quadrature(9)
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 internal}'). 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
class quadrature {
public:
- // typedefs:
- typedef quadrature_on_geo::size_type size_type;
typedef quadrature_option_type::family_type family_type;
typedef std::vector<weighted_point>::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;
friend std::ostream& operator<< (std::ostream&, const quadrature&);- protected:
- quadrature_option_type _options;
mutable quadrature_on_geo _quad [reference_element::max_size];
mutable std::vector<bool> _initialized;
void _initialize (reference_element hat_K) const; - private:
- quadrature (const quadrature&);
quadrature operator= (const quadrature&); - };