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 value_t, 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

Template Parameters:

value_t – type of coefficients

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 value_t, template<typename, typename...> typename _splitting_method_t, typename state_t, typename optional_args_t, typename ...Algorithms_t>
auto ponio::make_method(splitting::detail::splitting_tuple<_splitting_method_t, value_t, optional_args_t, Algorithms_t...> const &algos, state_t const &shadow_of_u0)#

generic factory for splitting methods to build a method from a tuple of algorithms and a state

Template Parameters:

  • _splitting_method_t – splitting method (Lie or Strang splitting)

  • value_t – type of coefficients and time step

  • state_t – type of state

  • optional_args_t – type of tuple of optional arguments to build _splitting_method_t object (void if not needed)

  • Algorithms_t – types of algorithms to solve each step of splitting

Parameters:

  • algos – tuple of algorithms and splitting method

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

An helper function for splitting method factory.

template<typename value_t, 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