`newton`

nonlinear solver

# 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`. 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 User's guide for more.

# Implementation

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

rheolef::newton
int newton(const Problem &P, Field &uh, Float &tol, size_t &max_iter, odiststream *p_derr=0)
see the newton page for the full documentation
Definition: newton.h:98
Float
see the Float page for the full documentation