NAME¶

continuation - nonlinear solver (rheolef-7.1)

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())

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(3) allows one to control some features of the algorithm.

The continuation algorithm bases on the damped_newton(3) method. In addition to the members required for the damped_newton(3) 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 usersguide 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

AUTHOR¶

Pierre Saramito <Pierre.Saramito@imag.fr>

COPYRIGHT¶

Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>. This is free software: you are free to change and redistribute it. There is NO WARRANTY, to the extent permitted by law.