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              : #include "NumericalAlgorithms/Strahlkorper/TagsTypeAliases.hpp"
       8              : 
       9              : /// \cond
      10              : class DataVector;
      11              : namespace gsl {
      12              : template <typename>
      13              : struct not_null;
      14              : }  // namespace gsl
      15              : /// \endcond
      16              : 
      17            0 : namespace gr::surfaces {
      18              : /// @{
      19              : /*!
      20              :  * \ingroup SurfacesGroup
      21              :  * \brief Area element of a 2D `Strahlkorper`.
      22              :  *
      23              :  * \details Implements Eq. (D.13), using Eqs. (D.4) and (D.5),
      24              :  * of \cite Baumgarte1996hh. Specifically, computes
      25              :  * \f$\sqrt{(\Theta^i\Theta_i)(\Phi^j\Phi_j)-(\Theta^i\Phi_i)^2}\f$,
      26              :  * \f$\Theta^i=\left(n^i(n_j-s_j) r J^j_\theta + r J^i_\theta\right)\f$,
      27              :  * \f$\Phi^i=\left(n^i(n_j-s_j)r J^j_\phi + r J^i_\phi\right)\f$,
      28              :  * and \f$\Theta^i\f$ and \f$\Phi^i\f$ are lowered by the
      29              :  * 3D spatial metric \f$g_{ij}\f$. Here \f$J^i_\alpha\f$, \f$s_j\f$,
      30              :  * \f$r\f$, and \f$n^i=n_i\f$ correspond to the input arguments
      31              :  * `jacobian`, `normal_one_form`, `radius`, and `r_hat`, respectively;
      32              :  * these input arguments depend only on the Strahlkorper, not on the
      33              :  * metric, and can be computed from a Strahlkorper using ComputeItems
      34              :  * in `ylm::Tags`. Note that this does not include the factor
      35              :  * of \f$\sin\theta\f$, i.e., this returns \f$r^2\f$ for a spherical
      36              :  * `Strahlkorper` in flat space.
      37              :  * This choice makes the area element returned here compatible with
      38              :  * `definite_integral` defined in `YlmSpherePack.hpp`.
      39              :  */
      40              : template <typename Frame>
      41            1 : void area_element(gsl::not_null<Scalar<DataVector>*> result,
      42              :                   const tnsr::ii<DataVector, 3, Frame>& spatial_metric,
      43              :                   const ylm::Tags::aliases::Jacobian<Frame>& jacobian,
      44              :                   const tnsr::i<DataVector, 3, Frame>& normal_one_form,
      45              :                   const Scalar<DataVector>& radius,
      46              :                   const tnsr::i<DataVector, 3, Frame>& r_hat);
      47              : 
      48              : template <typename Frame>
      49            1 : Scalar<DataVector> area_element(
      50              :     const tnsr::ii<DataVector, 3, Frame>& spatial_metric,
      51              :     const ylm::Tags::aliases::Jacobian<Frame>& jacobian,
      52              :     const tnsr::i<DataVector, 3, Frame>& normal_one_form,
      53              :     const Scalar<DataVector>& radius,
      54              :     const tnsr::i<DataVector, 3, Frame>& r_hat);
      55              : /// @}
      56              : 
      57              : /// @{
      58              : /*!
      59              :  * \ingroup SurfacesGroup
      60              :  * \brief Euclidean area element of a 2D `Strahlkorper`.
      61              :  *
      62              :  * This is useful for computing a flat-space integral over an
      63              :  * arbitrarily-shaped `Strahlkorper`.
      64              :  *
      65              :  * \details Implements Eq. (D.13), using Eqs. (D.4) and (D.5),
      66              :  * of \cite Baumgarte1996hh. Specifically, computes
      67              :  * \f$\sqrt{(\Theta^i\Theta_i)(\Phi^j\Phi_j)-(\Theta^i\Phi_i)^2}\f$,
      68              :  * \f$\Theta^i=\left(n^i(n_j-s_j) r J^j_\theta + r J^i_\theta\right)\f$,
      69              :  * \f$\Phi^i=\left(n^i(n_j-s_j)r J^j_\phi + r J^i_\phi\right)\f$,
      70              :  * and \f$\Theta^i\f$ and \f$\Phi^i\f$ are lowered by the
      71              :  * Euclidean spatial metric. Here \f$J^i_\alpha\f$, \f$s_j\f$,
      72              :  * \f$r\f$, and \f$n^i=n_i\f$ correspond to the input arguments
      73              :  * `jacobian`, `normal_one_form`, `radius`, and `r_hat`, respectively;
      74              :  * these input arguments depend only on the Strahlkorper, not on the
      75              :  * metric, and can be computed from a Strahlkorper using ComputeItems
      76              :  * in `ylm::Tags`. Note that this does not include the factor
      77              :  * of \f$\sin\theta\f$, i.e., this returns \f$r^2\f$ for a spherical
      78              :  * `Strahlkorper`.
      79              :  * This choice makes the area element returned here compatible with
      80              :  * `definite_integral` defined in `YlmSpherePack.hpp`.
      81              :  */
      82              : template <typename Frame>
      83            1 : void euclidean_area_element(
      84              :     gsl::not_null<Scalar<DataVector>*> result,
      85              :     const ylm::Tags::aliases::Jacobian<Frame>& jacobian,
      86              :     const tnsr::i<DataVector, 3, Frame>& normal_one_form,
      87              :     const Scalar<DataVector>& radius,
      88              :     const tnsr::i<DataVector, 3, Frame>& r_hat);
      89              : 
      90              : template <typename Frame>
      91            1 : Scalar<DataVector> euclidean_area_element(
      92              :     const ylm::Tags::aliases::Jacobian<Frame>& jacobian,
      93              :     const tnsr::i<DataVector, 3, Frame>& normal_one_form,
      94              :     const Scalar<DataVector>& radius,
      95              :     const tnsr::i<DataVector, 3, Frame>& r_hat);
      96              : /// @}
      97              : }  // namespace gr::surfaces