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annotate +sbp/+implementations/d1_upwind_7.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_7(m,h)
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3 BP = 6;
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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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8 Hv=ones(m,1);
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9 Hv(1:6) = [0.19087e5/0.60480e5; 0.84199e5/0.60480e5; 0.18869e5/0.30240e5; 0.37621e5/0.30240e5; 0.55031e5/0.60480e5; 0.61343e5/0.60480e5; ];
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10 Hv(m-5:m)=rot90(Hv(1:6),2);
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11 Hv = Hv*h;
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12 H = spdiag(Hv,0);
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13 HI = spdiag(1./Hv,0);
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14
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15 q_diags = [-3 -2 -1 0 1 2 3 4];
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16 q_stencil = [-1/105 +1/10 -3/5 -1/4 +1 -3/10 +1/15 -1/140];
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17 Qp = stripeMatrix(q_stencil, q_diags,m);
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18
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19 Q_U =[
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20 -0.265e3/0.300272e6 0.1587945773e10/0.2432203200e10 -0.1926361e7/0.25737600e8 -0.84398989e8/0.810734400e9 0.48781961e8/0.4864406400e10 0.3429119e7/0.202683600e9;
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21 -0.1570125773e10/0.2432203200e10 -0.26517e5/0.1501360e7 0.240029831e9/0.486440640e9 0.202934303e9/0.972881280e9 0.118207e6/0.13512240e8 -0.231357719e9/0.4864406400e10;
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22 0.1626361e7/0.25737600e8 -0.206937767e9/0.486440640e9 -0.61067e5/0.750680e6 0.49602727e8/0.81073440e8 -0.43783933e8/0.194576256e9 0.51815011e8/0.810734400e9;
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23 0.91418989e8/0.810734400e9 -0.53314099e8/0.194576256e9 -0.33094279e8/0.81073440e8 -0.18269e5/0.107240e6 0.440626231e9/0.486440640e9 -0.365711063e9/0.1621468800e10;
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24 -0.62551961e8/0.4864406400e10 0.799e3/0.35280e5 0.82588241e8/0.972881280e9 -0.279245719e9/0.486440640e9 -0.346583e6/0.1501360e7 0.2312302333e10/0.2432203200e10;
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25 -0.3375119e7/0.202683600e9 0.202087559e9/0.4864406400e10 -0.11297731e8/0.810734400e9 0.61008503e8/0.1621468800e10 -0.1360092253e10/0.2432203200e10 -0.10677e5/0.42896e5;
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26 ];
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27
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29 Qp(1:6,1:6)=Q_U;
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30 Qp(m-5:m,m-5:m)=rot90(Q_U,2)';
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32 Qm=-Qp';
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34 e_1=sparse(m,1);e_1(1)=1;
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35 e_m=sparse(m,1);e_m(m)=1;
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37 Dp=HI*(Qp-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ;
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39 Dm=HI*(Qm-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ;
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40 end