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annotate +sbp/+implementations/d1_upwind_8.m @ 1337:bf2554f1825d feature/D2_boundary_opt

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Add periodic D1 and D2 operators for orders 8,10,12
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 13 May 2022 13:28:10 +0200
parents f7ac3cd6eeaa
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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Martin Almquist <martin.almquist@it.uu.se>
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1 function [H, HI, Dp, Dm, e_1, e_m] = d1_upwind_8(m,h)
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2
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3 BP = 8;
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4 if(m<2*BP)
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5 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
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6 end
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7
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8 Hv=ones(m,1);
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9 Hv(1:8) = [0.7489399e7/0.25401600e8; 0.5537831e7/0.3628800e7; 0.103373e6/0.403200e6; 0.261259e6/0.145152e6; 0.298231e6/0.725760e6; 0.515917e6/0.403200e6; 0.3349159e7/0.3628800e7; 0.25639991e8/0.25401600e8];
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10 Hv(m-7:m)=rot90(Hv(1:8),2);
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11 Hv=Hv*h;
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12
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13 H = spdiag(Hv,0);
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14 HI = spdiag(1./Hv,0);
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15
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16 q_diags = [-3 -2 -1 0 1 2 3 4 5];
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17 q_stencil = [-1/168 +1/14 -1/2 -9/20 +5/4 -1/2 +1/6 -1/28 +1/280];
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18 Qp = stripeMatrix(q_stencil, q_diags,m);
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19
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20
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21 Q_U =[
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22 -0.16683e5/0.63018560e8 0.29345822969987e14/0.43354248537600e14 -0.2734625426591e13/0.40644608004000e14 -0.113480208109603e15/0.780376473676800e15 -0.830250230261e12/0.26012549122560e14 0.2500519492033e13/0.32515686403200e14 0.2235718279643e13/0.390188236838400e15 -0.388481888477e12/0.26543417472000e14;
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23 -0.29227665839987e14/0.43354248537600e14 -0.493793e6/0.63018560e8 0.8302717120817e13/0.26543417472000e14 0.3739408501537e13/0.9290196115200e13 0.2684481534461e13/0.13935294172800e14 -0.4450185662513e13/0.18580392230400e14 -0.1221838279381e13/0.37160784460800e14 0.90595000956023e14/0.1950941184192000e16;
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24 0.2505689537591e13/0.40644608004000e14 -0.7312922392817e13/0.26543417472000e14 -0.69332623e8/0.1323389760e10 0.10994933811709e14/0.18580392230400e14 -0.9270952411151e13/0.18580392230400e14 0.3191238635141e13/0.20644880256000e14 0.4442211176987e13/0.92901961152000e14 -0.940661365031e12/0.32515686403200e14;
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25 0.118016946570403e15/0.780376473676800e15 -0.4173878828737e13/0.9290196115200e13 -0.7990503962509e13/0.18580392230400e14 -0.207799621e9/0.1323389760e10 0.2044021560341e13/0.2477385630720e13 0.511197701761e12/0.18580392230400e14 0.1237681717213e13/0.13935294172800e14 -0.7784834666617e13/0.130062745612800e15;
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26 0.68609076271e11/0.2364777192960e13 -0.2235651762161e13/0.13935294172800e14 0.6527681584751e13/0.18580392230400e14 -0.1115980068821e13/0.2477385630720e13 -0.55386253e8/0.189055680e9 0.3208334350649e13/0.3716078446080e13 -0.407569013461e12/0.844563283200e12 0.136474842626653e15/0.780376473676800e15;
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27 -0.2487637785013e13/0.32515686403200e14 0.4244231077313e13/0.18580392230400e14 -0.1550378843141e13/0.20644880256000e14 -0.5726967564961e13/0.18580392230400e14 -0.1017898941929e13/0.3716078446080e13 -0.526653889e9/0.1323389760e10 0.45241297077547e14/0.37160784460800e14 -0.2279608411897e13/0.5080576000500e13;
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28 -0.2164019088443e13/0.390188236838400e15 0.1263196075861e13/0.37160784460800e14 -0.6600697610987e13/0.92901961152000e14 0.556610591687e12/0.13935294172800e14 0.926842346471e12/0.9290196115200e13 -0.18757693936747e14/0.37160784460800e14 -0.584765899e9/0.1323389760e10 0.204646287449e12/0.168431424000e12;
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29 0.387091928477e12/0.26543417472000e14 -0.90231551688023e14/0.1950941184192000e16 0.1032404418251e13/0.32515686403200e14 0.3502353445417e13/0.130062745612800e15 -0.15385068876253e14/0.780376473676800e15 0.262499068919e12/0.10161152001000e14 -0.867004691939e12/0.1852745664000e13 -0.85017967e8/0.189055680e9;
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30 ];
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31
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32 Qp(1:8,1:8)=Q_U;
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33 Qp(m-7:m,m-7:m)=rot90(Q_U,2)'; %%% This is different from standard SBP
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34
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35 Qm=-Qp';
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36
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37 e_1=sparse(m,1);e_1(1)=1;
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38 e_m=sparse(m,1);e_m(m)=1;
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39
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40 Dp=HI*(Qp-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ;
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42 Dm=HI*(Qm-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ;
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43 end