Classes
class	BSSN
	Driver class to initialize and store BSSN variables from an input spacetime metric. More...

class	BSSNAtildeTensor
	Computes the trace-free conformal extrinsic curvature tensor \( \tilde{A}_{ij} \) in the BSSN formalism. More...

class	BSSNChristoffel
	Compute the conformal Christoffel symbols \( \tilde{\Gamma}^k_{ij} \). More...

class	BSSNContractedGamma

struct	BSSNGrid
	Storage structure for all evolved BSSN variables on a single grid point or patch. More...

struct	ChiContext

class	ChristoffelSym
	Stores and computes Christoffel symbols \( \Gamma^\lambda_{\mu\nu} \). More...

class	ConstraintSolver

class	ExtrinsicCurvature
	Computes the extrinsic curvature tensor \( K_{ij} \) from BSSN variables. More...

class	Metric
	A callable 4D metric class for general relativity (Minkowski, Schwarzschild, Kerr, etc.) More...

class	RicciConformalTensor
	Provides methods to compute the \( \chi \)-dependent part of the Ricci tensor in the BSSN formalism. More...

class	RicciPhysicalTensor
	Computes the physical 3-Ricci tensor \( R_{ij} \) as the sum of conformal and conformal-factor contributions. More...

class	RicciTensor
	Computes the Ricci tensor and Ricci scalar from a 4D Riemann tensor. More...

class	RicciTildeTensor
	Provides methods to compute the conformal Ricci tensor \( \tilde{R}_{ij} \) in the BSSN formulation. More...

class	RiemannTensor
	Computes the 4D Riemann curvature tensor \( R^\rho_{\ \sigma\mu\nu} \). More...

class	TildeGamma
	Computes the contracted conformal Christoffel vector \( \tilde{\Gamma}^i \). More...

Enumerations
enum class	DiffMode { PARTIAL , COV , COV2 , SPEC }

Functions
template<typename T , typename ScalarFunc >
tensorium::Vector< T >	covariant_scalar (const tensorium::Vector< T > &X, T dx, T dy, T dz, ScalarFunc &&func, const tensorium::Tensor< T, 3 > &christoffel)

template<typename T , typename ScalarFunc >
tensorium::Tensor< T, 2 >	autodiff_scalar_second (const tensorium::Vector< T > &X, T dx, T dy, T dz, ScalarFunc &&func, const tensorium::Tensor< T, 3 > &christoffel)

template<typename T , typename ScalarFunc >
tensorium::Vector< T >	autodiff_rank0 (const tensorium::Vector< T > &X, T dx, T dy, T dz, ScalarFunc &&func, DiffMode mode, const tensorium::Tensor< T, 3 > &christoffel)

template<typename T , typename VectorFunc >
tensorium::Tensor< T, 2 >	autodiff_rank1 (const tensorium::Vector< T > &X, T dx, T dy, T dz, VectorFunc &&func, DiffMode mode, const tensorium::Tensor< T, 3 > &christoffel)

template<typename T , typename TensorFunc >
tensorium::Tensor< T, 3 >	autodiff_rank2_first (const tensorium::Vector< T > &X, T dx, T dy, T dz, TensorFunc &&func, DiffMode mode, const tensorium::Tensor< T, 3 > &christoffel)

template<typename T , typename FieldFunc >
auto	autodiff (const tensorium::Vector< T > &X, T dx, T dy, T dz, FieldFunc &&func, DiffMode mode, const tensorium::Tensor< T, 3 > &christoffel={})

template<typename T >
void	compute_partial_derivatives_3D (const tensorium::Tensor< T, 5 > &gamma_field, size_t i, size_t j, size_t k, T dx, T dy, T dz, tensorium::Tensor< T, 3 > &dgamma_out)
	Compute the 3D partial derivatives \( \partial_k \tilde{\gamma}_{ij} \) from a 5D field tensor.

template<typename T >
void	spectral_derivative_1D (tensorium::Vector< T > &field, tensorium::Vector< T > &dfield, T dx)

template<typename T >
void	spectral_partial_scalar_3D (const tensorium::Tensor< T, 3 > &scalar_field, T dx, T dy, T dz, tensorium::Tensor< T, 4 > &grad_out)

template<typename T , typename TensorFunc >
tensorium::Tensor< T, 3 >	spectral_partial_tensor2 (const tensorium::Vector< T > &X, T dx, T dy, T dz, TensorFunc &&func, size_t NX, size_t NY, size_t NZ)

template<typename T , typename ScalarFunc >
tensorium::Vector< T >	partial_scalar (const tensorium::Vector< T > &X, T dx, T dy, T dz, ScalarFunc &&func)

template<typename T , typename VectorFunc >
tensorium::Tensor< T, 2 >	partial_vector (const tensorium::Vector< T > &X, T dx, T dy, T dz, VectorFunc &&func)

template<typename T , typename TensorFunc >
void	compute_partial_derivatives_tensor2D (const tensorium::Vector< T > &X, T dx, T dy, T dz, TensorFunc &&func, tensorium::Tensor< T, 3 > &out)

template<typename T , typename TensorFunc >
void	compute_second_derivatives_tensor2D (const tensorium::Vector< T > &X, T dx, T dy, T dz, TensorFunc &&func, tensorium::Tensor< T, 4 > &out)

template<typename T , typename VectorFunc >
void	compute_partial_derivatives_vector (const tensorium::Vector< T > &X, T dx, T dy, T dz, VectorFunc &&func, tensorium::Tensor< T, 2 > &out)

template<typename T , typename ScalarFunc >
void	compute_partial_derivatives_scalar (const tensorium::Vector< T > &X, T dx, T dy, T dz, ScalarFunc &&func, tensorium::Vector< T > &out)

template<typename T >
tensorium::Tensor< T, 2 >	compute_dt_gamma_from_beta (const tensorium::Tensor< T, 2 > &gamma, const tensorium::Vector< T > &beta, const tensorium::Tensor< T, 2 > &partial_beta, const tensorium::Tensor< T, 3 > &christoffel)

template<typename T >
void	compute_partial_derivatives_vector3D (const tensorium::Tensor< T, 4 > &vec_field, size_t i, size_t j, size_t k, T dx, T dy, T dz, tensorium::Tensor< T, 2 > &dvec_out)

template<typename T , typename ScalarFunc >
void	compute_second_derivatives_scalar (const tensorium::Vector< T > &X, T dx, T dy, T dz, ScalarFunc &&func, tensorium::Tensor< T, 2 > &out)

template<typename T , typename ScalarFunc >
tensorium::Tensor< T, 2 >	covariant_scalar_second (const tensorium::Vector< T > &X, T dx, T dy, T dz, ScalarFunc &&func, const tensorium::Tensor< T, 3 > &christoffel)

template<typename T >
void	compute_second_derivatives_scalar3D (const tensorium::Tensor< T, 3 > &scalar_field, T dx, T dy, T dz, tensorium::Tensor< T, 5 > &hessian_out)

template<typename T >
tensorium::Tensor< T, 5 >	covariant_scalar_second_3D (const tensorium::Tensor< T, 3 > &chi, const tensorium::Tensor< T, 5 > &christoffel, T dx, T dy, T dz)

template<typename T , typename VectorFunc >
tensorium::Tensor< T, 2 >	covariant_vector (const tensorium::Vector< T > &X, T dx, T dy, T dz, VectorFunc &&func, const tensorium::Tensor< T, 3 > &Gamma)

template<typename T , typename TensorFunc >
tensorium::Tensor< T, 3 >	covariant_tensor2 (const tensorium::Vector< T > &X, T dx, T dy, T dz, TensorFunc &&func, const tensorium::Tensor< T, 3 > &Gamma)

template<typename T , typename TensorFunc >
tensorium::Tensor< T, 3 >	partial_tensor2 (const tensorium::Vector< T > &X, T dx, T dy, T dz, TensorFunc &&func)

template<typename T , typename TensorFunc >
tensorium::Tensor< T, 4 >	covariant_tensor2_second (const tensorium::Vector< T > &X, T dx, T dy, T dz, TensorFunc &&func, const tensorium::Tensor< T, 3 > &Gamma)

template<typename T , typename TensorFunc >
tensorium::Tensor< T, 3 >	populate_tensor3D_component (size_t i, size_t j, TensorFunc &&func, T dx, T dy, T dz, size_t NX, size_t NY, size_t NZ)

template<typename T >
tensorium::Tensor< T, 5 >	generate_conformal_metric_field (const tensorium_RG::Metric< T > &metric, size_t Nx, size_t Ny, size_t Nz, T dx, T dy, T dz)
	Generate the conformal 3-metric field \( \tilde{\gamma}_{ij}(x^i) \) on a 3D grid.

template<typename T >
void	print_tensor2 (const std::string &name, const tensorium::Tensor< T, 2 > &tensor)

template<typename T >
void	print_tensor3 (const std::string &name, const tensorium::Tensor< T, 3 > &tensor)

template<typename T >
void	print_vector (const std::string &name, const tensorium::Vector< T > &vec)

template<typename T >
	__attribute__ ((always_inline, hot, flatten)) inline tensorium
	Compute the inverse of a 2D metric tensor using local matrix inversion.

Enumeration Type Documentation

◆ DiffMode

enum class tensorium_RG::DiffMode

strong

Enumerator
PARTIAL
COV
COV2
SPEC

Function Documentation

◆ attribute()

template<typename T >

tensorium_RG::__attribute__ ( (always_inline, hot, flatten) )

Compute the inverse of a 2D metric tensor using local matrix inversion.

Compute Christoffel symbols at an offset position along one direction.

Converts the tensor to a matrix, computes the inverse, and converts back.

Template Parameters

T	Scalar type

Parameters

g	Metric tensor \( g_{\mu\nu} \)

Returns: Inverse tensor \( g^{\mu\nu} \)

Used in numerical relativity to evaluate derivatives of Christoffel symbols.

Template Parameters

T	Scalar type

Parameters

X	Base coordinate
direction	Axis of offset
offset	Value to add (positive or negative)
h	Finite difference step size
g	Output metric tensor
g_inv	Output inverse metric
Gamma_out	Output Christoffel tensor
metric	Metric object

References tensorium::Tensor< K, Rank >::dimensions.

◆ autodiff()

template<typename T , typename FieldFunc >

auto tensorium_RG::autodiff	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		FieldFunc &&	func,
		DiffMode	mode,
		const tensorium::Tensor< T, 3 > &	christoffel = {} )

Referenced by tensorium_RG::BSSN< T >::init_BSSN().

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◆ autodiff_rank0()

template<typename T , typename ScalarFunc >

tensorium::Vector< T > tensorium_RG::autodiff_rank0	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		ScalarFunc &&	func,
		DiffMode	mode,
		const tensorium::Tensor< T, 3 > &	christoffel )

References COV, covariant_scalar(), PARTIAL, partial_scalar(), and X().

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◆ autodiff_rank1()

template<typename T , typename VectorFunc >

tensorium::Tensor< T, 2 > tensorium_RG::autodiff_rank1	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		VectorFunc &&	func,
		DiffMode	mode,
		const tensorium::Tensor< T, 3 > &	christoffel )

References COV, covariant_vector(), PARTIAL, partial_vector(), and X().

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◆ autodiff_rank2_first()

template<typename T , typename TensorFunc >

tensorium::Tensor< T, 3 > tensorium_RG::autodiff_rank2_first	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		TensorFunc &&	func,
		DiffMode	mode,
		const tensorium::Tensor< T, 3 > &	christoffel )

References COV, covariant_tensor2(), PARTIAL, partial_tensor2(), SPEC, and X().

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◆ autodiff_scalar_second()

template<typename T , typename ScalarFunc >

tensorium::Tensor< T, 2 > tensorium_RG::autodiff_scalar_second	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		ScalarFunc &&	func,
		const tensorium::Tensor< T, 3 > &	christoffel )

References covariant_scalar_second(), and X().

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◆ compute_dt_gamma_from_beta()

template<typename T >

tensorium::Tensor< T, 2 > tensorium_RG::compute_dt_gamma_from_beta	(	const tensorium::Tensor< T, 2 > &	gamma,
		const tensorium::Vector< T > &	beta,
		const tensorium::Tensor< T, 2 > &	partial_beta,
		const tensorium::Tensor< T, 3 > &	christoffel )

References beta.

◆ compute_partial_derivatives_3D()

template<typename T >

void tensorium_RG::compute_partial_derivatives_3D	(	const tensorium::Tensor< T, 5 > &	gamma_field,
		size_t	i,
		size_t	j,
		size_t	k,
		T	dx,
		T	dy,
		T	dz,
		tensorium::Tensor< T, 3 > &	dgamma_out )

inline

Compute the 3D partial derivatives \( \partial_k \tilde{\gamma}_{ij} \) from a 5D field tensor.

Uses centered 4th-order or 2nd-order finite differences for inner and boundary points.

\[ \partial_k \tilde{\gamma}_{ij} = \begin{cases} \frac{-f(x+2h) + 8f(x+h) - 8f(x-h) + f(x-2h)}{12h} & \text{if inner} \\ \frac{f(x+h) - f(x-h)}{2h} & \text{if near boundary} \\ 0 & \text{otherwise} \end{cases} \]

Parameters

gamma_field	Field of type Tensor<T, 5> with dimensions [Nx, Ny, Nz, 3, 3]
i,j,k	Grid position
dx,dy,dz	Grid spacings
dgamma_out	Output tensor \( \partial_k \tilde{\gamma}_{ij} \)

References tensorium::Tensor< K, Rank >::resize(), and tensorium::Tensor< K, Rank >::shape().

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◆ compute_partial_derivatives_scalar()

template<typename T , typename ScalarFunc >

void tensorium_RG::compute_partial_derivatives_scalar	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		ScalarFunc &&	func,
		tensorium::Vector< T > &	out )

References tensorium::Tensor< K, Rank >::resize(), and X().

Referenced by covariant_scalar_second(), and covariant_scalar_second_3D().

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◆ compute_partial_derivatives_tensor2D()

template<typename T , typename TensorFunc >

void tensorium_RG::compute_partial_derivatives_tensor2D	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		TensorFunc &&	func,
		tensorium::Tensor< T, 3 > &	out )

References tensorium::Tensor< K, Rank >::resize(), and X().

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◆ compute_partial_derivatives_vector()

template<typename T , typename VectorFunc >

void tensorium_RG::compute_partial_derivatives_vector	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		VectorFunc &&	func,
		tensorium::Tensor< T, 2 > &	out )

References tensorium::Tensor< K, Rank >::resize(), and X().

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◆ compute_partial_derivatives_vector3D()

template<typename T >

void tensorium_RG::compute_partial_derivatives_vector3D	(	const tensorium::Tensor< T, 4 > &	vec_field,
		size_t	i,
		size_t	j,
		size_t	k,
		T	dx,
		T	dy,
		T	dz,
		tensorium::Tensor< T, 2 > &	dvec_out )

inline

References tensorium::Tensor< K, Rank >::resize(), and tensorium::Tensor< K, Rank >::shape().

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◆ compute_second_derivatives_scalar()

template<typename T , typename ScalarFunc >

void tensorium_RG::compute_second_derivatives_scalar	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		ScalarFunc &&	func,
		tensorium::Tensor< T, 2 > &	out )

inline

References tensorium::Tensor< K, Rank >::resize(), and X().

Referenced by tensorium_RG::ChiContext< T >::compute(), covariant_scalar_second(), and covariant_scalar_second_3D().

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◆ compute_second_derivatives_scalar3D()

template<typename T >

void tensorium_RG::compute_second_derivatives_scalar3D	(	const tensorium::Tensor< T, 3 > &	scalar_field,
		T	dx,
		T	dy,
		T	dz,
		tensorium::Tensor< T, 5 > &	hessian_out )

References tensorium::Tensor< K, Rank >::resize(), and tensorium::Tensor< K, Rank >::shape().

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◆ compute_second_derivatives_tensor2D()

template<typename T , typename TensorFunc >

void tensorium_RG::compute_second_derivatives_tensor2D	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		TensorFunc &&	func,
		tensorium::Tensor< T, 4 > &	out )

References X().

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◆ covariant_scalar()

template<typename T , typename ScalarFunc >

tensorium::Vector< T > tensorium_RG::covariant_scalar	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		ScalarFunc &&	func,
		const tensorium::Tensor< T, 3 > &	christoffel )

References partial_scalar(), and X().

Referenced by autodiff_rank0().

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◆ covariant_scalar_second()

template<typename T , typename ScalarFunc >

tensorium::Tensor< T, 2 > tensorium_RG::covariant_scalar_second	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		ScalarFunc &&	func,
		const tensorium::Tensor< T, 3 > &	christoffel )

References compute_partial_derivatives_scalar(), compute_second_derivatives_scalar(), and X().

Referenced by autodiff_scalar_second().

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◆ covariant_scalar_second_3D()

template<typename T >

tensorium::Tensor< T, 5 > tensorium_RG::covariant_scalar_second_3D	(	const tensorium::Tensor< T, 3 > &	chi,
		const tensorium::Tensor< T, 5 > &	christoffel,
		T	dx,
		T	dy,
		T	dz )

References chi, compute_partial_derivatives_scalar(), compute_second_derivatives_scalar(), tensorium::Tensor< K, Rank >::shape(), and X().

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◆ covariant_tensor2()

template<typename T , typename TensorFunc >

tensorium::Tensor< T, 3 > tensorium_RG::covariant_tensor2	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		TensorFunc &&	func,
		const tensorium::Tensor< T, 3 > &	Gamma )

References Gamma, partial_tensor2(), and X().

Referenced by autodiff_rank2_first().

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◆ covariant_tensor2_second()

template<typename T , typename TensorFunc >

tensorium::Tensor< T, 4 > tensorium_RG::covariant_tensor2_second	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		TensorFunc &&	func,
		const tensorium::Tensor< T, 3 > &	Gamma )

References Gamma, and X().

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◆ covariant_vector()

template<typename T , typename VectorFunc >

tensorium::Tensor< T, 2 > tensorium_RG::covariant_vector	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		VectorFunc &&	func,
		const tensorium::Tensor< T, 3 > &	Gamma )

References Gamma, partial_vector(), and X().

Referenced by autodiff_rank1().

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◆ generate_conformal_metric_field()

template<typename T >

tensorium::Tensor< T, 5 > tensorium_RG::generate_conformal_metric_field	(	const tensorium_RG::Metric< T > &	metric,
		size_t	Nx,
		size_t	Ny,
		size_t	Nz,
		T	dx,
		T	dy,
		T	dz )

Generate the conformal 3-metric field \( \tilde{\gamma}_{ij}(x^i) \) on a 3D grid.

For each spatial grid point \( (x, y, z) \), the spatial metric \( \gamma_{ij} \) is extracted from the given metric, the conformal factor \( \chi \) is computed, and the conformal metric is defined as:

\[ \tilde{\gamma}_{ij} = \chi \, \gamma_{ij} \]

Template Parameters

T	Scalar type (typically `double`)

Parameters

metric	A metric object providing `BSSN(X, α, β, γ)` and `compute_conformal_factor(γ)`
Nx,Ny,Nz	Grid resolution in x, y, z directions
dx,dy,dz	Grid spacings in x, y, z directions

Returns: A 5D tensor with shape \( (N_x, N_y, N_z, 3, 3) \) containing \( \tilde{\gamma}_{ij} \) at each grid point

< Coordinates X^μ = (t, x, y, z)

< Time is fixed at t = 0

References alpha, beta, tensorium_RG::Metric< T >::BSSN(), chi, tensorium_RG::Metric< T >::compute_conformal_factor(), tensorium_RG::Metric< T >::compute_conformal_metric(), gamma, and X().

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◆ partial_scalar()

template<typename T , typename ScalarFunc >

tensorium::Vector< T > tensorium_RG::partial_scalar	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		ScalarFunc &&	func )

References X().

Referenced by autodiff_rank0(), tensorium_RG::ChiContext< T >::compute(), tensorium_RG::RicciTildeTensor< T >::compute_dGamma_term(), and covariant_scalar().

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◆ partial_tensor2()

template<typename T , typename TensorFunc >

tensorium::Tensor< T, 3 > tensorium_RG::partial_tensor2	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		TensorFunc &&	func )

References X().

Referenced by autodiff_rank2_first(), and covariant_tensor2().

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◆ partial_vector()

template<typename T , typename VectorFunc >

tensorium::Tensor< T, 2 > tensorium_RG::partial_vector	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		VectorFunc &&	func )

References X().

Referenced by autodiff_rank1(), and covariant_vector().

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◆ populate_tensor3D_component()

template<typename T , typename TensorFunc >

tensorium::Tensor< T, 3 > tensorium_RG::populate_tensor3D_component	(	size_t	i,
		size_t	j,
		TensorFunc &&	func,
		T	dx,
		T	dy,
		T	dz,
		size_t	NX,
		size_t	NY,
		size_t	NZ )

References gamma, and X().

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◆ print_tensor2()

template<typename T >

void tensorium_RG::print_tensor2	(	const std::string &	name,
		const tensorium::Tensor< T, 2 > &	tensor )

inline

Referenced by tensorium_RG::BSSN< T >::init_BSSN().

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◆ print_tensor3()

template<typename T >

void tensorium_RG::print_tensor3	(	const std::string &	name,
		const tensorium::Tensor< T, 3 > &	tensor )

inline

Referenced by tensorium_RG::BSSN< T >::init_BSSN().

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◆ print_vector()

template<typename T >

void tensorium_RG::print_vector	(	const std::string &	name,
		const tensorium::Vector< T > &	vec )

inline

Referenced by tensorium_RG::BSSN< T >::init_BSSN().

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◆ spectral_derivative_1D()

template<typename T >

void tensorium_RG::spectral_derivative_1D	(	tensorium::Vector< T > &	field,
		tensorium::Vector< T > &	dfield,
		T	dx )

◆ spectral_partial_scalar_3D()

template<typename T >

void tensorium_RG::spectral_partial_scalar_3D	(	const tensorium::Tensor< T, 3 > &	scalar_field,
		T	dx,
		T	dy,
		T	dz,
		tensorium::Tensor< T, 4 > &	grad_out )

References real, tensorium::Tensor< K, Rank >::resize(), and tensorium::Tensor< K, Rank >::shape().

Referenced by spectral_partial_tensor2().

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◆ spectral_partial_tensor2()

template<typename T , typename TensorFunc >

tensorium::Tensor< T, 3 > tensorium_RG::spectral_partial_tensor2	(	const tensorium::Vector< T > &	X,
		T	dx,
		T	dy,
		T	dz,
		TensorFunc &&	func,
		size_t	NX,
		size_t	NY,
		size_t	NZ )

References gamma, spectral_partial_scalar_3D(), and X().

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Classes

Enumerations

Functions

Enumeration Type Documentation

◆ DiffMode

Function Documentation

◆ __attribute__()

◆ autodiff()

◆ autodiff_rank0()

◆ autodiff_rank1()

◆ autodiff_rank2_first()

◆ autodiff_scalar_second()

◆ compute_dt_gamma_from_beta()

◆ compute_partial_derivatives_3D()

◆ compute_partial_derivatives_scalar()

◆ compute_partial_derivatives_tensor2D()

◆ compute_partial_derivatives_vector()

◆ compute_partial_derivatives_vector3D()

◆ compute_second_derivatives_scalar()

◆ compute_second_derivatives_scalar3D()

◆ compute_second_derivatives_tensor2D()

◆ covariant_scalar()

◆ covariant_scalar_second()

◆ covariant_scalar_second_3D()

◆ covariant_tensor2()

◆ covariant_tensor2_second()

◆ covariant_vector()

◆ generate_conformal_metric_field()

◆ partial_scalar()

◆ partial_tensor2()

◆ partial_vector()

◆ populate_tensor3D_component()

◆ print_tensor2()

◆ print_tensor3()

◆ print_vector()

◆ spectral_derivative_1D()

◆ spectral_partial_scalar_3D()

◆ spectral_partial_tensor2()

◆ attribute()