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/Tensor/TypeAliases.hpp"
       9              : #include "Utilities/Gsl.hpp"
      10              : 
      11              : namespace Ccz4 {
      12              : /// @{
      13              : /*!
      14              :  * \brief Computes the gradient of the spatial part of the Z4 constraint
      15              :  *
      16              :  * \details Computes the gradient as:
      17              :  *
      18              :  * \f{align}
      19              :  *     \nabla_i Z_j &=
      20              :  *         D_{ijl} \left(\hat{\Gamma}^l - \tilde{\Gamma}^l\right) +
      21              :  *         \frac{1}{2} \tilde{\gamma}_{jl} \left(
      22              :  *             \partial_i \hat{\Gamma}^l - \partial_i \tilde{\Gamma}^l\right) -
      23              :  *         \Gamma^l_{ij} Z_l
      24              :  * \f}
      25              :  *
      26              :  * where \f$Z_i\f$ is the spatial Z4 constraint defined by
      27              :  * `Ccz4::Tags::SpatialZ4Constraint`, \f$\tilde{\gamma}_{ij}\f$ is the conformal
      28              :  * spatial metric defined by `Ccz4::Tags::ConformalMetric`, \f$\Gamma^k_{ij}\f$
      29              :  * is the spatial Christoffel symbols of the second kind defined by
      30              :  * `Ccz4::Tags::ChristoffelSecondKind`, \f$D_{ijk}\f$ is the CCZ4 auxiliary
      31              :  * variable defined by `Ccz4::Tags::FieldD`,
      32              :  * \f$\left(\hat{\Gamma}^i - \tilde{\Gamma}^i\right)\f$ is the CCZ4 temporary
      33              :  * expression defined by
      34              :  * `Ccz4::Tags::GammaHatMinusContractedConformalChristoffel`, and
      35              :  * \f$\left(\partial_i \hat{\Gamma}^j - \partial_i \tilde{\Gamma}^j\right)\f$ is
      36              :  * its spatial derivative.
      37              :  */
      38              : template <typename DataType, size_t Dim, typename Frame>
      39            1 : void grad_spatial_z4_constraint(
      40              :     const gsl::not_null<tnsr::ij<DataType, Dim, Frame>*> result,
      41              :     const tnsr::i<DataType, Dim, Frame>& spatial_z4_constraint,
      42              :     const tnsr::ii<DataType, Dim, Frame>& conformal_spatial_metric,
      43              :     const tnsr::Ijj<DataType, Dim, Frame>& christoffel_second_kind,
      44              :     const tnsr::ijj<DataType, Dim, Frame>& field_d,
      45              :     const tnsr::I<DataType, Dim, Frame>&
      46              :         gamma_hat_minus_contracted_conformal_christoffel,
      47              :     const tnsr::iJ<DataType, Dim, Frame>&
      48              :         d_gamma_hat_minus_contracted_conformal_christoffel);
      49              : 
      50              : template <typename DataType, size_t Dim, typename Frame>
      51            1 : tnsr::ij<DataType, Dim, Frame> grad_spatial_z4_constraint(
      52              :     const tnsr::i<DataType, Dim, Frame>& spatial_z4_constraint,
      53              :     const tnsr::ii<DataType, Dim, Frame>& conformal_spatial_metric,
      54              :     const tnsr::Ijj<DataType, Dim, Frame>& christoffel_second_kind,
      55              :     const tnsr::ijj<DataType, Dim, Frame>& field_d,
      56              :     const tnsr::I<DataType, Dim, Frame>&
      57              :         gamma_hat_minus_contracted_conformal_christoffel,
      58              :     const tnsr::iJ<DataType, Dim, Frame>&
      59              :         d_gamma_hat_minus_contracted_conformal_christoffel);
      60              : /// @}
      61              : }  // namespace Ccz4