Line data    Source code

       1            0 : // Distributed under the MIT License.
       2              : // See LICENSE.txt for details.
       3              : 
       4              : #pragma once
       5              : 
       6              : #include "DataStructures/Tensor/TypeAliases.hpp"
       7              : 
       8              : /// \cond
       9              : class DataVector;
      10              : namespace gsl {
      11              : template <typename>
      12              : struct not_null;
      13              : }  // namespace gsl
      14              : /// \endcond
      15              : 
      16              : namespace gr::surfaces {
      17              : /// @{
      18              : /// \ingroup SurfacesGroup
      19              : /// \brief Computes 3-covariant gradient \f$D_i S_j\f$ of a
      20              : /// Strahlkorper's normal.
      21              : ///
      22              : /// \details See Eqs. (1--9) of \cite Baumgarte1996hh.
      23              : /// Here \f$S_j\f$ is the (normalized) unit one-form to the surface,
      24              : /// and \f$D_i\f$ is the spatial covariant derivative.  Note that this
      25              : /// object is symmetric, even though this is not obvious from the
      26              : /// definition.  The input arguments `r_hat`, `radius`, and
      27              : /// `d2x_radius` depend on the Strahlkorper but not on the metric, and
      28              : /// can be computed from a Strahlkorper using ComputeItems in
      29              : /// `ylm::Tags`.  The input argument
      30              : /// `one_over_one_form_magnitude` is \f$1/\sqrt{g^{ij}n_i n_j}\f$,
      31              : /// where \f$n_i\f$ is `ylm::Tags::NormalOneForm` (i.e.  the
      32              : /// unnormalized one-form to the Strahlkorper); it can be computed
      33              : /// using (one over) the `magnitude` function.  The input argument
      34              : /// `unit_normal_one_form` is \f$S_j\f$,the normalized one-form.
      35              : template <typename Frame>
      36            1 : void grad_unit_normal_one_form(
      37              :     gsl::not_null<tnsr::ii<DataVector, 3, Frame>*> result,
      38              :     const tnsr::i<DataVector, 3, Frame>& r_hat,
      39              :     const Scalar<DataVector>& radius,
      40              :     const tnsr::i<DataVector, 3, Frame>& unit_normal_one_form,
      41              :     const tnsr::ii<DataVector, 3, Frame>& d2x_radius,
      42              :     const DataVector& one_over_one_form_magnitude,
      43              :     const tnsr::Ijj<DataVector, 3, Frame>& christoffel_2nd_kind);
      44              : 
      45              : template <typename Frame>
      46            1 : tnsr::ii<DataVector, 3, Frame> grad_unit_normal_one_form(
      47              :     const tnsr::i<DataVector, 3, Frame>& r_hat,
      48              :     const Scalar<DataVector>& radius,
      49              :     const tnsr::i<DataVector, 3, Frame>& unit_normal_one_form,
      50              :     const tnsr::ii<DataVector, 3, Frame>& d2x_radius,
      51              :     const DataVector& one_over_one_form_magnitude,
      52              :     const tnsr::Ijj<DataVector, 3, Frame>& christoffel_2nd_kind);
      53              : /// @}
      54              : }  // namespace gr::surfaces