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)