Line data    Source code

       1           0 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : #pragma once
       5             : 
       6             : #include <cstddef>
       7             : 
       8             : #include "Options/String.hpp"
       9             : #include "Time/TimeSteppers/ImexRungeKutta.hpp"
      10             : #include "Utilities/Serialization/CharmPupable.hpp"
      11             : #include "Utilities/TMPL.hpp"
      12             : 
      13             : namespace TimeSteppers {
      14             : /*!
      15             :  * \ingroup TimeSteppersGroup
      16             :  * \brief A second order continuous-extension RK method that provides 2nd-order
      17             :  * dense output.
      18             :  *
      19             :  * \f{eqnarray}{
      20             :  * \frac{du}{dt} & = & \mathcal{L}(t,u).
      21             :  * \f}
      22             :  * Given a solution \f$u(t^n)=u^n\f$, this stepper computes
      23             :  * \f$u(t^{n+1})=u^{n+1}\f$ using the following equations:
      24             :  *
      25             :  * \f{align}{
      26             :  * k^{(i)} & = \mathcal{L}(t^n + c_i \Delta t,
      27             :  *                         u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k^{(j)}),
      28             :  *                              \mbox{ } 1 \leq i \leq s,\\
      29             :  * u^{n+1}(t^n + \theta \Delta t) & = u^n + \Delta t \sum_{i=1}^{s} b_i(\theta)
      30             :  * k^{(i)}. \f}
      31             :  *
      32             :  * Here the coefficients \f$a_{ij}\f$, \f$b_i\f$, and \f$c_i\f$ are given
      33             :  * in \cite Gassner20114232. Note that \f$c_1 = 0\f$, \f$s\f$ is the number
      34             :  * of stages, and \f$\theta\f$ is the fraction of the step.
      35             :  *
      36             :  * When used as an IMEX method, the implicit portion uses the
      37             :  * trapezoid rule, which is stiffly accurate and A-stable.
      38             :  *
      39             :  * The CFL factor/stable step size is 1.0.
      40             :  */
      41           1 : class Heun2 : public ImexRungeKutta {
      42             :  public:
      43           0 :   using options = tmpl::list<>;
      44           0 :   static constexpr Options::String help = {
      45             :       "Heun's method, a 2nd order Runge-Kutta method."};
      46             : 
      47           0 :   Heun2() = default;
      48           0 :   Heun2(const Heun2&) = default;
      49           0 :   Heun2& operator=(const Heun2&) = default;
      50           0 :   Heun2(Heun2&&) = default;
      51           0 :   Heun2& operator=(Heun2&&) = default;
      52           0 :   ~Heun2() override = default;
      53             : 
      54           1 :   size_t order() const override;
      55             : 
      56           1 :   double stable_step() const override;
      57             : 
      58           1 :   size_t imex_order() const override;
      59             : 
      60           1 :   size_t implicit_stage_order() const override;
      61             : 
      62           0 :   WRAPPED_PUPable_decl_template(Heun2);  // NOLINT
      63             : 
      64           0 :   explicit Heun2(CkMigrateMessage* /*unused*/) {}
      65             : 
      66           0 :   const ButcherTableau& butcher_tableau() const override;
      67             : 
      68           0 :   const ImplicitButcherTableau& implicit_butcher_tableau() const override;
      69             : };
      70             : 
      71           0 : inline bool constexpr operator==(const Heun2& /*lhs*/, const Heun2& /*rhs*/) {
      72             :   return true;
      73             : }
      74             : 
      75           0 : inline bool constexpr operator!=(const Heun2& /*lhs*/, const Heun2& /*rhs*/) {
      76             :   return false;
      77             : }
      78             : }  // namespace TimeSteppers