riesz(4rheolef) [debian man page]

riesz(4rheolef) 						    rheolef-6.1 						   riesz(4rheolef)

NAME

       riesz - integrate a function by using quadrature formulae

DESCRIPTION

       The function riesz implements the approximation of an integral by using quadrature formulae.

SYNOPSYS

	template <class Function>
	field riesz (const space& Xh, const Function& f, quadrature_option_type qopt = default_value);

	template <class Function>
	field riesz (const space& Xh, const Function& f, const geo& domain, quadrature_option_type qopt = default_value);

EXAMPLE

       The following code compute the Riesz representant, denoted by lh of f(x), and the integral of f over the domain omega:

	 Float f(const point& x);
	 ...
	 space Xh (omega_h, "P1");
	 field lh = riesz (Xh, f);
	 Float int_f = dot(lh, 1);

       The Riesz representer is the lh vector of values:

	 lh(i) = integrate f(x) phi_i(x) dx

       where  phi_i is the i-th basis function in Xh and the integral is evaluated by using a quadrature formulae.  By default the quadrature for-
       mule is the Gauss one with the order equal to the polynomial order of Xh.  Alternative quadrature formulae and order is available by  pass-
       ing an optional variable to riesz.

OPTIONS

       An  optional  argument specifies the quadrature formulae used for the computation of the integral.  The domain of integration is by default
       the mesh associated to the finite element space.  An alternative domain dom, e.g. a part of the boundary can be supplied as an extra  argu-
       ment.  This domain can be also a band associated to the banded level set method.

IMPLEMENTATION

       template <class T, class M, class Function>
       field_basic<T,M>
       riesz (
	   const space_basic<T,M>&	 Xh,
	   const Function&		 f,
	   const quadrature_option_type& qopt
	      = quadrature_option_type(quadrature_option_type::max_family,0))

IMPLEMENTATION

       template <class T, class M, class Function>
       field_basic<T,M>
       riesz (
	   const space_basic<T,M>&	 Xh,
	   const Function&		 f,
	   const geo_basic<T,M>&	 dom,
	   const quadrature_option_type& qopt
	      = quadrature_option_type(quadrature_option_type::max_family,0))

IMPLEMENTATION

       template <class T, class M, class Function>
       field_basic<T,M>
       riesz (
	   const space_basic<T,M>&	 Xh,
	   const Function&		 f,
	   std::string			 dom_name,
	   const quadrature_option_type& qopt
	      = quadrature_option_type(quadrature_option_type::max_family,0))

IMPLEMENTATION

       template <class T, class M, class Function>
       field_basic<T,M>
       riesz (
	   const space_basic<T,M>&	 Xh,
	   const Function&		 f,
	   const band_basic<T,M>&	 gh,
	   const quadrature_option_type& qopt
	      = quadrature_option_type(quadrature_option_type::max_family,0))

rheolef-6.1							    rheolef-6.1 						   riesz(4rheolef)

Check Out this Related Man Page

quadrature(7rheolef)						    rheolef-6.1 					      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 refer-
       ence 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)

rheolef-6.1							    rheolef-6.1 					      quadrature(7rheolef)

Linux and UNIX Man Pages

riesz(4rheolef) [debian man page]

Check Out this Related Man Page