Mercurial > repos > public > sbplib
annotate +sbp/+implementations/d4_variable_8_higher_boundary_order.m @ 318:99005a80b4c2 feature/beams
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 | 7579c2abbf9f |
| 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_higher_boundary_order(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 %This is 3rd order accurate at the boundary. Not same norm as D1 operator | |
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19 |
| 312 | 20 H = diag(ones(m,1),0); |
| 21 H(1:8,1:8) = [ | |
| 22 0.7488203e7/0.25401600e8 0 0 0 0 0 0 0; | |
| 23 0 0.5539027e7/0.3628800e7 0 0 0 0 0 0; | |
| 24 0 0 0.308923e6/0.1209600e7 0 0 0 0 0; | |
| 25 0 0 0 0.1307491e7/0.725760e6 0 0 0 0; | |
| 26 0 0 0 0 0.59407e5/0.145152e6 0 0 0; | |
| 27 0 0 0 0 0 0.1548947e7/0.1209600e7 0 0; | |
| 28 0 0 0 0 0 0 0.3347963e7/0.3628800e7 0; | |
| 29 0 0 0 0 0 0 0 0.25641187e8/0.25401600e8; | |
| 30 ]; | |
| 31 | |
| 32 H(m-7:m,m-7:m) = fliplr(flipud(H(1:8,1:8))); | |
| 33 | |
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34 e_1 = zeros(m,1); |
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35 e_1(1) = 1; |
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36 e_m = zeros(m,1); |
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37 e_m(m) = 1; |
| 312 | 38 |
| 39 S_U = [-0.49e2/0.20e2 6 -0.15e2/0.2e1 0.20e2/0.3e1 -0.15e2/0.4e1 0.6e1/0.5e1 -0.1e1/0.6e1]/h; | |
| 40 S_1 = zeros(1,m); | |
| 41 S_1(1:7) = S_U; | |
| 42 S_m = zeros(1,m); | |
| 43 S_m(m-6:m) = fliplr(-S_U); | |
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44 |
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45 S2_U = [0.203e3/0.45e2 -0.87e2/0.5e1 0.117e3/0.4e1 -0.254e3/0.9e1 0.33e2/0.2e1 -0.27e2/0.5e1 0.137e3/0.180e3]/h^2; |
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46 S2_1 = zeros(1,m); |
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47 S2_1(1:7) = S2_U; |
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48 S2_m = zeros(1,m); |
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49 S2_m(m-6:m) = fliplr(S2_U); |
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50 |
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51 S3_U = [-0.49e2/0.8e1 29 -0.461e3/0.8e1 62 -0.307e3/0.8e1 13 -0.15e2/0.8e1]/h^3; |
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52 S3_1 = zeros(1,m); |
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53 S3_1(1:7) = S3_U; |
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54 S3_m = zeros(1,m); |
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55 S3_m(m-6:m) = fliplr(-S3_U); |
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56 |
| 312 | 57 H = h*H; |
| 58 HI = inv(H); | |
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59 |
| 312 | 60 % Fourth derivative, 1th order accurate at first 8 boundary points (still |
| 61 % yield 5th order convergence if stable: for example u_tt = -u_xxxx | |
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62 |
| 312 | 63 m5 = -0.41e2/0.7560e4; |
| 64 m4 = 0.1261e4/0.15120e5; | |
| 65 m3 = -0.541e3/0.840e3; | |
| 66 m2 = 0.4369e4/0.1260e4; | |
| 67 m1 = -0.1669e4/0.180e3; | |
| 68 m0 = 0.1529e4/0.120e3; | |
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69 |
| 312 | 70 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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parents:
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71 |
| 312 | 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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parents:
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73 |
| 312 | 74 M4_U = [ |
| 75 0.1031569831e10/0.155675520e9 -0.32874237931e11/0.1452971520e10 0.3069551773e10/0.90810720e8 -0.658395212131e12/0.21794572800e11 0.31068454007e11/0.1816214400e10 -0.39244130657e11/0.7264857600e10 0.1857767503e10/0.2724321600e10 0.1009939e7/0.49420800e8; | |
| 76 -0.32874237931e11/0.1452971520e10 0.12799022387e11/0.155675520e9 -0.134456503627e12/0.1037836800e10 0.15366749479e11/0.129729600e9 -0.207640325549e12/0.3113510400e10 0.5396424073e10/0.259459200e9 -0.858079351e9/0.345945600e9 -0.19806607e8/0.170270100e9; | |
| 77 0.3069551773e10/0.90810720e8 -0.134456503627e12/0.1037836800e10 0.6202056779e10/0.28828800e8 -0.210970327081e12/0.1037836800e10 0.2127730129e10/0.18532800e8 -0.4048692749e10/0.115315200e9 0.1025943959e10/0.259459200e9 0.71054663e8/0.290594304e9; | |
| 78 -0.658395212131e12/0.21794572800e11 0.15366749479e11/0.129729600e9 -0.210970327081e12/0.1037836800e10 0.31025293213e11/0.155675520e9 -0.1147729001e10/0.9884160e7 0.1178067773e10/0.32432400e8 -0.13487255581e11/0.3113510400e10 -0.231082547e9/0.1816214400e10; | |
| 79 0.31068454007e11/0.1816214400e10 -0.207640325549e12/0.3113510400e10 0.2127730129e10/0.18532800e8 -0.1147729001e10/0.9884160e7 0.11524865123e11/0.155675520e9 -0.29754506009e11/0.1037836800e10 0.14231221e8/0.2316600e7 -0.15030629699e11/0.21794572800e11; | |
| 80 -0.39244130657e11/0.7264857600e10 0.5396424073e10/0.259459200e9 -0.4048692749e10/0.115315200e9 0.1178067773e10/0.32432400e8 -0.29754506009e11/0.1037836800e10 0.572247737e9/0.28828800e8 -0.11322059051e11/0.1037836800e10 0.3345834083e10/0.908107200e9; | |
| 81 0.1857767503e10/0.2724321600e10 -0.858079351e9/0.345945600e9 0.1025943959e10/0.259459200e9 -0.13487255581e11/0.3113510400e10 0.14231221e8/0.2316600e7 -0.11322059051e11/0.1037836800e10 0.10478882597e11/0.778377600e9 -0.68446325191e11/0.7264857600e10; | |
| 82 0.1009939e7/0.49420800e8 -0.19806607e8/0.170270100e9 0.71054663e8/0.290594304e9 -0.231082547e9/0.1816214400e10 -0.15030629699e11/0.21794572800e11 0.3345834083e10/0.908107200e9 -0.68446325191e11/0.7264857600e10 0.9944747557e10/0.778377600e9; | |
| 83 ]; | |
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parents:
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84 |
| 312 | 85 M4(1:8,1:8) = M4_U; |
| 86 | |
| 87 M4(m-7:m,m-7:m) = flipud( fliplr( M4_U ) ); | |
| 88 M4 = M4/h^3; | |
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89 |
| 312 | 90 D4 = HI*(M4-e_1*S3_1+e_m*S3_m + S_1'*S2_1-S_m'*S2_m); |
| 91 end |