Opt/MassAssembling2DP1OptV2.m

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function M=MassAssembling2DP1OptV2(nq,nme,me,areas)
% function M=MassAssembling2DP1OptV2(nq,nme,me,areas)
%   Assembly of the Mass Matrix using `P_1`-Lagrange finite elements
%   - OptV2 version (see report).
%
%   The Mass Matrix `\Masse` 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 denoted by `\nq`,
%  nme: total number of triangles, also denoted by `\nme`,
%  me: Connectivity array, `3\times\nme` array. <br/>
%  `\me(\jl,k)` is the storage index of the
%  `\jl`-th  vertex of the `k`-th triangle in the array `\q` of vertices coordinates, `\jl\in\{1,2,3\}` and
%       `k\in{\ENS{1}{\nme}}`.
%  areas: Array of areas, `1\times\nme` array. areas(k) is the area of the `k`-th triangle.
%
% Return values:
%  M: Global mass matrix, `\nq\times\nq` sparse matrix.
%
% Example:
%  @verbatim 
%    Th=SquareMesh(10);
%    M=MassAssembling2DP1OptV2(Th.nq,Th.nme,Th.me,Th.areas);
%  @endverbatim
% Copyright:
%   See \ref license
Ig = me([1 2 3 1 2 3 1 2 3],:);
Jg = me([1 1 1 2 2 2 3 3 3],:);
a6=areas/6;
a12=areas/12;
Kg = [a6;a12;a12;a12;a6;a12;a12;a12;a6];
M = sparse(Ig,Jg,Kg,nq,nq);