continuation

nonlinear solver

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 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;
    };

Example

See the example combustion_continuation.cc example and the User's guide 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