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comparison +sbp/+implementations/d1_noneq_4.m @ 261:6009f2712d13 operator_remake

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Moved and renamned all implementations.
author Martin Almquist <martin.almquist@it.uu.se>
date Thu, 08 Sep 2016 15:35:45 +0200
parents
children bfa130b7abf6
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260:b4116ce49ac4 261:6009f2712d13
1 function [D1,H,x,h] = d1_noneq_4(N,L)
2
3 % L: Domain length
4 % N: Number of grid points
5 if(nargin < 2)
6 L = 1;
7 end
8
9 % BP: Number of boundary points
10 % m: Number of nonequidistant spacings
11 % order: Accuracy of interior stencil
12 BP = 4;
13 m = 2;
14 order = 4;
15
16 %%%% Non-equidistant grid points %%%%%
17 x0 = 0.0000000000000e+00;
18 x1 = 6.8764546205559e-01;
19 x2 = 1.8022115125776e+00;
20 x3 = 2.8022115125776e+00;
21 x4 = 3.8022115125776e+00;
22
23 xb = zeros(m+1,1);
24 for i = 0:m
25 xb(i+1) = eval(['x' num2str(i)]);
26 end
27 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
28
29 %%%% Compute h %%%%%%%%%%
30 h = L/(2*xb(end) + N-1-2*m);
31 %%%%%%%%%%%%%%%%%%%%%%%%%
32
33 %%%% Define grid %%%%%%%%
34 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
35 %%%%%%%%%%%%%%%%%%%%%%%%%
36
37 %%%% Norm matrix %%%%%%%%
38 P = zeros(BP,1);
39 %#ok<*NASGU>
40 P0 = 2.1259737557798e-01;
41 P1 = 1.0260290400758e+00;
42 P2 = 1.0775123588954e+00;
43 P3 = 9.8607273802835e-01;
44
45 for i = 0:BP-1
46 P(i+1) = eval(['P' num2str(i)]);
47 end
48
49 H = ones(N,1);
50 H(1:BP) = P;
51 H(end-BP+1:end) = flip(P);
52 H = spdiags(h*H,0,N,N);
53 %%%%%%%%%%%%%%%%%%%%%%%%%
54
55 %%%% Q matrix %%%%%%%%%%%
56
57 % interior stencil
58 switch order
59 case 2
60 d = [-1/2,0,1/2];
61 case 4
62 d = [1/12,-2/3,0,2/3,-1/12];
63 case 6
64 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
65 case 8
66 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
67 case 10
68 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
69 case 12
70 d = [1/5544,-1/385,1/56,-5/63,15/56,-6/7,0,6/7,-15/56,5/63,-1/56,1/385,-1/5544];
71 end
72 d = repmat(d,N,1);
73 Q = spdiags(d,-order/2:order/2,N,N);
74
75 % Boundaries
76 Q0_0 = -5.0000000000000e-01;
77 Q0_1 = 6.5605279837843e-01;
78 Q0_2 = -1.9875859409017e-01;
79 Q0_3 = 4.2705795711740e-02;
80 Q0_4 = 0.0000000000000e+00;
81 Q0_5 = 0.0000000000000e+00;
82 Q1_0 = -6.5605279837843e-01;
83 Q1_1 = 0.0000000000000e+00;
84 Q1_2 = 8.1236966439895e-01;
85 Q1_3 = -1.5631686602052e-01;
86 Q1_4 = 0.0000000000000e+00;
87 Q1_5 = 0.0000000000000e+00;
88 Q2_0 = 1.9875859409017e-01;
89 Q2_1 = -8.1236966439895e-01;
90 Q2_2 = 0.0000000000000e+00;
91 Q2_3 = 6.9694440364211e-01;
92 Q2_4 = -8.3333333333333e-02;
93 Q2_5 = 0.0000000000000e+00;
94 Q3_0 = -4.2705795711740e-02;
95 Q3_1 = 1.5631686602052e-01;
96 Q3_2 = -6.9694440364211e-01;
97 Q3_3 = 0.0000000000000e+00;
98 Q3_4 = 6.6666666666667e-01;
99 Q3_5 = -8.3333333333333e-02;
100 for i = 1:BP
101 for j = 1:BP
102 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
103 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
104 end
105 end
106 %%%%%%%%%%%%%%%%%%%%%%%%%%%
107
108 %%%% Difference operator %%
109 D1 = H\Q;
110 %%%%%%%%%%%%%%%%%%%%%%%%%%%