SpECTRE Documentation Coverage Report
Current view: top level - Evolution/Systems/Cce - NewmanPenrose.hpp Hit Total Coverage
Commit: 817e13c5144619b701c7cd870655d8dbf94ab8ce Lines: 4 17 23.5 %
Date: 2024-07-19 22:17:05
Legend: Lines: hit not hit

          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/SpinWeighted.hpp"
       7             : #include "DataStructures/Tensor/Tensor.hpp"
       8             : #include "Evolution/Systems/Cce/Tags.hpp"
       9             : #include "NumericalAlgorithms/SpinWeightedSphericalHarmonics/SwshDerivatives.hpp"
      10             : #include "NumericalAlgorithms/SpinWeightedSphericalHarmonics/SwshInterpolation.hpp"
      11             : #include "Utilities/Gsl.hpp"
      12             : #include "Utilities/TMPL.hpp"
      13             : 
      14             : /// \cond
      15             : class ComplexDataVector;
      16             : /// \endcond
      17             : 
      18             : namespace Cce {
      19             : 
      20             : /// \cond
      21             : namespace Tags {
      22             :   struct LMax;
      23             : } // namespace Tags
      24             : template <typename Tag>
      25             : struct VolumeWeyl;
      26             : /// \endcond
      27             : 
      28             : /*!
      29             :  * \brief Compute the Weyl scalar \f$\Psi_0\f$ in the volume according to a
      30             :  * standard set of Newman-Penrose vectors.
      31             :  *
      32             :  * \details The Bondi forms of the Newman-Penrose vectors that are needed for
      33             :  * \f$\Psi_0\f$ are:
      34             :  *
      35             :  * \f{align}{
      36             :  * \mathbf{l} &= \partial_r / \sqrt{2}\\
      37             :  * \mathbf{m} &= \frac{-1}{2 r} \left(\sqrt{1 + K} q^A \partial_A -
      38             :  *   \frac{J}{\sqrt{1 + K}}\bar{q}^A \partial_A \right)
      39             :  * \f}
      40             :  *
      41             :  * Then, we may compute \f$\Psi_0 =  l^\alpha m^\beta l^\mu m^\nu C_{\alpha
      42             :  * \beta \mu \nu}\f$ from the Bondi system, giving
      43             :  *
      44             :  * \f{align*}{
      45             :  * \Psi_0 = \frac{(1 - y)^4}{16 r^2 K}
      46             :  * \bigg[& \partial_y \beta \left((1 + K) (\partial_y J)
      47             :  * - \frac{J^2 \partial_y \bar J}{1 + K}\right)
      48             :  * - \frac{1}{2} (1 + K) (\partial_y^2 J)
      49             :  * + \frac{J^2 \partial_y^2 \bar J}{2(K + 1)}\\
      50             :  * & + \frac{1}{K^2} \left(- \frac{1}{4} J \left(\bar{J}^2 \left(\partial_y
      51             :  * J\right)^2 + J^2 \left(\partial_y \bar J\right)^2\right)
      52             :  * + \frac{1 + K^2}{2} J (\partial_y J) (\partial_y \bar J)
      53             :  * \right)\bigg].
      54             :  * \f}
      55             :  */
      56             : template <>
      57           1 : struct VolumeWeyl<Tags::Psi0> {
      58           0 :   using return_tags = tmpl::list<Tags::Psi0>;
      59           0 :   using argument_tags = tmpl::list<Tags::BondiJ, Tags::Dy<Tags::BondiJ>,
      60             :                                    Tags::Dy<Tags::Dy<Tags::BondiJ>>,
      61             :                                    Tags::BondiK, Tags::BondiR, Tags::OneMinusY>;
      62           0 :   static void apply(
      63             :       gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*> psi_0,
      64             :       const Scalar<SpinWeighted<ComplexDataVector, 2>>& bondi_j,
      65             :       const Scalar<SpinWeighted<ComplexDataVector, 2>>& dy_j,
      66             :       const Scalar<SpinWeighted<ComplexDataVector, 2>>& dy_dy_j,
      67             :       const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_k,
      68             :       const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r,
      69             :       const Scalar<SpinWeighted<ComplexDataVector, 0>>& one_minus_y);
      70             : };
      71             : 
      72             : /*!
      73             :  * \brief Transform `Tags::BondiJ` from the partially flat coordinates
      74             :  * to the Cauchy coordinates.
      75             :  *
      76             :  * \details The spin-2 quantity \f$\hat J\f$ transforms as
      77             :  * \f{align*}{
      78             :  * J = \frac{1}{4 \omega^2} (\bar d^2 \hat J + c^2 \bar{\hat J}
      79             :  * + 2 c \bar d \hat K )
      80             :  * \f}
      81             :  *
      82             :  * with
      83             :  * \f{align*}{
      84             :  * \hat K = \sqrt{1+\hat J \bar{\hat J}}
      85             :  * \f}
      86             :  */
      87           1 : struct TransformBondiJToCauchyCoords {
      88           0 :   using return_tags = tmpl::list<Tags::BondiJCauchyView>;
      89           0 :   using argument_tags = tmpl::list<
      90             :       Tags::CauchyGaugeC, Tags::BondiJ, Tags::CauchyGaugeD,
      91             :       Tags::CauchyGaugeOmega,
      92             :       Spectral::Swsh::Tags::SwshInterpolator<Tags::PartiallyFlatAngularCoords>,
      93             :       Tags::LMax>;
      94           0 :   static void apply(
      95             :       gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*>
      96             :           cauchy_view_volume_j,
      97             :       const Scalar<SpinWeighted<ComplexDataVector, 2>>& gauge_cauchy_c,
      98             :       const Scalar<SpinWeighted<ComplexDataVector, 2>>& volume_j,
      99             :       const Scalar<SpinWeighted<ComplexDataVector, 0>>& gauge_cauchy_d,
     100             :       const Scalar<SpinWeighted<ComplexDataVector, 0>>& omega_cauchy,
     101             :       const Spectral::Swsh::SwshInterpolator& interpolator,
     102             :       const size_t l_max);
     103             : };
     104             : 
     105             : /*!
     106             :  * \brief Compute the Weyl scalar \f$\Psi_0\f$ in the volume for the purpose
     107             :  * of CCM, the quantity is in the Cauchy coordinates.
     108             :  *
     109             :  * \details The Weyl scalar \f$\Psi_0\f$ is given by:
     110             :  *
     111             :  * \f{align*}{
     112             :  * \Psi_0 = \frac{(1 - y)^4}{16 r^2 K}
     113             :  * \bigg[& \partial_y \beta \left((1 + K) (\partial_y J)
     114             :  * - \frac{J^2 \partial_y \bar J}{1 + K}\right)
     115             :  * - \frac{1}{2} (1 + K) (\partial_y^2 J)
     116             :  * + \frac{J^2 \partial_y^2 \bar J}{2(K + 1)}\\
     117             :  * & + \frac{1}{K^2} \left(- \frac{1}{4} J \left(\bar{J}^2 \left(\partial_y
     118             :  * J\right)^2 + J^2 \left(\partial_y \bar J\right)^2\right)
     119             :  * + \frac{1 + K^2}{2} J (\partial_y J) (\partial_y \bar J)
     120             :  * \right)\bigg].
     121             :  * \f}
     122             :  *
     123             :  * The quantities above are all in the Cauchy coordinates, where \f$K\f$ is
     124             :  * updated from \f$J\f$ and \f$\bar J\f$, \f$(1-y)\f$ is invariant under
     125             :  * the coordinate transformation. \f$r\f$ transforms as
     126             :  *
     127             :  * \f{align*}{
     128             :  * r = \omega \hat r
     129             :  * \f}
     130             :  */
     131             : template <>
     132           1 : struct VolumeWeyl<Tags::Psi0Match> {
     133           0 :   using return_tags = tmpl::list<Tags::Psi0Match>;
     134           0 :   using argument_tags =
     135             :       tmpl::list<Tags::BondiJCauchyView, Tags::Dy<Tags::BondiJCauchyView>,
     136             :                  Tags::Dy<Tags::Dy<Tags::BondiJCauchyView>>,
     137             :                  Tags::BoundaryValue<Tags::BondiR>, Tags::OneMinusY,
     138             :                  Tags::LMax>;
     139           0 :   static void apply(
     140             :       gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*> psi_0,
     141             :       const Scalar<SpinWeighted<ComplexDataVector, 2>>& bondi_j_cauchy,
     142             :       const Scalar<SpinWeighted<ComplexDataVector, 2>>& dy_j_cauchy,
     143             :       const Scalar<SpinWeighted<ComplexDataVector, 2>>& dy_dy_j_cauchy,
     144             :       const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r_cauchy,
     145             :       const Scalar<SpinWeighted<ComplexDataVector, 0>>& one_minus_y,
     146             :       const size_t l_max);
     147             : };
     148             : 
     149             : /*!
     150             :  * \brief Compute the Weyl scalar \f$\Psi_0\f$ and its radial derivative
     151             :  * \f$\partial_\lambda \Psi_0\f$ on the inner boundary of CCE domain.
     152             :  * The quantities are in the Cauchy coordinates.
     153             :  *
     154             :  * \details The radial derivative of the Weyl scalar \f$\partial_\lambda
     155             :  * \Psi_0\f$ is given by
     156             :  *
     157             :  * \f{align*}{
     158             :  * \partial_\lambda \Psi_0 = \frac{(1-y)^2}{2r}e^{-2\beta}
     159             :  * \partial_y \Psi_0
     160             :  * \f}
     161             :  *
     162             :  * Note that \f$(1-y)\f$, \f$r\f$, and \f$\beta\f$ are in the Cauchy
     163             :  * coordinates, where \f$(1-y)\f$ is invariant under the coordinate
     164             :  * transformation, while \f$r\f$ and \f$\beta\f$ transform as
     165             :  *
     166             :  * \f{align*}{
     167             :  * &r = \omega \hat r
     168             :  * & \beta = \hat \beta - \frac{1}{2} \log \omega
     169             :  * \f}
     170             :  */
     171           1 : struct InnerBoundaryWeyl {
     172           0 :   using return_tags =
     173             :       tmpl::list<Tags::BoundaryValue<Tags::Psi0Match>,
     174             :                  Tags::BoundaryValue<Tags::Dlambda<Tags::Psi0Match>>>;
     175           0 :   using argument_tags =
     176             :       tmpl::list<Tags::Psi0Match, Tags::Dy<Tags::Psi0Match>, Tags::OneMinusY,
     177             :                  Tags::BoundaryValue<Tags::BondiR>,
     178             :                  Tags::BoundaryValue<Tags::BondiBeta>, Tags::LMax>;
     179           0 :   static void apply(
     180             :       gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*> psi_0_boundary,
     181             :       gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*>
     182             :           dlambda_psi_0_boundary,
     183             :       const Scalar<SpinWeighted<ComplexDataVector, 2>>& psi_0,
     184             :       const Scalar<SpinWeighted<ComplexDataVector, 2>>& dy_psi_0,
     185             :       const Scalar<SpinWeighted<ComplexDataVector, 0>>& one_minus_y,
     186             :       const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r_cauchy,
     187             :       const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_beta_cauchy,
     188             :       const size_t l_max);
     189             : };
     190             : }  // namespace Cce

Generated by: LCOV version 1.14