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comparison +sbp/+implementations/d1_noneq_4.m @ 423:a2cb0d4f4a02 feature/grids

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Merge in default.
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 07 Feb 2017 15:47:51 +0100
parents f7ac3cd6eeaa
children 4cb627c7fb90
comparison
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218:da058ce66876 423:a2cb0d4f4a02
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 if(N<8)
10 error('Operator requires at least 8 grid points');
11 end
12
13 % BP: Number of boundary points
14 % m: Number of nonequidistant spacings
15 % order: Accuracy of interior stencil
16 BP = 4;
17 m = 2;
18 order = 4;
19
20 %%%% Non-equidistant grid points %%%%%
21 x0 = 0.0000000000000e+00;
22 x1 = 6.8764546205559e-01;
23 x2 = 1.8022115125776e+00;
24 x3 = 2.8022115125776e+00;
25 x4 = 3.8022115125776e+00;
26
27 xb = sparse(m+1,1);
28 for i = 0:m
29 xb(i+1) = eval(['x' num2str(i)]);
30 end
31 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
32
33 %%%% Compute h %%%%%%%%%%
34 h = L/(2*xb(end) + N-1-2*m);
35 %%%%%%%%%%%%%%%%%%%%%%%%%
36
37 %%%% Define grid %%%%%%%%
38 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
39 %%%%%%%%%%%%%%%%%%%%%%%%%
40
41 %%%% Norm matrix %%%%%%%%
42 P = sparse(BP,1);
43 %#ok<*NASGU>
44 P0 = 2.1259737557798e-01;
45 P1 = 1.0260290400758e+00;
46 P2 = 1.0775123588954e+00;
47 P3 = 9.8607273802835e-01;
48
49 for i = 0:BP-1
50 P(i+1) = eval(['P' num2str(i)]);
51 end
52
53 H = ones(N,1);
54 H(1:BP) = P;
55 H(end-BP+1:end) = flip(P);
56 H = spdiags(h*H,0,N,N);
57 %%%%%%%%%%%%%%%%%%%%%%%%%
58
59 %%%% Q matrix %%%%%%%%%%%
60
61 % interior stencil
62 switch order
63 case 2
64 d = [-1/2,0,1/2];
65 case 4
66 d = [1/12,-2/3,0,2/3,-1/12];
67 case 6
68 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
69 case 8
70 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
71 case 10
72 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
73 case 12
74 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];
75 end
76 d = repmat(d,N,1);
77 Q = spdiags(d,-order/2:order/2,N,N);
78
79 % Boundaries
80 Q0_0 = -5.0000000000000e-01;
81 Q0_1 = 6.5605279837843e-01;
82 Q0_2 = -1.9875859409017e-01;
83 Q0_3 = 4.2705795711740e-02;
84 Q0_4 = 0.0000000000000e+00;
85 Q0_5 = 0.0000000000000e+00;
86 Q1_0 = -6.5605279837843e-01;
87 Q1_1 = 0.0000000000000e+00;
88 Q1_2 = 8.1236966439895e-01;
89 Q1_3 = -1.5631686602052e-01;
90 Q1_4 = 0.0000000000000e+00;
91 Q1_5 = 0.0000000000000e+00;
92 Q2_0 = 1.9875859409017e-01;
93 Q2_1 = -8.1236966439895e-01;
94 Q2_2 = 0.0000000000000e+00;
95 Q2_3 = 6.9694440364211e-01;
96 Q2_4 = -8.3333333333333e-02;
97 Q2_5 = 0.0000000000000e+00;
98 Q3_0 = -4.2705795711740e-02;
99 Q3_1 = 1.5631686602052e-01;
100 Q3_2 = -6.9694440364211e-01;
101 Q3_3 = 0.0000000000000e+00;
102 Q3_4 = 6.6666666666667e-01;
103 Q3_5 = -8.3333333333333e-02;
104 for i = 1:BP
105 for j = 1:BP
106 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
107 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
108 end
109 end
110 %%%%%%%%%%%%%%%%%%%%%%%%%%%
111
112 %%%% Difference operator %%
113 D1 = H\Q;
114 %%%%%%%%%%%%%%%%%%%%%%%%%%%