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comparison +sbp/+implementations/d1_noneq_6.m @ 284:dae8c3a56f5e

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Merged in operator_remake (pull request #2) Operator remake
author Jonatan Werpers <jonatan.werpers@it.uu.se>
date Mon, 12 Sep 2016 12:53:02 +0200
parents f7ac3cd6eeaa
children 4cb627c7fb90
comparison
equal deleted inserted replaced
282:18c023aaf3f7 284:dae8c3a56f5e
1 function [D1,H,x,h] = d1_noneq_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<12)
10 error('Operator requires at least 12 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 = 6;
17 m = 3;
18 order = 6;
19
20 %%%% Non-equidistant grid points %%%%%
21 x0 = 0.0000000000000e+00;
22 x1 = 4.4090263368623e-01;
23 x2 = 1.2855984345073e+00;
24 x3 = 2.2638953951239e+00;
25 x4 = 3.2638953951239e+00;
26 x5 = 4.2638953951239e+00;
27 x6 = 5.2638953951239e+00;
28
29 xb = sparse(m+1,1);
30 for i = 0:m
31 xb(i+1) = eval(['x' num2str(i)]);
32 end
33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
34
35 %%%% Compute h %%%%%%%%%%
36 h = L/(2*xb(end) + N-1-2*m);
37 %%%%%%%%%%%%%%%%%%%%%%%%%
38
39 %%%% Define grid %%%%%%%%
40 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
41 %%%%%%%%%%%%%%%%%%%%%%%%%
42
43 %%%% Norm matrix %%%%%%%%
44 P = sparse(BP,1);
45 %#ok<*NASGU>
46 P0 = 1.3030223027124e-01;
47 P1 = 6.8851501587715e-01;
48 P2 = 9.5166202564389e-01;
49 P3 = 9.9103890475697e-01;
50 P4 = 1.0028757074552e+00;
51 P5 = 9.9950151111941e-01;
52
53 for i = 0:BP-1
54 P(i+1) = eval(['P' num2str(i)]);
55 end
56
57 H = ones(N,1);
58 H(1:BP) = P;
59 H(end-BP+1:end) = flip(P);
60 H = spdiags(h*H,0,N,N);
61 %%%%%%%%%%%%%%%%%%%%%%%%%
62
63 %%%% Q matrix %%%%%%%%%%%
64
65 % interior stencil
66 switch order
67 case 2
68 d = [-1/2,0,1/2];
69 case 4
70 d = [1/12,-2/3,0,2/3,-1/12];
71 case 6
72 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
73 case 8
74 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
75 case 10
76 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
77 case 12
78 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];
79 end
80 d = repmat(d,N,1);
81 Q = spdiags(d,-order/2:order/2,N,N);
82
83 % Boundaries
84 Q0_0 = -5.0000000000000e-01;
85 Q0_1 = 6.6042071945824e-01;
86 Q0_2 = -2.2104152954203e-01;
87 Q0_3 = 7.6243679810093e-02;
88 Q0_4 = -1.7298206716724e-02;
89 Q0_5 = 1.6753369904210e-03;
90 Q0_6 = 0.0000000000000e+00;
91 Q0_7 = 0.0000000000000e+00;
92 Q0_8 = 0.0000000000000e+00;
93 Q1_0 = -6.6042071945824e-01;
94 Q1_1 = 0.0000000000000e+00;
95 Q1_2 = 8.7352798702787e-01;
96 Q1_3 = -2.6581719253084e-01;
97 Q1_4 = 5.7458484948314e-02;
98 Q1_5 = -4.7485599871040e-03;
99 Q1_6 = 0.0000000000000e+00;
100 Q1_7 = 0.0000000000000e+00;
101 Q1_8 = 0.0000000000000e+00;
102 Q2_0 = 2.2104152954203e-01;
103 Q2_1 = -8.7352798702787e-01;
104 Q2_2 = 0.0000000000000e+00;
105 Q2_3 = 8.1707122038457e-01;
106 Q2_4 = -1.8881125503769e-01;
107 Q2_5 = 2.4226492138960e-02;
108 Q2_6 = 0.0000000000000e+00;
109 Q2_7 = 0.0000000000000e+00;
110 Q2_8 = 0.0000000000000e+00;
111 Q3_0 = -7.6243679810093e-02;
112 Q3_1 = 2.6581719253084e-01;
113 Q3_2 = -8.1707122038457e-01;
114 Q3_3 = 0.0000000000000e+00;
115 Q3_4 = 7.6798636652679e-01;
116 Q3_5 = -1.5715532552963e-01;
117 Q3_6 = 1.6666666666667e-02;
118 Q3_7 = 0.0000000000000e+00;
119 Q3_8 = 0.0000000000000e+00;
120 Q4_0 = 1.7298206716724e-02;
121 Q4_1 = -5.7458484948314e-02;
122 Q4_2 = 1.8881125503769e-01;
123 Q4_3 = -7.6798636652679e-01;
124 Q4_4 = 0.0000000000000e+00;
125 Q4_5 = 7.5266872305402e-01;
126 Q4_6 = -1.5000000000000e-01;
127 Q4_7 = 1.6666666666667e-02;
128 Q4_8 = 0.0000000000000e+00;
129 Q5_0 = -1.6753369904210e-03;
130 Q5_1 = 4.7485599871040e-03;
131 Q5_2 = -2.4226492138960e-02;
132 Q5_3 = 1.5715532552963e-01;
133 Q5_4 = -7.5266872305402e-01;
134 Q5_5 = 0.0000000000000e+00;
135 Q5_6 = 7.5000000000000e-01;
136 Q5_7 = -1.5000000000000e-01;
137 Q5_8 = 1.6666666666667e-02;
138 for i = 1:BP
139 for j = 1:BP
140 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
141 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
142 end
143 end
144 %%%%%%%%%%%%%%%%%%%%%%%%%%%
145
146 %%%% Difference operator %%
147 D1 = H\Q;
148 %%%%%%%%%%%%%%%%%%%%%%%%%%%