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             : };
      58             : }  // namespace Elasticity