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annotate +sbp/blocknorm4.m @ 87:0a29a60e0b21

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In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
author Martin Almquist <martin.almquist@it.uu.se>
date Sun, 29 Nov 2015 22:23:09 +0100
parents 32b39dc44474
children
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29
32b39dc44474 Removed repository inside +sbp to make it part of the root repo.
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1 function [H, HI, D1, D2, e_1, e_m, M,Q S_1, S_m] = blocknorm4(m,h)
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2 H_U=[0.751e3 / 0.3456e4 0.661e3 / 0.3456e4 -0.515e3 / 0.3456e4 0.5e1 / 0.128e3; 0.661e3 / 0.3456e4 0.1405e4 / 0.1152e4 -0.3e1 / 0.128e3 0.29e2 / 0.3456e4; -0.515e3 / 0.3456e4 -0.3e1 / 0.128e3 0.989e3 / 0.1152e4 0.149e3 / 0.3456e4; 0.5e1 / 0.128e3 0.29e2 / 0.3456e4 0.149e3 / 0.3456e4 0.3407e4 / 0.3456e4;];
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5 H=eye(m);
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6 H(1:4,1:4)=H_U;
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7 H(m-3:m,m-3:m)=flipud( fliplr(H_U(1:4,1:4) ) );
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8 H=H*h;
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9 HI=inv(H);
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11 Q=(-1/12*diag(ones(m-2,1),2)+8/12*diag(ones(m-1,1),1)-8/12*diag(ones(m-1,1),-1)+1/12*diag(ones(m-2,1),-2));
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13 Q_U = [-0.1e1 / 0.2e1 0.55e2 / 0.72e2 -0.47e2 / 0.144e3 0.1e1 / 0.16e2; -0.55e2 / 0.72e2 0 0.43e2 / 0.48e2 -0.19e2 / 0.144e3; 0.47e2 / 0.144e3 -0.43e2 / 0.48e2 0 0.47e2 / 0.72e2; -0.1e1 / 0.16e2 0.19e2 / 0.144e3 -0.47e2 / 0.72e2 0;];
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15 Q(1:4,1:4)=Q_U;
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16 Q(m-3:m,m-3:m)=flipud( fliplr(-Q_U(1:4,1:4) ) );
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18 D1=HI*Q;
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20 M_U=[0.359e3 / 0.288e3 -0.443e3 / 0.288e3 0.97e2 / 0.288e3 -0.13e2 / 0.288e3; -0.51e2 / 0.32e2 0.325e3 / 0.96e2 -0.191e3 / 0.96e2 0.19e2 / 0.96e2; 0.43e2 / 0.96e2 -0.69e2 / 0.32e2 0.293e3 / 0.96e2 -0.137e3 / 0.96e2; -0.29e2 / 0.288e3 0.89e2 / 0.288e3 -0.427e3 / 0.288e3 0.727e3 / 0.288e3;];
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24 M=-(-1/12*diag(ones(m-2,1),2)+16/12*diag(ones(m-1,1),1)+16/12*diag(ones(m-1,1),-1)-1/12*diag(ones(m-2,1),-2)-30/12*diag(ones(m,1),0));
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26 M(1:4,1:4)=M_U;
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28 M(m-3:m,m-3:m)=flipud( fliplr( M_U ) );
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29 M=M/h;
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31 DS_U=[0.25e2 / 0.12e2 -4 3 -0.4e1 / 0.3e1 0.1e1 / 0.4e1;];
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32 DS=zeros(m,m);
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33 DS(1,1:5)=DS_U;
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34 DS(m,m-4:m)=fliplr(DS_U);
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35 DS=DS/h;
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36
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37 D2=HI*(-M+DS);
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38
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39 d3=[-1 3 -3 1];
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40 t3=sum(abs(d3));
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41 DD_3(1:1,1:4)=[d3];
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42 DD_3(m:m,m-3:m)=[d3];
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44 % This works for wave eq.
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45 % For studs interface in 1D no AD is needed.
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46 ADD=1*h/(t3)*DD_3'*DD_3;
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47
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48 e_1 = zeros(m,1);
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49 e_1(1)= 1;
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50 e_m = zeros(m,1);
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51 e_m(end)= 1;
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52 S_1 = -DS(1,:)';
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53 S_m = DS(end,:)';
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54
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55 Q = H*D1-(-e_1*e_1' + e_m*e_m');
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56 M = -(H*D2-(-e_1*S_1' + e_m*S_m'));
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57 end