SpECTRE Documentation Coverage Report
Current view: top level - PointwiseFunctions/GeneralRelativity/GeneralizedHarmonic - SpatialDerivOfLapse.hpp Hit Total Coverage
Commit: 664546099c4dbf27a1b708fac45e39c82dd743d2 Lines: 3 8 37.5 %
Date: 2024-04-19 16:28:01
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          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             : 
       8             : #include "DataStructures/DataBox/Prefixes.hpp"
       9             : #include "DataStructures/DataBox/Tag.hpp"
      10             : #include "DataStructures/DataVector.hpp"
      11             : #include "DataStructures/Tensor/Tensor.hpp"
      12             : #include "Evolution/Systems/GeneralizedHarmonic/Tags.hpp"
      13             : #include "NumericalAlgorithms/LinearOperators/PartialDerivatives.hpp"
      14             : #include "PointwiseFunctions/GeneralRelativity/Tags.hpp"
      15             : #include "Utilities/ContainerHelpers.hpp"
      16             : #include "Utilities/Gsl.hpp"
      17             : #include "Utilities/TMPL.hpp"
      18             : 
      19             : // IWYU pragma: no_forward_declare Tags::deriv
      20             : 
      21             : /// \cond
      22             : namespace domain {
      23             : namespace Tags {
      24             : template <size_t Dim, typename Frame>
      25             : struct Coordinates;
      26             : }  // namespace Tags
      27             : }  // namespace domain
      28             : class DataVector;
      29             : template <typename X, typename Symm, typename IndexList>
      30             : class Tensor;
      31             : /// \endcond
      32             : 
      33             : namespace gh {
      34             : /// @{
      35             : /*!
      36             :  * \ingroup GeneralRelativityGroup
      37             :  * \brief Computes spatial derivatives of lapse (\f$\alpha\f$) from the
      38             :  *        generalized harmonic variables and spacetime unit normal 1-form.
      39             :  *
      40             :  * \details If the generalized harmonic conjugate momentum and spatial
      41             :  * derivative variables are \f$\Pi_{ab} = -n^c \partial_c g_{ab} \f$ and
      42             :  * \f$\Phi_{iab} = \partial_i g_{ab} \f$, the spatial derivatives of
      43             :  * \f$\alpha\f$ can be obtained from:
      44             :  *
      45             :  * \f{align*}
      46             :  *      n^a n^b \Phi_{iab} =
      47             :  *          -\frac{1}{2\alpha} [\partial_i (-\alpha^2 + \beta_j\beta^j)-
      48             :  *                              2 \beta^j \partial_i \beta_j
      49             :  *                              + \beta^j \beta^k \partial_i \gamma_{jk}]
      50             :  *                         = -\frac{2}{\alpha} \partial_i \alpha,
      51             :  * \f}
      52             :  *
      53             :  * since
      54             :  *
      55             :  * \f[
      56             :  * \partial_i (\beta_j\beta^j) =
      57             :  *     2\beta^j \partial_i \beta_j - \beta^j \beta^k \partial_i \gamma_{jk}.
      58             :  * \f]
      59             :  *
      60             :  * \f[
      61             :  *     \Longrightarrow \partial_i \alpha = -(\alpha/2) n^a \Phi_{iab} n^b
      62             :  * \f]
      63             :  */
      64             : template <typename DataType, size_t SpatialDim, typename Frame>
      65           1 : void spatial_deriv_of_lapse(
      66             :     gsl::not_null<tnsr::i<DataType, SpatialDim, Frame>*> deriv_lapse,
      67             :     const Scalar<DataType>& lapse,
      68             :     const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,
      69             :     const tnsr::iaa<DataType, SpatialDim, Frame>& phi);
      70             : 
      71             : template <typename DataType, size_t SpatialDim, typename Frame>
      72           1 : tnsr::i<DataType, SpatialDim, Frame> spatial_deriv_of_lapse(
      73             :     const Scalar<DataType>& lapse,
      74             :     const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,
      75             :     const tnsr::iaa<DataType, SpatialDim, Frame>& phi);
      76             : /// @}
      77             : 
      78             : namespace Tags {
      79             : /*!
      80             :  * \brief Compute item to get spatial derivatives of lapse from the
      81             :  * generalized harmonic variables and spacetime unit normal one-form.
      82             :  *
      83             :  * \details See `spatial_deriv_of_lapse()`. Can be retrieved using
      84             :  * `gr::Tags::Lapse` wrapped in `::Tags::deriv`.
      85             :  */
      86             : template <size_t SpatialDim, typename Frame>
      87           1 : struct DerivLapseCompute : ::Tags::deriv<gr::Tags::Lapse<DataVector>,
      88             :                                          tmpl::size_t<SpatialDim>, Frame>,
      89             :                            db::ComputeTag {
      90           0 :   using argument_tags =
      91             :       tmpl::list<gr::Tags::Lapse<DataVector>,
      92             :                  gr::Tags::SpacetimeNormalVector<DataVector, SpatialDim, Frame>,
      93             :                  Phi<DataVector, SpatialDim, Frame>>;
      94             : 
      95           0 :   using return_type = tnsr::i<DataVector, SpatialDim, Frame>;
      96             : 
      97           0 :   static constexpr auto function = static_cast<void (*)(
      98             :       gsl::not_null<tnsr::i<DataVector, SpatialDim, Frame>*>,
      99             :       const Scalar<DataVector>&, const tnsr::A<DataVector, SpatialDim, Frame>&,
     100             :       const tnsr::iaa<DataVector, SpatialDim, Frame>&)>(
     101             :       &spatial_deriv_of_lapse<DataVector, SpatialDim, Frame>);
     102             : 
     103           0 :   using base = ::Tags::deriv<gr::Tags::Lapse<DataVector>,
     104             :                              tmpl::size_t<SpatialDim>, Frame>;
     105             : };
     106             : }  // namespace Tags
     107             : }  // namespace gh

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