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continuation(4rheolef) rheolef-7.0 continuation(4rheolef)

NAME

continuation -- continuation algorithm for nonlinear problems

DESCRIPTION

This function applies a continuation algorithm for the resolution of the following problem:



       F(lambda,u) = 0
where lambda is a parameter and u is the corresponding solution. The main idea is to follow a branch of solution 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 continuation algorithm bases on the damped_newton (see damped_newton(4)) and thus requirement for the my_problem class may contains methods for the evaluation of F (aka the residue) and its derivative: 



    class my_problem {


    public:


      typedef value_type;


      typedef float_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_versus_parameter (const field& uh) const;


      value_type derivative_solve      (const value_type& mrh) const;


      value_type derivative_trans_mult (const value_type& mrh) 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;


    };
See the example combustion.h in the user's documentation for more. The optional argument of type class continuation_option (see continuation_option(2)) allows one to control some features of the algorithm.

IMPLEMENTATION

template<class Problem>
void
continuation (


  Problem&                        F,


  typename Problem::value_type&   uh,


  odiststream*                    p_out,


  odiststream*                    p_err,


  const continuation_option& opts = continuation_option())

SEE ALSO

damped_newton(4), continuation_option(2)

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.

rheolef-7.0 rheolef-7.0