LORENE
map_et_poisson2d.C
1 /*
2  * Method of the class Map_et for the resolution of the 2-D Poisson
3  * equation.
4  *
5  * (see file map.h for documentation).
6  */
7 
8 /*
9  * Copyright (c) 2000-2001 Eric Gourgoulhon
10  *
11  * This file is part of LORENE.
12  *
13  * LORENE is free software; you can redistribute it and/or modify
14  * it under the terms of the GNU General Public License as published by
15  * the Free Software Foundation; either version 2 of the License, or
16  * (at your option) any later version.
17  *
18  * LORENE is distributed in the hope that it will be useful,
19  * but WITHOUT ANY WARRANTY; without even the implied warranty of
20  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21  * GNU General Public License for more details.
22  *
23  * You should have received a copy of the GNU General Public License
24  * along with LORENE; if not, write to the Free Software
25  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26  *
27  */
28 
29 
30 char map_et_poisson2d_C[] = "$Header: /cvsroot/Lorene/C++/Source/Map/map_et_poisson2d.C,v 1.4 2014/10/13 08:53:05 j_novak Exp $" ;
31 
32 /*
33  * $Id: map_et_poisson2d.C,v 1.4 2014/10/13 08:53:05 j_novak Exp $
34  * $Log: map_et_poisson2d.C,v $
35  * Revision 1.4 2014/10/13 08:53:05 j_novak
36  * Lorene classes and functions now belong to the namespace Lorene.
37  *
38  * Revision 1.3 2014/10/06 15:13:13 j_novak
39  * Modified #include directives to use c++ syntax.
40  *
41  * Revision 1.2 2002/02/07 14:55:58 e_gourgoulhon
42  * Corrected a bug when the source is known only in the coefficient
43  * space.
44  *
45  * Revision 1.1.1.1 2001/11/20 15:19:27 e_gourgoulhon
46  * LORENE
47  *
48  * Revision 2.4 2000/11/07 14:21:03 eric
49  * Correction d'une erreur dans le cas T_SIN_I (calcul de R(u)).
50  *
51  * Revision 2.3 2000/10/26 15:58:00 eric
52  * Correction cas T_COS_P : l'import de saff_q se fait par copie du Tbl.
53  *
54  * Revision 2.2 2000/10/12 15:37:43 eric
55  * Traitement des bases spectrales dans le cas T_COS_P.
56  *
57  * Revision 2.1 2000/10/11 15:15:43 eric
58  * 1ere version operationnelle.
59  *
60  * Revision 2.0 2000/10/09 13:47:17 eric
61  * *** empty log message ***
62  *
63  *
64  * $Header: /cvsroot/Lorene/C++/Source/Map/map_et_poisson2d.C,v 1.4 2014/10/13 08:53:05 j_novak Exp $
65  *
66  */
67 
68 // Headers C
69 #include <cmath>
70 
71 // Headers Lorene:
72 #include "map.h"
73 #include "cmp.h"
74 #include "param.h"
75 
76 //*****************************************************************************
77 
78 namespace Lorene {
79 
80 void Map_et::poisson2d(const Cmp& source_mat, const Cmp& source_quad,
81  Param& par, Cmp& uu) const {
82 
83  assert(source_mat.get_etat() != ETATNONDEF) ;
84  assert(source_quad.get_etat() != ETATNONDEF) ;
85  assert(source_mat.get_mp()->get_mg() == mg) ;
86  assert(source_quad.get_mp()->get_mg() == mg) ;
87  assert(uu.get_mp()->get_mg() == mg) ;
88 
89  assert( source_quad.check_dzpuis(4) ) ;
90 
91  double& lambda = par.get_double_mod(0) ;
92  int nz = mg->get_nzone() ;
93  int nzm1 = nz-1 ;
94 
95  // Special case of a vanishing source
96  // ----------------------------------
97 
98  if ( (source_mat.get_etat() == ETATZERO)
99  && (source_quad.get_etat() == ETATZERO) ) {
100 
101  uu = 0 ;
102  lambda = 1 ;
103  return ;
104  }
105 
106  int base_t = ((source_mat.va).base).get_base_t(0) ;
107 
108  switch (base_t) {
109 
110  //==================================================================
111  // case T_COS_P
112  //==================================================================
113 
114  case T_COS_P : {
115 
116  // Construction of a Map_af which coincides with *this on the equator
117  // ------------------------------------------------------------------
118 
119  double theta0 = M_PI / 2 ; // Equator
120  double phi0 = 0 ;
121 
122  Map_af mpaff(*this) ;
123 
124  for (int l=0 ; l<nz ; l++) {
125  double rmax = val_r(l, double(1), theta0, phi0) ;
126  switch ( mg->get_type_r(l) ) {
127  case RARE: {
128  double rmin = val_r(l, double(0), theta0, phi0) ;
129  mpaff.set_alpha(rmax - rmin, l) ;
130  mpaff.set_beta(rmin, l) ;
131  break ;
132  }
133 
134  case FIN: {
135  double rmin = val_r(l, double(-1), theta0, phi0) ;
136  mpaff.set_alpha( double(.5) * (rmax - rmin), l ) ;
137  mpaff.set_beta( double(.5) * (rmax + rmin), l) ;
138  break ;
139  }
140 
141  case UNSURR: {
142  double rmin = val_r(l, double(-1), theta0, phi0) ;
143  double umax = double(1) / rmin ;
144  double umin = double(1) / rmax ;
145  mpaff.set_alpha( double(.5) * (umin - umax), l) ;
146  mpaff.set_beta( double(.5) * (umin + umax), l) ;
147  break ;
148  }
149 
150  default: {
151  cout << "Map_et::poisson2d: unknown type_r ! " << endl ;
152  abort () ;
153  break ;
154  }
155 
156  }
157  }
158 
159  // Importation of source_mat and source_quad of the affine mapping
160  // ---------------------------------------------------------------
161  Cmp saff_m(mpaff) ;
162  saff_m.import( nzm1, source_mat ) ;
163  (saff_m.va).set_base( (source_mat.va).base ) ;
164 
165  Cmp saff_q(mpaff) ;
166 
167  // In order to use Cmp::import with dzpuis != 0 :
168  Cmp set_q = source_quad ;
169  set_q.set_dzpuis(0) ; // dzpuis artificially set to 0
170 
171  saff_q.import( nzm1, set_q ) ;
172  (saff_q.va).set_base( (set_q.va).base ) ;
173 
174  // Copy in the external domain :
175  if ( (set_q.va).get_etat() == ETATQCQ) {
176  (set_q.va).coef_i() ; // the values in configuration space are required
177  assert( (set_q.va).c->get_etat() == ETATQCQ ) ;
178  assert( (saff_q.va).c->get_etat() == ETATQCQ ) ;
179  *( (saff_q.va).c->t[nzm1] ) = *( (set_q.va).c->t[nzm1] ) ;
180  }
181 
182  // the true dzpuis is restored :
183  saff_q.set_dzpuis( source_quad.get_dzpuis() ) ;
184 
185  // Resolution of the 2-D Poisson equation on the spherical domains
186  // ---------------------------------------------------------------
187 
188  Cmp uaff(mpaff) ;
189 
190  mpaff.poisson2d(saff_m, saff_q, par, uaff) ;
191 
192  // Importation of the solution on the Map_et mapping *this
193  // -------------------------------------------------------
194 
195  uu.import(uaff) ;
196 
197  uu.va.set_base( uaff.va.base ) ; // same spectral bases
198 
199  break ;
200  }
201 
202  //==================================================================
203  // case T_SIN_I
204  //==================================================================
205 
206  case T_SIN_I : {
207 
208  //-------------------------------
209  // Computation of the prefactor a ---> Cmp apre
210  //-------------------------------
211 
212  Mtbl unjj = 1 + srdrdt*srdrdt ;
213 
214  Mtbl apre1(*mg) ;
215  apre1.set_etat_qcq() ;
216  for (int l=0; l<nz; l++) {
217  *(apre1.t[l]) = alpha[l]*alpha[l] ;
218  }
219 
220  apre1 = apre1 * dxdr * dxdr * unjj ;
221 
222  Cmp apre(*this) ;
223  apre = apre1 ;
224 
225  Tbl amax0 = max(apre1) ; // maximum values in each domain
226 
227  // The maximum values of a in each domain are put in a Mtbl
228  Mtbl amax1(*mg) ;
229  amax1.set_etat_qcq() ;
230  for (int l=0; l<nz; l++) {
231  *(amax1.t[l]) = amax0(l) ;
232  }
233 
234  Cmp amax(*this) ;
235  amax = amax1 ;
236 
237 
238  //-------------------
239  // Initializations
240  //-------------------
241 
242  int nitermax = par.get_int() ;
243  int& niter = par.get_int_mod() ;
244  double lambda_relax = par.get_double() ;
245  double unmlambda_relax = 1. - lambda_relax ;
246  double precis = par.get_double(1) ;
247 
248  Cmp& ssj = par.get_cmp_mod() ;
249 
250  Cmp ssjm1 = ssj ;
251  Cmp ssjm2 = ssjm1 ;
252 
253  Cmp ssj_q(*this) ;
254  ssj_q = 0 ;
255 
256  Valeur& vuu = uu.va ;
257 
258  Valeur vuujm1(*mg) ;
259  if (uu.get_etat() == ETATZERO) {
260  vuujm1 = 1 ; // to take relative differences
261  vuujm1.set_base( vuu.base ) ;
262  }
263  else{
264  vuujm1 = vuu ;
265  }
266 
267  // Affine mapping for the Laplacian-tilde
268 
269  Map_af mpaff(*this) ;
270 
271  cout << "Map_et::poisson2d : relat. diff. u^J <-> u^{J-1} : " << endl ;
272 
273 //==========================================================================
274 //==========================================================================
275 // Start of iteration
276 //==========================================================================
277 //==========================================================================
278 
279  Tbl tdiff(nz) ;
280  double diff ;
281  niter = 0 ;
282 
283  do {
284 
285  //====================================================================
286  // Computation of R(u) (the result is put in uu)
287  //====================================================================
288 
289 
290  //-----------------------
291  // First operations on uu
292  //-----------------------
293 
294  Valeur duudx = (uu.va).dsdx() ; // d/dx
295 
296  const Valeur& d2uudtdx = duudx.dsdt() ; // d^2/dxdtheta
297 
298  //-------------------
299  // 1/x d^2uu/dtheta^2
300  //-------------------
301 
302  Valeur sxlapang = uu.va ;
303 
304  sxlapang = sxlapang.d2sdt2() ;
305 
306  sxlapang = sxlapang.sx() ; // d^2(uu)/dth^2 /x in the nucleus
307  // d^2(uu)/dth^2 in the shells
308  // d^2(uu)/dth^2 /(x-1) in the ZEC
309 
310  //---------------------------------------------------------------
311  // Computation of
312  // [ (dR/dx)^{-1} ( A - 1 ) duu/dx + 1/R (B - 1) d^2uu/dth^2 ] / x
313  //
314  // with A = 1/(dRdx) R/(x+beta_l/alpha_l) unjj
315  // B = [1/(dRdx) R/(x+beta_l/alpha_l)]^2 unjj
316  //
317  // The result is put in uu (via vuu)
318  //---------------------------------------------------------------
319 
320  // Intermediate quantity jac which value is
321  // (dR/dx)^{-1} in the nucleus and the shells
322  // +(dU/dx)^{-1} in the ZEC
323 
324  Mtbl jac = dxdr ;
325  if (mg->get_type_r(nzm1) == UNSURR) {
326  jac.annule(nzm1, nzm1) ;
327  Mtbl jac_ext = dxdr ;
328  jac_ext.annule(0, nzm1-1) ;
329  jac_ext = - jac_ext ;
330  jac = jac + jac_ext ;
331  }
332 
333  uu.set_etat_qcq() ;
334 
335  Base_val sauve_base = duudx.base ;
336 
337  vuu = jac * ( rsxdxdr * unjj - 1.) * duudx
338  + ( rsxdxdr*rsxdxdr * unjj - 1.) * xsr * sxlapang ;
339 
340  vuu.set_base(sauve_base) ;
341 
342  vuu = vuu.sx() ;
343 
344  //---------------------------------------
345  // Computation of R(u)
346  //
347  // The result is put in uu (via vuu)
348  //---------------------------------------
349 
350 
351  sauve_base = vuu.base ;
352 
353  vuu = xsr * vuu
354  + 2. * dxdr * sr2drdt * d2uudtdx ;
355 
356  vuu += dxdr * ( sr2d2rdt2 + dxdr * (
357  dxdr* unjj * d2rdx2
358  - 2. * sr2drdt * d2rdtdx )
359  ) * duudx ;
360 
361  vuu.set_base(sauve_base) ;
362 
363  // Since the assignment is performed on vuu (uu.va), the treatment
364  // of uu.dzpuis must be performed by hand:
365 
366  uu.set_dzpuis(4) ;
367 
368  //====================================================================
369  // Computation of the effective source s^J of the ``affine''
370  // Poisson equation
371  //====================================================================
372 
373  ssj = lambda_relax * ssjm1 + unmlambda_relax * ssjm2 ;
374 
375  ssj = ( source_mat + source_quad + uu + (amax - apre) * ssj ) / amax ;
376 
377  (ssj.va).set_base((source_mat.va).base) ;
378 
379  //====================================================================
380  // Resolution of the ``affine'' Poisson equation
381  //====================================================================
382 
383  assert( uu.check_dzpuis( ssj.get_dzpuis() ) ) ;
384 
385  mpaff.poisson2d(ssj, ssj_q, par, uu) ;
386 
387  tdiff = diffrel(vuu, vuujm1) ;
388 
389  diff = max(tdiff) ;
390 
391 
392  cout << " step " << niter << " : " ;
393  for (int l=0; l<nz; l++) {
394  cout << tdiff(l) << " " ;
395  }
396  cout << endl ;
397 
398  //=================================
399  // Updates for the next iteration
400  //=================================
401 
402  ssjm2 = ssjm1 ;
403  ssjm1 = ssj ;
404  vuujm1 = vuu ;
405 
406  niter++ ;
407 
408  } // End of iteration
409  while ( (diff > precis) && (niter < nitermax) ) ;
410 
411 //==========================================================================
412 //==========================================================================
413 // End of iteration
414 //==========================================================================
415 //==========================================================================
416 
417 
418  break ;
419  }
420 
421  default : {
422  cout << "Map_et::poisson2d : unkown theta basis !" << endl ;
423  cout << " basis : " << hex << base_t << endl ;
424  abort() ;
425  break ;
426  }
427  } // End of switch on base_t
428 }
429 
430 
431 }
Lorene::Base_val
Bases of the spectral expansions.
Definition: base_val.h:322
Lorene::Valeur
Values and coefficients of a (real-value) function.
Definition: valeur.h:287
Lorene::Cmp::check_dzpuis
bool check_dzpuis(int dzi) const
Returns false if the last domain is compactified and *this is not zero in this domain and dzpuis is n...
Definition: cmp.C:715
Lorene::Map_radial::d2rdtdx
Coord d2rdtdx
in the nucleus and in the non-compactified shells; \ in the compactified outer domain.
Definition: map.h:1640
Lorene::Map_radial::sr2d2rdt2
Coord sr2d2rdt2
in the nucleus and in the non-compactified shells; \ in the compactified outer domain.
Definition: map.h:1657
Lorene::diffrel
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition: cmp_math.C:504
Lorene
Lorene prototypes.
Definition: app_hor.h:64
Lorene::Map_radial::xsr
Coord xsr
in the nucleus; \ 1/R in the non-compactified shells; \ in the compactified outer domain.
Definition: map.h:1549
Lorene::Mtbl::annule
void annule(int l_min, int l_max)
Sets the Mtbl to zero in some domains.
Definition: mtbl.C:329
Lorene::Mtbl
Multi-domain array.
Definition: mtbl.h:118
Lorene::Cmp::va
Valeur va
The numerical value of the Cmp
Definition: cmp.h:464
Lorene::Map::get_mg
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:765
Lorene::Cmp::get_etat
int get_etat() const
Returns the logical state.
Definition: cmp.h:899
Lorene::max
Tbl max(const Cmp &)
Maximum values of a Cmp in each domain.
Definition: cmp_math.C:435
Lorene::Mg3d::get_type_r
int get_type_r(int l) const
Returns the type of sampling in the radial direction in domain no.
Definition: grilles.h:474
Lorene::Param::get_int_mod
int & get_int_mod(int position=0) const
Returns the reference of a modifiable int stored in the list.
Definition: param.C:430
Lorene::Map_et::alpha
double * alpha
Array (size: mg->nzone ) of the values of in each domain.
Definition: map.h:2758
Lorene::Map_et::val_r
virtual double val_r(int l, double xi, double theta, double pphi) const
Returns the value of the radial coordinate r for a given in a given domain.
Definition: map_et_radius.C:92
Lorene::Map_radial::sr2drdt
Coord sr2drdt
in the nucleus and in the non-compactified shells; \ in the compactified outer domain.
Definition: map.h:1600
Lorene::Map_af::poisson2d
virtual void poisson2d(const Cmp &source_mat, const Cmp &source_quad, Param &par, Cmp &uu) const
Computes the solution of a 2-D Poisson equation.
Definition: map_af_poisson2d.C:81
Lorene::Map_radial::dxdr
Coord dxdr
in the nucleus and in the non-compactified shells; \ in the compactified outer domain.
Definition: map.h:1560
T_COS_P
#define T_COS_P
dev. cos seulement, harmoniques paires
Definition: type_parite.h:200
Lorene::Cmp
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition: cmp.h:446
Lorene::Param::get_double
const double & get_double(int position=0) const
Returns the reference of a double stored in the list.
Definition: param.C:361
Lorene::Tbl
Basic array class.
Definition: tbl.h:161
Lorene::Mg3d::get_nzone
int get_nzone() const
Returns the number of domains.
Definition: grilles.h:448
Lorene::Map_af::set_beta
void set_beta(double beta0, int l)
Modifies the value of in domain no. l.
Definition: map_af.C:641
Lorene::Cmp::get_dzpuis
int get_dzpuis() const
Returns dzpuis.
Definition: cmp.h:903
Lorene::Map_af
Affine radial mapping.
Definition: map.h:2027
Lorene::Valeur::set_base
void set_base(const Base_val &)
Sets the bases for spectral expansions (member base )
Definition: valeur.C:810
Lorene::Param::get_cmp_mod
Cmp & get_cmp_mod(int position=0) const
Returns the reference of a modifiable Cmp stored in the list.
Definition: param.C:1049
Lorene::Map_radial::d2rdx2
Coord d2rdx2
in the nucleus and in the non-compactified shells; \ in the compactified outer domain.
Definition: map.h:1619
Lorene::Valeur::dsdt
const Valeur & dsdt() const
Returns of *this.
Definition: valeur_dsdt.C:112
Lorene::Map_af::set_alpha
void set_alpha(double alpha0, int l)
Modifies the value of in domain no. l.
Definition: map_af.C:630
Lorene::Param::get_double_mod
double & get_double_mod(int position=0) const
Returns the reference of a stored modifiable double .
Definition: param.C:498
Lorene::Mtbl::t
Tbl ** t
Array (size nzone ) of pointers on the Tbl 's.
Definition: mtbl.h:132
Lorene::Param
Parameter storage.
Definition: param.h:125
Lorene::Cmp::import
void import(const Cmp &ci)
Assignment to another Cmp defined on a different mapping.
Definition: cmp_import.C:73
Lorene::Param::get_int
const int & get_int(int position=0) const
Returns the reference of a int stored in the list.
Definition: param.C:292
Lorene::Valeur::d2sdt2
const Valeur & d2sdt2() const
Returns of *this.
Definition: valeur_d2sdt2.C:107
Lorene::Valeur::base
Base_val base
Bases on which the spectral expansion is performed.
Definition: valeur.h:305
Lorene::Valeur::sx
const Valeur & sx() const
Returns (r -sampling = RARE ) \ Id (r sampling = FIN ) \ (r -sampling = UNSURR )
Definition: valeur_sx.C:110
Lorene::Map_radial::srdrdt
Coord srdrdt
in the nucleus and in the non-compactified shells; \ in the compactified outer domain.
Definition: map.h:1584
Lorene::Cmp::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: cmp.C:304
Lorene::Cmp::get_mp
const Map * get_mp() const
Returns the mapping.
Definition: cmp.h:901
Lorene::Map_et::rsxdxdr
Coord rsxdxdr
in the nucleus; \ in the shells; \ in the outermost compactified domain.
Definition: map.h:2834
Lorene::Cmp::set_dzpuis
void set_dzpuis(int)
Set a value to dzpuis.
Definition: cmp.C:654
Lorene::Mtbl::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: mtbl.C:299
Lorene::Map_et::poisson2d
virtual void poisson2d(const Cmp &source_mat, const Cmp &source_quad, Param &par, Cmp &uu) const
Computes the solution of a 2-D Poisson equation.
Definition: map_et_poisson2d.C:80
T_SIN_I
#define T_SIN_I
dev. sin seulement, harmoniques impaires
Definition: type_parite.h:206
Lorene::Map::mg
const Mg3d * mg
Pointer on the multi-grid Mgd3 on which this is defined
Definition: map.h:676