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 "DataStructures/TaggedVariant.hpp"
       9              : #include "Options/String.hpp"
      10              : #include "Time/TimeSteppers/ImexRungeKutta.hpp"
      11              : #include "Utilities/Serialization/CharmPupable.hpp"
      12              : #include "Utilities/TMPL.hpp"
      13              : 
      14              : namespace TimeSteppers {
      15              : /*!
      16              :  * \ingroup TimeSteppersGroup
      17              :  * \brief A second order continuous-extension RK method that provides 2nd-order
      18              :  * dense output.
      19              :  *
      20              :  * \f{eqnarray}{
      21              :  * \frac{du}{dt} & = & \mathcal{L}(t,u).
      22              :  * \f}
      23              :  * Given a solution \f$u(t^n)=u^n\f$, this stepper computes
      24              :  * \f$u(t^{n+1})=u^{n+1}\f$ using the following equations:
      25              :  *
      26              :  * \f{align}{
      27              :  * k^{(i)} & = \mathcal{L}(t^n + c_i \Delta t,
      28              :  *                         u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k^{(j)}),
      29              :  *                              \mbox{ } 1 \leq i \leq s,\\
      30              :  * u^{n+1}(t^n + \theta \Delta t) & = u^n + \Delta t \sum_{i=1}^{s} b_i(\theta)
      31              :  * k^{(i)}. \f}
      32              :  *
      33              :  * Here the coefficients \f$a_{ij}\f$, \f$b_i\f$, and \f$c_i\f$ are given
      34              :  * in \cite Gassner20114232. Note that \f$c_1 = 0\f$, \f$s\f$ is the number
      35              :  * of stages, and \f$\theta\f$ is the fraction of the step.
      36              :  *
      37              :  * When used as an IMEX method, the implicit portion uses the
      38              :  * trapezoid rule, which is stiffly accurate and A-stable.
      39              :  *
      40              :  * The CFL factor/stable step size is 1.0.
      41              :  */
      42            1 : class Heun2 : public ImexRungeKutta {
      43              :  public:
      44            0 :   using options = tmpl::list<>;
      45            0 :   static constexpr Options::String help = {
      46              :       "Heun's method, a 2nd order Runge-Kutta method."};
      47              : 
      48            0 :   Heun2() = default;
      49            0 :   Heun2(const Heun2&) = default;
      50            0 :   Heun2& operator=(const Heun2&) = default;
      51            0 :   Heun2(Heun2&&) = default;
      52            0 :   Heun2& operator=(Heun2&&) = default;
      53            0 :   ~Heun2() override = default;
      54              : 
      55            1 :   variants::TaggedVariant<Tags::FixedOrder, Tags::VariableOrder> order()
      56              :       const override;
      57              : 
      58            1 :   double stable_step() const override;
      59              : 
      60            1 :   size_t imex_order() const override;
      61              : 
      62            1 :   size_t implicit_stage_order() const override;
      63              : 
      64            0 :   WRAPPED_PUPable_decl_template(Heun2);  // NOLINT
      65              : 
      66            0 :   explicit Heun2(CkMigrateMessage* /*unused*/) {}
      67              : 
      68            0 :   const ButcherTableau& butcher_tableau() const override;
      69              : 
      70            0 :   const ImplicitButcherTableau& implicit_butcher_tableau() const override;
      71              : };
      72              : 
      73            0 : inline bool constexpr operator==(const Heun2& /*lhs*/, const Heun2& /*rhs*/) {
      74              :   return true;
      75              : }
      76              : 
      77            0 : inline bool constexpr operator!=(const Heun2& /*lhs*/, const Heun2& /*rhs*/) {
      78              :   return false;
      79              : }
      80              : }  // namespace TimeSteppers