LORENE
boson_star_equil.C
1/*
2 * Method Boson_star::equilibrium
3 *
4 * (see file boson_star.h for documentation).
5 */
6
7/*
8 * Copyright (c) 2012 Claire Some, Eric Gourgoulhon
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 as published by
14 * the Free Software Foundation; either version 2 of the License, or
15 * (at your option) any later version.
16 *
17 * LORENE is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU General Public License for more details.
21 *
22 * You should have received a copy of the GNU General Public License
23 * along with LORENE; if not, write to the Free Software
24 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25 *
26 */
27
28
29char 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 $" ;
30
31/*
32 * $Id: boson_star_equil.C,v 1.6 2014/10/13 08:52:49 j_novak Exp $
33 * $Log: boson_star_equil.C,v $
34 * Revision 1.6 2014/10/13 08:52:49 j_novak
35 * Lorene classes and functions now belong to the namespace Lorene.
36 *
37 * Revision 1.5 2014/10/06 15:13:04 j_novak
38 * Modified #include directives to use c++ syntax.
39 *
40 * Revision 1.4 2013/04/03 12:10:13 e_gourgoulhon
41 * Added member kk to Compobj; suppressed tkij
42 *
43 * Revision 1.3 2012/12/03 15:27:30 c_some
44 * Small changes
45 *
46 * Revision 1.2 2012/11/23 15:43:05 c_some
47 * Small changes
48 *
49 * Revision 1.1 2012/11/22 16:04:12 c_some
50 * New class Boson_star
51 *
52 *
53 * $Header: /cvsroot/Lorene/C++/Source/Compobj/boson_star_equil.C,v 1.6 2014/10/13 08:52:49 j_novak Exp $
54 *
55 */
56
57// Headers C
58#include <cmath>
59
60// Headers Lorene
61#include "boson_star.h"
62#include "param.h"
63#include "tenseur.h"
64
65#include "graphique.h"
66#include "utilitaires.h"
67#include "unites.h"
68
69namespace Lorene {
70void Boson_star::equilibrium(double, double,
71 int nzadapt, const Tbl& phi_limit, const Itbl& icontrol,
72 const Tbl& control, Tbl& diff, Param*) {
73
74 // Fundamental constants and units
75 // -------------------------------
76
77 using namespace Unites ;
78
79 // For the display
80 // ---------------
81 char display_bold[]="x[1m" ; display_bold[0] = 27 ;
82 char display_normal[] = "x[0m" ; display_normal[0] = 27 ;
83
84 // Grid parameters
85 // ---------------
86
87 const Mg3d* mg = mp.get_mg() ;
88 int nz = mg->get_nzone() ; // total number of domains
89
90 // The following is required to initialize mp_prev as a Map_et:
91 Map_et& mp_et = dynamic_cast<Map_et&>(mp) ;
92
93 // Index of the point at phi=0, theta=pi/2 at the surface of the star:
94
95 int nzet = nzadapt ; //## to be checked
96
97 assert(mg->get_type_t() == SYM) ;
98 int l_b = nzet - 1 ;
99 int j_b = mg->get_nt(l_b) - 1 ;
100 int k_b = 0 ;
101
102 // Value of the enthalpy defining the surface of the star
103 // double ent_b = phi_limit(nzet-1) ;
104
105 // Parameters to control the iteration
106 // -----------------------------------
107
108 int mer_max = icontrol(0) ;
109// int mer_rot = icontrol(1) ;
110// int mer_change_omega = icontrol(2) ;
111// int mer_fix_omega = icontrol(3) ;
112//## int mer_mass = icontrol(4) ;
113 int mermax_poisson = icontrol(5) ;
114 int mer_triax = icontrol(6) ;
115//## int delta_mer_kep = icontrol(7) ;
116
117
118 double precis = control(0) ;
119// double omega_ini = control(1) ;
120 double relax = control(2) ;
121 double relax_prev = double(1) - relax ;
122 double relax_poisson = control(3) ;
123// double thres_adapt = control(4) ;
124 double ampli_triax = control(5) ;
125 double precis_adapt = control(6) ;
126
127
128 // Error indicators
129 // ----------------
130
131 diff.set_etat_qcq() ;
132 double& diff_phi = diff.set(0) ;
133 double& diff_nuf = diff.set(1) ;
134 double& diff_nuq = diff.set(2) ;
135// double& diff_dzeta = diff.set(3) ;
136// double& diff_ggg = diff.set(4) ;
137 double& diff_shift_x = diff.set(5) ;
138 double& diff_shift_y = diff.set(6) ;
139 double& vit_triax = diff.set(7) ;
140
141 // Parameters for the function Map_et::adapt
142 // -----------------------------------------
143
144 Param par_adapt ;
145 int nitermax = 100 ;
146 int niter ;
147 int adapt_flag = 1 ; // 1 = performs the full computation,
148 // 0 = performs only the rescaling by
149 // the factor alpha_r
150 int nz_search = nzet + 1 ; // Number of domains for searching the enthalpy
151 // isosurfaces
152 double alpha_r ;
153 double reg_map = 1. ; // 1 = regular mapping, 0 = contracting mapping
154
155 par_adapt.add_int(nitermax, 0) ; // maximum number of iterations to
156 // locate zeros by the secant method
157 par_adapt.add_int(nzadapt, 1) ; // number of domains where the adjustment
158 // to the isosurfaces of ent is to be
159 // performed
160 par_adapt.add_int(nz_search, 2) ; // number of domains to search for
161 // the enthalpy isosurface
162 par_adapt.add_int(adapt_flag, 3) ; // 1 = performs the full computation,
163 // 0 = performs only the rescaling by
164 // the factor alpha_r
165 par_adapt.add_int(j_b, 4) ; // theta index of the collocation point
166 // (theta_*, phi_*)
167 par_adapt.add_int(k_b, 5) ; // theta index of the collocation point
168 // (theta_*, phi_*)
169
170 par_adapt.add_int_mod(niter, 0) ; // number of iterations actually used in
171 // the secant method
172
173 par_adapt.add_double(precis_adapt, 0) ; // required absolute precision in
174 // the determination of zeros by
175 // the secant method
176 par_adapt.add_double(reg_map, 1) ; // 1. = regular mapping, 0 = contracting mapping
177
178 par_adapt.add_double(alpha_r, 2) ; // factor by which all the radial
179 // distances will be multiplied
180
181 par_adapt.add_tbl(phi_limit, 0) ; // array of values of the field Phi
182 // to define the isosurfaces.
183
184 // Parameters for the function Map_et::poisson for nuf
185 // ----------------------------------------------------
186
187 double precis_poisson = 1.e-16 ;
188
189 // Preparations
190 // ------------
191
192 // Cartesian components of the shift vector are required
194
195
196 Cmp cssjm1_nuf(ssjm1_nuf) ;
197 Cmp cssjm1_nuq(ssjm1_nuq) ;
198 Cmp cssjm1_tggg(ssjm1_tggg) ;
199 Cmp cssjm1_khi(ssjm1_khi) ;
200 Tenseur cssjm1_wshift(mp, 1, CON, mp.get_bvect_cart() ) ;
201 cssjm1_wshift.set_etat_qcq() ;
202 for (int i=1; i<=3; i++) {
203 cssjm1_wshift.set(i-1) = ssjm1_wshift(i) ;
204 }
205
206 Tenseur cshift(mp, 1, CON, mp.get_bvect_cart() ) ;
207 cshift.set_etat_qcq() ;
208 for (int i=1; i<=3; i++) {
209 cshift.set(i-1) = -beta(i) ;
210 }
211
212 Tenseur cw_shift(mp, 1, CON, mp.get_bvect_cart() ) ;
213 cw_shift.set_etat_qcq() ;
214 for (int i=1; i<=3; i++) {
215 cw_shift.set(i-1) = w_shift(i) ;
216 }
217
218 Tenseur ckhi_shift(mp) ;
219 ckhi_shift.set_etat_qcq() ;
220 ckhi_shift.set() = khi_shift ;
221
222 Param par_poisson_nuf ;
223 par_poisson_nuf.add_int(mermax_poisson, 0) ; // maximum number of iterations
224 par_poisson_nuf.add_double(relax_poisson, 0) ; // relaxation parameter
225 par_poisson_nuf.add_double(precis_poisson, 1) ; // required precision
226 par_poisson_nuf.add_int_mod(niter, 0) ; // number of iterations actually used
227 par_poisson_nuf.add_cmp_mod( cssjm1_nuf ) ;
228
229 Param par_poisson_nuq ;
230 par_poisson_nuq.add_int(mermax_poisson, 0) ; // maximum number of iterations
231 par_poisson_nuq.add_double(relax_poisson, 0) ; // relaxation parameter
232 par_poisson_nuq.add_double(precis_poisson, 1) ; // required precision
233 par_poisson_nuq.add_int_mod(niter, 0) ; // number of iterations actually used
234 par_poisson_nuq.add_cmp_mod( cssjm1_nuq ) ;
235
236 Param par_poisson_tggg ;
237 par_poisson_tggg.add_int(mermax_poisson, 0) ; // maximum number of iterations
238 par_poisson_tggg.add_double(relax_poisson, 0) ; // relaxation parameter
239 par_poisson_tggg.add_double(precis_poisson, 1) ; // required precision
240 par_poisson_tggg.add_int_mod(niter, 0) ; // number of iterations actually used
241 par_poisson_tggg.add_cmp_mod( cssjm1_tggg ) ;
242 double lambda_tggg ;
243 par_poisson_tggg.add_double_mod( lambda_tggg ) ;
244
245 Param par_poisson_dzeta ;
246 double lbda_grv2 ;
247 par_poisson_dzeta.add_double_mod( lbda_grv2 ) ;
248
249 // Parameters for the function Scalar::poisson_vect
250 // -------------------------------------------------
251
252 Param par_poisson_vect ;
253
254 par_poisson_vect.add_int(mermax_poisson, 0) ; // maximum number of iterations
255 par_poisson_vect.add_double(relax_poisson, 0) ; // relaxation parameter
256 par_poisson_vect.add_double(precis_poisson, 1) ; // required precision
257 par_poisson_vect.add_cmp_mod( cssjm1_khi ) ;
258 par_poisson_vect.add_tenseur_mod( cssjm1_wshift ) ;
259 par_poisson_vect.add_int_mod(niter, 0) ;
260
261
262 // Initializations
263 // ---------------
264
265 //## Spherical components of the shift vector are restored
267 update_metric() ;
268 //## Back to Cartesian components
270
271
272 // Quantities at the previous step :
273 Map_et mp_prev = mp_et ;
274 Scalar rphi_prev = rphi ;
275 Scalar logn_prev = logn ;
276 Scalar dzeta_prev = dzeta ;
277
278 // Creation of uninitialized tensors:
279 Scalar source_nuf(mp) ; // source term in the equation for nuf
280 Scalar source_nuq(mp) ; // source term in the equation for nuq
281 Scalar source_dzf(mp) ; // matter source term in the eq. for dzeta
282 Scalar source_dzq(mp) ; // quadratic source term in the eq. for dzeta
283 Scalar source_tggg(mp) ; // source term in the eq. for tggg
284 Vector source_shift(mp, CON, mp.get_bvect_cart()) ;
285 // source term for shift
286
287
288 ofstream fichconv("convergence.d") ; // Output file for diff_phi
289 fichconv << "# diff_phi GRV2 max_triax vit_triax" << endl ;
290
291
292 ofstream fichevol("evolution.d") ; // Output file for various quantities
293 fichevol <<
294 "# |dH/dr_eq/dH/dr_pole| r_pole/r_eq rphi_c"
295 << endl ;
296
297 diff_phi = 1 ;
298 double err_grv2 = 1 ;
299 double max_triax_prev = 0 ; // Triaxial amplitude at previous step
300
301 //=========================================================================
302 // Start of iteration
303 //=========================================================================
304
305 for(int mer=0 ; (diff_phi > precis) && (mer<mer_max) ; mer++ ) {
306
307 cout << "-----------------------------------------------" << endl ;
308 cout << "step: " << mer << endl ;
309 cout << "diff_phi = " << display_bold << diff_phi << display_normal
310 << endl ;
311 cout << "err_grv2 = " << err_grv2 << endl ;
312 fichconv << mer ;
313 fichevol << mer ;
314
315
316 //-----------------------------------------------
317 // Sources of the Poisson equations
318 //-----------------------------------------------
319
320 // Source for nu
321 // -------------
322 Scalar bet = log(bbb) ;
323 bet.std_spectral_base() ;
324
325 Vector d_logn = logn.derive_cov( mp.flat_met_spher() ) ;
326 Vector d_bet = bet.derive_cov( mp.flat_met_spher() ) ;
327
328 Scalar s_euler = stress_euler.trace(gamma) ;
329 source_nuf = qpig * a_car *( ener_euler + s_euler ) ;
330
331 source_nuq = ak_car - d_logn(1)*(d_logn(1)+d_bet(1))
332 - d_logn(2)*(d_logn(2)+d_bet(2))
333 - d_logn(3)*(d_logn(3)+d_bet(3)) ;
334
335 source_nuf.std_spectral_base() ;
336 source_nuq.std_spectral_base() ;
337
338 // Source for dzeta
339 // ----------------
340 source_dzf = 2 * qpig * a_car * b_car * stress_euler(3,3) ;
341 source_dzf.std_spectral_base() ;
342
343 source_dzq = 1.5 * ak_car
344 - d_logn(1)*d_logn(1) - d_logn(2)*d_logn(2) - d_logn(3)*d_logn(3) ;
345 source_dzq.std_spectral_base() ;
346
347 // Source for tggg
348 // ---------------
349
350 source_tggg = 2 * qpig * nn * a_car * bbb * (s_euler - b_car * stress_euler(3,3)) ;
351 source_tggg.std_spectral_base() ;
352
353 source_tggg.mult_rsint() ;
354
355
356 // Source for shift
357 // ----------------
358
359 // Matter term:
360 Vector mom_euler_cart = mom_euler ;
361 mom_euler_cart.change_triad(mp.get_bvect_cart()) ;
362 source_shift = (-4*qpig) * nn * a_car * mom_euler_cart ;
363
364 // Quadratic terms:
365 Vector vtmp = 6 * bet.derive_con( mp.flat_met_spher() )
366 - 2 * logn.derive_con( mp.flat_met_spher() ) ;
367
368 Vector squad = nn * contract(kk, 1, vtmp, 0) / b_car ;
370
371 source_shift = source_shift + squad.up(0, mp.flat_met_cart() ) ;
372
373 //----------------------------------------------
374 // Resolution of the Poisson equation for nuf
375 //----------------------------------------------
376
377 source_nuf.poisson(par_poisson_nuf, nuf) ;
378
379 cout << "Test of the Poisson equation for nuf :" << endl ;
380 Tbl err = source_nuf.test_poisson(nuf, cout, true) ;
381 diff_nuf = err(0, 0) ;
382
383 //---------------------------------------
384 // Triaxial perturbation of nuf
385 //---------------------------------------
386
387 if (mer == mer_triax) {
388
389 if ( mg->get_np(0) == 1 ) {
390 cout <<
391 "Boson_star::equilibrium: np must be stricly greater than 1"
392 << endl << " to set a triaxial perturbation !" << endl ;
393 abort() ;
394 }
395
396 const Coord& phi = mp.phi ;
397 const Coord& sint = mp.sint ;
398 Scalar perturb(mp) ;
399 perturb = 1 + ampli_triax * sint*sint * cos(2*phi) ;
400 nuf = nuf * perturb ;
401
402 nuf.std_spectral_base() ; // set the bases for spectral expansions
403 // to be the standard ones for a
404 // scalar field
405
406 }
407
408 // Monitoring of the triaxial perturbation
409 // ---------------------------------------
410
411 const Valeur& va_nuf = nuf.get_spectral_va() ;
412 va_nuf.coef() ; // Computes the spectral coefficients
413 double max_triax = 0 ;
414
415 if ( mg->get_np(0) > 1 ) {
416
417 for (int l=0; l<nz; l++) { // loop on the domains
418 for (int j=0; j<mg->get_nt(l); j++) {
419 for (int i=0; i<mg->get_nr(l); i++) {
420
421 // Coefficient of cos(2 phi) :
422 double xcos2p = (*(va_nuf.c_cf))(l, 2, j, i) ;
423
424 // Coefficient of sin(2 phi) :
425 double xsin2p = (*(va_nuf.c_cf))(l, 3, j, i) ;
426
427 double xx = sqrt( xcos2p*xcos2p + xsin2p*xsin2p ) ;
428
429 max_triax = ( xx > max_triax ) ? xx : max_triax ;
430 }
431 }
432 }
433
434 }
435
436 cout << "Triaxial part of nuf : " << max_triax << endl ;
437
438 //----------------------------------------------
439 // Resolution of the Poisson equation for nuq
440 //----------------------------------------------
441
442 source_nuq.poisson(par_poisson_nuq, nuq) ;
443
444 cout << "Test of the Poisson equation for nuq :" << endl ;
445 err = source_nuq.test_poisson(nuq, cout, true) ;
446 diff_nuq = err(0, 0) ;
447
448 //---------------------------------------------------------
449 // Resolution of the vector Poisson equation for the shift
450 //---------------------------------------------------------
451
452
453 for (int i=1; i<=3; i++) {
454 if(source_shift(i).get_etat() != ETATZERO) {
455 if(source_shift(i).dz_nonzero()) {
456 assert( source_shift(i).get_dzpuis() == 4 ) ;
457 }
458 else{
459 (source_shift.set(i)).set_dzpuis(4) ;
460 }
461 }
462 }
463
464 double lambda_shift = double(1) / double(3) ;
465
466 if ( mg->get_np(0) == 1 ) {
467 lambda_shift = 0 ;
468 }
469
470 Tenseur csource_shift(mp, 1, CON, mp.get_bvect_cart() ) ;
471 csource_shift.set_etat_qcq() ;
472 for (int i=1; i<=3; i++) {
473 csource_shift.set(i-1) = source_shift(i) ;
474 }
475 csource_shift.set(2).set_etat_zero() ; //## bizarre...
476
477 csource_shift.poisson_vect(lambda_shift, par_poisson_vect,
478 cshift, cw_shift, ckhi_shift) ;
479
480 for (int i=1; i<=3; i++) {
481 beta.set(i) = - cshift(i-1) ;
482 beta.set(i).set_dzpuis(0) ; //## bizarre...
483 w_shift.set(i) = cw_shift(i-1) ;
484 }
485 khi_shift = ckhi_shift() ;
486
487 cout << "Test of the Poisson equation for shift_x :" << endl ;
488 err = source_shift(1).test_poisson(-beta(1), cout, true) ;
489 diff_shift_x = err(0, 0) ;
490
491 cout << "Test of the Poisson equation for shift_y :" << endl ;
492 err = source_shift(2).test_poisson(-beta(2), cout, true) ;
493 diff_shift_y = err(0, 0) ;
494
495 // Computation of tnphi and nphi from the Cartesian components
496 // of the shift
497 // -----------------------------------------------------------
498
499 fait_nphi() ;
500
501
502
503 //----------------------------------------------------
504 // Adaptation of the mapping to the new enthalpy field
505 //----------------------------------------------------
506
507 // Shall the adaptation be performed ?
508 // ---------------------------------
509
510 adapt_flag = 0 ; // No adaptation of the mapping
511
512 mp_prev = mp_et ;
513
514
515 //---------------------------------------------------------
516 // Matter source terms in the gravitational field equations
517 //---------------------------------------------------------
518
519 //## Computation of tnphi and nphi from the Cartesian components
520 // of the shift for the test in hydro_euler():
521
522 fait_nphi() ;
523
524 // Update of the energy-momentum tensor
525 update_ener_mom() ;
526
527
528 //-------------------------------------------------------
529 // 2-D Poisson equation for tggg
530 //-------------------------------------------------------
531
532 Cmp csource_tggg(source_tggg) ;
533 Cmp ctggg(tggg) ;
534 mp.poisson2d(csource_tggg, mp.cmp_zero(), par_poisson_tggg,
535 ctggg) ;
536 tggg = ctggg ;
537
538
539 //-------------------------------------------------------
540 // 2-D Poisson equation for dzeta
541 //-------------------------------------------------------
542
543 Cmp csource_dzf(source_dzf) ;
544 Cmp csource_dzq(source_dzq) ;
545 Cmp cdzeta(dzeta) ;
546 mp.poisson2d(csource_dzf, csource_dzq, par_poisson_dzeta,
547 cdzeta) ;
548 dzeta = cdzeta ;
549
550 err_grv2 = lbda_grv2 - 1;
551 cout << "GRV2: " << err_grv2 << endl ;
552
553
554 //---------------------------------------
555 // Computation of the metric coefficients (except for N^phi)
556 //---------------------------------------
557
558 // Relaxations on nu and dzeta :
559
560 if (mer >= 10) {
561 logn = relax * logn + relax_prev * logn_prev ;
562
563 dzeta = relax * dzeta + relax_prev * dzeta_prev ;
564 }
565
566 // Update of the metric coefficients N, A, B and computation of K_ij :
567
568 //## Spherical components of the shift vector are restored
570 update_metric() ;
571 //## Back to Cartesian components
573
574 //-----------------------
575 // Informations display
576 //-----------------------
577
578 cout << *this << endl ;
579
580
581 //------------------------------------------------------------
582 // Relative change in Phi with respect to previous step
583 //------------------------------------------------------------
584
585 Tbl diff_phi_tbl = diffrel( rphi, rphi_prev ) ;
586 diff_phi = diff_phi_tbl(0) ;
587 for (int l=1; l<nzet; l++) {
588 diff_phi += diff_phi_tbl(l) ;
589 }
590 diff_phi /= nzet ;
591
592 fichconv << " " << log10( fabs(diff_phi) + 1.e-16 ) ;
593 fichconv << " " << log10( fabs(err_grv2) + 1.e-16 ) ;
594 fichconv << " " << log10( fabs(max_triax) + 1.e-16 ) ;
595
596 vit_triax = 0 ;
597 if ( (mer > mer_triax+1) && (max_triax_prev > 1e-13) ) {
598 vit_triax = (max_triax - max_triax_prev) / max_triax_prev ;
599 }
600
601 fichconv << " " << vit_triax ;
602
603 //------------------------------
604 // Recycling for the next step
605 //------------------------------
606
607 rphi_prev = rphi ;
608 logn_prev = logn ;
609 dzeta_prev = dzeta ;
610 max_triax_prev = max_triax ;
611
612 fichconv << endl ;
613 fichevol << endl ;
614 fichconv.flush() ;
615 fichevol.flush() ;
616
617 } // End of main loop
618
619 //=========================================================================
620 // End of iteration
621 //=========================================================================
622
623 ssjm1_nuf = cssjm1_nuf ;
624 ssjm1_nuq = cssjm1_nuq ;
625 ssjm1_tggg = cssjm1_tggg ;
626 ssjm1_khi = cssjm1_khi ;
627 for (int i=1; i<=3; i++) {
628 ssjm1_wshift.set(i) = cssjm1_wshift(i-1) ;
629 }
630
631 // Spherical components of the shift vector are restored
633
634 fichconv.close() ;
635 fichevol.close() ;
636
637}
638}
Scalar rphi
Real part of the scalar field Phi.
Definition boson_star.h:72
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.
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
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition cmp.h:446
void set_etat_zero()
Sets the logical state to ETATZERO (zero).
Definition cmp.C:289
Scalar ak_car
Scalar .
Definition compobj.h:315
Scalar b_car
Square of the metric factor B.
Definition compobj.h:293
Scalar bbb
Metric factor B.
Definition compobj.h:290
Scalar a_car
Square of the metric factor A.
Definition compobj.h:287
Sym_tensor kk
Extrinsic curvature tensor
Definition compobj.h:153
Vector mom_euler
Total 3-momentum density in the Eulerian frame.
Definition compobj.h:147
Sym_tensor stress_euler
Stress tensor with respect to the Eulerian observer.
Definition compobj.h:150
Scalar ener_euler
Total energy density E in the Eulerian frame.
Definition compobj.h:144
Metric gamma
3-metric
Definition compobj.h:141
Scalar nn
Lapse function N .
Definition compobj.h:135
Vector beta
Shift vector .
Definition compobj.h:138
Map & mp
Mapping describing the coordinate system (r,theta,phi)
Definition compobj.h:132
Active physical coordinates and mapping derivatives.
Definition coord.h:90
Basic integer array class.
Definition itbl.h:122
Radial mapping of rather general form.
Definition map.h:2752
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 sint
Definition map.h:721
const Base_vect_spher & get_bvect_spher() const
Returns the orthonormal vectorial basis associated with the coordinates of the mapping.
Definition map.h:783
const Cmp & cmp_zero() const
Returns the null Cmp defined on *this.
Definition map.h:807
const Metric_flat & flat_met_cart() const
Returns the flat metric associated with the Cartesian coordinates and with components expressed in th...
Definition map.C:331
virtual void poisson2d(const Cmp &source_mat, const Cmp &source_quad, Param &par, Cmp &uu) const =0
Computes the solution of a 2-D Poisson equation.
Coord phi
coordinate centered on the grid
Definition map.h:720
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition map.h:765
const Metric_flat & flat_met_spher() const
Returns the flat metric associated with the spherical coordinates and with components expressed in th...
Definition map.C:321
Multi-domain grid.
Definition grilles.h:273
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
int get_np(int l) const
Returns the number of points in the azimuthal direction ( ) in domain no. l.
Definition grilles.h:462
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition grilles.h:457
int get_nzone() const
Returns the number of domains.
Definition grilles.h:448
int get_nr(int l) const
Returns the number of points in the radial direction ( ) in domain no. l.
Definition grilles.h:452
Parameter storage.
Definition param.h:125
void add_double(const double &x, int position=0)
Adds the the address of a new double to the list.
Definition param.C:315
void add_cmp_mod(Cmp &ti, int position=0)
Adds the address of a new modifiable Cmp to the list.
Definition param.C:1004
void add_double_mod(double &x, int position=0)
Adds the address of a new modifiable double to the list.
Definition param.C:453
void add_int_mod(int &n, int position=0)
Adds the address of a new modifiable int to the list.
Definition param.C:385
void add_tenseur_mod(Tenseur &ti, int position=0)
Adds the address of a new modifiable Tenseur to the list.
Definition param.C:1142
void add_int(const int &n, int position=0)
Adds the address of a new int to the list.
Definition param.C:246
void add_tbl(const Tbl &ti, int position=0)
Adds the address of a new Tbl to the list.
Definition param.C:522
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
Scalar poisson() const
Solves the scalar Poisson equation with *this as a source.
Definition scalar_pde.C:136
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
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.
const Valeur & get_spectral_va() const
Returns va (read only version)
Definition scalar.h:601
void mult_rsint()
Multiplication by everywhere; dzpuis is not changed.
void set_dzpuis(int)
Modifies the dzpuis flag.
Definition scalar.C:808
const Vector & derive_con(const Metric &gam) const
Returns the "contravariant" derivative of *this with respect to some metric , by raising the index of...
Vector w_shift
Vector used in the decomposition of shift , following Shibata's prescription [Prog.
Definition compobj.h:529
Scalar logn
Logarithm of the lapse N .
Definition compobj.h:495
Scalar nuq
Part of the Metric potential = logn generated by the quadratic terms.
Definition compobj.h:510
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
Scalar nuf
Part of the Metric potential = logn generated by the matter terms.
Definition compobj.h:505
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
void update_metric()
Computes metric coefficients from known potentials.
Definition star_QI.C:410
Vector ssjm1_wshift
Effective source at the previous step for the resolution of the vector Poisson equation for .
Definition compobj.h:578
void fait_nphi()
Computes tnphi and nphi from the Cartesian components of the shift, stored in shift .
Definition star_QI.C:386
Scalar khi_shift
Scalar used in the decomposition of shift , following Shibata's prescription [Prog.
Definition compobj.h:539
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
Scalar tggg
Metric potential .
Definition compobj.h:516
Scalar ssjm1_tggg
Effective source at the previous step for the resolution of the Poisson equation for tggg .
Definition compobj.h:561
Scalar dzeta
Metric potential .
Definition compobj.h:513
Basic array class.
Definition tbl.h:161
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tbl.C:361
double & set(int i)
Read/write of a particular element (index i) (1D case)
Definition tbl.h:281
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition tenseur.h:301
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition tenseur.C:824
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tenseur.C:636
void poisson_vect(double lambda, Param &par, Tenseur &shift, Tenseur &vect, Tenseur &scal) const
Solves the vectorial Poisson equation : .
Values and coefficients of a (real-value) function.
Definition valeur.h:287
Mtbl_cf * c_cf
Coefficients of the spectral expansion of the function.
Definition valeur.h:302
void coef() const
Computes the coeffcients of *this.
Tensor field of valence 1.
Definition vector.h:188
virtual void change_triad(const Base_vect &)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Scalar & set(int)
Read/write access to a component.
Definition vector.C:296
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Cmp log10(const Cmp &)
Basis 10 logarithm.
Definition cmp_math.C:322
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition cmp_math.C:504
Cmp cos(const Cmp &)
Cosine.
Definition cmp_math.C:94
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
Tensor up(int ind, const Metric &gam) const
Computes a new tensor by raising an index of *this.
Tensor trace(int ind1, int ind2) const
Trace on two different type indices.
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Lorene prototypes.
Definition app_hor.h:64
Standard units of space, time and mass.