/usr/include/lorene/C++/Include/excision_surf.h is in liblorene-dev 0.0.0~cvs20161116+dfsg-1.
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* Definition of Lorene class Excision_surf, friend class of Spheroid.
*
*/
/*
* Copyright (c) 2008 Jose-Luis Jaramillo & Nicolas Vasset
*
* This file is part of LORENE.
*
* LORENE is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2
* as published by the Free Software Foundation.
*
* LORENE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
#ifndef __EXCISIONSURF_H_
#define __EXCISIONSURF_H_
/*
* $Header: /cvsroot/Lorene/C++/Include/excision_surf.h,v 1.7 2014/10/13 08:52:34 j_novak Exp $
*
*/
#include "metric.h"
#include "spheroid.h"
namespace Lorene {
/**
* Surface where boundary conditions for quantities in the bulk will be calculated
* It relies on geometrical properties of the associated Spheroid\ingroup (star)
* (*** WARNING! under development***)
*
*/
class Excision_surf {
// Data :
// -----
protected:
/// The associated Spheroid object
Spheroid sph ;
///The value of the conformal factor on the 3-slice
Scalar conf_fact ;
/** The lapse defined on the 3 slice*/
Scalar lapse ;
/** The Shift 3-vector on the slice **/
Vector shift ;
/** The 3-d metric on the slice*/
Metric gamij ;
/** The 3-d extrinsic curvature on the slice */
Sym_tensor Kij ;
/** The time step for evolution in parabolic drivers */
double delta_t;
/** The internal number of timesteps for one iteration. */
double no_of_steps;
/** The 2d expansion, directly evolved from the initial excision with Einstein Equations */
Scalar expa;
/** The time derivative of the expansion, derived from Einstein equations and arbitrary evolution */
Scalar dt_expa;
// Derived data :
// ------------
protected:
mutable Scalar* p_get_BC_conf_fact_1 ; ///< Source of Neumann boundary condition on \f$ \psi \f$,
mutable Scalar* p_get_BC_lapse_1 ; ///< Source of Dirichlet boundary condition of \f$ N \f$
mutable Vector* p_get_BC_shift_1 ; ///< Source of Dirichlet BC for the shift vector \f$ \beta^{i} \f$
mutable Scalar* p_get_BC_Npsi_1 ; ///< Source of Neumann boundary condition on \f$ \psi \f$.
mutable Scalar* p_get_BC_conf_fact_2 ; ///< Source of Neumann boundary condition on \f$ \psi \f$,
mutable Scalar* p_get_BC_conf_fact_3 ; ///< Source of Neumann boundary condition on \f$ \psi \f$,
mutable Scalar* p_get_BC_conf_fact_4 ; ///< Source of Birichlet boundary condition on \f$ \psi \f$,
mutable Scalar* p_get_BC_lapse_2 ; ///< Source of Dirichlet boundary condition of \f$ N \f$
mutable Scalar* p_get_BC_lapse_3 ; ///< Source of Dirichlet condtion on \f$ N \f$, based on einstein equations.
mutable Scalar* p_get_BC_lapse_4 ; ///< Source of Dirichlet condtion on \f$ N \f$, based on einstein equations (conservation of isotropic gauge)
mutable Scalar* p_derive_t_expa ; ///< Computation of an updated expansion scalar.
mutable Vector* p_get_BC_shift_2 ; ///< Source of Dirichlet BC for the shift vector \f$ \beta^{i} \f$
mutable Vector* p_get_BC_shift_3 ; ///< Source of Dirichlet BC for the shift vector \f$ \beta^{i} \f$, partly derived from kinematical relation
mutable Vector* p_get_BC_shift_4 ; ///< Source of Dirichlet BC for the shift vector \f$ \beta^{i} \f$, partly from projection of Einstein Equations
mutable Scalar* p_get_BC_Npsi_2 ; ///< Source of Dirichlet boundary condition on \f$ N \psi \f$.
mutable Scalar* p_get_BC_Npsi_3 ; ///< Source of Dirichlet boundary condition on \f$ N \psi \f$.
mutable Scalar* p_get_BC_Npsi_4 ; ///< Source of Dirichlet boundary condition on \f$ N \psi \f$.
mutable Scalar* p_get_BC_Npsi_5 ; ///< Source of Neumann boundary condition on \f$ N \psi \f$.
// Constructors - Destructor
// -------------------------
public:
/** Constructor of an excision surface embedded in a 3-slice (\c Time_slice ) of 3+1
* formalism.
* This is done from the \c Time_slice data.
* @param h_in : the location of the surface \e r = h_in (WARNING:must be
defined on a mono-domain angular grid)
* @param gij : the 3-metric on the 3slice
* @param Kij : the extrinsic curvature of the 3-slice
* (covariant representation)
* @param timestep : time interval associated with the parabolic-driven boundary conditions.
* @param int_nos : Number of iterations to be done during timestep.
*/
Excision_surf(const Scalar& h_in, const Metric& gij, const Sym_tensor& Kij2, const Scalar& ppsi, const Scalar& nn, const Vector& beta, double timestep, int int_nos) ;
Excision_surf(const Excision_surf& ) ; ///< Copy constructor
/// Constructor from a file (see \c sauve(FILE*) )
Excision_surf(FILE* ) ;
virtual ~Excision_surf() ; ///< Destructor
// Memory management
// -----------------
protected:
/// Deletes all the derived quantities
virtual void del_deriv() const ;
/// Sets to \c 0x0 all the pointers on derived quantities
void set_der_0x0() const ;
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Excision_surf
void operator=(const Excision_surf&) ;
// Functions/Accessors
//---------------------
/** Computes the parameters for the hyperbolic evolution in set_expa_hyperb(), so that the expansion has a C1 matching
* with initial data. Sets also values for expa() and dt_expa() accordingly with initial conditions */
void get_evol_params_from_ID(double alpha, double beta, double gamma, Scalar& Ee, Vector& Jj, Sym_tensor& Ss) ;
///Sets a new value for expansion rescaled over lapse (and its derivative), obtained by parabolic evolution.
void set_expa_parab(double c_theta_lap, double c_theta_fin, Scalar& expa_fin) ;
/**Sets a new value for expansion rescaled over lapse (and its derivative), obtained by hyperbolic evolution.
* Parameters for the hyperbolic driver are determined by the function Excision_surf::get_evol_params_from_ID()
* so that the expansion stays of regularity $C^{1}$ throughout.
* All manipulated quantities are 2-dimensional.
*/
void set_expa_hyperb(double alph0, double beta0, double gamma0) ;
// Accessors
// ---------
public:
/// Returns the spheroid
const Spheroid& get_sph() const {return sph; };
/// Returns the conformal factor associated with the surface
const Scalar& get_conf_fact() const {return conf_fact; } ;
/// Returns the lapse function
const Scalar& get_lapse() const {return lapse ; } ;
/// Returns the shift vector field.
const Vector& get_shift() const {return shift ; } ;
/// Returns the symmetric tensor \f$ gamij \f$
const Metric& get_gamij() const {return gamij ; } ;
/// returns the 3-d extrinsic curvature \f$ K_{ij}\f$
const Sym_tensor& get_Kij() const {return Kij ; } ;
/// Returns the timestep used for evolution.
double get_delta_t() const {return delta_t ;};
/// Returns the internal number of timesteps for one iteration.
double get_no_of_steps() const {return no_of_steps ;};
/// Returns the assumed expansion associated to the excised surface at t.
const Scalar & get_expa() const {return expa; };
/// Returns the assumed time derivative of the expansion at t, evolved by functions of this class;
const Scalar& get_dt_expa() const {return dt_expa;} ;
/// Sets a new spheroid from data
Spheroid& set_sph() {del_deriv() ; return sph ;};
/// Sets the value of the conformal factor
Scalar& set_conf_fact() {del_deriv() ; return conf_fact ; } ;
/// Sets the lapse function
Scalar& set_lapse() {del_deriv() ; return lapse ; } ;
/// Sets the shift vector field
Vector& set_shift() {del_deriv() ; return shift ; } ;
/// Sets the 3d metric of the TimeSlice
Metric& set_gamij() {del_deriv() ; return gamij ; } ;
/// Sets the extrinsic curvature
Sym_tensor& set_Kij() {del_deriv() ; return Kij ; } ;
double set_delta_t() {del_deriv() ; return delta_t ; } ;
double set_no_of_steps() {del_deriv() ; return no_of_steps ; } ;
/// Sets the expansion function on the surface at time t (considering to protect this function)
Scalar& set_expa() {del_deriv(); return expa;};
/// Sets the time derivative of the expansion function on the surface at time t (considering to protect this function)
Scalar& set_dt_expa() {del_deriv(); return dt_expa;};
// Computational functions
// -----------------------
public:
/// Source for a Neumann BC on the conformal factor. If boolean isMOTS is false, it is based on expansion value of the spheroid or the value of exppa; it is based on zero expansion if isMOTS is true.
const Scalar& get_BC_conf_fact_1(bool isMOTS = false) const ;
// Source for an arbitrary Dirichlet BC on the lapse
const Scalar& get_BC_lapse_1(double value) const ;
// Source for a global Dirichlet BC on the shift, imposing a conformal Killing symmetry on \f$ \varphi \f$.
const Vector& get_BC_shift_1(double Omega) const ;
// Source for a Dirichlet arbitrary BC on (N*Psi1)
const Scalar& get_BC_Npsi_1(double value) const ;
/// Source for the Dirichlet BC on the conformal factor, based on a parabolic driver for the conformal factor
const Scalar& get_BC_conf_fact_2(double c_psi_lap, double c_psi_fin, Scalar& expa_fin) const ;
/// Source for the Neumann BC on the conformal factor, based on a parabolic driver for the expansio
const Scalar& get_BC_conf_fact_3(double c_theta_lap, double c_theta_fin, Scalar& expa_fin) const ;
/// Source for the Dirchlet BC on the conformal factor, based on the consistency condition derived from the trace
const Scalar& get_BC_conf_fact_4() const ;
/// Source for Dirichlet BC on the lapse, based on a parabolic driver towards arbitrary constant value
const Scalar& get_BC_lapse_2(double lapse_fin, double c_lapse_lap, double c_lapse_fi) const ;
/// Source for Dirichlet BC on the lapse, based on einstein equations
const Scalar& get_BC_lapse_3(Scalar& dttheta, Scalar& Ee, Vector& Jj, Sym_tensor& Sij, bool sph_sym = true) const ;
/// Source for Dirichlet BC on the lapse, based on einstein equations (conservation of isotropic gauge)
const Scalar& get_BC_lapse_4 (Scalar& old_nn, Vector& beta_point, Sym_tensor& strain_tens) const ;
/// Forms the prospective time derivative for the expansion using projected Einstein equations. Does NOT modify the member dt_expa: do it by hand!
const Scalar& derive_t_expa(Scalar& Ee, Vector& Jj, Sym_tensor& Sij) const;
/// Source for a Dirichlet BC on the shift, based on a Parabolic driver; no assumptions are made except a global conformal Killing symmetry.
const Vector& get_BC_shift_2(double c_bb_lap, double c_bb_fin, double c_V_lap, double epsilon) const ;
/// Source for a Dirichlet BC on the shift, based on a Parabolic driver; Radial part is dealt with using a kinematical relation.
const Vector& get_BC_shift_3(Scalar& dtpsi, double c_V_lap, double epsilon) const ;
/// Source for a Dirichlet BC on the shift, based on a Parabolic driver; Radial part is dealt with using projection of Einstein Equations.
const Vector & get_BC_shift_4(Scalar& dttheta, Scalar& Ee, Vector& Jj, Sym_tensor& Sij, double c_V_lap, double epsilon, bool sph_sym= true) const ;
/// Source for the Dirichlet BC on (N*Psi1), based on a parabolic driver.
const Scalar& get_BC_Npsi_2(double value, double c_npsi_lap, double c_npsi_fin) const ;
/// Source for the Dirichlet BC on (N*Psi1), with Kerr_Schild-like form for the lapse boundary.
const Scalar& get_BC_Npsi_3(double n_0, double beta) const ;
/// Source for a Dirichlet BC on (N*Psi1), fixing a constant surface gravity in space and time.
const Scalar& get_BC_Npsi_4(double Kappa) const ;
/// Source for a Neumann BC on (N*Psi1), fixing a constant surface gravity in space and time.
const Scalar& get_BC_Npsi_5(double Kappa) const ;
// Outputs
// -------
public:
virtual void sauve(FILE *) const ; ///< Save in a file
/// Display
friend ostream& operator<<(ostream& , const Spheroid& ) ;
};
ostream& operator<<(ostream& , const Spheroid& ) ;
}
#endif
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