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comparison +sbp/+implementations/d1_noneq_minimal_6.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_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 % BP: Number of boundary points
10 % m: Number of nonequidistant spacings
11 % order: Accuracy of interior stencil
12 BP = 5;
13 m = 2;
14 order = 6;
15
16 %%%% Non-equidistant grid points %%%%%
17 x0 = 0.0000000000000e+00;
18 x1 = 4.0842950991998e-01;
19 x2 = 1.1968523189207e+00;
20 x3 = 2.1968523189207e+00;
21 x4 = 3.1968523189207e+00;
22 x5 = 4.1968523189207e+00;
23
24 xb = zeros(m+1,1);
25 for i = 0:m
26 xb(i+1) = eval(['x' num2str(i)]);
27 end
28 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
29
30 %%%% Compute h %%%%%%%%%%
31 h = L/(2*xb(end) + N-1-2*m);
32 %%%%%%%%%%%%%%%%%%%%%%%%%
33
34 %%%% Define grid %%%%%%%%
35 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
36 %%%%%%%%%%%%%%%%%%%%%%%%%
37
38 %%%% Norm matrix %%%%%%%%
39 P = zeros(BP,1);
40 %#ok<*NASGU>
41 P0 = 1.2740260779883e-01;
42 P1 = 6.1820981002054e-01;
43 P2 = 9.4308973897679e-01;
44 P3 = 1.0093019060199e+00;
45 P4 = 9.9884825610465e-01;
46
47 for i = 0:BP-1
48 P(i+1) = eval(['P' num2str(i)]);
49 end
50
51 H = ones(N,1);
52 H(1:BP) = P;
53 H(end-BP+1:end) = flip(P);
54 H = spdiags(h*H,0,N,N);
55 %%%%%%%%%%%%%%%%%%%%%%%%%
56
57 %%%% Q matrix %%%%%%%%%%%
58
59 % interior stencil
60 switch order
61 case 2
62 d = [-1/2,0,1/2];
63 case 4
64 d = [1/12,-2/3,0,2/3,-1/12];
65 case 6
66 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
67 case 8
68 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
69 case 10
70 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
71 case 12
72 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];
73 end
74 d = repmat(d,N,1);
75 Q = spdiags(d,-order/2:order/2,N,N);
76
77 % Boundaries
78 Q0_0 = -5.0000000000000e-01;
79 Q0_1 = 6.3217364546846e-01;
80 Q0_2 = -1.6411963429825e-01;
81 Q0_3 = 3.6495407984639e-02;
82 Q0_4 = -4.5494191548490e-03;
83 Q0_5 = 0.0000000000000e+00;
84 Q0_6 = 0.0000000000000e+00;
85 Q0_7 = 0.0000000000000e+00;
86 Q1_0 = -6.3217364546846e-01;
87 Q1_1 = 0.0000000000000e+00;
88 Q1_2 = 8.0515625504417e-01;
89 Q1_3 = -2.0755653563249e-01;
90 Q1_4 = 3.4573926056780e-02;
91 Q1_5 = 0.0000000000000e+00;
92 Q1_6 = 0.0000000000000e+00;
93 Q1_7 = 0.0000000000000e+00;
94 Q2_0 = 1.6411963429825e-01;
95 Q2_1 = -8.0515625504417e-01;
96 Q2_2 = 0.0000000000000e+00;
97 Q2_3 = 7.9402676057785e-01;
98 Q2_4 = -1.6965680649860e-01;
99 Q2_5 = 1.6666666666667e-02;
100 Q2_6 = 0.0000000000000e+00;
101 Q2_7 = 0.0000000000000e+00;
102 Q3_0 = -3.6495407984639e-02;
103 Q3_1 = 2.0755653563249e-01;
104 Q3_2 = -7.9402676057785e-01;
105 Q3_3 = 0.0000000000000e+00;
106 Q3_4 = 7.5629896626333e-01;
107 Q3_5 = -1.5000000000000e-01;
108 Q3_6 = 1.6666666666667e-02;
109 Q3_7 = 0.0000000000000e+00;
110 Q4_0 = 4.5494191548490e-03;
111 Q4_1 = -3.4573926056780e-02;
112 Q4_2 = 1.6965680649860e-01;
113 Q4_3 = -7.5629896626333e-01;
114 Q4_4 = 0.0000000000000e+00;
115 Q4_5 = 7.5000000000000e-01;
116 Q4_6 = -1.5000000000000e-01;
117 Q4_7 = 1.6666666666667e-02;
118 for i = 1:BP
119 for j = 1:BP
120 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
121 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
122 end
123 end
124 %%%%%%%%%%%%%%%%%%%%%%%%%%%
125
126 %%%% Difference operator %%
127 D1 = H\Q;
128 %%%%%%%%%%%%%%%%%%%%%%%%%%%