/usr/share/octave/packages/bim-1.1.5/bim1a_advection_upwind.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 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 | ## Copyright (C) 2010-2014 Carlo de Falco
##
## 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>
## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{A}]} = bim1a_advection_upwind (@var{mesh}, @var{beta})
##
## Build the UW stabilized stiffness matrix for an advection problem.
##
## The equation taken into account is:
##
## (@var{beta} u)' = f
##
## where @var{beta} is an element-wise constant.
##
## Instead of passing the vector field @var{beta} directly one can pass
## a piecewise linear conforming scalar function @var{phi} as the last
## input. In such case @var{beta} = grad @var{phi} is assumed.
##
## If @var{phi} is a single scalar value @var{beta} is assumed to be 0
## in the whole domain.
##
## @seealso{bim1a_rhs, bim1a_reaction, bim1a_laplacian, bim2a_advection_diffusion}
## @end deftypefn
function A = bim1a_advection_upwind (x, beta)
## Check input
if nargin != 2
error("bim1a_advection_upwind: wrong number of input parameters.");
endif
nnodes = length(x);
nelem = nnodes-1;
if (length(beta) == 1)
vk = zeros(nelem,1);
elseif (length(beta) == nelem)
vk = beta;
elseif (length(beta) == nnodes)
vk = diff(beta);
else
error("bim1a_advection_upwind: coefficient beta has wrong dimensions.");
endif
bmk = (vk+abs(vk))/2;
bpk = -(vk-abs(vk))/2;
dm1 = [-bmk; NaN];
dp1 = [NaN; -bpk];
d0 = [bmk(1); bmk(2:end) + bpk(1:end-1); bpk(end)];
A = spdiags([dm1, d0, dp1],-1:1,nnodes,nnodes);
endfunction
%!test
%! n = 200;
%! mesh = linspace(0,1,n+1)';
%! uex = @(r) - r.^2 + 1;
%! Nnodes = numel(mesh);
%! Nelements = Nnodes-1;
%! D = 1; v = 1; sigma = 0;
%! alpha = D*ones(Nelements,1);
%! gamma = ones(Nnodes,1);
%! eta = ones(Nnodes,1);
%! beta = 1/D*v*ones(Nelements,1);
%! delta = ones(Nelements,1);
%! zeta = sigma*ones(Nnodes,1);
%! f = @(r) 2*D - 2*v.*r + sigma*uex(r);
%! rhs = bim1a_rhs(mesh, ones(Nelements,1), f(mesh));
%! S = bim1a_laplacian(mesh,alpha,gamma);
%! A = bim1a_advection_upwind(mesh, beta);
%! R = bim1a_reaction(mesh, delta, zeta);
%! S += (A+R);
%! u = zeros(Nnodes,1); u([1 end]) = uex(mesh([1 end]));
%! u(2:end-1) = S(2:end-1,2:end-1)\(rhs(2:end-1) - S(2:end-1,[1 end])*u([1 end]));
%! assert(u,uex(mesh),1e-3)
|