MassWAssemblingP1base.m

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function M=MassWAssemblingP1base(nq,nme,me,areas,Tw)
% function M=MassWAssemblingP1base(nq,nme,me,areas,Tw)
%   Assembling Mass Weight Matrix by `P_1`-Lagrange finite elements
%   using "base" version (see report).
%
%   The Mass Weight Matrix 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 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.
%  Tw: `\nme` 'double' array, `Tw(i)=w(\q^i),` `\forall i\in\ENS{1}{\nq}`.
%
% Return values:
%  M: `\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=MassWAssemblingP1base(Th.nq,Th.nme,Th.me,Th.areas,Tw);
%  @endverbatim
%
% See also:
%   #SquareMesh
M=sparse(nq,nq);
for k=1:nme
    for il=1:3
        i=me(il,k);
        Twloc(il)=Tw(i);
    end
    E=ElemMassWMatP1(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