.TH "continuation" 3rheolef "Sat Mar 13 2021" "Version 7.1" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
continuation \- nonlinear solver (rheolef-7\&.1)
.PP
  
.SH "SYNOPSIS"
.PP
.PP
.nf
template<class Problem>
void continuation (
  Problem&                        F,
  typename Problem::value_type&   uh,
  odiststream*                    p_out,
  odiststream*                    p_err,
  const continuation_option& opts = continuation_option())
.fi
.PP
 
.SH "DESCRIPTION"
.PP
This function implements a generic damped Newton method for the resolution of the following problem: 
.PP
.nf
    F(lambda,u) = 0

.fi
.PP
 where \fClambda\fP is a parameter and \fCu\fP is the corresponding solution, that depends upon \fClambda\fP\&. The main idea is to follow a branch of solution denoted as \fCu(lambda)\fP when the parameter \fClambda\fP varies\&. A simple call to the algorithm writes: 
.PP
.nf
    my_problem P;
    field uh (Vh,0);
    continuation (P, uh, &dout, &derr);

.fi
.PP
 The optional argument \fBcontinuation_option(3)\fP allows one to control some features of the algorithm\&.
.PP
The continuation algorithm bases on the \fBdamped_newton(3)\fP method\&. In addition to the members required for the \fBdamped_newton(3)\fP method, several additional members are required for the continuation one\&. The requirements are: 
.PP
.nf
    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;
    };

.fi
.PP
 
.SH "EXAMPLE"
.PP
See the example \fBcombustion_continuation\&.cc\fP example and the \fBusersguide\fP for more\&.
.SH "ADAPTIVE MESH"
.PP
There are two versions of this algorithm:
.PP
.IP "\(bu" 2
one with imbedded mesh adaptation loop
.IP "\(bu" 2
one without this feature
.PP
.PP
The algorithm is automatically selected when there is an \fCadapt()\fP method in the problem definition\&.
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file main/lib/continuation\&.h 
.SH AUTHOR
Pierre  Saramito  <Pierre.Saramito@imag.fr>
.SH 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.