level_set(4rheolef) [debian man page]

level_set(4rheolef)						    rheolef-6.1 					       level_set(4rheolef)

NAME

       level_set - compute a level set from a function

SYNOPSYS

       geo level_set (const field& fh);

DESCRIPTION

       Given  a  function fh defined in a domain Lambda, compute the level set defined by {x in Lambda, fh(x) = 0}.  This level set is represented
       by the geo class.

OPTIONS

       The option class leve_set_option_type controls the slit of quadrilaterals into triangles for tridimensional intersected	surface  and  also
       the zero machine precision, epsilon.

IMPLEMENTATION

       struct level_set_option_type {
	   bool split_to_triangle;
	   Float epsilon;
	   level_set_option_type()
	    : split_to_triangle(true),
	      epsilon(100*std::numeric_limits<Float>::epsilon())
	      {}
       };
       template <class T, class M>
       geo_basic<T,M> level_set (
	 const field_basic<T,M>& fh,
	 const level_set_option_type& opt = level_set_option_type());

rheolef-6.1							    rheolef-6.1 					       level_set(4rheolef)

newton(4rheolef)						    rheolef-6.1 						  newton(4rheolef)

NAME

       newton -- Newton nonlinear algorithm

DESCRIPTION

       Nonlinear Newton algorithm for the resolution of the following problem:

	      F(u) = 0

       A simple call to the algorithm writes:

	   my_problem P;
	   field uh (Vh);
	   newton (P, uh, tol, max_iter);

       The my_problem class may contains methods for the evaluation of F (aka residue) and its derivative:

	   class my_problem {
	   public:
	     my_problem();
	     field residue (const field& uh) const;
	     void update_derivative (const field& uh) const;
	     field derivative_solve (const field& mrh) const;
	     Float norm (const field& uh) const;
	     Float dual_norm (const field& Muh) const;
	   };

       See the example p-laplacian.h in the user's documentation for more.

IMPLEMENTATION

       template <class Problem, class Field>
       int newton (Problem P, Field& uh, Float& tol, size_t& max_iter, odiststream *p_derr = 0) {
	   if (p_derr) *p_derr << "# Newton: n r" << std::endl;
	   for (size_t n = 0; true; n++) {
	     Field rh = P.residue(uh);
	     Float r = P.dual_norm(rh);
	     if (p_derr) *p_derr << n << " " << r << std::endl;
	     if (r <= tol) { tol = r; max_iter = n; return 0; }
	     if (n == max_iter) { tol = r; return 1; }
	     P.update_derivative (uh);
	     Field delta_uh = P.derivative_solve (-rh);
	     uh += delta_uh;
	   }
       }

rheolef-6.1							    rheolef-6.1 						  newton(4rheolef)