/usr/share/octave/packages/bim-1.1.5/bim3a_laplacian.m is in octave-bim 1.1.5-4.
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##
## 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>
## -*- texinfo -*-
## @deftypefn {Function File} @
## {@var{A}} = bim3a_laplacian (@var{mesh}, @var{epsilon}, @var{kappa})
##
## Build the standard finite element stiffness matrix for a diffusion
## problem.
##
## The equation taken into account is:
##
## - (@var{epsilon} * @var{kappa} ( u' ))' = f
##
## where @var{epsilon} is an element-wise constant scalar function,
## while @var{kappa} is a piecewise linear conforming scalar function.
##
## @seealso{bim3a_rhs, bim3a_reaction, bim2a_laplacian, bim3a_laplacian}
## @end deftypefn
function [A] = bim3a_laplacian (mesh,epsilon,kappa)
## Check input
if nargin != 3
error("bim3a_laplacian: wrong number of input parameters.");
elseif !(isstruct(mesh) && isfield(mesh,"p") &&
isfield (mesh,"t") && isfield(mesh,"e"))
error("bim3a_laplacian: first input is not a valid mesh structure.");
endif
p = mesh.p;
t = mesh.t;
nnodes = columns(p);
nelem = columns(t);
## Turn scalar input to a vector of appropriate size
if isscalar(epsilon)
epsilon = epsilon * ones(nelem,1);
endif
if isscalar(kappa)
kappa = kappa*ones(nnodes,1);
endif
if !( isvector(epsilon) && isvector(kappa) )
error("bim3a_laplacian: coefficients are not valid vectors.");
elseif (numel (epsilon) != nelem)
error("bim3a_laplacian: length of epsilon is not equal to the number of elements.");
elseif (numel (kappa) != nnodes)
error("bim2a_laplacian: length of kappa is not equal to the number of nodes.");
endif
## Local contributions
Lloc = zeros(4,4,nelem);
epsilonareak = reshape (epsilon .* mesh.area',1,1,nelem);
shg = mesh.shg(:,:,:);
## Computation
for inode = 1:4
for jnode = 1:4
ginode(inode,jnode,:) = mesh.t(inode,:);
gjnode(inode,jnode,:) = mesh.t(jnode,:);
Lloc(inode,jnode,:) = sum( kappa(inode) * shg(:,inode,:) .* shg(:,jnode,:),1) .* epsilonareak;
endfor
endfor
## Assembly
A = sparse(ginode(:),gjnode(:),Lloc(:));
endfunction
%!shared mesh,epsilon,kappa,nnodes,nelem
% x = y = z = linspace(0,1,4);
% [mesh] = msh3m_structured_mesh(x,y,z,1,1:6);
% [mesh] = bim3c_mesh_properties(mesh);
% nnodes = columns(mesh.p);
% nelem = columns(mesh.t);
% epsilon = ones(columns(mesh.t),1);
% kappa = ones(columns(mesh.p),1);
%!test
% [A] = bim3a_laplacian(mesh,epsilon,kappa);
% assert(size(A),[nnodes, nnodes]);
%!test
% [A1] = bim3a_laplacian(mesh,3*epsilon,kappa);
% [A2] = bim3a_laplacian(mesh,epsilon,3*kappa);
% assert(A1,A2);
%!test
% [A1] = bim3a_laplacian(mesh,epsilon,kappa);
% [A2] = bim3a_laplacian(mesh,1,1);
% assert(A1,A2);
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