---
name: "continuation"
section: "3rheolef"
platform: "linux"
package: "librheolef-dev"
version: "7.2-4"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/continuation"
---

# continuation(3rheolef)

nonlinear solver (rheolef-7.2)

## 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.