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<tt>continuation</tt>

nonlinear solver

# Synopsis

template<class Problem>
void continuation (
Problem& F,
typename Problem::value_type& uh,
odiststream* p_out,
odiststream* p_err,
const continuation_option& opts = continuation_option())
rheolef::continuation
void continuation(Problem &F, typename Problem::value_type &uh, odiststream *p_out, odiststream *p_err, const continuation_option &opts=continuation_option())
see the continuation page for the full documentation
Definition continuation.h:303

# Description

This function implements a generic damped Newton method for the resolution of the following problem:

        F(lambda,u) = 0

where `lambda` is a parameter and `u` is the corresponding solution, that depends upon `lambda`. The main idea is to follow a branch of solution denoted as `u(lambda)` when the parameter `lambda` varies. A simple call to the algorithm writes:

        my_problem P;
        field uh (Vh,0);
        continuation (P, uh, &dout, &derr);

The optional argument `continuation_option` allows one to control some features of the algorithm.

The continuation algorithm bases on the `damped_newton` method. In addition to the members required for the `damped_newton` method, several additional members are required for the continuation one. The requirements are:

        class my_problem {
        public:
          typedef float_type;
          typedef value_type;
          string parameter_name() const;
          float_type parameter() const;
          void set_parameter (float_type lambda);
          value_type residue          (const value_type& uh) const;
          void update_derivative      (const value_type& uh) const;
          csr<float_type> derivative  (const value_type& uh) const;
          value_type derivative_solve      (const value_type& mrh) const;
          value_type derivative_trans_mult (const value_type& mrh) const;
          value_type derivative_versus_parameter (const field& uh) const;
          bool stop (const value_type& xh) const;
          idiststream& get (idiststream& is,       value_type& uh);
          odiststream& put (odiststream& os, const value_type& uh) const;
          float_type space_norm (const value_type& uh) const;
          float_type dual_space_norm (const value_type& mrh) const;
          float_type space_dot (const value_type& xh, const value_type& yh) const;
          float_type dual_space_dot (const value_type& mrh, const value_type& msh) const;
          value_type massify   (const value_type& uh) const;
          value_type unmassify (const value_type& mrh) const;
        };

# Example

See the example combustion_continuation.cc example and the User's guide for more.

# Adaptive mesh

There are two versions of this algorithm:

- one with imbedded mesh adaptation loop
- one without this feature

The algorithm is automatically selected when there is an `adapt()` method in the problem definition.

# Implementation

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