NAME¶

newton - nonlinear solver (rheolef-7.1)

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.