base/MassWAssembling2DP1base.m

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function M=MassWAssembling2DP1base(nq,nme,me,areas,Tw)
% function M=MassWAssembling2DP1base(nq,nme,me,areas,Tw)
%   Assembly of the Weighted Mass Matrix by `P_1`-Lagrange finite elements
%   - Basic version (see report).
%
%   The Weighted Mass Matrix `\MasseF{w}` is given by 
%   ``\MasseF{w}_{i,j}=\int_\DOMH w(\q)\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`, `\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.
%  Tw: Array of vertices weight `w` function values,
%  `1\times\nq` array.<br/>
%  `Tw(i)=w(\q^i),` `\forall i\in\ENS{1}{\nq}`.
%
% Return values:
%  M: Global weighted mass matrix, `\nq\times\nq` sparse matrix.
%
% Example:
%  @verbatim 
%    Th=SquareMesh(10);
%    w=@(x,y) cos(x+y);
%    Tw=w(Th.q(1,:),Th.q(2,:));
%    Mw=MassWAssembling2DP1base(Th.nq,Th.nme,Th.me,Th.areas,Tw);
%  @endverbatim
%
% See also:
%   #ElemMassWMat2DP1
% Copyright:
%   See \ref license
M=sparse(nq,nq);
for k=1:nme
    for il=1:3
        i=me(il,k);
        Twloc(il)=Tw(i);
    end
    E=ElemMassWMat2DP1(areas(k),Twloc);
    for il=1:3
        i=me(il,k);
        for jl=1:3
            j=me(jl,k);
            M(i,j)=M(i,j)+E(il,jl);
        end
    end
end