LORENE
star_bin_upmetr_der_xcts.C
1 /*
2  * Methods Star_bin_xcts::update_metric_der_comp
3  * (see file star.h for documentation)
4  */
5 
6 /*
7  * Copyright (c) 2010 Michal Bejger
8  *
9  * This file is part of LORENE.
10  *
11  * LORENE is free software; you can redistribute it and/or modify
12  * it under the terms of the GNU General Public License version 2
13  * as published by the Free Software Foundation.
14  *
15  * LORENE is distributed in the hope that it will be useful,
16  * but WITHOUT ANY WARRANTY; without even the implied warranty of
17  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18  * GNU General Public License for more details.
19  *
20  * You should have received a copy of the GNU General Public License
21  * along with LORENE; if not, write to the Free Software
22  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
23  *
24  */
25 
26 char star_bin_upmetr_der_xcts_C[] = "$Header: /cvsroot/Lorene/C++/Source/Star/star_bin_upmetr_der_xcts.C,v 1.6 2014/10/13 08:53:38 j_novak Exp $" ;
27 
28 /*
29  * $Id: star_bin_upmetr_der_xcts.C,v 1.6 2014/10/13 08:53:38 j_novak Exp $
30  * $Log: star_bin_upmetr_der_xcts.C,v $
31  * Revision 1.6 2014/10/13 08:53:38 j_novak
32  * Lorene classes and functions now belong to the namespace Lorene.
33  *
34  * Revision 1.5 2014/10/06 15:13:17 j_novak
35  * Modified #include directives to use c++ syntax.
36  *
37  * Revision 1.4 2010/12/09 10:44:42 m_bejger
38  * Cosmetic changes
39  *
40  * Revision 1.3 2010/06/15 14:58:19 m_bejger
41  * Companion D^j beta^i computed in companion frame and imported
42  *
43  * Revision 1.2 2010/06/15 08:09:43 m_bejger
44  * *** empty log message ***
45  *
46  * Revision 1.1 2010/05/04 07:51:05 m_bejger
47  * Initial version
48  *
49  * $Header: /cvsroot/Lorene/C++/Source/Star/star_bin_upmetr_der_xcts.C,v 1.6 2014/10/13 08:53:38 j_novak Exp $
50  *
51  */
52 
53 // C headers
54 #include <cmath>
55 
56 // Headers Lorene
57 #include "star.h"
58 #include "utilitaires.h"
59 #include "graphique.h"
60 
61 namespace Lorene {
63 
64  // Derivatives of metric coefficients
65  // ----------------------------------
66 
67  // Computation of dcov_Psi
68  Vector temp = (comp.Psi_auto).derive_cov(comp.flat) ;
69 
70  temp.dec_dzpuis(2) ;
72 
73  assert ( *(temp.get_triad()) == *(dcov_Psi.get_triad())) ;
74 
75  for(int i=1; i<=3; i++) {
76 
77  dcov_Psi.set(i).import(temp(i)) ;
78  dcov_Psi.set(i).set_spectral_va().set_base(temp(i).get_spectral_va().get_base()) ;
79 
80  }
81  dcov_Psi.inc_dzpuis(2) ;
82 
84 
85  // Computation of dcov_chi
86  temp = (comp.chi_auto).derive_cov(comp.flat) ;
87 
88  temp.dec_dzpuis(2) ;
90 
91  assert ( *(temp.get_triad()) == *(dcov_chi.get_triad())) ;
92 
93  for(int i=1; i<=3; i++) {
94 
95  dcov_chi.set(i).import(temp(i)) ;
96  dcov_chi.set(i).set_spectral_va().set_base(temp(i).get_spectral_va().get_base()) ;
97 
98  }
99  dcov_chi.inc_dzpuis(2) ;
100 
102 
103  // Computation of \hat{A}^{ij}_{comp}
104  // ----------------------------------
105 
106  // D^j beta^i
107 
108  Tensor temp_beta = (comp.beta_auto).derive_con(comp.flat) ;
109  temp_beta.dec_dzpuis(2) ;
110  temp_beta.change_triad(mp.get_bvect_cart()) ;
111 
112  Tensor dbeta_comp(mp, 2, CON, mp.get_bvect_cart()) ;
113 
114  assert ( *(temp_beta.get_triad()) == *(dbeta_comp.get_triad()) ) ;
115 
116  for(int i=1; i<=3; i++)
117  for(int j=1; j<=3; j++) {
118 
119  // importing
120  (dbeta_comp.set(i,j)).import( (temp_beta)(i,j) );
121  // setting appropriate bases
122  (dbeta_comp.set(i,j)).set_spectral_va().set_base(temp_beta(i,j).get_spectral_va().get_base()) ;
123 
124  }
125 
126  dbeta_comp.inc_dzpuis(2) ;
127 
128  // Trace of D_j beta^i :
129  Scalar divbeta_comp = beta_comp.divergence(flat) ;
130 
131  for (int i=1; i<=3; i++)
132  for (int j=1; j<=i; j++) {
133 //##
134 // for (int j=i; j<=3; j++) {
135 
136  haij_comp.set(i, j) = dbeta_comp(i, j) + dbeta_comp(j, i)
137  - double(2) /double(3) * divbeta_comp * (flat.con())(i,j) ;
138 
139  }
140 
141  // Computation of (\hat{A}_{ij}\hat{A}^{ij})_{comp}
142  // ------------------------------------------------
143 
144  Sym_tensor haij_auto_cov = haij_auto.up_down(flat) ;
145 
146  haij_comp = 0.5 * pow(Psi, 7.) / chi * haij_comp ;
147  //## for comparison: old formulation
148  //haij_comp = 0.5 * haij_comp / nn ;
149  haij_comp.std_spectral_base() ;
150 
151  hacar_comp = contract(haij_auto_cov, 0, 1, haij_comp, 0, 1, true) ;
152 
153  // The derived quantities are obsolete
154  // -----------------------------------
155 
156  del_deriv() ;
157 
158 }
159 }
Scalar chi
Total function .
Definition: star.h:1155
Vector dcov_chi
Covariant derivative of the function .
Definition: star.h:1174
Map & mp
Mapping associated with the star.
Definition: star.h:180
Lorene prototypes.
Definition: app_hor.h:64
Tensor field of valence 0 (or component of a tensorial field).
Definition: scalar.h:387
Tensor up_down(const Metric &gam) const
Computes a new tensor by raising or lowering all the indices of *this .
Vector dcov_Psi
Covariant derivative of the conformal factor .
Definition: star.h:1171
Class for stars in binary system in eXtended Conformal Thin Sandwich formulation. ...
Definition: star.h:1091
virtual void change_triad(const Base_vect &)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Tensor field of valence 1.
Definition: vector.h:188
Sym_tensor haij_auto
Part of the extrinsic curvature tensor generated by beta_auto.
Definition: star.h:1193
void set_base(const Base_val &)
Sets the bases for spectral expansions (member base )
Definition: valeur.C:810
virtual void dec_dzpuis(int dec=1)
Decreases by dec units the value of dzpuis and changes accordingly the values in the compactified ext...
Definition: tensor.C:808
virtual const Sym_tensor & con() const
Read-only access to the contravariant representation.
Definition: metric_flat.C:153
Sym_tensor haij_comp
Part of the extrinsic curvature tensor generated by beta_comp.
Definition: star.h:1199
Scalar Psi_auto
Scalar field generated principally by the star.
Definition: star.h:1144
const Base_vect * get_triad() const
Returns the vectorial basis (triad) on which the components are defined.
Definition: tensor.h:866
Vector beta_comp
Part of the shift vector generated principally by the star (Spherical components with respect to the ...
Definition: star.h:1187
const Scalar & divergence(const Metric &) const
The divergence of this with respect to a Metric .
Definition: vector.C:381
Cmp pow(const Cmp &, int)
Power .
Definition: cmp_math.C:348
Scalar chi_auto
Scalar field generated principally by the star.
Definition: star.h:1134
Tensor handling.
Definition: tensor.h:288
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
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
Metric_flat flat
Flat metric defined on the mapping (Spherical components with respect to the mapping of the star) ...
Definition: star.h:1177
void import(const Scalar &ci)
Assignment to another Scalar defined on a different mapping.
Definition: scalar_import.C:68
Scalar Psi
Total conformal factor .
Definition: star.h:1152
void update_metric_der_comp(const Star_bin_xcts &comp)
Computes the derivative of metric functions related to the companion star.
const Base_vect_cart & get_bvect_cart() const
Returns the Cartesian basis associated with the coordinates (x,y,z) of the mapping, i.e.
Definition: map.h:791
Scalar & set(const Itbl &ind)
Returns the value of a component (read/write version).
Definition: tensor.C:654
Vector beta_auto
Part of the shift vector generated principally by the star (Spherical components with respect to the ...
Definition: star.h:1182
virtual void del_deriv() const
Deletes all the derived quantities.
virtual void change_triad(const Base_vect &new_triad)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Scalar hacar_comp
Part of the scalar generated by beta_auto and beta_comp, i.e.
Definition: star.h:1211
Valeur & set_spectral_va()
Returns va (read/write version)
Definition: scalar.h:604
Scalar & set(int)
Read/write access to a component.
Definition: vector.C:296
const Vector & derive_cov(const Metric &gam) const
Returns the gradient (1-form = covariant vector) of *this.
Definition: scalar_deriv.C:390
virtual void std_spectral_base()
Sets the standard spectal bases of decomposition for each component.
Definition: tensor.C:926
Class intended to describe valence-2 symmetric tensors.
Definition: sym_tensor.h:223