/usr/share/octave/packages/bim-1.1.5/bim2a_axisymmetric_laplacian.m is in octave-bim 1.1.5-4.
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 | ## Copyright (C) 2006-2014 Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
## BIM - Diffusion Advection Reaction PDE Solver
##
## BIM 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.
##
## BIM 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 BIM; If not, see <http://www.gnu.org/licenses/>.
##
## author: Carlo de Falco <cdf _AT_ users.sourceforge.net>
## author: Massimiliano Culpo <culpo _AT_ users.sourceforge.net>
## author: Matteo porro <meoo85 _AT_ users.sourceforge.net>
## author: Emanuela Abbate <emanuela.abbate _AT_ mail.polimi.it>
## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {@var{A}} = bim2a_axisymmetric_laplacian (@var{mesh},@var{epsilon},@var{kappa})
##
## Build the standard finite element stiffness matrix for a diffusion
## problem in cylindrical coordinates with axisymmetric configuration.
## Rotational symmetry is assumed with respect to be the vertical axis r=0.
## Only plane geometries that DO NOT intersect the symmetry axis are admitted.
##
##@example
##@group
## | ____ _|____
## | | \ \ | |
## z | | \ OK \| | NO!
## | |______\ |\___|
## | r |
#@end group
#@end example
##
## The equation taken into account is:
##
## 1/r * d(r * Fr)/dr + dFz/dz = f
##
## with
##
## F = [Fr, Fz]' = - @var{epsilon} * @var{kappa} grad (u)
##
## where @var{epsilon} is an element-wise constant scalar function,
## while @var{kappa} is a piecewise linear conforming scalar function.
##
## @seealso{bim2a_axisymmetric_rhs, bim2a_axisymmetric_reaction,
## bim2a_axisymmetric_advection_diffusion, bim2a_laplacian, bim1a_laplacian,
## bim3a_laplacian}
## @end deftypefn
function [A] = bim2a_axisymmetric_laplacian(mesh,epsilon,kappa)
## Check input
if nargin != 3
error("bim2a_axisymmetric_laplacian: wrong number of input parameters.");
elseif !(all(mesh.p(1,:) >= 0) || all(mesh.p(1,:) <= 0))
error("bim2a_axisymmetric_laplacian: the input mesh cannot intersect the rotation axis r=0.");
endif
## Input check inside bim2a_axisymmetric_advection_diffusion
nnodes = columns(mesh.p);
nelem = columns(mesh.t);
A = bim2a_axisymmetric_advection_diffusion (mesh,epsilon,kappa,ones(nnodes,1),0);
endfunction
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