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