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

using	return_tags = tmpl::list< Spectral::Swsh::Tags::Derivative< ArgumentTag, Spectral::Swsh::Tags::EthbarEthbar > >

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::Ethbar > >

Static Public Member Functions
template<typename DyArgumentType , typename DyDyArgumentType , typename EthbarDyArgumentType >
static void	apply (const gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, spin > > * > ethbar_ethbar_argument, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &one_minus_y, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &eth_r_divided_by_r, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &eth_eth_r_divided_by_r, const DyArgumentType &dy_argument, const DyDyArgumentType &dy_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::EthbarEthbar > >

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

Details

The implemented equation is:

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

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