/usr/share/octave/packages/bim-1.1.5/bim1a_axisymmetric_reaction.m is in octave-bim 1.1.5-4.
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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 | ## Copyright (C) 2006-2014 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>
## author: Emanuela Abbate <emanuela.abbate _AT_ mail.polimi.it>
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{C}]} = @
## bim1a_axisymmetric_reaction(@var{mesh},@var{delta},@var{zeta})
##
## Build the lumped finite element mass matrix for a diffusion
## problem in cylindrical coordinates with axisymmetric configuration.
##
## The equation taken into account is:
##
## @var{delta} * @var{zeta} * u = f
##
## where @var{delta} is an element-wise constant scalar function, while
## @var{zeta} is a piecewise linear conforming scalar function.
##
## @seealso{bim1a_axisymmetric_rhs, bim1a_axisymmetric_advection_diffusion, bim1a_axisymmetric_laplacian,
## bim2a_reaction, bim3a_reaction}
## @end deftypefn
function [C] = bim1a_axisymmetric_reaction(mesh,delta,zeta)
## Check input
if nargin != 3
error("bim1a_axisymmetric_reaction: wrong number of input parameters.");
elseif !isvector(mesh)
error("bim1a_axisymmetric_reaction: first argument is not a valid vector.");
endif
mesh = reshape(mesh,[],1);
nnodes = length(mesh);
nelems = nnodes-1;
## Turn scalar input to a vector of appropriate size
if isscalar(delta)
delta = delta*ones(nelems,1);
endif
if isscalar(zeta)
zeta = zeta*ones(nnodes,1);
endif
if !( isvector(delta) && isvector(zeta) )
error("bim1a_axisymmetric_reaction: coefficients are not valid vectors.");
elseif length(delta) != nelems
error("bim1a_axisymmetric_reaction: length of delta is not equal to the number of elements.");
elseif length(zeta) != nnodes
error("bim1a_axisymmetric_reaction: length of zeta is not equal to the number of nodes.");
endif
h = (mesh(2:end)-mesh(1:end-1)).*delta;
d0 = zeta.*[h(1)/2; (h(1:end-1)+h(2:end))/2; h(end)/2];
C = spdiags(d0.*abs(mesh), 0, nnodes,nnodes);
endfunction
%!test
%! n = 100;
%! mesh = linspace(0,1,n+1)';
%! cm = (mesh(1:end-1) + mesh(2:end))/2;
%! uex = @(r) - r.^2 + 1;
%! Nnodes = numel(mesh);
%! Nelements = Nnodes-1;
%! D = 1; v = cm; sigma = 1;
%! alpha = D*ones(Nelements,1);
%! gamma = ones(Nnodes,1);
%! eta = ones(Nnodes,1);
%! beta = 0;
%! delta = ones(Nelements,1);
%! zeta = sigma*ones(Nnodes,1);
%! f = @(r) 4*D + sigma*uex(r);
%! rhs = bim1a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh));
%! S = bim1a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! R = bim1a_axisymmetric_reaction(mesh, delta, zeta);
%! S += R;
%! u = zeros(Nnodes,1); u(end) = uex(mesh(end));
%! u(1:end-1) = S(1:end-1,1:end-1)\(rhs(1:end-1) - S(1:end-1,end)*u(end));
%! assert(u,uex(mesh),1e-3)
%!test
%! n = 100;
%! mesh = linspace(0,1,n+1)';
%! cm = (mesh(1:end-1) + mesh(2:end))/2;
%! uex = @(r) - r.^2 + 1;
%! Nnodes = numel(mesh);
%! Nelements = Nnodes-1;
%! D = 1; v = cm; sigma = 1;
%! alpha = D*ones(Nelements,1);
%! gamma = ones(Nnodes,1);
%! eta = ones(Nnodes,1);
%! beta = 1/D*v;
%! delta = ones(Nelements,1);
%! zeta = sigma*ones(Nnodes,1);
%! f = @(r) 4*D + 2 - 4*r.^2 + sigma*uex(r);
%! rhs = bim1a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh));
%! S = bim1a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! R = bim1a_axisymmetric_reaction(mesh, delta, zeta);
%! S += R;
%! u = zeros(Nnodes,1); u(end) = uex(mesh(end));
%! u(1:end-1) = S(1:end-1,1:end-1)\(rhs(1:end-1) - S(1:end-1,end)*u(end));
%! assert(u,uex(mesh),1e-3)
%!test
%! x = linspace(0,1,101);
%! A = bim1a_axisymmetric_reaction(x,1,1);
%! delta = ones(100,1);
%! zeta = ones(101,1);
%! B = bim1a_axisymmetric_reaction(x,delta,zeta);
%! assert(A,B)
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