damped_newton(4) damped Newton nonlinear algorithm


Nonlinear damped Newton algorithm for the resolution of the following problem:

       F(u) = 0

A simple call to the algorithm writes:

    my_problem P;
    field uh (Vh);
    damped_newton (P, uh, tol, max_iter);

The my_problem class may contains methods for the evaluation of F (aka residue) and its derivative:

    class my_problem {
      field residue (const field& uh) const;
      void update_derivative (const field& uh) const;
      field derivative_trans_mult (const field& mrh) const;
      field derivative_solve (const field& mrh) const;
      Float norm (const field& uh) const;
      Float dual_norm (const field& Muh) const;

See the example p-laplacian.h in the user's documentation for more.


template <class Problem, class Field, class Real, class Size>
int damped_newton (Problem P, Field& u, Real& tol, Size& max_iter, odiststream* p_derr=0) {
  return damped_newton(P, newton_identity_preconditioner(), u, tol, max_iter, p_derr);