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 [AT] 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.