TRUSTSchema_RK.h

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#ifndef TRUSTSchema_RK_included
#define TRUSTSchema_RK_included
 
#include <Domaine_Cl_dis_base.h>
#include <Schema_Temps_base.h>
#include <Equation_base.h>
#include <type_traits>
 
using ARR1 = std::array<double, 1>; // OK je sais mais bon ... ne demande pas alors :-)
using ARR2 = std::array<double, 2>;
using ARR3 = std::array<double, 3>;
using ARR4 = std::array<double, 4>;
 
enum class Ordre_RK { UN , RATIO_DEUX , DEUX_CLASSIQUE , DEUX_WILLIAMSON , TROIS_CLASSIQUE , TROIS_WILLIAMSON , QUATRE_CLASSIQUE , QUATRE_CLASSIQUE_3_8 , QUATRE_WILLIAMSON };
 
template <Ordre_RK _ORDRE_ >
class TRUSTSchema_RK : public Schema_Temps_base
{
  // Renvoie le nombre de valeurs temporelles a conserver. Ici : n et n+1, donc 2.
  int nb_valeurs_temporelles() const override { return 2 ; }
 
  // Renvoie le nombre de valeurs temporelles futures. Ici : n+1, donc 1.
  int nb_valeurs_futures() const override { return 1 ; }
 
  // Renvoie le le temps a la i-eme valeur future. Ici : t(n+1)
  double temps_futur(int i) const override
  {
    assert(i == 1);
    return temps_courant() + pas_de_temps();
  }
 
  // Renvoie le le temps le temps que doivent rendre les champs a l'appel de valeurs(). Ici : t(n+1)
  double temps_defaut() const override { return temps_courant() + pas_de_temps(); }
 
  // a surcharger si utile
  void completer() override { /* Do nothing */ }
 
  friend class RK3_FT; // pour trio
  int faire_un_pas_de_temps_eqn_base(Equation_base& eq) override { return faire_un_pas_de_temps_eqn_base_generique<_ORDRE_>(eq); } // SFINAE :-)
 
protected:
  static constexpr int NW = 100;
 
  inline void print_warning(const int nw)
  {
    Cerr << finl << "**** Advice (printed only on the first " << nw << " time steps) ****" << finl;
    Cerr << "You are using Runge Kutta schema ! If you wish to increase the time step, try facsec between 1 and 2/3/4 (depends on the order of the scheme)." << finl;
  }
 
private:
  static constexpr double SQRT2 = 1.4142135623730950488016887242096980785696718753769480731766797, SQRT2_2 = SQRT2 / 2.;
 
  // RK low storage : See Williamson RK series https://www.sciencedirect.com/science/article/pii/0021999180900339
  static constexpr ARR2 A2 = { 0.0, SQRT2 - 2. };
  static constexpr ARR2 B2 = { SQRT2_2, SQRT2_2 };
 
  static constexpr ARR3 A3 = { 0.0, -5. / 9., -153. / 128. };
  static constexpr ARR3 B3 = { 1. / 3., 15. / 16., 8. / 15. };
 
  static constexpr ARR3 A4 = { 0.0, -1. /2. , -2. };
  static constexpr ARR3 B4 = { 1. / 2., 1. , 1. / 6. };
 
  // RK CLASSIQUE : see https://en.wikipedia.org/wiki/List_of_Runge%E2%80%93Kutta_methods
  static constexpr std::array<ARR1, 1> BUTCHER_2 = { { { 1. / 2. } } }; /* RK2 */
  static constexpr std::array<ARR2, 2> BUTCHER_3 = { { { 1. / 2., 0. }, { -1., 2. } } }; /* RK3 */
  static constexpr std::array<ARR3, 3> BUTCHER_4 = { { { 1. / 2., 0. , 0.}, { 0., 1. / 2., 0.}, { 0. , 0., 1. } } }; /* RK4 */
  static constexpr std::array<ARR3, 3> BUTCHER_4_3_8 = { { { 1. / 3., 0. , 0.}, { -1. / 3., 1., 0.}, { 1. , -1., 1. } } }; /* RK4 3/8 rule */
 
  static constexpr std::array<ARR4, 4> BUTCHER_TAB = { {
      { 0., 1., 0., 0. }, /* RK2 classique*/
      { 1. / 6., 2. / 3., 1. / 6., 0. }, /* RK3 classique*/
      { 1. / 6., 1. / 3., 1. / 3., 1. / 6. }, /* RK4 classique*/
      { 1. / 8., 3. / 8., 3. / 8., 1. / 8. } /* RK4 3/8 rule */
    }
  };
 
  // SFINAE template functions
  template<Ordre_RK _O_ = _ORDRE_, int NB>
  std::enable_if_t<_O_ == Ordre_RK::DEUX_WILLIAMSON, std::array<double, NB>>
  inline const get_a() { return A2; }
 
  template<Ordre_RK _O_ = _ORDRE_, int NB>
  std::enable_if_t<_O_ != Ordre_RK::DEUX_WILLIAMSON, std::array<double, NB>>
  inline const get_a() { return _ORDRE_ == Ordre_RK::TROIS_WILLIAMSON ? A3 : A4; }
 
  template<Ordre_RK _O_ = _ORDRE_, int NB>
  std::enable_if_t<_O_ == Ordre_RK::DEUX_WILLIAMSON, std::array<double, NB>>
  inline const get_b() { return B2; }
 
  template<Ordre_RK _O_ = _ORDRE_, int NB>
  std::enable_if_t<_O_ != Ordre_RK::DEUX_WILLIAMSON, std::array<double, NB>>
  inline const get_b() { return _ORDRE_ == Ordre_RK::TROIS_WILLIAMSON ? B3 : B4; }
 
  template<Ordre_RK _O_ = _ORDRE_>
  std::enable_if_t<_O_ == Ordre_RK::DEUX_WILLIAMSON || _O_ == Ordre_RK::TROIS_WILLIAMSON || _O_ == Ordre_RK::QUATRE_WILLIAMSON, int>
  faire_un_pas_de_temps_eqn_base_generique(Equation_base& eq);
 
  template<Ordre_RK _O_ = _ORDRE_, int NB>
  std::enable_if_t<_O_ == Ordre_RK::DEUX_CLASSIQUE, std::array<std::array<double, NB>, NB> >
  inline const get_butcher_coeff() { return BUTCHER_2; }
 
  template<Ordre_RK _O_ = _ORDRE_, int NB>
  std::enable_if_t<_O_ == Ordre_RK::TROIS_CLASSIQUE, std::array<std::array<double, NB>, NB> >
  inline const get_butcher_coeff() { return BUTCHER_3; }
 
  template<Ordre_RK _O_ = _ORDRE_, int NB>
  std::enable_if_t<_O_ == Ordre_RK::QUATRE_CLASSIQUE || _O_ == Ordre_RK::QUATRE_CLASSIQUE_3_8, std::array<std::array<double, NB>, NB> >
  inline const get_butcher_coeff() { return _O_ == Ordre_RK::QUATRE_CLASSIQUE ? BUTCHER_4 : BUTCHER_4_3_8; }
 
  template<Ordre_RK _O_ = _ORDRE_>
  std::enable_if_t<_O_ == Ordre_RK::DEUX_CLASSIQUE || _O_ == Ordre_RK::TROIS_CLASSIQUE || _O_ == Ordre_RK::QUATRE_CLASSIQUE || _O_ == Ordre_RK::QUATRE_CLASSIQUE_3_8, int>
  faire_un_pas_de_temps_eqn_base_generique(Equation_base& eq);
 
  // DANGER : SHOULD NOT GO HERE
  template<Ordre_RK _O_ = _ORDRE_> std::enable_if_t<_O_ == Ordre_RK::UN || _O_ == Ordre_RK::RATIO_DEUX, int>
  faire_un_pas_de_temps_eqn_base_generique(Equation_base& eq) { throw; } // From VTABLE
  DoubleTabs ki_;
};
 
// XXX : CAN BE REMOVED WHEN WE PASS TO C++17
// see https://stackoverflow.com/questions/40690260/undefined-reference-error-for-static-constexpr-member
template <Ordre_RK _ORDRE_ >
constexpr std::array<ARR1, 1> TRUSTSchema_RK<_ORDRE_>::BUTCHER_2;
 
template <Ordre_RK _ORDRE_ >
constexpr std::array<ARR2, 2> TRUSTSchema_RK<_ORDRE_>::BUTCHER_3;
 
template <Ordre_RK _ORDRE_ >
constexpr std::array<ARR3, 3> TRUSTSchema_RK<_ORDRE_>::BUTCHER_4;
 
template <Ordre_RK _ORDRE_ >
constexpr std::array<ARR3, 3> TRUSTSchema_RK<_ORDRE_>::BUTCHER_4_3_8;
 
template <Ordre_RK _ORDRE_ >
constexpr std::array<ARR4, 4> TRUSTSchema_RK<_ORDRE_>::BUTCHER_TAB;
 
template <Ordre_RK _ORDRE_ >
constexpr ARR2 TRUSTSchema_RK<_ORDRE_>::A2;
 
template <Ordre_RK _ORDRE_ >
constexpr ARR2 TRUSTSchema_RK<_ORDRE_>::B2;
 
template <Ordre_RK _ORDRE_ >
constexpr ARR3 TRUSTSchema_RK<_ORDRE_>::A3;
 
template <Ordre_RK _ORDRE_ >
constexpr ARR3 TRUSTSchema_RK<_ORDRE_>::B3;
 
template <Ordre_RK _ORDRE_ >
constexpr ARR3 TRUSTSchema_RK<_ORDRE_>::A4;
 
template <Ordre_RK _ORDRE_ >
constexpr ARR3 TRUSTSchema_RK<_ORDRE_>::B4;
 
#include <TRUSTSchema_RK.tpp>
 
#endif /* TRUSTSchema_RK_included */