GetFEM  5.4.2
gmm_solver_Schwarz_additive.h
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30 ===========================================================================*/
31 
32 /**@file gmm_solver_Schwarz_additive.h
33  @author Yves Renard <[email protected]>
34  @author Michel Fournie <[email protected]>
35  @date October 13, 2002.
36 */
37 
38 #ifndef GMM_SOLVERS_SCHWARZ_ADDITIVE_H__
39 #define GMM_SOLVERS_SCHWARZ_ADDITIVE_H__
40 
41 #include "gmm_kernel.h"
42 #include "gmm_superlu_interface.h"
43 #include "gmm_solver_cg.h"
44 #include "gmm_solver_gmres.h"
45 #include "gmm_solver_bicgstab.h"
46 #include "gmm_solver_qmr.h"
47 
48 namespace gmm {
49 
50  /* ******************************************************************** */
51  /* Additive Schwarz interfaced local solvers */
52  /* ******************************************************************** */
53 
54  struct using_cg {};
55  struct using_gmres {};
56  struct using_bicgstab {};
57  struct using_qmr {};
58 
59  template <typename P, typename local_solver, typename Matrix>
60  struct actual_precond {
61  typedef P APrecond;
62  static const APrecond &transform(const P &PP) { return PP; }
63  };
64 
65  template <typename Matrix1, typename Precond, typename Vector>
66  void AS_local_solve(using_cg, const Matrix1 &A, Vector &x, const Vector &b,
67  const Precond &P, iteration &iter)
68  { cg(A, x, b, P, iter); }
69 
70  template <typename Matrix1, typename Precond, typename Vector>
71  void AS_local_solve(using_gmres, const Matrix1 &A, Vector &x,
72  const Vector &b, const Precond &P, iteration &iter)
73  { gmres(A, x, b, P, 100, iter); }
74 
75  template <typename Matrix1, typename Precond, typename Vector>
76  void AS_local_solve(using_bicgstab, const Matrix1 &A, Vector &x,
77  const Vector &b, const Precond &P, iteration &iter)
78  { bicgstab(A, x, b, P, iter); }
79 
80  template <typename Matrix1, typename Precond, typename Vector>
81  void AS_local_solve(using_qmr, const Matrix1 &A, Vector &x,
82  const Vector &b, const Precond &P, iteration &iter)
83  { qmr(A, x, b, P, iter); }
84 
85 #if defined(GMM_USES_SUPERLU)
86  struct using_superlu {};
87 
88  template <typename P, typename Matrix>
89  struct actual_precond<P, using_superlu, Matrix> {
90  typedef typename linalg_traits<Matrix>::value_type value_type;
91  typedef SuperLU_factor<value_type> APrecond;
92  template <typename PR>
93  static APrecond transform(const PR &) { return APrecond(); }
94  static const APrecond &transform(const APrecond &PP) { return PP; }
95  };
96 
97  template <typename Matrix1, typename Precond, typename Vector>
98  void AS_local_solve(using_superlu, const Matrix1 &, Vector &x,
99  const Vector &b, const Precond &P, iteration &iter)
100  { P.solve(x, b); iter.set_iteration(1); }
101 #endif
102 
103  /* ******************************************************************** */
104  /* Additive Schwarz Linear system */
105  /* ******************************************************************** */
106 
107  template <typename Matrix1, typename Matrix2, typename Precond,
108  typename local_solver>
109  struct add_schwarz_mat{
110  typedef typename linalg_traits<Matrix1>::value_type value_type;
111 
112  const Matrix1 *A;
113  const std::vector<Matrix2> *vB;
114  std::vector<Matrix2> vAloc;
115  mutable iteration iter;
116  double residual;
117  mutable size_type itebilan;
118  mutable std::vector<std::vector<value_type> > gi, fi;
119  std::vector<typename actual_precond<Precond, local_solver,
120  Matrix1>::APrecond> precond1;
121 
122  void init(const Matrix1 &A_, const std::vector<Matrix2> &vB_,
123  iteration iter_, const Precond &P, double residual_);
124 
125  add_schwarz_mat(void) {}
126  add_schwarz_mat(const Matrix1 &A_, const std::vector<Matrix2> &vB_,
127  iteration iter_, const Precond &P, double residual_)
128  { init(A_, vB_, iter_, P, residual_); }
129  };
130 
131  template <typename Matrix1, typename Matrix2, typename Precond,
132  typename local_solver>
133  void add_schwarz_mat<Matrix1, Matrix2, Precond, local_solver>::init(
134  const Matrix1 &A_, const std::vector<Matrix2> &vB_,
135  iteration iter_, const Precond &P, double residual_) {
136 
137  vB = &vB_; A = &A_; iter = iter_;
138  residual = residual_;
139 
140  size_type nb_sub = vB->size();
141  vAloc.resize(nb_sub);
142  gi.resize(nb_sub); fi.resize(nb_sub);
143  precond1.resize(nb_sub);
144  std::fill(precond1.begin(), precond1.end(),
145  actual_precond<Precond, local_solver, Matrix1>::transform(P));
146  itebilan = 0;
147 
148  if (iter.get_noisy()) cout << "Init pour sub dom ";
149 #ifdef GMM_USES_MPI
150  int size,tranche,borne_sup,borne_inf,rank,tag1=11,tag2=12,tag3=13,sizepr = 0;
151  // int tab[4];
152  double t_ref,t_final;
153  MPI_Status status;
154  t_ref=MPI_Wtime();
155  MPI_Comm_rank(MPI_COMM_WORLD, &rank);
156  MPI_Comm_size(MPI_COMM_WORLD, &size);
157  tranche=nb_sub/size;
158  borne_inf=rank*tranche;
159  borne_sup=(rank+1)*tranche;
160  // if (rank==size-1) borne_sup = nb_sub;
161 
162  cout << "Nombre de sous domaines " << borne_sup - borne_inf << endl;
163 
164  int sizeA = mat_nrows(*A);
165  gmm::csr_matrix<value_type> Acsr(sizeA, sizeA), Acsrtemp(sizeA, sizeA);
166  gmm::copy(gmm::eff_matrix(*A), Acsr);
167  int next = (rank + 1) % size;
168  int previous = (rank + size - 1) % size;
169  //communication of local information on ring pattern
170  //Each process receive Nproc-1 contributions
171 
172  for (int nproc = 0; nproc < size; ++nproc) {
173  for (size_type i = size_type(borne_inf); i < size_type(borne_sup); ++i) {
174 // for (size_type i = 0; i < nb_sub/size; ++i) {
175 // for (size_type i = 0; i < nb_sub; ++i) {
176  // size_type i=(rank+size*(j-1)+nb_sub)%nb_sub;
177 
178  cout << "Sous domaines " << i << " : " << mat_ncols((*vB)[i]) << endl;
179 #else
180  for (size_type i = 0; i < nb_sub; ++i) {
181 #endif
182 
183  if (iter.get_noisy()) cout << i << " " << std::flush;
184  Matrix2 Maux(mat_ncols((*vB)[i]), mat_nrows((*vB)[i]));
185 
186 #ifdef GMM_USES_MPI
187  Matrix2 Maux2(mat_ncols((*vB)[i]), mat_ncols((*vB)[i]));
188  if (nproc == 0) {
189  gmm::resize(vAloc[i], mat_ncols((*vB)[i]), mat_ncols((*vB)[i]));
190  gmm::clear(vAloc[i]);
191  }
192  gmm::mult(gmm::transposed((*vB)[i]), Acsr, Maux);
193  gmm::mult(Maux, (*vB)[i], Maux2);
194  gmm::add(Maux2, vAloc[i]);
195 #else
196  gmm::resize(vAloc[i], mat_ncols((*vB)[i]), mat_ncols((*vB)[i]));
197  gmm::mult(gmm::transposed((*vB)[i]), *A, Maux);
198  gmm::mult(Maux, (*vB)[i], vAloc[i]);
199 #endif
200 
201 #ifdef GMM_USES_MPI
202  if (nproc == size - 1 ) {
203 #endif
204  precond1[i].build_with(vAloc[i]);
205  gmm::resize(fi[i], mat_ncols((*vB)[i]));
206  gmm::resize(gi[i], mat_ncols((*vB)[i]));
207 #ifdef GMM_USES_MPI
208  }
209 #else
210  }
211 #endif
212 #ifdef GMM_USES_MPI
213  }
214  if (nproc != size - 1) {
215  MPI_Sendrecv(&(Acsr.jc[0]), sizeA+1, MPI_INT, next, tag2,
216  &(Acsrtemp.jc[0]), sizeA+1, MPI_INT, previous, tag2,
217  MPI_COMM_WORLD, &status);
218  if (Acsrtemp.jc[sizeA] > size_type(sizepr)) {
219  sizepr = Acsrtemp.jc[sizeA];
220  gmm::resize(Acsrtemp.pr, sizepr);
221  gmm::resize(Acsrtemp.ir, sizepr);
222  }
223  MPI_Sendrecv(&(Acsr.ir[0]), Acsr.jc[sizeA], MPI_INT, next, tag1,
224  &(Acsrtemp.ir[0]), Acsrtemp.jc[sizeA], MPI_INT, previous, tag1,
225  MPI_COMM_WORLD, &status);
226 
227  MPI_Sendrecv(&(Acsr.pr[0]), Acsr.jc[sizeA], mpi_type(value_type()), next, tag3,
228  &(Acsrtemp.pr[0]), Acsrtemp.jc[sizeA], mpi_type(value_type()), previous, tag3,
229  MPI_COMM_WORLD, &status);
230  gmm::copy(Acsrtemp, Acsr);
231  }
232  }
233  t_final=MPI_Wtime();
234  cout<<"temps boucle precond "<< t_final-t_ref<<endl;
235 #endif
236  if (iter.get_noisy()) cout << "\n";
237  }
238 
239  template <typename Matrix1, typename Matrix2, typename Precond,
240  typename Vector2, typename Vector3, typename local_solver>
241  void mult(const add_schwarz_mat<Matrix1, Matrix2, Precond, local_solver> &M,
242  const Vector2 &p, Vector3 &q) {
243  size_type itebilan = 0;
244 #ifdef GMM_USES_MPI
245  static double tmult_tot = 0.0;
246  double t_ref = MPI_Wtime();
247 #endif
248  // cout << "tmult AS begin " << endl;
249  mult(*(M.A), p, q);
250 #ifdef GMM_USES_MPI
251  tmult_tot += MPI_Wtime()-t_ref;
252  cout << "tmult_tot = " << tmult_tot << endl;
253 #endif
254  std::vector<double> qbis(gmm::vect_size(q));
255  std::vector<double> qter(gmm::vect_size(q));
256 #ifdef GMM_USES_MPI
257  // MPI_Status status;
258  // MPI_Request request,request1;
259  // int tag=111;
260  int size,tranche,borne_sup,borne_inf,rank;
261  size_type nb_sub=M.fi.size();
262  MPI_Comm_rank(MPI_COMM_WORLD, &rank);
263  MPI_Comm_size(MPI_COMM_WORLD, &size);
264  tranche=nb_sub/size;
265  borne_inf=rank*tranche;
266  borne_sup=(rank+1)*tranche;
267  // if (rank==size-1) borne_sup=nb_sub;
268  // int next = (rank + 1) % size;
269  // int previous = (rank + size - 1) % size;
270  t_ref = MPI_Wtime();
271  for (size_type i = size_type(borne_inf); i < size_type(borne_sup); ++i)
272 // for (size_type i = 0; i < nb_sub/size; ++i)
273  // for (size_type j = 0; j < nb_sub; ++j)
274 #else
275  for (size_type i = 0; i < M.fi.size(); ++i)
276 #endif
277  {
278 #ifdef GMM_USES_MPI
279  // size_type i=j; // (rank+size*(j-1)+nb_sub)%nb_sub;
280 #endif
281  gmm::mult(gmm::transposed((*(M.vB))[i]), q, M.fi[i]);
282  M.iter.init();
283  AS_local_solve(local_solver(), (M.vAloc)[i], (M.gi)[i],
284  (M.fi)[i],(M.precond1)[i],M.iter);
285  itebilan = std::max(itebilan, M.iter.get_iteration());
286  }
287 
288 #ifdef GMM_USES_MPI
289  cout << "First AS loop time " << MPI_Wtime() - t_ref << endl;
290 #endif
291 
292  gmm::clear(q);
293 #ifdef GMM_USES_MPI
294  t_ref = MPI_Wtime();
295  // for (size_type j = 0; j < nb_sub; ++j)
296  for (size_type i = size_type(borne_inf); i < size_type(borne_sup); ++i)
297 
298 #else
299  for (size_type i = 0; i < M.gi.size(); ++i)
300 #endif
301  {
302 
303 #ifdef GMM_USES_MPI
304  // size_type i=j; // (rank+size*(j-1)+nb_sub)%nb_sub;
305 // gmm::mult((*(M.vB))[i], M.gi[i], qbis,qbis);
306  gmm::mult((*(M.vB))[i], M.gi[i], qter);
307  add(qter,qbis,qbis);
308 #else
309  gmm::mult((*(M.vB))[i], M.gi[i], q, q);
310 #endif
311  }
312 #ifdef GMM_USES_MPI
313  //WARNING this add only if you use the ring pattern below
314  // need to do this below if using a n explicit ring pattern communication
315 
316 // add(qbis,q,q);
317  cout << "Second AS loop time " << MPI_Wtime() - t_ref << endl;
318 #endif
319 
320 
321 #ifdef GMM_USES_MPI
322  // int tag1=11;
323  static double t_tot = 0.0;
324  double t_final;
325  t_ref=MPI_Wtime();
326 // int next = (rank + 1) % size;
327 // int previous = (rank + size - 1) % size;
328  //communication of local information on ring pattern
329  //Each process receive Nproc-1 contributions
330 
331 // if (size > 1) {
332 // for (int nproc = 0; nproc < size-1; ++nproc)
333 // {
334 
335 // MPI_Sendrecv(&(qbis[0]), gmm::vect_size(q), MPI_DOUBLE, next, tag1,
336 // &(qter[0]), gmm::vect_size(q),MPI_DOUBLE,previous,tag1,
337 // MPI_COMM_WORLD,&status);
338 // gmm::copy(qter, qbis);
339 // add(qbis,q,q);
340 // }
341 // }
342  MPI_Allreduce(&(qbis[0]), &(q[0]),gmm::vect_size(q), MPI_DOUBLE,
343  MPI_SUM,MPI_COMM_WORLD);
344  t_final=MPI_Wtime();
345  t_tot += t_final-t_ref;
346  cout<<"["<< rank<<"] temps reduce Resol "<< t_final-t_ref << " t_tot = " << t_tot << endl;
347 #endif
348 
349  if (M.iter.get_noisy() > 0) cout << "itebloc = " << itebilan << endl;
350  M.itebilan += itebilan;
351  M.iter.set_resmax((M.iter.get_resmax() + M.residual) * 0.5);
352  }
353 
354  template <typename Matrix1, typename Matrix2, typename Precond,
355  typename Vector2, typename Vector3, typename local_solver>
356  void mult(const add_schwarz_mat<Matrix1, Matrix2, Precond, local_solver> &M,
357  const Vector2 &p, const Vector3 &q) {
358  mult(M, p, const_cast<Vector3 &>(q));
359  }
360 
361  template <typename Matrix1, typename Matrix2, typename Precond,
362  typename Vector2, typename Vector3, typename Vector4,
363  typename local_solver>
364  void mult(const add_schwarz_mat<Matrix1, Matrix2, Precond, local_solver> &M,
365  const Vector2 &p, const Vector3 &p2, Vector4 &q)
366  { mult(M, p, q); add(p2, q); }
367 
368  template <typename Matrix1, typename Matrix2, typename Precond,
369  typename Vector2, typename Vector3, typename Vector4,
370  typename local_solver>
371  void mult(const add_schwarz_mat<Matrix1, Matrix2, Precond, local_solver> &M,
372  const Vector2 &p, const Vector3 &p2, const Vector4 &q)
373  { mult(M, p, const_cast<Vector4 &>(q)); add(p2, q); }
374 
375  /* ******************************************************************** */
376  /* Additive Schwarz interfaced global solvers */
377  /* ******************************************************************** */
378 
379  template <typename ASM_type, typename Vect>
380  void AS_global_solve(using_cg, const ASM_type &ASM, Vect &x,
381  const Vect &b, iteration &iter)
382  { cg(ASM, x, b, *(ASM.A), identity_matrix(), iter); }
383 
384  template <typename ASM_type, typename Vect>
385  void AS_global_solve(using_gmres, const ASM_type &ASM, Vect &x,
386  const Vect &b, iteration &iter)
387  { gmres(ASM, x, b, identity_matrix(), 100, iter); }
388 
389  template <typename ASM_type, typename Vect>
390  void AS_global_solve(using_bicgstab, const ASM_type &ASM, Vect &x,
391  const Vect &b, iteration &iter)
392  { bicgstab(ASM, x, b, identity_matrix(), iter); }
393 
394  template <typename ASM_type, typename Vect>
395  void AS_global_solve(using_qmr,const ASM_type &ASM, Vect &x,
396  const Vect &b, iteration &iter)
397  { qmr(ASM, x, b, identity_matrix(), iter); }
398 
399 #if defined(GMM_USES_SUPERLU)
400  template <typename ASM_type, typename Vect>
401  void AS_global_solve(using_superlu, const ASM_type &, Vect &,
402  const Vect &, iteration &) {
403  GMM_ASSERT1(false, "You cannot use SuperLU as "
404  "global solver in additive Schwarz meethod");
405  }
406 #endif
407 
408  /* ******************************************************************** */
409  /* Linear Additive Schwarz method */
410  /* ******************************************************************** */
411  /* ref : Domain decomposition algorithms for the p-version finite */
412  /* element method for elliptic problems, Luca F. Pavarino, */
413  /* PhD thesis, Courant Institute of Mathematical Sciences, 1992. */
414  /* ******************************************************************** */
415 
416  /** Function to call if the ASM matrix is precomputed for successive solve
417  * with the same system.
418  */
419  template <typename Matrix1, typename Matrix2,
420  typename Vector2, typename Vector3, typename Precond,
421  typename local_solver, typename global_solver>
423  add_schwarz_mat<Matrix1, Matrix2, Precond, local_solver> &ASM, Vector3 &u,
424  const Vector2 &f, iteration &iter, const global_solver&) {
425 
426  typedef typename linalg_traits<Matrix1>::value_type value_type;
427 
428  size_type nb_sub = ASM.vB->size(), nb_dof = gmm::vect_size(f);
429  ASM.itebilan = 0;
430  std::vector<value_type> g(nb_dof);
431  std::vector<value_type> gbis(nb_dof);
432 #ifdef GMM_USES_MPI
433  double t_init=MPI_Wtime();
434  int size,tranche,borne_sup,borne_inf,rank;
435  MPI_Comm_rank(MPI_COMM_WORLD, &rank);
436  MPI_Comm_size(MPI_COMM_WORLD, &size);
437  tranche=nb_sub/size;
438  borne_inf=rank*tranche;
439  borne_sup=(rank+1)*tranche;
440  // if (rank==size-1) borne_sup=nb_sub*size;
441  for (size_type i = size_type(borne_inf); i < size_type(borne_sup); ++i)
442 // for (size_type i = 0; i < nb_sub/size; ++i)
443  // for (size_type j = 0; j < nb_sub; ++j)
444  // for (size_type i = rank; i < nb_sub; i+=size)
445 #else
446  for (size_type i = 0; i < nb_sub; ++i)
447 #endif
448  {
449 
450 #ifdef GMM_USES_MPI
451  // size_type i=j; // (rank+size*(j-1)+nb_sub)%nb_sub;
452 #endif
453  gmm::mult(gmm::transposed((*(ASM.vB))[i]), f, ASM.fi[i]);
454  ASM.iter.init();
455  AS_local_solve(local_solver(), ASM.vAloc[i], ASM.gi[i], ASM.fi[i],
456  ASM.precond1[i], ASM.iter);
457  ASM.itebilan = std::max(ASM.itebilan, ASM.iter.get_iteration());
458 #ifdef GMM_USES_MPI
459  gmm::mult((*(ASM.vB))[i], ASM.gi[i], gbis,gbis);
460 #else
461  gmm::mult((*(ASM.vB))[i], ASM.gi[i], g, g);
462 #endif
463  }
464 #ifdef GMM_USES_MPI
465  cout<<"temps boucle init "<< MPI_Wtime()-t_init<<endl;
466  double t_ref,t_final;
467  t_ref=MPI_Wtime();
468  MPI_Allreduce(&(gbis[0]), &(g[0]),gmm::vect_size(g), MPI_DOUBLE,
469  MPI_SUM,MPI_COMM_WORLD);
470  t_final=MPI_Wtime();
471  cout<<"temps reduce init "<< t_final-t_ref<<endl;
472 #endif
473 #ifdef GMM_USES_MPI
474  t_ref=MPI_Wtime();
475  cout<<"begin global AS"<<endl;
476 #endif
477  AS_global_solve(global_solver(), ASM, u, g, iter);
478 #ifdef GMM_USES_MPI
479  t_final=MPI_Wtime();
480  cout<<"temps AS Global Solve "<< t_final-t_ref<<endl;
481 #endif
482  if (iter.get_noisy())
483  cout << "Total number of internal iterations : " << ASM.itebilan << endl;
484  }
485 
486  /** Global function. Compute the ASM matrix and call the previous function.
487  * The ASM matrix represent the preconditionned linear system.
488  */
489  template <typename Matrix1, typename Matrix2,
490  typename Vector2, typename Vector3, typename Precond,
491  typename local_solver, typename global_solver>
492  void additive_schwarz(const Matrix1 &A, Vector3 &u,
493  const Vector2 &f, const Precond &P,
494  const std::vector<Matrix2> &vB,
495  iteration &iter, local_solver,
496  global_solver) {
497  iter.set_rhsnorm(vect_norm2(f));
498  if (iter.get_rhsnorm() == 0.0) { gmm::clear(u); return; }
499  iteration iter2 = iter; iter2.reduce_noisy();
500  iter2.set_maxiter(size_type(-1));
501  add_schwarz_mat<Matrix1, Matrix2, Precond, local_solver>
502  ASM(A, vB, iter2, P, iter.get_resmax());
503  additive_schwarz(ASM, u, f, iter, global_solver());
504  }
505 
506  /* ******************************************************************** */
507  /* Sequential Non-Linear Additive Schwarz method */
508  /* ******************************************************************** */
509  /* ref : Nonlinearly Preconditionned Inexact Newton Algorithms, */
510  /* Xiao-Chuan Cai, David E. Keyes, */
511  /* SIAM J. Sci. Comp. 24: p183-200. l */
512  /* ******************************************************************** */
513 
514  template <typename Matrixt, typename MatrixBi>
515  class NewtonAS_struct {
516 
517  public :
518  typedef Matrixt tangent_matrix_type;
519  typedef MatrixBi B_matrix_type;
520  typedef typename linalg_traits<Matrixt>::value_type value_type;
521  typedef std::vector<value_type> Vector;
522 
523  virtual size_type size(void) = 0;
524  virtual const std::vector<MatrixBi> &get_vB() = 0;
525 
526  virtual void compute_F(Vector &f, Vector &x) = 0;
527  virtual void compute_tangent_matrix(Matrixt &M, Vector &x) = 0;
528  // compute Bi^T grad(F(X)) Bi
529  virtual void compute_sub_tangent_matrix(Matrixt &Mloc, Vector &x,
530  size_type i) = 0;
531  // compute Bi^T F(X)
532  virtual void compute_sub_F(Vector &fi, Vector &x, size_type i) = 0;
533 
534  virtual ~NewtonAS_struct() {}
535  };
536 
537  template <typename Matrixt, typename MatrixBi>
538  struct AS_exact_gradient {
539  const std::vector<MatrixBi> &vB;
540  std::vector<Matrixt> vM;
541  std::vector<Matrixt> vMloc;
542 
543  void init(void) {
544  for (size_type i = 0; i < vB.size(); ++i) {
545  Matrixt aux(gmm::mat_ncols(vB[i]), gmm::mat_ncols(vM[i]));
546  gmm::resize(vMloc[i], gmm::mat_ncols(vB[i]), gmm::mat_ncols(vB[i]));
547  gmm::mult(gmm::transposed(vB[i]), vM[i], aux);
548  gmm::mult(aux, vB[i], vMloc[i]);
549  }
550  }
551  AS_exact_gradient(const std::vector<MatrixBi> &vB_) : vB(vB_) {
552  vM.resize(vB.size()); vMloc.resize(vB.size());
553  for (size_type i = 0; i < vB.size(); ++i) {
554  gmm::resize(vM[i], gmm::mat_nrows(vB[i]), gmm::mat_nrows(vB[i]));
555  }
556  }
557  };
558 
559  template <typename Matrixt, typename MatrixBi,
560  typename Vector2, typename Vector3>
561  void mult(const AS_exact_gradient<Matrixt, MatrixBi> &M,
562  const Vector2 &p, Vector3 &q) {
563  gmm::clear(q);
564  typedef typename gmm::linalg_traits<Vector3>::value_type T;
565  std::vector<T> v(gmm::vect_size(p)), w, x;
566  for (size_type i = 0; i < M.vB.size(); ++i) {
567  w.resize(gmm::mat_ncols(M.vB[i]));
568  x.resize(gmm::mat_ncols(M.vB[i]));
569  gmm::mult(M.vM[i], p, v);
570  gmm::mult(gmm::transposed(M.vB[i]), v, w);
571  double rcond;
572  SuperLU_solve(M.vMloc[i], x, w, rcond);
573  // gmm::iteration iter(1E-10, 0, 100000);
574  //gmm::gmres(M.vMloc[i], x, w, gmm::identity_matrix(), 50, iter);
575  gmm::mult_add(M.vB[i], x, q);
576  }
577  }
578 
579  template <typename Matrixt, typename MatrixBi,
580  typename Vector2, typename Vector3>
581  void mult(const AS_exact_gradient<Matrixt, MatrixBi> &M,
582  const Vector2 &p, const Vector3 &q) {
583  mult(M, p, const_cast<Vector3 &>(q));
584  }
585 
586  template <typename Matrixt, typename MatrixBi,
587  typename Vector2, typename Vector3, typename Vector4>
588  void mult(const AS_exact_gradient<Matrixt, MatrixBi> &M,
589  const Vector2 &p, const Vector3 &p2, Vector4 &q)
590  { mult(M, p, q); add(p2, q); }
591 
592  template <typename Matrixt, typename MatrixBi,
593  typename Vector2, typename Vector3, typename Vector4>
594  void mult(const AS_exact_gradient<Matrixt, MatrixBi> &M,
595  const Vector2 &p, const Vector3 &p2, const Vector4 &q)
596  { mult(M, p, const_cast<Vector4 &>(q)); add(p2, q); }
597 
598  struct S_default_newton_line_search {
599 
600  double conv_alpha, conv_r;
601  size_t it, itmax, glob_it;
602 
603  double alpha, alpha_old, alpha_mult, first_res, alpha_max_ratio;
604  double alpha_min_ratio, alpha_min;
605  size_type count, count_pat;
606  bool max_ratio_reached;
607  double alpha_max_ratio_reached, r_max_ratio_reached;
608  size_type it_max_ratio_reached;
609 
610 
611  double converged_value(void) { return conv_alpha; };
612  double converged_residual(void) { return conv_r; };
613 
614  virtual void init_search(double r, size_t git, double = 0.0) {
615  alpha_min_ratio = 0.9;
616  alpha_min = 1e-10;
617  alpha_max_ratio = 10.0;
618  alpha_mult = 0.25;
619  itmax = size_type(-1);
620  glob_it = git; if (git <= 1) count_pat = 0;
621  conv_alpha = alpha = alpha_old = 1.;
622  conv_r = first_res = r; it = 0;
623  count = 0;
624  max_ratio_reached = false;
625  }
626  virtual double next_try(void) {
627  alpha_old = alpha;
628  if (alpha >= 0.4) alpha *= 0.5; else alpha *= alpha_mult; ++it;
629  return alpha_old;
630  }
631  virtual bool is_converged(double r, double = 0.0) {
632  // cout << "r = " << r << " alpha = " << alpha / alpha_mult << " count_pat = " << count_pat << endl;
633  if (!max_ratio_reached && r < first_res * alpha_max_ratio) {
634  alpha_max_ratio_reached = alpha_old; r_max_ratio_reached = r;
635  it_max_ratio_reached = it; max_ratio_reached = true;
636  }
637  if (max_ratio_reached && r < r_max_ratio_reached * 0.5
638  && r > first_res * 1.1 && it <= it_max_ratio_reached+1) {
639  alpha_max_ratio_reached = alpha_old; r_max_ratio_reached = r;
640  it_max_ratio_reached = it;
641  }
642  if (count == 0 || r < conv_r)
643  { conv_r = r; conv_alpha = alpha_old; count = 1; }
644  if (conv_r < first_res) ++count;
645 
646  if (r < first_res * alpha_min_ratio)
647  { count_pat = 0; return true; }
648  if (count >= 5 || (alpha < alpha_min && max_ratio_reached)) {
649  if (conv_r < first_res * 0.99) count_pat = 0;
650  if (/*gmm::random() * 50. < -log(conv_alpha)-4.0 ||*/ count_pat >= 3)
651  { conv_r=r_max_ratio_reached; conv_alpha=alpha_max_ratio_reached; }
652  if (conv_r >= first_res * 0.9999) count_pat++;
653  return true;
654  }
655  return false;
656  }
657  S_default_newton_line_search(void) { count_pat = 0; }
658  };
659 
660 
661 
662  template <typename Matrixt, typename MatrixBi, typename Vector,
663  typename Precond, typename local_solver, typename global_solver>
664  void Newton_additive_Schwarz(NewtonAS_struct<Matrixt, MatrixBi> &NS,
665  const Vector &u_,
666  iteration &iter, const Precond &P,
667  local_solver, global_solver) {
668  Vector &u = const_cast<Vector &>(u_);
669  typedef typename linalg_traits<Vector>::value_type value_type;
670  typedef typename number_traits<value_type>::magnitude_type mtype;
671  typedef actual_precond<Precond, local_solver, Matrixt> chgt_precond;
672 
673  double residual = iter.get_resmax();
674 
675  S_default_newton_line_search internal_ls;
676  S_default_newton_line_search external_ls;
677 
678  typename chgt_precond::APrecond PP = chgt_precond::transform(P);
679  iter.set_rhsnorm(mtype(1));
680  iteration iternc(iter);
681  iternc.reduce_noisy(); iternc.set_maxiter(size_type(-1));
682  iteration iter2(iternc);
683  iteration iter3(iter2); iter3.reduce_noisy();
684  iteration iter4(iter3);
685  iternc.set_name("Local Newton");
686  iter2.set_name("Linear System for Global Newton");
687  iternc.set_resmax(residual/100.0);
688  iter3.set_resmax(residual/10000.0);
689  iter2.set_resmax(residual/1000.0);
690  iter4.set_resmax(residual/1000.0);
691  std::vector<value_type> rhs(NS.size()), x(NS.size()), d(NS.size());
692  std::vector<value_type> xi, xii, fi, di;
693 
694  std::vector< std::vector<value_type> > vx(NS.get_vB().size());
695  for (size_type i = 0; i < NS.get_vB().size(); ++i) // for exact gradient
696  vx[i].resize(NS.size()); // for exact gradient
697 
698  Matrixt Mloc, M(NS.size(), NS.size());
699  NS.compute_F(rhs, u);
700  mtype act_res=gmm::vect_norm2(rhs), act_res_new(0), precond_res = act_res;
701  mtype alpha;
702 
703  while(!iter.finished(std::min(act_res, precond_res))) {
704  for (int SOR_step = 0; SOR_step >= 0; --SOR_step) {
705  gmm::clear(rhs);
706  for (size_type isd = 0; isd < NS.get_vB().size(); ++isd) {
707  const MatrixBi &Bi = (NS.get_vB())[isd];
708  size_type si = mat_ncols(Bi);
709  gmm::resize(Mloc, si, si);
710  xi.resize(si); xii.resize(si); fi.resize(si); di.resize(si);
711 
712  iternc.init();
713  iternc.set_maxiter(30); // ?
714  if (iternc.get_noisy())
715  cout << "Non-linear local problem " << isd << endl;
716  gmm::clear(xi);
717  gmm::copy(u, x);
718  NS.compute_sub_F(fi, x, isd); gmm::scale(fi, value_type(-1));
719  mtype r = gmm::vect_norm2(fi), r_t(r);
720  if (r > value_type(0)) {
721  iternc.set_rhsnorm(std::max(r, mtype(1)));
722  while(!iternc.finished(r)) {
723  NS.compute_sub_tangent_matrix(Mloc, x, isd);
724 
725  PP.build_with(Mloc);
726  iter3.init();
727  AS_local_solve(local_solver(), Mloc, di, fi, PP, iter3);
728 
729  internal_ls.init_search(r, iternc.get_iteration());
730  do {
731  alpha = internal_ls.next_try();
732  gmm::add(xi, gmm::scaled(di, -alpha), xii);
733  gmm::mult(Bi, gmm::scaled(xii, -1.0), u, x);
734  NS.compute_sub_F(fi, x, isd); gmm::scale(fi, value_type(-1));
735  r_t = gmm::vect_norm2(fi);
736  } while (!internal_ls.is_converged(r_t));
737 
738  if (alpha != internal_ls.converged_value()) {
739  alpha = internal_ls.converged_value();
740  gmm::add(xi, gmm::scaled(di, -alpha), xii);
741  gmm::mult(Bi, gmm::scaled(xii, -1.0), u, x);
742  NS.compute_sub_F(fi, x, isd); gmm::scale(fi, value_type(-1));
743  r_t = gmm::vect_norm2(fi);
744  }
745  gmm::copy(x, vx[isd]); // for exact gradient
746 
747  if (iternc.get_noisy()) cout << "(step=" << alpha << ")\t";
748  ++iternc; r = r_t; gmm::copy(xii, xi);
749  }
750  if (SOR_step) gmm::mult(Bi, gmm::scaled(xii, -1.0), u, u);
751  gmm::mult(Bi, gmm::scaled(xii, -1.0), rhs, rhs);
752  }
753  }
754  precond_res = gmm::vect_norm2(rhs);
755  if (SOR_step) cout << "SOR step residual = " << precond_res << endl;
756  if (precond_res < residual) break;
757  cout << "Precond residual = " << precond_res << endl;
758  }
759 
760  iter2.init();
761  // solving linear system for the global Newton method
762  if (0) {
763  NS.compute_tangent_matrix(M, u);
764  add_schwarz_mat<Matrixt, MatrixBi, Precond, local_solver>
765  ASM(M, NS.get_vB(), iter4, P, iter.get_resmax());
766  AS_global_solve(global_solver(), ASM, d, rhs, iter2);
767  }
768  else { // for exact gradient
769  AS_exact_gradient<Matrixt, MatrixBi> eg(NS.get_vB());
770  for (size_type i = 0; i < NS.get_vB().size(); ++i) {
771  NS.compute_tangent_matrix(eg.vM[i], vx[i]);
772  }
773  eg.init();
774  gmres(eg, d, rhs, gmm::identity_matrix(), 50, iter2);
775  }
776 
777  // gmm::add(gmm::scaled(rhs, 0.1), u); ++iter;
778  external_ls.init_search(act_res, iter.get_iteration());
779  do {
780  alpha = external_ls.next_try();
781  gmm::add(gmm::scaled(d, alpha), u, x);
782  NS.compute_F(rhs, x);
783  act_res_new = gmm::vect_norm2(rhs);
784  } while (!external_ls.is_converged(act_res_new));
785 
786  if (alpha != external_ls.converged_value()) {
787  alpha = external_ls.converged_value();
788  gmm::add(gmm::scaled(d, alpha), u, x);
789  NS.compute_F(rhs, x);
790  act_res_new = gmm::vect_norm2(rhs);
791  }
792 
793  if (iter.get_noisy() > 1) cout << endl;
794  act_res = act_res_new;
795  if (iter.get_noisy()) cout << "(step=" << alpha << ")\t unprecond res = " << act_res << " ";
796 
797 
798  ++iter; gmm::copy(x, u);
799  }
800  }
801 
802 }
803 
804 
805 #endif // GMM_SOLVERS_SCHWARZ_ADDITIVE_H__
gmm_solver_bicgstab.h
BiCGStab iterative solver.
gmm::qmr
void qmr(const Matrix &A, Vector &x, const VectorB &b, const Precond1 &M1, iteration &iter)
Quasi-Minimal Residual.
Definition: gmm_solver_qmr.h:94
gmm::additive_schwarz
void additive_schwarz(add_schwarz_mat< Matrix1, Matrix2, Precond, local_solver > &ASM, Vector3 &u, const Vector2 &f, iteration &iter, const global_solver &)
Function to call if the ASM matrix is precomputed for successive solve with the same system.
Definition: gmm_solver_Schwarz_additive.h:422
gmm::resize
void resize(M &v, size_type m, size_type n)
*‍/
Definition: gmm_blas.h:231
bgeot::size_type
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:49
gmm::clear
void clear(L &l)
clear (fill with zeros) a vector or matrix.
Definition: gmm_blas.h:59
gmm::gmres
void gmres(const Mat &A, Vec &x, const VecB &b, const Precond &M, int restart, iteration &outer, Basis &KS)
Generalized Minimum Residual.
Definition: gmm_solver_gmres.h:90
gmm_solver_cg.h
Conjugate gradient iterative solver.
gmm_solver_gmres.h
GMRES (Generalized Minimum Residual) iterative solver.
gmm_solver_qmr.h
Quasi-Minimal Residual iterative solver.
gmm::iteration
The Iteration object calculates whether the solution has reached the desired accuracy,...
Definition: gmm_iter.h:53
gmm_superlu_interface.h
Interface with SuperLU (LU direct solver for sparse matrices).
gmm::resize
void resize(V &v, size_type n)
*‍/
Definition: gmm_blas.h:209
gmm::vect_norm2
number_traits< typename linalg_traits< V >::value_type >::magnitude_type vect_norm2(const V &v)
Euclidean norm of a vector.
Definition: gmm_blas.h:557
bgeot::alpha
size_type alpha(short_type n, short_type d)
Return the value of which is the number of monomials of a polynomial of variables and degree .
Definition: bgeot_poly.cc:47
gmm_kernel.h
Include the base gmm files.
gmm::mult_add
void mult_add(const L1 &l1, const L2 &l2, L3 &l3)
*‍/
Definition: gmm_blas.h:1781
gmm::add
void add(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:1268