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quadrature - quadrature formulae on the reference lement

quadrature(7rheolef) rheolef-6.7 quadrature(7rheolef)

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)
rheolef-6.7 rheolef-6.7