LORENE
et_rot_mag_mag_plus.C
1 /*
2  * Computes magnetic fields and derived quantities for rotating equilibrium
3  *
4  * (see file et_rot_mag.h for documentation)
5  *
6  */
7 
8 /*
9  * Copyright (c) 2002 Emmanuel Marcq
10  * Copyright (c) 2002 Jerome Novak
11  *
12  * This file is part of LORENE.
13  *
14  * LORENE is free software; you can redistribute it and/or modify
15  * it under the terms of the GNU General Public License as published by
16  * the Free Software Foundation; either version 2 of the License, or
17  * (at your option) any later version.
18  *
19  * LORENE is distributed in the hope that it will be useful,
20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22  * GNU General Public License for more details.
23  *
24  * You should have received a copy of the GNU General Public License
25  * along with LORENE; if not, write to the Free Software
26  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
27  *
28  */
29 
30 char et_rot_mag_mag_plus_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_mag_mag_plus.C,v 1.3 2014/10/13 08:52:58 j_novak Exp $" ;
31 
32 /*
33  * $Id: et_rot_mag_mag_plus.C,v 1.3 2014/10/13 08:52:58 j_novak Exp $
34  * $Log: et_rot_mag_mag_plus.C,v $
35  * Revision 1.3 2014/10/13 08:52:58 j_novak
36  * Lorene classes and functions now belong to the namespace Lorene.
37  *
38  * Revision 1.2 2014/10/06 15:13:09 j_novak
39  * Modified #include directives to use c++ syntax.
40  *
41  * Revision 1.1 2012/08/12 17:48:35 p_cerda
42  * Magnetstar: New classes for magnetstar. Allowing for non-equatorial symmetry in Etoile et al. Adding B_phi in Et_rot_mag.
43  *
44  * Revision 1.14 2005/06/03 15:31:56 j_novak
45  * Better computation when more than one point in phi.
46  *
47  * Revision 1.13 2003/10/03 15:58:47 j_novak
48  * Cleaning of some headers
49  *
50  * Revision 1.12 2002/09/09 13:00:39 e_gourgoulhon
51  * Modification of declaration of Fortran 77 prototypes for
52  * a better portability (in particular on IBM AIX systems):
53  * All Fortran subroutine names are now written F77_* and are
54  * defined in the new file C++/Include/proto_f77.h.
55  *
56  * Revision 1.11 2002/06/05 15:15:59 j_novak
57  * The case of non-adapted mapping is treated.
58  * parmag.d and parrot.d have been merged.
59  *
60  * Revision 1.10 2002/06/03 13:23:16 j_novak
61  * The case when the mapping is not adapted is now treated
62  *
63  * Revision 1.9 2002/06/03 13:00:45 e_marcq
64  *
65  * conduc parameter read in parmag.d
66  *
67  * Revision 1.7 2002/05/20 10:31:59 j_novak
68  * *** empty log message ***
69  *
70  * Revision 1.6 2002/05/17 15:08:01 e_marcq
71  *
72  * Rotation progressive plug-in, units corrected, Q and a_j new member data
73  *
74  * Revision 1.5 2002/05/16 10:02:09 j_novak
75  * Errors in stress energy tensor corrected
76  *
77  * Revision 1.4 2002/05/15 09:54:00 j_novak
78  * First operational version
79  *
80  * Revision 1.3 2002/05/14 13:38:36 e_marcq
81  *
82  *
83  * Unit update, new outputs
84  *
85  * Revision 1.1 2002/05/10 09:26:52 j_novak
86  * Added new class Et_rot_mag for magnetized rotating neutron stars (under development)
87  *
88  *
89  * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_mag_mag_plus.C,v 1.3 2014/10/13 08:52:58 j_novak Exp $
90  *
91  */
92 
93 // Headers C
94 #include <cstdlib>
95 #include <cmath>
96 
97 // Headers Lorene
98 #include "et_rot_mag.h"
99 #include "utilitaires.h"
100 #include "param.h"
101 #include "proto_f77.h"
102 #include "graphique.h"
103 #include "unites.h"
104 
105 namespace Lorene {
106 
107 // Algo du papier de 1995
108 
109  using namespace Unites ;
110 
111 void Et_rot_mag::magnet_comput_plus(const int adapt_flag,
112  const int initial_j,
113  const Tbl an_j,
114  Cmp (*f_j)(const Cmp&, const Tbl),
115  const Tbl bn_j,
116  Cmp (*g_j)(const Cmp&, const Tbl),
117  Cmp (*N_j)(const Cmp&, const Tbl),
118  Param& par_poisson_At,
119  Param& par_poisson_Avect){
120  double relax_mag = 1.0 ;
121 
122  int Z = mp.get_mg()->get_nzone();
123 
124  if(is_conduct()) {
125  bool adapt(adapt_flag) ;
126  /****************************************************************
127  * Assertion that all zones have same number of points in theta
128  ****************************************************************/
129  int nt = mp.get_mg()->get_nt(nzet-1) ;
130  for (int l=0; l<Z; l++) assert(mp.get_mg()->get_nt(l) == nt) ;
131 
132  Tbl Rsurf(nt) ;
133  Rsurf.set_etat_qcq() ;
134  mp.r.fait() ;
135  mp.tet.fait() ;
136  Mtbl* theta = mp.tet.c ;
137  const Map_radial* mpr = dynamic_cast<const Map_radial*>(&mp) ;
138  assert (mpr != 0x0) ;
139  for (int j=0; j<nt; j++)
140  Rsurf.set(j) = mpr->val_r_jk(l_surf()(0,j), xi_surf()(0,j), j, 0) ;
141 
142 
143  // Calcul de A_0t dans l'etoile (conducteur parfait)
144 
145  Cmp A_0t(- omega * A_phi) ;
146  A_0t.annule(nzet,Z-1) ;
147 
148  Tenseur ATTENS(A_t) ;
149  Tenseur APTENS(A_phi) ;
150  Tenseur BMN(-logn) ;
151  BMN = BMN + log(bbb) ;
152  BMN.set_std_base() ;
153 
154 
156  nphi.gradient_spher())());
158  nphi.gradient_spher())()) ;
160  BMN.gradient_spher())()
161  + 2*nphi()*flat_scalar_prod_desal(APTENS.gradient_spher(),
162  BMN.gradient_spher())()) ;
163 
164  Cmp ATANT(A_phi.srdsdt()); // Constrction par copie pour mapping
165 
166  ATANT.va = ATANT.va.mult_ct().ssint() ;
167 
168  Cmp ttnphi(tnphi()) ;
169  ttnphi.mult_rsint() ;
170  Cmp BLAH(- b_car()/(nnn()*nnn())*ttnphi*grad1) ;
171  BLAH -= (1+b_car()/(nnn()*nnn())*tnphi()*tnphi())*grad2 ;
172  Cmp nphisr(nphi()) ;
173  nphisr.div_r() ;
174  Cmp npgrada(2*nphisr*(A_phi.dsdr()+ATANT )) ;
175  npgrada.inc2_dzpuis() ;
176  BLAH -= grad3 + npgrada ;
177  Cmp gtt(-nnn()*nnn()+b_car()*tnphi()*tnphi()) ;
178  Cmp gtphi( - b_car()*ttnphi) ;
179 
180  // Calcul de j_t grace a Maxwell-Gauss
181  Cmp tmp(((BLAH - A_0t.laplacien())/a_car() - gtphi*j_phi)
182  / gtt);
183  tmp.annule(nzet, Z-1) ;
184  if (adapt) {
185  j_t = tmp ;
186  }
187  else {
188  j_t.allocate_all() ;
189  for (int j=0; j<nt; j++)
190  for (int l=0; l<nzet; l++)
191  for (int i=0; i<mp.get_mg()->get_nr(l); i++)
192  j_t.set(l,0,j,i) = ( (*mp.r.c)(l,0,j,i) > Rsurf(j) ?
193  0. : tmp(l,0,j,i) ) ;
194  j_t.annule(nzet,Z-1) ;
195  }
196  j_t.std_base_scal() ;
197 
198  // Calcul du courant j_phi
199 
200  Tbl maxA_phi = max(abs(A_phi));
201 
202  if (maxA_phi.set(0) == 0) {
203 
204  cout << "Initializing j_phi" << endl;
205 
206  double aini = 0.;
207  int nd = an_j.get_dim(0);
208  for (int i=0; i<nd - 4;i++){
209  aini = aini + fabs(an_j(i));
210  }
211  aini = aini + fabs (an_j(3)) + fabs (an_j(5));
212  double bini = 0.;
213  nd = bn_j.get_dim(0);
214  for (int i=0; i<nd;i++){
215  bini = bini + fabs(bn_j(i));
216  }
217 
218  switch (initial_j) {
219  case 0 :
220  j_phi = (ener() + press())*aini + bini ;
221  j_phi.std_base_scal() ;
222  j_phi.annule(nzet,Z-1) ;
223  j_phi.std_base_scal() ;
224  break;
225 
226  case 1 :
227  j_phi = (ener() + press())*aini + bini;
228  j_phi.std_base_scal() ;
229  j_phi.mult_rsint();
230  j_phi.annule(nzet,Z-1) ;
231  j_phi.std_base_scal() ;
232  break;
233 
234  case 2 :
235  j_phi = (ener() + press())*aini + bini ;
236  j_phi.std_base_scal() ;
237  j_phi.mult_cost();
238  j_phi.mult_rsint();
239  j_phi.set_dzpuis(2);
240  j_phi.mult_r();
241  j_phi.annule(nzet,Z-1) ;
242  j_phi.std_base_scal() ;
243  break;
244 
245  default :
246  cout << "ERROR" << endl;
247  cout << "initial_j = " << initial_j << endl;
248  abort();
249  }
250 
251 
252  }else{
253 
254 
255 
256  double maxA_phi_surf = 0.;
257  for (int j = 0; j < nt ; j++ ) {
258  // double maxA_phi_surf_tmp = fabs(A_phi(nzet-1,0,j,mp.get_mg()->get_nr(nzet-1)-1));
259  double maxA_phi_surf_tmp = fabs(A_phi(nzet,0,j,0));
260  maxA_phi_surf= max(maxA_phi_surf, maxA_phi_surf_tmp);
261  }
262 
263  Cmp A_phi_scaled = A_phi / maxA_phi.set(0);
264  Cmp A_phi_scaled2 = (A_phi - maxA_phi_surf)/ maxA_phi.set(0);
265 
266  A_phi_scaled2.allocate_all() ;
267  for (int j=0; j<nt; j++) {
268  for (int l=0; l<Z; l++) {
269  for (int i=0; i<mp.get_mg()->get_nr(l); i++) {
270  if (A_phi_scaled2(l,0,j,i) < 0.) {
271  A_phi_scaled2.set(l,0,j,i) = 0 ;
272  }
273  }
274  }
275  }
276  A_phi_scaled2.std_base_scal() ;
277 
278 
279  Cmp j_phi_ff = g_j (A_phi_scaled2, bn_j)/maxA_phi.set(0);
280  //Cmp j_phi_ff = A_phi_scaled ;
281  j_phi_ff.std_base_scal() ;
282  j_phi_ff.div_rsint();
283  j_phi_ff.div_rsint();
284  j_phi_ff = j_phi_ff / b_car() / nnn() / nnn();
285 
286  j_phi = omega * j_t
287  + (ener() + press())*f_j(A_phi_scaled, an_j)/maxA_phi.set(0)/g_si
288  + j_phi_ff;
289 
290  j_phi.annule(nzet,Z-1) ;
291  j_phi.std_base_scal() ;
292 
293 
294 
295  B_phi = N_j (A_phi_scaled2, bn_j);
296  B_phi.std_base_scal() ;
297  B_phi = B_phi / nnn();
298 
299 
300 
301  }
302  // des_coupe_y(A_phi, 0., nzet, "Magnetic field") ;
303  // des_coupe_y(j_phi, 0., nzet, "Current",0x0,1.2,true,30) ;
304 
305  // Resolution de Maxwell Ampere (-> A_phi)
306  // Calcul des termes sources avec A-t du pas precedent.
307 
309  BMN.gradient_spher())());
310 
311  Tenseur source_tAphi(mp, 1, CON, mp.get_bvect_spher()) ;
312 
313  source_tAphi.set_etat_qcq() ;
314  Cmp tjphi(j_phi) ;
315  tjphi.mult_rsint() ;
316  Cmp tgrad1(grad1) ;
317  tgrad1.mult_rsint() ;
318  Cmp d_grad4(grad4) ;
319  d_grad4.div_rsint() ;
320  source_tAphi.set(0)=0 ;
321  source_tAphi.set(1)=0 ;
322  source_tAphi.set(2)= -b_car()*a_car()*(tjphi-tnphi()*j_t)
323  + b_car()/(nnn()*nnn())*(tgrad1+tnphi()*grad2)+d_grad4 ;
324 
325  source_tAphi.change_triad(mp.get_bvect_cart());
326 
327  Tenseur WORK_VECT(mp, 1, CON, mp.get_bvect_cart()) ;
328  WORK_VECT.set_etat_qcq() ;
329  for (int i=0; i<3; i++) {
330  WORK_VECT.set(i) = 0 ;
331  }
332  Tenseur WORK_SCAL(mp) ;
333  WORK_SCAL.set_etat_qcq() ;
334  WORK_SCAL.set() = 0 ;
335 
336  double lambda_mag = 0. ; // No 3D version !
337 
338  Tenseur AVECT(source_tAphi) ;
339  if (source_tAphi.get_etat() != ETATZERO) {
340 
341  for (int i=0; i<3; i++) {
342  if(source_tAphi(i).dz_nonzero()) {
343  assert( source_tAphi(i).get_dzpuis() == 4 ) ;
344  }
345  else{
346  (source_tAphi.set(i)).set_dzpuis(4) ;
347  }
348  }
349 
350  }
351  source_tAphi.poisson_vect(lambda_mag, par_poisson_Avect, AVECT, WORK_VECT,
352  WORK_SCAL) ;
353  AVECT.change_triad(mp.get_bvect_spher());
354  Cmp A_phi_n(AVECT(2));
355  A_phi_n.mult_rsint() ;
356 
357  // Resolution de Maxwell-Ampere : A_1
358 
359  Cmp source_A_1t(-a_car()*(j_t*gtt + j_phi*gtphi) + BLAH);
360 
361  Cmp A_1t(mp);
362  A_1t = 0 ;
363  source_A_1t.poisson(par_poisson_At, A_1t) ;
364 
365  int L = mp.get_mg()->get_nt(0);
366 
367  Tbl MAT(L,L) ;
368  Tbl MAT_PHI(L,L);
369  Tbl VEC(L) ;
370 
371  MAT.set_etat_qcq() ;
372  VEC.set_etat_qcq() ;
373  MAT_PHI.set_etat_qcq() ;
374 
375  Tbl leg(L,2*L) ;
376  leg.set_etat_qcq() ;
377 
378  Cmp psi(mp);
379  Cmp psi2(mp);
380  psi.allocate_all() ;
381  psi2.allocate_all() ;
382 
383  for (int p=0; p<mp.get_mg()->get_np(0); p++) {
384  // leg[k,l] : legendre_l(cos(theta_k))
385  // Construction par recurrence de degre 2
386  for(int k=0;k<L;k++){
387  for(int l=0;l<2*L;l++){
388 
389  if(l==0) leg.set(k,l)=1. ;
390  if(l==1) leg.set(k,l)=cos((*theta)(l_surf()(p,k),p,k,0)) ;
391  if(l>=2) leg.set(k,l) = double(2*l-1)/double(l)
392  * cos((*theta)(l_surf()(p,k),p,k,0))
393  * leg(k,l-1)-double(l-1)/double(l)*leg(k,l-2) ;
394  }
395  }
396 
397  for(int k=0;k<L;k++){
398 
399  // Valeurs a la surface trouvees via va.val_point_jk(l,xisurf,k,p)
400 
401  VEC.set(k) = A_0t.va.val_point_jk(l_surf()(p,k), xi_surf()(p,k), k, p)
402  -A_1t.va.val_point_jk(l_surf()(p,k), xi_surf()(p,k), k, p);
403 
404  for(int l=0;l<L;l++) MAT.set(l,k) = leg(k,2*l)/pow(Rsurf(k),2*l+1);
405 
406  }
407  // appel fortran :
408 
409  int* IPIV=new int[L] ;
410  int INFO ;
411 
412  Tbl MAT_SAVE(MAT) ;
413  Tbl VEC2(L) ;
414  VEC2.set_etat_qcq() ;
415  int un = 1 ;
416 
417  F77_dgesv(&L, &un, MAT.t, &L, IPIV, VEC.t, &L, &INFO) ;
418 
419  // coeffs a_l dans VEC
420 
421  for(int k=0;k<L;k++) {VEC2.set(k)=1. ; }
422 
423  F77_dgesv(&L, &un, MAT_SAVE.t, &L, IPIV, VEC2.t, &L, &INFO) ;
424 
425  delete [] IPIV ;
426 
427  for(int nz=0;nz < Z; nz++){
428  for(int i=0;i< mp.get_mg()->get_nr(nz);i++){
429  for(int k=0;k<L;k++){
430  psi.set(nz,p,k,i) = 0. ;
431  psi2.set(nz,p,k,i) = 0. ;
432  for(int l=0;l<L;l++){
433  psi.set(nz,p,k,i) += VEC(l)*leg(k,2*l) /
434  pow((*mp.r.c)(nz,p,k,i),2*l+1);
435  psi2.set(nz,p,k,i) += VEC2(l)*leg(k,2*l)/
436  pow((*mp.r.c)(nz, p, k,i),2*l+1);
437  }
438  }
439  }
440  }
441  }
442  psi.std_base_scal() ;
443  psi2.std_base_scal() ;
444 
445  assert(psi.get_dzpuis() == 0) ;
446  int dif = A_1t.get_dzpuis() ;
447  if (dif > 0) {
448  for (int d=0; d<dif; d++) A_1t.dec_dzpuis() ;
449  }
450 
451  if (adapt) {
452  Cmp A_t_ext(A_1t + psi) ;
453  A_t_ext.annule(0,nzet-1) ;
454  A_0t += A_t_ext ;
455  }
456  else {
457  tmp = A_0t ;
458  A_0t.allocate_all() ;
459  for (int j=0; j<nt; j++)
460  for (int l=0; l<Z; l++)
461  for (int i=0; i<mp.get_mg()->get_nr(l); i++)
462  A_0t.set(l,0,j,i) = ( (*mp.r.c)(l,0,j,i) > Rsurf(j) ?
463  A_1t(l,0,j,i) + psi(l,0,j,i) : tmp(l,0,j,i) ) ;
464  }
465  A_0t.std_base_scal() ;
466 
467  Valeur** asymp = A_0t.asymptot(1) ;
468 
469  double Q_0 = -4*M_PI*(*asymp[1])(Z-1,0,0,0) ; // utilise A_0t plutot que E
470  delete asymp[0] ;
471  delete asymp[1] ;
472 
473  delete [] asymp ;
474 
475  asymp = psi2.asymptot(1) ;
476 
477  double Q_2 = -4*M_PI*(*asymp[1])(Z-1,0,0,0) ; // A_2t = psi2 a l'infini
478  delete asymp[0] ;
479  delete asymp[1] ;
480 
481  delete [] asymp ;
482 
483  // solution definitive de A_t:
484 
485  double C = (Q-Q_0)/Q_2 ;
486 
487  assert(psi2.get_dzpuis() == 0) ;
488  dif = A_0t.get_dzpuis() ;
489  if (dif > 0) {
490  for (int d=0; d<dif; d++) A_0t.dec_dzpuis() ;
491  }
492  Cmp A_t_n(mp) ;
493  if (adapt) {
494  A_t_n = A_0t + C ;
495  Cmp A_t_ext(A_0t + C*psi2) ;
496  A_t_ext.annule(0,nzet-1) ;
497  A_t_n.annule(nzet,Z-1) ;
498  A_t_n += A_t_ext ;
499  }
500  else {
501  A_t_n.allocate_all() ;
502  for (int j=0; j<nt; j++)
503  for (int l=0; l<Z; l++)
504  for (int i=0; i<mp.get_mg()->get_nr(l); i++)
505  A_t_n.set(l,0,j,i) = ( (*mp.r.c)(l,0,j,i) > Rsurf(j) ?
506  A_0t(l,0,j,i) + C*psi2(l,0,j,i) :
507  A_0t(l,0,j,i) + C ) ;
508  }
509  A_t_n.std_base_scal() ;
510 
511  asymp = A_t_n.asymptot(1) ;
512 
513  delete asymp[0] ;
514  delete asymp[1] ;
515 
516  delete [] asymp ;
517  A_t = relax_mag*A_t_n + (1.-relax_mag)*A_t ;
518  A_phi = relax_mag*A_phi_n + (1. - relax_mag)*A_phi ;
519 
520 
521  }else{
522  cout << "not implemented" << endl;
523  abort();
524 
525  }
526 
527 
528 }
529 
530 
531 
532 
533 
534 
535 
536 
537 
538 
539 
540 
541 
542 }
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition: cmp.h:446
void mult_rsint()
Multiplication by .
Definition: cmp_r_manip.C:116
void allocate_all()
Sets the logical state to ETATQCQ (ordinary state) and performs the memory allocation of all the elem...
Definition: cmp.C:323
void div_r()
Division by r everywhere.
Definition: cmp_r_manip.C:78
void dec_dzpuis()
Decreases by 1 the value of dzpuis and changes accordingly the values of the Cmp in the external comp...
Definition: cmp_r_manip.C:154
Valeur va
The numerical value of the Cmp
Definition: cmp.h:464
void std_base_scal()
Sets the spectral bases of the Valeur va to the standard ones for a scalar.
Definition: cmp.C:644
void annule(int l)
Sets the Cmp to zero in a given domain.
Definition: cmp.C:348
const Cmp & laplacien(int zec_mult_r=4) const
Returns the Laplacian of *this.
Definition: cmp_deriv.C:242
int get_dzpuis() const
Returns dzpuis.
Definition: cmp.h:903
void inc2_dzpuis()
Increases by 2 the value of dzpuis and changes accordingly the values of the Cmp in the external comp...
Definition: cmp_r_manip.C:192
Valeur ** asymptot(int n, const int flag=0) const
Asymptotic expansion at r = infinity.
Definition: cmp_asymptot.C:71
Cmp poisson() const
Solves the scalar Poisson equation with *this as a source.
Definition: cmp_pde.C:94
Tbl & set(int l)
Read/write of the value in a given domain.
Definition: cmp.h:724
virtual void magnet_comput_plus(const int adapt_flag, const int initial_j, const Tbl an_j, Cmp(*f_j)(const Cmp &x, const Tbl), const Tbl bn_j, Cmp(*g_j)(const Cmp &x, const Tbl), Cmp(*N_j)(const Cmp &x, const Tbl), Param &par_poisson_At, Param &par_poisson_Avect)
Computes the electromagnetic quantities solving the Maxwell equations (6) and (7) of [Bocquet,...
Base class for pure radial mappings.
Definition: map.h:1536
virtual double val_r_jk(int l, double xi, int j, int k) const =0
Returns the value of the radial coordinate r for a given and a given collocation point in in a give...
Multi-domain array.
Definition: mtbl.h:118
Parameter storage.
Definition: param.h:125
Basic array class.
Definition: tbl.h:161
double & set(int i)
Read/write of a particular element (index i) (1D case)
Definition: tbl.h:281
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tbl.C:361
double * t
The array of double.
Definition: tbl.h:173
int get_dim(int i) const
Gives the i-th dimension (ie dim.dim[i])
Definition: tbl.h:403
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 set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition: tenseur.C:1170
const Tenseur & gradient_spher() const
Returns the gradient of *this (Spherical coordinates) (scalar field only).
Definition: tenseur.C:1548
void change_triad(const Base_vect &new_triad)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Definition: tenseur.C:668
void poisson_vect(double lambda, Param &par, Tenseur &shift, Tenseur &vect, Tenseur &scal) const
Solves the vectorial Poisson equation : .
Definition: tenseur_pde.C:118
int get_etat() const
Returns the logical state.
Definition: tenseur.h:707
Values and coefficients of a (real-value) function.
Definition: valeur.h:287
const Valeur & mult_ct() const
Returns applied to *this.
double val_point_jk(int l, double x, int j, int k) const
Computes the value of the field represented by *this at an arbitrary point in , but collocation point...
Definition: valeur.C:900
const Valeur & ssint() const
Returns of *this.
Definition: valeur_ssint.C:112
Tbl max(const Cmp &)
Maximum values of a Cmp in each domain.
Definition: cmp_math.C:435
Cmp pow(const Cmp &, int)
Power .
Definition: cmp_math.C:348
Cmp cos(const Cmp &)
Cosine.
Definition: cmp_math.C:94
Cmp abs(const Cmp &)
Absolute value.
Definition: cmp_math.C:410
Cmp log(const Cmp &)
Neperian logarithm.
Definition: cmp_math.C:296
Tenseur flat_scalar_prod_desal(const Tenseur &t1, const Tenseur &t2)
Same as flat_scalar_prod but with desaliasing.
Lorene prototypes.
Definition: app_hor.h:64
Standard units of space, time and mass.