1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
|
/*
* Resolution of the divergence-free vector Poisson equation
*
* (see file vector.h for documentation).
*
*/
/*
* Copyright (c) 2003 Eric Gourgoulhon & Jerome Novak
*
* 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 version 2
* as published by the Free Software Foundation.
*
* 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 vector_df_poisson_C[] = "$Header: /cvsroot/Lorene/C++/Source/Tensor/vector_df_poisson.C,v 1.15 2014/10/13 08:53:44 j_novak Exp $" ;
/*
* $Id: vector_df_poisson.C,v 1.15 2014/10/13 08:53:44 j_novak Exp $
* $Log: vector_df_poisson.C,v $
* Revision 1.15 2014/10/13 08:53:44 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.14 2014/10/06 15:13:20 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.13 2005/02/15 09:45:22 j_novak
* Correction of an error in the matching.
*
* Revision 1.12 2005/02/09 16:53:11 j_novak
* Now V^r and eta are matched across domains, but not any of their derivatives.
*
* Revision 1.11 2005/02/09 14:52:01 j_novak
* Better solution in the shells.
*
* Revision 1.10 2005/02/09 13:20:27 j_novak
* Completely new way of solving the vector Poisson equation in the Div_free
* case: the system is inverted "as a whole" for V^r and eta. This works only
* with Map_af...
*
*
* $Header: /cvsroot/Lorene/C++/Source/Tensor/vector_df_poisson.C,v 1.15 2014/10/13 08:53:44 j_novak Exp $
*
*/
// C headers
#include <cassert>
#include <cmath>
// Lorene headers
#include "tensor.h"
#include "diff.h"
#include "proto.h"
#include "param.h"
namespace Lorene {
Vector_divfree Vector_divfree::poisson(Param& par ) const {
// All this has a meaning only for spherical components:
#ifndef NDEBUG
const Base_vect_spher* bvs = dynamic_cast<const Base_vect_spher*>(triad) ;
assert(bvs != 0x0) ;
#endif
int nitermax = par.get_int() ;
int& niter = par.get_int_mod() ;
double relax = par.get_double() ;
double precis = par.get_double(1) ;
Cmp& ss_khi = par.get_cmp_mod(0) ;
Cmp& ss_mu = par.get_cmp_mod(1) ;
// Solution for the r-component
// ----------------------------
Scalar source_r = *(cmp[0]) ;
source_r.mult_r() ;
Param par_khi ;
par_khi.add_int(nitermax, 0) ;
par_khi.add_int_mod(niter, 0) ;
par_khi.add_double(relax, 0) ;
par_khi.add_double(precis, 1) ;
par_khi.add_cmp_mod(ss_khi, 0) ;
Scalar khi (*mp) ;
khi.set_etat_zero() ;
source_r.poisson(par_khi, khi) ;
khi.div_r() ; // khi now contains V^r
// Solution for mu
// ---------------
Param par_mu ;
par_mu.add_int(nitermax, 0) ;
par_mu.add_int_mod(niter, 0) ;
par_mu.add_double(relax, 0) ;
par_mu.add_double(precis, 1) ;
par_mu.add_cmp_mod(ss_mu, 0) ;
Scalar mu_resu (*mp) ;
mu_resu.set_etat_zero() ;
mu().poisson(par_mu, mu_resu) ;
// Final result
// ------------
Vector_divfree resu(*mp, *triad, *met_div) ;
resu.set_vr_mu(khi, mu_resu) ;
return resu ;
}
/*
* In the case without parameters, first is solved the equation for mu and then
* the system of equations for (eta, V^r) is inverted as a whole:
* d2 eta / dr2 + 2/r d eta / dr - 1/r d V^r / dr = S(eta)
* d V^r / dr + 2/r V^r - l(l+1)/r eta = 0 (div free condition)
*
* There is no l=0 contribution (divergence free in all space!).
* In the nucleus and the CED the system is inverted for h(r) and v(r) ,
* such that eta = r^2 h and V^r = r^2 v in the nucleus,
* in the compactified domain one has eta = u^2 h and V^r = u^2 v (where u=1/r);
* In the shells, both equations are multiplied by r.
* These methods are used only to get particular solutions.
*
* Homogeneous solutions are known analitically: r^(l-1) and/or 1/r^(l+2)
* It is then only possible to match eta and V^r, but not their derivatives,
* due to the div-free condition.
*/
Vector_divfree Vector_divfree::poisson() const {
const Map_af* mpaff = dynamic_cast<const Map_af*>(mp) ;
#ifndef NDEBUG
for (int i=0; i<3; i++)
assert(cmp[i]->check_dzpuis(4)) ;
// All this has a meaning only for spherical components:
const Base_vect_spher* bvs = dynamic_cast<const Base_vect_spher*>(triad) ;
assert(bvs != 0x0) ;
//## ... and affine mapping, for the moment!
assert( mpaff != 0x0) ;
#endif
// Final result
// ------------
Vector_divfree resu(*mpaff, *triad, *met_div) ;
// Solution for mu
// ---------------
Scalar mu_resu = mu().poisson() ;
Scalar f_r(*mpaff) ;
if (cmp[0]->get_etat() == ETATZERO) { // no work needed ...
f_r.set_etat_zero() ;
resu.set_vr_mu(f_r, mu_resu) ;
return resu ;
}
// Some working objects
//---------------------
const Mg3d& mg = *mpaff->get_mg() ;
int nz = mg.get_nzone() ; int nzm1 = nz - 1;
assert(mg.get_type_r(0) == RARE) ;
assert(mg.get_type_r(nzm1) == UNSURR) ;
Scalar S_r = *cmp[0] ;
Scalar S_eta = eta() ;
S_r.set_spectral_va().ylm() ;
S_eta.set_spectral_va().ylm() ;
const Base_val& base = S_eta.get_spectral_va().base ;
Mtbl_cf sol_part_eta(mg, base) ; sol_part_eta.annule_hard() ;
Mtbl_cf sol_part_vr(mg, base) ; sol_part_vr.annule_hard() ;
Mtbl_cf solution_hom_un(mg, base) ; solution_hom_un.annule_hard() ;
Mtbl_cf solution_hom_deux(mg, base) ; solution_hom_deux.annule_hard() ;
// Build-up & inversion of the system for (eta, V^r) in each domain
//-----------------------------------------------------------------
// Nucleus
//--------
int nr = mg.get_nr(0) ;
int nt = mg.get_nt(0) ;
int np = mg.get_np(0) ;
double alpha = mpaff->get_alpha()[0] ;
double beta = mpaff->get_beta()[0] ;
int l_q = 0 ; int m_q = 0; int base_r = 0 ;
int nr0 = nr - 1 ; //one degree of freedom less because of division by r^2
// Loop on l and m
//----------------
for (int k=0 ; k<np+1 ; k++) {
for (int j=0 ; j<nt ; j++) {
base.give_quant_numbers(0, k, j, m_q, l_q, base_r) ;
if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q != 0) ) {
int dege1 = (l_q <3 ? 0 : 1) ; //degeneracy of eq.1
int dege2 = 0 ; //degeneracy of eq.2
int nr_eq1 = nr0 - dege1 ; //Eq.1 is for h (eta/r^2)
int nr_eq2 = nr0 - dege2 ; //Eq.2 is the div-free condition
int nrtot = nr_eq1 + nr_eq2 ;
Matrice oper(nrtot, nrtot) ; oper.set_etat_qcq() ;
Tbl sec_membre(nrtot) ; sec_membre.set_etat_qcq() ;
Diff_x2dsdx2 d2(base_r, nr) ; const Matrice& md2 = d2.get_matrice() ;
Diff_xdsdx xd(base_r, nr) ; const Matrice& mxd = xd.get_matrice() ;
Diff_id id(base_r, nr) ; const Matrice& mid = id.get_matrice() ;
// Building the operator
//----------------------
for (int lin=0; lin<nr_eq1; lin++) { //eq.1
for (int col=dege1; col<nr0; col++)
oper.set(lin,col-dege1)
= md2(lin,col) + 6*mxd(lin,col) + 6*mid(lin,col) ;
for (int col=dege2; col<nr0; col++)
oper.set(lin,col-dege2+nr_eq1) = -mxd(lin,col) -2*mid(lin,col) ;
}
for (int lin=0; lin<nr0; lin++) { //eq.2
for (int col=dege1; col<nr0; col++)
oper.set(lin+nr_eq1,col-dege1) = -l_q*(l_q+1)*mid(lin,col) ;
for (int col=dege2; col<nr0; col++)
oper.set(lin+nr_eq1, col-dege2+nr_eq1) = mxd(lin,col) + 4*mid(lin,col) ;
}
oper.set_lu() ;
// Filling the r.h.s
//------------------
for (int i=0; i<nr_eq1; i++) //eq.1
sec_membre.set(i) = (*S_eta.get_spectral_va().c_cf)(0, k, j, i) ;
for (int i=0; i<nr0; i++) //eq.2
sec_membre.set(i+nr_eq1) = 0 ;
// Inversion of the "big" operator
//--------------------------------
Tbl big_res = oper.inverse(sec_membre) ;
Tbl res_eta(nr) ; res_eta.set_etat_qcq() ;
Tbl res_vr(nr) ; res_vr.set_etat_qcq() ;
// Putting coefficients of h and v to individual arrays
//-----------------------------------------------------
for (int i=0; i<dege1; i++)
res_eta.set(i) = 0 ;
for (int i=dege1; i<nr0; i++)
res_eta.set(i) = big_res(i-dege1) ;
res_eta.set(nr0) = 0 ;
for (int i=0; i<dege2; i++)
res_vr.set(i) = 0 ;
for (int i=dege2; i<nr0; i++)
res_vr.set(i) = big_res(i-dege2+nr_eq1) ;
res_vr.set(nr0) = 0 ;
// Multiplication by xi^2 (the alpha^2 factor comes soon)
//-------------------------------------------------------
multx2_1d(nr, &res_eta.t, base_r) ;
multx2_1d(nr, &res_vr.t, base_r) ;
// Homogeneous solution (only r^(l-1) in the nucleus)
Tbl sol_hom = solh(nr, l_q-1, 0., base_r) ;
for (int i=0 ; i<nr ; i++) {
sol_part_eta.set(0, k, j, i) = alpha*alpha*res_eta(i) ;
sol_part_vr.set(0, k, j, i) = alpha*alpha*res_vr(i) ;
solution_hom_un.set(0, k, j, i) = sol_hom(i) ;
solution_hom_deux.set(0, k, j, i) = 0. ;
}
}
}
}
// Shells
//-------
for (int zone=1 ; zone<nzm1 ; zone++) {
nr = mg.get_nr(zone) ;
assert (nr > 5) ;
assert(nt == mg.get_nt(zone)) ;
assert(np == mg.get_np(zone)) ;
alpha = mpaff->get_alpha()[zone] ;
beta = mpaff->get_beta()[zone] ;
double ech = beta / alpha ;
// Loop on l and m
//----------------
for (int k=0 ; k<np+1 ; k++) {
for (int j=0 ; j<nt ; j++) {
base.give_quant_numbers(zone, k, j, m_q, l_q, base_r) ;
if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q != 0) ) {
int dege1 = 2 ; //degeneracy of eq.1
int dege2 = 0 ; //degeneracy of eq.2
int nr_eq1 = nr - dege1 ; //Eq.1 is for eta
int nr_eq2 = nr - dege2 ; //Eq.2 is the div-free condition
int nrtot = nr_eq1 + nr_eq2 + 1;
Matrice oper(nrtot, nrtot) ; oper.set_etat_qcq() ;
Tbl sec_membre(nrtot) ; sec_membre.set_etat_qcq() ;
Diff_x2dsdx2 x2d2(base_r, nr+1); const Matrice& m2d2 = x2d2.get_matrice() ;
Diff_xdsdx2 xd2(base_r, nr+1) ; const Matrice& mxd2 = xd2.get_matrice() ;
Diff_dsdx2 d2(base_r, nr+1) ; const Matrice& md2 = d2.get_matrice() ;
Diff_xdsdx xd(base_r, nr+1) ; const Matrice& mxd = xd.get_matrice() ;
Diff_dsdx d1(base_r, nr+1) ; const Matrice& md = d1.get_matrice() ;
Diff_id id(base_r, nr+1) ; const Matrice& mid = id.get_matrice() ;
// Building the operator
//----------------------
for (int lin=0; lin<nr_eq1; lin++) {
for (int col=dege1; col<nr; col++)
oper.set(lin,col-dege1)
= mxd2(lin,col) + ech*md2(lin,col) + 2*md(lin,col) ;
for (int col=dege2; col<nr+1; col++)
oper.set(lin,col-dege2+nr_eq1) = -md(lin,col) ;
}
for (int lin=0; lin<nr_eq2; lin++) {
for (int col=dege1; col<nr; col++)
oper.set(lin+nr_eq1,col-dege1) = -l_q*(l_q+1)*mid(lin,col) ;
for (int col=dege2; col<nr+1; col++)
oper.set(lin+nr_eq1, col-dege2+nr_eq1) =
mxd(lin,col) + ech*md(lin,col) + 2*mid(lin,col) ;
}
//Additional line to avoid spurious homogeneous solutions
//this line is the first one of the V^r eq.
for (int col=dege1; col<nr; col++)
oper.set(nrtot-1, col-dege1) = 0 ;
for (int col=dege2; col<nr+1; col++)
oper.set(nrtot-1, col-dege2+nr_eq1) =
m2d2(0,col) + ech*(2*mxd2(0,col) + ech*md2(0,col))
+4*(mxd(0,col) +ech*md(0,col))
+(2 - l_q*(l_q+1))*mid(0,col) ;
oper.set_lu() ;
// Filling the r.h.s
//------------------
Tbl sr(5) ; sr.set_etat_qcq() ;
Tbl seta(nr) ; seta.set_etat_qcq() ;
for (int i=0; i<5; i++) {
sr.set(i) = (*S_r.get_spectral_va().c_cf)(zone, k, j, i);
seta.set(i) = (*S_eta.get_spectral_va().c_cf)(zone, k, j, i) ;
}
for (int i=5; i<nr; i++)
seta.set(i) = (*S_eta.get_spectral_va().c_cf)(zone, k, j, i) ;
Tbl xsr= sr ; Tbl x2sr= sr ;
Tbl xseta= seta ;
multx2_1d(5, &x2sr.t, base_r) ; multx_1d(5, &xsr.t, base_r) ;
multx_1d(nr, &xseta.t, base_r) ;
for (int i=0; i<nr_eq1; i++)
sec_membre.set(i) = alpha*(alpha*xseta(i) + beta*seta(i)) ;
for (int i=0; i<nr_eq2; i++)
sec_membre.set(i+nr_eq1) = 0 ;
sec_membre.set(nr_eq1+nr_eq2) = alpha*alpha*x2sr(0) + 2*alpha*beta*xsr(0)
+ beta*beta*sr(0) ;
// Inversion of the "big" operator
//--------------------------------
Tbl big_res = oper.inverse(sec_membre) ;
Tbl res_eta(nr) ; res_eta.set_etat_qcq() ;
Tbl res_vr(nr) ; res_vr.set_etat_qcq() ;
// Putting coefficients of h and v to individual arrays
//-----------------------------------------------------
for (int i=0; i<dege1; i++)
res_eta.set(i) = 0 ;
for (int i=dege1; i<nr; i++)
res_eta.set(i) = big_res(i-dege1) ;
for (int i=0; i<dege2; i++)
res_vr.set(i) = 0 ;
for (int i=dege2; i<nr; i++)
res_vr.set(i) = big_res(i-dege2+nr_eq1) ;
//homogeneous solutions
Tbl sol_hom1 = solh(nr, l_q-1, ech, base_r) ;
Tbl sol_hom2 = solh(nr, l_q+1, ech, base_r) ;
for (int i=0 ; i<nr ; i++) {
sol_part_eta.set(zone, k, j, i) = res_eta(i) ;
sol_part_vr.set(zone, k, j, i) = res_vr(i) ;
solution_hom_un.set(zone, k, j, i) = sol_hom1(0,i) ;
solution_hom_deux.set(zone, k, j, i) = sol_hom2(1,i) ;
}
}
}
}
}
// Compactified external domain
//-----------------------------
nr = mg.get_nr(nzm1) ;
assert(nt == mg.get_nt(nzm1)) ;
assert(np == mg.get_np(nzm1)) ;
alpha = mpaff->get_alpha()[nzm1] ;
assert (nr > 4) ;
nr0 = nr - 2 ; //two degrees of freedom less because of division by r^2
// Loop on l and m
//----------------
for (int k=0 ; k<np+1 ; k++) {
for (int j=0 ; j<nt ; j++) {
base.give_quant_numbers(nzm1, k, j, m_q, l_q, base_r) ;
if ( (nullite_plm(j, nt, k, np, base) == 1) && (l_q != 0) ) {
int dege1 = 0; //degeneracy of eq.1
int dege2 = 1; //degeneracy of eq.2
int nr_eq1 = nr0 - dege1 ; //Eq.1 is for eta
int nr_eq2 = nr0 - dege2 ; //Eq.2 is the div-free condition
int nrtot = nr_eq1 + nr_eq2 ;
Matrice oper(nrtot, nrtot) ; oper.set_etat_qcq() ;
Tbl sec_membre(nrtot) ; sec_membre.set_etat_qcq() ;
Diff_x2dsdx2 x2d2(base_r, nr) ; const Matrice& m2d2 = x2d2.get_matrice() ;
Diff_xdsdx xd(base_r, nr) ; const Matrice& mxd = xd.get_matrice() ;
Diff_id id(base_r, nr) ; const Matrice& mid = id.get_matrice() ;
// Building the operator
//----------------------
for (int lin=0; lin<nr_eq1; lin++) {
for (int col=dege1; col<nr0; col++)
oper.set(lin,col-dege1)
= m2d2(lin,col) + 4*mxd(lin,col) + 2*mid(lin,col) ;
for (int col=dege2; col<nr0; col++)
oper.set(lin,col-dege2+nr_eq1) =
mxd(lin,col) + 2*mid(lin,col) ;
}
for (int lin=0; lin<nr_eq2; lin++) {
for (int col=dege1; col<nr0; col++)
oper.set(lin+nr_eq1,col-dege1) = l_q*(l_q+1)*mid(lin,col) ;
for (int col=dege2; col<nr0; col++)
oper.set(lin+nr_eq1, col-dege2+nr_eq1) = mxd(lin,col) ;
}
oper.set_lu() ;
// Filling the r.h.s
//------------------
for (int i=0; i<nr_eq1; i++)
sec_membre.set(i) = (*S_eta.get_spectral_va().c_cf)(nzm1, k, j, i) ;
for (int i=0; i<nr_eq2; i++)
sec_membre.set(i+nr_eq1) = 0 ;
Tbl big_res = oper.inverse(sec_membre) ;
Tbl res_eta(nr) ; res_eta.set_etat_qcq() ;
Tbl res_vr(nr) ; res_vr.set_etat_qcq() ;
// Putting coefficients of h and v to individual arrays
//-----------------------------------------------------
for (int i=0; i<dege1; i++)
res_eta.set(i) = 0 ;
for (int i=dege1; i<nr0; i++)
res_eta.set(i) = big_res(i-dege1) ;
res_eta.set(nr0) = 0 ;
res_eta.set(nr0+1) = 0 ;
for (int i=0; i<dege2; i++)
res_vr.set(i) = 0 ;
for (int i=dege2; i<nr0; i++)
res_vr.set(i) = big_res(i-dege2+nr_eq1) ;
res_vr.set(nr0) = 0 ;
res_vr.set(nr0+1) = 0 ;
// Multiplication by r^2
//-----------------------
Tbl res_v2(nr) ; res_v2.set_etat_qcq() ;
Tbl res_e2(nr) ; res_e2.set_etat_qcq() ;
mult2_xm1_1d_cheb(nr, res_eta.t, res_e2.t) ;
mult2_xm1_1d_cheb(nr, res_vr.t, res_v2.t) ;
// Homogeneous solution (only 1/r^(l+2) in the CED)
Tbl sol_hom = solh(nr, l_q+1, 0., base_r) ;
for (int i=0 ; i<nr ; i++) {
sol_part_eta.set(nzm1, k, j, i) = alpha*alpha*res_e2(i) ;
sol_part_vr.set(nzm1, k, j, i) = alpha*alpha*res_v2(i) ;
solution_hom_un.set(nzm1, k, j, i) = sol_hom(i) ;
solution_hom_deux.set(nzm1, k, j, i) = 0. ;
}
}
}
}
// Now let's match everything ...
//-------------------------------
// Resulting V^r & eta
Scalar vr(*mpaff) ; vr.set_etat_qcq() ;
vr.set_spectral_base(base) ;
vr.set_spectral_va().set_etat_cf_qcq() ;
Mtbl_cf& cf_vr = *vr.set_spectral_va().c_cf ;
cf_vr.annule_hard() ;
Scalar het(*mpaff) ; het.set_etat_qcq() ;
het.set_spectral_base(base) ;
het.set_spectral_va().set_etat_cf_qcq() ;
Mtbl_cf& cf_eta = *het.set_spectral_va().c_cf ;
cf_eta.annule_hard() ;
int taille = 2*nzm1 ;
Tbl sec_membre(taille) ;
Matrice systeme(taille, taille) ;
systeme.set_etat_qcq() ;
int ligne ; int colonne ;
// Loop on l and m
//----------------
for (int k=0 ; k<np+1 ; k++)
for (int j=0 ; j<nt ; j++) {
base.give_quant_numbers(0, k, j, m_q, l_q, base_r) ;
if ((nullite_plm(j, nt, k, np, base) == 1)&&(l_q != 0)) {
ligne = 0 ;
colonne = 0 ;
sec_membre.annule_hard() ;
for (int l=0; l<taille; l++)
for (int c=0; c<taille; c++)
systeme.set(l,c) = 0 ;
//Nucleus
nr = mg.get_nr(0) ;
alpha = mpaff->get_alpha()[0] ;
// value of x^(l-1) at 1 ...
systeme.set(ligne, colonne) = 1. ;
for (int i=0 ; i<nr ; i++)
sec_membre.set(ligne) -= sol_part_eta(0, k, j, i) ;
ligne++ ;
// ... and of its couterpart for V^r
systeme.set(ligne, colonne) = l_q;
for (int i=0; i<nr; i++)
sec_membre.set(ligne) -= sol_part_vr(0,k,j,i) ;
colonne++ ;
//shells
for (int zone=1 ; zone<nzm1 ; zone++) {
nr = mg.get_nr(zone) ;
alpha = mpaff->get_alpha()[zone] ;
double echelle = mpaff->get_beta()[zone]/alpha ;
ligne -- ;
//value of (x+echelle)^(l-1) at -1
systeme.set(ligne, colonne) = -pow(echelle-1., double(l_q-1)) ;
// value of 1/(x+echelle) ^(l+2) at -1
systeme.set(ligne, colonne+1) = -1/pow(echelle-1., double(l_q+2)) ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0)
sec_membre.set(ligne) += sol_part_eta(zone, k, j, i) ;
else sec_membre.set(ligne) -= sol_part_eta(zone, k, j, i) ;
ligne++ ;
// ... and their couterparts for V^r
systeme.set(ligne, colonne) = -l_q*pow(echelle-1., double(l_q-1)) ;
systeme.set(ligne, colonne+1) = (l_q+1)/pow(echelle-1., double(l_q+2));
for (int i=0 ; i<nr ; i++)
if (i%2 == 0)
sec_membre.set(ligne) += sol_part_vr(zone, k, j, i) ;
else sec_membre.set(ligne) -= sol_part_vr(zone, k, j, i) ;
ligne++ ;
//value of (x+echelle)^(l-1) at 1 :
systeme.set(ligne, colonne) = pow(echelle+1., double(l_q-1)) ;
// value of 1/(x+echelle)^(l+2) at 1 :
systeme.set(ligne, colonne+1) = 1./pow(echelle+1., double(l_q+2)) ;
for (int i=0 ; i<nr ; i++)
sec_membre.set(ligne) -= sol_part_eta(zone, k, j, i) ;
ligne ++ ;
//... and their couterparts for V^r
systeme.set(ligne, colonne) = l_q*pow(echelle+1., double(l_q-1)) ;
systeme.set(ligne, colonne+1) = -double(l_q+1)
/ pow(echelle+1., double(l_q+2)) ;
for (int i=0 ; i<nr ; i++)
sec_membre.set(ligne) -= sol_part_vr(zone, k, j, i);
colonne += 2 ;
}
//Compactified external domain
nr = mg.get_nr(nzm1) ;
alpha = mpaff->get_alpha()[nzm1] ;
ligne -- ;
//value of (x-1)^(l+2) at -1 :
systeme.set(ligne, colonne) = -pow(-2, double(l_q+2)) ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0) sec_membre.set(ligne) += sol_part_eta(nzm1, k, j, i) ;
else sec_membre.set(ligne) -= sol_part_eta(nzm1, k, j, i) ;
//... and of its couterpart for V^r
systeme.set(ligne+1, colonne) = double(l_q+1)*pow(-2, double(l_q+2)) ;
for (int i=0 ; i<nr ; i++)
if (i%2 == 0) sec_membre.set(ligne+1) += sol_part_vr(nzm1, k, j, i) ;
else sec_membre.set(ligne+1) -= sol_part_vr(nzm1, k, j, i) ;
// Solution of the system giving the coefficients for the homogeneous
// solutions
//-------------------------------------------------------------------
if (taille > 2) systeme.set_band(2,2) ;
else systeme.set_band(1,1) ;
systeme.set_lu() ;
Tbl facteurs(systeme.inverse(sec_membre)) ;
int conte = 0 ;
// everything is put to the right place, the same combination of hom.
// solutions (with some l or -(l+1) factors) must be used for V^r
//-------------------------------------------------------------------
nr = mg.get_nr(0) ; //nucleus
for (int i=0 ; i<nr ; i++) {
cf_eta.set(0, k, j, i) = sol_part_eta(0, k, j, i)
+facteurs(conte)*solution_hom_un(0, k, j, i) ;
cf_vr.set(0, k, j, i) = sol_part_vr(0, k, j, i)
+double(l_q)*facteurs(conte)*solution_hom_un(0, k, j, i) ;
}
conte++ ;
for (int zone=1 ; zone<nzm1 ; zone++) { //shells
nr = mg.get_nr(zone) ;
for (int i=0 ; i<nr ; i++) {
cf_eta.set(zone, k, j, i) =
sol_part_eta(zone, k, j, i)
+facteurs(conte)*solution_hom_un(zone, k, j, i)
+facteurs(conte+1)*solution_hom_deux(zone, k, j, i) ;
cf_vr.set(zone, k, j, i) = sol_part_vr(zone, k, j, i)
+double(l_q)*facteurs(conte)*solution_hom_un(zone, k, j, i)
-double(l_q+1)*facteurs(conte+1)*solution_hom_deux(zone, k, j, i) ;
}
conte+=2 ;
}
nr = mg.get_nr(nz-1) ; //compactified external domain
for (int i=0 ; i<nr ; i++) {
cf_eta.set(nzm1, k, j, i) = sol_part_eta(nzm1, k, j, i)
+facteurs(conte)*solution_hom_un(nzm1, k, j, i) ;
cf_vr.set(nzm1, k, j, i) = sol_part_vr(nzm1, k, j, i)
-double(l_q+1)*facteurs(conte)*solution_hom_un(nzm1, k, j, i) ;
}
} // End of nullite_plm
} //End of loop on theta
vr.set_spectral_va().ylm_i() ;
het.set_spectral_va().ylm_i() ;
resu.set_vr_eta_mu(vr, het, mu_resu) ;
return resu ;
}
}
|
