NAME

       newton - nonlinear solver (rheolef-7.2)

SYNOPSIS

       template <class Problem, class Field>
       int newton (const Problem& P, Field& uh, Float& tol, size_t& max_iter, odiststream *p_derr = 0)

DESCRIPTION

       This function implements a generic Newton method for the resolution of the following
       problem:

           F(u) = 0

        A simple call to the algorithm writes:

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

        The my_problem class should contain some methods for the evaluation of F, i.e. the
       residue of the problem, and its derivative. The minimal requirements are:

           class my_problem {
           public:
             typedef value_type;
             value_type residue           (const value_type& uh)  const;
             void update_derivative       (const value_type& uh)  const;
             value_type  derivative_solve (const value_type& mrh) const;
             Float dual_space_norm        (const value_type& mrh) const;
           };

        The value_type could be a field(2). The Newton method could also be applied when
       value_type is a simple Float scalar. Conversely, it supports multi-field extensions.

       The update_derivative and derivative_solver members are called at each step of the Newton
       algorithm.

       The dual_space_norm member function returns a scalar from the weighted residual field term
       mrh returned by the residue function: this scalar is used as the stopping criterion of the
       algorithm.

EXAMPLE

       See the p_laplacian_newton.cc example and the usersguide for more.

IMPLEMENTATION

       This documentation has been generated from file main/lib/newton.h

AUTHOR

       Pierre  Saramito  <Pierre.Saramito@imag.fr>

COPYRIGHT

       Copyright   (C)  2000-2018  Pierre  Saramito  <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL
       version 3 or later  <http://gnu.org/licenses/gpl.html>.  This  is  free  software:  you
       are free to change and redistribute it.  There is NO WARRANTY, to the extent permitted by
       law.