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comparison +sbp/+implementations/d4_variable_8_higher_boundary_order.m @ 323:7579c2abbf9f feature/beams

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Cleaning d4_variable_8_higher_boundary_order.m
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 26 Sep 2016 09:19:08 +0200
parents 99005a80b4c2
children c0cbffcf6513
comparison
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322:def409c10800 323:7579c2abbf9f
15 %%% Dissipationen uppbyggd av D4: %%% 15 %%% Dissipationen uppbyggd av D4: %%%
16 %%% DI=D4*B*H*D4 %%% 16 %%% DI=D4*B*H*D4 %%%
17 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 17 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
18 %This is 3rd order accurate at the boundary. Not same norm as D1 operator 18 %This is 3rd order accurate at the boundary. Not same norm as D1 operator
19 19
20 H = diag(ones(m,1),0); 20 BP = 8;
21 H(1:8,1:8) = [ 21 if(m<2*BP)
22 0.7488203e7/0.25401600e8 0 0 0 0 0 0 0; 22 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
23 0 0.5539027e7/0.3628800e7 0 0 0 0 0 0; 23 end
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 24
32 H(m-7:m,m-7:m) = fliplr(flipud(H(1:8,1:8))); 25 % Norm
26 Hv = ones(m,1);
27 Hv(1:8) = [0.7488203e7/0.25401600e8, 0.5539027e7/0.3628800e7, 0.308923e6/0.1209600e7, 0.1307491e7/0.725760e6, 0.59407e5/0.145152e6, 0.1548947e7/0.1209600e7, 0.3347963e7/0.3628800e7, 0.25641187e8/0.25401600e8];
28 Hv(m-7:m) = rot90(Hv(1:8),2);
29 Hv = h*Hv;
30 H = spdiag(Hv, 0);
31 HI = spdiag(1./Hv, 0);
33 32
34 e_1 = zeros(m,1);
35 e_1(1) = 1;
36 e_m = zeros(m,1);
37 e_m(m) = 1;
38 33
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; 34 % Boundary operators
40 S_1 = zeros(1,m); 35 e_l = sparse(m,1);
41 S_1(1:7) = S_U; 36 e_l(1) = 1;
42 S_m = zeros(1,m); 37 e_r = rot90(e_l, 2);
43 S_m(m-6:m) = fliplr(-S_U);
44 38
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; 39 d1_l = sparse(m,1);
46 S2_1 = zeros(1,m); 40 d1_l(1:7) = [-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;
47 S2_1(1:7) = S2_U; 41 d1_r = -rot90(d1_l);
48 S2_m = zeros(1,m);
49 S2_m(m-6:m) = fliplr(S2_U);
50 42
51 S3_U = [-0.49e2/0.8e1 29 -0.461e3/0.8e1 62 -0.307e3/0.8e1 13 -0.15e2/0.8e1]/h^3; 43 d2_l = sparse(m,1);
52 S3_1 = zeros(1,m); 44 d2_l(1:7) = [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;
53 S3_1(1:7) = S3_U; 45 d2_r = rot90(d2_l, 2);
54 S3_m = zeros(1,m);
55 S3_m(m-6:m) = fliplr(-S3_U);
56 46
57 H = h*H; 47 d3_l = sparse(m,1);
58 HI = inv(H); 48 d3_l(1:7) = [-0.49e2/0.8e1 29 -0.461e3/0.8e1 62 -0.307e3/0.8e1 13 -0.15e2/0.8e1]/h^3;
49 d3_r = -rot90(d3_l, 2);
50
51
59 52
60 % Fourth derivative, 1th order accurate at first 8 boundary points (still 53 % Fourth derivative, 1th order accurate at first 8 boundary points (still
61 % yield 5th order convergence if stable: for example u_tt = -u_xxxx 54 % yield 5th order convergence if stable: for example u_tt = -u_xxxx
62 55
63 m5 = -0.41e2/0.7560e4; 56 stencil = [-0.41e2/0.7560e4, 0.1261e4/0.15120e5, -0.541e3/0.840e3, 0.4369e4/0.1260e4, -0.1669e4/0.180e3, 0.1529e4/0.120e3, -0.1669e4/0.180e3, 0.4369e4/0.1260e4, -0.541e3/0.840e3, 0.1261e4/0.15120e5,-0.41e2/0.7560e4];
64 m4 = 0.1261e4/0.15120e5; 57 diags = -5:5;
65 m3 = -0.541e3/0.840e3;
66 m2 = 0.4369e4/0.1260e4;
67 m1 = -0.1669e4/0.180e3;
68 m0 = 0.1529e4/0.120e3;
69
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);
71
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));
73 58
74 M4_U = [ 59 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; 60 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; 61 -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; 62 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;
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; 66 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; 67 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 ]; 68 ];
84 69
85 M4(1:8,1:8) = M4_U; 70 M4(1:8,1:8) = M4_U;
71 M4(m-7:m,m-7:m) = rot90(M4_U, 2);
72 M4 = 1/h^3*M4;
86 73
87 M4(m-7:m,m-7:m) = flipud( fliplr( M4_U ) ); 74 D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r');
88 M4 = M4/h^3;
89
90 D4 = HI*(M4-e_1*S3_1+e_m*S3_m + S_1'*S2_1-S_m'*S2_m);
91 end 75 end