damped_newton - nonlinear solver (rheolef-7.2)

       Pierre  Saramito  <Pierre.Saramito@imag.fr>

       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.

rheolef                                            Version 7.2                           damped_newton(3rheolef)

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

           F(u) = 0

        Recall that the damped Newton method is more robust than the basic Newton one: it converges from any
       initial value.

       A simple call to the algorithm writes:

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

        In addition to the members required for the newton(3) method, two additional members are required for
       the damped variant:

           class my_problem {
           public:
             ...
             value_type derivative_trans_mult (const value_type& mrh) const;
             Float space_norm (const value_type& uh) const;
           };

        The derivative_trans_mult is used for computing the damping coefficient. The space_norm represents
       usually a L2 norm e.g. formally:

                                 /
           space_norm(uh) = sqrt |       |uh(x)|^2 dx
                                 / Omega

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

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

       damped_newton - nonlinear solver (rheolef-7.2)

       template <class Problem, class Field, class Real, class Size>
       int damped_newton (const Problem& F, Field& u, Real& tol, Size& max_iter, odiststream* p_derr=0)