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