NAME

       continuation - nonlinear solver (rheolef-7.2)

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.