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 gh {
      12             : namespace gauges {
      13             : namespace DampedHarmonicGauge_detail {
      14             : /*
      15             :  * Spatial weight function used in the damped harmonic gauge source
      16             :  * function.
      17             :  *
      18             :  * The spatial weight function is:
      19             :  * \f{align*}{
      20             :  *   W(x^i) = \exp(- (r / \sigma_r)^2),
      21             :  * \f}
      22             :  *
      23             :  * where \f$r=\sqrt{x^i\delta_{ij}x^j}\f$ is the coordinate radius, and
      24             :  * \f$\sigma_r\f$ is the width of the Gaussian.
      25             :  *
      26             :  * This function can be written with an extra factor inside the exponent in
      27             :  * literature, e.g. \cite Deppe2018uye. We absorb that in \f$\sigma_r\f$.
      28             :  */
      29             : template <typename DataType, size_t SpatialDim, typename Frame>
      30             : void spatial_weight_function(gsl::not_null<Scalar<DataType>*> weight,
      31             :                              const tnsr::I<DataType, SpatialDim, Frame>& coords,
      32             :                              double sigma_r);
      33             : 
      34             : /*
      35             :  * Spacetime derivatives of the spatial weight function that enters the
      36             :  * damped harmonic gauge source function.
      37             :  *
      38             :  * Compute the derivatives:
      39             :  * \f{align*}{
      40             :  * \partial_a W(x^i)= \partial_a \exp(- (r/\sigma_r)^2)
      41             :  *                  = (-2 * x^i / \sigma_r^2) * exp(-(r/\sigma_r)^2)
      42             :  * \f}
      43             :  *
      44             :  * where \f$r=\sqrt{x^i\delta_{ij}x^j}\f$ is the coordinate radius, and
      45             :  * \f$\sigma_r\f$ is the width of the Gaussian. Since the weight function is
      46             :  * spatial, the time derivative is always zero.
      47             :  */
      48             : template <typename DataType, size_t SpatialDim, typename Frame>
      49             : void spacetime_deriv_of_spatial_weight_function(
      50             :     gsl::not_null<tnsr::a<DataType, SpatialDim, Frame>*> d4_weight,
      51             :     const tnsr::I<DataType, SpatialDim, Frame>& coords, double sigma_r,
      52             :     const Scalar<DataType>& weight_function);
      53             : 
      54             : /*
      55             :  * The log factor that appears in damped harmonic gauge source function.
      56             :  *
      57             :  * Calculates:  \f$ logF = \mathrm{log}(g^p/N) \f$.
      58             :  */
      59             : template <typename DataType>
      60             : void log_factor_metric_lapse(gsl::not_null<Scalar<DataType>*> logfac,
      61             :                              const Scalar<DataType>& lapse,
      62             :                              const Scalar<DataType>& sqrt_det_spatial_metric,
      63             :                              double exponent);
      64             : 
      65             : template <typename DataType>
      66             : Scalar<DataType> log_factor_metric_lapse(
      67             :     const Scalar<DataType>& lapse,
      68             :     const Scalar<DataType>& sqrt_det_spatial_metric, double exponent);
      69             : 
      70             : }  // namespace DampedHarmonicGauge_detail
      71             : }  // namespace gauges
      72             : }  // namespace gh