SpECTRE  v2024.06.05
Cce::ApplySwshJacobianInplace< Spectral::Swsh::Tags::Derivative< ArgumentTag, Spectral::Swsh::Tags::EthbarEth > > Struct Template Reference

Specialization for the spin-weighted derivative \(\bar{\eth} \eth\). More...

#include <SwshDerivatives.hpp>

Public Types

using pre_swsh_derivative_tags = tmpl::list<>
using swsh_derivative_tags = tmpl::list<>
using integration_independent_tags = tmpl::list< Tags::OneMinusY, Tags::EthRDividedByR, Tags::EthEthbarRDividedByR >
using return_tags = tmpl::list< Spectral::Swsh::Tags::Derivative< ArgumentTag, Spectral::Swsh::Tags::EthbarEth > >
using argument_tags = tmpl::append< integration_independent_tags >
using on_demand_argument_tags = tmpl::list< Tags::Dy< ArgumentTag >, Tags::Dy< Tags::Dy< ArgumentTag > >, Spectral::Swsh::Tags::Derivative< Tags::Dy< ArgumentTag >, Spectral::Swsh::Tags::Eth >, Spectral::Swsh::Tags::Derivative< Tags::Dy< ArgumentTag >, Spectral::Swsh::Tags::Ethbar > >

Static Public Member Functions

template<typename DyArgumentType , typename DyDyArgumentType , typename EthDyArgumentType , typename EthbarDyArgumentType >
static void apply (const gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, spin > > * > ethbar_eth_argument, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &one_minus_y, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &eth_r_divided_by_r, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &eth_ethbar_r_divided_by_r, const DyArgumentType &dy_argument, const DyDyArgumentType &dy_dy_argument, const EthDyArgumentType &eth_dy_argument, const EthbarDyArgumentType ethbar_dy_argument)

Static Public Attributes

static constexpr int spin

Detailed Description

template<typename ArgumentTag>
struct Cce::ApplySwshJacobianInplace< Spectral::Swsh::Tags::Derivative< ArgumentTag, Spectral::Swsh::Tags::EthbarEth > >

Specialization for the spin-weighted derivative \(\bar{\eth} \eth\).


The implemented equation is:

\[ \bar{\eth} \eth F = \bar{\eth}^\prime \eth^\prime F - \frac{\eth R \bar{\eth} R}{R^2} (1 - y)^2 \partial_y^2 F - (1 - y)\left(\frac{\eth R}{R} \bar{\eth} \partial_y F + \frac{\bar{\eth} R}{R} \eth \partial_y F + \frac{\eth \bar\eth R}{R} \partial_y F\right), \]

where \(\bar{\eth} \eth\) is the derivative at constant Bondi radius \(r\) and \(\bar{\eth}^\prime \eth^\prime\) is the derivative at constant numerical radius \(y\).

Member Data Documentation

◆ spin

template<typename ArgumentTag >
constexpr int Cce::ApplySwshJacobianInplace< Spectral::Swsh::Tags::Derivative< ArgumentTag, Spectral::Swsh::Tags::EthbarEth > >::spin
Initial value:
Prefix tag representing the spin-weighted derivative of a spin-weighted scalar.
Definition: SwshTags.hpp:151
Struct for labeling the spin-weighted derivative in tags.
Definition: SwshTags.hpp:41

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