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 [AT] imag.fr>
COPYRIGHT
Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito [AT] 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.