : public smart_pointer<quadrature_rep<T> > {
public:
// typedefs:


    typedef quadrature_rep<T>              rep;


    typedef smart_pointer<rep>             base;


    typedef typename rep::size_type        size_type;


    typedef typename rep::family_type      family_type;


    typedef typename rep::const_iterator   const_iterator;


    typedef typename rep::orientation_type orientation_type;
// allocators:


    quadrature (quadrature_option opt = quadrature_option())


     : base(new_macro(rep(opt))) {}
// modifiers:


    void set_order  (size_type order) { base::data().set_order(order); }


    void set_family (family_type ft)  { base::data().set_family(ft); }
// accessors:


    size_type      get_order() const { return base::data().get_order();}


    family_type    get_family() const { return base::data().get_family();}


    std::string    get_family_name() const { return base::data().get_family_name();}


    const quadrature_option& get_options() const { return base::data().get_options(); }


    size_type      size  (reference_element hat_K) const { return base::data().size(hat_K); }


    const_iterator begin (reference_element hat_K) const { return base::data().begin(hat_K); }


    const_iterator end   (reference_element hat_K) const { return base::data().end(hat_K); }


    const weighted_point<T>& operator() (reference_element hat_K, size_type q) const


                                                         { return base::data().operator() (hat_K,q); }
// side accessor:


    void side_initialize (


        reference_element             tilde_K,


        size_type                     loc_isid,


        reference_element             hat_S,


        size_type                     shift,


        orientation_type              orient) const {


            base::data().side_initialize (tilde_K, loc_isid, hat_S, shift, orient);


    }
};

SEE ALSO¶

reference_element(2)

COPYRIGHT¶

Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>. This is free software: you are free to change and redistribute it. There is NO WARRANTY, to the extent permitted by law.