MassVFAssembling3DP1OptV2.m

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function M=MassVFAssembling3DP1OptV2(nq,nme,me,volumes,Num)
% function M=MassVFAssembling3DP1OptV2(nq,nme,me,volumes,Num)
%   Assembly of the Mass vectors fields Matrix by `P_1`-Lagrange finite elements in 3D
%   using OptV2 version (see report).
%
%   The Mass vectors fields is given by 
%   ``\MassVF_{i,j}=\int_\DOMH \DOT{\BasisFuncTwoD_m(\q)}{ \BasisFuncTwoD_l(\q)}d(\q), \ \forall (m,l)\in\ENS{1}{3\,\nq}^2,``
%   where `\BasisFuncTwoD_m` are `P_1`-Lagrange vector 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.
%  Num: 
%    - 0 global alternate numbering with local alternate numbering (classical method), 
%    - 1 global block numbering with local alternate numbering,
%    - 2 global alternate numbering with local block numbering,
%    - 3 global block numbering with local block numbering.
%
% Return values:
%  M: `3\nq\times 3\nq` Global Mass vectors fields sparse matrix
%
% Example:
%  @verbatim 
%    Th=CubeMesh(10);
%    Mvf=MassVFAssembling3DP1OptV2(Th.nq,Th.nme,Th.me,Th.areas,0);@endverbatim
%  
% See also:
%   #BuildIgJgP1VF, #BuildElemMassVFMatFunc
% Copyright:
%   See \ref license

ElemMassVFMat=BuildElemMassVFMatFunc(Num);
E=ElemMassVFMat(20);
E=E(:)';
[Ig,Jg]=BuildIgJgP1VF(Num,me,nq);
Kg=zeros(144,nme);

It=find(E==2);
Vt=volumes/10;
for i=It
  Kg(i,:)=Vt;
end

It=find(E==1);
Vt=volumes/20;
for i=It
  Kg(i,:)=Vt;
end

M=sparse(Ig(:),Jg(:),Kg(:),3*nq,3*nq);