Enumerations
enum	Axis { X = 0 , Y = 1 , Z = 2 }

Functions
template<typename Field>
double	get (const Field &f, size_t i, size_t j, size_t k)
	Utility accessor that forwards to Field3D::idx / raw pointer storage.
template<typename Field>
double	Dx (const Field &f, size_t i, size_t j, size_t k, double dx)
	4th-order centered derivative along x.
template<typename Field>
double	Dy (const Field &f, size_t i, size_t j, size_t k, double dy)
	4th-order centered derivative along y.
template<typename Field>
double	Dz (const Field &f, size_t i, size_t j, size_t k, double dz)
	4th-order centered derivative along z.
template<typename Field>
double	Dxx (const Field &f, size_t i, size_t j, size_t k, double dx)
	4th-order approximation to \(\partial_{xx} f\).
template<typename Field>
double	Dyy (const Field &f, size_t i, size_t j, size_t k, double dy)
template<typename Field>
double	Dzz (const Field &f, size_t i, size_t j, size_t k, double dz)
template<typename Field>
double	Dxy (const Field &f, size_t i, size_t j, size_t k, double dx, double dy)
	Mixed second derivative using the compact second-order stencil.
template<typename Field>
double	Dxz (const Field &f, size_t i, size_t j, size_t k, double dx, double dz)
template<typename Field>
double	Dyz (const Field &f, size_t i, size_t j, size_t k, double dy, double dz)
template<typename Field>
double	Dxy4 (const Field &f, size_t i, size_t j, size_t k, double dx, double dy)
	Tensor-product 4th-order approximation to \(\partial_{xy} f\).
template<typename Field>
double	Dxz4 (const Field &f, size_t i, size_t j, size_t k, double dx, double dz)
template<typename Field>
double	Dyz4 (const Field &f, size_t i, size_t j, size_t k, double dy, double dz)
template<typename Field>
double	D (const Field &f, size_t i, size_t j, size_t k, Axis a, double dx, double dy, double dz)
	Axis selector that forwards to Dx/Dy/Dz for compile-time loops.
template<typename Field>
double	KO6_axis (const Field &f, size_t i, size_t j, size_t k, Axis axis)
	One-dimensional slice of the 6th-order Kreiss–Oliger filter.
template<typename Field>
double	KO6 (const Field &f, size_t i, size_t j, size_t k, double sigma)
	Dimension-summed Kreiss–Oliger dissipation scaled by \(\sigma\).
template<typename Field>
double	Dx_upwind (const Field &f, size_t i, size_t j, size_t k, double dx, double beta)
	Third-order upwind derivative along x used for shift advection terms.
template<typename Field>
double	Dy_upwind (const Field &f, size_t i, size_t j, size_t k, double dy, double beta)
template<typename Field>
double	Dz_upwind (const Field &f, size_t i, size_t j, size_t k, double dz, double beta)

Enumeration Type Documentation

◆ Axis

enum tensorium_RG::fd::Axis

Enumerator
X
Y
Z

Function Documentation

◆ D()

template<typename Field>

double tensorium_RG::fd::D	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		Axis	a,
		double	dx,
		double	dy,
		double	dz )

inline

Axis selector that forwards to Dx/Dy/Dz for compile-time loops.

References Dx(), Dy(), Dz(), X, and Y.

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◆ Dx()

template<typename Field>

double tensorium_RG::fd::Dx	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dx )

inline

4th-order centered derivative along x.

Implements the stencil shown in the file-level documentation.

Parameters

f	Field to differentiate.
dx	Grid spacing \(\Delta x\).

References get().

Referenced by tensorium_RG::bssn::compute_bssn_constraints(), tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_chi(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_gamma_tilde(), tensorium_RG::bssn::compute_rhs_K(), tensorium_RG::bssn::compute_ricci_bssn(), D(), and tensorium_RG::bssn::detail::diff_gamma_tilde_inv_component().

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◆ Dx_upwind()

template<typename Field>

double tensorium_RG::fd::Dx_upwind	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dx,
		double	beta )

inline

Third-order upwind derivative along x used for shift advection terms.

Parameters

beta	Sign of the advecting velocity (typically \(\beta^x\)) determines the biased stencil.

References get().

Referenced by tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_alpha(), tensorium_RG::bssn::compute_rhs_chi(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_gamma_tilde(), and tensorium_RG::bssn::compute_rhs_K().

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◆ Dxx()

template<typename Field>

double tensorium_RG::fd::Dxx	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dx )

inline

4th-order approximation to \(\partial_{xx} f\).

Note: Uses the classic \((-1,16,-30,16,-1)/12\) stencil scaled by \(1/\Delta x^2\).

References get().

Referenced by tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_K(), and tensorium_RG::bssn::compute_ricci_bssn().

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◆ Dxy()

template<typename Field>

double tensorium_RG::fd::Dxy	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dx,
		double	dy )

inline

Mixed second derivative using the compact second-order stencil.

Useful near where 4th-order cross derivatives would require larger halos.

References get().

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◆ Dxy4()

template<typename Field>

double tensorium_RG::fd::Dxy4	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dx,
		double	dy )

inline

Tensor-product 4th-order approximation to \(\partial_{xy} f\).

Expands the 1D \((-1,8,-8,1)/12\) derivative in both axes and rescales by \(144\,\Delta x\,\Delta y\) so Ricci builders can reuse it for the \(\tilde{R}_{ij}\) terms.

References get().

Referenced by tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_K(), and tensorium_RG::bssn::compute_ricci_bssn().

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◆ Dxz()

template<typename Field>

double tensorium_RG::fd::Dxz	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dx,
		double	dz )

inline

References get().

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◆ Dxz4()

template<typename Field>

double tensorium_RG::fd::Dxz4	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dx,
		double	dz )

inline

References get().

Referenced by tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_K(), and tensorium_RG::bssn::compute_ricci_bssn().

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◆ Dy()

template<typename Field>

double tensorium_RG::fd::Dy	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dy )

inline

4th-order centered derivative along y.

References get().

Referenced by tensorium_RG::bssn::compute_bssn_constraints(), tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_chi(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_gamma_tilde(), tensorium_RG::bssn::compute_rhs_K(), tensorium_RG::bssn::compute_ricci_bssn(), D(), and tensorium_RG::bssn::detail::diff_gamma_tilde_inv_component().

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◆ Dy_upwind()

template<typename Field>

double tensorium_RG::fd::Dy_upwind	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dy,
		double	beta )

inline

References get().

Referenced by tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_alpha(), tensorium_RG::bssn::compute_rhs_chi(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_gamma_tilde(), and tensorium_RG::bssn::compute_rhs_K().

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◆ Dyy()

template<typename Field>

double tensorium_RG::fd::Dyy	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dy )

inline

References get().

Referenced by tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_K(), and tensorium_RG::bssn::compute_ricci_bssn().

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◆ Dyz()

template<typename Field>

double tensorium_RG::fd::Dyz	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dy,
		double	dz )

inline

References get().

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◆ Dyz4()

template<typename Field>

double tensorium_RG::fd::Dyz4	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dy,
		double	dz )

inline

References get().

Referenced by tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_K(), and tensorium_RG::bssn::compute_ricci_bssn().

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◆ Dz()

template<typename Field>

double tensorium_RG::fd::Dz	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dz )

inline

4th-order centered derivative along z.

References get().

Referenced by tensorium_RG::bssn::compute_bssn_constraints(), tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_chi(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_gamma_tilde(), tensorium_RG::bssn::compute_rhs_K(), tensorium_RG::bssn::compute_ricci_bssn(), D(), and tensorium_RG::bssn::detail::diff_gamma_tilde_inv_component().

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◆ Dz_upwind()

template<typename Field>

double tensorium_RG::fd::Dz_upwind	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dz,
		double	beta )

inline

References get().

Referenced by tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_alpha(), tensorium_RG::bssn::compute_rhs_chi(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_gamma_tilde(), and tensorium_RG::bssn::compute_rhs_K().

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◆ Dzz()

template<typename Field>

double tensorium_RG::fd::Dzz	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	dz )

inline

References get().

Referenced by tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_K(), and tensorium_RG::bssn::compute_ricci_bssn().

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◆ get()

template<typename Field>

double tensorium_RG::fd::get	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k )

inline

Utility accessor that forwards to Field3D::idx / raw pointer storage.

Referenced by Dx(), Dx_upwind(), Dxx(), Dxy(), Dxy4(), Dxz(), Dxz4(), Dy(), Dy_upwind(), Dyy(), Dyz(), Dyz4(), Dz(), Dz_upwind(), Dzz(), and KO6_axis().

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◆ KO6()

template<typename Field>

double tensorium_RG::fd::KO6	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		double	sigma )

inline

Dimension-summed Kreiss–Oliger dissipation scaled by \(\sigma\).

Note: RHS kernels typically set \(\sigma=0.1\) following the module conventions.

References KO6_axis(), X, Y, and Z.

Referenced by tensorium_RG::bssn::compute_rhs_A_tilde(), tensorium_RG::bssn::compute_rhs_alpha(), tensorium_RG::bssn::compute_rhs_chi(), tensorium_RG::bssn::compute_rhs_Gamma(), tensorium_RG::bssn::compute_rhs_gamma_tilde(), and tensorium_RG::bssn::compute_rhs_K().

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◆ KO6_axis()

template<typename Field>

double tensorium_RG::fd::KO6_axis	(	const Field &	f,
		size_t	i,
		size_t	j,
		size_t	k,
		Axis	axis )

inline

One-dimensional slice of the 6th-order Kreiss–Oliger filter.

Implements \(\mathcal{D}_6[f]_j = (f_{j-3} - 6f_{j-2} + 15 f_{j-1} - 20 f_j + 15 f_{j+1} - 6 f_{j+2} + f_{j+3})/64\).

References get(), X, and Y.

Referenced by KO6().

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Enumerations

Functions

Enumeration Type Documentation

◆ Axis

Function Documentation

◆ D()

◆ Dx()

◆ Dx_upwind()

◆ Dxx()

◆ Dxy()

◆ Dxy4()

◆ Dxz()

◆ Dxz4()

◆ Dy()

◆ Dy_upwind()

◆ Dyy()

◆ Dyz()

◆ Dyz4()

◆ Dz()

◆ Dz_upwind()

◆ Dzz()

◆ get()

◆ KO6()

◆ KO6_axis()