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/DataBox/PrefixHelpers.hpp"
       9              : #include "DataStructures/DataBox/Prefixes.hpp"
      10              : #include "Elliptic/BoundaryConditions/BoundaryCondition.hpp"
      11              : #include "Elliptic/Protocols/FirstOrderSystem.hpp"
      12              : #include "Elliptic/Systems/Elasticity/Equations.hpp"
      13              : #include "Elliptic/Systems/Elasticity/Tags.hpp"
      14              : #include "NumericalAlgorithms/LinearOperators/PartialDerivatives.hpp"
      15              : #include "PointwiseFunctions/Elasticity/ConstitutiveRelations/ConstitutiveRelation.hpp"
      16              : #include "Utilities/ProtocolHelpers.hpp"
      17              : #include "Utilities/TMPL.hpp"
      18              : 
      19              : namespace Elasticity {
      20              : 
      21              : /*!
      22              :  * \brief The linear elasticity equation formulated as a set of coupled
      23              :  * first-order PDEs.
      24              :  *
      25              :  * This system formulates the elasticity equation (see `Elasticity`):
      26              :  *
      27              :  * \f{align*}
      28              :  * \nabla_i T^{ij} = f_\mathrm{ext}^j \\
      29              :  * T^{ij} = -Y^{ijkl} \nabla_{(k} \xi_{l)}
      30              :  * \f}
      31              :  *
      32              :  * The system can be formulated in terms of these fluxes and sources (see
      33              :  * `elliptic::protocols::FirstOrderSystem`):
      34              :  *
      35              :  * \f{align*}
      36              :  * F^{ij} &= -T^{ij} = Y^{ijkl} \nabla_{(k} \xi_{l)} \\
      37              :  * S^j &= 0 \\
      38              :  * f^j &= f_\mathrm{ext}^j \text{.}
      39              :  * \f}
      40              :  */
      41              : template <size_t Dim>
      42            1 : struct FirstOrderSystem
      43              :     : tt::ConformsTo<elliptic::protocols::FirstOrderSystem> {
      44            0 :   static constexpr size_t volume_dim = Dim;
      45              : 
      46            0 :   using primal_fields = tmpl::list<Tags::Displacement<Dim>>;
      47            0 :   using primal_fluxes = tmpl::list<Tags::MinusStress<Dim>>;
      48              : 
      49            0 :   using background_fields = tmpl::list<>;
      50            0 :   using inv_metric_tag = void;
      51              : 
      52            0 :   using fluxes_computer = Fluxes<Dim>;
      53            0 :   using sources_computer = void;
      54              : 
      55            0 :   using boundary_conditions_base =
      56              :       elliptic::BoundaryConditions::BoundaryCondition<Dim>;
      57            0 :   using modify_boundary_data = void;
      58              : };
      59              : }  // namespace Elasticity