debian man page for characteristic

characteristic(2rheolef)					    rheolef-6.1 					  characteristic(2rheolef)

NAME
       characteristic - the Lagrange-Galerkin method implemented

SYNOPSYS
	The class characteristic implements the Lagrange-Galerkin method:
	It is the extension of the method of characteristic from the finite
	difference to the finite element context.

EXAMPLE
	The following code compute the Riesz representer (see riesz(4)),
	denoted by lh of u(x)=uh(x+dh(x)) where ah is the
	deformation vector field. The deformation field dh=-dt*uh
	in Lagrange-Galerkin methods, where ah is the advection field
	and dt a time step.

	 geo omega;
	 field dh = ...;
	 field uh = ...;
	 characteristic X (dh);
	 field lh = riesz(Xh, compose(uh, X));

	The Riesz representer is the lh vector field defined by:

	       lh(i) = integrate uh(x+dh(x)) phi_i(x) dx

	where phi_i is the i-th basis function in the space Xh
	and the integral is evaluated by using a quadrature formulae.
	By default the quadrature formule is Gauss-Lobatto with
	the order equal to the polynomial order of Xh
	(order 1: trapeze, order 2: simpson, etc).
	Recall that this choice of quadrature formulae guaranties inconditional
	stability at any polynomial order.
	Alternative quadrature formulae or order can be used by using the
	additional quadrature option argument to the riesz function.

IMPLEMENTATION
       template<class T, class M = rheo_default_memory_model>
       class characteristic_basic : public smart_pointer<characteristic_rep<T,M> > {
       public:
	 typedef characteristic_rep<T,M> rep;
	 typedef smart_pointer<rep>	 base;

       // allocator:

	 characteristic_basic(const field_basic<T,M>& dh);

       // accesors:

	 const field_basic<T,M>& get_displacement() const;

	 const characteristic_on_quadrature<T,M>&
	 get_pre_computed (
	   const space_basic<T,M>&	 Xh,
	   const field_basic<T,M>&	 dh,
	   const quadrature_option_type& qopt) const;

       };
       typedef characteristic_basic<Float> characteristic;

IMPLEMENTATION
       template<class T, class M>
       inline
       field_o_characteristic<T,M>
       compose (const field_basic<T,M>& uh, characteristic_basic<T,M>& X)

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

SEE ALSO
       riesz(4)

rheolef-6.1							    rheolef-6.1 					  characteristic(2rheolef)