Spacelike time slice of a 3+1 spacetime with conformal decomposition in the maximal slicing and Dirac gauge. More...

#include <time_slice.h>

Inheritance diagram for Lorene::Tslice_dirac_max:

Public Member Functions
	Tslice_dirac_max (const Scalar &lapse_in, const Vector &shift_in, const Metric_flat &ff_in, const Scalar &psi_in, const Sym_tensor_trans &hh_in, const Sym_tensor &hata_in, int depth_in=3)
	Constructor from conformal decomposition.
	Tslice_dirac_max (const Map &mp, const Base_vect &triad, const Metric_flat &ff_in, int depth_in=3)
	Constructor as standard time slice of flat spacetime (Minkowski).
	Tslice_dirac_max (const Map &mp, const Base_vect &triad, const Metric_flat &ff_in, FILE *fich, bool partial_read, int depth_in=3)
	Constructor from binary file.
	Tslice_dirac_max (const Star_rot_Dirac &star, double pdt, int depth_in=3)
	Construnction of a stationary slice from a rotating star.
	Tslice_dirac_max (const Tslice_dirac_max &)
	Copy constructor.
virtual	~Tslice_dirac_max ()
	Destructor.
void	operator= (const Tslice_dirac_max &)
	Assignment to another Tslice_dirac_max.
virtual void	set_hh (const Sym_tensor &hh_in)
	Sets the deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .
virtual void	initial_data_cts (const Sym_tensor &uu, const Scalar &trk_in, const Scalar &trk_point, double pdt, double precis=1.e-12, int method_poisson_vect=6, const char graph_device=0x0, const Scalar ener_dens=0x0, const Vector mom_dens=0x0, const Scalar trace_stress=0x0)
	Computes valid initial data by solving the constraint equations in the conformal thin-sandwich approach.
virtual void	set_khi_mu (const Scalar &khi_in, const Scalar &mu_in)
	Sets the potentials $\chi$ and $\mu$ of the TT part $\bar{h}^{ij}$ of $h^{ij}$ (see the documentation of `Sym_tensor_tt` for details).
virtual void	set_AB_hh (const Scalar &A_in, const Scalar &B_in)
	Sets the potentials A and $\tilde{B}$ of the TT part $\bar{h}^{ij}$ of $h^{ij}$ (see the documentation of `Sym_tensor` for details).
virtual void	set_trh (const Scalar &trh_in)
	Sets the trace, with respect to the flat metric `ff` , of $h^{ij}$ .
virtual Scalar	solve_psi (const Scalar *ener_dens=0x0) const
	Solves the elliptic equation for the conformal factor $\Psi$ (Hamiltonian constraint).
virtual Scalar	solve_npsi (const Scalar ener_dens=0x0, const Scalar trace_stress=0x0) const
	Solves the elliptic equation for $N\Psi$ (maximal slicing condition + Hamiltonian constraint).
virtual Vector	solve_beta (int method=6) const
	Solves the elliptic equation for the shift vector $\beta^i$ from $A^{ij}$ (Eq.
void	evolve (double pdt, int nb_time_steps, int niter_elliptic, double relax_elliptic, int check_mod, int save_mod, int method_poisson_vect=6, int nopause=1, const char graph_device=0x0, bool verbose=true, const Scalar ener_euler=0x0, const Vector mom_euler=0x0, const Scalar s_euler=0x0, const Sym_tensor *strain_euler=0x0)
	Time evolution by resolution of Einstein equations.
virtual double	adm_mass () const
	Returns the ADM mass at (geometrical units) the current step.
virtual const Sym_tensor &	hh (Param par_bc=0x0, Param par_mat=0x0) const
	Deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .
virtual const Scalar &	trk () const
	Trace K of the extrinsic curvature at the current time step (`jtime` ).
virtual const Vector &	hdirac () const
	Vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ which vanishes in Dirac gauge.
virtual const Scalar &	A_hh () const
	Returns the potential A of $\bar{h}^{ij}$ .
virtual const Scalar &	B_hh () const
	Returns the potential $\tilde{B}$ of $\bar{h}^{ij}$ .
virtual const Scalar &	trh () const
	Computes the trace `h`, with respect to the flat metric `ff` , of $h^{ij}$ .
virtual void	set_psi_del_npsi (const Scalar &psi_in)
	Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .
virtual void	set_psi_del_n (const Scalar &psi_in)
	Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .
virtual void	set_npsi_del_psi (const Scalar &npsi_in)
	Sets the factor $N\Psi$ at the current time step (`jtime` ) and deletes the value of $\Psi$ .
virtual void	set_npsi_del_n (const Scalar &npsi_in)
	Sets the factor $N\Psi$ at the current time step (`jtime` ) and deletes the value of N.
virtual void	set_hata (const Sym_tensor &hata_in)
	Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .
virtual void	set_hata_TT (const Sym_tensor_tt &hata_tt)
	Sets the TT part of $\hat{A}^{ij}$ (see member `hata_evol` ).
virtual void	set_hata_from_XAB (Param par_bc=0x0, Param par_mat=0x0)
	Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature from its potentials A, $\tilde{B}$ and .
virtual const Scalar &	nn () const
	Lapse function N at the current time step (`jtime` ).
virtual const Sym_tensor &	gam_dd () const
	Induced metric (covariant components $\gamma_{ij}$ ) at the current time step (`jtime` ).
virtual const Sym_tensor &	gam_uu () const
	Induced metric (contravariant components $\gamma^{ij}$ ) at the current time step (`jtime` ).
virtual const Sym_tensor &	k_dd () const
	Extrinsic curvature tensor (covariant components $K_{ij}$ ) at the current time step (`jtime` ).
virtual const Sym_tensor &	k_uu () const
	Extrinsic curvature tensor (contravariant components $K^{ij}$ ) at the current time step (`jtime` ).
virtual const Scalar &	A_hata () const
	Returns the potential A of $\hat{A}^{ij}$ .
virtual const Scalar &	B_hata () const
	Returns the potential $\tilde{B}$ of $\hat{A}^{ij}$ .
virtual const Scalar &	psi () const
	Conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .
const Scalar &	psi4 () const
	Factor $\Psi^4$ at the current time step (`jtime` ).
const Scalar &	ln_psi () const
	Logarithm of $\Psi$ at the current time step (`jtime` ).
virtual const Scalar &	npsi () const
	Factor $N\Psi$ at the current time step (`jtime` ).
virtual const Metric &	tgam () const
	Conformal metric $\tilde\gamma_{ij} = \Psi^{-4} \gamma_{ij}$ Returns the value at the current time step (`jtime` ).
virtual const Sym_tensor &	hata () const
	Conformal representation $\hat{A}^{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .
virtual Sym_tensor	aa () const
	Conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .
virtual const Vector &	vec_X (int method_poisson=6) const
	Vector representing the longitudinal part of $\hat{A}^{ij}$ .
void	compute_X_from_momentum_constraint (const Vector &hat_S, const Sym_tensor_tt &hata_tt, int iter_max=200, double precis=1.e-12, double relax=0.8, int methode_poisson=6)
	Computes the vector from the conformally-rescaled momentum $\hat{S}^i = \Psi^6 S^i$ , using the momentum constraint.
virtual void	set_AB_hata (const Scalar &A_in, const Scalar &B_in)
	Sets the potentials A and $\tilde{B}$ of the TT part $\hat{A}^{ij}$ (see the documentation of `Sym_tensor` for details).
void	check_psi_dot (Tbl &tlnpsi_dot, Tbl &tdiff, Tbl &tdiff_rel) const
	Checks the $\frac{\partial}{\partial t} \ln\Psi$ relation.
void	set_scheme_order (int ord)
	Sets the order of the finite-differences scheme.
int	get_scheme_order () const
	Gets the order of the finite-differences scheme.
int	get_latest_j () const
	Gets the latest value of time step index.
const Evolution_std< double > &	get_time () const
	Gets the time coordinate t at successive time steps.
virtual const Vector &	beta () const
	shift vector $\beta^i$ at the current time step (`jtime` )
const Metric &	gam () const
	Induced metric $\mathbf{\gamma}$ at the current time step (`jtime` ).
Tbl	check_hamiltonian_constraint (const Scalar *energy_density=0x0, ostream &ost=cout, bool verb=true) const
	Checks the level at which the hamiltonian constraint is verified.
Tbl	check_momentum_constraint (const Vector *momentum_density=0x0, ostream &ost=cout, bool verb=true) const
	Checks the level at which the momentum constraints are verified.
Tbl	check_dynamical_equations (const Sym_tensor strain_tensor=0x0, const Scalar energy_density=0x0, ostream &ost=cout, bool verb=true) const
	Checks the level at which the dynamical equations are verified.
void	save (const char *rootname) const
	Saves in a binary file.

Protected Member Functions
void	compute_sources (const Sym_tensor *strain_tensor=0x0) const
	Computes the sources `source_A_XXX_evol` and `source_B_XXX_evol` , for the solution of the evolution equation for $h^{ij}$ and $\hat{A}^{ij}$ .
void	initialize_sources_copy () const
	Copy the sources `source_A_XXX_evol` and `source_B_XXX_evol` to all time-steps.
void	hh_det_one (int j, Param par_bc=0x0, Param par_mat=0x0) const
	Computes $h^{ij}$ from the values of A and $\tilde{B}$ and using the condition $\det\tilde\gamma^{ij} = \det f^{ij}$ , which fixes the trace of $h^{ij}$ .
void	hh_det_one (const Sym_tensor_tt &hijtt, Param *par_mat=0x0) const
	Computes $h^{ij}$ from the TT part using the condition $\det\tilde\gamma^{ij} = \det f^{ij}$ , which fixes the trace of $h^{ij}$ .
virtual ostream &	operator>> (ostream &) const
	Operator >> (virtual function called by the operator<<).
virtual void	sauve (FILE *fich, bool partial_save) const
	Total or partial saves in a binary file.
virtual void	del_deriv () const
	Deletes all the derived quantities.
void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities.

Protected Attributes
Evolution_std< Scalar >	A_hh_evol
	The A potential of $\bar{h}^{ij}$ .
Evolution_std< Scalar >	B_hh_evol
	The $\tilde{B}$ potential of $\bar{h}^{ij}$ .
Evolution_std< Scalar >	source_A_hh_evol
	The A potential of the source of equation for $\bar{h}^{ij}$ .
Evolution_std< Scalar >	source_B_hh_evol
	The $\tilde{B}$ potential of the source of equation for $\bar{h}^{ij}$ .
Evolution_std< Scalar >	source_A_hata_evol
	The potential A of the source of equation for $\hat{A}^{ij}$ .
Evolution_std< Scalar >	source_B_hata_evol
	The potential $\tilde{B}$ of the source of equation for $\hat{A}^{ij}$ .
Evolution_std< Scalar >	trh_evol
	The trace, with respect to the flat metric `ff` , of $h^{ij}$ .
const Metric_flat &	ff
	Pointer on the flat metric $f_{ij}$ with respect to which the conformal decomposition is performed.
Evolution_std< Scalar >	psi_evol
	Values at successive time steps of the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .
Evolution_std< Scalar >	npsi_evol
	Values at successive time steps of the factor $N\Psi$ .
Evolution_std< Sym_tensor >	hh_evol
	Values at successive time steps of the components $h^{ij}$ .
Evolution_std< Sym_tensor >	hata_evol
	Values at successive time steps of the components $\hat{A}^{ij}$ .
Evolution_std< Scalar >	A_hata_evol
	Potential A associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ .
Evolution_std< Scalar >	B_hata_evol
	Potential $\tilde{B}$ associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ .
Metric *	p_tgamma
	Pointer on the conformal metric $\tilde\gamma_{ij}$ at the current time step (`jtime`).
Scalar *	p_psi4
	Pointer on the factor $\Psi^4$ at the current time step (`jtime`).
Scalar *	p_ln_psi
	Pointer on the logarithm of $\Psi$ at the current time step (`jtime`).
Vector *	p_hdirac
	Pointer on the vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ (which vanishes in Dirac gauge), at the current time step (`jtime`).
Vector *	p_vec_X
	Pointer on the vector representing the longitudinal part of $\hat{A}^{ij}$ .
int	depth
	Number of stored time slices.
int	scheme_order
	Order of the finite-differences scheme for the computation of time derivatives.
int	jtime
	Time step index of the latest slice.
Evolution_std< double >	the_time
	Time label of each slice.
Evolution_std< Sym_tensor >	gam_dd_evol
	Values at successive time steps of the covariant components of the induced metric $\gamma_{ij}$ .
Evolution_std< Sym_tensor >	gam_uu_evol
	Values at successive time steps of the contravariant components of the induced metric $\gamma^{ij}$ .
Evolution_std< Sym_tensor >	k_dd_evol
	Values at successive time steps of the covariant components of the extrinsic curvature tensor $K_{ij}$ .
Evolution_std< Sym_tensor >	k_uu_evol
	Values at successive time steps of the contravariant components of the extrinsic curvature tensor $K^{ij}$ .
Evolution_std< Scalar >	n_evol
	Values at successive time steps of the lapse function N.
Evolution_std< Vector >	beta_evol
	Values at successive time steps of the shift vector $\beta^i$ .
Evolution_std< Scalar >	trk_evol
	Values at successive time steps of the trace K of the extrinsic curvature.
Evolution_full< Tbl >	adm_mass_evol
	ADM mass at each time step, since the creation of the slice.
Metric *	p_gamma
	Pointer on the induced metric at the current time step (`jtime`).

Detailed Description

Spacelike time slice of a 3+1 spacetime with conformal decomposition in the maximal slicing and Dirac gauge.

()

Definition at line 971 of file time_slice.h.

Constructor & Destructor Documentation

◆ Tslice_dirac_max() [1/5]

Lorene::Tslice_dirac_max::Tslice_dirac_max	(	const Scalar &	lapse_in,
		const Vector &	shift_in,
		const Metric_flat &	ff_in,
		const Scalar &	psi_in,
		const Sym_tensor_trans &	hh_in,
		const Sym_tensor &	hata_in,
		int	depth_in = 3 )

Constructor from conformal decomposition.

Parameters

lapse_in	lapse function N
shift_in	shift vector
ff_in	reference flat metric with respect to which the conformal decomposition is performed
psi_in	conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$
hh_in	deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ . $h^{ij}$ must be such that $\det\tilde\gamma^{ij} = f^{-1}$ .
hata_in	conformal representation $\hat{A}^{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ , with K = 0 in the present case
depth_in	number of stored time slices; this parameter is used to set the `scheme_order` member with `scheme_order` = `depth_in` - 1. `scheme_order` can be changed afterwards by the method `set_scheme_order(int)`.

Definition at line 152 of file tslice_dirac_max.C.

References A_hh_evol, B_hh_evol, source_A_hata_evol, source_A_hh_evol, source_B_hata_evol, source_B_hh_evol, Lorene::Time_slice_conf::Time_slice_conf(), and trh_evol.

◆ Tslice_dirac_max() [2/5]

Lorene::Tslice_dirac_max::Tslice_dirac_max	(	const Map &	mp,
		const Base_vect &	triad,
		const Metric_flat &	ff_in,
		int	depth_in = 3 )

Constructor as standard time slice of flat spacetime (Minkowski).

Parameters

mp	Mapping on which the various Lorene fields will be constructed
triad	vector basis with respect to which the various tensor components will be defined
ff_in	reference flat metric with respect to which the conformal decomposition is performed
depth_in	number of stored time slices; this parameter is used to set the `scheme_order` member with `scheme_order` = `depth_in` - 1. `scheme_order` can be changed afterwards by the method `set_scheme_order(int)`.

Definition at line 166 of file tslice_dirac_max.C.

References A_hh_evol, B_hh_evol, Lorene::Time_slice::jtime, Lorene::Map(), Lorene::Scalar::set_etat_zero(), source_A_hata_evol, source_A_hh_evol, source_B_hata_evol, source_B_hh_evol, Lorene::Time_slice::the_time, Lorene::Time_slice_conf::Time_slice_conf(), and trh_evol.

◆ Tslice_dirac_max() [3/5]

Lorene::Tslice_dirac_max::Tslice_dirac_max	(	const Map &	mp,
		const Base_vect &	triad,
		const Metric_flat &	ff_in,
		FILE *	fich,
		bool	partial_read,
		int	depth_in = 3 )

Constructor from binary file.

The binary file must have been created by method save.

Parameters

mp	Mapping on which the various Lorene fields will be constructed
triad	vector basis with respect to which the various tensor components will be defined
ff_in	reference flat metric with respect to which the conformal decomposition is performed
fich	file containing the saved `Tslice_dirac_max`
partial_read	indicates whether the full object must be read in file or whether the final construction is devoted to a constructor of a derived class
depth_in	number of stored time slices; the given must coincide with that stored in the file.

Definition at line 196 of file tslice_dirac_max.C.

References A_hh_evol, B_hh_evol, Lorene::Time_slice::depth, Lorene::fread_be(), Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, Lorene::Map(), source_A_hata_evol, source_A_hh_evol, source_B_hata_evol, source_B_hh_evol, Lorene::Time_slice::the_time, Lorene::Time_slice_conf::Time_slice_conf(), and trh_evol.

◆ Tslice_dirac_max() [4/5]

Lorene::Tslice_dirac_max::Tslice_dirac_max	(	const Star_rot_Dirac &	star,
		double	pdt,
		int	depth_in = 3 )

Construnction of a stationary slice from a rotating star.

Definition at line 250 of file tslice_dirac_max.C.

◆ Tslice_dirac_max() [5/5]

Lorene::Tslice_dirac_max::Tslice_dirac_max ( const Tslice_dirac_max & tin )

Copy constructor.

Definition at line 302 of file tslice_dirac_max.C.

References A_hh_evol, B_hh_evol, source_A_hata_evol, source_A_hh_evol, source_B_hata_evol, source_B_hh_evol, Lorene::Time_slice_conf::Time_slice_conf(), trh_evol, and Tslice_dirac_max().

◆ ~Tslice_dirac_max()

Lorene::Tslice_dirac_max::~Tslice_dirac_max ( )

virtual

Destructor.

Definition at line 317 of file tslice_dirac_max.C.

Member Function Documentation

◆ A_hata()

const Scalar & Lorene::Time_slice_conf::A_hata ( ) const

virtualinherited

Returns the potential A of $\hat{A}^{ij}$ .

See the documentation of Sym_tensor for details. Returns the value at the current time step (jtime ).

Definition at line 667 of file time_slice_conf.C.

References A_hata_evol, Lorene::Scalar::dec_dzpuis(), Lorene::Scalar::get_dzpuis(), hata_evol, Lorene::Time_slice::jtime, and Lorene::Time_slice::the_time.

◆ A_hh()

const Scalar & Lorene::Tslice_dirac_max::A_hh ( ) const

virtual

Returns the potential A of $\bar{h}^{ij}$ .

See the documentation of Sym_tensor for details. Returns the value at the current time step (jtime ).

Definition at line 528 of file tslice_dirac_max.C.

References A_hh_evol, Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, and Lorene::Time_slice::the_time.

◆ aa()

Sym_tensor Lorene::Time_slice_conf::aa ( ) const

virtualinherited

Conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .

Returns the value at the current time step (jtime ).

Definition at line 768 of file time_slice_conf.C.

References hata(), psi(), and psi4().

◆ adm_mass()

double Lorene::Tslice_dirac_max::adm_mass ( ) const

virtual

Returns the ADM mass at (geometrical units) the current step.

Moreover this method updates adm_mass_evol if necessary.

Reimplemented from Lorene::Time_slice_conf.

Definition at line 146 of file tslice_adm_mass.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Scalar::derive_con(), Lorene::Time_slice_conf::ff, Lorene::Vector::flux(), Lorene::Tensor::get_mp(), Lorene::Tbl::get_taille(), hh(), Lorene::Time_slice::jtime, Lorene::Map(), Lorene::Time_slice_conf::psi(), Lorene::Tbl::set(), Lorene::Tbl::set_etat_qcq(), Lorene::Time_slice::the_time, and Lorene::Tensor::trace().

◆ B_hata()

const Scalar & Lorene::Time_slice_conf::B_hata ( ) const

virtualinherited

Returns the potential $\tilde{B}$ of $\hat{A}^{ij}$ .

See the documentation of Sym_tensor_tt for details. Returns the value at the current time step (jtime ).

Definition at line 681 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, Lorene::Scalar::dec_dzpuis(), Lorene::Scalar::get_dzpuis(), hata_evol, Lorene::Time_slice::jtime, and Lorene::Time_slice::the_time.

◆ B_hh()

const Scalar & Lorene::Tslice_dirac_max::B_hh ( ) const

virtual

Returns the potential $\tilde{B}$ of $\bar{h}^{ij}$ .

See the documentation of Sym_tensor_tt for details. Returns the value at the current time step (jtime ).

Definition at line 539 of file tslice_dirac_max.C.

References B_hh_evol, Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, and Lorene::Time_slice::the_time.

◆ beta()

const Vector & Lorene::Time_slice::beta ( ) const

virtualinherited

shift vector $\beta^i$ at the current time step (jtime )

Definition at line 90 of file time_slice_access.C.

References beta_evol, and jtime.

◆ check_dynamical_equations()

Tbl Lorene::Time_slice::check_dynamical_equations	(	const Sym_tensor *	strain_tensor = 0x0,
		const Scalar *	energy_density = 0x0,
		ostream &	ost = cout,
		bool	verb = true ) const

inherited

Checks the level at which the dynamical equations are verified.

$\‍[ \frac{\partial K_{ij}}{\partial t} - \pounds_{\mbox{\boldmath{$\beta $}}} K_{ij} = - D_i D_j N + N \left[ R_{ij} - 2 K_{ik} K^k_{\ j} + K K_{ij} + 4\pi \left( (S-E)\gamma_{ij} - 2 S_{ij} \right) \right] \‍]$

Parameters

strain_tensor	: a pointer on the strain_tensor $S_{ij}$ measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer, it is assumed that $S_{ij}$ = 0 (vacuum).
energy_density	: a pointer on the energy density E (see `check_hamiltonian_constraint`)
ost	: output stream for a formatted output of the result

Returns: Tbl 3D of size the number of domains times 3 times 3 (corresponding to the rank-2 tensor, with the symmetry in the components) containing the absolute ( if = 0 ) or the relative (in presence of matter) error in max version.

Definition at line 142 of file tslice_check_einstein.C.

References Lorene::Tensor::annule_domain(), Lorene::Tbl::annule_hard(), beta(), Lorene::contract(), Lorene::Scalar::derive_con(), Lorene::Tensor::derive_con(), Lorene::Sym_tensor::derive_lie(), gam(), Lorene::Tbl::get_dim(), Lorene::Tensor::get_mp(), jtime, k_dd(), k_dd_evol, k_uu(), Lorene::maxabs(), nn(), Lorene::Tensor_sym::position(), Lorene::Metric::ricci(), scheme_order, Lorene::Itbl::set(), Lorene::Tbl::set(), Lorene::Tensor::trace(), trk(), and Lorene::Tensor::up_down().

◆ check_hamiltonian_constraint()

Tbl Lorene::Time_slice::check_hamiltonian_constraint	(	const Scalar *	energy_density = 0x0,
		ostream &	ost = cout,
		bool	verb = true ) const

inherited

Checks the level at which the hamiltonian constraint is verified.

$\‍[R + K^2 - K_{ij}K^{ij} = 16\pi E \‍]$

Parameters

energy_density	: a pointer on the energy density E measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer, it is assumed that E = 0 (vacuum).
ost	: output stream for a formatted output of the result

Returns: Tbl of size the number of domains containing the absolute ( if E = 0 ) or the relative (in presence of matter) error in max version.

Definition at line 82 of file tslice_check_einstein.C.

References Lorene::contract(), Lorene::Scalar::dec_dzpuis(), gam(), k_dd(), k_uu(), Lorene::maxabs(), Lorene::Metric::ricci_scal(), and trk().

◆ check_momentum_constraint()

Tbl Lorene::Time_slice::check_momentum_constraint	(	const Vector *	momentum_density = 0x0,
		ostream &	ost = cout,
		bool	verb = true ) const

inherited

Checks the level at which the momentum constraints are verified.

$\‍[D_j K_i^{\ j} - D_i K = 8 \pi J_i \‍]$

Parameters

momentum_density	: a pointer on the momentum density measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer, it is assumed that = 0 (vacuum).
ost	: output stream for a formatted output of the result

Returns: Tbl 2D of size the number of domains times 3 (components)containing the absolute ( if = 0 ) or the relative (in presence of matter) error in max version.

Definition at line 112 of file tslice_check_einstein.C.

References Lorene::Scalar::derive_con(), Lorene::Sym_tensor::divergence(), gam(), Lorene::Tensor::get_index_type(), k_uu(), Lorene::maxabs(), and trk().

◆ check_psi_dot()

void Lorene::Time_slice_conf::check_psi_dot	(	Tbl &	tlnpsi_dot,
		Tbl &	tdiff,
		Tbl &	tdiff_rel ) const

inherited

Checks the $\frac{\partial}{\partial t} \ln\Psi$ relation.

Parameters

tlnpsi_dot	[output] maximun value in each domain of $\left\| \frac{\partial}{\partial t} \ln\Psi \right\|$
tdiff	[output] maximum value in each domain of $\left\| \frac{\partial}{\partial t} \ln\Psi - \beta^i {\cal D}_i \ln \Psi - \frac{1}{6} ( {\cal D}_i \beta^i - N K) \right\|$
tdiff_rel	[output] relative error on the above relation in each domain.

Definition at line 907 of file time_slice_conf.C.

References Lorene::abs(), Lorene::Time_slice::beta(), Lorene::contract(), Lorene::Scalar::dec_dzpuis(), Lorene::Vector::divergence(), ff, Lorene::Time_slice::jtime, ln_psi(), Lorene::max(), Lorene::Time_slice::n_evol, nn(), npsi(), npsi_evol, psi(), psi_evol, Lorene::Time_slice::scheme_order, and trk().

◆ compute_sources()

void Lorene::Tslice_dirac_max::compute_sources ( const Sym_tensor * strain_tensor = 0x0 ) const

protected

Computes the sources source_A_XXX_evol and source_B_XXX_evol , for the solution of the evolution equation for $h^{ij}$ and $\hat{A}^{ij}$ .

Parameters

strain_tensor [input] : a pointer on the strain_tensor $S^{ij}$ measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer (default value), it is assumed that $S_{ij}$ = 0 (vacuum).

Definition at line 222 of file tslice_dirac_max_setAB.C.

◆ compute_X_from_momentum_constraint()

void Lorene::Time_slice_conf::compute_X_from_momentum_constraint	(	const Vector &	hat_S,
		const Sym_tensor_tt &	hata_tt,
		int	iter_max = 200,
		double	precis = 1.e-12,
		double	relax = 0.8,
		int	methode_poisson = 6 )

inherited

Computes the vector $ X^i $ from the conformally-rescaled momentum $\hat{S}^i = \Psi^6 S^i$ , using the momentum constraint.

Definition at line 839 of file time_slice_conf.C.

References Lorene::abs(), Lorene::Metric::connect(), Lorene::contract(), ff, Lorene::Connection::get_delta(), Lorene::Tensor::get_index_type(), hata_evol, hh_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, Lorene::max(), p_vec_X, Lorene::Vector::poisson(), psi(), psi4(), tgam(), Lorene::Time_slice::the_time, and trk().

◆ del_deriv()

void Lorene::Time_slice_conf::del_deriv ( ) const

protectedvirtualinherited

Deletes all the derived quantities.

Reimplemented from Lorene::Time_slice.

Definition at line 350 of file time_slice_conf.C.

References Lorene::Time_slice::del_deriv(), p_hdirac, p_ln_psi, p_psi4, p_tgamma, p_vec_X, and set_der_0x0().

◆ evolve()

void Lorene::Tslice_dirac_max::evolve	(	double	pdt,
		int	nb_time_steps,
		int	niter_elliptic,
		double	relax_elliptic,
		int	check_mod,
		int	save_mod,
		int	method_poisson_vect = 6,
		int	nopause = 1,
		const char *	graph_device = 0x0,
		bool	verbose = true,
		const Scalar *	ener_euler = 0x0,
		const Vector *	mom_euler = 0x0,
		const Scalar *	s_euler = 0x0,
		const Sym_tensor *	strain_euler = 0x0 )

Time evolution by resolution of Einstein equations.

Parameters

pdt	time step dt.
nb_time_steps	number of time steps for the evolution
niter_elliptic	number of iterations if the resolution of elliptic equations
relax_elliptic	relaxation factor for the elliptic equations
check_mod	determines the frequency of check of the constraint equations: they are checked every `check_mod` time step
save_mod	determines the frequency of writing to file the monotoring quantities: they are written to file every `save_mod` time step
method	method_poisson_vect to be used for solving vector Poisson equation (for the shift), see `Vector::poisson(double, const Metric_flat&, int) const`.
nopause	= 1 if no pause between each time step, 0 otherwise
graph_device	name of type of graphical device: 0x0 (default value) will result in interactive choice; "/xwin" in X-Window display and "/n" in no output.

Definition at line 123 of file tslice_dirac_max_evolve.C.

◆ gam()

const Metric & Lorene::Time_slice::gam ( ) const

inherited

Induced metric $\mathbf{\gamma}$ at the current time step (jtime ).

Definition at line 98 of file time_slice_access.C.

References gam_dd(), and p_gamma.

◆ gam_dd()

const Sym_tensor & Lorene::Time_slice_conf::gam_dd ( ) const

virtualinherited

Induced metric (covariant components $\gamma_{ij}$ ) at the current time step (jtime ).

Reimplemented from Lorene::Time_slice.

Definition at line 611 of file time_slice_conf.C.

References Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::jtime, psi4(), tgam(), and Lorene::Time_slice::the_time.

◆ gam_uu()

const Sym_tensor & Lorene::Time_slice_conf::gam_uu ( ) const

virtualinherited

Induced metric (contravariant components $\gamma^{ij}$ ) at the current time step (jtime ).

Reimplemented from Lorene::Time_slice.

Definition at line 622 of file time_slice_conf.C.

References Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice::jtime, psi4(), tgam(), and Lorene::Time_slice::the_time.

◆ get_latest_j()

int Lorene::Time_slice::get_latest_j ( ) const

inlineinherited

Gets the latest value of time step index.

Definition at line 346 of file time_slice.h.

References jtime.

◆ get_scheme_order()

int Lorene::Time_slice::get_scheme_order ( ) const

inlineinherited

Gets the order of the finite-differences scheme.

Definition at line 343 of file time_slice.h.

References scheme_order.

◆ get_time()

const Evolution_std< double > & Lorene::Time_slice::get_time ( ) const

inlineinherited

Gets the time coordinate t at successive time steps.

Definition at line 349 of file time_slice.h.

References the_time.

◆ hata()

const Sym_tensor & Lorene::Time_slice_conf::hata ( ) const

virtualinherited

Conformal representation $\hat{A}^{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .

Returns the value at the current time step (jtime ).

Definition at line 775 of file time_slice_conf.C.

References Lorene::Time_slice::beta(), Lorene::Sym_tensor::derive_lie(), Lorene::Vector::divergence(), ff, hata_evol, hh(), hh_evol, Lorene::Tensor::inc_dzpuis(), Lorene::Time_slice::jtime, nn(), Lorene::Vector::ope_killing_conf(), psi(), psi4(), Lorene::Time_slice::scheme_order, and Lorene::Time_slice::the_time.

◆ hdirac()

const Vector & Lorene::Tslice_dirac_max::hdirac ( ) const

virtual

Vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ which vanishes in Dirac gauge.

It is null in the present case...

Reimplemented from Lorene::Time_slice_conf.

Definition at line 510 of file tslice_dirac_max.C.

References Lorene::Time_slice_conf::ff, and Lorene::Time_slice_conf::p_hdirac.

◆ hh()

const Sym_tensor & Lorene::Tslice_dirac_max::hh	(	Param *	par_bc = 0x0,
		Param *	par_mat = 0x0 ) const

virtual

Deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .

Returns the value at the current time step (jtime ).

Reimplemented from Lorene::Time_slice_conf.

Definition at line 477 of file tslice_dirac_max.C.

References A_hh_evol, B_hh_evol, hh_det_one(), Lorene::Time_slice_conf::hh_evol, and Lorene::Time_slice::jtime.

◆ hh_det_one() [1/2]

void Lorene::Tslice_dirac_max::hh_det_one	(	const Sym_tensor_tt &	hijtt,
		Param *	par_mat = 0x0 ) const

protected

Computes $h^{ij}$ from the TT part using the condition $\det\tilde\gamma^{ij} = \det f^{ij}$ , which fixes the trace of $h^{ij}$ .

Parameters

hijtt : the TT part.

Definition at line 171 of file tslice_dirac_max_setAB.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Time_slice_conf::ff, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Tensor::get_mp(), Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, Lorene::Map(), Lorene::maxabs(), Lorene::Time_slice::p_gamma, Lorene::Time_slice_conf::p_hdirac, Lorene::Time_slice_conf::p_tgamma, Lorene::Tensor::set_etat_zero(), Lorene::Sym_tensor::set_longit_trans(), Lorene::Sym_tensor_trans::set_tt_part_det_one(), Lorene::Time_slice_conf::tgam(), Lorene::Time_slice::the_time, Lorene::Sym_tensor_trans::the_trace(), and trh_evol.

◆ hh_det_one() [2/2]

void Lorene::Tslice_dirac_max::hh_det_one	(	int	j,
		Param *	par_bc = 0x0,
		Param *	par_mat = 0x0 ) const

protected

Computes $h^{ij}$ from the values of A and $\tilde{B}$ and using the condition $\det\tilde\gamma^{ij} = \det f^{ij}$ , which fixes the trace of $h^{ij}$ .

Parameters

j	time step at which the computation of $h^{ij}$ is required.

Definition at line 112 of file tslice_dirac_max_setAB.C.

◆ initial_data_cts()

void Lorene::Tslice_dirac_max::initial_data_cts	(	const Sym_tensor &	uu,
		const Scalar &	trk_in,
		const Scalar &	trk_point,
		double	pdt,
		double	precis = 1.e-12,
		int	method_poisson_vect = 6,
		const char *	graph_device = 0x0,
		const Scalar *	ener_dens = 0x0,
		const Vector *	mom_dens = 0x0,
		const Scalar *	trace_stress = 0x0 )

virtual

Computes valid initial data by solving the constraint equations in the conformal thin-sandwich approach.

Parameters

uu	value of ${\tilde u}^{ij} = \partial h^{ij} /\partial t$ (freely specifiable data). This quantity must be trace-free with respect to the conformal metric $\tilde\gamma_{ij}$ , reflecting the unimodular character of $\tilde\gamma_{ij}$ .
trk_in	value of $K = K_i^{\ i}$ (freely specifiable data)
trk_point	value of $\partial K / \partial t$ (freely specifiable data)
pdt	time step, to be used in order to fill `depth` slices
precis	convergence threshold required to stop the iteration
method_poisson_vect	method to be used for solving vector Poisson equation (for the shift), see `Vector::poisson(double, const Metric_flat&, int) const`.
graph_device	name of type of graphical device: 0x0 (default value) will result in interactive choice; "/xwin" in X-Window display and "/n" in no output.
ener_dens	matter energy density E as measured by the Eulerian observer; this quantity is passed as a pointer, the null value of which (default) meaning E=0.
mom_dens	matter momentum density J as measured by the Eulerian observer; this quantity is passed as a pointer, the null value of which (default) meaning J=0.
trace_stress	trace of the matter stress S as measured by the Eulerian observer; this quantity is passed as a pointer, the null value of which (default) meaning S=0.

Reimplemented from Lorene::Time_slice_conf.

Definition at line 355 of file tslice_dirac_max.C.

References Lorene::Time_slice_conf::A_hata_evol, A_hh_evol, Lorene::Tensor::annule_domain(), Lorene::Time_slice_conf::B_hata_evol, B_hh_evol, compute_sources(), Lorene::Time_slice_conf::del_deriv(), Lorene::Time_slice::depth, Lorene::Scalar::get_etat(), Lorene::Tensor::get_mp(), Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice_conf::initial_data_cts(), initialize_sources_copy(), Lorene::Time_slice::jtime, Lorene::maxabs(), Lorene::Scalar::set_dzpuis(), and Lorene::Time_slice::the_time.

◆ initialize_sources_copy()

void Lorene::Tslice_dirac_max::initialize_sources_copy ( ) const

protected

Copy the sources source_A_XXX_evol and source_B_XXX_evol to all time-steps.

Definition at line 414 of file tslice_dirac_max_setAB.C.

References Lorene::Time_slice::depth, Lorene::Time_slice::jtime, source_A_hata_evol, source_A_hh_evol, source_B_hata_evol, source_B_hh_evol, and Lorene::Time_slice::the_time.

◆ k_dd()

const Sym_tensor & Lorene::Time_slice_conf::k_dd ( ) const

virtualinherited

Extrinsic curvature tensor (covariant components $K_{ij}$ ) at the current time step (jtime ).

Reimplemented from Lorene::Time_slice.

Definition at line 633 of file time_slice_conf.C.

References Lorene::Time_slice::gam(), Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, k_uu(), and Lorene::Time_slice::the_time.

◆ k_uu()

const Sym_tensor & Lorene::Time_slice_conf::k_uu ( ) const

virtualinherited

Extrinsic curvature tensor (contravariant components $K^{ij}$ ) at the current time step (jtime ).

Reimplemented from Lorene::Time_slice.

Definition at line 646 of file time_slice_conf.C.

References Lorene::Time_slice::gam(), hata(), Lorene::Time_slice::jtime, Lorene::Time_slice::k_uu_evol, psi(), psi4(), Lorene::Time_slice::the_time, and trk().

◆ ln_psi()

const Scalar & Lorene::Time_slice_conf::ln_psi ( ) const

inherited

Logarithm of $\Psi$ at the current time step (jtime ).

Definition at line 722 of file time_slice_conf.C.

References Lorene::log(), p_ln_psi, and psi().

◆ nn()

const Scalar & Lorene::Time_slice_conf::nn ( ) const

virtualinherited

Lapse function N at the current time step (jtime ).

Reimplemented from Lorene::Time_slice.

Definition at line 594 of file time_slice_conf.C.

References Lorene::Time_slice::jtime, Lorene::Time_slice::n_evol, npsi_evol, psi_evol, and Lorene::Time_slice::the_time.

◆ npsi()

const Scalar & Lorene::Time_slice_conf::npsi ( ) const

virtualinherited

Factor $N\Psi$ at the current time step (jtime ).

Definition at line 735 of file time_slice_conf.C.

References Lorene::Time_slice::jtime, Lorene::Time_slice::n_evol, npsi_evol, psi_evol, and Lorene::Time_slice::the_time.

◆ operator=()

void Lorene::Tslice_dirac_max::operator= ( const Tslice_dirac_max & tin )

Assignment to another Tslice_dirac_max.

Definition at line 324 of file tslice_dirac_max.C.

References A_hh_evol, B_hh_evol, Lorene::Time_slice_conf::operator=(), source_A_hata_evol, source_A_hh_evol, source_B_hata_evol, source_B_hh_evol, trh_evol, and Tslice_dirac_max().

◆ operator>>()

ostream & Lorene::Tslice_dirac_max::operator>> ( ostream & flux ) const

protectedvirtual

Operator >> (virtual function called by the operator<<).

Reimplemented from Lorene::Time_slice_conf.

Definition at line 569 of file tslice_dirac_max.C.

References A_hh_evol, B_hh_evol, Lorene::Time_slice::jtime, Lorene::maxabs(), Lorene::Time_slice_conf::operator>>(), and trh_evol.

◆ psi()

const Scalar & Lorene::Time_slice_conf::psi ( ) const

virtualinherited

Conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\‍[ \Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12} \‍]$

Returns the value at the current time step (jtime ).

Definition at line 696 of file time_slice_conf.C.

References Lorene::Time_slice::jtime, Lorene::Time_slice::n_evol, npsi_evol, psi_evol, and Lorene::Time_slice::the_time.

◆ psi4()

const Scalar & Lorene::Time_slice_conf::psi4 ( ) const

inherited

Factor $\Psi^4$ at the current time step (jtime ).

Definition at line 710 of file time_slice_conf.C.

References p_psi4, Lorene::pow(), and psi().

◆ sauve()

void Lorene::Tslice_dirac_max::sauve	(	FILE *	fich,
		bool	partial_save ) const

protectedvirtual

Total or partial saves in a binary file.

This protected method is to be called either from public method save or from method sauve of a derived class.

Parameters

fich	binary file
partial_save	indicates whether the whole object must be saved.

Reimplemented from Lorene::Time_slice_conf.

Definition at line 590 of file tslice_dirac_max.C.

References A_hh(), A_hh_evol, B_hh(), B_hh_evol, Lorene::Time_slice::depth, Lorene::fwrite_be(), Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, and Lorene::Time_slice_conf::sauve().

◆ save()

void Lorene::Time_slice::save ( const char * rootname ) const

inherited

Saves in a binary file.

The saved data is sufficient to restore the whole time slice via the constructor from file.

Parameters

rootname root for the file name; the current time step index will be appended to it.

Definition at line 464 of file time_slice.C.

References beta(), depth, Lorene::fwrite_be(), Lorene::Tensor::get_mp(), Lorene::Tensor::get_triad(), jtime, Lorene::Map(), nn(), Lorene::Base_vect::sauve(), Lorene::Mg3d::sauve(), and sauve().

◆ set_AB_hata()

void Lorene::Time_slice_conf::set_AB_hata	(	const Scalar &	A_in,
		const Scalar &	B_in )

virtualinherited

Sets the potentials A and $\tilde{B}$ of the TT part $\hat{A}^{ij}$ (see the documentation of Sym_tensor for details).

Sets the value at the current time step (jtime ).

Definition at line 894 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, hata_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, and Lorene::Time_slice::the_time.

◆ set_AB_hh()

void Lorene::Tslice_dirac_max::set_AB_hh	(	const Scalar &	A_in,
		const Scalar &	B_in )

virtual

Sets the potentials A and $\tilde{B}$ of the TT part $\bar{h}^{ij}$ of $h^{ij}$ (see the documentation of Sym_tensor for details).

$h^{ij}$ is not modified. Sets the value at the current time step (jtime ).

Definition at line 87 of file tslice_dirac_max_setAB.C.

References A_hh_evol, Lorene::Time_slice::adm_mass_evol, B_hh_evol, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::p_gamma, Lorene::Time_slice_conf::p_hdirac, Lorene::Time_slice_conf::p_tgamma, Lorene::Time_slice::the_time, and trh_evol.

◆ set_der_0x0()

void Lorene::Time_slice_conf::set_der_0x0 ( ) const

protectedinherited

Sets to 0x0 all the pointers on derived quantities.

Definition at line 364 of file time_slice_conf.C.

References p_hdirac, p_ln_psi, p_psi4, p_tgamma, and p_vec_X.

◆ set_hata()

void Lorene::Time_slice_conf::set_hata ( const Sym_tensor & hata_in )

virtualinherited

Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .

Sets the value at the current time step (jtime ), and updates the potentials A_hata_evol, B_hata_evol and p_vec_X accordingly.

Definition at line 537 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, hata_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, and Lorene::Time_slice::the_time.

◆ set_hata_from_XAB()

void Lorene::Time_slice_conf::set_hata_from_XAB	(	Param *	par_bc = 0x0,
		Param *	par_mat = 0x0 )

virtualinherited

Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature from its potentials A, $\tilde{B}$ and $ X^i $ .

These potentials must be up-to-date. It sets the value at the current time step (jtime ).

Definition at line 569 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, ff, hata_evol, Lorene::Tensor::inc_dzpuis(), Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, Lorene::Map(), p_vec_X, Lorene::Sym_tensor_tt::set_A_tildeB(), and Lorene::Time_slice::the_time.

◆ set_hata_TT()

void Lorene::Time_slice_conf::set_hata_TT ( const Sym_tensor_tt & hata_tt )

virtualinherited

Sets the TT part of $\hat{A}^{ij}$ (see member hata_evol ).

Sets the value at current time-step (jtime ) and updates the potentials A and $\tilde{B}$ .

Definition at line 549 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, Lorene::Sym_tensor::compute_A(), Lorene::Sym_tensor::compute_tilde_B_tt(), Lorene::Scalar::dec_dzpuis(), Lorene::Scalar::get_dzpuis(), hata_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, and Lorene::Time_slice::the_time.

◆ set_hh()

void Lorene::Tslice_dirac_max::set_hh ( const Sym_tensor & hh_in )

virtual

Sets the deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .

$h^{ij}$ must be such that $\det\tilde\gamma^{ij} = f^{-1}$ . Sets the value at the current time step (jtime ).

Reimplemented from Lorene::Time_slice_conf.

Definition at line 339 of file tslice_dirac_max.C.

References A_hh_evol, B_hh_evol, Lorene::Time_slice::jtime, Lorene::Time_slice_conf::set_hh(), source_A_hata_evol, source_A_hh_evol, source_B_hata_evol, source_B_hh_evol, and trh_evol.

◆ set_khi_mu()

void Lorene::Tslice_dirac_max::set_khi_mu	(	const Scalar &	khi_in,
		const Scalar &	mu_in )

virtual

Sets the potentials $\chi$ and $\mu$ of the TT part $\bar{h}^{ij}$ of $h^{ij}$ (see the documentation of Sym_tensor_tt for details).

The value of $h^{ij}$ is then deduced from the unimodularity condition on the conformal metric. Sets the value at the current time step (jtime ).

Definition at line 411 of file tslice_dirac_max.C.

References Lorene::Scalar::dec_dzpuis(), Lorene::Time_slice_conf::ff, Lorene::Tensor::get_mp(), Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, Lorene::Map(), Lorene::Tensor::set_etat_zero(), Lorene::Sym_tensor_tt::set_khi_mu(), Lorene::Sym_tensor::set_longit_trans(), Lorene::Time_slice::the_time, Lorene::Sym_tensor_trans::the_trace(), Lorene::Sym_tensor_trans::trace_from_det_one(), and trh_evol.

◆ set_npsi_del_n()

void Lorene::Time_slice_conf::set_npsi_del_n ( const Scalar & npsi_in )

virtualinherited

Sets the factor $N\Psi$ at the current time step (jtime ) and deletes the value of N.

Definition at line 481 of file time_slice_conf.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::n_evol, npsi_evol, and Lorene::Time_slice::the_time.

◆ set_npsi_del_psi()

void Lorene::Time_slice_conf::set_npsi_del_psi ( const Scalar & npsi_in )

virtualinherited

Sets the factor $N\Psi$ at the current time step (jtime ) and deletes the value of $\Psi$ .

Definition at line 456 of file time_slice_conf.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice::jtime, npsi_evol, Lorene::Time_slice::p_gamma, p_ln_psi, p_psi4, psi_evol, and Lorene::Time_slice::the_time.

◆ set_psi_del_n()

void Lorene::Time_slice_conf::set_psi_del_n ( const Scalar & psi_in )

virtualinherited

Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\‍[ \Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12} \‍]$

Sets the value at the current time step (jtime ) and deletes the value of N.

Definition at line 431 of file time_slice_conf.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::n_evol, Lorene::Time_slice::p_gamma, p_ln_psi, p_psi4, psi_evol, and Lorene::Time_slice::the_time.

◆ set_psi_del_npsi()

void Lorene::Time_slice_conf::set_psi_del_npsi ( const Scalar & psi_in )

virtualinherited

Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\‍[ \Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12} \‍]$

Sets the value at the current time step (jtime ) and deletes the value of $N\Psi$ .

Definition at line 407 of file time_slice_conf.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice::jtime, npsi_evol, Lorene::Time_slice::p_gamma, p_ln_psi, p_psi4, psi_evol, and Lorene::Time_slice::the_time.

◆ set_scheme_order()

void Lorene::Time_slice::set_scheme_order ( int ord )

inlineinherited

Sets the order of the finite-differences scheme.

Definition at line 334 of file time_slice.h.

References scheme_order.

◆ set_trh()

void Lorene::Tslice_dirac_max::set_trh ( const Scalar & trh_in )

virtual

Sets the trace, with respect to the flat metric ff , of $h^{ij}$ .

Sets the value at the current time step (jtime ). Note that this method does not ensure that the conformal metric is unimodular.

Definition at line 440 of file tslice_dirac_max.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::p_gamma, Lorene::Time_slice_conf::p_hdirac, Lorene::Time_slice_conf::p_tgamma, source_A_hata_evol, source_A_hh_evol, source_B_hata_evol, source_B_hh_evol, Lorene::Time_slice::the_time, and trh_evol.

◆ solve_beta()

Vector Lorene::Tslice_dirac_max::solve_beta ( int method = 6 ) const

virtual

Solves the elliptic equation for the shift vector $\beta^i$ from $A^{ij}$ (Eq.

(73) of Bonazzola et al. 2004).

Parameters

method method to be used for solving vector Poisson equation (for the shift), see Vector::poisson(double, const Metric_flat&, int) const.

Returns: solution $\beta^i_{\rm new}$ of the elliptic equation (flat vector Laplacian) for the shift with the source computed from the quantities at the current time step.

Definition at line 227 of file tslice_dirac_max_solve.C.

References Lorene::Time_slice_conf::aa(), Lorene::Time_slice::beta(), Lorene::contract(), Lorene::Scalar::derive_con(), Lorene::Tensor::derive_con(), Lorene::Sym_tensor::divergence(), Lorene::Vector::divergence(), Lorene::Time_slice_conf::ff, hh(), Lorene::Tensor::inc_dzpuis(), Lorene::maxabs(), Lorene::Time_slice_conf::nn(), and Lorene::Vector::poisson().

◆ solve_npsi()

Scalar Lorene::Tslice_dirac_max::solve_npsi	(	const Scalar *	ener_dens = 0x0,
		const Scalar *	trace_stress = 0x0 ) const

virtual

Solves the elliptic equation for $N\Psi$ (maximal slicing condition + Hamiltonian constraint).

Parameters

ener_dens	conformal matter energy density $\hat{E} = \Psi^6 E$ , where E is measured by the Eulerian observer; this quantity is passed as a pointer, the null value of which (default) meaning E=0.
trace_stress	trace of the conformal matter stress $S^* = \Psi^6 S$ , where S is measured by the Eulerian observer; this quantity is passed as a pointer, the null value of which (default) meaning S=0.

Returns: solution $(N\Psi)_{\rm new}$ of the elliptic equation (flat Laplacian) for $N\Psi$ with the source computed from the quantities at the current time step.

Definition at line 121 of file tslice_dirac_max_solve.C.

References Lorene::Time_slice_conf::aa(), Lorene::contract(), Lorene::Metric::cov(), Lorene::Scalar::derive_cov(), Lorene::Tensor::derive_cov(), Lorene::Tensor_sym::derive_cov(), Lorene::Time_slice_conf::ff, Lorene::Scalar::get_etat(), Lorene::Tensor::get_mp(), hh(), Lorene::Scalar::inc_dzpuis(), Lorene::Scalar::laplacian(), Lorene::Map(), Lorene::maxabs(), Lorene::Time_slice_conf::npsi(), Lorene::Scalar::poisson(), Lorene::Time_slice_conf::psi(), Lorene::Time_slice_conf::psi4(), Lorene::Scalar::set_etat_zero(), Lorene::Scalar::std_spectral_base(), Lorene::Time_slice_conf::tgam(), and Lorene::Tensor::up_down().

◆ solve_psi()

Scalar Lorene::Tslice_dirac_max::solve_psi ( const Scalar * ener_dens = 0x0 ) const

virtual

Solves the elliptic equation for the conformal factor $\Psi$ (Hamiltonian constraint).

Parameters

ener_dens conformal matter energy density $\hat{E} = \Psi^6 E$ , where E is measured by the Eulerian observer; this quantity is passed as a pointer, the null value of which (default) meaning E=0.

Returns: solution $\Psi_{\rm new}$ of the elliptic equation (flat Laplacian) for the lapse with the source computed from the quantities at the current time step.

Definition at line 175 of file tslice_dirac_max_solve.C.

References Lorene::contract(), Lorene::Metric::cov(), Lorene::Scalar::derive_cov(), Lorene::Tensor::derive_cov(), Lorene::Tensor_sym::derive_cov(), Lorene::Time_slice_conf::ff, Lorene::Scalar::get_etat(), Lorene::Tensor::get_mp(), Lorene::Time_slice_conf::hata(), hh(), Lorene::Scalar::inc_dzpuis(), Lorene::Scalar::laplacian(), Lorene::Map(), Lorene::maxabs(), Lorene::Scalar::poisson(), Lorene::pow(), Lorene::Time_slice_conf::psi(), Lorene::Scalar::set_etat_zero(), Lorene::Scalar::std_spectral_base(), Lorene::Time_slice_conf::tgam(), and Lorene::Tensor::up_down().

◆ tgam()

const Metric & Lorene::Time_slice_conf::tgam ( ) const

virtualinherited

Conformal metric $\tilde\gamma_{ij} = \Psi^{-4} \gamma_{ij}$ Returns the value at the current time step (jtime ).

Reimplemented in Lorene::Isol_hor.

Definition at line 750 of file time_slice_conf.C.

References ff, hh(), and p_tgamma.

◆ trh()

const Scalar & Lorene::Tslice_dirac_max::trh ( ) const

virtual

Computes the trace h, with respect to the flat metric ff , of $h^{ij}$ .

Returns the value at the current time step (jtime ).

Definition at line 550 of file tslice_dirac_max.C.

References hh_det_one(), Lorene::Time_slice::jtime, and trh_evol.

◆ trk()

const Scalar & Lorene::Tslice_dirac_max::trk ( ) const

virtual

Trace K of the extrinsic curvature at the current time step (jtime ).

It is null in the present case (maximal slicing)

Reimplemented from Lorene::Time_slice_conf.

Definition at line 494 of file tslice_dirac_max.C.

References Lorene::Time_slice_conf::ff, Lorene::Time_slice::jtime, Lorene::Scalar::set_etat_zero(), Lorene::Time_slice::the_time, and Lorene::Time_slice::trk_evol.

◆ vec_X()

const Vector & Lorene::Time_slice_conf::vec_X ( int method_poisson = 6 ) const

virtualinherited

Vector $ X^i $ representing the longitudinal part of $\hat{A}^{ij}$ .

(see the documentation of hata_evol)

Definition at line 828 of file time_slice_conf.C.

References ff, hata_evol, Lorene::Tensor::inc_dzpuis(), Lorene::Time_slice::jtime, p_vec_X, and Lorene::Vector::poisson().

Member Data Documentation

◆ A_hata_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::A_hata_evol

mutableprotectedinherited

Potential A associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ .

(see documentation of Sym_tensor::p_aaa).

Definition at line 550 of file time_slice.h.

◆ A_hh_evol

Evolution_std<Scalar> Lorene::Tslice_dirac_max::A_hh_evol

mutableprotected

The A potential of $\bar{h}^{ij}$ .

(see the documentation of Sym_tensor::p_aaa for details).

Definition at line 980 of file time_slice.h.

◆ adm_mass_evol

Evolution_full<Tbl> Lorene::Time_slice::adm_mass_evol

mutableprotectedinherited

ADM mass at each time step, since the creation of the slice.

At a given time step j, adm_mass_evol[j] is a 1-D Tbl of size the number nz of domains, containing the "ADM mass" evaluated at the outer boundary of each domain. The true ADM mass is thus the last value, i.e. adm_mass_evol[j](nz-1).

Definition at line 236 of file time_slice.h.

◆ B_hata_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::B_hata_evol

mutableprotectedinherited

Potential $\tilde{B}$ associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ .

(see documentation of Sym_tensor::p_tilde_b).

Definition at line 555 of file time_slice.h.

◆ B_hh_evol

Evolution_std<Scalar> Lorene::Tslice_dirac_max::B_hh_evol

mutableprotected

The $\tilde{B}$ potential of $\bar{h}^{ij}$ .

(see the documentation of Sym_tensor::p_tilde_b for details).

Definition at line 986 of file time_slice.h.

◆ beta_evol

Evolution_std<Vector> Lorene::Time_slice::beta_evol

mutableprotectedinherited

Values at successive time steps of the shift vector $\beta^i$ .

Definition at line 222 of file time_slice.h.

◆ depth

int Lorene::Time_slice::depth

protectedinherited

Number of stored time slices.

Definition at line 182 of file time_slice.h.

◆ ff

const Metric_flat& Lorene::Time_slice_conf::ff

protectedinherited

Pointer on the flat metric $f_{ij}$ with respect to which the conformal decomposition is performed.

Definition at line 510 of file time_slice.h.

◆ gam_dd_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::gam_dd_evol

mutableprotectedinherited

Values at successive time steps of the covariant components of the induced metric $\gamma_{ij}$ .

Definition at line 201 of file time_slice.h.

◆ gam_uu_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::gam_uu_evol

mutableprotectedinherited

Values at successive time steps of the contravariant components of the induced metric $\gamma^{ij}$ .

Definition at line 206 of file time_slice.h.

◆ hata_evol

Evolution_std<Sym_tensor> Lorene::Time_slice_conf::hata_evol

mutableprotectedinherited

Values at successive time steps of the components $\hat{A}^{ij}$ .

It is the conformal representation of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ . One can uniquely (up to the boundary conditions) define the decomposition: $\hat{A}^{ij} = {\cal D}^i X^j + {\cal D}^j X^i - \frac{2}{3} {\cal D}_k X^k f^{ij} + \hat{A}^{ij}_{TT}$ , where $ X^i $ represents the longitudinal part and $\hat{A}^{ij}_{TT}$ is the transverse-traceless part.

Definition at line 545 of file time_slice.h.

◆ hh_evol

Evolution_std<Sym_tensor> Lorene::Time_slice_conf::hh_evol

mutableprotectedinherited

Values at successive time steps of the components $h^{ij}$ .

It is the deviation of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .

Definition at line 533 of file time_slice.h.

◆ jtime

int Lorene::Time_slice::jtime

protectedinherited

Time step index of the latest slice.

Definition at line 193 of file time_slice.h.

◆ k_dd_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::k_dd_evol

mutableprotectedinherited

Values at successive time steps of the covariant components of the extrinsic curvature tensor $K_{ij}$ .

Definition at line 211 of file time_slice.h.

◆ k_uu_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::k_uu_evol

mutableprotectedinherited

Values at successive time steps of the contravariant components of the extrinsic curvature tensor $K^{ij}$ .

Definition at line 216 of file time_slice.h.

◆ n_evol

Evolution_std<Scalar> Lorene::Time_slice::n_evol

mutableprotectedinherited

Values at successive time steps of the lapse function N.

Definition at line 219 of file time_slice.h.

◆ npsi_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::npsi_evol

mutableprotectedinherited

Values at successive time steps of the factor $N\Psi$ .

Definition at line 525 of file time_slice.h.

◆ p_gamma

Metric* Lorene::Time_slice::p_gamma

mutableprotectedinherited

Pointer on the induced metric at the current time step (jtime).

Definition at line 242 of file time_slice.h.

◆ p_hdirac

Vector* Lorene::Time_slice_conf::p_hdirac

mutableprotectedinherited

Pointer on the vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ (which vanishes in Dirac gauge), at the current time step (jtime).

Definition at line 574 of file time_slice.h.

◆ p_ln_psi

Scalar* Lorene::Time_slice_conf::p_ln_psi

mutableprotectedinherited

Pointer on the logarithm of $\Psi$ at the current time step (jtime).

Definition at line 569 of file time_slice.h.

◆ p_psi4

Scalar* Lorene::Time_slice_conf::p_psi4

mutableprotectedinherited

Pointer on the factor $\Psi^4$ at the current time step (jtime).

Definition at line 566 of file time_slice.h.

◆ p_tgamma

Metric* Lorene::Time_slice_conf::p_tgamma

mutableprotectedinherited

Pointer on the conformal metric $\tilde\gamma_{ij}$ at the current time step (jtime).

Definition at line 563 of file time_slice.h.

◆ p_vec_X

Vector* Lorene::Time_slice_conf::p_vec_X

mutableprotectedinherited

Pointer on the vector $ X^i $ representing the longitudinal part of $\hat{A}^{ij}$ .

(see the documentation of hata_evol)

Definition at line 580 of file time_slice.h.

◆ psi_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::psi_evol

mutableprotectedinherited

Values at successive time steps of the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\‍[ \Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12} \‍]$

Definition at line 520 of file time_slice.h.

◆ scheme_order

int Lorene::Time_slice::scheme_order

protectedinherited

Order of the finite-differences scheme for the computation of time derivatives.

This order is not constant and can be adjusted via set_scheme_order() .

Definition at line 190 of file time_slice.h.

◆ source_A_hata_evol

Evolution_std<Scalar> Lorene::Tslice_dirac_max::source_A_hata_evol

mutableprotected

The potential A of the source of equation for $\hat{A}^{ij}$ .

(see the documentation of Sym_tensor::p_aaa for details).

Definition at line 1004 of file time_slice.h.

◆ source_A_hh_evol

Evolution_std<Scalar> Lorene::Tslice_dirac_max::source_A_hh_evol

mutableprotected

The A potential of the source of equation for $\bar{h}^{ij}$ .

(see the documentation of Sym_tensor::p_aaa for details).

Definition at line 992 of file time_slice.h.

◆ source_B_hata_evol

Evolution_std<Scalar> Lorene::Tslice_dirac_max::source_B_hata_evol

mutableprotected

The potential $\tilde{B}$ of the source of equation for $\hat{A}^{ij}$ .

(see the documentation of Sym_tensor::p_tilde_b for details).

Definition at line 1010 of file time_slice.h.

◆ source_B_hh_evol

Evolution_std<Scalar> Lorene::Tslice_dirac_max::source_B_hh_evol

mutableprotected

The $\tilde{B}$ potential of the source of equation for $\bar{h}^{ij}$ .

(see the documentation of Sym_tensor::p_tilde_b for details).

Definition at line 998 of file time_slice.h.

◆ the_time

Evolution_std<double> Lorene::Time_slice::the_time

protectedinherited

Time label of each slice.

Definition at line 196 of file time_slice.h.

◆ trh_evol

Evolution_std<Scalar> Lorene::Tslice_dirac_max::trh_evol

mutableprotected

The trace, with respect to the flat metric ff , of $h^{ij}$ .

Definition at line 1013 of file time_slice.h.

◆ trk_evol

Evolution_std<Scalar> Lorene::Time_slice::trk_evol

mutableprotectedinherited

Values at successive time steps of the trace K of the extrinsic curvature.

Definition at line 227 of file time_slice.h.

The documentation for this class was generated from the following files:

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Tslice_dirac_max() [1/5]

◆ Tslice_dirac_max() [2/5]

◆ Tslice_dirac_max() [3/5]

◆ Tslice_dirac_max() [4/5]

◆ Tslice_dirac_max() [5/5]

◆ ~Tslice_dirac_max()

Member Function Documentation

◆ A_hata()

◆ A_hh()

◆ aa()

◆ adm_mass()

◆ B_hata()

◆ B_hh()

◆ beta()

◆ check_dynamical_equations()

◆ check_hamiltonian_constraint()

◆ check_momentum_constraint()

◆ check_psi_dot()

◆ compute_sources()

◆ compute_X_from_momentum_constraint()

◆ del_deriv()

◆ evolve()

◆ gam()

◆ gam_dd()

◆ gam_uu()

◆ get_latest_j()

◆ get_scheme_order()

◆ get_time()

◆ hata()

◆ hdirac()

◆ hh()

◆ hh_det_one() [1/2]

◆ hh_det_one() [2/2]

◆ initial_data_cts()

◆ initialize_sources_copy()

◆ k_dd()

◆ k_uu()

◆ ln_psi()

◆ nn()

◆ npsi()

◆ operator=()

◆ operator>>()

◆ psi()

◆ psi4()

◆ sauve()

◆ save()

◆ set_AB_hata()

◆ set_AB_hh()

◆ set_der_0x0()

◆ set_hata()

◆ set_hata_from_XAB()

◆ set_hata_TT()

◆ set_hh()

◆ set_khi_mu()

◆ set_npsi_del_n()

◆ set_npsi_del_psi()

◆ set_psi_del_n()

◆ set_psi_del_npsi()

◆ set_scheme_order()

◆ set_trh()

◆ solve_beta()

◆ solve_npsi()

◆ solve_psi()

◆ tgam()

◆ trh()

◆ trk()

◆ vec_X()

Member Data Documentation

◆ A_hata_evol

◆ A_hh_evol

◆ adm_mass_evol

◆ B_hata_evol

◆ B_hh_evol

◆ beta_evol

◆ depth