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comparison +sbp/+implementations/d4_variable_8_min_boundary_points.m @ 320:3955ccffb7c8 feature/beams

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Cleaned d4_variable_8_min_boundary_points
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 26 Sep 2016 08:57:25 +0200
parents 99005a80b4c2
children c0cbffcf6513
comparison
equal deleted inserted replaced
319:fc91e3a2d44a 320:3955ccffb7c8
14 %%% RR ?r dissipation) %%% 14 %%% RR ?r dissipation) %%%
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 18
19 H = diag(ones(m,1),0); 19 BP = 8;
20 H(1:8,1:8) = diag([1498139/5080320, 1107307/725760, 20761/80640, 1304999/725760, 299527/725760, 103097/80640, 670091/725760, 5127739/5080320]); 20 if(m<2*BP)
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]))); 21 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
22 end
23
24 % Norm
25 Hv = ones(m,1);
26 Hv(1:8) = [1498139/5080320, 1107307/725760, 20761/80640, 1304999/725760, 299527/725760, 103097/80640, 670091/725760, 5127739/5080320];
27 Hv(m-7:m) = rot90(Hv(1:8),2);
28 Hv = h*Hv;
29 H = spdiag(Hv, 0);
30 HI = spdiag(1./Hv, 0);
22 31
23 32
24 e_1 = zeros(m,1); 33 % Boundary operators
25 e_1(1) = 1; 34 e_l = sparse(m,1);
26 e_m = zeros(m,1); 35 e_l(1) = 1;
27 e_m(m) = 1; 36 e_r = rot90(e_l, 2);
28 37
29 S_U = [-0.137e3/0.60e2 5 -5 0.10e2/0.3e1 -0.5e1/0.4e1 0.1e1/0.5e1;]/h; 38 d1_l = sparse(m,1);
30 S_1 = zeros(1,m); 39 d1_l(1:6) = [-0.137e3/0.60e2 5 -5 0.10e2/0.3e1 -0.5e1/0.4e1 0.1e1/0.5e1;]/h;
31 S_1(1:6) = S_U; 40 d1_r = -rot90(d1_l);
32 S_m = zeros(1,m);
33 S_m(m-5:m) = fliplr(-S_U);
34 41
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; 42 d2_l = sparse(m,1);
36 S2_1 = zeros(1,m); 43 d2_l(1:6) = [0.15e2/0.4e1 -0.77e2/0.6e1 0.107e3/0.6e1 -13 0.61e2/0.12e2 -0.5e1/0.6e1;]/h^2;
37 S2_1(1:6) = S2_U; 44 d2_r = rot90(d2_l, 2);
38 S2_m = zeros(1,m);
39 S2_m(m-5:m) = fliplr(S2_U);
40 45
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; 46 d3_l = sparse(m,1);
42 S3_1 = zeros(1,m); 47 d3_l(1:6) = [-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;
43 S3_1(1:6) = S3_U; 48 d3_r = -rot90(d3_l, 2);
44 S3_m = zeros(1,m);
45 S3_m(m-5:m) = fliplr(-S3_U);
46 49
47 50
48 H = h*H; 51 % Fourth derivative, 1th order accurate at first 8 boundary points
49 HI = inv(H);
50 52
53 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];
54 diags = -5:5;
55 M4 = stripeMatrix(stencil, diags, m);
51 56
52 57 M4_U = [
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
55
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;
62
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);
64
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));
66
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; 58 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; 59 -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; 60 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; 61 -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; 62 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;
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; 64 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; 65 -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 ]; 66 ];
77 67
78 M4(1:8,1:8) = M4_U; 68 M4(1:8,1:8) = M4_U;
69 M4(m-7:m,m-7:m) = rot90(M4_U, 2);
70 M4 = 1/h^3*M4;
79 71
80 M4(m-7:m,m-7:m) = flipud( fliplr( M4_U ) ); 72 D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r');
81 M4 = M4/h^3;
82
83 D4=HI*(M4-e_1*S3_1+e_m*S3_m + S_1'*S2_1-S_m'*S2_m);
84 end 73 end