LORENE
star_bin_upmetr_der.C
1/*
2 * Methods Star_bin::update_metric_der_comp
3 *
4 * (see file star.h for documentation)
5 *
6 */
7
8/*
9 * Copyright (c) 2004 Francois Limousin
10 *
11 * This file is part of LORENE.
12 *
13 * LORENE is free software; you can redistribute it and/or modify
14 * it under the terms of the GNU General Public License as published by
15 * the Free Software Foundation; either version 2 of the License, or
16 * (at your option) any later version.
17 *
18 * LORENE is distributed in the hope that it will be useful,
19 * but WITHOUT ANY WARRANTY; without even the implied warranty of
20 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21 * GNU General Public License for more details.
22 *
23 * You should have received a copy of the GNU General Public License
24 * along with LORENE; if not, write to the Free Software
25 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26 *
27 */
28
29
30char star_bin_upmetr_der_C[] = "$Header: /cvsroot/Lorene/C++/Source/Star/star_bin_upmetr_der.C,v 1.17 2014/10/13 08:53:38 j_novak Exp $" ;
31
32/*
33 * $Id: star_bin_upmetr_der.C,v 1.17 2014/10/13 08:53:38 j_novak Exp $
34 * $Log: star_bin_upmetr_der.C,v $
35 * Revision 1.17 2014/10/13 08:53:38 j_novak
36 * Lorene classes and functions now belong to the namespace Lorene.
37 *
38 * Revision 1.16 2014/10/06 15:13:17 j_novak
39 * Modified #include directives to use c++ syntax.
40 *
41 * Revision 1.15 2006/05/24 16:52:50 f_limousin
42 * New computation of tkij_comp
43 *
44 * Revision 1.14 2005/09/13 19:38:31 f_limousin
45 * Reintroduction of the resolution of the equations in cartesian coordinates.
46 *
47 * Revision 1.13 2005/02/24 16:26:46 f_limousin
48 * Add the name of the variable for the companion which is now used
49 * to compute dlogn_comp, dlnq_comp...
50 *
51 * Revision 1.12 2005/02/24 16:07:23 f_limousin
52 * Improve the computation of dlogn, dlnq and dlnpsi. We import the part
53 * coming from the companion and add the auto part.
54 *
55 * Revision 1.11 2005/02/18 13:14:18 j_novak
56 * Changing of malloc/free to new/delete + suppression of some unused variables
57 * (trying to avoid compilation warnings).
58 *
59 * Revision 1.10 2005/02/17 17:34:28 f_limousin
60 * Change the name of some quantities to be consistent with other classes
61 * (for instance nnn is changed to nn, shift to beta, beta to lnq...)
62 *
63 * Revision 1.9 2004/06/22 12:52:47 f_limousin
64 * Change qq, qq_auto and qq_comp to beta, beta_auto and beta_comp.
65 *
66 * Revision 1.8 2004/06/07 16:25:14 f_limousin
67 * Minor modif.
68 *
69 * Revision 1.7 2004/04/08 16:33:32 f_limousin
70 * The new variable is ln(Q) instead of Q=psi^2*N. It improves the
71 * convergence of the code.
72 *
73 * Revision 1.6 2004/03/23 10:00:09 f_limousin
74 * We now make the derivation with respect to the metric tilde
75 * instead of the flat metric for the computation of dshift_comp.
76 *
77 * Revision 1.5 2004/02/27 09:53:14 f_limousin
78 * Correction of an error on the computation of kcar_comp.
79 *
80 * Revision 1.4 2004/02/18 18:47:01 e_gourgoulhon
81 * divshift_comp now computed via Tensor::divergence, the
82 * method Tensor::scontract having disappeared.
83 *
84 * Revision 1.3 2004/01/20 15:20:23 f_limousin
85 * First version
86 *
87 *
88 * $Header: /cvsroot/Lorene/C++/Source/Star/star_bin_upmetr_der.C,v 1.17 2014/10/13 08:53:38 j_novak Exp $
89 *
90 */
91
92// C headers
93#include <cmath>
94
95// Headers Lorene
96#include "star.h"
97#include "utilitaires.h"
98#include "graphique.h"
99
100namespace Lorene {
102
103 // Derivatives of metric coefficients
104 // ----------------------------------
105
106 // dcov_logn
107 Vector temp ((comp.logn_auto).derive_cov(comp.get_flat())) ;
108 temp.dec_dzpuis(2) ;
109 temp.change_triad(temp.get_mp().get_bvect_cart()) ;
110 temp.change_triad(mp.get_bvect_cart()) ;
111 Base_val sauve_base1 (temp(1).get_spectral_va().get_base()) ;
112 Base_val sauve_base2 (temp(2).get_spectral_va().get_base()) ;
113 Base_val sauve_base3 (temp(3).get_spectral_va().get_base()) ;
114 assert ( *(temp.get_triad()) == *(dcov_logn.get_triad())) ;
115
116 dcov_logn.set(1).import(temp(1)) ;
117 dcov_logn.set(2).import(temp(2)) ;
118 dcov_logn.set(3).import(temp(3)) ;
119
124
126
127 // dcon_logn
128 Vector temp_con((comp.logn_auto).derive_con(comp.get_flat())) ;
129 temp_con.dec_dzpuis(2) ;
130 temp_con.change_triad(temp_con.get_mp().get_bvect_cart()) ;
131 temp_con.change_triad(mp.get_bvect_cart()) ;
132 sauve_base1 = temp_con(1).get_spectral_va().get_base() ;
133 sauve_base2 = temp_con(2).get_spectral_va().get_base() ;
134 sauve_base3 = temp_con(3).get_spectral_va().get_base() ;
135 assert ( *(temp_con.get_triad()) == *(dcon_logn.get_triad())) ;
136
140
145
147
148 // dcov_phi
149 temp = (0.5*(comp.lnq_auto-comp.logn_auto)).derive_cov(comp.get_flat()) ;
150 temp.dec_dzpuis(2) ;
151 temp.change_triad(temp.get_mp().get_bvect_cart()) ;
152 temp.change_triad(mp.get_bvect_cart()) ;
153 sauve_base1 = temp(1).get_spectral_va().get_base() ;
154 sauve_base2 = temp(2).get_spectral_va().get_base() ;
155 sauve_base3 = temp(3).get_spectral_va().get_base() ;
156 assert ( *(temp.get_triad()) == *(dcov_phi.get_triad())) ;
157
158 dcov_phi.set(1).import(temp(1)) ;
159 dcov_phi.set(2).import(temp(2)) ;
160 dcov_phi.set(3).import(temp(3)) ;
161
166
167 dcov_phi = dcov_phi + 0.5*(lnq_auto - logn_auto).derive_cov(flat) ;
168
169 // dcon_phi
170 temp_con = (0.5*(comp.lnq_auto-comp.logn_auto))
171 .derive_con(comp.get_flat()) ;
172 temp_con.dec_dzpuis(2) ;
173 temp_con.change_triad(temp_con.get_mp().get_bvect_cart()) ;
174 temp_con.change_triad(mp.get_bvect_cart()) ;
175 sauve_base1 = temp_con(1).get_spectral_va().get_base() ;
176 sauve_base2 = temp_con(2).get_spectral_va().get_base() ;
177 sauve_base3 = temp_con(3).get_spectral_va().get_base() ;
178 assert ( *(temp_con.get_triad()) == *(dcon_phi.get_triad())) ;
179
180 dcon_phi.set(1).import(temp_con(1)) ;
181 dcon_phi.set(2).import(temp_con(2)) ;
182 dcon_phi.set(3).import(temp_con(3)) ;
183
188
189 dcon_phi = dcon_phi + 0.5*(lnq_auto - logn_auto).derive_con(flat) ;
190
191
192 // Construction of Omega d/dphi
193 // ----------------------------
194
195 const Mg3d* mg = mp.get_mg() ;
196 int nz = mg->get_nzone() ; // total number of domains
197 Vector omdsdp (mp, CON, mp.get_bvect_cart()) ;
198 Scalar yya (mp) ;
199 yya = mp.ya ;
200 Scalar xxa (mp) ;
201 xxa = mp.xa ;
202
203 if (fabs(mp.get_rot_phi()) < 1e-10){
204 omdsdp.set(1) = - om * yya ;
205 omdsdp.set(2) = om * xxa ;
206 omdsdp.set(3).annule_hard() ;
207 }
208 else{
209 omdsdp.set(1) = om * yya ;
210 omdsdp.set(2) = - om * xxa ;
211 omdsdp.set(3).annule_hard() ;
212 }
213
214 omdsdp.set(1).set_spectral_va()
215 .set_base(*(mp.get_mg()->std_base_vect_cart()[0])) ;
216 omdsdp.set(2).set_spectral_va()
217 .set_base(*(mp.get_mg()->std_base_vect_cart()[1])) ;
218 omdsdp.set(3).set_spectral_va()
219 .set_base(*(mp.get_mg()->std_base_vect_cart()[2])) ;
220
221 omdsdp.annule_domain(nz-1) ;
222
223 // Computation of tkij_comp
224 // ------------------------
225
226 // Gradient tilde (partial derivatives with respect to
227 // the cartesian coordinates of the mapping)
228 // D~^j beta^i
229
231
232 // Trace of D~_j beta^i :
234
235 // Computation of K^{ij}
236 // -------------------------
237
238 for (int i=1; i<=3; i++)
239 for (int j=i; j<=3; j++) {
240
241 tkij_comp.set(i, j) = dbeta_comp(i, j) + dbeta_comp(j, i) -
242 double(2) /double(3) * divbeta_comp * (gtilde.con())(i,j) ;
243 }
244
245 // Addition (or not !) of u^{ij}
247
248 tkij_comp = 0.5 * tkij_comp / nn ;
249
250 /*
251 Sym_tensor aa_comp (mp, CON, mp.get_bvect_cart()) ;
252 aa_comp.set_etat_qcq() ;
253 Sym_tensor comp_aa (comp.get_tkij_auto()) ;
254 comp_aa.dec_dzpuis(2) ;
255 comp_aa.change_triad(mp.get_bvect_cart()) ;
256
257
258 assert(*(aa_comp.get_triad()) == *(comp_aa.get_triad())) ;
259 // importations :
260 for (int i=1 ; i<=3 ; i++)
261 for (int j=i ; j<=3 ; j++) {
262 aa_comp.set(i, j).import(comp_aa(i, j)) ;
263 aa_comp.set(i, j).set_spectral_va().set_base(comp_aa(i, j).
264 get_spectral_va().get_base()) ;
265 }
266 aa_comp.inc_dzpuis(2) ;
267
268 for (int i=1 ; i<=3 ; i++)
269 for (int j=i ; j<=3 ; j++)
270 for (int l=0 ; l<=nz-2 ; l++)
271 tkij_comp.set(i,j).set_domain(l) = aa_comp(i,j).domain(l) ;
272 */
273
274
275 // Computation of kcar_comp
276 // ------------------------
277
279
280 kcar_comp = contract(tkij_auto_cov, 0, 1, tkij_comp, 0, 1,true) ;
281
282 // The derived quantities are obsolete
283 // -----------------------------------
284
285 del_deriv() ;
286
287}
288
289}
Bases of the spectral expansions.
Definition base_val.h:322
Time evolution with partial storage (*** under development ***).
Definition evolution.h:371
const Base_vect_cart & get_bvect_cart() const
Returns the Cartesian basis associated with the coordinates (x,y,z) of the mapping,...
Definition map.h:791
Coord ya
Absolute y coordinate.
Definition map.h:731
double get_rot_phi() const
Returns the angle between the x –axis and X –axis.
Definition map.h:775
Coord xa
Absolute x coordinate.
Definition map.h:730
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition map.h:765
virtual const Sym_tensor & con() const
Read-only access to the contravariant representation.
Definition metric.C:290
Multi-domain grid.
Definition grilles.h:273
int get_nzone() const
Returns the number of domains.
Definition grilles.h:448
Tensor field of valence 0 (or component of a tensorial field).
Definition scalar.h:387
const Vector & derive_cov(const Metric &gam) const
Returns the gradient (1-form = covariant vector) of *this
Valeur & set_spectral_va()
Returns va (read/write version)
Definition scalar.h:604
const Vector & derive_con(const Metric &gam) const
Returns the "contravariant" derivative of *this with respect to some metric , by raising the index of...
void import(const Scalar &ci)
Assignment to another Scalar defined on a different mapping.
Class for stars in binary system.
Definition star.h:483
Scalar lnq_auto
Scalar field generated principally by the star.
Definition star.h:543
Vector dcon_logn
Contravariant derivative of the total logarithm of the lapse.
Definition star.h:538
Vector dcon_phi
Contravariant derivative of the logarithm of the conformal factor.
Definition star.h:557
Sym_tensor hij_comp
Deviation of the inverse conformal metric from the inverse flat metric generated principally by the ...
Definition star.h:594
virtual void del_deriv() const
Deletes all the derived quantities.
Definition star_bin.C:369
Vector beta_comp
Part of the shift vector generated principally by the star (Spherical components with respect to the ...
Definition star.h:575
Vector dcov_logn
Covariant derivative of the total logarithm of the lapse.
Definition star.h:535
Scalar logn_auto
Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principally by...
Definition star.h:527
Scalar kcar_comp
Part of the scalar generated by beta_auto and beta_comp, i.e.
Definition star.h:618
Sym_tensor tkij_comp
Part of the extrinsic curvature tensor generated by beta_comp.
Definition star.h:606
Sym_tensor tkij_auto
Part of the extrinsic curvature tensor generated by beta_auto.
Definition star.h:600
Vector dcov_phi
Covariant derivative of the logarithm of the conformal factor.
Definition star.h:555
Metric_flat flat
Flat metric defined on the mapping (Spherical components with respect to the mapping of the star) .
Definition star.h:562
void update_metric_der_comp(const Star_bin &comp, double omega)
Computes the derivative of metric functions related to the companion star.
Metric gtilde
Conformal metric .
Definition star.h:565
Scalar nn
Lapse function N .
Definition star.h:225
Map & mp
Mapping associated with the star.
Definition star.h:180
Class intended to describe valence-2 symmetric tensors.
Definition sym_tensor.h:223
Sym_tensor derive_lie(const Vector &v) const
Computes the Lie derivative of this with respect to some vector field v.
Definition sym_tensor.C:360
Tensor handling.
Definition tensor.h:288
void set_base(const Base_val &)
Sets the bases for spectral expansions (member base )
Definition valeur.C:810
Tensor field of valence 1.
Definition vector.h:188
const Scalar & divergence(const Metric &) const
The divergence of this with respect to a Metric .
Definition vector.C:381
Scalar & set(int)
Read/write access to a component.
Definition vector.C:296
Tensor up_down(const Metric &gam) const
Computes a new tensor by raising or lowering all the indices of *this .
const Tensor & derive_con(const Metric &gam) const
Returns the "contravariant" derivative of this with respect to some metric , by raising the last inde...
Definition tensor.C:1014
virtual void inc_dzpuis(int inc=1)
Increases by inc units the value of dzpuis and changes accordingly the values in the compactified ext...
Definition tensor.C:816
const Base_vect * get_triad() const
Returns the vectorial basis (triad) on which the components are defined.
Definition tensor.h:866
Scalar & set(const Itbl &ind)
Returns the value of a component (read/write version).
Definition tensor.C:654
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Lorene prototypes.
Definition app_hor.h:64