grad_grad(3rheolef) [debian man page]

grad_grad(3rheolef)						    rheolef-6.1 					       grad_grad(3rheolef)

NAME

       grad_grad -- -Laplacian operator

SYNOPSIS

	     form(const space V, const space& V, "grad_grad");

DESCRIPTION

       Assembly the form associated to the Laplacian operator on a finite element space V:

		      /
		      |
	     a(u,v) = |  grad(u).grad(v) dx
		      |
		      / Omega

       The V space may be a either P1 , P2  or P1d  finite element space.  See also form(2) and space(2).

EXAMPLE

       The following piece of code build the Laplacian form associated to the P1 approximation:

	       geo g("square");
	       space V(g, "P1");
	       form a(V, V, "grad_grad");

SEE ALSO

       form(2), space(2)

rheolef-6.1							    rheolef-6.1 					       grad_grad(3rheolef)

form_element(7rheolef)						    rheolef-6.1 					    form_element(7rheolef)

NAME

       form_element - bilinear form on a single element

SYNOPSYS

       The form_element class defines functions that compute a bilinear form defined between two polynomial basis on a single geometrical element.
       This bilinear form is represented by a matrix.

       The bilinear form is designated by a string, e.g. "mass", "grad_grad", ...  indicating the form. The form depends also of  the  geometrical
       element: triangle, square, tetrahedron (see geo_element(2)).

IMPLEMENTATION NOTE

       The  form_element class is managed by (see smart_pointer(2)).  This class uses a pointer on a pure virtual class form_element_rep while the
       effective code refers to the specific concrete derived classes: mass, grad_grad, etc.

IMPLEMENTATION

       template <class T, class M>
       class form_element : public smart_pointer<form_element_rep<T,M> > {
       public:

       // typedefs:

	   typedef form_element_rep<T,M>	 rep;
	   typedef smart_pointer<rep>		 base;
	   typedef typename rep::size_type	 size_type;
	   typedef typename rep::vertex_type	 vertex_type;
	   typedef typename rep::space_type	 space_type;
	   typedef typename rep::geo_type	 geo_type;
	   typedef typename rep::coordinate_type coordinate_type;

       // constructors:

	   form_element ();
	   form_element (
	       std::string	     name,
	       const space_type&     X,
	       const space_type&     Y,
	       const geo_type&	     omega,
	       const quadrature_option_type& qopt);

       // accessors & modifier:

	   void operator() (const geo_element& K, ublas::matrix<T>& m) const;
	   virtual bool is_symmetric () const;

       // for scalar-weighted forms:

	   void set_weight (const field_basic<T,M>& wh) const;
	   bool is_weighted() const;
	   const field_basic<T,M>& get_weight () const;

       // for banded level set method:

	   bool is_on_band() const;
	   const band_basic<T,M>& get_band() const;
	   void set_band (const band_basic<T,M>& bh) const;

       };

SEE ALSO

       geo_element(2), smart_pointer(2)

rheolef-6.1							    rheolef-6.1 					    form_element(7rheolef)