/usr/include/getfem/getfem_model_solvers.h is in libgetfem++-dev 4.2.1~beta1~svn4482~dfsg-2build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 | /* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
Copyright (C) 2004-2012 Yves Renard
This file is a part of GETFEM++
Getfem++ is free software; you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version along with the GCC Runtime Library
Exception either version 3.1 or (at your option) any later version.
This program 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 Lesser General Public
License and GCC Runtime Library Exception for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
As a special exception, you may use this file as it is a part of a free
software library without restriction. Specifically, if other files
instantiate templates or use macros or inline functions from this file,
or you compile this file and link it with other files to produce an
executable, this file does not by itself cause the resulting executable
to be covered by the GNU Lesser General Public License. This exception
does not however invalidate any other reasons why the executable file
might be covered by the GNU Lesser General Public License.
===========================================================================*/
/**
@file getfem_model_solvers.h
@author Yves Renard <Yves.Renard@insa-lyon.fr>
@date June 15, 2004.
@brief Standard solvers for model bricks
@see getfem_modeling.h
*/
#ifndef GETFEM_MODEL_SOLVERS_H__
#define GETFEM_MODEL_SOLVERS_H__
#include "getfem_models.h"
#include "gmm/gmm_MUMPS_interface.h"
#include "gmm/gmm_iter.h"
#include "gmm/gmm_iter_solvers.h"
#include "gmm/gmm_dense_qr.h"
//#include "gmm/gmm_inoutput.h"
namespace getfem {
template <typename T> struct sort_abs_val_
{ bool operator()(T x, T y) { return (gmm::abs(x) < gmm::abs(y)); } };
template <typename MAT> void print_eigval(const MAT &M) {
// just to test a stiffness matrix if needing
typedef typename gmm::linalg_traits<MAT>::value_type T;
size_type n = gmm::mat_nrows(M);
gmm::dense_matrix<T> MM(n, n), Q(n, n);
std::vector<T> eigval(n);
gmm::copy(M, MM);
// gmm::symmetric_qr_algorithm(MM, eigval, Q);
gmm::implicit_qr_algorithm(MM, eigval, Q);
std::sort(eigval.begin(), eigval.end(), sort_abs_val_<T>());
cout << "eival = " << eigval << endl;
// cout << "vectp : " << gmm::mat_col(Q, n-1) << endl;
// cout << "vectp : " << gmm::mat_col(Q, n-2) << endl;
// double emax, emin;
// cout << "condition number" << condition_number(MM,emax,emin) << endl;
// cout << "emin = " << emin << endl;
// cout << "emax = " << emax << endl;
}
/* ***************************************************************** */
/* Linear solvers definition */
/* ***************************************************************** */
template <typename MAT, typename VECT>
struct abstract_linear_solver {
virtual void operator ()(const MAT &, VECT &, const VECT &,
gmm::iteration &) const = 0;
virtual ~abstract_linear_solver() {}
};
template <typename MAT, typename VECT>
struct linear_solver_cg_preconditioned_ildlt
: public abstract_linear_solver<MAT, VECT> {
void operator ()(const MAT &M, VECT &x, const VECT &b,
gmm::iteration &iter) const {
gmm::ildlt_precond<MAT> P(M);
gmm::cg(M, x, b, P, iter);
if (!iter.converged()) GMM_WARNING2("cg did not converge!");
}
};
template <typename MAT, typename VECT>
struct linear_solver_gmres_preconditioned_ilu
: public abstract_linear_solver<MAT, VECT> {
void operator ()(const MAT &M, VECT &x, const VECT &b,
gmm::iteration &iter) const {
gmm::ilu_precond<MAT> P(M);
gmm::gmres(M, x, b, P, 500, iter);
if (!iter.converged()) GMM_WARNING2("gmres did not converge!");
}
};
template <typename MAT, typename VECT>
struct linear_solver_gmres_unpreconditioned
: public abstract_linear_solver<MAT, VECT> {
void operator ()(const MAT &M, VECT &x, const VECT &b,
gmm::iteration &iter) const {
gmm::identity_matrix P;
gmm::gmres(M, x, b, P, 500, iter);
if (!iter.converged()) GMM_WARNING2("gmres did not converge!");
}
};
template <typename MAT, typename VECT>
struct linear_solver_gmres_preconditioned_ilut
: public abstract_linear_solver<MAT, VECT> {
void operator ()(const MAT &M, VECT &x, const VECT &b,
gmm::iteration &iter) const {
gmm::ilut_precond<MAT> P(M, 40, 1E-7);
gmm::gmres(M, x, b, P, 500, iter);
if (!iter.converged()) GMM_WARNING2("gmres did not converge!");
}
};
template <typename MAT, typename VECT>
struct linear_solver_gmres_preconditioned_ilutp
: public abstract_linear_solver<MAT, VECT> {
void operator ()(const MAT &M, VECT &x, const VECT &b,
gmm::iteration &iter) const {
gmm::ilutp_precond<MAT> P(M, 20, 1E-7);
gmm::gmres(M, x, b, P, 500, iter);
if (!iter.converged()) GMM_WARNING2("gmres did not converge!");
}
};
template <typename MAT, typename VECT>
struct linear_solver_superlu
: public abstract_linear_solver<MAT, VECT> {
void operator ()(const MAT &M, VECT &x, const VECT &b,
gmm::iteration &iter) const {
double rcond;
/*gmm::HarwellBoeing_IO::write("test.hb", M);
std::fstream f("bbb", std::ios::out);
for (unsigned i=0; i < gmm::vect_size(b); ++i) f << b[i] << "\n";*/
int info = SuperLU_solve(M, x, b, rcond);
iter.enforce_converged(info == 0);
if (iter.get_noisy()) cout << "condition number: " << 1.0/rcond<< endl;
}
};
#ifdef GMM_USES_MUMPS
template <typename MAT, typename VECT>
struct linear_solver_mumps : public abstract_linear_solver<MAT, VECT> {
void operator ()(const MAT &M, VECT &x, const VECT &b,
gmm::iteration &iter) const {
bool ok = gmm::MUMPS_solve(M, x, b, false);
iter.enforce_converged(ok);
}
};
template <typename MAT, typename VECT>
struct linear_solver_mumps_sym : public abstract_linear_solver<MAT, VECT> {
void operator ()(const MAT &M, VECT &x, const VECT &b,
gmm::iteration &iter) const {
bool ok = gmm::MUMPS_solve(M, x, b, true);
iter.enforce_converged(ok);
}
};
#endif
#if GETFEM_PARA_LEVEL > 1 && GETFEM_PARA_SOLVER == MUMPS_PARA_SOLVER
template <typename MAT, typename VECT>
struct linear_solver_distributed_mumps
: public abstract_linear_solver<MAT, VECT> {
void operator ()(const MAT &M, VECT &x, const VECT &b,
gmm::iteration &iter) const {
double tt_ref=MPI_Wtime();
bool ok = MUMPS_distributed_matrix_solve(M, x, b, false);
iter.enforce_converged(ok);
if (MPI_IS_MASTER()) cout<<"UNSYMMETRIC MUMPS time "<< MPI_Wtime() - tt_ref<<endl;
}
};
template <typename MAT, typename VECT>
struct linear_solver_distributed_mumps_sym
: public abstract_linear_solver<MAT, VECT> {
void operator ()(const MAT &M, VECT &x, const VECT &b,
gmm::iteration &iter) const {
double tt_ref=MPI_Wtime();
bool ok = MUMPS_distributed_matrix_solve(M, x, b, true);
iter.enforce_converged(ok);
if (MPI_IS_MASTER()) cout<<"SYMMETRIC MUMPS time "<< MPI_Wtime() - tt_ref<<endl;
}
};
#endif
/* ***************************************************************** */
/* Newton Line search definition */
/* ***************************************************************** */
struct abstract_newton_line_search {
double conv_alpha, conv_r;
size_t it, itmax, glob_it;
// size_t tot_it;
virtual void init_search(double r, size_t git, double R0 = 0.0) = 0;
virtual double next_try(void) = 0;
virtual bool is_converged(double, double R1 = 0.0) = 0;
virtual double converged_value(void) {
// tot_it += it; cout << "tot_it = " << tot_it << endl; it = 0;
return conv_alpha;
};
virtual double converged_residual(void) { return conv_r; };
virtual ~abstract_newton_line_search() { }
};
struct quadratic_newton_line_search : public abstract_newton_line_search {
double R0_, R1_;
double alpha, alpha_mult, first_res, alpha_max_ratio, alpha_min;
virtual void init_search(double r, size_t git, double R0 = 0.0) {
GMM_ASSERT1(R0 != 0.0, "You have to specify R0");
glob_it = git;
conv_alpha = alpha = double(1); conv_r = first_res = r; it = 0;
R0_ = R0;
}
virtual double next_try(void) {
++it;
if (it == 1) return double(1);
GMM_ASSERT1(R1_ != 0.0, "You have to specify R1");
double a = R0_ / R1_;
return (a < 0) ? (a*0.5 + sqrt(a*a*0.25-a)) : a*0.5;
}
virtual bool is_converged(double r, double R1 = 0.0) {
conv_r = r;
R1_ = R1; return ((gmm::abs(R1_) < gmm::abs(R0_*0.5)) || it >= itmax);
}
quadratic_newton_line_search(size_t imax = size_t(-1)) { itmax = imax; }
};
struct simplest_newton_line_search : public abstract_newton_line_search {
double alpha, alpha_mult, first_res, alpha_max_ratio, alpha_min;
virtual void init_search(double r, size_t git, double = 0.0) {
glob_it = git;
conv_alpha = alpha = double(1); conv_r = first_res = r; it = 0;
}
virtual double next_try(void)
{ conv_alpha = alpha; alpha *= alpha_mult; ++it; return conv_alpha; }
virtual bool is_converged(double r, double = 0.0) {
conv_r = r;
return ((it <= 1 && r < first_res)
|| (r <= first_res * alpha_max_ratio)
|| (conv_alpha <= alpha_min)
|| it >= itmax);
}
simplest_newton_line_search
(size_t imax = size_t(-1), double a_max_ratio = 6.0/5.0,
double a_min = 1.0/1000.0, double a_mult = 3.0/5.0)
: alpha_mult(a_mult), alpha_max_ratio(a_max_ratio), alpha_min(a_min)
{ itmax = imax; }
};
struct default_newton_line_search : public abstract_newton_line_search {
// This line search try to detect where is the minimum, dividing the step
// by a factor two each time.
// - it stops if the residual is less than the previous residual
// times alpha_min_ratio (= 0.9).
// - if the minimal step is reached with a residual greater than
// the previous residual times alpha_min_ratio then it decides
// between two options :
// - return with the step corresponding to the smallest residual
// - return with a greater residual corresponding to a residual
// less than the previous residual times alpha_max_ratio.
// the decision is taken regarding the previous iterations.
// - in order to shorten the line search, the process stops when
// the residual increases three times consecutively.
// possible improvment : detect the curvature at the origin
// (only one evaluation) and take it into account.
// Fitted to some experiments in contrib/tests_newton
double alpha, alpha_old, alpha_mult, first_res, alpha_max_ratio;
double alpha_min_ratio, alpha_min;
size_type count, count_pat;
bool max_ratio_reached;
double alpha_max_ratio_reached, r_max_ratio_reached;
size_type it_max_ratio_reached;
virtual void init_search(double r, size_t git, double = 0.0);
virtual double next_try(void);
virtual bool is_converged(double r, double = 0.0);
default_newton_line_search(void) { count_pat = 0; }
};
/* the former default_newton_line_search */
struct basic_newton_line_search : public abstract_newton_line_search {
double alpha, alpha_mult, first_res, alpha_max_ratio;
double alpha_min, prev_res, alpha_max_augment;
virtual void init_search(double r, size_t git, double = 0.0) {
glob_it = git;
conv_alpha = alpha = double(1);
prev_res = conv_r = first_res = r; it = 0;
}
virtual double next_try(void)
{ conv_alpha = alpha; alpha *= alpha_mult; ++it; return conv_alpha; }
virtual bool is_converged(double r, double = 0.0) {
if (glob_it == 0 || (r < first_res / double(2))
|| (conv_alpha <= alpha_min && r < first_res * alpha_max_augment)
|| it >= itmax)
{ conv_r = r; return true; }
if (it > 1 && r > prev_res && prev_res < alpha_max_ratio * first_res)
return true;
prev_res = conv_r = r;
return false;
}
basic_newton_line_search
(size_t imax = size_t(-1),
double a_max_ratio = 5.0/3.0,
double a_min = 1.0/1000.0, double a_mult = 3.0/5.0, double a_augm = 2.0)
: alpha_mult(a_mult), alpha_max_ratio(a_max_ratio),
alpha_min(a_min), alpha_max_augment(a_augm) { itmax = imax; }
};
struct systematic_newton_line_search : public abstract_newton_line_search {
double alpha, alpha_mult, first_res;
double alpha_min, prev_res;
bool first;
virtual void init_search(double r, size_t git, double = 0.0) {
glob_it = git;
conv_alpha = alpha = double(1);
prev_res = conv_r = first_res = r; it = 0; first = true;
}
virtual double next_try(void)
{ double a = alpha; alpha *= alpha_mult; ++it; return a; }
virtual bool is_converged(double r, double = 0.0) {
// cout << "a = " << alpha / alpha_mult << " r = " << r << endl;
if (r < conv_r || first)
{ conv_r = r; conv_alpha = alpha / alpha_mult; first = false; }
if ((alpha <= alpha_min*alpha_mult) || it >= itmax) return true;
return false;
}
systematic_newton_line_search
(size_t imax = size_t(-1),
double a_min = 1.0/10000.0, double a_mult = 3.0/5.0)
: alpha_mult(a_mult), alpha_min(a_min) { itmax = imax; }
};
/* ***************************************************************** */
/* Newton algorithm. */
/* ***************************************************************** */
template <typename PB>
void classical_Newton(PB &pb, gmm::iteration &iter,
const abstract_linear_solver<typename PB::MATRIX,
typename PB::VECTOR> &linear_solver) {
typedef typename gmm::linalg_traits<typename PB::VECTOR>::value_type T;
typedef typename gmm::number_traits<T>::magnitude_type R;
gmm::iteration iter_linsolv0 = iter;
iter_linsolv0.reduce_noisy();
iter_linsolv0.set_resmax(iter.get_resmax()/20.0);
iter_linsolv0.set_maxiter(10000); // arbitrary
pb.compute_residual();
typename PB::VECTOR dr(gmm::vect_size(pb.residual()));
typename PB::VECTOR b(gmm::vect_size(pb.residual()));
scalar_type crit = pb.residual_norm()
/ std::max(1E-25, pb.approx_external_load_norm());
while (!iter.finished(crit)) {
gmm::iteration iter_linsolv = iter_linsolv0;
if (iter.get_noisy() > 1)
cout << "starting computing tangent matrix" << endl;
int is_singular = 1;
while (is_singular) {
pb.compute_tangent_matrix();
gmm::clear(dr);
gmm::copy(gmm::scaled(pb.residual(), pb.scale_residual()), b);
if (iter.get_noisy() > 1) cout << "starting linear solver" << endl;
iter_linsolv.init();
linear_solver(pb.tangent_matrix(), dr, b, iter_linsolv);
if (!iter_linsolv.converged()) {
is_singular++;
if (is_singular <= 4) {
if (iter.get_noisy())
cout << "Singular tangent matrix:"
" perturbation of the state vector." << endl;
pb.perturbation();
pb.compute_residual();
} else {
if (iter.get_noisy())
cout << "Singular tangent matrix: perturbation failed, aborting."
<< endl;
return;
}
}
else is_singular = 0;
}
if (iter.get_noisy() > 1) cout << "linear solver done" << endl;
R alpha = pb.line_search(dr, iter); //it is assumed that the linesearch
//executes a pb.compute_residual();
if (iter.get_noisy()) cout << "alpha = " << alpha << " ";
++iter;
crit = std::min(pb.residual_norm()
/ std::max(1E-25, pb.approx_external_load_norm()),
gmm::vect_norm1(dr) / std::max(1E-25, pb.state_norm()));
}
}
/* ***************************************************************** */
/* Intermediary structure for Newton algorithms with getfem::model. */
/* ***************************************************************** */
#define TRACE_SOL 0
template <typename MAT, typename VEC>
struct model_pb {
typedef MAT MATRIX;
typedef VEC VECTOR;
typedef typename gmm::linalg_traits<VECTOR>::value_type T;
typedef typename gmm::number_traits<T>::magnitude_type R;
model &md;
bool is_reduced;
std::vector<size_type> &sind;
gmm::sub_index I;
abstract_newton_line_search &ls;
VECTOR stateinit, &state;
const VECTOR &rhs;
const MATRIX &K;
MATRIX Kr;
VECTOR rhsr;
bool with_pseudo_potential;
void compute_tangent_matrix(void) {
md.to_variables(state);
md.assembly(model::BUILD_MATRIX);
if (is_reduced) {
gmm::resize(Kr, sind.size(), sind.size());
gmm::copy(gmm::sub_matrix(K, I, I), Kr);
}
}
const MATRIX &tangent_matrix(void) { return (is_reduced ? Kr : K); }
inline T scale_residual(void) const { return T(1); }
void compute_residual(void) {
md.to_variables(state);
md.assembly(model::BUILD_RHS);
if (is_reduced) {
gmm::resize(rhsr, sind.size());
gmm::copy(gmm::sub_vector(rhs, I), rhsr);
}
}
void compute_pseudo_potential(void)
{ md.to_variables(state); md.assembly(model::BUILD_PSEUDO_POTENTIAL); }
void perturbation(void) {
R res = gmm::vect_norm2(state), ampl = std::max(res*R(1E-20), R(1E-50));
std::vector<R> V(gmm::vect_size(state));
gmm::fill_random(V);
gmm::add(gmm::scaled(V, ampl), state);
}
const VECTOR &residual(void) { return (is_reduced ? rhsr : rhs); }
R state_norm(void) const
{ return gmm::vect_norm1(gmm::sub_vector(state, I)); }
R approx_external_load_norm(void)
{ return md.approx_external_load(); }
R residual_norm(void) { // A norm1 seems to be better than a norm2
// at least for contact problems.
return (is_reduced ? gmm::vect_norm1(rhsr) : gmm::vect_norm1(rhs));
}
R compute_res(bool comp = true) {
if (with_pseudo_potential) {
compute_pseudo_potential();
return md.pseudo_potential();
} else {
if (comp) compute_residual();
return residual_norm();
}
}
R line_search(VECTOR &dr, const gmm::iteration &iter) {
size_type nit = 0;
gmm::resize(stateinit, md.nb_dof());
gmm::copy(state, stateinit);
R alpha(1), res, /* res_init, */ R0;
/* res_init = */ res = compute_res(false);
// cout << "first residual = " << residual() << endl << endl;
R0 = (is_reduced ? gmm::real(gmm::vect_sp(dr, rhsr))
: gmm::real(gmm::vect_sp(dr, rhs)));
#if TRACE_SOL
static int trace_number = 0;
int trace_iter = 0;
{
std::stringstream trace_name;
trace_name << "line_search_state" << std::setfill('0')
<< std::setw(3) << trace_number << "_000_init";
gmm::vecsave(trace_name.str(),stateinit);
}
trace_number++;
#endif
ls.init_search(res, iter.get_iteration(), R0);
do {
alpha = ls.next_try();
gmm::add(gmm::sub_vector(stateinit, I), gmm::scaled(dr, alpha),
gmm::sub_vector(state, I));
#if TRACE_SOL
{
trace_iter++;
std::stringstream trace_name;
trace_name << "line_search_state" << std::setfill('0')
<< std::setw(3) << trace_number << "_"
<< std::setfill('0') << std::setw(3) << trace_iter;
gmm::vecsave(trace_name.str(), state);
}
#endif
res = compute_res();
// cout << "residual = " << residual() << endl << endl;
R0 = (is_reduced ? gmm::real(gmm::vect_sp(dr, rhsr))
: gmm::real(gmm::vect_sp(dr, rhs)));
++ nit;
} while (!ls.is_converged(res, R0));
if (alpha != ls.converged_value() || with_pseudo_potential) {
alpha = ls.converged_value();
gmm::add(gmm::sub_vector(stateinit, I), gmm::scaled(dr, alpha),
gmm::sub_vector(state, I));
res = ls.converged_residual();
compute_residual();
}
return alpha;
}
model_pb(model &m, abstract_newton_line_search &ls_, VECTOR &st,
const VECTOR &rhs_, const MATRIX &K_, bool reduced_,
std::vector<size_type> &sind_,
bool with_pseudo_pot = false)
: md(m), is_reduced(reduced_), sind(sind_), I(sind_), ls(ls_), state(st),
rhs(rhs_), K(K_), with_pseudo_potential(with_pseudo_pot) {}
};
//---------------------------------------------------------------------
// Default linear solver.
//---------------------------------------------------------------------
typedef abstract_linear_solver<model_real_sparse_matrix,
model_real_plain_vector> rmodel_linear_solver;
typedef dal::shared_ptr<rmodel_linear_solver> rmodel_plsolver_type;
typedef abstract_linear_solver<model_complex_sparse_matrix,
model_complex_plain_vector>
cmodel_linear_solver;
typedef dal::shared_ptr<cmodel_linear_solver> cmodel_plsolver_type;
template<typename MATRIX, typename VECTOR>
dal::shared_ptr<abstract_linear_solver<MATRIX, VECTOR> >
default_linear_solver(const model &md) {
dal::shared_ptr<abstract_linear_solver<MATRIX, VECTOR> > p;
#if GETFEM_PARA_LEVEL == 1 && GETFEM_PARA_SOLVER == MUMPS_PARA_SOLVER
if (md.is_symmetric())
p.reset(new linear_solver_mumps_sym<MATRIX, VECTOR>);
else
p.reset(new linear_solver_mumps<MATRIX, VECTOR>);
#elif GETFEM_PARA_LEVEL > 1 && GETFEM_PARA_SOLVER == MUMPS_PARA_SOLVER
if (md.is_symmetric())
p.reset(new linear_solver_distributed_mumps_sym<MATRIX, VECTOR>);
else
p.reset(new linear_solver_distributed_mumps<MATRIX, VECTOR>);
#else
size_type ndof = md.nb_dof(), max3d = 15000, dim = md.leading_dimension();
# ifdef GMM_USES_MUMPS
max3d = 250000;
# endif
if ((ndof<300000 && dim<=2) || (ndof<max3d && dim<=3) || (ndof<1000)) {
# ifdef GMM_USES_MUMPS
if (md.is_symmetric())
p.reset(new linear_solver_mumps_sym<MATRIX, VECTOR>);
else
p.reset(new linear_solver_mumps<MATRIX, VECTOR>);
# else
p.reset(new linear_solver_superlu<MATRIX, VECTOR>);
# endif
}
else {
if (md.is_coercive())
p.reset(new linear_solver_cg_preconditioned_ildlt<MATRIX, VECTOR>);
else {
if (dim <= 2)
p.reset(new
linear_solver_gmres_preconditioned_ilut<MATRIX,VECTOR>);
else
p.reset(new
linear_solver_gmres_preconditioned_ilu<MATRIX,VECTOR>);
}
}
#endif
return p;
}
template <typename MATRIX, typename VECTOR>
dal::shared_ptr<abstract_linear_solver<MATRIX, VECTOR> >
select_linear_solver(const model &md, const std::string &name) {
dal::shared_ptr<abstract_linear_solver<MATRIX, VECTOR> > p;
if (bgeot::casecmp(name, "superlu") == 0)
p.reset(new linear_solver_superlu<MATRIX, VECTOR>);
else if (bgeot::casecmp(name, "mumps") == 0) {
#ifdef GMM_USES_MUMPS
# if GETFEM_PARA_LEVEL <= 1
p.reset(new linear_solver_mumps<MATRIX, VECTOR>);
# else
p.reset(new linear_solver_distributed_mumps<MATRIX, VECTOR>);
# endif
#else
GMM_ASSERT1(false, "Mumps is not interfaced");
#endif
}
else if (bgeot::casecmp(name, "cg/ildlt") == 0)
p.reset(new linear_solver_cg_preconditioned_ildlt<MATRIX, VECTOR>);
else if (bgeot::casecmp(name, "gmres/ilu") == 0)
p.reset(new linear_solver_gmres_preconditioned_ilu<MATRIX, VECTOR>);
else if (bgeot::casecmp(name, "gmres/ilut") == 0)
p.reset(new linear_solver_gmres_preconditioned_ilut<MATRIX, VECTOR>);
else if (bgeot::casecmp(name, "gmres/ilutp") == 0)
p.reset(new linear_solver_gmres_preconditioned_ilutp<MATRIX, VECTOR>);
else if (bgeot::casecmp(name, "auto") == 0)
p = default_linear_solver<MATRIX, VECTOR>(md);
else
GMM_ASSERT1(false, "Unknown linear solver");
return p;
}
inline rmodel_plsolver_type rselect_linear_solver(const model &md,
const std::string &name) {
return select_linear_solver<model_real_sparse_matrix,
model_real_plain_vector>(md, name);
}
inline cmodel_plsolver_type cselect_linear_solver(const model &md,
const std::string &name) {
return select_linear_solver<model_complex_sparse_matrix,
model_complex_plain_vector>(md, name);
}
//---------------------------------------------------------------------
// Standard solve.
//---------------------------------------------------------------------
/** A default solver for the model brick system.
Of course it could be not very well suited for a particular
problem, so it could be copied and adapted to change solvers,
add a special traitement on the problem, etc ... This is in
fact a model for your own solver.
For small problems, a direct solver is used
(getfem::SuperLU_solve), for larger problems, a conjugate
gradient gmm::cg (if the problem is coercive) or a gmm::gmres is
used (preconditionned with an incomplete factorization).
When MPI/METIS is enabled, a partition is done via METIS, and a parallel
solver can be used.
Note that it is possible to disable some variables
(see the md.disable_variable(varname) method) in order to
solve the problem only with respect to a subset of variables (the
disabled variables are the considered as data) for instance to
replace the global Newton strategy with a fixed point one.
@ingroup bricks
*/
void standard_solve(model &md, gmm::iteration &iter,
rmodel_plsolver_type lsolver,
abstract_newton_line_search &ls,
bool with_pseudo_potential = false);
void standard_solve(model &md, gmm::iteration &iter,
cmodel_plsolver_type lsolver,
abstract_newton_line_search &ls,
bool with_pseudo_potential = false);
void standard_solve(model &md, gmm::iteration &iter,
rmodel_plsolver_type lsolver,
bool with_pseudo_potential = false);
void standard_solve(model &md, gmm::iteration &iter,
cmodel_plsolver_type lsolver,
bool with_pseudo_potential = false);
void standard_solve(model &md, gmm::iteration &iter,
bool with_pseudo_potential = false);
}
//---------------------------------------------------------------------
//
// Solvers for the old brick system. Kept for compatibility reasons.
//
//---------------------------------------------------------------------
#include "getfem_modeling.h"
namespace getfem {
#if GETFEM_PARA_LEVEL > 1 && GETFEM_PARA_SOLVER == SCHWARZADD_PARA_SOLVER
template <typename MODEL_STATE, typename MAT, typename VECT>
struct linear_solver_para_schwarzadd
: public abstract_linear_solver<MAT, VECT> {
typedef typename MODEL_STATE::value_type value_type;
const mdbrick_abstract<MODEL_STATE> &problem;
int nblocsubdom; // Number of sub-domains per process
linear_solver_para_schwarzadd(const mdbrick_abstract<MODEL_STATE> &problem_,
int nblocsubdom_)
: problem(problem_), nblocsubdom(nblocsubdom_) {}
void operator ()(const MAT &M, VECT &x, const VECT &b,
gmm::iteration &iter) const {
double tt_ref=MPI_Wtime();
// Meshes sub-partition.
std::set<const mesh *> mesh_set;
for (size_type i = 0; i < problem.nb_mesh_fems(); ++i)
mesh_set.insert(&(problem.get_mesh_fem(i).linked_mesh()));
std::vector< std::vector<int> > eparts(mesh_set.size());
int size, rank, nset = 0;
size_type ndof = problem.nb_dof();
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
MPI_Comm_size(MPI_COMM_WORLD, &size);
for (std::set<const mesh *>::iterator it = mesh_set.begin();
it != mesh_set.end(); ++it, ++nset) {
int ne = int((*it)->get_mpi_region().nb_convex());
std::vector<int> xadj(ne+1), adjncy, numelt((*it)->convex_index().last_true()+1), numeltinv(ne), npart(ne);
int j = 0, k = 0;
bgeot::mesh_structure::ind_set s;
for (mr_visitor ic((*it)->get_mpi_region()); !ic.finished();++ic,++j)
{ numelt[ic.cv()] = j; numeltinv[j] = ic.cv(); }
j = 0;
for (mr_visitor ic((*it)->get_mpi_region()); !ic.finished();++ic,++j) {
xadj[j] = k;
(*it)->neighbours_of_convex(ic.cv(), s);
for (bgeot::mesh_structure::ind_set::iterator iti = s.begin();
iti != s.end(); ++iti)
if ((*it)->get_mpi_region().is_in(*iti))
{ adjncy.push_back(numelt[*iti]); ++k; }
}
xadj[j] = k;
int wgtflag = 0, edgecut, numflag = 0, options[5] = {0,0,0,0,0};
int nbbl = nblocsubdom/size;
// The mpi region is partitionned into nblocsubdom sub-domains.
METIS_PartGraphKway(&ne, &(xadj[0]), &(adjncy[0]), 0, 0, &wgtflag,
&numflag, &nbbl, options, &edgecut,
&(npart[0]));
eparts[nset].resize(0);
eparts[nset].resize((*it)->convex_index().last()+1, size_type(-1));
for (size_type i = 0; i < size_type(ne); ++i)
eparts[nset][numeltinv[i]] = npart[i];
}
// To be completeted for non-finite element dofs
// nblocsubdom is number of sub dom per proc
// std::vector<dal::bit_vector> Bidof(nblocsubdom);
// nblocsubdom is the global number of sub dom
std::vector<dal::bit_vector> Bidof(nblocsubdom/size);
size_type apos = 0;
for (size_type i = 0; i < problem.nb_mesh_fems(); ++i) {
const mesh_fem &mf = problem.get_mesh_fem(i);
nset = 0;
for (std::set<const mesh *>::iterator it = mesh_set.begin();
it != mesh_set.end(); ++it, ++nset)
if (*it == &(mf.linked_mesh())) break;
size_type pos = problem.get_mesh_fem_position(i);
GMM_ASSERT1(pos == apos, "Multipliers are not taken into account");
size_type length = mf.nb_dof();
apos += length;
for (dal::bv_visitor j(mf.convex_index()); !j.finished(); ++j) {
size_type k = eparts[nset][j];
if (k != size_type(-1))
for (size_type l = 0; l < mf.nb_dof_of_element(j); ++l)
Bidof[k].add(mf.ind_dof_of_element(j)[l] + pos);
}
GMM_ASSERT1(apos == ndof, "Multipliers are not taken into account");
}
// nblocsubdom is number of sub dom per proc
// std::vector< gmm::row_matrix< gmm::rsvector<value_type> > > Bi(nblocsubdom*size);
// nblocsubdom is the global number of sub dom
std::vector< gmm::row_matrix< gmm::rsvector<value_type> > > Bi(nblocsubdom);
// nblocsubdom is number of sub dom per proc
// for (size_type i = 0; i < size_type(nblocsubdom); ++i) {
// nblocsubdom is the global number of sub dom
for (size_type i = 0; i < size_type(nblocsubdom/size); ++i) {
// nblocsubdom is number of sub dom per proc
// gmm::resize(Bi[size*rank + i], ndof, Bidof[i].card());
// nblocsubdom is the global number of sub dom
gmm::resize(Bi[(nblocsubdom/size)*rank + i], ndof, Bidof[i].card());
size_type k = 0;
for (dal::bv_visitor j(Bidof[i]); !j.finished(); ++j, ++k)
// nblocsubdom is number of sub dom per proc
// Bi[size*rank + i](j, k) = value_type(1);
// nblocsubdom is the global number of sub dom
Bi[(nblocsubdom/size)*rank + i](j, k) = value_type(1);
}
gmm::mpi_distributed_matrix<MAT> mpiM(ndof, ndof);
gmm::copy(M, mpiM.local_matrix());
additive_schwarz(mpiM, x, b, gmm::identity_matrix(), Bi, iter,
gmm::using_superlu(), gmm::using_cg());
cout<<"temps SCHWARZ ADD "<< MPI_Wtime() - tt_ref<<endl;
}
};
#endif
template <typename MODEL_STATE> struct useful_types {
TYPEDEF_MODEL_STATE_TYPES;
typedef abstract_linear_solver<T_MATRIX, VECTOR> lsolver_type;
typedef dal::shared_ptr<lsolver_type> plsolver_type;
};
template <typename MODEL_STATE>
typename useful_types<MODEL_STATE>::plsolver_type
default_linear_solver(const mdbrick_abstract<MODEL_STATE> &problem) {
typedef typename MODEL_STATE::tangent_matrix_type T_MATRIX;
typedef typename MODEL_STATE::vector_type VECTOR;
typename useful_types<MODEL_STATE>::plsolver_type p;
#if GETFEM_PARA_LEVEL == 1 && GETFEM_PARA_SOLVER == MUMPS_PARA_SOLVER
p.reset(new linear_solver_mumps<T_MATRIX, VECTOR>);
#elif GETFEM_PARA_LEVEL > 1 && GETFEM_PARA_SOLVER == MUMPS_PARA_SOLVER
p.reset(new linear_solver_distributed_mumps<T_MATRIX, VECTOR>);
#elif GETFEM_PARA_LEVEL > 1 && GETFEM_PARA_SOLVER == SCHWARZADD_PARA_SOLVER
int size;
// MPI_Comm_size(MPI_COMM_WORLD, &size);
size=32;//global number of sub_dom
p.reset(new linear_solver_para_schwarzadd<MODEL_STATE, T_MATRIX, VECTOR>(problem, size));
#else
size_type ndof = problem.nb_dof(), max3d = 15000, dim = problem.dim();
# ifdef GMM_USES_MUMPS
max3d = 100000;
# endif
if ((ndof<200000 && dim<=2) || (ndof<max3d && dim<=3) || (ndof<1000)) {
# ifdef GMM_USES_MUMPS
p.reset(new linear_solver_mumps<T_MATRIX, VECTOR>);
# else
p.reset(new linear_solver_superlu<T_MATRIX, VECTOR>);
# endif
}
else {
if (problem.is_coercive())
p.reset(new linear_solver_cg_preconditioned_ildlt<T_MATRIX, VECTOR>);
else if (problem.mixed_variables().card() == 0) {
if (dim <= 2)
p.reset(new
linear_solver_gmres_preconditioned_ilu<T_MATRIX,VECTOR>);
else
p.reset(new
linear_solver_gmres_preconditioned_ilu<T_MATRIX,VECTOR>);
}
else {
if (dim <= 2)
p.reset(new
linear_solver_gmres_preconditioned_ilu<T_MATRIX,VECTOR>);
else
p.reset(new
linear_solver_gmres_preconditioned_ilu<T_MATRIX,VECTOR>);
}
}
#endif
return p;
}
template <typename MODEL_STATE>
typename useful_types<MODEL_STATE>::plsolver_type
select_linear_solver(const mdbrick_abstract<MODEL_STATE> &problem,
const std::string &name) {
typedef typename MODEL_STATE::tangent_matrix_type T_MATRIX;
typedef typename MODEL_STATE::vector_type VECTOR;
typename useful_types<MODEL_STATE>::plsolver_type p;
if (bgeot::casecmp(name, "superlu") == 0)
p.reset(new linear_solver_superlu<T_MATRIX, VECTOR>);
else if (bgeot::casecmp(name, "mumps") == 0) {
#ifdef GMM_USES_MUMPS
# if GETFEM_PARA_LEVEL <= 1
p.reset(new linear_solver_mumps<T_MATRIX, VECTOR>);
# else
p.reset(new linear_solver_distributed_mumps<T_MATRIX, VECTOR>);
# endif
#else
GMM_ASSERT1(false, "Mumps is not interfaced");
#endif
}
else if (bgeot::casecmp(name, "cg/ildlt") == 0)
p.reset(new linear_solver_cg_preconditioned_ildlt<T_MATRIX, VECTOR>);
else if (bgeot::casecmp(name, "gmres/ilu") == 0)
p.reset(new linear_solver_gmres_preconditioned_ilu<T_MATRIX, VECTOR>);
else if (bgeot::casecmp(name, "gmres/ilut") == 0)
p.reset(new linear_solver_gmres_preconditioned_ilut<T_MATRIX, VECTOR>);
else if (bgeot::casecmp(name, "gmres/ilutp") == 0)
p.reset(new linear_solver_gmres_preconditioned_ilutp<T_MATRIX, VECTOR>);
else if (bgeot::casecmp(name, "auto") == 0)
p = default_linear_solver(problem);
else
GMM_ASSERT1(false, "Unknown linear solver");
return p;
}
/* ***************************************************************** */
/* Intermediary structure for Newton algorithms with MODEL_STATE. */
/* ***************************************************************** */
template <typename MODEL_STATE>
struct model_problem {
TYPEDEF_MODEL_STATE_TYPES;
typedef T_MATRIX MATRIX;
typedef typename gmm::linalg_traits<VECTOR>::value_type T;
MODEL_STATE &MS;
mdbrick_abstract<MODEL_STATE> &pb;
abstract_newton_line_search &ls;
VECTOR stateinit, d;
void compute_tangent_matrix(void) {
pb.compute_tangent_matrix(MS);
if (pb.nb_constraints() > 0) {
pb.compute_residual(MS);
MS.compute_reduced_system();
}
}
void perturbation(void) {
R res = gmm::vect_norm2(MS.state()), ampl = res / R(1000);
if (res == R(0)) ampl = 1E-30;
VECTOR V(gmm::vect_size(MS.state()));
gmm::fill_random(V);
gmm::add(gmm::scaled(V, ampl), MS.state());
}
inline T scale_residual(void) const { return T(-1); }
const T_MATRIX &tangent_matrix(void)
{ return MS.reduced_tangent_matrix(); }
void compute_residual(void) {
pb.compute_residual(MS);
if (pb.nb_constraints() > 0) MS.compute_reduced_residual();
}
const VECTOR &residual(void) { return MS.reduced_residual(); }
R residual_norm(void) { return MS.reduced_residual_norm(); }
R approx_external_load_norm(void) { return R(1);} // Not taken into account
R state_norm(void) const { return R(0); } // Not taken into account
R line_search(VECTOR &dr, const gmm::iteration &iter) {
gmm::resize(d, pb.nb_dof());
gmm::resize(stateinit, pb.nb_dof());
gmm::copy(MS.state(), stateinit);
MS.unreduced_solution(dr, d);
R alpha(1), res, R0;
R0 = gmm::real(gmm::vect_sp(dr, residual()));
ls.init_search(MS.reduced_residual_norm(), iter.get_iteration(), R0);
do {
alpha = ls.next_try();
gmm::add(stateinit, gmm::scaled(d, alpha), MS.state());
compute_residual();
res = MS.reduced_residual_norm();
R0 = gmm::real(gmm::vect_sp(dr, residual()));
} while (!ls.is_converged(res));
if (alpha != ls.converged_value()) {
alpha = ls.converged_value();
gmm::add(stateinit, gmm::scaled(d, alpha), MS.state());
res = ls.converged_residual();
compute_residual();
}
return alpha;
}
model_problem(MODEL_STATE &MS_, mdbrick_abstract<MODEL_STATE> &pb_,
abstract_newton_line_search &ls_)
: MS(MS_), pb(pb_), ls(ls_) {}
};
/* ***************************************************************** */
/* Standard solve. */
/* ***************************************************************** */
/** A default solver for the old model brick system.
Of course it could be not very well suited for a particular
problem, so it could be copied and adapted to change solvers,
add a special traitement on the problem, etc ... This is in
fact a model for your own solver.
For small problems, a direct solver is used
(getfem::SuperLU_solve), for larger problems, a conjugate
gradient gmm::cg (if the problem is coercive) or a gmm::gmres is
used (preconditionned with an incomplete factorization).
When MPI/METIS is enabled, a partition is done via METIS, and a
parallel solver can be used.
@ingroup bricks
*/
template <typename MODEL_STATE> void
standard_solve
(MODEL_STATE &MS, mdbrick_abstract<MODEL_STATE> &problem,
gmm::iteration &iter,
typename useful_types<MODEL_STATE>::plsolver_type lsolver,
abstract_newton_line_search &ls) {
typedef typename MODEL_STATE::vector_type VECTOR;
// typedef typename MODEL_STATE::tangent_matrix_type T_MATRIX;
// typedef typename MODEL_STATE::constraints_matrix_type C_MATRIX;
typedef typename MODEL_STATE::value_type value_type;
// typedef typename gmm::number_traits<value_type>::magnitude_type R;
// typedef typename gmm::sub_vector_type<VECTOR *,
// gmm::sub_interval>::vector_type SUBVECTOR
model_problem<MODEL_STATE> mdpb(MS, problem, ls);
MS.adapt_sizes(problem); // to be sure it is ok, but should be done before
if (problem.is_linear()) {
mdpb.compute_tangent_matrix();
mdpb.compute_residual();
VECTOR dr(gmm::vect_size(mdpb.residual())), d(problem.nb_dof());
VECTOR b(gmm::vect_size(dr));
gmm::copy(gmm::scaled(mdpb.residual(), value_type(-1)), b);
// cout << "tg matrix = " << mdpb.tangent_matrix() << endl;
// print_eigval(mdpb.tangent_matrix());
(*lsolver)(mdpb.tangent_matrix(), dr, b, iter);
MS.unreduced_solution(dr, d);
gmm::add(d, MS.state());
}
else
classical_Newton(mdpb, iter, *lsolver);
}
template <typename MODEL_STATE> void
standard_solve(MODEL_STATE &MS, mdbrick_abstract<MODEL_STATE> &problem,
gmm::iteration &iter,
typename useful_types<MODEL_STATE>::plsolver_type lsolver) {
default_newton_line_search ls;
standard_solve(MS, problem, iter, lsolver, ls);
}
template <typename MODEL_STATE> void
standard_solve(MODEL_STATE &MS, mdbrick_abstract<MODEL_STATE> &problem,
gmm::iteration &iter) {
getfem::default_newton_line_search ls;
standard_solve(MS, problem, iter, default_linear_solver(problem), ls);
}
} /* end of namespace getfem. */
#endif /* GETFEM_MODEL_SOLVERS_H__ */
|