function R=StiffAssemblingP1OptV0(nq,nme,q,me,areas)
% function R=StiffAssemblingP1OptV0(nq,nme,q,me,areas)
%   Assembly of the Stiffness Matrix by P1-Lagrange finite elements
%   - OptV0 version (see report).
%
% Parameters:
%  nq: total number of nodes of the mesh,
%  nme: total number of triangles,
%  q: Array of vertices coordinates, 2-by-nq array.
%     q(il,j) is the il-th coordinate of the j-th vertex, il in {1,2}
%     and j in {1,...,nq}.
%  me: Connectivity array, 3-by-nme array.
%      me(jl,k) is the storage index of the jl-th  vertex 
%      of the k-th triangle in the array q of vertices coordinates,
%  areas: Array of areas, 1-by-nme array. areas(k) is the area 
%         of the k-th triangle.
%
% Return values:
%  R: Global stiffness matrix, nq-by-nq sparse matrix.
%
% Example:
%    Th=SquareMesh(10);
%    R=StiffAssemblingP1OptV0(Th.nq,Th.nme,Th.q,Th.me,Th.areas);

%
% OptFEM2DP1 [V1.2b1] -    Copyright (C) 2013  CJS (LAGA)
%
%   This file is part of OptFEM2DP1.
%   OptFEM2DP1 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 3 of the License, or
%   (at your option) any later version.
%
%   OptFEM2DP1 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 this program.  If not, see <http://www.gnu.org/licenses/>.
R=sparse(nq,nq);
for k=1:nme
  I=me(:,k);
  Me=ElemStiffMatP1(q(:,me(1,k)),q(:,me(2,k)),q(:,me(3,k)),areas(k));
  R(I,I)=R(I,I)+Me;
end
