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

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Opt/StiffElasAssembling2DP1OptV2.m
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    00001 function [K]=StiffElasAssembling2DP1OptV2(nq,nme,q,me,areas,lambda,mu,Num)
    00002 % function K=StiffElasAssembling2DP1OptV2(nq,nme,q,me,areas,lambda,mu,Num)
    00003 %   Assembly of the Stiffness Elasticity Matrix by `P_1`-Lagrange finite elements
    00004 %   using "OptV2" version (see report).
    00005 %
    00006 %   The Stiffness Elasticity Matrix is given by
    00007 %   ``\StiffElas_{m,l}=\int_{\DOMH} \Odv^t(\BasisFuncTwoD_m) \Ocv(\BasisFuncTwoD_l)dT, \ \forall (m,l)\in\ENS{1}{2\,\nq}^2,``
    00008 %   where `\BasisFuncTwoD_m` are `P_1`-Lagrange vector basis functions.
    00009 %   Here `\Ocv=(\Occ_{xx},\Occ_{yy},\Occ_{xy})^t` and `\Odv=(\Odc_{xx},\Odc_{yy},2\Odc_{xy})^t`
    00010 %   are the elastic stress and strain tensors respectively.
    00011 %
    00012 % Parameters:
    00013 %  nq: total number of nodes in the mesh, also denoted by `\nq`.
    00014 %  nme: total number of triangles, also denoted by `\nme`.
    00015 %  q: Array of vertices coordinates, `2\times\nq` array. <br/>
    00016 %  `{\q}(\il,j)` is the
    00017 %  `\il`-th coordinate of the `j`-th vertex, `\il\in\{1,2\}` and
    00018 %  `j\in\ENS{1}{\nq}`
    00019 %  me: Connectivity array, `3\times\nme` array. <br/>
    00020 %  `\me(\jl,k)` is the storage index of the
    00021 %  `\jl`-th  vertex of the `k`-th triangle in the array `\q`, `\jl\in\{1,2,3\}` and
    00022 %       `k\in{\ENS{1}{\nme}}`.
    00023 %  areas: Array of areas, `1\times\nme` array. areas(k) is the area of the `k`-th triangle.
    00024 %  lambda: the first Lame coefficient in Hooke's law
    00025 %  mu: the second Lame coefficient in Hooke's law
    00026 %  Num:
    00027 %    - 0 global alternate numbering with local alternate numbering (classical method),
    00028 %    - 1 global block numbering with local alternate numbering,
    00029 %    - 2 global alternate numbering with local block numbering,
    00030 %    - 3 global block numbering with local block numbering.
    00031 %
    00032 % Return values:
    00033 %  K: `2\nq\times 2\nq` stiffness elasticity sparse matrix
    00034 %
    00035 % Example:
    00036 %  @verbatim
    00037 %    Th=SquareMesh(10);
    00038 %    lambda=1; mu=1;
    00039 %    Num = 0;
    00040 %    KK=StiffElasAssembling2DP1OptV2(Th.nq,Th.nme,Th.q,Th.me,Th.areas,lambda,mu,Num);@endverbatim
    00041 %
    00042 % See also:
    00043 %   #BuildIgJgP1VF, #ElemStiffElasMatBaVec2DP1, #ElemStiffElasMatBbVec2DP1
    00044 % Copyright:
    00045 %   See \ref license
    00046 [Ig,Jg]=BuildIgJgP1VF(Num,me,nq);
    00047 switch Num
    00048 case {0,1}
    00049   Kg=ElemStiffElasMatBaVec2DP1(q,me,areas,lambda,mu);
    00050 case {2,3}
    00051   Kg=ElemStiffElasMatBbVec2DP1(q,me,areas,lambda,mu);
    00052 end
    00053 K = sparse(Ig(:),Jg(:),Kg(:),2*nq,2*nq);

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