Lorene::Time_slice_conf Class Reference
Time evolution (<em><strong>under development</strong></em>)

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

`#include <time_slice.h>`

Inheritance diagram for Lorene::Time_slice_conf:

## 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 relating the physical metric to the conformal one: .
virtual void | set_psi_del_n (const Scalar &psi_in)
| Sets the conformal factor relating the physical metric to the conformal one: .
virtual void | set_npsi_del_psi (const Scalar &npsi_in)
| Sets the factor at the current time step (`jtime` ) and deletes the value of .
virtual void | set_npsi_del_n (const Scalar &npsi_in)
| Sets the factor at the current time step (`jtime` ) and deletes the value of N.
virtual void | set_hh (const Sym_tensor &hh_in)
| Sets the deviation of the conformal metric from the flat metric : .
virtual void | set_hata (const Sym_tensor &hata_in)
| Sets the conformal representation of the traceless part of the extrinsic curvature: .
virtual void | set_hata_TT (const Sym_tensor_tt &hata_tt)
| Sets the TT part of (see member `hata_evol` ).
virtual void | set_hata_from_XAB (Param *par_bc=0x0, Param *par_mat=0x0)
| Sets the conformal representation of the traceless part of the extrinsic curvature from its potentials A, 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 ) at the current time step (`jtime` ).
virtual const Sym_tensor & | gam_uu () const
| Induced metric (contravariant components ) at the current time step (`jtime` ).
virtual const Sym_tensor & | k_dd () const
| Extrinsic curvature tensor (covariant components ) at the current time step (`jtime` ).
virtual const Sym_tensor & | k_uu () const
| Extrinsic curvature tensor (contravariant components ) at the current time step (`jtime` ).
virtual const Scalar & | A_hata () const
| Returns the potential A of .
virtual const Scalar & | B_hata () const
| Returns the potential of .
virtual const Scalar & | psi () const
| Conformal factor relating the physical metric to the conformal one: .
const Scalar & | psi4 () const
| Factor at the current time step (`jtime` ).
const Scalar & | ln_psi () const
| Logarithm of at the current time step (`jtime` ).
virtual const Scalar & | npsi () const
| Factor at the current time step (`jtime` ).
virtual const Metric & | tgam () const
| Conformal metric Returns the value at the current time step (`jtime` ).
virtual const Sym_tensor & | hh (Param *=0x0, Param *=0x0) const
| Deviation of the conformal metric from the flat metric : .
virtual const Sym_tensor & | hata () const
| Conformal representation of the traceless part of the extrinsic curvature: .
virtual Sym_tensor | aa () const
| Conformal representation of the traceless part of the extrinsic curvature: .
virtual const Scalar & | trk () const
| Trace K of the extrinsic curvature at the current time step (`jtime` ).
virtual const Vector & | hdirac () const
| Vector which vanishes in Dirac gauge.
virtual const Vector & | vec_X (int method_poisson=6) const
| Vector representing the longitudinal part of .
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 , 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 at the current time step (`jtime` )
const Metric & | gam () const
| Induced metric 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 with respect to which the conformal decomposition is performed.
Evolution_std< Scalar > | psi_evol
| Values at successive time steps of the conformal factor relating the physical metric to the conformal one: .
Evolution_std< Scalar > | npsi_evol
| Values at successive time steps of the factor .
Evolution_std< Sym_tensor > | hh_evol
| Values at successive time steps of the components .
Evolution_std< Sym_tensor > | hata_evol
| Values at successive time steps of the components .
Evolution_std< Scalar > | A_hata_evol
| Potential A associated with the symmetric tensor .
Evolution_std< Scalar > | B_hata_evol
| Potential associated with the symmetric tensor .
Metric * | p_tgamma
| Pointer on the conformal metric at the current time step (`jtime`).
Scalar * | p_psi4
| Pointer on the factor at the current time step (`jtime`).
Scalar * | p_ln_psi
| Pointer on the logarithm of at the current time step (`jtime`).
Vector * | p_hdirac
| Pointer on the vector (which vanishes in Dirac gauge), at the current time step (`jtime`).
Vector * | p_vec_X
| Pointer on the vector representing the longitudinal part of .
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 .
Evolution_std< Sym_tensor > | gam_uu_evol
| Values at successive time steps of the contravariant components of the induced metric .
Evolution_std< Sym_tensor > | k_dd_evol
| Values at successive time steps of the covariant components of the extrinsic curvature tensor .
Evolution_std< Sym_tensor > | k_uu_evol
| Values at successive time steps of the contravariant components of the extrinsic curvature tensor .
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 .
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.

()

Definition at line 498 of file time_slice.h.

## Constructor & Destructor Documentation

## Time_slice_conf() [1/5]

Lorene::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 relating the physical metric to the conformal one:
  hh_in | deviation of the conformal metric from the flat metric : . must be such that .
  hata_in | conformal representation of the traceless part of the extrinsic curvature:
  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 118 of file time_slice_conf.C.

References A_hata(), A_hata_evol, B_hata(), B_hata_evol, Lorene::Time_slice::beta_evol, Lorene::Metric_flat::con(), ff, Lorene::Tensor::get_index_type(), hata_evol, hh_evol, Lorene::Time_slice::jtime, Lorene::max(), Lorene::maxabs(), Lorene::Time_slice::n_evol, npsi_evol, psi_evol, set_der_0x0(), Lorene::Time_slice::the_time, Lorene::Time_slice::Time_slice(), and Lorene::Time_slice::trk_evol.

## Time_slice_conf() [2/5]

Lorene::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 172 of file time_slice_conf.C.

References A_hata(), A_hata_evol, B_hata(), B_hata_evol, ff, hata_evol, hh_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_uu(), npsi_evol, Lorene::Time_slice::p_gamma, p_psi4, Lorene::pow(), psi_evol, set_der_0x0(), Lorene::Scalar::std_spectral_base(), Lorene::Time_slice::the_time, Lorene::Time_slice::Time_slice(), and Lorene::Time_slice::trk_evol.

## Time_slice_conf() [3/5]

Lorene::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 209 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, ff, hata_evol, hh_evol, Lorene::Time_slice::jtime, Lorene::Map(), npsi_evol, psi_evol, set_der_0x0(), Lorene::Scalar::set_etat_one(), Lorene::Scalar::set_etat_zero(), Lorene::Tensor::set_etat_zero(), Lorene::Scalar::std_spectral_base(), Lorene::Time_slice::the_time, and Lorene::Time_slice::Time_slice().

## Time_slice_conf() [4/5]

Lorene::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 250 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, Lorene::Time_slice::depth, ff, Lorene::fread_be(), hata_evol, hh_evol, Lorene::Time_slice::jtime, Lorene::Map(), npsi_evol, psi_evol, set_der_0x0(), Lorene::Time_slice::the_time, and Lorene::Time_slice::Time_slice().

## Time_slice_conf() [5/5]

Lorene::Time_slice_conf::Time_slice_conf | ( | const Time_slice_conf & | tin | ) |

Copy constructor.

Definition at line 320 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, ff, hata_evol, hh_evol, npsi_evol, psi_evol, set_der_0x0(), Lorene::Time_slice::Time_slice(), and Time_slice_conf().

## ~Time_slice_conf()

Lorene::Time_slice_conf::~Time_slice_conf | ( |  | ) |

virtual

Destructor.

Definition at line 337 of file time_slice_conf.C.

References del_deriv().

## Member Function Documentation

## A_hata()

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

virtual

Returns the potential A of .

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

Definition at line 664 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.

## aa()

Sym_tensor Lorene::Time_slice_conf::aa | ( |  | ) | const

virtual

Conformal representation of the traceless part of the extrinsic curvature: .

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

Definition at line 765 of file time_slice_conf.C.

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

## adm_mass()

double Lorene::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 Lorene::Tslice_dirac_max.

Definition at line 74 of file tslice_adm_mass.C.

References adm_mass_evol, Lorene::Tensor::derive_con(), Lorene::Tensor_sym::derive_con(), Lorene::Vector::flux(), gam_dd(), Lorene::Tensor::get_mp(), Lorene::Tbl::get_taille(), jtime, Lorene::Map(), Lorene::Tbl::set(), Lorene::Tbl::set_etat_qcq(), the_time, Lorene::Tensor::trace(), and Lorene::Tensor::up().

## B_hata()

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

virtual

Returns the potential of .

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

Definition at line 678 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.

## beta()

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

virtual inherited

shift vector at the current time step (`jtime` )

Definition at line 87 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.

Parameters

  strain_tensor | : a pointer on the strain_tensor measured by the Eulerian observer of 4-velocity ; if this is the null pointer, it is assumed that = 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 139 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.

Parameters

  energy_density | : a pointer on the energy density E measured by the Eulerian observer of 4-velocity ; 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 79 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.

Parameters

  momentum_density | : a pointer on the momentum density measured by the Eulerian observer of 4-velocity ; 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 109 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().

## 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 )

Computes the vector from the conformally-rescaled momentum , using the momentum constraint.

Definition at line 836 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

protected virtual

Deletes all the derived quantities.

Reimplemented from Lorene::Time_slice.

Definition at line 347 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().

## gam()

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

inherited

Induced metric at the current time step (`jtime` ).

Definition at line 95 of file time_slice_access.C.

References gam_dd(), and p_gamma.

## gam_dd()

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

virtual

Induced metric (covariant components ) at the current time step (`jtime` ).

Reimplemented from Lorene::Time_slice.

Definition at line 608 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

virtual

Induced metric (contravariant components ) at the current time step (`jtime` ).

Reimplemented from Lorene::Time_slice.

Definition at line 619 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

inline inherited

Gets the latest value of time step index.

Definition at line 343 of file time_slice.h.

References jtime.

## get_scheme_order()

int Lorene::Time_slice::get_scheme_order | ( |  | ) | const

inline inherited

Gets the order of the finite-differences scheme.

Definition at line 340 of file time_slice.h.

References scheme_order.

## get_time()

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

inline inherited

Gets the time coordinate t at successive time steps.

Definition at line 346 of file time_slice.h.

References the_time.

## hata()

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

virtual

Conformal representation of the traceless part of the extrinsic curvature: .

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

Definition at line 772 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::Time_slice_conf::hdirac | ( |  | ) | const

virtual

Vector which vanishes in Dirac gauge.

Reimplemented in Lorene::Tslice_dirac_max.

Definition at line 815 of file time_slice_conf.C.

References ff, hh(), and p_hdirac.

## hh()

const Sym_tensor & Lorene::Time_slice_conf::hh | ( | Param * | = 0x0,
|  | Param * | = 0x0 ) const

virtual

Deviation of the conformal metric from the flat metric : .

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

Reimplemented in Lorene::Tslice_dirac_max.

Definition at line 758 of file time_slice_conf.C.

References hh_evol, and Lorene::Time_slice::jtime.

## k_dd()

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

virtual

Extrinsic curvature tensor (covariant components ) at the current time step (`jtime` ).

Reimplemented from Lorene::Time_slice.

Definition at line 630 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

virtual

Extrinsic curvature tensor (contravariant components ) at the current time step (`jtime` ).

Reimplemented from Lorene::Time_slice.

Definition at line 643 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

Logarithm of at the current time step (`jtime` ).

Definition at line 719 of file time_slice_conf.C.

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

## nn()

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

virtual

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

Reimplemented from Lorene::Time_slice.

Definition at line 591 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

virtual

Factor at the current time step (`jtime` ).

Definition at line 732 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=() [1/2]

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

Assignment to a `Time_slice`.

Definition at line 391 of file time_slice_conf.C.

References del_deriv(), Lorene::Time_slice::operator=(), and Lorene::Time_slice::Time_slice().

## operator=() [2/2]

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

Assignment to another `Time_slice_conf`.

Definition at line 376 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, del_deriv(), hata_evol, hh_evol, npsi_evol, Lorene::Time_slice::operator=(), psi_evol, and Time_slice_conf().

## operator>>()

ostream & Lorene::Time_slice::operator>> | ( | ostream & | flux | ) | const

protected virtual inherited

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

Reimplemented in Lorene::Isol_hor.

Definition at line 411 of file time_slice.C.

References adm_mass(), adm_mass_evol, beta_evol, depth, gam_dd_evol, gam_uu_evol, jtime, k_dd_evol, k_uu_evol, Lorene::maxabs(), n_evol, p_gamma, scheme_order, the_time, and trk_evol.

## psi()

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

virtual

Conformal factor relating the physical metric to the conformal one: .

is defined by

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

Definition at line 693 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

Factor at the current time step (`jtime` ).

Definition at line 707 of file time_slice_conf.C.

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

## sauve()

void Lorene::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 Lorene::Isol_hor, and Lorene::Tslice_dirac_max.

Definition at line 507 of file time_slice.C.

References beta(), beta_evol, depth, Lorene::fwrite_be(), jtime, n_evol, nn(), scheme_order, and the_time.

## 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 461 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_der_0x0()

void Lorene::Time_slice_conf::set_der_0x0 | ( |  | ) | const

protected

Sets to `0x0` all the pointers on derived quantities.

Definition at line 361 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 | ) |

virtual

Sets the conformal representation of the traceless part of the extrinsic curvature: .

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 534 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 )

virtual

Sets the conformal representation of the traceless part of the extrinsic curvature from its potentials A, and .

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

Definition at line 566 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 | ) |

virtual

Sets the TT part of (see member `hata_evol` ).

Sets the value at current time-step (`jtime` ) and updates the potentials A and .

Definition at line 546 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::Time_slice_conf::set_hh | ( | const Sym_tensor & | hh_in | ) |

virtual

Sets the deviation of the conformal metric from the flat metric : .

must be such that . Sets the value at the current time step (`jtime` ).

Reimplemented in Lorene::Tslice_dirac_max.

Definition at line 489 of file time_slice_conf.C.

References Lorene::Time_slice::adm_mass_evol, ff, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, hh_evol, Lorene::Time_slice::jtime, Lorene::max(), Lorene::maxabs(), Lorene::Time_slice::p_gamma, p_hdirac, p_tgamma, and Lorene::Time_slice::the_time.

## set_npsi_del_n()

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

virtual

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

Definition at line 478 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 | ) |

virtual

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

Definition at line 453 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 | ) |

virtual

Sets the conformal factor relating the physical metric to the conformal one: .

is defined by

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

Definition at line 428 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 | ) |

virtual

Sets the conformal factor relating the physical metric to the conformal one: .

is defined by

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

Definition at line 404 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 | ) |

inline inherited

Sets the order of the finite-differences scheme.

Definition at line 331 of file time_slice.h.

References scheme_order.

## tgam()

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

virtual

Conformal metric Returns the value at the current time step (`jtime` ).

Reimplemented in Lorene::Isol_hor.

Definition at line 747 of file time_slice_conf.C.

References ff, hh(), and p_tgamma.

## trk()

const Scalar & Lorene::Time_slice_conf::trk | ( |  | ) | const

virtual

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

Reimplemented from Lorene::Time_slice.

Reimplemented in Lorene::Tslice_dirac_max.

Definition at line 796 of file time_slice_conf.C.

References Lorene::Time_slice::beta(), Lorene::contract(), Lorene::Vector::divergence(), ff, Lorene::Scalar::inc_dzpuis(), Lorene::Time_slice::jtime, ln_psi(), nn(), psi(), psi_evol, Lorene::Time_slice::scheme_order, 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

virtual

Vector representing the longitudinal part of .

(see the documentation of `hata_evol`)

Definition at line 825 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

mutable protected

Potential A associated with the symmetric tensor .

(see documentation of `Sym_tensor::p_aaa`).

Definition at line 547 of file time_slice.h.

## adm_mass_evol

Evolution_full<Tbl> Lorene::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 233 of file time_slice.h.

## B_hata_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::B_hata_evol

mutable protected

Potential associated with the symmetric tensor .

(see documentation of `Sym_tensor::p_tilde_b`).

Definition at line 552 of file time_slice.h.

## beta_evol

Evolution_std<Vector> Lorene::Time_slice::beta_evol

mutable protected inherited

Values at successive time steps of the shift vector .

Definition at line 219 of file time_slice.h.

## depth

int Lorene::Time_slice::depth

protected inherited

Number of stored time slices.

Definition at line 179 of file time_slice.h.

## ff

const Metric_flat& Lorene::Time_slice_conf::ff

protected

Pointer on the flat metric with respect to which the conformal decomposition is performed.

Definition at line 507 of file time_slice.h.

## gam_dd_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::gam_dd_evol

mutable protected inherited

Values at successive time steps of the covariant components of the induced metric .

Definition at line 198 of file time_slice.h.

## gam_uu_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::gam_uu_evol

mutable protected inherited

Values at successive time steps of the contravariant components of the induced metric .

Definition at line 203 of file time_slice.h.

## hata_evol

Evolution_std<Sym_tensor> Lorene::Time_slice_conf::hata_evol

mutable protected

Values at successive time steps of the components .

It is the conformal representation of the traceless part of the extrinsic curvature: . One can uniquely (up to the boundary conditions) define the decomposition: , where represents the longitudinal part and is the transverse-traceless part.

Definition at line 542 of file time_slice.h.

## hh_evol

Evolution_std<Sym_tensor> Lorene::Time_slice_conf::hh_evol

mutable protected

Values at successive time steps of the components .

It is the deviation of the conformal metric from the flat metric : .

Definition at line 530 of file time_slice.h.

## jtime

int Lorene::Time_slice::jtime

protected inherited

Time step index of the latest slice.

Definition at line 190 of file time_slice.h.

## k_dd_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::k_dd_evol

mutable protected inherited

Values at successive time steps of the covariant components of the extrinsic curvature tensor .

Definition at line 208 of file time_slice.h.

## k_uu_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::k_uu_evol

mutable protected inherited

Values at successive time steps of the contravariant components of the extrinsic curvature tensor .

Definition at line 213 of file time_slice.h.

## n_evol

Evolution_std<Scalar> Lorene::Time_slice::n_evol

mutable protected inherited

Values at successive time steps of the lapse function N.

Definition at line 216 of file time_slice.h.

## npsi_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::npsi_evol

mutable protected

Values at successive time steps of the factor .

Definition at line 522 of file time_slice.h.

## p_gamma

Metric* Lorene::Time_slice::p_gamma

mutable protected inherited

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

Definition at line 239 of file time_slice.h.

## p_hdirac

Vector* Lorene::Time_slice_conf::p_hdirac

mutable protected

Pointer on the vector (which vanishes in Dirac gauge), at the current time step (`jtime`).

Definition at line 571 of file time_slice.h.

## p_ln_psi

Scalar* Lorene::Time_slice_conf::p_ln_psi

mutable protected

Pointer on the logarithm of at the current time step (`jtime`).

Definition at line 566 of file time_slice.h.

## p_psi4

Scalar* Lorene::Time_slice_conf::p_psi4

mutable protected

Pointer on the factor at the current time step (`jtime`).

Definition at line 563 of file time_slice.h.

## p_tgamma

Metric* Lorene::Time_slice_conf::p_tgamma

mutable protected

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

Definition at line 560 of file time_slice.h.

## p_vec_X

Vector* Lorene::Time_slice_conf::p_vec_X

mutable protected

Pointer on the vector representing the longitudinal part of .

(see the documentation of `hata_evol`)

Definition at line 577 of file time_slice.h.

## psi_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::psi_evol

mutable protected

Values at successive time steps of the conformal factor relating the physical metric to the conformal one: .

is defined by

Definition at line 517 of file time_slice.h.

## scheme_order

int Lorene::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 187 of file time_slice.h.

## the_time

Evolution_std<double> Lorene::Time_slice::the_time

protected inherited

Time label of each slice.

Definition at line 193 of file time_slice.h.

## trk_evol

Evolution_std<Scalar> Lorene::Time_slice::trk_evol

mutable protected inherited

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

Definition at line 224 of file time_slice.h.

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

- time_slice.h
- time_slice_conf.C