Functions
template<typename T>
void	print_ricci_samples (const BSSNGridSoA< T > &G)
	Print Ricci tensor samples at representative radii for diagnostic purposes.
template<typename T>
void	invert_gamma_tilde (BSSNGridSoA< T > &G, size_t i, size_t j, size_t k)
	Explicit 3x3 inversion of \(\tilde{\gamma}_{ij}\) at a given grid index.
template<typename T>
void	minkowski (BSSNGridSoA< T > &G, T M, T xc=T(0), T yc=T(0), T zc=T(0), T r_floor=T(1e-6))
	Populate the grid with Minkowski (flat) initial data.
template<typename T>
void	schwarzschild_isotropic (BSSNGridSoA< T > &G, T M, T xc=T(0), T yc=T(0), T zc=T(0), T r_floor=T(1e-6))
	Construct an isotropic Schwarzschild puncture with conformal factor \(\psi=1+M/(2r)\).
template<typename T>
void	binary_schwarzschild_isotropic_2centers (BSSNGridSoA< T > &G, T m1, T x1, T y1, T z1, T m2, T x2, T y2, T z2, T r_floor=T(1e-6))
	Superpose two isotropic Schwarzschild conformal factors for binary puncture data.
template<typename T>
void	binary_bowen_york_puncture_init (BSSNGridSoA< T > &G, T m1, T x1, T y1, T z1, const T P1[3], const T S1[3], T m2, T x2, T y2, T z2, const T P2[3], const T S2[3], T r_floor=T(1e-6))
template<typename T>
static void	by_add_momentum_TF (T A[3][3], const T n[3], const T P[3], T r)
	Add the trace-free momentum component \(\tilde{A}_{ij}^P\) to \(\tilde{A}_{ij}\).
template<typename T>
static void	by_add_spin_TF (T A[3][3], const T n[3], const T S[3], T r)
	Add the spin component \(\tilde{A}_{ij}^S\) derived from \(S^i\).
template<typename T>
void	fill_Atilde_bowen_york_binary (BSSNGridSoA< T > &G, T x1, T y1, T z1, const T P1[3], const T S1[3], T x2, T y2, T z2, const T P2[3], const T S2[3], T r_floor=T(1e-6))
	Populate \(\tilde{A}_{ij}\) with the superposition of two Bowen–York punctures.
template<typename T>
static T	Atilde_sq_flat_from_soa (const BSSNGridSoA< T > &G, size_t id)
	Compute \(\tilde{A}_{ij}\tilde{A}^{ij}\) assuming \(\tilde{\gamma}_{ij}=\delta_{ij}\).
template<typename T>
void	solve_lichnerowicz_u_SOR (BSSNGridSoA< T > &G, T m1, T x1, T y1, T z1, T m2, T x2, T y2, T z2, T r_floor=T(1e-6), int maxIter=4000, T tol=T(1e-10), T omega=T(1.6))
	Solve the Lichnerowicz equation \(\Delta u = -\frac{1}{8}\psi^{-7}\tilde{A}_{ij}\tilde{A}^{ij}\) via red-black SOR.

Function Documentation

◆ Atilde_sq_flat_from_soa()

template<typename T>

T tensorium_RG::init::Atilde_sq_flat_from_soa	(	const BSSNGridSoA< T > &	G,
		size_t	id )

inlinestatic

Compute \(\tilde{A}_{ij}\tilde{A}^{ij}\) assuming \(\tilde{\gamma}_{ij}=\delta_{ij}\).

References tensorium_RG::XX, tensorium_RG::XY, tensorium_RG::XZ, tensorium_RG::YY, tensorium_RG::YZ, and tensorium_RG::ZZ.

Referenced by solve_lichnerowicz_u_SOR().

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◆ binary_bowen_york_puncture_init()

template<typename T>

void tensorium_RG::init::binary_bowen_york_puncture_init	(	BSSNGridSoA< T > &	G,
		T	m1,
		T	x1,
		T	y1,
		T	z1,
		const T	P1[3],
		const T	S1[3],
		T	m2,
		T	x2,
		T	y2,
		T	z2,
		const T	P2[3],
		const T	S2[3],
		T	r_floor = T(1e-6) )

inline

References tensorium_RG::bssn::apply_halos_grid(), tensorium_RG::bssn::assert_invariants(), tensorium_RG::bssn::compute_ricci_bssn(), tensorium_RG::bssn::compute_tildeGamma_contracted(), fill_Atilde_bowen_york_binary(), invert_gamma_tilde(), print_ricci_samples(), tensorium_RG::bssn::project_bssn_state(), solve_lichnerowicz_u_SOR(), tensorium_RG::XX, tensorium_RG::XY, tensorium_RG::XZ, tensorium_RG::YY, tensorium_RG::YZ, and tensorium_RG::ZZ.

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◆ binary_schwarzschild_isotropic_2centers()

template<typename T>

void tensorium_RG::init::binary_schwarzschild_isotropic_2centers	(	BSSNGridSoA< T > &	G,
		T	m1,
		T	x1,
		T	y1,
		T	z1,
		T	m2,
		T	x2,
		T	y2,
		T	z2,
		T	r_floor = T(1e-6) )

inline

Superpose two isotropic Schwarzschild conformal factors for binary puncture data.

Uses \(\psi = 1 + m_1/(2 r_1) + m_2/(2 r_2)\) with centers at \((x_a,y_a,z_a)\) and enforces the algebraic constraints afterwards. Generates conformally flat, time-symmetric data ( \(K=0\)).

References tensorium_RG::bssn::apply_halos_grid(), tensorium_RG::bssn::assert_invariants(), tensorium_RG::bssn::compute_bssn_constraints(), tensorium_RG::bssn::compute_ricci_bssn(), tensorium_RG::bssn::compute_tildeGamma_contracted(), invert_gamma_tilde(), tensorium_RG::bssn::print_constraint_norms(), print_ricci_samples(), tensorium_RG::bssn::project_bssn_state(), tensorium_RG::XX, tensorium_RG::XY, tensorium_RG::XZ, tensorium_RG::YY, tensorium_RG::YZ, and tensorium_RG::ZZ.

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◆ by_add_momentum_TF()

template<typename T>

void tensorium_RG::init::by_add_momentum_TF	(	T	A[3][3],
		const T	n[3],
		const T	P[3],
		T	r )

inlinestatic

Add the trace-free momentum component \(\tilde{A}_{ij}^P\) to \(\tilde{A}_{ij}\).

Referenced by fill_Atilde_bowen_york_binary().

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◆ by_add_spin_TF()

template<typename T>

void tensorium_RG::init::by_add_spin_TF	(	T	A[3][3],
		const T	n[3],
		const T	S[3],
		T	r )

inlinestatic

Add the spin component \(\tilde{A}_{ij}^S\) derived from \(S^i\).

Referenced by fill_Atilde_bowen_york_binary().

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◆ fill_Atilde_bowen_york_binary()

template<typename T>

void tensorium_RG::init::fill_Atilde_bowen_york_binary	(	BSSNGridSoA< T > &	G,
		T	x1,
		T	y1,
		T	z1,
		const T	P1[3],
		const T	S1[3],
		T	x2,
		T	y2,
		T	z2,
		const T	P2[3],
		const T	S2[3],
		T	r_floor = T(1e-6) )

inline

Populate \(\tilde{A}_{ij}\) with the superposition of two Bowen–York punctures.

Parameters

x1,y1,z1,x2,y2,z2	Centers of punctures 1 and 2.
P1,S1	Linear momentum and spin of puncture 1; analogous for puncture 2.
r_floor	Minimum radius enforced when normalizing \(n_i\).

References by_add_momentum_TF(), by_add_spin_TF(), tensorium_RG::XX, tensorium_RG::XY, tensorium_RG::XZ, tensorium_RG::YY, tensorium_RG::YZ, and tensorium_RG::ZZ.

Referenced by binary_bowen_york_puncture_init().

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◆ invert_gamma_tilde()

template<typename T>

void tensorium_RG::init::invert_gamma_tilde	(	BSSNGridSoA< T > &	G,
		size_t	i,
		size_t	j,
		size_t	k )

inline

Explicit 3x3 inversion of \(\tilde{\gamma}_{ij}\) at a given grid index.

Used by initial-data routines after writing the conformal metric to keep the inverse cache synchronized without invoking the global projector.

References tensorium_RG::XX, tensorium_RG::XY, tensorium_RG::XZ, tensorium_RG::YY, tensorium_RG::YZ, and tensorium_RG::ZZ.

Referenced by binary_bowen_york_puncture_init(), binary_schwarzschild_isotropic_2centers(), and schwarzschild_isotropic().

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◆ minkowski()

template<typename T>

void tensorium_RG::init::minkowski	(	BSSNGridSoA< T > &	G,
		T	M,
		T	xc = T(0),
		T	yc = T(0),
		T	zc = T(0),
		T	r_floor = T(1e-6) )

inline

Populate the grid with Minkowski (flat) initial data.

Parameters

M	Unused placeholder (kept for interface compatibility with Schwarzschild builders).
xc,yc,zc	Center of the coordinate system used for diagnostics.
r_floor	Minimum radius when sampling Ricci/constraint monitors.

Sets \(\alpha=1,\chi=1,\tilde{\gamma}_{ij}=\delta_{ij},\tilde{A}_{ij}=0,K=0,\beta^i=B^i=0,\tilde{\Gamma}^i=0\). After filling halos it recomputes Christoffels, Ricci, constraints, and enforces invariants.

References tensorium_RG::bssn::apply_halos_grid(), tensorium_RG::bssn::assert_invariants(), tensorium_RG::bssn::compute_bssn_constraints(), tensorium_RG::bssn::compute_ricci_bssn(), tensorium_RG::bssn::compute_tildeGamma_contracted(), tensorium_RG::bssn::print_constraint_norms(), print_ricci_samples(), tensorium_RG::bssn::project_bssn_state(), tensorium_RG::XX, tensorium_RG::XY, tensorium_RG::XZ, tensorium_RG::YY, tensorium_RG::YZ, and tensorium_RG::ZZ.

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◆ print_ricci_samples()

template<typename T>

void tensorium_RG::init::print_ricci_samples ( const BSSNGridSoA< T > & G )

Print Ricci tensor samples at representative radii for diagnostic purposes.

Evaluates \(R_{ij}\) at three locations (near, mid, far) along the x-axis to verify that the initial data satisfy \(R_{ij}=0\) away from punctures. Used after Minkowski/Schwarzschild set-up.

References tensorium_RG::XX, tensorium_RG::XY, tensorium_RG::XZ, tensorium_RG::YY, tensorium_RG::YZ, and tensorium_RG::ZZ.

Referenced by binary_bowen_york_puncture_init(), binary_schwarzschild_isotropic_2centers(), minkowski(), and schwarzschild_isotropic().

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◆ schwarzschild_isotropic()

template<typename T>

void tensorium_RG::init::schwarzschild_isotropic	(	BSSNGridSoA< T > &	G,
		T	M,
		T	xc = T(0),
		T	yc = T(0),
		T	zc = T(0),
		T	r_floor = T(1e-6) )

inline

Construct an isotropic Schwarzschild puncture with conformal factor \(\psi=1+M/(2r)\).

Parameters

M	Puncture mass parameter.
xc,yc,zc	Puncture center.
r_floor	Regularization radius to avoid division by zero at the puncture.

Sets \(\alpha=\psi^{-2}\), \(\chi=\psi^{-4}\), \(\tilde{\gamma}_{ij}=\delta_{ij}\), and \(\tilde{A}_{ij}=K=0\). The routine clamps \(r\ge r_{\text{floor}}\), applies halo BCs, recomputes \(\tilde{\Gamma}^i\) and \(R_{ij}\), then prints Ricci and constraint diagnostics.

References tensorium_RG::bssn::apply_halos_grid(), tensorium_RG::bssn::assert_invariants(), tensorium_RG::bssn::compute_bssn_constraints(), tensorium_RG::bssn::compute_ricci_bssn(), tensorium_RG::bssn::compute_tildeGamma_contracted(), invert_gamma_tilde(), tensorium_RG::bssn::print_constraint_norms(), print_ricci_samples(), tensorium_RG::bssn::project_bssn_state(), tensorium_RG::XX, tensorium_RG::XY, tensorium_RG::XZ, tensorium_RG::YY, tensorium_RG::YZ, and tensorium_RG::ZZ.

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◆ solve_lichnerowicz_u_SOR()

template<typename T>

void tensorium_RG::init::solve_lichnerowicz_u_SOR	(	BSSNGridSoA< T > &	G,
		T	m1,
		T	x1,
		T	y1,
		T	z1,
		T	m2,
		T	x2,
		T	y2,
		T	z2,
		T	r_floor = T(1e-6),
		int	maxIter = 4000,
		T	tol = T(1e-10),
		T	omega = T(1.6) )

inline

Solve the Lichnerowicz equation \(\Delta u = -\frac{1}{8}\psi^{-7}\tilde{A}_{ij}\tilde{A}^{ij}\) via red-black SOR.

Parameters

m1,m2,x1,...	Coordinates and bare masses entering the Brill–Lindquist conformal factor.
maxIter,tol,omega	Solver controls (iterations, residual tolerance, relaxation factor).

The discrete Laplacian uses standard 2nd-order stencils to balance efficiency with robustness. After convergence the routine updates \(\chi=\psi^{-4}\) and \(\alpha=\psi^{-2}\) and reprojects the grid.

References tensorium_RG::bssn::assert_invariants(), Atilde_sq_flat_from_soa(), tensorium_RG::bssn::compute_tildeGamma_contracted(), and tensorium_RG::bssn::project_bssn_state().

Referenced by binary_bowen_york_puncture_init().

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Functions

Function Documentation

◆ Atilde_sq_flat_from_soa()

◆ binary_bowen_york_puncture_init()

◆ binary_schwarzschild_isotropic_2centers()

◆ by_add_momentum_TF()

◆ by_add_spin_TF()

◆ fill_Atilde_bowen_york_binary()

◆ invert_gamma_tilde()

◆ minkowski()

◆ print_ricci_samples()

◆ schwarzschild_isotropic()

◆ solve_lichnerowicz_u_SOR()