/usr/include/rheolef/newton.h is in librheolef-dev 6.5-1+b1.
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 | # ifndef _RHEO_NEWTON_H
# define _RHEO_NEWTON_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
///
/// =========================================================================
namespace rheolef {
/*Class:newton
NAME: @code{newton} -- Newton nonlinear algorithm
@findex newton
@cindex nonlinear problem
@cindex Newton method
DESCRIPTION:
@noindent
Nonlinear Newton algorithm for the resolution of the following problem:
@example
F(u) = 0
@end example
A simple call to the algorithm writes:
@example
my_problem P;
field uh (Vh);
newton (P, uh, tol, max_iter);
@end example
The @code{my_problem} class may contains methods for the evaluation
of F (aka residue) and its derivative:
@example
class my_problem @{
public:
my_problem();
field residue (const field& uh) const;
Float dual_space_norm (const field& mrh) const;
void update_derivative (const field& uh) const;
field derivative_solve (const field& mrh) const;
@};
@end example
The @code{dual_space_norm} returns a scalar from the weighted residual field term
@code{mrh} returned by the @code{residue} function:
this scalar is used as stopping criteria for the algorithm.
The @code{update_derivative} and @code{derivative_solver}
members are called at each step of the Newton algorithm.
See the example @code{p_laplacian.h} in the user's documentation for more.
AUTHOR:
| Pierre.Saramito@imag.fr
LJK, 38041 Grenoble cedex 9, France
DATE: 14 oct 2009
METHODS: @newton
End:
*/
//<newton:
template <class Problem, class Field>
int newton (Problem P, Field& uh, Float& tol, size_t& max_iter, odiststream *p_derr = 0) {
if (p_derr) *p_derr << "# Newton:" << std::endl << "# n r" << std::endl << std::flush;
for (size_t n = 0; true; n++) {
Field rh = P.residue(uh);
Float r = P.dual_space_norm(rh);
if (p_derr) *p_derr << n << " " << r << std::endl << std::flush;
if (r <= tol) { tol = r; max_iter = n; return 0; }
if (n == max_iter) { tol = r; return 1; }
P.update_derivative (uh);
Field delta_uh = P.derivative_solve (-rh);
uh += delta_uh;
}
}
//>newton:
}// namespace rheolef
# endif // _RHEO_NEWTON_H
|