Mercurial > repos > public > sbplib
annotate +sbp/+implementations/d4_variable_8_min_boundary_points.m @ 319:fc91e3a2d44a feature/beams
Cleaned d4_variable_6_min_boundary_points.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Mon, 26 Sep 2016 08:52:03 +0200 |
| parents | 99005a80b4c2 |
| children | 3955ccffb7c8 |
| rev | line source |
|---|---|
| 312 | 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_8_min_boundary_points(m,h) |
| 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 3 %%% 8:te ordn. SBP Finita differens %%% | |
| 4 %%% operatorer med diagonal norm %%% | |
| 5 %%% %%% | |
| 6 %%% %%% | |
| 7 %%% H (Normen) %%% | |
| 8 %%% D1=H^(-1)Q (approx f?rsta derivatan) %%% | |
| 9 %%% D2 (approx andra derivatan) %%% | |
| 10 %%% D2=HI*(R+C*D*S %%% | |
| 11 %%% %%% | |
| 12 %%% R=-D1'*H*C*D1-RR %%% | |
| 13 %%% %%% | |
| 14 %%% RR ?r dissipation) %%% | |
| 15 %%% Dissipationen uppbyggd av D4: %%% | |
| 16 %%% DI=D4*B*H*D4 %%% | |
| 17 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 18 | |
| 19 H = diag(ones(m,1),0); | |
| 20 H(1:8,1:8) = diag([1498139/5080320, 1107307/725760, 20761/80640, 1304999/725760, 299527/725760, 103097/80640, 670091/725760, 5127739/5080320]); | |
| 21 H(m-7:m,m-7:m) = fliplr(flipud(diag([1498139/5080320, 1107307/725760, 20761/80640, 1304999/725760, 299527/725760, 103097/80640, 670091/725760, 5127739/5080320]))); | |
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22 |
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23 |
| 312 | 24 e_1 = zeros(m,1); |
| 25 e_1(1) = 1; | |
| 26 e_m = zeros(m,1); | |
| 27 e_m(m) = 1; | |
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28 |
| 312 | 29 S_U = [-0.137e3/0.60e2 5 -5 0.10e2/0.3e1 -0.5e1/0.4e1 0.1e1/0.5e1;]/h; |
| 30 S_1 = zeros(1,m); | |
| 31 S_1(1:6) = S_U; | |
| 32 S_m = zeros(1,m); | |
| 33 S_m(m-5:m) = fliplr(-S_U); | |
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34 |
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35 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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36 S2_1 = zeros(1,m); |
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37 S2_1(1:6) = S2_U; |
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38 S2_m = zeros(1,m); |
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39 S2_m(m-5:m) = fliplr(S2_U); |
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40 |
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41 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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42 S3_1 = zeros(1,m); |
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43 S3_1(1:6) = S3_U; |
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44 S3_m = zeros(1,m); |
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45 S3_m(m-5:m) = fliplr(-S3_U); |
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46 |
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47 |
| 312 | 48 H = h*H; |
| 49 HI = inv(H); | |
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50 |
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51 |
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52 |
| 312 | 53 % Fourth derivative, 1th order accurate at first 8 boundary points (still |
| 54 % yield 5th order convergence if stable: for example u_tt = -u_xxxx | |
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55 |
| 312 | 56 m5 = -0.41e2/0.7560e4; |
| 57 m4 = 0.1261e4/0.15120e5; | |
| 58 m3 = -0.541e3/0.840e3; | |
| 59 m2 = 0.4369e4/0.1260e4; | |
| 60 m1 = -0.1669e4/0.180e3; | |
| 61 m0 = 0.1529e4/0.120e3; | |
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62 |
| 312 | 63 M4=m5*(diag(ones(m-5,1),5)+diag(ones(m-5,1),-5))+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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64 |
| 312 | 65 %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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66 |
| 312 | 67 M4_U=[ |
| 68 0.151705142321e12/0.29189160000e11 -0.25643455801727e14/0.1634592960000e13 0.286417898677e12/0.15135120000e11 -0.4038072020317e13/0.326918592000e12 0.96455968907e11/0.20432412000e11 -0.151076916769e12/0.181621440000e12 0.14511526363e11/0.408648240000e12 -0.196663079e9/0.33359040000e11; | |
| 69 -0.25643455801727e14/0.1634592960000e13 0.735383382473e12/0.14594580000e11 -0.5035391734409e13/0.77837760000e11 0.20392440917e11/0.467026560e9 -0.109540902413e12/0.6671808000e10 0.2488686539e10/0.884520000e9 -0.2798067539e10/0.33359040000e11 0.6433463591e10/0.408648240000e12; | |
| 70 0.286417898677e12/0.15135120000e11 -0.5035391734409e13/0.77837760000e11 0.145019791981e12/0.1621620000e10 -0.333577111061e12/0.5189184000e10 0.18928722391e11/0.778377600e9 -0.93081704557e11/0.25945920000e11 -0.372660319e9/0.3243240000e10 0.2861399869e10/0.544864320000e12; | |
| 71 -0.4038072020317e13/0.326918592000e12 0.20392440917e11/0.467026560e9 -0.333577111061e12/0.5189184000e10 0.59368471277e11/0.1167566400e10 -0.201168708569e12/0.9340531200e10 0.1492314487e10/0.432432000e9 0.1911896257e10/0.9340531200e10 0.24383341e8/0.2554051500e10; | |
| 72 0.96455968907e11/0.20432412000e11 -0.109540902413e12/0.6671808000e10 0.18928722391e11/0.778377600e9 -0.201168708569e12/0.9340531200e10 0.1451230301e10/0.106142400e9 -0.103548247007e12/0.15567552000e11 0.27808437809e11/0.11675664000e11 -0.36870830713e11/0.65383718400e11; | |
| 73 -0.151076916769e12/0.181621440000e12 0.2488686539e10/0.884520000e9 -0.93081704557e11/0.25945920000e11 0.1492314487e10/0.432432000e9 -0.103548247007e12/0.15567552000e11 0.1229498243e10/0.115830000e9 -0.32222519717e11/0.3706560000e10 0.470092704233e12/0.136216080000e12; | |
| 74 0.14511526363e11/0.408648240000e12 -0.2798067539e10/0.33359040000e11 -0.372660319e9/0.3243240000e10 0.1911896257e10/0.9340531200e10 0.27808437809e11/0.11675664000e11 -0.32222519717e11/0.3706560000e10 0.11547819313e11/0.912161250e9 -0.15187033999199e14/0.1634592960000e13; | |
| 75 -0.196663079e9/0.33359040000e11 0.6433463591e10/0.408648240000e12 0.2861399869e10/0.544864320000e12 0.24383341e8/0.2554051500e10 -0.36870830713e11/0.65383718400e11 0.470092704233e12/0.136216080000e12 -0.15187033999199e14/0.1634592960000e13 0.33832994693e11/0.2653560000e10; | |
| 76 ]; | |
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77 |
| 312 | 78 M4(1:8,1:8) = M4_U; |
| 79 | |
| 80 M4(m-7:m,m-7:m) = flipud( fliplr( M4_U ) ); | |
| 81 M4 = M4/h^3; | |
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82 |
| 312 | 83 D4=HI*(M4-e_1*S3_1+e_m*S3_m + S_1'*S2_1-S_m'*S2_m); |
| 84 end |