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 ylm {
      11              : template <typename Frame>
      12              : class Strahlkorper;
      13              : }  // namespace ylm
      14              : /// \endcond
      15              : 
      16              : namespace gr::surfaces {
      17              : /*!
      18              :  * \ingroup SurfacesGroup
      19              :  * \brief Euclidean surface integral of a vector on a 2D `Strahlkorper`
      20              :  *
      21              :  * \details Computes the surface integral
      22              :  * \f$\oint V^i s_i (s_j s_k \delta^{jk})^{-1/2} d^2S\f$ for a
      23              :  * vector \f$V^i\f$ on a `Strahlkorper` with area element \f$d^2S\f$ and
      24              :  * normal one-form \f$s_i\f$.  Here \f$\delta^{ij}\f$ is the Euclidean
      25              :  * metric (i.e. the Kronecker delta). Note that the input `normal_one_form`
      26              :  * is not assumed to be normalized; the denominator of the integrand
      27              :  * effectively normalizes it using the Euclidean metric.
      28              :  * The area element can be computed via
      29              :  * `gr::surfaces::euclidean_area_element()`.
      30              :  */
      31              : template <typename Frame>
      32            1 : double euclidean_surface_integral_of_vector(
      33              :     const Scalar<DataVector>& area_element,
      34              :     const tnsr::I<DataVector, 3, Frame>& vector,
      35              :     const tnsr::i<DataVector, 3, Frame>& normal_one_form,
      36              :     const ylm::Strahlkorper<Frame>& strahlkorper);
      37              : }  // namespace gr::surfaces