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)

domain_indirect(7rheolef)					    rheolef-6.1 					 domain_indirect(7rheolef)

NAME

       domain_indirect - a named part of a finite element mesh

DESCRIPTION

       The  domain_indirect  class  defines  a	container for a part of a finite element mesh.	This describes the connectivity of edges or faces.
       This class is usefull for boundary condition setting.

IMPLEMENTATION NOTE

       The domain class is splitted into two parts.  The first one is the domain_indirect class, that contains the main renumbering  features:	it
       acts  as  a  indirect  on  a  geo class(see geo(2)).  The second one is the domain class, that simply contains two smart_pointers: one on a
       domain_indirect and the second on the geo where renumbering is acting.  Thus, the domain class develops a complete geo-like interface,  via
       the  geo_abstract_rep  pure virtual class derivation, and can be used by the space class (see space(2)).  The split between domain_indirect
       and domain is necessary, because the geo class contains a list of domain_indirect.  It cannot contains  a  list	of  domain  classes,  that
       refers to the geo class itself: a loop in reference counting leads to a blocking situation in the automatic deallocation.

IMPLEMENTATION

       template <>
       class domain_indirect_basic<sequential> : public smart_pointer<domain_indirect_rep<sequential> > {
       public:

       // typedefs:

	   typedef domain_indirect_rep<sequential> rep;
	   typedef smart_pointer<rep>	     base;
	   typedef rep::size_type	     size_type;
	   typedef rep::iterator_ioige	     iterator_ioige;
	   typedef rep::const_iterator_ioige const_iterator_ioige;

       // allocators:

	   domain_indirect_basic ();

	   template <class T>
	   domain_indirect_basic (
	       const geo_basic<T,sequential>&  omega,
	       const std::string&	       name,
	       size_type		       map_dim,
	       const communicator&	       comm,
	       const std::vector<size_type>&   ie_list);

	   template <class U>
	   domain_indirect_basic (
	       array<geo_element_auto<heap_allocator<size_type> >,sequential, heap_allocator<size_type> >&
					       d_tmp,
	       const geo_basic<U, sequential>& omega,
	       std::vector<index_set>*	       ball);

	   void resize (size_type n);

       // accessors:

	   size_type size()	const;
	   size_type dis_size() const;
	   const distributor& ownership() const;

	   const_iterator_ioige ioige_begin() const;
	   const_iterator_ioige ioige_end()   const;
		 iterator_ioige ioige_begin();
		 iterator_ioige ioige_end();

	   const geo_element_indirect& oige (size_type ioige) const;

	   void set_name (std::string name);
	   void set_map_dimension (size_type map_dim);
	   std::string name ()	  const;
	   size_type map_dimension () const;

       // i/o:

	   odiststream& put (odiststream&) const;
	   template <class T>
	   idiststream& get (idiststream& ips, const geo_rep<T,sequential>& omega, std::vector<index_set> *ball);
       };

IMPLEMENTATION

       template <>
       class domain_indirect_basic<distributed> : public smart_pointer<domain_indirect_rep<distributed> > {
       public:

       // typedefs:

	   typedef domain_indirect_rep<distributed>  rep;
	   typedef smart_pointer<rep>		 base;
	   typedef rep::size_type		 size_type;

       // allocators:

	   domain_indirect_basic ();
	   template<class T>
	   domain_indirect_basic (
	       const geo_basic<T,distributed>& omega,
	       const std::string&	     name,
	       size_type		     map_dim,
	       const communicator&	     comm,
	       const std::vector<size_type>& ie_list);

       // accessors/modifiers:

	   size_type size()	const;
	   size_type dis_size() const;
	   const distributor& ownership() const;

	   const geo_element_indirect& oige (size_type ioige) const;

	   void set_name (std::string name);
	   void set_map_dimension (size_type map_dim);
	   std::string name () const;
	   size_type map_dimension () const;

       // distributed specific acessors:

	   const distributor& ini_ownership() const;
	   size_type ioige2ini_dis_ioige (size_type ioige) const;
	   size_type ini_ioige2dis_ioige (size_type ini_ioige) const;

       // i/o:

	   template <class T>
	   idiststream& get (idiststream& ips, const geo_rep<T,distributed>& omega);
	   template <class T>
	   odiststream& put (odiststream& ops, const geo_rep<T,distributed>& omega) const;
       };

SEE ALSO

       geo(2), space(2)

rheolef-6.1							    rheolef-6.1 					 domain_indirect(7rheolef)