Method class

Note

Naming convention: about type name of template parameter.

• Algorithm_t matches to an algorithm i.e. a class that contains stages of a Runge-Kutta method. It needs to provide an operator () with the following definition:

  state_t operator()( Stage<s>, Problem_t& f, value_t tn, state_t const& un, ArrayKi_t const& ki, value_t dt)
  

• Method_t matches to the ponio::method class, and provides the following operator ():

  state_t operator()(Problem_t& f, value_t tn, state_t const& un, value_t dt)
  

template<typename Algorithm_t, typename state_t>
class method

define a time method

A method is define by its algorithm (how compute \(u^{n+1}\) from \((t^n,u^n,\Delta t)\)) and store possible substeps. Actually this class avoid the user to specify a template parameter, while making it easy to add new methods.

Template Parameters:

• Algorithm_t – type of the algorithm which define properly the method

• state_t – type of \(u^n\)

There is 0 overloading of ponio::make_method function, one for generic algorithm, and one for each implemanted splitting method (Lie splitting method and Strang splitting method).

template<typename Algorithm_t, typename state_t>
auto ponio::make_method(Algorithm_t const &algo, state_t const &shadow_of_u0)

generic factory to build a method from an algoritm, it only reuses method constructor

Parameters:

• algo – a Algorithm_t objet with predifined stages of the method

• shadow_of_u0 – an object with the same size of computed value for allocation

template<typename ...Algorithms_t, typename state_t>
auto ponio::make_method(splitting::lie::lie_tuple<Algorithms_t...> const &algos, state_t const &shadow_of_u0)

generic factory to build a method from an algoritm, it only reuses method constructor

Parameters:

• algos – a variadic splitting::lie_tuple of Algorithms_t

• shadow_of_u0 – an object with the same size of computed value for allocation

template<typename ...Algorithms_t, typename state_t>
auto ponio::make_method(splitting::strang::strang_tuple<Algorithms_t...> const &algos, state_t const &shadow_of_u0)

generic factory to build a method from an algoritm, it only reuses method constructor

Parameters:

• algos – a variadic splitting::strang_tuple of Algorithms_t

• shadow_of_u0 – an object with the same size of computed value for allocation

An helper function for splitting method factory.

template<typename state_t, typename ...Algorithms_t>
auto ponio::make_tuple_methods(std::tuple<Algorithms_t...> const &algos, state_t const &shadow_of_u0)

factory of tuple of methods from a tuple of Algorithm_t

this factory is to prevent duplucation of code in factory of methods for splitting methods (Lie or Strang method).

Parameters:

• algos – a tuple of Algorithm_t objets with predifined stages

• shadow_of_u0 – an object with the same size of computed value for allocation