Time_slice_conf Class Reference
[Time evolution (under development)]

Spacelike time slice of a 3+1 spacetime with conformal decomposition. More...

#include <time_slice.h>

Inheritance diagram for Time_slice_conf:
Time_slice Isol_hor Tslice_dirac_max

List of all members.

Public Member Functions

 Time_slice_conf (const Scalar &lapse_in, const Vector &shift_in, const Metric_flat &ff_in, const Scalar &psi_in, const Sym_tensor &hh_in, const Sym_tensor &hata_in, const Scalar &trk_in, int depth_in=3)
 Constructor from conformal decomposition.
 Time_slice_conf (const Scalar &lapse_in, const Vector &shift_in, const Sym_tensor &gamma_in, const Sym_tensor &kk_in, const Metric_flat &ff_in, int depth_in=3)
 Constructor from physical metric.
 Time_slice_conf (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).
 Time_slice_conf (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.
 Time_slice_conf (const Time_slice_conf &)
 Copy constructor.
virtual ~Time_slice_conf ()
 Destructor.
void operator= (const Time_slice_conf &)
 Assignment to another Time_slice_conf.
void operator= (const Time_slice &)
 Assignment to a Time_slice.
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_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 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 $ X^i $.
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 & hh (Param *=0x0, Param *=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 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 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 Vector & vec_X (int method_poisson=6) const
 Vector $ X^i $ 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 $ X^i $ from the conformally-rescaled momentum $ \hat{S}^i = \Psi^6 S^i $, using the momentum constraint.
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.
virtual double adm_mass () const
 Returns the ADM mass (geometrical units) at the current step.
void save (const char *rootname) const
 Saves in a binary file.

Protected Member Functions

virtual void del_deriv () const
 Deletes all the derived quantities.
void set_der_0x0 () const
 Sets to 0x0 all the pointers on derived quantities.
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.

Protected Attributes

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 $ X^i $ 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).

Friends

ostream & operator<< (ostream &, const Time_slice &)
 Display.

Detailed Description

Spacelike time slice of a 3+1 spacetime with conformal decomposition.

()

Definition at line 494 of file time_slice.h.

Constructor & Destructor Documentation

Time_slice_conf::Time_slice_conf ( const Scalar &  lapse_in,
const Vector &  shift_in,
const Metric_flat &  ff_in,
const Scalar &  psi_in,
const Sym_tensor &  hh_in,
const Sym_tensor &  hata_in,
const Scalar &  trk_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 $ 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) $
trk_in trace K of the extrinsic curvature
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 114 of file time_slice_conf.C.

References A_hata(), B_hata(), Time_slice::beta_evol, Metric_flat::con(), Metric_flat::determinant(), ff, Tensor::get_index_type(), Time_slice::jtime, max(), maxabs(), Time_slice::n_evol, set_der_0x0(), Time_slice::the_time, Time_slice::trk_evol, and Evolution_std< TyT >::update().

Time_slice_conf::Time_slice_conf ( const Scalar &  lapse_in,
const Vector &  shift_in,
const Sym_tensor &  gamma_in,
const Sym_tensor &  kk_in,
const Metric_flat &  ff_in,
int  depth_in = 3 
)

Constructor from physical metric.

The conformal decomposition is performed by the constructor.

Parameters:
lapse_in lapse function N
shift_in shift vector
gamma_in induced metric (covariant or contravariant components)
kk_in extrinsic curvature (covariant or contravariant components)
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 168 of file time_slice_conf.C.

References A_hata(), B_hata(), Metric_flat::con(), Metric::con(), Metric_flat::determinant(), Metric::determinant(), ff, hata_evol, hh_evol, Time_slice::jtime, Time_slice::k_uu(), Time_slice::p_gamma, p_psi4, pow(), psi_evol, set_der_0x0(), Scalar::std_spectral_base(), Time_slice::the_time, Time_slice::trk_evol, and Evolution_std< TyT >::update().

Time_slice_conf::Time_slice_conf ( 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 205 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, hata_evol, hh_evol, Time_slice::jtime, npsi_evol, psi_evol, set_der_0x0(), Scalar::set_etat_one(), Scalar::set_etat_zero(), Tensor::set_etat_zero(), Scalar::std_spectral_base(), Time_slice::the_time, and Evolution_std< TyT >::update().

Time_slice_conf::Time_slice_conf ( 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 Time_slice_conf
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 246 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, Time_slice::depth, fread_be(), Map::get_mg(), hata_evol, Time_slice::jtime, psi_evol, set_der_0x0(), Time_slice::the_time, and Evolution_std< TyT >::update().

Time_slice_conf::Time_slice_conf ( const Time_slice_conf &  tin  ) 

Copy constructor.

Definition at line 316 of file time_slice_conf.C.

References set_der_0x0().

Time_slice_conf::~Time_slice_conf (  )  [virtual]

Destructor.

Definition at line 333 of file time_slice_conf.C.

References del_deriv().

Member Function Documentation

const Scalar & Time_slice_conf::A_hata (  )  const [virtual]

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 660 of file time_slice_conf.C.

References A_hata_evol, hata_evol, Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::the_time, and Evolution_std< TyT >::update().

Sym_tensor Time_slice_conf::aa (  )  const [virtual]

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 761 of file time_slice_conf.C.

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

double Time_slice::adm_mass (  )  const [virtual, inherited]

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

Moreover this method updates adm_mass_evol if necessary.

Reimplemented in Tslice_dirac_max.

Definition at line 70 of file tslice_adm_mass.C.

References Time_slice::adm_mass_evol, Tensor::derive_con(), Tensor_sym::derive_con(), Vector::flux(), Time_slice::gam_dd(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), Tbl::get_taille(), Time_slice::jtime, Tbl::set(), Tbl::set_etat_qcq(), Time_slice::the_time, Tensor::trace(), Tensor::up(), Evolution_full< TyT >::update(), and Map::val_r().

const Scalar & Time_slice_conf::B_hata (  )  const [virtual]

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 674 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, hata_evol, Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::the_time, and Evolution_std< TyT >::update().

const Vector & Time_slice::beta (  )  const [virtual, inherited]

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

Definition at line 83 of file time_slice_access.C.

References Time_slice::beta_evol, Evolution< TyT >::is_known(), and Time_slice::jtime.

Tbl 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 $ J_i $ = 0 ) or the relative (in presence of matter) error in max version.

Definition at line 135 of file tslice_check_einstein.C.

References Tensor::annule_domain(), Time_slice::beta(), Metric::con(), contract(), Tensor::derive_con(), Scalar::derive_con(), Sym_tensor::derive_lie(), Time_slice::gam(), Tbl::get_dim(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), Time_slice::jtime, Time_slice::k_dd(), Time_slice::k_dd_evol, Time_slice::k_uu(), maxabs(), Time_slice::nn(), Tensor_sym::position(), Metric::ricci(), Time_slice::scheme_order, Itbl::set(), Evolution< TyT >::time_derive(), Tensor::trace(), Time_slice::trk(), and Tensor::up_down().

Tbl 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 75 of file tslice_check_einstein.C.

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

Tbl 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 $ J_i $ measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer, it is assumed that$ J_i $ = 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 $ J_i $ = 0 ) or the relative (in presence of matter) error in max version.

Definition at line 105 of file tslice_check_einstein.C.

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

void 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 
)

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

Definition at line 833 of file time_slice_conf.C.

References abs(), contract(), Tensor::get_index_type(), max(), and Vector::poisson().

void Time_slice_conf::del_deriv (  )  const [protected, virtual]

Deletes all the derived quantities.

Reimplemented from Time_slice.

Definition at line 343 of file time_slice_conf.C.

References p_hdirac, p_ln_psi, p_psi4, p_tgamma, p_vec_X, and set_der_0x0().

const Metric & Time_slice::gam (  )  const [inherited]

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

Definition at line 91 of file time_slice_access.C.

References Time_slice::gam_dd(), and Time_slice::p_gamma.

const Sym_tensor & Time_slice_conf::gam_dd (  )  const [virtual]

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

Reimplemented from Time_slice.

Definition at line 604 of file time_slice_conf.C.

References Time_slice::gam_dd_evol, Evolution< TyT >::is_known(), Time_slice::jtime, psi4(), tgam(), Time_slice::the_time, and Evolution_std< TyT >::update().

const Sym_tensor & Time_slice_conf::gam_uu (  )  const [virtual]

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

Reimplemented from Time_slice.

Definition at line 615 of file time_slice_conf.C.

References Time_slice::gam_uu_evol, Evolution< TyT >::is_known(), Time_slice::jtime, psi4(), tgam(), Time_slice::the_time, and Evolution_std< TyT >::update().

int Time_slice::get_latest_j (  )  const [inline, inherited]

Gets the latest value of time step index.

Definition at line 339 of file time_slice.h.

References Time_slice::jtime.

int Time_slice::get_scheme_order (  )  const [inline, inherited]

Gets the order of the finite-differences scheme.

Definition at line 336 of file time_slice.h.

References Time_slice::scheme_order.

const Evolution_std<double>& Time_slice::get_time (  )  const [inline, inherited]

Gets the time coordinate t at successive time steps.

Definition at line 342 of file time_slice.h.

References Time_slice::the_time.

const Sym_tensor & Time_slice_conf::hata (  )  const [virtual]

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 768 of file time_slice_conf.C.

References Time_slice::beta(), Sym_tensor::derive_lie(), Vector::divergence(), ff, hata_evol, hh(), hh_evol, Tensor::inc_dzpuis(), Evolution< TyT >::is_known(), Time_slice::jtime, nn(), Vector::ope_killing_conf(), psi(), psi4(), Time_slice::scheme_order, Time_slice::the_time, Evolution< TyT >::time_derive(), and Evolution_std< TyT >::update().

const Vector & Time_slice_conf::hdirac (  )  const [virtual]

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

Reimplemented in Tslice_dirac_max.

Definition at line 811 of file time_slice_conf.C.

References ff, hh(), and p_hdirac.

const Sym_tensor & Time_slice_conf::hh ( Param *  = 0x0,
Param *  = 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 in Tslice_dirac_max.

Definition at line 754 of file time_slice_conf.C.

References hh_evol, Evolution< TyT >::is_known(), and Time_slice::jtime.

const Sym_tensor & Time_slice_conf::k_dd (  )  const [virtual]

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

Reimplemented from Time_slice.

Definition at line 626 of file time_slice_conf.C.

References Time_slice::gam(), Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::k_dd_evol, k_uu(), Time_slice::the_time, and Evolution_std< TyT >::update().

const Sym_tensor & Time_slice_conf::k_uu (  )  const [virtual]

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

Reimplemented from Time_slice.

Definition at line 639 of file time_slice_conf.C.

References Time_slice::gam(), hata(), Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::k_uu_evol, psi(), psi4(), Time_slice::the_time, trk(), and Evolution_std< TyT >::update().

const Scalar & Time_slice_conf::ln_psi (  )  const

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

Definition at line 715 of file time_slice_conf.C.

References log(), p_ln_psi, psi(), and Scalar::std_spectral_base().

const Scalar & Time_slice_conf::nn (  )  const [virtual]

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

Reimplemented from Time_slice.

Definition at line 587 of file time_slice_conf.C.

References Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::n_evol, npsi_evol, psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

const Scalar & Time_slice_conf::npsi (  )  const [virtual]

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

Definition at line 728 of file time_slice_conf.C.

References Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::n_evol, npsi_evol, psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::operator= ( const Time_slice &  tin  ) 

Assignment to a Time_slice.

Definition at line 387 of file time_slice_conf.C.

References del_deriv(), and operator=().

void Time_slice_conf::operator= ( const Time_slice_conf &  tin  ) 

Assignment to another Time_slice_conf.

Reimplemented from Time_slice.

Reimplemented in Isol_hor, and Tslice_dirac_max.

Definition at line 372 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, del_deriv(), hata_evol, hh_evol, npsi_evol, and psi_evol.

ostream & Time_slice::operator>> ( ostream &  flux  )  const [protected, virtual, inherited]

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

Reimplemented in Isol_hor, and Tslice_dirac_max.

Definition at line 407 of file time_slice.C.

References Time_slice::adm_mass(), Time_slice::adm_mass_evol, Time_slice::beta_evol, Time_slice::depth, Time_slice::gam_dd_evol, Time_slice::gam_uu_evol, Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::k_dd_evol, Time_slice::k_uu_evol, maxabs(), Time_slice::n_evol, Time_slice::p_gamma, Time_slice::scheme_order, Time_slice::the_time, and Time_slice::trk_evol.

const Scalar & Time_slice_conf::psi (  )  const [virtual]

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 689 of file time_slice_conf.C.

References Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::n_evol, npsi_evol, psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

const Scalar & Time_slice_conf::psi4 (  )  const

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

Definition at line 703 of file time_slice_conf.C.

References p_psi4, pow(), psi(), and Scalar::std_spectral_base().

void Time_slice::sauve ( FILE *  fich,
bool  partial_save 
) const [protected, virtual, inherited]

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 in Isol_hor, and Tslice_dirac_max.

Definition at line 503 of file time_slice.C.

References Time_slice::beta(), Time_slice::beta_evol, Time_slice::depth, fwrite_be(), Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::n_evol, Time_slice::nn(), Time_slice::scheme_order, and Time_slice::the_time.

void 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 457 of file time_slice.C.

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

void Time_slice_conf::set_der_0x0 (  )  const [protected]

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Time_slice.

Definition at line 357 of file time_slice_conf.C.

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

void Time_slice_conf::set_hata ( const Sym_tensor &  hata_in  )  [virtual]

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 530 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, Evolution< TyT >::downdate(), hata_evol, Time_slice::jtime, Time_slice::k_dd_evol, Time_slice::k_uu_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_hata_from_XAB ( Param *  par_bc = 0x0,
Param *  par_mat = 0x0 
) [virtual]

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 562 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, Evolution< TyT >::downdate(), ff, Tensor::get_mp(), hata_evol, Map::inc_dzpuis(), Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::k_dd_evol, Time_slice::k_uu_evol, Vector::ope_killing_conf(), p_vec_X, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_hata_TT ( const Sym_tensor_tt &  hata_tt  )  [virtual]

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 542 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, Sym_tensor::compute_A(), Sym_tensor::compute_tilde_B_tt(), Scalar::dec_dzpuis(), Evolution< TyT >::downdate(), Scalar::get_dzpuis(), hata_evol, Time_slice::jtime, Time_slice::k_dd_evol, Time_slice::k_uu_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::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 in Tslice_dirac_max.

Definition at line 485 of file time_slice_conf.C.

References Time_slice::adm_mass_evol, Metric_flat::con(), Metric_flat::determinant(), Evolution< TyT >::downdate(), ff, Time_slice::gam_dd_evol, Time_slice::gam_uu_evol, hh_evol, Time_slice::jtime, max(), maxabs(), Time_slice::p_gamma, p_hdirac, p_tgamma, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_npsi_del_n ( const Scalar &  npsi_in  )  [virtual]

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

Definition at line 474 of file time_slice_conf.C.

References Time_slice::adm_mass_evol, Evolution< TyT >::downdate(), Time_slice::jtime, Time_slice::n_evol, npsi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_npsi_del_psi ( const Scalar &  npsi_in  )  [virtual]

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

Definition at line 449 of file time_slice_conf.C.

References Time_slice::adm_mass_evol, Evolution< TyT >::downdate(), Time_slice::gam_dd_evol, Time_slice::gam_uu_evol, Time_slice::jtime, npsi_evol, Time_slice::p_gamma, p_ln_psi, p_psi4, psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_psi_del_n ( const Scalar &  psi_in  )  [virtual]

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 424 of file time_slice_conf.C.

References Time_slice::adm_mass_evol, Evolution< TyT >::downdate(), Time_slice::gam_dd_evol, Time_slice::gam_uu_evol, Time_slice::jtime, Time_slice::n_evol, Time_slice::p_gamma, p_ln_psi, p_psi4, psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_psi_del_npsi ( const Scalar &  psi_in  )  [virtual]

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 400 of file time_slice_conf.C.

References Time_slice::adm_mass_evol, Evolution< TyT >::downdate(), Time_slice::gam_dd_evol, Time_slice::gam_uu_evol, Time_slice::jtime, npsi_evol, Time_slice::p_gamma, p_ln_psi, p_psi4, psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice::set_scheme_order ( int  ord  )  [inline, inherited]

Sets the order of the finite-differences scheme.

Definition at line 327 of file time_slice.h.

References Time_slice::scheme_order.

const Metric & Time_slice_conf::tgam (  )  const [virtual]

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

Reimplemented in Isol_hor.

Definition at line 743 of file time_slice_conf.C.

References Metric_flat::con(), ff, hh(), and p_tgamma.

const Scalar & Time_slice_conf::trk (  )  const [virtual]

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

Reimplemented from Time_slice.

Reimplemented in Tslice_dirac_max.

Definition at line 792 of file time_slice_conf.C.

References Time_slice::beta(), contract(), Vector::divergence(), ff, Scalar::inc_dzpuis(), Evolution< TyT >::is_known(), Time_slice::jtime, ln_psi(), nn(), psi(), psi_evol, Time_slice::scheme_order, Time_slice::the_time, Evolution< TyT >::time_derive(), Time_slice::trk_evol, and Evolution_std< TyT >::update().

const Vector & Time_slice_conf::vec_X ( int  method_poisson = 6  )  const [virtual]

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

(see the documentation of hata_evol)

Definition at line 821 of file time_slice_conf.C.

References ff, hata_evol, Evolution< TyT >::is_known(), Time_slice::jtime, and p_vec_X.

Friends And Related Function Documentation

ostream& operator<< ( ostream &  ,
const Time_slice &   
) [friend, inherited]

Display.

Member Data Documentation

Evolution_std<Scalar> Time_slice_conf::A_hata_evol [mutable, protected]

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

(see documentation of Sym_tensor::p_aaa).

Definition at line 543 of file time_slice.h.

Evolution_full<Tbl> Time_slice::adm_mass_evol [mutable, protected, inherited]

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 229 of file time_slice.h.

Evolution_std<Scalar> Time_slice_conf::B_hata_evol [mutable, protected]

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

(see documentation of Sym_tensor::p_tilde_b).

Definition at line 548 of file time_slice.h.

Evolution_std<Vector> Time_slice::beta_evol [mutable, protected, inherited]

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

Definition at line 215 of file time_slice.h.

int Time_slice::depth [protected, inherited]

Number of stored time slices.

Definition at line 175 of file time_slice.h.

const Metric_flat& Time_slice_conf::ff [protected]

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

Definition at line 503 of file time_slice.h.

Evolution_std<Sym_tensor> Time_slice::gam_dd_evol [mutable, protected, inherited]

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

Definition at line 194 of file time_slice.h.

Evolution_std<Sym_tensor> Time_slice::gam_uu_evol [mutable, protected, inherited]

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

Definition at line 199 of file time_slice.h.

Evolution_std<Sym_tensor> Time_slice_conf::hata_evol [mutable, protected]

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 538 of file time_slice.h.

Evolution_std<Sym_tensor> Time_slice_conf::hh_evol [mutable, protected]

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 526 of file time_slice.h.

int Time_slice::jtime [protected, inherited]

Time step index of the latest slice.

Definition at line 186 of file time_slice.h.

Evolution_std<Sym_tensor> Time_slice::k_dd_evol [mutable, protected, inherited]

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

Definition at line 204 of file time_slice.h.

Evolution_std<Sym_tensor> Time_slice::k_uu_evol [mutable, protected, inherited]

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

Definition at line 209 of file time_slice.h.

Evolution_std<Scalar> Time_slice::n_evol [mutable, protected, inherited]

Values at successive time steps of the lapse function N.

Definition at line 212 of file time_slice.h.

Evolution_std<Scalar> Time_slice_conf::npsi_evol [mutable, protected]

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

Definition at line 518 of file time_slice.h.

Metric* Time_slice::p_gamma [mutable, protected, inherited]

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

Definition at line 235 of file time_slice.h.

Vector* Time_slice_conf::p_hdirac [mutable, protected]

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 567 of file time_slice.h.

Scalar* Time_slice_conf::p_ln_psi [mutable, protected]

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

Definition at line 562 of file time_slice.h.

Scalar* Time_slice_conf::p_psi4 [mutable, protected]

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

Definition at line 559 of file time_slice.h.

Metric* Time_slice_conf::p_tgamma [mutable, protected]

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

Definition at line 556 of file time_slice.h.

Vector* Time_slice_conf::p_vec_X [mutable, protected]

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

(see the documentation of hata_evol)

Definition at line 573 of file time_slice.h.

Evolution_std<Scalar> Time_slice_conf::psi_evol [mutable, protected]

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 513 of file time_slice.h.

int Time_slice::scheme_order [protected, inherited]

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 183 of file time_slice.h.

Evolution_std<double> Time_slice::the_time [protected, inherited]

Time label of each slice.

Definition at line 189 of file time_slice.h.

Evolution_std<Scalar> Time_slice::trk_evol [mutable, protected, inherited]

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

Definition at line 220 of file time_slice.h.

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