| OptFEM2DP1 Toolbox 1.2b4 Matlab/Octave Optimized P1-Lagrange Finite Element Method in 2D

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Opt/StiffAssembling2DP1OptV1.m
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    00001 function R=StiffAssembling2DP1OptV1(nq,nme,q,me,areas)
    00002 % function R=StiffAssembling2DP1OptV1(nq,nme,q,me,areas)
    00003 %   Assembly of the Stiffness Matrix using `P_1`-Lagrange finite elements
    00004 %   - OptV1 version (see report).
    00005 %
    00006 %   The Stiffness Matrix `\Stiff` is given by
    00007 %   ``\Stiff_{i,j}=\int_\DOMH \DOT{\GRAD\FoncBase_i(\q)}{\GRAD\FoncBase_j(\q)}d\q,\ \forall (i,j)\in{\ENS{1}{\nq}}^2``
    00008 %   where `\FoncBase_i` are `P_1`-Lagrange basis functions.
    00009 %
    00010 % Parameters:
    00011 %  nq: total number of nodes of the mesh, also denoted by `\nq`.
    00012 %  nme: total number of triangles, also denoted by `\nme`.
    00013 %  q: Array of vertices coordinates, `2\times\nq` array. <br/>
    00014 %  `{\q}(\il,j)` is the
    00015 %  `\il`-th coordinate of the `j`-th vertex, `\il\in\{1,2\}` and
    00016 %  `j\in\ENS{1}{\nq}`
    00017 %  me: Connectivity array, `3\times\nme` array.<br/>
    00018 %  `\me(\jl,k)` is the storage index of the
    00019 %  `\jl`-th  vertex of the `k`-th triangle in the array `\q` of vertices coordinates, `\jl\in\{1,2,3\}` and
    00020 %       `k\in{\ENS{1}{\nme}}`.
    00021 %  areas: Array of areas, `1\times\nme` array. areas(k) is the area of the `k`-th triangle.
    00022 %
    00023 % Return values:
    00024 %  R: Stiffness Matrix, `\nq\times\nq` sparse matrix.
    00025 %
    00026 % Example:
    00027 %  @verbatim
    00028 %    Th=SquareMesh(10);
    00029 %    R=StiffAssembling2DP1OptV1(Th.nq,Th.nme,Th.me,Th.q,Th.areas);
    00030 %  @endverbatim
    00031 %
    00032 % See also:
    00033 %   #ElemStiffMat2DP1
    00034 % Copyright:
    00035 %   See \ref license
    00036 Ig=zeros(nme*9,1);Jg=zeros(nme*9,1);
    00037 Kg=zeros(nme*9,1);
    00038
    00039 ii=[1 2 3 1 2 3 1 2 3];
    00040 jj=[1 1 1 2 2 2 3 3 3];
    00041 kk=1:9;
    00042 for k=1:nme
    00043   Me=ElemStiffMat2DP1(q(:,me(1,k)),q(:,me(2,k)),q(:,me(3,k)),areas(k));
    00044   Ig(kk)=me(ii,k);
    00045   Jg(kk)=me(jj,k);
    00046   Kg(kk)=Me(:);
    00047   kk=kk+9;
    00048 end
    00049 R=sparse(Ig,Jg,Kg,nq,nq);

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