/usr/include/rheolef/uzawa_abtbc.h is in librheolef-dev 5.93-2.
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 | # ifndef _RHEO_UZAWA_ABTBC_H
# define _RHEO_UZAWA_ABTBC_H
///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef 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 General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
///
/// =========================================================================
/*Class:uzawa_abtbc
NAME: @code{uzawa_abtbc}, @code{uzs_abtbc} -- stabilized mixed linear solver
@findex uzawa\_abtbc
@cindex mixed linear problem
@cindex Stokes problem
@cindex Uzawa algorithm
@cindex finite element method
@cindex stabilized mixed finite element method
@cindex incompresible elasticity
DESCRIPTION:
@noindent
Uzawa algorithm applied to the mixed problem
@example
[ a b^T ] [ u ] [ f ]
[ ] [ ] = [ ]
[ b -c ] [ p ] [ g ]
@end example
with the bock diagonal preconditionner : (inv(a),I).
Such mixed linear problems appears for instance with the discretization
of Stokes problems with stabilized P1-P1 element, or with nearly
incompressible elasticity.
The algorithm requires the resolution of linear
systems such as: @code{a*x = b}.
These systems may be solved either by direct or iterative
algorithms. Thus, a general matrix solver class is submitted
to the algorithm.
@noindent
@code{uzawa_abtb} is a specialization of the @code{uzs_abtbc} that
uses a direct solver.
DATE: 15 nov 1997
METHODS: @uzs_abtbc
End:
*/
#include "rheolef/matrix_solver.h"
namespace rheolef {
//<uzawa_abtbc:
template<
class MatrixSolver,
class MatrixPreconditioner,
class Matrix,
class DiagMatrix,
class Vector,
class Real>
int
uzs_abtbc(
const MatrixSolver& m_solver,
const Matrix& a,
const MatrixPreconditioner& ap,
const Matrix& b,
const Matrix& c,
const DiagMatrix& I,
Vector& u,
Vector& p,
const Vector& f,
const Vector& g,
const Real& rho,
int& max_iter,
Real& tol,
ostream* p_cres = 0)
{
Float residu = 1. ;
for (int k=1 ; k <= max_iter ; k++) {
Vector oldp = p;
Vector oldu = u;
int status_ms = m_solver(a, ap, u, f - b.trans_mult(p));
Vector r = I.solve(b*u - g + c*p);
p = p + rho*r;
residu = norm(r);
if (p_cres) *p_cres << "[uzawa_abtbc] " << k << " " << residu << "\n";
if (residu <= tol) {
tol = residu;
max_iter = k;
return 0;
}
}
tol = residu;
return 1;
}
template<
class MatrixPreconditionner,
class Matrix,
class Vector,
class Real>
int
uzawa_abtbc(
const Matrix& a,
const MatrixPreconditionner& ap,
const Matrix& b,
const Matrix& c,
Vector& u,
Vector& p,
const Vector& f,
const Vector& g,
const Real& rho,
int& max_iter,
Real& tol,
ostream* p_cres = &std::cerr)
{
return uzs_abtbc (ldlt_solver<MatrixPreconditionner, Matrix, Vector, Vector>(),
a, ap, b, c, EYE, u, p, f, g, rho, max_iter, tol, p_cres);
}
//>uzawa_abtbc:
}// namespace rheolef
# endif // _RHEO_UZAWA_ABTBC_H
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