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             : #include <utility>
       8             : 
       9             : /// \cond
      10             : class DataVector;
      11             : template <size_t>
      12             : class Mesh;
      13             : namespace Spectral {
      14             : enum class Basis : uint8_t;
      15             : enum class Quadrature : uint8_t;
      16             : }  // namespace Spectral
      17             : /// \endcond
      18             : 
      19             : namespace Spectral {
      20             : /// @{
      21             : /*!
      22             :  * \brief Interpolates values from the boundary into the volume, which is needed
      23             :  * when applying time derivative or Bjorhus-type boundary conditions in a
      24             :  * discontinuous Galerkin scheme using Gauss points.
      25             :  *
      26             :  * Assumes that the logical coordinates are \f$[-1, 1]\f$.
      27             :  * The interpolation is done by assuming the time derivative correction is zero
      28             :  * on interior nodes. With a nodal Lagrange polynomial basis this means that
      29             :  * only the \f$\ell^{\mathrm{Gauss-Lobatto}}_{0}\f$ and
      30             :  * \f$\ell^{\mathrm{Gauss-Lobatto}}_{N}\f$ polynomials/basis functions
      31             :  * contribute to the correction. In order to interpolate the correction from the
      32             :  * nodes at the boundary, the Gauss-Lobatto Lagrange polynomials  must be
      33             :  * evaluated at the Gauss grid points. The returned pair of `DataVector`s stores
      34             :  *
      35             :  * \f{align*}{
      36             :  *   &\ell^{\mathrm{Gauss-Lobatto}}_{0}(\xi_j^{\mathrm{Gauss}}), \\
      37             :  *   &\ell^{\mathrm{Gauss-Lobatto}}_{N}(\xi_j^{\mathrm{Gauss}}).
      38             :  * \f}
      39             :  *
      40             :  * This is a different correction from lifting. Lifting is done using the mass
      41             :  * matrix, which is an integral over the basis functions, while here we use
      42             :  * interpolation.
      43             :  *
      44             :  * \warning This can only be called with Gauss points.
      45             :  */
      46           1 : const std::pair<DataVector, DataVector>& boundary_interpolation_term(
      47             :     const Mesh<1>& mesh);
      48             : 
      49             : template <Basis BasisType, Quadrature QuadratureType>
      50           1 : const std::pair<DataVector, DataVector>& boundary_interpolation_term(
      51             :     size_t num_points);
      52             : /// @}
      53             : }  // namespace Spectral