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:

// typedefs:

    typedef typename quadrature_on_geo<T>::size_type                 size_type;
    typedef quadrature_option_type::family_type                      family_type;
    typedef typename std::vector<weighted_point<T> >::const_iterator const_iterator;

// allocators:

    quadrature (quadrature_option_type opt = quadrature_option_type());

// modifiers:

    void set_order  (size_type order);
    void set_family (family_type ft);

// accessors:

    size_type      get_order() const;
    family_type    get_family() const;
    std::string    get_family_name() const;
    size_type      size  (reference_element hat_K) const;
    const_iterator begin (reference_element hat_K) const;
    const_iterator end   (reference_element hat_K) const;
    template<class U>
    friend std::ostream& operator<< (std::ostream&, const quadrature<U>&);
protected:
    quadrature_option_type        _options;
    mutable quadrature_on_geo<T>  _quad [reference_element::max_variant];
    mutable std::vector<bool>     _initialized;
    void _initialize (reference_element hat_K) const;
private:
    quadrature (const quadrature<T>&);
    quadrature operator= (const quadrature<T>&);
};
 

SEE ALSO¶

reference_element(2)