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annotate +sbp/+implementations/d4_variable_6_3.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 def409c10800
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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_3(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 7 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 2 fria parametrar att optimera
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22
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24
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25 H=diag(ones(m,1),0);
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26 H(1:7,1:7)=[
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27 0.414837907e9/0.1191965760e10 0 0 0 0 0 0;
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28 0 0.475278367e9/0.397321920e9 0 0 0 0 0;
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29 0 0 0.13872751e8/0.12416310e8 0 0 0 0;
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30 0 0 0 0.346739027e9/0.595982880e9 0 0 0;
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31 0 0 0 0 0.560227469e9/0.397321920e9 0 0;
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32 0 0 0 0 0 0.322971631e9/0.397321920e9 0;
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33 0 0 0 0 0 0 0.616122491e9/0.595982880e9;
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34 ];
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35
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36 H(m-6:m,m-6:m) = fliplr(flipud(H(1:7,1:7)));
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38
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39 e_1=zeros(m,1);
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40 e_1(1)=1;
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41 e_m=zeros(m,1);
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42 e_m(m)=1;
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43
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44 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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45 S_1=zeros(1,m);
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46 S_1(1:6)=S_U;
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47 S_m=zeros(1,m);
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48 S_m(m-5:m)=fliplr(-S_U);
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50
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51 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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52 S2_1 = zeros(1,m);
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53 S2_1(1:6) = S2_U;
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54 S2_m = zeros(1,m);
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55 S2_m(m-5:m) = fliplr(S2_U);
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56
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57
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58 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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59 S3_1 = zeros(1,m);
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60 S3_1(1:6) = S3_U;
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61 S3_m = zeros(1,m);
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62 S3_m(m-5:m) = fliplr(-S3_U);
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63
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64 %DS=zeros(m,m);
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65 %DS(1,1:5)=-[-25/12, 4, -3, 4/3, -1/4];
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66 %DS(m,m-4:m)=fliplr(-[-25/12, 4, -3, 4/3, -1/4]);
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67 %DS=diag(c)*DS/h;
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70 H=h*H;
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71 HI=inv(H);
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74 % Fourth derivative, 1th order accurate at first 8 boundary points (still
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75 % yield 5th order convergence if stable: for example u_tt=-u_xxxx
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76
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77 m4 = 7/240;
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78 m3 = -2/5;
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79 m2 = 169/60;
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80 m1 = -122/15;
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81 m0 = 91/8;
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82
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83 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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84
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85 %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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87 M4_U = [
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88 0.1399708478939e13/0.263487168000e12 -0.13482796013041e14/0.834376032000e12 0.344344095859e12/0.17565811200e11 -0.3166261424681e13/0.250312809600e12 0.1508605165681e13/0.333750412800e12 -0.486270829441e12/0.834376032000e12 -0.221976356359e12/0.5006256192000e13;
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89 -0.13482796013041e14/0.834376032000e12 0.7260475818391e13/0.139062672000e12 -0.27224036353e11/0.406022400e9 0.1847477458951e13/0.41718801600e11 -0.848984558161e12/0.55625068800e11 0.247494925991e12/0.139062672000e12 0.165585445559e12/0.834376032000e12;
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90 0.344344095859e12/0.17565811200e11 -0.27224036353e11/0.406022400e9 0.2044938640393e13/0.22250027520e11 -0.1071086785417e13/0.16687520640e11 0.502199537033e12/0.22250027520e11 -0.143589154441e12/0.55625068800e11 -0.88181965559e11/0.333750412800e12;
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91 -0.3166261424681e13/0.250312809600e12 0.1847477458951e13/0.41718801600e11 -0.1071086785417e13/0.16687520640e11 0.628860435593e12/0.12515640480e11 -0.73736245829e11/0.3337504128e10 0.195760572271e12/0.41718801600e11 -0.81156046361e11/0.250312809600e12;
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92 0.1508605165681e13/0.333750412800e12 -0.848984558161e12/0.55625068800e11 0.502199537033e12/0.22250027520e11 -0.73736245829e11/0.3337504128e10 0.76725285869e11/0.4450005504e10 -0.3912429433e10/0.406022400e9 0.53227370659e11/0.17565811200e11;
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93 -0.486270829441e12/0.834376032000e12 0.247494925991e12/0.139062672000e12 -0.143589154441e12/0.55625068800e11 0.195760572271e12/0.41718801600e11 -0.3912429433e10/0.406022400e9 0.1699707221791e13/0.139062672000e12 -0.6959018412841e13/0.834376032000e12;
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94 -0.221976356359e12/0.5006256192000e13 0.165585445559e12/0.834376032000e12 -0.88181965559e11/0.333750412800e12 -0.81156046361e11/0.250312809600e12 0.53227370659e11/0.17565811200e11 -0.6959018412841e13/0.834376032000e12 0.3012195053939e13/0.263487168000e12;
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95 ];
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96
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97 M4(1:7,1:7) = M4_U;
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98
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99 M4(m-6:m,m-6:m) = flipud( fliplr( M4_U ) );
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100 M4 = M4/h^3;
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101
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102 D4 = HI*(M4-e_1*S3_1+e_m*S3_m + S_1'*S2_1-S_m'*S2_m);
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103 end