integrate(4rheolef) [debian man page]

integrate(4rheolef)						    rheolef-6.1 					       integrate(4rheolef)

NAME

       integrate - integrate a function

DESCRIPTION

       Integrate a function over a domain by using a quadrature formulae.

SYNOPSYS

	template <class T, class M, class Function>
	T integrate (const geo_basic<T,M>& g, Function f, quadrature_option_type qopt)

EXAMPLE

	 Float f(const point& x);
	 ...
	 Float value = integrate (omega, f, quadrature_option);

	An optional argument specifies the quadrature formulae used
	for the computation of the integral.

IMPLEMENTATION

       template <class T, class M, class Function>
       T integrate (const geo_basic<T,M>& g, Function f, const quadrature_option_type& qopt)
       {
	   space_basic<T,M> Xh (g, "P0");
	   field_basic<T,M> int_K_f_dx = riesz (Xh, f, qopt);
	   return dot (1, int_K_f_dx);
       }

rheolef-6.1							    rheolef-6.1 					       integrate(4rheolef)

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)