boson_star_equil.C
/*
* Method Boson_star::equilibrium
*
* (see file boson_star.h for documentation).
*/
/*
* Copyright (c) 2012 Claire Some, Eric Gourgoulhon
*
* 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 as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* 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
*
*/
char boson_star_equil_C[] = "$Header: /cvsroot/Lorene/C++/Source/Compobj/boson_star_equil.C,v 1.6 2014/10/13 08:52:49 j_novak Exp $" ;
/*
* $Id: boson_star_equil.C,v 1.6 2014/10/13 08:52:49 j_novak Exp $
* $Log: boson_star_equil.C,v $
* Revision 1.6 2014/10/13 08:52:49 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.5 2014/10/06 15:13:04 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.4 2013/04/03 12:10:13 e_gourgoulhon
* Added member kk to Compobj; suppressed tkij
*
* Revision 1.3 2012/12/03 15:27:30 c_some
* Small changes
*
* Revision 1.2 2012/11/23 15:43:05 c_some
* Small changes
*
* Revision 1.1 2012/11/22 16:04:12 c_some
* New class Boson_star
*
*
* $Header: /cvsroot/Lorene/C++/Source/Compobj/boson_star_equil.C,v 1.6 2014/10/13 08:52:49 j_novak Exp $
*
*/
// Headers C
#include <cmath>
// Headers Lorene
#include "boson_star.h"
#include "param.h"
#include "tenseur.h"
#include "graphique.h"
#include "utilitaires.h"
#include "unites.h"
namespace Lorene {
void Boson_star::equilibrium(double, double,
int nzadapt, const Tbl& phi_limit, const Itbl& icontrol,
const Tbl& control, Tbl& diff, Param*) {
// Fundamental constants and units
// -------------------------------
using namespace Unites ;
// For the display
// ---------------
char display_bold[]="x[1m" ; display_bold[0] = 27 ;
char display_normal[] = "x[0m" ; display_normal[0] = 27 ;
// Grid parameters
// ---------------
const Mg3d* mg = mp.get_mg() ;
int nz = mg->get_nzone() ; // total number of domains
// The following is required to initialize mp_prev as a Map_et:
Map_et& mp_et = dynamic_cast<Map_et&>(mp) ;
// Index of the point at phi=0, theta=pi/2 at the surface of the star:
int nzet = nzadapt ; //## to be checked
assert(mg->get_type_t() == SYM) ;
int l_b = nzet - 1 ;
int j_b = mg->get_nt(l_b) - 1 ;
int k_b = 0 ;
// Value of the enthalpy defining the surface of the star
// double ent_b = phi_limit(nzet-1) ;
// Parameters to control the iteration
// -----------------------------------
int mer_max = icontrol(0) ;
// int mer_rot = icontrol(1) ;
// int mer_change_omega = icontrol(2) ;
// int mer_fix_omega = icontrol(3) ;
//## int mer_mass = icontrol(4) ;
int mermax_poisson = icontrol(5) ;
int mer_triax = icontrol(6) ;
//## int delta_mer_kep = icontrol(7) ;
double precis = control(0) ;
// double omega_ini = control(1) ;
double relax = control(2) ;
double relax_prev = double(1) - relax ;
double relax_poisson = control(3) ;
// double thres_adapt = control(4) ;
double ampli_triax = control(5) ;
double precis_adapt = control(6) ;
// Error indicators
// ----------------
diff.set_etat_qcq() ;
double& diff_phi = diff.set(0) ;
double& diff_nuf = diff.set(1) ;
double& diff_nuq = diff.set(2) ;
// double& diff_dzeta = diff.set(3) ;
// double& diff_ggg = diff.set(4) ;
double& diff_shift_x = diff.set(5) ;
double& diff_shift_y = diff.set(6) ;
double& vit_triax = diff.set(7) ;
// Parameters for the function Map_et::adapt
// -----------------------------------------
Param par_adapt ;
int nitermax = 100 ;
int niter ;
int adapt_flag = 1 ; // 1 = performs the full computation,
// 0 = performs only the rescaling by
// the factor alpha_r
int nz_search = nzet + 1 ; // Number of domains for searching the enthalpy
// isosurfaces
double alpha_r ;
double reg_map = 1. ; // 1 = regular mapping, 0 = contracting mapping
par_adapt.add_int(nitermax, 0) ; // maximum number of iterations to
// locate zeros by the secant method
par_adapt.add_int(nzadapt, 1) ; // number of domains where the adjustment
// to the isosurfaces of ent is to be
// performed
par_adapt.add_int(nz_search, 2) ; // number of domains to search for
// the enthalpy isosurface
par_adapt.add_int(adapt_flag, 3) ; // 1 = performs the full computation,
// 0 = performs only the rescaling by
// the factor alpha_r
par_adapt.add_int(j_b, 4) ; // theta index of the collocation point
// (theta_*, phi_*)
par_adapt.add_int(k_b, 5) ; // theta index of the collocation point
// (theta_*, phi_*)
par_adapt.add_int_mod(niter, 0) ; // number of iterations actually used in
// the secant method
par_adapt.add_double(precis_adapt, 0) ; // required absolute precision in
// the determination of zeros by
// the secant method
par_adapt.add_double(reg_map, 1) ; // 1. = regular mapping, 0 = contracting mapping
par_adapt.add_double(alpha_r, 2) ; // factor by which all the radial
// distances will be multiplied
par_adapt.add_tbl(phi_limit, 0) ; // array of values of the field Phi
// to define the isosurfaces.
// Parameters for the function Map_et::poisson for nuf
// ----------------------------------------------------
double precis_poisson = 1.e-16 ;
// Preparations
// ------------
// Cartesian components of the shift vector are required
beta.change_triad( mp.get_bvect_cart() ) ;
Cmp cssjm1_nuf(ssjm1_nuf) ;
Cmp cssjm1_nuq(ssjm1_nuq) ;
Cmp cssjm1_tggg(ssjm1_tggg) ;
Cmp cssjm1_khi(ssjm1_khi) ;
Tenseur cssjm1_wshift(mp, 1, CON, mp.get_bvect_cart() ) ;
cssjm1_wshift.set_etat_qcq() ;
for (int i=1; i<=3; i++) {
cssjm1_wshift.set(i-1) = ssjm1_wshift(i) ;
}
Tenseur cshift(mp, 1, CON, mp.get_bvect_cart() ) ;
cshift.set_etat_qcq() ;
for (int i=1; i<=3; i++) {
cshift.set(i-1) = -beta(i) ;
}
Tenseur cw_shift(mp, 1, CON, mp.get_bvect_cart() ) ;
cw_shift.set_etat_qcq() ;
for (int i=1; i<=3; i++) {
cw_shift.set(i-1) = w_shift(i) ;
}
Tenseur ckhi_shift(mp) ;
ckhi_shift.set_etat_qcq() ;
ckhi_shift.set() = khi_shift ;
Param par_poisson_nuf ;
par_poisson_nuf.add_int(mermax_poisson, 0) ; // maximum number of iterations
par_poisson_nuf.add_double(relax_poisson, 0) ; // relaxation parameter
par_poisson_nuf.add_double(precis_poisson, 1) ; // required precision
par_poisson_nuf.add_int_mod(niter, 0) ; // number of iterations actually used
par_poisson_nuf.add_cmp_mod( cssjm1_nuf ) ;
Param par_poisson_nuq ;
par_poisson_nuq.add_int(mermax_poisson, 0) ; // maximum number of iterations
par_poisson_nuq.add_double(relax_poisson, 0) ; // relaxation parameter
par_poisson_nuq.add_double(precis_poisson, 1) ; // required precision
par_poisson_nuq.add_int_mod(niter, 0) ; // number of iterations actually used
par_poisson_nuq.add_cmp_mod( cssjm1_nuq ) ;
Param par_poisson_tggg ;
par_poisson_tggg.add_int(mermax_poisson, 0) ; // maximum number of iterations
par_poisson_tggg.add_double(relax_poisson, 0) ; // relaxation parameter
par_poisson_tggg.add_double(precis_poisson, 1) ; // required precision
par_poisson_tggg.add_int_mod(niter, 0) ; // number of iterations actually used
par_poisson_tggg.add_cmp_mod( cssjm1_tggg ) ;
double lambda_tggg ;
par_poisson_tggg.add_double_mod( lambda_tggg ) ;
Param par_poisson_dzeta ;
double lbda_grv2 ;
par_poisson_dzeta.add_double_mod( lbda_grv2 ) ;
// Parameters for the function Scalar::poisson_vect
// -------------------------------------------------
Param par_poisson_vect ;
par_poisson_vect.add_int(mermax_poisson, 0) ; // maximum number of iterations
par_poisson_vect.add_double(relax_poisson, 0) ; // relaxation parameter
par_poisson_vect.add_double(precis_poisson, 1) ; // required precision
par_poisson_vect.add_cmp_mod( cssjm1_khi ) ;
par_poisson_vect.add_tenseur_mod( cssjm1_wshift ) ;
par_poisson_vect.add_int_mod(niter, 0) ;
// Initializations
// ---------------
//## Spherical components of the shift vector are restored
beta.change_triad( mp.get_bvect_spher() ) ;
update_metric() ;
//## Back to Cartesian components
beta.change_triad( mp.get_bvect_cart() ) ;
// Quantities at the previous step :
Map_et mp_prev = mp_et ;
Scalar rphi_prev = rphi ;
Scalar logn_prev = logn ;
Scalar dzeta_prev = dzeta ;
// Creation of uninitialized tensors:
Scalar source_nuf(mp) ; // source term in the equation for nuf
Scalar source_nuq(mp) ; // source term in the equation for nuq
Scalar source_dzf(mp) ; // matter source term in the eq. for dzeta
Scalar source_dzq(mp) ; // quadratic source term in the eq. for dzeta
Scalar source_tggg(mp) ; // source term in the eq. for tggg
Vector source_shift(mp, CON, mp.get_bvect_cart()) ;
// source term for shift
ofstream fichconv("convergence.d") ; // Output file for diff_phi
fichconv << "# diff_phi GRV2 max_triax vit_triax" << endl ;
ofstream fichevol("evolution.d") ; // Output file for various quantities
fichevol <<
"# |dH/dr_eq/dH/dr_pole| r_pole/r_eq rphi_c"
<< endl ;
diff_phi = 1 ;
double err_grv2 = 1 ;
double max_triax_prev = 0 ; // Triaxial amplitude at previous step
//=========================================================================
// Start of iteration
//=========================================================================
for(int mer=0 ; (diff_phi > precis) && (mer<mer_max) ; mer++ ) {
cout << "-----------------------------------------------" << endl ;
cout << "step: " << mer << endl ;
cout << "diff_phi = " << display_bold << diff_phi << display_normal
<< endl ;
cout << "err_grv2 = " << err_grv2 << endl ;
fichconv << mer ;
fichevol << mer ;
//-----------------------------------------------
// Sources of the Poisson equations
//-----------------------------------------------
// Source for nu
// -------------
Scalar bet = log(bbb) ;
bet.std_spectral_base() ;
Vector d_logn = logn.derive_cov( mp.flat_met_spher() ) ;
Vector d_bet = bet.derive_cov( mp.flat_met_spher() ) ;
Scalar s_euler = stress_euler.trace(gamma) ;
source_nuf = qpig * a_car *( ener_euler + s_euler ) ;
source_nuq = ak_car - d_logn(1)*(d_logn(1)+d_bet(1))
- d_logn(2)*(d_logn(2)+d_bet(2))
- d_logn(3)*(d_logn(3)+d_bet(3)) ;
source_nuf.std_spectral_base() ;
source_nuq.std_spectral_base() ;
// Source for dzeta
// ----------------
source_dzf = 2 * qpig * a_car * b_car * stress_euler(3,3) ;
source_dzf.std_spectral_base() ;
source_dzq = 1.5 * ak_car
- d_logn(1)*d_logn(1) - d_logn(2)*d_logn(2) - d_logn(3)*d_logn(3) ;
source_dzq.std_spectral_base() ;
// Source for tggg
// ---------------
source_tggg = 2 * qpig * nn * a_car * bbb * (s_euler - b_car * stress_euler(3,3)) ;
source_tggg.std_spectral_base() ;
source_tggg.mult_rsint() ;
// Source for shift
// ----------------
// Matter term:
Vector mom_euler_cart = mom_euler ;
mom_euler_cart.change_triad(mp.get_bvect_cart()) ;
source_shift = (-4*qpig) * nn * a_car * mom_euler_cart ;
// Quadratic terms:
Vector vtmp = 6 * bet.derive_con( mp.flat_met_spher() )
- 2 * logn.derive_con( mp.flat_met_spher() ) ;
Vector squad = nn * contract(kk, 1, vtmp, 0) / b_car ;
squad.change_triad(mp.get_bvect_cart()) ;
source_shift = source_shift + squad.up(0, mp.flat_met_cart() ) ;
//----------------------------------------------
// Resolution of the Poisson equation for nuf
//----------------------------------------------
source_nuf.poisson(par_poisson_nuf, nuf) ;
cout << "Test of the Poisson equation for nuf :" << endl ;
Tbl err = source_nuf.test_poisson(nuf, cout, true) ;
diff_nuf = err(0, 0) ;
//---------------------------------------
// Triaxial perturbation of nuf
//---------------------------------------
if (mer == mer_triax) {
if ( mg->get_np(0) == 1 ) {
cout <<
"Boson_star::equilibrium: np must be stricly greater than 1"
<< endl << " to set a triaxial perturbation !" << endl ;
abort() ;
}
const Coord& phi = mp.phi ;
const Coord& sint = mp.sint ;
Scalar perturb(mp) ;
perturb = 1 + ampli_triax * sint*sint * cos(2*phi) ;
nuf = nuf * perturb ;
nuf.std_spectral_base() ; // set the bases for spectral expansions
// to be the standard ones for a
// scalar field
}
// Monitoring of the triaxial perturbation
// ---------------------------------------
const Valeur& va_nuf = nuf.get_spectral_va() ;
va_nuf.coef() ; // Computes the spectral coefficients
double max_triax = 0 ;
if ( mg->get_np(0) > 1 ) {
for (int l=0; l<nz; l++) { // loop on the domains
for (int j=0; j<mg->get_nt(l); j++) {
for (int i=0; i<mg->get_nr(l); i++) {
// Coefficient of cos(2 phi) :
double xcos2p = (*(va_nuf.c_cf))(l, 2, j, i) ;
// Coefficient of sin(2 phi) :
double xsin2p = (*(va_nuf.c_cf))(l, 3, j, i) ;
double xx = sqrt( xcos2p*xcos2p + xsin2p*xsin2p ) ;
max_triax = ( xx > max_triax ) ? xx : max_triax ;
}
}
}
}
cout << "Triaxial part of nuf : " << max_triax << endl ;
//----------------------------------------------
// Resolution of the Poisson equation for nuq
//----------------------------------------------
source_nuq.poisson(par_poisson_nuq, nuq) ;
cout << "Test of the Poisson equation for nuq :" << endl ;
err = source_nuq.test_poisson(nuq, cout, true) ;
diff_nuq = err(0, 0) ;
//---------------------------------------------------------
// Resolution of the vector Poisson equation for the shift
//---------------------------------------------------------
for (int i=1; i<=3; i++) {
if(source_shift(i).get_etat() != ETATZERO) {
if(source_shift(i).dz_nonzero()) {
assert( source_shift(i).get_dzpuis() == 4 ) ;
}
else{
(source_shift.set(i)).set_dzpuis(4) ;
}
}
}
double lambda_shift = double(1) / double(3) ;
if ( mg->get_np(0) == 1 ) {
lambda_shift = 0 ;
}
Tenseur csource_shift(mp, 1, CON, mp.get_bvect_cart() ) ;
csource_shift.set_etat_qcq() ;
for (int i=1; i<=3; i++) {
csource_shift.set(i-1) = source_shift(i) ;
}
csource_shift.set(2).set_etat_zero() ; //## bizarre...
csource_shift.poisson_vect(lambda_shift, par_poisson_vect,
cshift, cw_shift, ckhi_shift) ;
for (int i=1; i<=3; i++) {
beta.set(i) = - cshift(i-1) ;
beta.set(i).set_dzpuis(0) ; //## bizarre...
w_shift.set(i) = cw_shift(i-1) ;
}
khi_shift = ckhi_shift() ;
cout << "Test of the Poisson equation for shift_x :" << endl ;
err = source_shift(1).test_poisson(-beta(1), cout, true) ;
diff_shift_x = err(0, 0) ;
cout << "Test of the Poisson equation for shift_y :" << endl ;
err = source_shift(2).test_poisson(-beta(2), cout, true) ;
diff_shift_y = err(0, 0) ;
// Computation of tnphi and nphi from the Cartesian components
// of the shift
// -----------------------------------------------------------
fait_nphi() ;
//----------------------------------------------------
// Adaptation of the mapping to the new enthalpy field
//----------------------------------------------------
// Shall the adaptation be performed ?
// ---------------------------------
adapt_flag = 0 ; // No adaptation of the mapping
mp_prev = mp_et ;
//---------------------------------------------------------
// Matter source terms in the gravitational field equations
//---------------------------------------------------------
//## Computation of tnphi and nphi from the Cartesian components
// of the shift for the test in hydro_euler():
fait_nphi() ;
// Update of the energy-momentum tensor
update_ener_mom() ;
//-------------------------------------------------------
// 2-D Poisson equation for tggg
//-------------------------------------------------------
Cmp csource_tggg(source_tggg) ;
Cmp ctggg(tggg) ;
mp.poisson2d(csource_tggg, mp.cmp_zero(), par_poisson_tggg,
ctggg) ;
tggg = ctggg ;
//-------------------------------------------------------
// 2-D Poisson equation for dzeta
//-------------------------------------------------------
Cmp csource_dzf(source_dzf) ;
Cmp csource_dzq(source_dzq) ;
Cmp cdzeta(dzeta) ;
mp.poisson2d(csource_dzf, csource_dzq, par_poisson_dzeta,
cdzeta) ;
dzeta = cdzeta ;
err_grv2 = lbda_grv2 - 1;
cout << "GRV2: " << err_grv2 << endl ;
//---------------------------------------
// Computation of the metric coefficients (except for N^phi)
//---------------------------------------
// Relaxations on nu and dzeta :
if (mer >= 10) {
logn = relax * logn + relax_prev * logn_prev ;
dzeta = relax * dzeta + relax_prev * dzeta_prev ;
}
// Update of the metric coefficients N, A, B and computation of K_ij :
//## Spherical components of the shift vector are restored
beta.change_triad( mp.get_bvect_spher() ) ;
update_metric() ;
//## Back to Cartesian components
beta.change_triad( mp.get_bvect_cart() ) ;
//-----------------------
// Informations display
//-----------------------
cout << *this << endl ;
//------------------------------------------------------------
// Relative change in Phi with respect to previous step
//------------------------------------------------------------
Tbl diff_phi_tbl = diffrel( rphi, rphi_prev ) ;
diff_phi = diff_phi_tbl(0) ;
for (int l=1; l<nzet; l++) {
diff_phi += diff_phi_tbl(l) ;
}
diff_phi /= nzet ;
fichconv << " " << log10( fabs(diff_phi) + 1.e-16 ) ;
fichconv << " " << log10( fabs(err_grv2) + 1.e-16 ) ;
fichconv << " " << log10( fabs(max_triax) + 1.e-16 ) ;
vit_triax = 0 ;
if ( (mer > mer_triax+1) && (max_triax_prev > 1e-13) ) {
vit_triax = (max_triax - max_triax_prev) / max_triax_prev ;
}
fichconv << " " << vit_triax ;
//------------------------------
// Recycling for the next step
//------------------------------
rphi_prev = rphi ;
logn_prev = logn ;
dzeta_prev = dzeta ;
max_triax_prev = max_triax ;
fichconv << endl ;
fichevol << endl ;
fichconv.flush() ;
fichevol.flush() ;
} // End of main loop
//=========================================================================
// End of iteration
//=========================================================================
ssjm1_nuf = cssjm1_nuf ;
ssjm1_nuq = cssjm1_nuq ;
ssjm1_tggg = cssjm1_tggg ;
ssjm1_khi = cssjm1_khi ;
for (int i=1; i<=3; i++) {
ssjm1_wshift.set(i) = cssjm1_wshift(i-1) ;
}
// Spherical components of the shift vector are restored
beta.change_triad( mp.get_bvect_spher() ) ;
fichconv.close() ;
fichevol.close() ;
}
}
Lorene::Boson_star::rphi
Scalar rphi
Real part of the scalar field Phi.
Definition boson_star.h:72
Lorene::Boson_star::equilibrium
virtual void equilibrium(double rphi_c, double iphi_c, int nzadapt, const Tbl &ent_limit, const Itbl &icontrol, const Tbl &control, Tbl &diff, Param *=0x0)
Solves the equation satisfied by the scalar field.
Definition boson_star_equil.C:70
Lorene::Boson_star::update_ener_mom
void update_ener_mom()
Computes the 3+1 components of the energy-momentum tensor (E, P_i and S_{ij}) from the values of the ...
Definition boson_star.C:211
Lorene::Cmp
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition cmp.h:446
Lorene::Cmp::set_etat_zero
void set_etat_zero()
Sets the logical state to ETATZERO (zero).
Definition cmp.C:289
Lorene::Compobj_QI::ak_car
Scalar ak_car
Scalar .
Definition compobj.h:315
Lorene::Compobj_QI::b_car
Scalar b_car
Square of the metric factor B.
Definition compobj.h:293
Lorene::Compobj_QI::bbb
Scalar bbb
Metric factor B.
Definition compobj.h:290
Lorene::Compobj_QI::a_car
Scalar a_car
Square of the metric factor A.
Definition compobj.h:287
Lorene::Compobj::kk
Sym_tensor kk
Extrinsic curvature tensor .
Definition compobj.h:153
Lorene::Compobj::mom_euler
Vector mom_euler
Total 3-momentum density in the Eulerian frame.
Definition compobj.h:147
Lorene::Compobj::stress_euler
Sym_tensor stress_euler
Stress tensor with respect to the Eulerian observer.
Definition compobj.h:150
Lorene::Compobj::ener_euler
Scalar ener_euler
Total energy density E in the Eulerian frame.
Definition compobj.h:144
Lorene::Compobj::gamma
Metric gamma
3-metric
Definition compobj.h:141
Lorene::Compobj::nn
Scalar nn
Lapse function N .
Definition compobj.h:135
Lorene::Compobj::beta
Vector beta
Shift vector .
Definition compobj.h:138
Lorene::Compobj::mp
Map & mp
Mapping describing the coordinate system (r,theta,phi).
Definition compobj.h:132
Lorene::Coord
Active physical coordinates and mapping derivatives.
Definition coord.h:90
Lorene::Itbl
Basic integer array class.
Definition itbl.h:122
Lorene::Map_et
Radial mapping of rather general form.
Definition map.h:2752
Lorene::Mg3d
Multi-domain grid.
Definition grilles.h:273
Lorene::Mg3d::get_type_t
int get_type_t() const
Returns the type of sampling in the direction: SYM : : symmetry with respect to the equatorial pl...
Definition grilles.h:485
Lorene::Mg3d::get_np
int get_np(int l) const
Returns the number of points in the azimuthal direction ( ) in domain no. l.
Definition grilles.h:462
Lorene::Mg3d::get_nt
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition grilles.h:457
Lorene::Mg3d::get_nzone
int get_nzone() const
Returns the number of domains.
Definition grilles.h:448
Lorene::Mg3d::get_nr
int get_nr(int l) const
Returns the number of points in the radial direction ( ) in domain no. l.
Definition grilles.h:452
Lorene::Param
Parameter storage.
Definition param.h:125
Lorene::Param::add_double
void add_double(const double &x, int position=0)
Adds the the address of a new double to the list.
Definition param.C:315
Lorene::Param::add_cmp_mod
void add_cmp_mod(Cmp &ti, int position=0)
Adds the address of a new modifiable Cmp to the list.
Definition param.C:1004
Lorene::Param::add_double_mod
void add_double_mod(double &x, int position=0)
Adds the address of a new modifiable double to the list.
Definition param.C:453
Lorene::Param::add_int_mod
void add_int_mod(int &n, int position=0)
Adds the address of a new modifiable int to the list.
Definition param.C:385
Lorene::Param::add_tenseur_mod
void add_tenseur_mod(Tenseur &ti, int position=0)
Adds the address of a new modifiable Tenseur to the list.
Definition param.C:1142
Lorene::Param::add_int
void add_int(const int &n, int position=0)
Adds the address of a new int to the list.
Definition param.C:246
Lorene::Param::add_tbl
void add_tbl(const Tbl &ti, int position=0)
Adds the address of a new Tbl to the list.
Definition param.C:522
Lorene::Scalar
Tensor field of valence 0 (or component of a tensorial field).
Definition scalar.h:387
Lorene::Scalar::derive_cov
const Vector & derive_cov(const Metric &gam) const
Returns the gradient (1-form = covariant vector) of *this.
Definition scalar_deriv.C:390
Lorene::Scalar::poisson
Scalar poisson() const
Solves the scalar Poisson equation with *this as a source.
Definition scalar_pde.C:136
Lorene::Scalar::std_spectral_base
virtual void std_spectral_base()
Sets the spectral bases of the Valeur va to the standard ones for a scalar field.
Definition scalar.C:784
Lorene::Scalar::test_poisson
Tbl test_poisson(const Scalar &uu, ostream &ostr, bool detail=false) const
Checks if a Poisson equation with *this as a source has been correctly solved.
Definition scalar_test_poisson.C:60
Lorene::Scalar::mult_rsint
void mult_rsint()
Multiplication by everywhere; dzpuis is not changed.
Definition scalar_r_manip.C:281
Lorene::Scalar::derive_con
const Vector & derive_con(const Metric &gam) const
Returns the "contravariant" derivative of *this with respect to some metric , by raising the index of...
Definition scalar_deriv.C:402
Lorene::Star_QI::w_shift
Vector w_shift
Vector used in the decomposition of shift , following Shibata's prescription [Prog.
Definition compobj.h:529
Lorene::Star_QI::logn
Scalar logn
Logarithm of the lapse N .
Definition compobj.h:495
Lorene::Star_QI::nuq
Scalar nuq
Part of the Metric potential = logn generated by the quadratic terms.
Definition compobj.h:510
Lorene::Star_QI::ssjm1_khi
Scalar ssjm1_khi
Effective source at the previous step for the resolution of the Poisson equation for the scalar by m...
Definition compobj.h:569
Lorene::Star_QI::nuf
Scalar nuf
Part of the Metric potential = logn generated by the matter terms.
Definition compobj.h:505
Lorene::Star_QI::ssjm1_nuq
Scalar ssjm1_nuq
Effective source at the previous step for the resolution of the Poisson equation for nuq by means of ...
Definition compobj.h:551
Lorene::Star_QI::update_metric
void update_metric()
Computes metric coefficients from known potentials.
Definition star_QI.C:410
Lorene::Star_QI::ssjm1_wshift
Vector ssjm1_wshift
Effective source at the previous step for the resolution of the vector Poisson equation for .
Definition compobj.h:578
Lorene::Star_QI::fait_nphi
void fait_nphi()
Computes tnphi and nphi from the Cartesian components of the shift, stored in shift .
Definition star_QI.C:386
Lorene::Star_QI::khi_shift
Scalar khi_shift
Scalar used in the decomposition of shift , following Shibata's prescription [Prog.
Definition compobj.h:539
Lorene::Star_QI::ssjm1_nuf
Scalar ssjm1_nuf
Effective source at the previous step for the resolution of the Poisson equation for nuf by means of ...
Definition compobj.h:545
Lorene::Star_QI::tggg
Scalar tggg
Metric potential .
Definition compobj.h:516
Lorene::Star_QI::ssjm1_tggg
Scalar ssjm1_tggg
Effective source at the previous step for the resolution of the Poisson equation for tggg .
Definition compobj.h:561
Lorene::Star_QI::dzeta
Scalar dzeta
Metric potential .
Definition compobj.h:513
Lorene::Tbl
Basic array class.
Definition tbl.h:161
Lorene::Tbl::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tbl.C:361
Lorene::Tbl::set
double & set(int i)
Read/write of a particular element (index i) (1D case).
Definition tbl.h:281
Lorene::Tenseur
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition tenseur.h:301
Lorene::Tenseur::set
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition tenseur.C:824
Lorene::Tenseur::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tenseur.C:636
Lorene::Tenseur::poisson_vect
void poisson_vect(double lambda, Param &par, Tenseur &shift, Tenseur &vect, Tenseur &scal) const
Solves the vectorial Poisson equation : .
Definition tenseur_pde.C:118
Lorene::Valeur
Values and coefficients of a (real-value) function.
Definition valeur.h:287
Lorene::Valeur::c_cf
Mtbl_cf * c_cf
Coefficients of the spectral expansion of the function.
Definition valeur.h:302
Lorene::Valeur::coef
void coef() const
Computes the coeffcients of *this.
Definition valeur_coef.C:148
Lorene::Vector
Tensor field of valence 1.
Definition vector.h:188
Lorene::Vector::change_triad
virtual void change_triad(const Base_vect &)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Definition vector_change_triad.C:75
Lorene::Vector::set
Scalar & set(int)
Read/write access to a component.
Definition vector.C:296
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Lorene::log10
Cmp log10(const Cmp &)
Basis 10 logarithm.
Definition cmp_math.C:322
Lorene::diffrel
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition cmp_math.C:504
Lorene::cos
Cmp cos(const Cmp &)
Cosine.
Definition cmp_math.C:94
Lorene::log
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
Lorene::Tensor::up
Tensor up(int ind, const Metric &gam) const
Computes a new tensor by raising an index of *this.
Definition tensor_calculus.C:225
Lorene::contract
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Definition tenseur_operateur.C:279
Lorene
Lorene prototypes.
Definition app_hor.h:64
Lorene::phi
Coord phi
coordinate centered on the grid
Definition map.h:720
Lorene::sint
Coord sint
Definition map.h:721
Unites
Standard units of space, time and mass.