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