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

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MassWAssemblingP1OptV2.m
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1 function M=MassWAssemblingP1OptV2(nq,nme,me,areas,Tw)
2 % function M=MassWAssemblingP1OptV2(nq,nme,me,areas,Tw)
3 % Assembly of the Weighted Mass Matrix using `P_1`-Lagrange finite elements
4 % - OptV2 version (see report).
5 %
6 % The Weighted Mass Matrix `\MasseF{w}` is given by
7 % ``\MasseF{w}_{i,j}=\int_\DOMH w(\q)\;\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 % Tw: Array containing the values of `w` at the vertices,
18 % `1\times\nq` array.<br/>
19 % `Tw(i)=w(\q^i),` `\forall i\in\ENS{1}{\nq}`.
20 %
21 % Return values:
22 % M: Global weighted mass matrix, `\nq\times\nq` sparse matrix.
23 %
24 % Example:
25 % @verbatim
26 % Th=SquareMesh(10);
27 % w=@(x,y) cos(x+y);
28 % Tw=w(Th.q(1,:),Th.q(2,:));
29 % Mw=MassWAssemblingP1OptV2(Th.nq,Th.nme,Th.me,Th.areas,Tw);
30 % @endverbatim
31 %
32 % OptFEM2DP1 [V1.2b1] - Copyright (C) 2013 CJS (LAGA)
33 %
34 % This file is part of OptFEM2DP1.
35 % OptFEM2DP1 is free software: you can redistribute it and/or modify
36 % it under the terms of the GNU General Public License as published by
37 % the Free Software Foundation, either version 3 of the License, or
38 % (at your option) any later version.
39 %
40 % OptFEM2DP1 is distributed in the hope that it will be useful,
41 % but WITHOUT ANY WARRANTY; without even the implied warranty of
42 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
43 % GNU General Public License for more details.
44 %
45 % You should have received a copy of the GNU General Public License
46 % along with this program. If not, see <http://www.gnu.org/licenses/>.
47 Ig = me([1 2 3 1 2 3 1 2 3],:);
48 Jg = me([1 1 1 2 2 2 3 3 3],:);
49 W=Tw(me).*(ones(3,1)*areas/30);
50 Kg=zeros(9,length(areas));
51 Kg(1,:)=3*W(1,:)+W(2,:)+W(3,:);
52 Kg(2,:)=W(1,:)+W(2,:)+W(3,:)/2;
53 Kg(3,:)=W(1,:)+W(2,:)/2+W(3,:);
54 Kg(5,:)=W(1,:)+3*W(2,:)+W(3,:);
55 Kg(6,:)=W(1,:)/2+W(2,:)+W(3,:);
56 Kg(9,:)=W(1,:)+W(2,:)+3*W(3,:);
57 Kg([4, 7, 8],:)=Kg([2, 3, 6],:);
58 M = sparse(Ig,Jg,Kg,nq,nq);