NAME¶

quadrature - quadrature formulae on the reference lement

SYNOPSYS¶

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_type opt = quadrature_option_type())
     : 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_type& 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); }
    template<class U>
    friend std::ostream& operator<< (std::ostream& os, const quadrature<U>& q) {
        return os << q.data(); }

// 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)