LORENE
sym_tensor.h
1 /*
2  * Definition of Lorene class Sym_tensor,
3  * as well as derived classes Sym_tensor_trans and Sym_tensor_tt
4  *
5  */
6 
7 /*
8  * Copyright (c) 2003-2004 Eric Gourgoulhon & Jerome Novak
9  *
10  * This file is part of LORENE.
11  *
12  * LORENE is free software; you can redistribute it and/or modify
13  * it under the terms of the GNU General Public License version 2
14  * as published by the Free Software Foundation.
15  *
16  * LORENE is distributed in the hope that it will be useful,
17  * but WITHOUT ANY WARRANTY; without even the implied warranty of
18  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19  * GNU General Public License for more details.
20  *
21  * You should have received a copy of the GNU General Public License
22  * along with LORENE; if not, write to the Free Software
23  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
24  *
25  */
26 
27 #ifndef __SYM_TENSOR_H_
28 #define __SYM_TENSOR_H_
29 
30 /*
31  * $Id: sym_tensor.h,v 1.50 2019/08/16 08:47:36 j_novak Exp $
32  * $Log: sym_tensor.h,v $
33  * Revision 1.50 2019/08/16 08:47:36 j_novak
34  * *** empty log message ***
35  *
36  * Revision 1.49 2014/10/13 08:52:36 j_novak
37  * Lorene classes and functions now belong to the namespace Lorene.
38  *
39  * Revision 1.48 2010/10/11 10:23:03 j_novak
40  * Removed methods Sym_tensor_trans::solve_hrr() and Sym_tensor_trans::set_WX_det_one(), as they are no longer relevant.
41  *
42  * Revision 1.47 2008/12/05 08:46:19 j_novak
43  * New method Sym_tensor_trans_aux::set_tt_part_det_one.
44  *
45  * Revision 1.46 2008/12/03 10:18:56 j_novak
46  * Method 6 is now the default for calls to vector Poisson solver.
47  *
48  * Revision 1.45 2008/08/20 14:39:53 n_vasset
49  * New Dirac solvers handling degenerate elliptic operators on excised spacetimes.
50  *
51  * Revision 1.44 2007/12/21 16:06:16 j_novak
52  * Methods to filter Tensor, Vector and Sym_tensor objects.
53  *
54  * Revision 1.43 2007/11/27 15:48:52 n_vasset
55  * New member p_tilde_c for class Sym_tensor
56  *
57  * Revision 1.42 2007/05/04 16:43:50 n_vasset
58  * adding of functions sol_Dirac_BC2 and sol_Dirac_A2
59  *
60  * Revision 1.41 2006/10/24 13:03:17 j_novak
61  * New methods for the solution of the tensor wave equation. Perhaps, first
62  * operational version...
63  *
64  * Revision 1.40 2006/08/31 12:13:21 j_novak
65  * Added an argument of type Param to Sym_tensor_trans::sol_ rac_A().
66  *
67  * Revision 1.39 2006/06/20 12:07:13 j_novak
68  * Improved execution speed for sol_Dirac_tildeB...
69  *
70  * Revision 1.38 2006/06/14 10:04:19 j_novak
71  * New methods sol_Dirac_l01, set_AtB_det_one and set_AtB_trace_zero.
72  *
73  * Revision 1.37 2006/06/13 13:30:12 j_novak
74  * New members sol_Dirac_A and sol_Dirac_tildeB (see documentation).
75  *
76  * Revision 1.36 2006/06/12 13:37:23 j_novak
77  * Added bounds in l (multipolar momentum) for Sym_tensor_trans::solve_hrr.
78  *
79  * Revision 1.35 2006/06/12 07:42:28 j_novak
80  * Fields A and tilde{B} are defined only for l>1.
81  *
82  * Revision 1.34 2006/06/12 07:27:18 j_novak
83  * New members concerning A and tilde{B}, dealing with the transverse part of the
84  * Sym_tensor.
85  *
86  * Revision 1.33 2005/11/28 14:45:14 j_novak
87  * Improved solution of the Poisson tensor equation in the case of a transverse
88  * tensor.
89  *
90  * Revision 1.32 2005/09/16 13:58:10 j_novak
91  * New Poisson solver for a Sym_tensor_trans.
92  *
93  * Revision 1.31 2005/09/07 16:47:42 j_novak
94  * Removed method Sym_tensor_trans::T_from_det_one
95  * Modified Sym_tensor::set_auxiliary, so that it takes eta/r and mu/r as
96  * arguments.
97  * Modified Sym_tensor_trans::set_hrr_mu.
98  * Added new protected method Sym_tensor_trans::solve_hrr
99  *
100  * Revision 1.30 2005/04/08 08:22:04 j_novak
101  * New methods set_hrr_mu_det_one() and set_WX_det_one(). Not tested yet...
102  *
103  * Revision 1.29 2005/04/06 15:43:58 j_novak
104  * New method Sym_tensor_trans::T_from_det_one(...).
105  *
106  * Revision 1.28 2005/04/04 15:25:22 j_novak
107  * Added new members www, xxx, ttt and the associated methods.
108  *
109  * Revision 1.27 2005/04/01 14:28:31 j_novak
110  * Members p_eta and p_mu are now defined in class Sym_tensor.
111  *
112  * Revision 1.26 2005/01/03 08:34:58 f_limousin
113  * Come back to the previous version.
114  *
115  * Revision 1.25 2005/01/03 08:15:39 f_limousin
116  * The first argument of the function trace_from_det_one(...) is now
117  * a Sym_tensor_trans instead of a Sym_tensor_tt (because of a
118  * compilation error with some compilators).
119  *
120  * Revision 1.24 2004/12/28 14:21:46 j_novak
121  * Added the method Sym_tensor_trans::trace_from_det_one
122  *
123  * Revision 1.23 2004/12/28 10:37:22 j_novak
124  * Better way of enforcing zero divergence.
125  *
126  * Revision 1.22 2004/06/14 20:44:44 e_gourgoulhon
127  * Added argument method_poisson to Sym_tensor::longit_pot and
128  * Sym_tensor::transverse.
129  *
130  * Revision 1.21 2004/05/25 14:57:20 f_limousin
131  * Add parameters in argument of functions transverse, longit_pot,
132  * set_tt_trace, tt_part and set_khi_mu for the case of a Map_et.
133  *
134  * Revision 1.20 2004/05/24 13:44:54 e_gourgoulhon
135  * Added parameter dzp to method Sym_tensor_tt::update.
136  *
137  * Revision 1.19 2004/04/08 16:37:54 e_gourgoulhon
138  * Sym_tensor_tt::set_khi_mu: added argument dzp (dzpuis of resulting h^{ij}).
139  *
140  * Revision 1.18 2004/03/30 14:01:19 j_novak
141  * Copy constructors and operator= now copy the "derived" members.
142  *
143  * Revision 1.17 2004/03/29 16:13:06 j_novak
144  * New methods set_longit_trans and set_tt_trace .
145  *
146  * Revision 1.16 2004/03/22 13:12:43 j_novak
147  * Modification of comments to use doxygen instead of doc++
148  *
149  * Revision 1.15 2004/03/03 13:54:16 j_novak
150  * Error in comments corrected.
151  *
152  * Revision 1.14 2004/03/03 13:16:20 j_novak
153  * New potential khi (p_khi) and the functions manipulating it.
154  *
155  * Revision 1.13 2004/02/26 22:45:13 e_gourgoulhon
156  * Added method derive_lie.
157  *
158  * Revision 1.12 2004/02/18 18:43:22 e_gourgoulhon
159  * Method trace() renamed the_trace() in order to avoid
160  * any confusion with new method Tensor::trace().
161  *
162  * Revision 1.11 2004/01/04 20:49:06 e_gourgoulhon
163  * Sym_tensor is now a derived class of Tensor_sym.
164  * Suppressed methods Sym_tensor::indices and Sym_tensor::position:
165  * they are now implemented at the Tensor_sym level.
166  *
167  * Revision 1.10 2003/11/27 16:05:11 e_gourgoulhon
168  * Changed return value of methods transverse( ) and longit_pot( ).
169  *
170  * Revision 1.9 2003/11/26 21:56:21 e_gourgoulhon
171  * Class Sym_tensor: added the members p_transverse and p_longit_pot,
172  * and the associated methods transverse( ), longit_pot( ),
173  * del_deriv_met( ) and set_der_met_0x0( ).
174  *
175  * Revision 1.8 2003/11/07 16:54:23 e_gourgoulhon
176  * Added method Sym_tensor_tt::poisson().
177  *
178  * Revision 1.7 2003/11/06 14:43:37 e_gourgoulhon
179  * Gave a name to const arguments in certain method prototypes (e.g.
180  * constructors) to correct a bug of DOC++.
181  *
182  * Revision 1.6 2003/11/05 15:26:31 e_gourgoulhon
183  * Modif documentation.
184  *
185  * Revision 1.5 2003/11/04 22:57:26 e_gourgoulhon
186  * Class Sym_tensor_tt: method set_eta_mu renamed set_rr_eta_mu
187  * method update_tp() renamed update()
188  * added method set_rr_mu.
189  *
190  * Revision 1.4 2003/11/03 22:29:54 e_gourgoulhon
191  * Class Sym_tensor_tt: added functions set_eta_mu and update_tp.
192  *
193  * Revision 1.3 2003/11/03 17:09:30 e_gourgoulhon
194  * Class Sym_tensor_tt: added the methods eta() and mu().
195  *
196  * Revision 1.2 2003/10/28 21:22:51 e_gourgoulhon
197  * Class Sym_tensor_trans: added methods trace() and tt_part().
198  *
199  * Revision 1.1 2003/10/27 10:45:19 e_gourgoulhon
200  * New derived classes Sym_tensor_trans and Sym_tensor_tt.
201  *
202  *
203  * $Header: /cvsroot/Lorene/C++/Include/sym_tensor.h,v 1.50 2019/08/16 08:47:36 j_novak Exp $
204  *
205  */
206 
207 namespace Lorene {
208 class Sym_tensor_trans ;
209 class Sym_tensor_tt ;
210 
211 
212 
213 
214  //---------------------------------//
215  // class Sym_tensor //
216  //---------------------------------//
217 
226 class Sym_tensor : public Tensor_sym {
227 
228  // Derived data :
229  // ------------
230  protected:
242  mutable Sym_tensor_trans* p_transverse[N_MET_MAX] ;
243 
249  mutable Vector* p_longit_pot[N_MET_MAX] ;
250 
263  mutable Scalar* p_eta ;
264 
277  mutable Scalar* p_mu ;
278 
296  mutable Scalar* p_www ;
297 
315  mutable Scalar* p_xxx ;
316 
318  mutable Scalar* p_ttt ;
319 
325  mutable Scalar* p_aaa ;
326 
337  mutable Scalar* p_tilde_b ;
338 
349  mutable Scalar* p_tilde_c ;
350 
351 
352 
353 
354 
355 
356  // Constructors - Destructor :
357  // -------------------------
358 
359  public:
373  Sym_tensor(const Map& map, const Itbl& tipe, const Base_vect& triad_i) ;
374 
383  Sym_tensor(const Map& map, int tipe, const Base_vect& triad_i) ;
384 
385  Sym_tensor(const Sym_tensor& a) ;
386 
390  Sym_tensor(const Tensor& a) ;
391 
402  Sym_tensor(const Map& map, const Base_vect& triad_i, FILE* fich) ;
403 
404  virtual ~Sym_tensor() ;
405 
406 
407 
408  // Memory management
409  // -----------------
410  protected:
411  virtual void del_deriv() const;
412 
414  void set_der_0x0() const ;
415 
420  virtual void del_derive_met(int i) const ;
421 
425  void set_der_met_0x0(int i) const ;
426 
427 
428  // Mutators / assignment
429  // ---------------------
430  public:
432  virtual void operator=(const Sym_tensor& a) ;
433 
435  virtual void operator=(const Tensor_sym& a) ;
436 
442  virtual void operator=(const Tensor& a) ;
443 
449  void set_longit_trans( const Vector& v, const Sym_tensor_trans& a) ;
450 
457  void set_auxiliary( const Scalar& trr, const Scalar& eta_over_r, const
458  Scalar& mu_over_r, const Scalar& www, const Scalar&
459  xxx, const Scalar& ttt ) ;
460 
466  virtual void exponential_filter_r(int lzmin, int lzmax, int p,
467  double alpha= -16.) ;
468 
474  virtual void exponential_filter_ylm(int lzmin, int lzmax, int p,
475  double alpha= -16.) ;
476 
477  // Computation of derived members
478  // ------------------------------
479  public:
480 
481 
485  const Vector& divergence(const Metric&) const ;
486 
490  Sym_tensor derive_lie(const Vector& v) const ;
491 
509  const Sym_tensor_trans& transverse(const Metric& gam, Param* par = 0x0,
510  int method_poisson = 6) const ;
511 
522  const Vector& longit_pot(const Metric& gam, Param* par = 0x0,
523  int method_poisson = 6) const ;
524 
526  virtual const Scalar& eta(Param* par = 0x0) const ;
527 
529  const Scalar& mu(Param* par = 0x0) const ;
530 
532  const Scalar& www() const ;
533 
535  const Scalar& xxx() const ;
536 
538  const Scalar& ttt() const ;
539 
545  const Scalar& compute_A(bool output_ylm = true, Param* par = 0x0) const ;
546 
552  const Scalar& compute_tilde_B(bool output_ylm = true, Param* par = 0x0) const ;
553 
560  Scalar compute_tilde_B_tt(bool output_ylm = true, Param* par = 0x0) const ;
561 
567  const Scalar& compute_tilde_C(bool output_ylm = true, Param* par = 0x0) const ;
568 
569 
570 
571 
572 
573  protected:
577  Scalar get_tilde_B_from_TT_trace(const Scalar& tilde_B_tt_in, const Scalar&
578  trace) const ;
579 
580  // Mathematical operators
581  // ----------------------
582  protected:
587  Sym_tensor* inverse() const ;
588 
589  // Friend classes
590  //-----------------
591  friend class Metric ;
592 
593 } ;
594 
595 
596  //---------------------------------//
597  // class Sym_tensor_trans //
598  //---------------------------------//
599 
600 
612 
613  // Data :
614  // -----
615  protected:
617  const Metric* const met_div ;
618 
620  mutable Scalar* p_trace ;
621 
623  mutable Sym_tensor_tt* p_tt ;
624 
625  // Constructors - Destructor
626  // -------------------------
627  public:
635  Sym_tensor_trans(const Map& map, const Base_vect& triad_i,
636  const Metric& met) ;
637 
639 
651  Sym_tensor_trans(const Map& map, const Base_vect& triad_i,
652  const Metric& met, FILE* fich) ;
653 
654  virtual ~Sym_tensor_trans() ;
655 
656 
657  // Memory management
658  // -----------------
659  protected:
660  virtual void del_deriv() const;
661 
663  void set_der_0x0() const ;
664 
665 
666  // Accessors
667  // ---------
668  public:
672  const Metric& get_met_div() const {return *met_div ; } ;
673 
674  // Mutators / assignment
675  // ---------------------
676 
677  public:
679  virtual void operator=(const Sym_tensor_trans& a) ;
680 
682  virtual void operator=(const Sym_tensor& a) ;
683 
685  virtual void operator=(const Tensor_sym& a) ;
686 
688  virtual void operator=(const Tensor& a) ;
689 
695  void set_tt_trace(const Sym_tensor_tt& a, const Scalar& h,
696  Param* par = 0x0) ;
697 
698  // Computational methods
699  // ---------------------
701  const Scalar& the_trace() const ;
702 
707  const Sym_tensor_tt& tt_part(Param* par = 0x0) const ;
708 
709  protected:
725  void sol_Dirac_A(const Scalar& aaa, Scalar& tilde_mu, Scalar& xxx,
726  const Param* par_bc = 0x0) const ;
727 
728 
755  void sol_Dirac_tilde_B(const Scalar& tilde_b, const Scalar& hh, Scalar& hrr,
756  Scalar& tilde_eta, Scalar& www, Param* par_bc=0x0,
757  Param* par_mat=0x0) const ;
758 
763  void sol_Dirac_l01(const Scalar& hh, Scalar& hrr, Scalar& tilde_eta,
764  Param* par_mat) const ;
765 
766 
767 
768  public:
769 
770 
771 
777  void sol_Dirac_Abound(const Scalar& aaa, Scalar& tilde_mu, Scalar& x_new,
778  Scalar bound_mu, const Param* par_bc);
779 
780 
787  void sol_Dirac_A2(const Scalar& aaa, Scalar& tilde_mu, Scalar& x_new,
788  Scalar bound_mu, const Param* par_bc);
789 
795  void sol_Dirac_BC2(const Scalar& bb, const Scalar& cc, const Scalar& hh,
796  Scalar& hrr, Scalar& tilde_eta, Scalar& ww, Scalar bound_eta,double dir, double neum, double rhor, Param* par_bc, Param* par_mat);
797 
798 
804  void sol_Dirac_BC3(const Scalar& bb, const Scalar& hh,
805  Scalar& hrr, Scalar& tilde_eta, Scalar& ww, Scalar bound_hrr, Scalar bound_eta, Param* par_bc, Param* par_mat);
806 
807 
808 
809  // Solving the electric system for l=0 and l=1 only (simpler case), with boundary conditions imposed by the degenerate elliptic system.
810 
811  void sol_Dirac_l01_bound(const Scalar& hh, Scalar& hrr, Scalar& tilde_eta, Scalar& bound_hrr, Scalar& bound_eta, Param* par_mat) ;
812 
813  // Provisory: just for compilation, to be removed
814  void sol_Dirac_l01_2(const Scalar& hh, Scalar& hrr, Scalar& tilde_eta, Param* par_mat) ;
815 
816 
830  void trace_from_det_one(const Sym_tensor_tt& htt,
831  double precis = 1.e-14, int it_max = 100) ;
832 
847  void set_hrr_mu_det_one(const Scalar& hrr, const Scalar& mu_in,
848  double precis = 1.e-14, int it_max = 100) ;
849 
864  void set_tt_part_det_one(const Sym_tensor_tt& hijtt, const
865  Scalar* h_prev = 0x0, Param* par_mat = 0x0,
866  double precis = 1.e-14, int it_max = 100) ;
867 
886  void set_AtBtt_det_one(const Scalar& a_in, const Scalar& tbtt_in,
887  const Scalar* h_prev = 0x0, Param* par_bc = 0x0,
888  Param* par_mat = 0x0, double precis = 1.e-14,
889  int it_max = 100) ;
890 
898  void set_AtB_trace(const Scalar& a_in, const Scalar& tb_in, const
899  Scalar& trace, Param* par_bc = 0x0, Param* par_mat = 0x0) ;
900 
914  Sym_tensor_trans poisson(const Scalar* h_guess = 0x0) const ;
915 } ;
916 
917 
918  //------------------------------//
919  // class Sym_tensor_tt //
920  //------------------------------//
921 
922 
934 
935  // Data :
936  // -----
937 
938  protected:
941  mutable Scalar* p_khi ;
942 
943 
944  // Constructors - Destructor
945  // -------------------------
946  public:
954  Sym_tensor_tt(const Map& map, const Base_vect& triad_i,
955  const Metric& met) ;
956 
957  Sym_tensor_tt(const Sym_tensor_tt& ) ;
958 
970  Sym_tensor_tt(const Map& map, const Base_vect& triad_i,
971  const Metric& met, FILE* fich) ;
972 
973  virtual ~Sym_tensor_tt() ;
974 
975 
976  // Memory management
977  // -----------------
978  protected:
979  virtual void del_deriv() const;
980 
982  void set_der_0x0() const ;
983 
984 
985  // Mutators / assignment
986  // ---------------------
987 
988  public:
990  virtual void operator=(const Sym_tensor_tt& a) ;
991 
993  virtual void operator=(const Sym_tensor_trans& a) ;
994 
996  virtual void operator=(const Sym_tensor& a) ;
997 
999  virtual void operator=(const Tensor_sym& a) ;
1000 
1002  virtual void operator=(const Tensor& a) ;
1003 
1015  void set_rr_eta_mu(const Scalar& hrr, const Scalar& eta_i,
1016  const Scalar& mu_i) ;
1017 
1029  void set_rr_mu(const Scalar& hrr, const Scalar& mu_i) ;
1030 
1031 
1043  void set_khi_eta_mu(const Scalar& khi_i, const Scalar& eta_i,
1044  const Scalar& mu_i) ;
1045 
1059  void set_khi_mu(const Scalar& khi_i, const Scalar& mu_i, int dzp = 0,
1060  Param* par1 = 0x0, Param* par2 = 0x0,
1061  Param* par3 = 0x0) ;
1062 
1070  void set_A_tildeB(const Scalar& a_in, const Scalar& tb_in, Param* par_bc = 0x0,
1071  Param* par_mat = 0x0) ;
1072 
1073  // Computational methods
1074  // ---------------------
1075 
1076  public:
1080  const Scalar& khi() const ;
1081 
1083  virtual const Scalar& eta(Param* par = 0x0) const ;
1084 
1085  protected:
1092  void update(int dzp, Param* par1 = 0x0, Param* par2 = 0x0) ;
1093 
1094  public:
1106  Sym_tensor_tt poisson(int dzfin = 2) const ;
1107 
1108 
1109 
1110 } ;
1111 
1112 
1113 
1114 
1115 }
1116 #endif
virtual void exponential_filter_ylm(int lzmin, int lzmax, int p, double alpha=-16.)
Applies exponential filters to all components (see Scalar::exponential_filter_ylm )...
Definition: sym_tensor.C:474
Scalar * p_mu
Field such that the components of the tensor are written (has only meaning with spherical component...
Definition: sym_tensor.h:277
Sym_tensor_tt poisson(int dzfin=2) const
Computes the solution of a tensorial TT Poisson equation with *this as a source: ...
Metric for tensor calculation.
Definition: metric.h:90
const Scalar & mu(Param *par=0x0) const
Gives the field (see member p_mu ).
Scalar * p_tilde_b
Field defined from and h insensitive to the longitudinal part of the Sym_tensor.
Definition: sym_tensor.h:337
const Metric *const met_div
Metric with respect to which the divergence and the trace are defined.
Definition: sym_tensor.h:617
Sym_tensor * inverse() const
Returns a pointer on the inverse of the Sym_tensor (seen as a matrix).
Definition: sym_tensor.C:375
virtual void exponential_filter_r(int lzmin, int lzmax, int p, double alpha=-16.)
Applies exponential filters to all components (see Scalar::exponential_filter_r ).
Definition: sym_tensor.C:449
Lorene prototypes.
Definition: app_hor.h:67
void set_rr_eta_mu(const Scalar &hrr, const Scalar &eta_i, const Scalar &mu_i)
Sets the component , as well as the angular potentials and (see members p_eta and p_mu )...
virtual void del_derive_met(int i) const
Logical destructor of the derivatives depending on the i-th element of met_depend specific to the cla...
Definition: sym_tensor.C:323
Tensor field of valence 0 (or component of a tensorial field).
Definition: scalar.h:393
const Scalar & xxx() const
Gives the field X (see member p_xxx ).
Base class for coordinate mappings.
Definition: map.h:688
void sol_Dirac_Abound(const Scalar &aaa, Scalar &tilde_mu, Scalar &x_new, Scalar bound_mu, const Param *par_bc)
Same resolution as sol_Dirac_A, but with inner boundary conditions added.
Sym_tensor_tt(const Map &map, const Base_vect &triad_i, const Metric &met)
Standard constructor.
Definition: sym_tensor_tt.C:78
Basic integer array class.
Definition: itbl.h:122
virtual void operator=(const Sym_tensor_tt &a)
Assignment to another Sym_tensor_tt.
void sol_Dirac_A(const Scalar &aaa, Scalar &tilde_mu, Scalar &xxx, const Param *par_bc=0x0) const
Solves a system of two coupled first-order PDEs obtained from the divergence-free condition (Dirac ga...
Scalar * p_trace
Trace with respect to the metric *met_div.
Definition: sym_tensor.h:620
Scalar * p_www
Field W such that the components and of the tensor are written (has only meaning with spherical com...
Definition: sym_tensor.h:296
void set_tt_trace(const Sym_tensor_tt &a, const Scalar &h, Param *par=0x0)
Assigns the derived members p_tt and p_trace and updates the components accordingly.
const Scalar & compute_tilde_C(bool output_ylm=true, Param *par=0x0) const
Gives the field (see member p_tilde_c ).
virtual void operator=(const Sym_tensor &a)
Assignment to another Sym_tensor.
Definition: sym_tensor.C:237
Tensor field of valence 1.
Definition: vector.h:188
Vectorial bases (triads) with respect to which the tensorial components are defined.
Definition: base_vect.h:105
Scalar get_tilde_B_from_TT_trace(const Scalar &tilde_B_tt_in, const Scalar &trace) const
Computes (see Sym_tensor::p_tilde_b ) from its transverse-traceless part and the trace...
Sym_tensor(const Map &map, const Itbl &tipe, const Base_vect &triad_i)
Standard constructor.
Definition: sym_tensor.C:145
const Scalar & ttt() const
Gives the field T (see member p_ttt ).
virtual void operator=(const Sym_tensor_trans &a)
Assignment to another Sym_tensor_trans.
Scalar trace() const
Trace on two different type indices for a valence 2 tensor.
virtual void del_deriv() const
Deletes the derived quantities.
void set_der_0x0() const
Sets the pointers on derived quantities to 0x0.
Definition: sym_tensor.C:308
Scalar * p_eta
Field such that the components of the tensor are written (has only meaning with spherical component...
Definition: sym_tensor.h:263
void set_A_tildeB(const Scalar &a_in, const Scalar &tb_in, Param *par_bc=0x0, Param *par_mat=0x0)
Assigns the derived members A and .
Scalar * p_aaa
Field A defined from X and insensitive to the longitudinal part of the Sym_tensor (only for )...
Definition: sym_tensor.h:325
const Scalar & www() const
Gives the field W (see member p_www ).
const Sym_tensor_trans & transverse(const Metric &gam, Param *par=0x0, int method_poisson=6) const
Computes the transverse part of the tensor with respect to a given metric, transverse meaning diverg...
Sym_tensor_tt * p_tt
Traceless part with respect to the metric *met_div.
Definition: sym_tensor.h:623
void set_der_0x0() const
Sets the pointers on derived quantities to 0x0.
void set_AtBtt_det_one(const Scalar &a_in, const Scalar &tbtt_in, const Scalar *h_prev=0x0, Param *par_bc=0x0, Param *par_mat=0x0, double precis=1.e-14, int it_max=100)
Assigns the derived member A and computes from its TT-part (see Sym_tensor::compute_tilde_B_tt() )...
const Vector & divergence(const Metric &) const
Returns the divergence of this with respect to a Metric .
Definition: sym_tensor.C:352
void set_AtB_trace(const Scalar &a_in, const Scalar &tb_in, const Scalar &trace, Param *par_bc=0x0, Param *par_mat=0x0)
Assigns the derived members A , and the trace.
virtual void del_deriv() const
Deletes the derived quantities.
void sol_Dirac_l01(const Scalar &hh, Scalar &hrr, Scalar &tilde_eta, Param *par_mat) const
Solves the same system as Sym_tensor_trans::sol_Dirac_tilde_B but only for .
virtual void del_deriv() const
Deletes the derived quantities.
Definition: sym_tensor.C:289
void set_der_0x0() const
Sets the pointers on derived quantities to 0x0.
void set_khi_eta_mu(const Scalar &khi_i, const Scalar &eta_i, const Scalar &mu_i)
Sets the component , as well as the angular potentials and (see members p_khi , p_eta and p_mu )...
const Scalar & khi() const
Gives the field such that the component .
virtual ~Sym_tensor()
Destructor.
Definition: sym_tensor.C:225
void set_rr_mu(const Scalar &hrr, const Scalar &mu_i)
Sets the component , as well as the angular potential (see member p_mu ).
const Scalar & compute_A(bool output_ylm=true, Param *par=0x0) const
Gives the field A (see member p_aaa ).
virtual const Scalar & eta(Param *par=0x0) const
Gives the field (see member p_eta ).
void sol_Dirac_BC3(const Scalar &bb, const Scalar &hh, Scalar &hrr, Scalar &tilde_eta, Scalar &ww, Scalar bound_hrr, Scalar bound_eta, Param *par_bc, Param *par_mat)
Same resolution as sol_Dirac_Abound, but here the boundary conditions are the degenerate elliptic con...
const Sym_tensor_tt & tt_part(Param *par=0x0) const
Returns the transverse traceless part of the tensor, the trace being defined with respect to metric *...
Scalar * p_xxx
Field X such that the components and of the tensor are written (has only meaning with spherical com...
Definition: sym_tensor.h:315
virtual ~Sym_tensor_trans()
Destructor.
const Scalar & compute_tilde_B(bool output_ylm=true, Param *par=0x0) const
Gives the field (see member p_tilde_b ).
Parameter storage.
Definition: param.h:125
void sol_Dirac_BC2(const Scalar &bb, const Scalar &cc, const Scalar &hh, Scalar &hrr, Scalar &tilde_eta, Scalar &ww, Scalar bound_eta, double dir, double neum, double rhor, Param *par_bc, Param *par_mat)
Same resolution as sol_Dirac_tilde_B, but with inner boundary conditions added.
Vector * p_longit_pot[N_MET_MAX]
Array of the vector potential of the longitudinal part of the tensor with respect to various metrics ...
Definition: sym_tensor.h:249
void set_tt_part_det_one(const Sym_tensor_tt &hijtt, const Scalar *h_prev=0x0, Param *par_mat=0x0, double precis=1.e-14, int it_max=100)
Assignes the TT-part of the tensor.
const Metric & get_met_div() const
Returns the metric with respect to which the divergence and the trace are defined.
Definition: sym_tensor.h:672
Scalar * p_tilde_c
Field defined from and h insensitive to the longitudinal part of the Sym_tensor.
Definition: sym_tensor.h:349
void trace_from_det_one(const Sym_tensor_tt &htt, double precis=1.e-14, int it_max=100)
Assigns the derived member p_tt and computes the trace so that *this + the flat metric has a determin...
Tensor handling.
Definition: tensor.h:294
void set_khi_mu(const Scalar &khi_i, const Scalar &mu_i, int dzp=0, Param *par1=0x0, Param *par2=0x0, Param *par3=0x0)
Sets the component , as well as the angular potential (see member p_khi and p_mu )...
void set_der_met_0x0(int i) const
Sets all the i-th components of met_depend specific to the class Sym_tensor (p_transverse ...
Definition: sym_tensor.C:338
void sol_Dirac_tilde_B(const Scalar &tilde_b, const Scalar &hh, Scalar &hrr, Scalar &tilde_eta, Scalar &www, Param *par_bc=0x0, Param *par_mat=0x0) const
Solves a system of three coupled first-order PDEs obtained from divergence-free conditions (Dirac gau...
Transverse symmetric tensors of rank 2.
Definition: sym_tensor.h:611
virtual ~Sym_tensor_tt()
Destructor.
virtual const Scalar & eta(Param *par=0x0) const
Gives the field (see member p_eta ).
void set_auxiliary(const Scalar &trr, const Scalar &eta_over_r, const Scalar &mu_over_r, const Scalar &www, const Scalar &xxx, const Scalar &ttt)
Assigns the component and the derived members p_eta , p_mu , p_www, p_xxx and p_ttt ...
Scalar * p_ttt
Field T defined as .
Definition: sym_tensor.h:318
void update(int dzp, Param *par1=0x0, Param *par2=0x0)
Computes the components , , , and , from and the potentials and .
void set_longit_trans(const Vector &v, const Sym_tensor_trans &a)
Assigns the derived members p_longit_pot and p_transverse and updates the components accordingly...
Scalar compute_tilde_B_tt(bool output_ylm=true, Param *par=0x0) const
Gives the field (see member p_tilde_b ) associated with the TT-part of the Sym_tensor ...
void sol_Dirac_A2(const Scalar &aaa, Scalar &tilde_mu, Scalar &x_new, Scalar bound_mu, const Param *par_bc)
Same resolution as sol_Dirac_Abound, but here the boundary conditions are the degenerate elliptic con...
Sym_tensor_trans poisson(const Scalar *h_guess=0x0) const
Computes the solution of a tensorial transverse Poisson equation with *this as a source: In particu...
Scalar * p_khi
Field such that the component .
Definition: sym_tensor.h:941
Sym_tensor_trans(const Map &map, const Base_vect &triad_i, const Metric &met)
Standard constructor.
void set_hrr_mu_det_one(const Scalar &hrr, const Scalar &mu_in, double precis=1.e-14, int it_max=100)
Assigns the rr component and the derived member .
Symmetric tensors (with respect to two of their arguments).
Definition: tensor.h:1050
const Vector & longit_pot(const Metric &gam, Param *par=0x0, int method_poisson=6) const
Computes the vector potential of longitudinal part of the tensor (see documentation of method transv...
const Scalar & the_trace() const
Returns the trace of the tensor with respect to metric *met_div.
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:363
Class intended to describe valence-2 symmetric tensors.
Definition: sym_tensor.h:226
Transverse and traceless symmetric tensors of rank 2.
Definition: sym_tensor.h:933
Sym_tensor_trans * p_transverse[N_MET_MAX]
Array of the transverse part of the tensor with respect to various metrics, transverse meaning diver...
Definition: sym_tensor.h:242