Rheolef
7.2
an efficient C++ finite element environment
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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; };
See the example combustion_continuation.cc example and the User's guide for more.
There are two versions of this algorithm:
The algorithm is automatically selected when there is an adapt()
method in the problem definition.
This documentation has been generated from file main/lib/continuation.h