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annotate toolbox/wathen.m @ 2:c124219d7bfa draft

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Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 07 May 2015 18:36:24 +0200
parents 8f23314345f4
children
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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1 function A = wathen(nx, ny, k)
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2 %WATHEN Wathen matrix - a finite element matrix (sparse, random entries).
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3 % A = WATHEN(NX,NY) is a sparse random N-by-N finite element matrix
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4 % where N = 3*NX*NY + 2*NX + 2*NY + 1.
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5 % A is precisely the `consistent mass matrix' for a regular NX-by-NY
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6 % grid of 8-node (serendipity) elements in 2 space dimensions.
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7 % A is symmetric positive definite for any (positive) values of
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8 % the `density', RHO(NX,NY), which is chosen randomly in this routine.
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9 % In particular, if D = DIAG(DIAG(A)), then
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10 % 0.25 <= EIG(INV(D)*A) <= 4.5
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11 % for any positive integers NX and NY and any densities RHO(NX,NY).
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12 % This diagonally scaled matrix is returned by WATHEN(NX,NY,1).
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13
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14 % Reference:
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15 % A.J. Wathen, Realistic eigenvalue bounds for the Galerkin
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16 % mass matrix, IMA J. Numer. Anal., 7 (1987), pp. 449-457.
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18 if nargin < 2, error('Two dimensioning arguments must be specified.'), end
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19 if nargin < 3, k = 0; end
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21 e1 = [6 -6 2 -8;-6 32 -6 20;2 -6 6 -6;-8 20 -6 32];
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22 e2 = [3 -8 2 -6;-8 16 -8 20;2 -8 3 -8;-6 20 -8 16];
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23 e = [e1 e2; e2' e1]/45;
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24 n = 3*nx*ny+2*nx+2*ny+1;
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25 A = sparse(n,n);
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26
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27 RHO = 100*rand(nx,ny);
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29 for j=1:ny
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30 for i=1:nx
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31
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32 nn(1) = 3*j*nx+2*i+2*j+1;
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33 nn(2) = nn(1)-1;
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34 nn(3) = nn(2)-1;
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35 nn(4) = (3*j-1)*nx+2*j+i-1;
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36 nn(5) = 3*(j-1)*nx+2*i+2*j-3;
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37 nn(6) = nn(5)+1;
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38 nn(7) = nn(6)+1;
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39 nn(8) = nn(4)+1;
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40
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41 em = e*RHO(i,j);
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42
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43 for krow=1:8
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44 for kcol=1:8
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45 A(nn(krow),nn(kcol)) = A(nn(krow),nn(kcol))+em(krow,kcol);
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46 end
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47 end
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49 end
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50 end
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52 if k == 1
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53 A = diag(diag(A)) \ A;
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54 end