`damped_newton`

nonlinear solver

# 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` 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 User's guide for more.

# Implementation

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

u
Definition: leveque.h:25
rheolef::damped_newton
int damped_newton(const Problem &P, const Preconditioner &T, Field &u, Real &tol, Size &max_iter, odiststream *p_derr=0)
see the damped_newton page for the full documentation
Definition: damped-newton-generic.h:29