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comparison +sbp/+implementations/d1_noneq_minimal_8.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_8(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 = 6;
13 m = 2;
14 order = 8;
15
16 %%%% Non-equidistant grid points %%%%%
17 x0 = 0.0000000000000e+00;
18 x1 = 4.9439570885261e-01;
19 x2 = 1.4051531374839e+00;
20 x3 = 2.4051531374839e+00;
21 x4 = 3.4051531374839e+00;
22 x5 = 4.4051531374839e+00;
23 x6 = 5.4051531374839e+00;
24
25 xb = zeros(m+1,1);
26 for i = 0:m
27 xb(i+1) = eval(['x' num2str(i)]);
28 end
29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
30
31 %%%% Compute h %%%%%%%%%%
32 h = L/(2*xb(end) + N-1-2*m);
33 %%%%%%%%%%%%%%%%%%%%%%%%%
34
35 %%%% Define grid %%%%%%%%
36 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
37 %%%%%%%%%%%%%%%%%%%%%%%%%
38
39 %%%% Norm matrix %%%%%%%%
40 P = zeros(BP,1);
41 %#ok<*NASGU>
42 P0 = 1.4523997892351e-01;
43 P1 = 7.6864793350174e-01;
44 P2 = 9.9116487068535e-01;
45 P3 = 9.9992473335107e-01;
46 P4 = 1.0002097054636e+00;
47 P5 = 9.9996591555866e-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 = 6.6697342753834e-01;
82 Q0_2 = -2.2919342278749e-01;
83 Q0_3 = 7.4283116457276e-02;
84 Q0_4 = -1.2020661178873e-02;
85 Q0_5 = -4.2460029252999e-05;
86 Q0_6 = 0.0000000000000e+00;
87 Q0_7 = 0.0000000000000e+00;
88 Q0_8 = 0.0000000000000e+00;
89 Q0_9 = 0.0000000000000e+00;
90 Q1_0 = -6.6697342753834e-01;
91 Q1_1 = 0.0000000000000e+00;
92 Q1_2 = 8.8241196934163e-01;
93 Q1_3 = -2.6653314104602e-01;
94 Q1_4 = 5.5302527504316e-02;
95 Q1_5 = -4.2079282615860e-03;
96 Q1_6 = 0.0000000000000e+00;
97 Q1_7 = 0.0000000000000e+00;
98 Q1_8 = 0.0000000000000e+00;
99 Q1_9 = 0.0000000000000e+00;
100 Q2_0 = 2.2919342278749e-01;
101 Q2_1 = -8.8241196934163e-01;
102 Q2_2 = 0.0000000000000e+00;
103 Q2_3 = 8.2904844081126e-01;
104 Q2_4 = -2.1156614214635e-01;
105 Q2_5 = 3.9307676460659e-02;
106 Q2_6 = -3.5714285714286e-03;
107 Q2_7 = 0.0000000000000e+00;
108 Q2_8 = 0.0000000000000e+00;
109 Q2_9 = 0.0000000000000e+00;
110 Q3_0 = -7.4283116457276e-02;
111 Q3_1 = 2.6653314104602e-01;
112 Q3_2 = -8.2904844081126e-01;
113 Q3_3 = 0.0000000000000e+00;
114 Q3_4 = 8.0305501223679e-01;
115 Q3_5 = -2.0078040553808e-01;
116 Q3_6 = 3.8095238095238e-02;
117 Q3_7 = -3.5714285714286e-03;
118 Q3_8 = 0.0000000000000e+00;
119 Q3_9 = 0.0000000000000e+00;
120 Q4_0 = 1.2020661178873e-02;
121 Q4_1 = -5.5302527504316e-02;
122 Q4_2 = 2.1156614214635e-01;
123 Q4_3 = -8.0305501223679e-01;
124 Q4_4 = 0.0000000000000e+00;
125 Q4_5 = 8.0024692689207e-01;
126 Q4_6 = -2.0000000000000e-01;
127 Q4_7 = 3.8095238095238e-02;
128 Q4_8 = -3.5714285714286e-03;
129 Q4_9 = 0.0000000000000e+00;
130 Q5_0 = 4.2460029252999e-05;
131 Q5_1 = 4.2079282615860e-03;
132 Q5_2 = -3.9307676460659e-02;
133 Q5_3 = 2.0078040553808e-01;
134 Q5_4 = -8.0024692689207e-01;
135 Q5_5 = 0.0000000000000e+00;
136 Q5_6 = 8.0000000000000e-01;
137 Q5_7 = -2.0000000000000e-01;
138 Q5_8 = 3.8095238095238e-02;
139 Q5_9 = -3.5714285714286e-03;
140 for i = 1:BP
141 for j = 1:BP
142 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
143 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
144 end
145 end
146 %%%%%%%%%%%%%%%%%%%%%%%%%%%
147
148 %%%% Difference operator %%
149 D1 = H\Q;
150 %%%%%%%%%%%%%%%%%%%%%%%%%%%