You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
210 lines
7.9 KiB
210 lines
7.9 KiB
/* -*- c++ -*- (enables emacs c++ mode) */
|
|
/*===========================================================================
|
|
|
|
Copyright (C) 2002-2012 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.
|
|
|
|
===========================================================================*/
|
|
|
|
// This file is a modified version of qmr.h from ITL.
|
|
// See http://osl.iu.edu/research/itl/
|
|
// Following the corresponding Copyright notice.
|
|
//===========================================================================
|
|
//
|
|
// Copyright (c) 1997-2001, The Trustees of Indiana University.
|
|
// All rights reserved.
|
|
// Redistribution and use in source and binary forms, with or without
|
|
// modification, are permitted provided that the following conditions are met:
|
|
//
|
|
// * Redistributions of source code must retain the above copyright
|
|
// notice, this list of conditions and the following disclaimer.
|
|
// * Redistributions in binary form must reproduce the above copyright
|
|
// notice, this list of conditions and the following disclaimer in the
|
|
// documentation and/or other materials provided with the distribution.
|
|
// * Neither the name of the University of Notre Dame nor the
|
|
// names of its contributors may be used to endorse or promote products
|
|
// derived from this software without specific prior written permission.
|
|
//
|
|
// THIS SOFTWARE IS PROVIDED BY THE TRUSTEES OF INDIANA UNIVERSITY AND
|
|
// CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
|
|
// BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
|
// FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE TRUSTEES
|
|
// OF INDIANA UNIVERSITY AND CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
|
// INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
|
|
// NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
|
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
|
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
|
|
// THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
//
|
|
//===========================================================================
|
|
|
|
/**@file gmm_solver_qmr.h
|
|
@author Andrew Lumsdaine <lums@osl.iu.edu>
|
|
@author Lie-Quan Lee <llee@osl.iu.edu>
|
|
@author Yves Renard <Yves.Renard@insa-lyon.fr>
|
|
@date October 13, 2002.
|
|
@brief Quasi-Minimal Residual iterative solver.
|
|
*/
|
|
#ifndef GMM_QMR_H
|
|
#define GMM_QMR_H
|
|
|
|
#include "gmm_kernel.h"
|
|
#include "gmm_iter.h"
|
|
|
|
namespace gmm {
|
|
|
|
/** Quasi-Minimal Residual.
|
|
|
|
This routine solves the unsymmetric linear system Ax = b using
|
|
the Quasi-Minimal Residual method.
|
|
|
|
See: R. W. Freund and N. M. Nachtigal, A quasi-minimal residual
|
|
method for non-Hermitian linear systems, Numerical Math.,
|
|
60(1991), pp. 315-339
|
|
|
|
Preconditioner - Incomplete LU, Incomplete LU with threshold,
|
|
SSOR or identity_preconditioner.
|
|
*/
|
|
template <typename Matrix, typename Vector, typename VectorB,
|
|
typename Precond1>
|
|
void qmr(const Matrix &A, Vector &x, const VectorB &b, const Precond1 &M1,
|
|
iteration& iter) {
|
|
|
|
typedef typename linalg_traits<Vector>::value_type T;
|
|
typedef typename number_traits<T>::magnitude_type R;
|
|
|
|
T delta(0), ep(0), beta(0), theta_1(0), gamma_1(0);
|
|
T theta(0), gamma(1), eta(-1);
|
|
R rho_1(0), rho, xi;
|
|
|
|
typedef typename temporary_vector<Vector>::vector_type TmpVec;
|
|
size_type nn = vect_size(x);
|
|
TmpVec r(nn), v_tld(nn), y(nn), w_tld(nn), z(nn), v(nn), w(nn);
|
|
TmpVec y_tld(nn), z_tld(nn), p(nn), q(nn), p_tld(nn), d(nn), s(nn);
|
|
|
|
iter.set_rhsnorm(double(gmm::vect_norm2(b)));
|
|
if (iter.get_rhsnorm() == 0.0) { clear(x); return; }
|
|
|
|
gmm::mult(A, gmm::scaled(x, T(-1)), b, r);
|
|
gmm::copy(r, v_tld);
|
|
|
|
gmm::left_mult(M1, v_tld, y);
|
|
rho = gmm::vect_norm2(y);
|
|
|
|
gmm::copy(r, w_tld);
|
|
gmm::transposed_right_mult(M1, w_tld, z);
|
|
xi = gmm::vect_norm2(z);
|
|
|
|
while (! iter.finished_vect(r)) {
|
|
|
|
if (rho == R(0) || xi == R(0)) {
|
|
if (iter.get_maxiter() == size_type(-1))
|
|
{ GMM_ASSERT1(false, "QMR failed to converge"); }
|
|
else { GMM_WARNING1("QMR failed to converge"); return; }
|
|
}
|
|
gmm::copy(gmm::scaled(v_tld, T(R(1)/rho)), v);
|
|
gmm::scale(y, T(R(1)/rho));
|
|
|
|
gmm::copy(gmm::scaled(w_tld, T(R(1)/xi)), w);
|
|
gmm::scale(z, T(R(1)/xi));
|
|
|
|
delta = gmm::vect_sp(z, y);
|
|
if (delta == T(0)) {
|
|
if (iter.get_maxiter() == size_type(-1))
|
|
{ GMM_ASSERT1(false, "QMR failed to converge"); }
|
|
else { GMM_WARNING1("QMR failed to converge"); return; }
|
|
}
|
|
gmm::right_mult(M1, y, y_tld);
|
|
gmm::transposed_left_mult(M1, z, z_tld);
|
|
|
|
if (iter.first()) {
|
|
gmm::copy(y_tld, p);
|
|
gmm::copy(z_tld, q);
|
|
} else {
|
|
gmm::add(y_tld, gmm::scaled(p, -(T(xi * delta) / ep)), p);
|
|
gmm::add(z_tld, gmm::scaled(q, -(T(rho * delta) / ep)), q);
|
|
}
|
|
|
|
gmm::mult(A, p, p_tld);
|
|
|
|
ep = gmm::vect_sp(q, p_tld);
|
|
if (ep == T(0)) {
|
|
if (iter.get_maxiter() == size_type(-1))
|
|
{ GMM_ASSERT1(false, "QMR failed to converge"); }
|
|
else { GMM_WARNING1("QMR failed to converge"); return; }
|
|
}
|
|
beta = ep / delta;
|
|
if (beta == T(0)) {
|
|
if (iter.get_maxiter() == size_type(-1))
|
|
{ GMM_ASSERT1(false, "QMR failed to converge"); }
|
|
else { GMM_WARNING1("QMR failed to converge"); return; }
|
|
}
|
|
gmm::add(p_tld, gmm::scaled(v, -beta), v_tld);
|
|
gmm::left_mult(M1, v_tld, y);
|
|
|
|
rho_1 = rho;
|
|
rho = gmm::vect_norm2(y);
|
|
|
|
gmm::mult(gmm::transposed(A), q, w_tld);
|
|
gmm::add(w_tld, gmm::scaled(w, -beta), w_tld);
|
|
gmm::transposed_right_mult(M1, w_tld, z);
|
|
|
|
xi = gmm::vect_norm2(z);
|
|
|
|
gamma_1 = gamma;
|
|
theta_1 = theta;
|
|
|
|
theta = rho / (gamma_1 * beta);
|
|
gamma = T(1) / gmm::sqrt(T(1) + gmm::sqr(theta));
|
|
|
|
if (gamma == T(0)) {
|
|
if (iter.get_maxiter() == size_type(-1))
|
|
{ GMM_ASSERT1(false, "QMR failed to converge"); }
|
|
else { GMM_WARNING1("QMR failed to converge"); return; }
|
|
}
|
|
eta = -eta * T(rho_1) * gmm::sqr(gamma) / (beta * gmm::sqr(gamma_1));
|
|
|
|
if (iter.first()) {
|
|
gmm::copy(gmm::scaled(p, eta), d);
|
|
gmm::copy(gmm::scaled(p_tld, eta), s);
|
|
} else {
|
|
T tmp = gmm::sqr(theta_1 * gamma);
|
|
gmm::add(gmm::scaled(p, eta), gmm::scaled(d, tmp), d);
|
|
gmm::add(gmm::scaled(p_tld, eta), gmm::scaled(s, tmp), s);
|
|
}
|
|
gmm::add(d, x);
|
|
gmm::add(gmm::scaled(s, T(-1)), r);
|
|
|
|
++iter;
|
|
}
|
|
}
|
|
|
|
|
|
}
|
|
|
|
#endif
|
|
|