SpECTRE  v2021.11.01
Cce::GaugeUpdateJacobianFromCoordinates< GaugeFactorSpin2, GaugeFactorSpin0, AngularCoordinateTag, CartesianCoordinateTag > Struct Template Reference

From the angular coordinates AngularCoordinateTag and the Cartesian coordinates CartesianCoordinateTag, determine the spin-weighted Jacobian factors GaugeFactorSpin2 and GaugeFactorSpin0. More...

#include <GaugeTransformBoundaryData.hpp>

Public Types

using return_tags = tmpl::list< GaugeFactorSpin2, GaugeFactorSpin0, AngularCoordinateTag >
 
using argument_tags = tmpl::list< CartesianCoordinateTag, Tags::LMax >
 

Static Public Member Functions

static void apply (const gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 2 > > * > gauge_factor_spin_2, const gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 0 > > * > gauge_factor_spin_0, const gsl::not_null< tnsr::i< DataVector, 2, ::Frame::Spherical<::Frame::Inertial > > * > angular_source_coordinates, const tnsr::i< DataVector, 3 > &cartesian_source_coordinates, const size_t l_max)
 

Detailed Description

template<typename GaugeFactorSpin2, typename GaugeFactorSpin0, typename AngularCoordinateTag, typename CartesianCoordinateTag>
struct Cce::GaugeUpdateJacobianFromCoordinates< GaugeFactorSpin2, GaugeFactorSpin0, AngularCoordinateTag, CartesianCoordinateTag >

From the angular coordinates AngularCoordinateTag and the Cartesian coordinates CartesianCoordinateTag, determine the spin-weighted Jacobian factors GaugeFactorSpin2 and GaugeFactorSpin0.

Details

This is most often used in the context of generating the Jacobians in the evolution-gauge coordinates from the Cauchy collocation points as a function of the evolution gauge coordinates. In this concrete case, the GaugeFactorSpin2 is the gauge factor \(\hat c\) and takes the value

\begin{align*} \hat c = \hat q^{\hat A} \partial_{\hat A}(x^A) q_A, \end{align*}

and the GaugeFactorSpin0 is the gauge factor \(\hat d\) and takes the value

\begin{align*} \hat d = \hat{\bar q}^{\hat A} \partial_{\hat A}(x^A) q_A. \end{align*}

The more generic template construction is employed so that the spin-weighted Jacobians can also be computed between two arbitrary gauges, including the inverse Jacobians associated with moving from the evolution gauge to the Cauchy gauge.


The documentation for this struct was generated from the following file: