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comparison +sbp/+implementations/d4_variable_6_min_boundary_points.m @ 319:fc91e3a2d44a feature/beams

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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 c0cbffcf6513
comparison
equal deleted inserted replaced
318:99005a80b4c2 319:fc91e3a2d44a
16 %%% DI=D4*B*H*D4 %%% 16 %%% DI=D4*B*H*D4 %%%
17 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 17 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
18 18
19 % H?r med 6 RP ist?llet f?r 8 f?r D4 operatorn, dock samma randderivator 19 % H?r med 6 RP ist?llet f?r 8 f?r D4 operatorn, dock samma randderivator
20 20
21 H = diag(ones(m,1),0); 21 BP = 6;
22 H(1:6,1:6) = diag([13649/43200,12013/8640,2711/4320,5359/4320,7877/8640, 43801/43200]); 22 if(m<2*BP)
23 H(m-5:m,m-5:m) = fliplr(flipud(diag([13649/43200,12013/8640, 2711/4320,5359/4320,7877/8640,43801/43200]))); 23 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
24 end
24 25
25 e_1 = zeros(m,1);e_1(1)=1; 26 % Norm
26 e_m = zeros(m,1);e_m(m)=1; 27 Hv = ones(m,1);
27 28 Hv(1:6) = [13649/43200,12013/8640,2711/4320,5359/4320,7877/8640, 43801/43200];
28 S_U = [-25/12, 4, -3, 4/3, -1/4]/h; 29 Hv(m-5:m) = rot90(Hv(1:6),2);
29 S_1 = zeros(1,m); 30 Hv = h*Hv;
30 S_1(1:5) = S_U; 31 H = spdiag(Hv, 0);
31 S_m = zeros(1,m); 32 HI = spdiag(1./Hv, 0);
32 S_m(m-4:m) = fliplr(-S_U);
33
34 S2_U = [0.35e2/0.12e2 -0.26e2/0.3e1 0.19e2/0.2e1 -0.14e2/0.3e1 0.11e2/0.12e2;]/h^2;
35 S2_1 = zeros(1,m);
36 S2_1(1:5) = S2_U;
37 S2_m = zeros(1,m);
38 S2_m(m-4:m) = fliplr(S2_U);
39
40 S3_U = [-0.5e1/0.2e1 9 -12 7 -0.3e1/0.2e1;]/h^3;
41 S3_1 = zeros(1,m);
42 S3_1(1:5) = S3_U;
43 S3_m = zeros(1,m);
44 S3_m(m-4:m) = fliplr(-S3_U);
45 33
46 34
47 x1=0.70127127127127; 35 % Boundary operators
36 e_l = sparse(m,1);
37 e_l(1) = 1;
38 e_r = rot90(e_l, 2);
48 39
40 d1_l = sparse(m,1);
41 d1_l(1:5) = [-25/12, 4, -3, 4/3, -1/4]/h;
42 d1_r = -rot90(d1_l);
49 43
50 D1=(1/60*diag(ones(m-3,1),3)-9/60*diag(ones(m-2,1),2)+45/60*diag(ones(m-1,1),1)-45/60*diag(ones(m-1,1),-1)+9/60*diag(ones(m-2,1),-2)-1/60*diag(ones(m-3,1),-3)); 44 d2_l = sparse(m,1);
45 d2_l(1:5) = [0.35e2/0.12e2 -0.26e2/0.3e1 0.19e2/0.2e1 -0.14e2/0.3e1 0.11e2/0.12e2;]/h^2;
46 d2_r = rot90(d2_l, 2);
51 47
52 D1(1:6,1:9) = [ 48 d3_l = sparse(m,1);
53 -21600/13649, 43200/13649*x1-7624/40947, -172800/13649*x1+ 715489/81894, 259200/13649*x1-187917/13649, -172800/13649* x1+735635/81894, 43200/13649*x1-89387/40947, 0, 0, 0; 49 d3_l(1:5) = [-0.5e1/0.2e1 9 -12 7 -0.3e1/0.2e1;]/h^3;
54 -8640/12013*x1+7624/180195, 0, 86400/12013*x1-57139/12013, -172800/12013*x1+745733/72078, 129600/12013*x1-91715/12013, -34560/12013*x1+240569/120130, 0, 0, 0; 50 d3_r = -rot90(d3_l, 2);
55 17280/2711*x1-715489/162660, -43200/2711*x1+57139/5422, 0, 86400/2711*x1-176839/8133, -86400/2711*x1+242111/10844, 25920/2711*x1-182261/27110, 0, 0, 0;
56 -25920/5359*x1+187917/53590, 86400/5359*x1-745733/64308, -86400/5359*x1+176839/16077, 0, 43200/5359*x1-165041/32154, -17280/5359*x1+710473/321540, 72/5359, 0, 0;
57 34560/7877*x1-147127/47262, -129600/7877*x1+91715/7877, 172800/7877*x1-242111/15754, -86400/7877*x1+165041/23631, 0, 8640/7877*x1, -1296/7877, 144/7877, 0;
58 -43200/43801*x1+89387/131403, 172800/43801*x1-240569/87602, -259200/43801*x1+182261/43801, 172800/43801*x1-710473/262806, -43200/43801*x1, 0, 32400/43801, -6480/43801, 720/43801
59 ];
60 D1(m-5:m,m-8:m) = flipud( fliplr(-D1(1:6,1:9)));
61 D1 = D1/h;
62 51
63
64 H = h*H;
65 HI = inv(H);
66
67
68 D2 = [];
69 52
70 % Fourth derivative, 1th order accurate at first 8 boundary points (still 53 % Fourth derivative, 1th order accurate at first 8 boundary points (still
71 % 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
72 55
73 m4 = 7/240; 56 stencil = [7/240, -2/5, 169/60, -122/15, 91/8, -122/15, 169/60, -2/5, 7/240];
74 m3 = -2/5; 57 diags = -4:4;
75 m2 = 169/60; 58 M4 = stripeMatrix(stencil, diags, m);
76 m1 = -122/15;
77 m0 = 91/8;
78
79 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);
80
81 %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));
82 59
83 M4_U=[ 60 M4_U=[
84 0.3504379e7/0.907200e6 -0.4613983e7/0.453600e6 0.4260437e7/0.453600e6 -0.418577e6/0.113400e6 0.524579e6/0.907200e6 0.535e3/0.18144e5; 61 0.3504379e7/0.907200e6 -0.4613983e7/0.453600e6 0.4260437e7/0.453600e6 -0.418577e6/0.113400e6 0.524579e6/0.907200e6 0.535e3/0.18144e5;
85 -0.4613983e7/0.453600e6 0.5186159e7/0.181440e6 -0.81121e5/0.2835e4 0.218845e6/0.18144e5 -0.159169e6/0.90720e5 -0.94669e5/0.907200e6; 62 -0.4613983e7/0.453600e6 0.5186159e7/0.181440e6 -0.81121e5/0.2835e4 0.218845e6/0.18144e5 -0.159169e6/0.90720e5 -0.94669e5/0.907200e6;
86 0.4260437e7/0.453600e6 -0.81121e5/0.2835e4 0.147695e6/0.4536e4 -0.384457e6/0.22680e5 0.339653e6/0.90720e5 -0.18233e5/0.113400e6; 63 0.4260437e7/0.453600e6 -0.81121e5/0.2835e4 0.147695e6/0.4536e4 -0.384457e6/0.22680e5 0.339653e6/0.90720e5 -0.18233e5/0.113400e6;
88 0.524579e6/0.907200e6 -0.159169e6/0.90720e5 0.339653e6/0.90720e5 -0.22762e5/0.2835e4 0.2006171e7/0.181440e6 -0.3647647e7/0.453600e6; 65 0.524579e6/0.907200e6 -0.159169e6/0.90720e5 0.339653e6/0.90720e5 -0.22762e5/0.2835e4 0.2006171e7/0.181440e6 -0.3647647e7/0.453600e6;
89 0.535e3/0.18144e5 -0.94669e5/0.907200e6 -0.18233e5/0.113400e6 0.1181753e7/0.453600e6 -0.3647647e7/0.453600e6 0.10305271e8/0.907200e6; 66 0.535e3/0.18144e5 -0.94669e5/0.907200e6 -0.18233e5/0.113400e6 0.1181753e7/0.453600e6 -0.3647647e7/0.453600e6 0.10305271e8/0.907200e6;
90 ]; 67 ];
91 68
92 M4(1:6,1:6) = M4_U; 69 M4(1:6,1:6) = M4_U;
70 M4(m-5:m,m-5:m) = rot90(M4_U, 2);
71 M4 = 1/h^3*M4;
93 72
94 M4(m-5:m,m-5:m) = flipud( fliplr( M4_U ) ); 73 D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r');
95 M4 = M4/h^3;
96
97 D4 = HI*(M4-e_1*S3_1+e_m*S3_m + S_1'*S2_1-S_m'*S2_m);
98
99 end 74 end