NAME

damped_newton - nonlinear solver (rheolef-7.1)

SYNOPSIS

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)

DESCRIPTION

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

EXAMPLE

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

IMPLEMENTATION

This documentation has been generated from file main/lib/damped_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.