NAME
damped_newton - nonlinear solver (rheolef-7.2)
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 [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.