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annotate +sbp/+implementations/d4_variable_6_2.m @ 318:99005a80b4c2 feature/beams

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Cleaned up d4_variable_4_min_boundary. Removed incorrect D2s from a bunch of files.
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 26 Sep 2016 08:44:17 +0200
parents 203afa156f59
children 5c9e5ba1c1ab
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1 function [H, HI, D1, D2, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = d4_variable_6_2(m,h)
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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3 %%% 6:te ordn. SBP Finita differens %%%
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4 %%% operatorer med diagonal norm %%%
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5 %%% Extension to variable koeff %%%
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6 %%% %%%
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7 %%% H (Normen) %%%
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8 %%% D1=H^(-1)Q (approx f?rsta derivatan) %%%
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9 %%% D2 (approx andra derivatan) %%%
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10 %%% D2=HI*(R+C*D*S %%%
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11 %%% %%%
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12 %%% R=-D1'*H*C*D1-RR %%%
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13 %%% %%%
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14 %%% RR ?r dissipation) %%%
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15 %%% Dissipationen uppbyggd av D4: %%%
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16 %%% DI=D4*B*H*D4 %%%
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17 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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18
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19 % H?r med 6 RP ist?llet f?r 8 f?r D4 operatorn, dock samma randderivator
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20 % Denna ?r noggrannare, och har 2a ordningens randdslutning och b?r ge 6te
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21 % ordningens konvergens. Hade dock ingen fri parameter att optimera
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23
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24 H = diag(ones(m,1),0);
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25 H(1:6,1:6) = [
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26 0.181e3/0.576e3 0 0 0 0 0;
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27 0 0.1343e4/0.960e3 0 0 0 0;
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28 0 0 0.293e3/0.480e3 0 0 0;
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29 0 0 0 0.1811e4/0.1440e4 0 0;
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30 0 0 0 0 0.289e3/0.320e3 0;
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31 0 0 0 0 0 0.65e2/0.64e2;
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32 ];
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33 H(m-5:m,m-5:m) = fliplr(flipud(H(1:6,1:6)));
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35
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36 e_1 = zeros(m,1);e_1(1) = 1;
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37 e_m = zeros(m,1);e_m(m) = 1;
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38
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39 S_U = [-0.137e3/0.60e2 5 -5 0.10e2/0.3e1 -0.5e1/0.4e1 0.1e1/0.5e1;]/h;
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40 S_1 = zeros(1,m);
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41 S_1(1:6) = S_U;
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42 S_m = zeros(1,m);
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43 S_m(m-5:m) = fliplr(-S_U);
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44
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45 S2_U = [0.15e2/0.4e1 -0.77e2/0.6e1 0.107e3/0.6e1 -13 0.61e2/0.12e2 -0.5e1/0.6e1;]/h^2;
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46 S2_1 = zeros(1,m);
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47 S2_1(1:6) = S2_U;
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48 S2_m = zeros(1,m);
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49 S2_m(m-5:m) = fliplr(S2_U);
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51 S3_U = [-0.17e2/0.4e1 0.71e2/0.4e1 -0.59e2/0.2e1 0.49e2/0.2e1 -0.41e2/0.4e1 0.7e1/0.4e1;]/h^3;
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52 S3_1 = zeros(1,m);
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53 S3_1(1:6) = S3_U;
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54 S3_m = zeros(1,m);
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55 S3_m(m-5:m) = fliplr(-S3_U);
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58 H = h*H;
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59 HI = inv(H);
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61 % Fourth derivative, 1th order accurate at first 8 boundary points (still
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62 % yield 5th order convergence if stable: for example u_tt = -u_xxxx
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63
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64 m4 = 7/240;
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65 m3 = -2/5;
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66 m2 = 169/60;
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67 m1 = -122/15;
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68 m0 = 91/8;
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70 M4 = m4*(diag(ones(m-4,1),4)+diag(ones(m-4,1),-4))+m3*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3))+m2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2))+m1*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1))+m0*diag(ones(m,1),0);
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72 %M4 = (-1/6*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3) ) + 2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2)) -13/2*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1)) + 28/3*diag(ones(m,1),0));
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74 M4_U = [
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75 0.1009e4/0.192e3 -0.7657e4/0.480e3 0.9307e4/0.480e3 -0.509e3/0.40e2 0.4621e4/0.960e3 -0.25e2/0.32e2;
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76 -0.7657e4/0.480e3 0.49513e5/0.960e3 -0.4007e4/0.60e2 0.21799e5/0.480e3 -0.8171e4/0.480e3 0.2657e4/0.960e3;
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77 0.9307e4/0.480e3 -0.4007e4/0.60e2 0.1399e4/0.15e2 -0.2721e4/0.40e2 0.12703e5/0.480e3 -0.521e3/0.120e3;
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78 -0.509e3/0.40e2 0.21799e5/0.480e3 -0.2721e4/0.40e2 0.3349e4/0.60e2 -0.389e3/0.15e2 0.559e3/0.96e2;
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79 0.4621e4/0.960e3 -0.8171e4/0.480e3 0.12703e5/0.480e3 -0.389e3/0.15e2 0.17857e5/0.960e3 -0.1499e4/0.160e3;
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80 -0.25e2/0.32e2 0.2657e4/0.960e3 -0.521e3/0.120e3 0.559e3/0.96e2 -0.1499e4/0.160e3 0.2225e4/0.192e3;
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81 ];
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82
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83 M4(1:6,1:6) = M4_U;
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84
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85 M4(m-5:m,m-5:m) = flipud( fliplr( M4_U ) );
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86 M4 = M4/h^3;
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87
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88 D4 = HI*(M4-e_1*S3_1+e_m*S3_m + S_1'*S2_1-S_m'*S2_m);
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89 end