| OptFEM2D Toolbox for Matlab V1.2b1 Matlab/Octave Optimized P1-Lagrange Finite Element Method in 2D

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MassAssemblingP1OptV1.m
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1 function M=MassAssemblingP1OptV1(nq,nme,me,areas)
2 % function M=MassAssemblingP1OptV1(nq,nme,me,areas)
3 % Assembly of the Mass Matrix using `P_1`-Lagrange finite elements
4 % - OptV1 version (see report).
5 %
6 % The Mass Matrix `\Masse` is given by
7 % ``\Masse_{i,j}=\int_\DOMH \FoncBase_i(\q) \FoncBase_j(\q) d\q,\ \forall (i,j)\in{\ENS{1}{\nq}}^2``
8 % where `\FoncBase_i` are `P_1`-Lagrange basis functions
9 % Parameters:
10 % nq: total number of nodes of the mesh, also denoted by `\nq`,
11 % nme: total number of triangles, also denoted by `\nme`,
12 % me: Connectivity array, `3\times\nme` array. <br/>
13 % `\me(\jl,k)` is the storage index of the
14 % `\jl`-th vertex of the `k`-th triangle in the array `\q` of vertices coordinates, `\jl\in\{1,2,3\}` and
15 % `k\in{\ENS{1}{\nme}}`.
16 % areas: Array of areas, `1\times\nme` array. areas(k) is the area of the `k`-th triangle.
17 %
18 % Return values:
19 % M: Global mass matrix, `\nq\times\nq` sparse matrix.
20 %
21 % Example:
22 % @verbatim
23 % Th=SquareMesh(10);
24 % M=MassAssemblingP1OptV1(Th.nq,Th.nme,Th.me,Th.areas);
25 % @endverbatim
26 %
27 % OptFEM2DP1 [V1.2b1] - Copyright (C) 2013 CJS (LAGA)
28 %
29 % This file is part of OptFEM2DP1.
30 % OptFEM2DP1 is free software: you can redistribute it and/or modify
31 % it under the terms of the GNU General Public License as published by
32 % the Free Software Foundation, either version 3 of the License, or
33 % (at your option) any later version.
34 %
35 % OptFEM2DP1 is distributed in the hope that it will be useful,
36 % but WITHOUT ANY WARRANTY; without even the implied warranty of
37 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
38 % GNU General Public License for more details.
39 %
40 % You should have received a copy of the GNU General Public License
41 % along with this program. If not, see <http://www.gnu.org/licenses/>.
42 Ig=zeros(9*nme,1);Jg=zeros(9*nme,1);Kg=zeros(9*nme,1);
43
44 ii=[1 2 3 1 2 3 1 2 3];
45 jj=[1 1 1 2 2 2 3 3 3];
46 kk=1:9;
47 for k=1:nme
48 E=ElemMassMatP1(areas(k));
49 Ig(kk)=me(ii,k);
50 Jg(kk)=me(jj,k);
51 Kg(kk)=E(:);
52 kk=kk+9;
53 end
54 M=sparse(Ig,Jg,Kg,nq,nq);
55 %*****