MassAssemblingP1OptV1.m

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function M=MassAssemblingP1OptV1(nq,nme,me,areas)
% function M=MassAssemblingP1OptV1(nq,nme,me,areas)
%   Assembling Mass Matrix by `P_1`-Lagrange finite elements
%   using "OptV1" version (see report).
%
%   The Mass Matrix is given by 
%   ``\Masse_{i,j}=\int_\DOMH \FoncBase_i(\q) \FoncBase_j(\q) d\q,\ \forall (i,j)\in\ENS{1}{\nq}^2``
%   where `\FoncBase_i` are `P_1`-Lagrange basis functions
% Parameters:
%  nq: total number of nodes of the mesh, also noted `\nq`,
%  nme: number of triangles, also noted `\nme`,
%  me: `3\times\nme` 'int32' array,`\me(\jl,k)` index of storage, in the array `q`, of the `\jl`-th
%       vertex of the triangle of index `k`, `\jl\in\{1,2,3\}` and `k\in\{1,\hdots,\nme\}.`
%       Also noted `\me`.
%  areas: `1\times\nme` array, areas(k) is the area of triangle k.
%
% Return values:
%  M: `\nq\times\nq` sparse matrix
%
% Example:
%  @verbatim 
%    Th=SquareMesh(10);
%    M=MassAssemblingP1OptV1(Th.nq,Th.nme,Th.me,Th.areas);
%  @endverbatim
%
% See also:
%   #SquareMesh
%
% @author Francois Cuvelier @date 2012-05-31
%
% @new{1,1,fc,2012-11-22} Added doxygen documentation using mtoc++ tool
%   - \c Homepage http://www.morepas.org/software/mtocpp/.
%   - \c License http://www.morepas.org/software/mtocpp/docs/licensing.html
%
% @change{1,1,fc,2012-11-22}
% - ...
%
% Copyright (c) 2012, Francois Cuvelier, Gilles Scarella
% All rights reserved.
%
% Redistribution and use in source and binary forms, with or without
% modification, are permitted only in compliance with the BSD license, see
% http://www.opensource.org/licenses/bsd-license.php
Ig=zeros(9*nme,1);Jg=zeros(9*nme,1);Kg=zeros(9*nme,1);

ii=[1 2 3 1 2 3 1 2 3];
jj=[1 1 1 2 2 2 3 3 3];
kk=1:9;
for k=1:nme
  E=ElemMassMatP1(areas(k));
  Ig(kk)=me(ii,k); 
  Jg(kk)=me(jj,k);
  Kg(kk)=E(:);
  kk=kk+9;
end
M=sparse(Ig,Jg,Kg,nq,nq);
%*****