LORENE
helmholtz_minus_mat.C
1 /*
2  * Copyright (c) 1999-2001 Philippe Grandclement
3  *
4  * This file is part of LORENE.
5  *
6  * LORENE is free software; you can redistribute it and/or modify
7  * it under the terms of the GNU General Public License as published by
8  * the Free Software Foundation; either version 2 of the License, or
9  * (at your option) any later version.
10  *
11  * LORENE is distributed in the hope that it will be useful,
12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14  * GNU General Public License for more details.
15  *
16  * You should have received a copy of the GNU General Public License
17  * along with LORENE; if not, write to the Free Software
18  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
19  *
20  */
21 
22 
23 char helmholtz_minus_mat_C[] = "$$" ;
24 
25 /*
26  * $Id: helmholtz_minus_mat.C,v 1.8 2014/10/13 08:53:28 j_novak Exp $
27  * $Log: helmholtz_minus_mat.C,v $
28  * Revision 1.8 2014/10/13 08:53:28 j_novak
29  * Lorene classes and functions now belong to the namespace Lorene.
30  *
31  * Revision 1.7 2014/10/06 15:16:08 j_novak
32  * Modified #include directives to use c++ syntax.
33  *
34  * Revision 1.6 2008/07/09 06:51:58 p_grandclement
35  * some corrections to helmholtz minus in the nucleus
36  *
37  * Revision 1.5 2008/07/08 11:45:28 p_grandclement
38  * Add helmholtz_minus in the nucleus
39  *
40  * Revision 1.4 2004/08/24 09:14:44 p_grandclement
41  * Addition of some new operators, like Poisson in 2d... It now requieres the
42  * GSL library to work.
43  *
44  * Also, the way a variable change is stored by a Param_elliptic is changed and
45  * no longer uses Change_var but rather 2 Scalars. The codes using that feature
46  * will requiere some modification. (It should concern only the ones about monopoles)
47  *
48  * Revision 1.3 2004/01/15 09:15:37 p_grandclement
49  * Modification and addition of the Helmholtz operators
50  *
51  * Revision 1.2 2003/12/11 15:57:26 p_grandclement
52  * include stdlib.h encore ...
53  *
54  * Revision 1.1 2003/12/11 14:48:49 p_grandclement
55  * Addition of ALL (and that is a lot !) the files needed for the general elliptic solver ... UNDER DEVELOPEMENT...
56  *
57  *
58  * $Header: /cvsroot/Lorene/C++/Source/Non_class_members/PDE/helmholtz_minus_mat.C,v 1.8 2014/10/13 08:53:28 j_novak Exp $
59  *
60  */
61 #include <cstdlib>
62 
63 #include "matrice.h"
64 #include "type_parite.h"
65 #include "proto.h"
66 #include "diff.h"
67 
68  //-----------------------------------
69  // Routine pour les cas non prevus --
70  //-----------------------------------
71 
72 namespace Lorene {
73 Matrice _helmholtz_minus_mat_pas_prevu(int, int, double, double, double) {
74  cout << "Helmholtz minus : base not implemented..." << endl ;
75  abort() ;
76  exit(-1) ;
77  Matrice res(1, 1) ;
78  return res;
79 }
80 
81  //-------------------------
82  //-- CAS R_CHEBU -----
83  //------------------------
84 
85 Matrice _helmholtz_minus_mat_r_chebu (int n, int lq, double alpha,
86  double, double masse) {
87 
88  assert (masse > 0) ;
89 
90  Matrice res(n-2, n-2) ;
91  res.set_etat_qcq() ;
92 
93  double* vect = new double[n] ;
94  double* vect_bis = new double[n] ;
95  double* vect_dd = new double[n] ;
96 
97  for (int i=0 ; i<n-2 ; i++) {
98 
99  for (int j=0 ; j<n ; j++)
100  vect[j] = 0 ;
101  vect[i] = 2*i+3 ;
102  vect[i+1] = -4*i-4 ;
103  vect[i+2] = 2*i+1 ;
104 
105  for (int j=0 ; j<n ; j++)
106  vect_bis[j] = vect[j] ;
107 
108  d2sdx2_1d (n, &vect_bis, R_CHEBU) ; // appel dans le cas unsurr
109  mult2_xm1_1d_cheb (n, vect_bis, vect_dd) ; // multiplication par (x-1)^2
110 
111  // Mass term
112  for (int j=0 ; j<n ; j++)
113  vect_bis[j] = vect[j] ;
114  sx2_1d (n, &vect_bis, R_CHEBU) ;
115 
116  for (int j=0 ; j<n-2 ; j++)
117  res.set(j,i) = vect_dd[j] - lq*(lq+1)*vect[j]
118  - masse*masse*vect_bis[j]/alpha/alpha ;
119  }
120 
121  delete [] vect ;
122  delete [] vect_bis ;
123  delete [] vect_dd ;
124 
125  return res ;
126 }
127 
128 
129  //-------------------------
130  //-- CAS R_CHEB -----
131  //------------------------
132 
133 Matrice _helmholtz_minus_mat_r_cheb (int n, int lq, double alpha, double beta,
134  double masse) {
135 
136  assert (masse > 0) ;
137 
138  double echelle = beta / alpha ;
139 
140  Matrice dd(n, n) ;
141  dd.set_etat_qcq() ;
142  Matrice xd(n, n) ;
143  xd.set_etat_qcq() ;
144  Matrice xx(n, n) ;
145  xx.set_etat_qcq() ;
146 
147  double* vect = new double[n] ;
148 
149  for (int i=0 ; i<n ; i++) {
150  for (int j=0 ; j<n ; j++)
151  vect[j] = 0 ;
152  vect[i] = 1 ;
153  d2sdx2_1d (n, &vect, R_CHEB) ; // appel dans le cas fin
154  vect[i] -= masse*masse*alpha*alpha ;
155  for (int j=0 ; j<n ; j++)
156  dd.set(j, i) = vect[j]*echelle*echelle ;
157  }
158 
159  for (int i=0 ; i<n ; i++) {
160  for (int j=0 ; j<n ; j++)
161  vect[j] = 0 ;
162  vect[i] = 1 ;
163  d2sdx2_1d (n, &vect, R_CHEB) ; // appel dans le cas fin
164  vect[i] -= masse*masse*alpha*alpha ;
165  multx_1d (n, &vect, R_CHEB) ;
166  for (int j=0 ; j<n ; j++)
167  dd.set(j, i) += 2*echelle*vect[j] ;
168  }
169 
170  for (int i=0 ; i<n ; i++) {
171  for (int j=0 ; j<n ; j++)
172  vect[j] = 0 ;
173  vect[i] = 1 ;
174  d2sdx2_1d (n, &vect, R_CHEB) ; // appel dans le cas fin
175  vect[i] -= masse*masse*alpha*alpha ;
176  multx_1d (n, &vect, R_CHEB) ;
177  multx_1d (n, &vect, R_CHEB) ;
178  for (int j=0 ; j<n ; j++)
179  dd.set(j, i) += vect[j] ;
180  }
181 
182  for (int i=0 ; i<n ; i++) {
183  for (int j=0 ; j<n ; j++)
184  vect[j] = 0 ;
185  vect[i] = 1 ;
186  sxdsdx_1d (n, &vect, R_CHEB) ;
187  for (int j=0 ; j<n ; j++)
188  xd.set(j, i) = vect[j]*echelle ;
189  }
190 
191  for (int i=0 ; i<n ; i++) {
192  for (int j=0 ; j<n ; j++)
193  vect[j] = 0 ;
194  vect[i] = 1 ;
195  sxdsdx_1d (n, &vect, R_CHEB) ;
196  multx_1d (n, &vect, R_CHEB) ;
197  for (int j=0 ; j<n ; j++)
198  xd.set(j, i) += vect[j] ;
199  }
200 
201  for (int i=0 ; i<n ; i++) {
202  for (int j=0 ; j<n ; j++)
203  vect[j] = 0 ;
204  vect[i] = 1 ;
205  sx2_1d (n, &vect, R_CHEB) ;
206  for (int j=0 ; j<n ; j++)
207  xx.set(j, i) = vect[j] ;
208  }
209 
210  delete [] vect ;
211 
212  Matrice res(n, n) ;
213  res = dd+2*xd - lq*(lq+1)*xx;
214 
215  return res ;
216 }
217 
218 
219  //-------------------------
220  //-- CAS R_CHEBP -----
221  //--------------------------
222 
223 
224 Matrice _helmholtz_minus_mat_r_chebp (int n, int lq, double alpha, double, double masse) {
225 
226  if (lq==0) {
227  Diff_dsdx2 d2(R_CHEBP, n) ;
228  Diff_sxdsdx sxd(R_CHEBP, n) ;
229  Diff_id xx (R_CHEBP, n) ;
230 
231  return Matrice(d2 + 2.*sxd -masse*masse*alpha*alpha*xx) ;
232  }
233  else {
234  Matrice res(n-1, n-1) ;
235  res.set_etat_qcq() ;
236 
237  double* vect = new double[n] ;
238 
239  double* vect_sx2 = new double[n] ;
240  double* vect_sxd = new double[n] ;
241  double* vect_dd = new double[n] ;
242 
243  for (int i=0 ; i<n-1 ; i++) {
244  for (int j=0 ; j<n ; j++)
245  vect[j] = 0 ;
246  vect[i] = 1. ;
247  vect[i+1] = 1. ;
248 
249 
250  for (int j=0 ; j<n ; j++)
251  vect_dd[j] = vect[j] ;
252  d2sdx2_1d (n, &vect_dd, R_CHEBP) ; // appel dans le cas chebp
253  for (int j=0 ; j<n ; j++)
254  vect_sxd[j] = vect[j] ;
255  sxdsdx_1d (n, &vect_sxd, R_CHEBP) ; // appel dans le cas chebp
256  for (int j=0 ; j<n ; j++)
257  vect_sx2[j] = vect[j] ;
258  sx2_1d (n, &vect_sx2, R_CHEBP) ; // appel dans le cas chebp
259 
260  for (int j=0 ; j<n-1 ; j++)
261  res.set(j,i) = vect_dd[j] +2*vect_sxd[j] - lq*(lq+1)*vect_sx2[j] - masse*masse*alpha*alpha*vect[j] ;
262  }
263  delete [] vect ;
264  delete [] vect_sx2 ;
265  delete [] vect_sxd ;
266  delete [] vect_dd ;
267 
268  return res ;
269  }
270 }
271 
272 
273 
274  //------------------------
275  //-- CAS R_CHEBI ----
276  //------------------------
277 
278 
279 Matrice _helmholtz_minus_mat_r_chebi (int n, int lq, double alpha, double, double masse) {
280 
281  if (lq==1) {
282  Diff_dsdx2 d2(R_CHEBI, n) ;
283  Diff_sxdsdx sxd(R_CHEBI, n) ;
284  Diff_sx2 sx2(R_CHEBI, n) ;
285  Diff_id xx(R_CHEBI, n) ;
286 
287  return Matrice(d2 + 2.*sxd - (lq*(lq+1))*sx2- masse*masse*alpha*alpha*xx) ;
288  }
289  else {
290  Matrice res(n-1, n-1) ;
291  res.set_etat_qcq() ;
292 
293  double* vect = new double[n] ;
294 
295  double* vect_sx2 = new double[n] ;
296  double* vect_sxd = new double[n] ;
297  double* vect_dd = new double[n] ;
298 
299  for (int i=0 ; i<n-1 ; i++) {
300  for (int j=0 ; j<n ; j++)
301  vect[j] = 0 ;
302  vect[i] = (2*i+3) ;
303  vect[i+1] = (2*i+1) ;
304 
305 
306  for (int j=0 ; j<n ; j++)
307  vect_dd[j] = vect[j] ;
308  d2sdx2_1d (n, &vect_dd, R_CHEBI) ; // appel dans le cas chebi
309  for (int j=0 ; j<n ; j++)
310  vect_sxd[j] = vect[j] ;
311  sxdsdx_1d (n, &vect_sxd, R_CHEBI) ; // appel dans le cas chebi
312  for (int j=0 ; j<n ; j++)
313  vect_sx2[j] = vect[j] ;
314  sx2_1d (n, &vect_sx2, R_CHEBI) ; // appel dans le cas chebi
315 
316  for (int j=0 ; j<n-1 ; j++)
317  res.set(j,i) = vect_dd[j] +2*vect_sxd[j] - lq*(lq+1)*vect_sx2[j] - masse*masse*alpha*alpha*vect[j] ;
318  }
319  delete [] vect ;
320  delete [] vect_sx2 ;
321  delete [] vect_sxd ;
322  delete [] vect_dd ;
323 
324  return res ;
325  }
326 }
327 
328 
329 
330  //--------------------------
331  //- La routine a appeler ---
332  //----------------------------
333 
334 Matrice helmholtz_minus_mat(int n, int lq,
335  double alpha, double beta, double masse,
336  int base_r)
337 {
338 
339  // Routines de derivation
340  static Matrice (*helmholtz_minus_mat[MAX_BASE])(int, int,
341  double, double, double);
342  static int nap = 0 ;
343 
344  // Premier appel
345  if (nap==0) {
346  nap = 1 ;
347  for (int i=0 ; i<MAX_BASE ; i++) {
348  helmholtz_minus_mat[i] = _helmholtz_minus_mat_pas_prevu ;
349  }
350  // Les routines existantes
351  helmholtz_minus_mat[R_CHEB >> TRA_R] = _helmholtz_minus_mat_r_cheb ;
352  helmholtz_minus_mat[R_CHEBU >> TRA_R] = _helmholtz_minus_mat_r_chebu ;
353  helmholtz_minus_mat[R_CHEBP >> TRA_R] = _helmholtz_minus_mat_r_chebp ;
354  helmholtz_minus_mat[R_CHEBI >> TRA_R] = _helmholtz_minus_mat_r_chebi ;
355  }
356 
357  Matrice res(helmholtz_minus_mat[base_r](n, lq, alpha, beta, masse)) ;
358  return res ;
359 }
360 
361 }
#define MAX_BASE
Nombre max. de bases differentes.
Definition: type_parite.h:144
#define R_CHEBU
base de Chebychev ordinaire (fin), dev. en 1/r
Definition: type_parite.h:180
#define R_CHEBI
base de Cheb. impaire (rare) seulement
Definition: type_parite.h:170
#define TRA_R
Translation en R, used for a bitwise shift (in hex)
Definition: type_parite.h:158
#define R_CHEB
base de Chebychev ordinaire (fin)
Definition: type_parite.h:166
#define R_CHEBP
base de Cheb. paire (rare) seulement
Definition: type_parite.h:168
Lorene prototypes.
Definition: app_hor.h:64