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comparison +sbp/+implementations/d1_noneq_minimal_6.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_minimal_6(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<10)
10 error('Operator requires at least 10 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 = 5;
17 m = 2;
18 order = 6;
19
20 %%%% Non-equidistant grid points %%%%%
21 x0 = 0.0000000000000e+00;
22 x1 = 4.0842950991998e-01;
23 x2 = 1.1968523189207e+00;
24 x3 = 2.1968523189207e+00;
25 x4 = 3.1968523189207e+00;
26 x5 = 4.1968523189207e+00;
27
28 xb = sparse(m+1,1);
29 for i = 0:m
30 xb(i+1) = eval(['x' num2str(i)]);
31 end
32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
33
34 %%%% Compute h %%%%%%%%%%
35 h = L/(2*xb(end) + N-1-2*m);
36 %%%%%%%%%%%%%%%%%%%%%%%%%
37
38 %%%% Define grid %%%%%%%%
39 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
40 %%%%%%%%%%%%%%%%%%%%%%%%%
41
42 %%%% Norm matrix %%%%%%%%
43 P = sparse(BP,1);
44 %#ok<*NASGU>
45 P0 = 1.2740260779883e-01;
46 P1 = 6.1820981002054e-01;
47 P2 = 9.4308973897679e-01;
48 P3 = 1.0093019060199e+00;
49 P4 = 9.9884825610465e-01;
50
51 for i = 0:BP-1
52 P(i+1) = eval(['P' num2str(i)]);
53 end
54
55 H = ones(N,1);
56 H(1:BP) = P;
57 H(end-BP+1:end) = flip(P);
58 H = spdiags(h*H,0,N,N);
59 %%%%%%%%%%%%%%%%%%%%%%%%%
60
61 %%%% Q matrix %%%%%%%%%%%
62
63 % interior stencil
64 switch order
65 case 2
66 d = [-1/2,0,1/2];
67 case 4
68 d = [1/12,-2/3,0,2/3,-1/12];
69 case 6
70 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
71 case 8
72 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
73 case 10
74 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
75 case 12
76 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];
77 end
78 d = repmat(d,N,1);
79 Q = spdiags(d,-order/2:order/2,N,N);
80
81 % Boundaries
82 Q0_0 = -5.0000000000000e-01;
83 Q0_1 = 6.3217364546846e-01;
84 Q0_2 = -1.6411963429825e-01;
85 Q0_3 = 3.6495407984639e-02;
86 Q0_4 = -4.5494191548490e-03;
87 Q0_5 = 0.0000000000000e+00;
88 Q0_6 = 0.0000000000000e+00;
89 Q0_7 = 0.0000000000000e+00;
90 Q1_0 = -6.3217364546846e-01;
91 Q1_1 = 0.0000000000000e+00;
92 Q1_2 = 8.0515625504417e-01;
93 Q1_3 = -2.0755653563249e-01;
94 Q1_4 = 3.4573926056780e-02;
95 Q1_5 = 0.0000000000000e+00;
96 Q1_6 = 0.0000000000000e+00;
97 Q1_7 = 0.0000000000000e+00;
98 Q2_0 = 1.6411963429825e-01;
99 Q2_1 = -8.0515625504417e-01;
100 Q2_2 = 0.0000000000000e+00;
101 Q2_3 = 7.9402676057785e-01;
102 Q2_4 = -1.6965680649860e-01;
103 Q2_5 = 1.6666666666667e-02;
104 Q2_6 = 0.0000000000000e+00;
105 Q2_7 = 0.0000000000000e+00;
106 Q3_0 = -3.6495407984639e-02;
107 Q3_1 = 2.0755653563249e-01;
108 Q3_2 = -7.9402676057785e-01;
109 Q3_3 = 0.0000000000000e+00;
110 Q3_4 = 7.5629896626333e-01;
111 Q3_5 = -1.5000000000000e-01;
112 Q3_6 = 1.6666666666667e-02;
113 Q3_7 = 0.0000000000000e+00;
114 Q4_0 = 4.5494191548490e-03;
115 Q4_1 = -3.4573926056780e-02;
116 Q4_2 = 1.6965680649860e-01;
117 Q4_3 = -7.5629896626333e-01;
118 Q4_4 = 0.0000000000000e+00;
119 Q4_5 = 7.5000000000000e-01;
120 Q4_6 = -1.5000000000000e-01;
121 Q4_7 = 1.6666666666667e-02;
122 for i = 1:BP
123 for j = 1:BP
124 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
125 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
126 end
127 end
128 %%%%%%%%%%%%%%%%%%%%%%%%%%%
129
130 %%%% Difference operator %%
131 D1 = H\Q;
132 %%%%%%%%%%%%%%%%%%%%%%%%%%%