MassAssembling3DP1base.m

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function M=MassAssembling3DP1base(nq,nme,me,volumes)
% function M=MassAssembling3DP1base(nq,nme,me,volumes)
%   Assembly of the Mass Matrix by `P_1`-Lagrange finite elements in 3D
%   - Basic 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 vertices, also denoted by `\nq`.
%  nme: total number of elements, also denoted by `\nme`.
%  me: Connectivity array, `4\times\nme` array. <br/>
%  `\me(\jl,k)` is the storage index of the
%  `\jl`-th  vertex of the `k`-th tetrahedron in the array `\q` of vertices coordinates, `\jl\in\{1,2,3,4\}` and
%       `k\in{\ENS{1}{\nme}}`.
%  volumes: Array of volumes, `1\times\nme array`. volumes(k) is the volume
%         of the k-th tetrahedron.
%
% Return values:
%  M: Global mass matrix, `\nq\times\nq` sparse matrix.
%
% Example:
%  @verbatim 
%    Th=CubeMesh(10);
%    M=MassAssembling3DP1base(Th.nq,Th.nme,Th.me,Th.volumes);
%  @endverbatim
%
% See also:
%   #ElemMassMat3DP1D0
% Copyright:
%   See \ref license
M=sparse(nq,nq);
for k=1:nme
    E=ElemMassMat3DP1D0(volumes(k));
    for il=1:4
        i=me(il,k);
        for jl=1:4
            j=me(jl,k);
            M(i,j)=M(i,j)+E(il,jl);
        end
    end
end