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