Mercurial > repos > public > sbplib
view +sbp/+implementations/d1_noneq_10.m @ 1337:bf2554f1825d feature/D2_boundary_opt
Add periodic D1 and D2 operators for orders 8,10,12
author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
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date | Fri, 13 May 2022 13:28:10 +0200 |
parents | 4cb627c7fb90 |
children |
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function [D1,H] = d1_noneq_10(N,h) % N: Number of grid points if(N<20) error('Operator requires at least 20 grid points'); end % BP: Number of boundary points BP = 10; %%%% Norm matrix %%%%%%%% P = sparse(BP,1); %#ok<*NASGU> P0 = 1.0000000000000e-01; P1 = 5.8980851260667e-01; P2 = 9.5666820955973e-01; P3 = 1.1500297411596e+00; P4 = 1.1232986993248e+00; P5 = 1.0123020150951e+00; P6 = 9.9877122702527e-01; P7 = 1.0000873322761e+00; P8 = 1.0000045540888e+00; P9 = 9.9999861455083e-01; for i = 0:BP-1 P(i+1) = eval(['P' num2str(i)]); end H = ones(N,1); H(1:BP) = P; H(end-BP+1:end) = flip(P); H = spdiags(h*H,0,N,N); %%%%%%%%%%%%%%%%%%%%%%%%% %%%% Q matrix %%%%%%%%%%% % interior stencil order = 10; d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260]; d = repmat(d,N,1); Q = spdiags(d,-order/2:order/2,N,N); % Boundaries Q0_0 = -5.0000000000000e-01; Q0_1 = 6.7548747038002e-01; Q0_2 = -2.6691978151546e-01; Q0_3 = 1.4438714982130e-01; Q0_4 = -7.7273673750760e-02; Q0_5 = 2.5570078343005e-02; Q0_6 = 4.2808774693299e-03; Q0_7 = -8.2902108933389e-03; Q0_8 = 3.2031176427908e-03; Q0_9 = -4.4502749689556e-04; Q0_10 = 0.0000000000000e+00; Q0_11 = 0.0000000000000e+00; Q0_12 = 0.0000000000000e+00; Q0_13 = 0.0000000000000e+00; Q0_14 = 0.0000000000000e+00; Q1_0 = -6.7548747038002e-01; Q1_1 = 0.0000000000000e+00; Q1_2 = 9.5146052715180e-01; Q1_3 = -4.2442349882626e-01; Q1_4 = 2.1538865145190e-01; Q1_5 = -7.1939778160350e-02; Q1_6 = -8.2539187832840e-03; Q1_7 = 1.9930661669090e-02; Q1_8 = -7.7433256989613e-03; Q1_9 = 1.0681515760869e-03; Q1_10 = 0.0000000000000e+00; Q1_11 = 0.0000000000000e+00; Q1_12 = 0.0000000000000e+00; Q1_13 = 0.0000000000000e+00; Q1_14 = 0.0000000000000e+00; Q2_0 = 2.6691978151546e-01; Q2_1 = -9.5146052715180e-01; Q2_2 = 0.0000000000000e+00; Q2_3 = 9.6073770842387e-01; Q2_4 = -3.9378595264609e-01; Q2_5 = 1.3302097358959e-01; Q2_6 = 8.1200458151489e-05; Q2_7 = -2.3849770528789e-02; Q2_8 = 9.6600442856829e-03; Q2_9 = -1.3234579460680e-03; Q2_10 = 0.0000000000000e+00; Q2_11 = 0.0000000000000e+00; Q2_12 = 0.0000000000000e+00; Q2_13 = 0.0000000000000e+00; Q2_14 = 0.0000000000000e+00; Q3_0 = -1.4438714982130e-01; Q3_1 = 4.2442349882626e-01; Q3_2 = -9.6073770842387e-01; Q3_3 = 0.0000000000000e+00; Q3_4 = 9.1551097634196e-01; Q3_5 = -2.8541713079648e-01; Q3_6 = 4.1398809121293e-02; Q3_7 = 1.7256059167927e-02; Q3_8 = -9.4349194803610e-03; Q3_9 = 1.3875650645663e-03; Q3_10 = 0.0000000000000e+00; Q3_11 = 0.0000000000000e+00; Q3_12 = 0.0000000000000e+00; Q3_13 = 0.0000000000000e+00; Q3_14 = 0.0000000000000e+00; Q4_0 = 7.7273673750760e-02; Q4_1 = -2.1538865145190e-01; Q4_2 = 3.9378595264609e-01; Q4_3 = -9.1551097634196e-01; Q4_4 = 0.0000000000000e+00; Q4_5 = 8.3519401865051e-01; Q4_6 = -2.0586492924974e-01; Q4_7 = 3.1230261235901e-02; Q4_8 = -2.0969453466651e-04; Q4_9 = -5.0965470499782e-04; Q4_10 = 0.0000000000000e+00; Q4_11 = 0.0000000000000e+00; Q4_12 = 0.0000000000000e+00; Q4_13 = 0.0000000000000e+00; Q4_14 = 0.0000000000000e+00; Q5_0 = -2.5570078343005e-02; Q5_1 = 7.1939778160350e-02; Q5_2 = -1.3302097358959e-01; Q5_3 = 2.8541713079648e-01; Q5_4 = -8.3519401865051e-01; Q5_5 = 0.0000000000000e+00; Q5_6 = 8.1046389580138e-01; Q5_7 = -2.1879194972141e-01; Q5_8 = 5.2977237804899e-02; Q5_9 = -9.0146730522360e-03; Q5_10 = 7.9365079365079e-04; Q5_11 = 0.0000000000000e+00; Q5_12 = 0.0000000000000e+00; Q5_13 = 0.0000000000000e+00; Q5_14 = 0.0000000000000e+00; Q6_0 = -4.2808774693299e-03; Q6_1 = 8.2539187832840e-03; Q6_2 = -8.1200458151489e-05; Q6_3 = -4.1398809121293e-02; Q6_4 = 2.0586492924974e-01; Q6_5 = -8.1046389580138e-01; Q6_6 = 0.0000000000000e+00; Q6_7 = 8.2787884456005e-01; Q6_8 = -2.3582460382545e-01; Q6_9 = 5.9178678209520e-02; Q6_10 = -9.9206349206349e-03; Q6_11 = 7.9365079365079e-04; Q6_12 = 0.0000000000000e+00; Q6_13 = 0.0000000000000e+00; Q6_14 = 0.0000000000000e+00; Q7_0 = 8.2902108933389e-03; Q7_1 = -1.9930661669090e-02; Q7_2 = 2.3849770528789e-02; Q7_3 = -1.7256059167927e-02; Q7_4 = -3.1230261235901e-02; Q7_5 = 2.1879194972141e-01; Q7_6 = -8.2787884456005e-01; Q7_7 = 0.0000000000000e+00; Q7_8 = 8.3301028859275e-01; Q7_9 = -2.3804321850015e-01; Q7_10 = 5.9523809523809e-02; Q7_11 = -9.9206349206349e-03; Q7_12 = 7.9365079365079e-04; Q7_13 = 0.0000000000000e+00; Q7_14 = 0.0000000000000e+00; Q8_0 = -3.2031176427908e-03; Q8_1 = 7.7433256989613e-03; Q8_2 = -9.6600442856829e-03; Q8_3 = 9.4349194803610e-03; Q8_4 = 2.0969453466651e-04; Q8_5 = -5.2977237804899e-02; Q8_6 = 2.3582460382545e-01; Q8_7 = -8.3301028859275e-01; Q8_8 = 0.0000000000000e+00; Q8_9 = 8.3333655748509e-01; Q8_10 = -2.3809523809524e-01; Q8_11 = 5.9523809523809e-02; Q8_12 = -9.9206349206349e-03; Q8_13 = 7.9365079365079e-04; Q8_14 = 0.0000000000000e+00; Q9_0 = 4.4502749689556e-04; Q9_1 = -1.0681515760869e-03; Q9_2 = 1.3234579460680e-03; Q9_3 = -1.3875650645663e-03; Q9_4 = 5.0965470499782e-04; Q9_5 = 9.0146730522360e-03; Q9_6 = -5.9178678209520e-02; Q9_7 = 2.3804321850015e-01; Q9_8 = -8.3333655748509e-01; Q9_9 = 0.0000000000000e+00; Q9_10 = 8.3333333333333e-01; Q9_11 = -2.3809523809524e-01; Q9_12 = 5.9523809523809e-02; Q9_13 = -9.9206349206349e-03; Q9_14 = 7.9365079365079e-04; for i = 1:BP for j = 1:BP Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]); Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]); end end %%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% Difference operator %% D1 = H\Q; %%%%%%%%%%%%%%%%%%%%%%%%%%%