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comparison +sbp/+implementations/d1_noneq_10.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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equal deleted inserted replaced
260:b4116ce49ac4 261:6009f2712d13
1 function [D1,H,x,h] = d1_noneq_10(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 = 10;
13 m = 5;
14 order = 10;
15
16 %%%% Non-equidistant grid points %%%%%
17 x0 = 0.0000000000000e+00;
18 x1 = 3.5902433622052e-01;
19 x2 = 1.1436659188355e+00;
20 x3 = 2.2144895894456e+00;
21 x4 = 3.3682742337736e+00;
22 x5 = 4.4309689056870e+00;
23 x6 = 5.4309689056870e+00;
24 x7 = 6.4309689056870e+00;
25 x8 = 7.4309689056870e+00;
26 x9 = 8.4309689056870e+00;
27 x10 = 9.4309689056870e+00;
28
29 xb = zeros(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 = zeros(BP,1);
45 %#ok<*NASGU>
46 P0 = 1.0000000000000e-01;
47 P1 = 5.8980851260667e-01;
48 P2 = 9.5666820955973e-01;
49 P3 = 1.1500297411596e+00;
50 P4 = 1.1232986993248e+00;
51 P5 = 1.0123020150951e+00;
52 P6 = 9.9877122702527e-01;
53 P7 = 1.0000873322761e+00;
54 P8 = 1.0000045540888e+00;
55 P9 = 9.9999861455083e-01;
56
57 for i = 0:BP-1
58 P(i+1) = eval(['P' num2str(i)]);
59 end
60
61 H = ones(N,1);
62 H(1:BP) = P;
63 H(end-BP+1:end) = flip(P);
64 H = spdiags(h*H,0,N,N);
65 %%%%%%%%%%%%%%%%%%%%%%%%%
66
67 %%%% Q matrix %%%%%%%%%%%
68
69 % interior stencil
70 switch order
71 case 2
72 d = [-1/2,0,1/2];
73 case 4
74 d = [1/12,-2/3,0,2/3,-1/12];
75 case 6
76 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
77 case 8
78 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
79 case 10
80 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
81 case 12
82 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];
83 end
84 d = repmat(d,N,1);
85 Q = spdiags(d,-order/2:order/2,N,N);
86
87 % Boundaries
88 Q0_0 = -5.0000000000000e-01;
89 Q0_1 = 6.7548747038002e-01;
90 Q0_2 = -2.6691978151546e-01;
91 Q0_3 = 1.4438714982130e-01;
92 Q0_4 = -7.7273673750760e-02;
93 Q0_5 = 2.5570078343005e-02;
94 Q0_6 = 4.2808774693299e-03;
95 Q0_7 = -8.2902108933389e-03;
96 Q0_8 = 3.2031176427908e-03;
97 Q0_9 = -4.4502749689556e-04;
98 Q0_10 = 0.0000000000000e+00;
99 Q0_11 = 0.0000000000000e+00;
100 Q0_12 = 0.0000000000000e+00;
101 Q0_13 = 0.0000000000000e+00;
102 Q0_14 = 0.0000000000000e+00;
103 Q1_0 = -6.7548747038002e-01;
104 Q1_1 = 0.0000000000000e+00;
105 Q1_2 = 9.5146052715180e-01;
106 Q1_3 = -4.2442349882626e-01;
107 Q1_4 = 2.1538865145190e-01;
108 Q1_5 = -7.1939778160350e-02;
109 Q1_6 = -8.2539187832840e-03;
110 Q1_7 = 1.9930661669090e-02;
111 Q1_8 = -7.7433256989613e-03;
112 Q1_9 = 1.0681515760869e-03;
113 Q1_10 = 0.0000000000000e+00;
114 Q1_11 = 0.0000000000000e+00;
115 Q1_12 = 0.0000000000000e+00;
116 Q1_13 = 0.0000000000000e+00;
117 Q1_14 = 0.0000000000000e+00;
118 Q2_0 = 2.6691978151546e-01;
119 Q2_1 = -9.5146052715180e-01;
120 Q2_2 = 0.0000000000000e+00;
121 Q2_3 = 9.6073770842387e-01;
122 Q2_4 = -3.9378595264609e-01;
123 Q2_5 = 1.3302097358959e-01;
124 Q2_6 = 8.1200458151489e-05;
125 Q2_7 = -2.3849770528789e-02;
126 Q2_8 = 9.6600442856829e-03;
127 Q2_9 = -1.3234579460680e-03;
128 Q2_10 = 0.0000000000000e+00;
129 Q2_11 = 0.0000000000000e+00;
130 Q2_12 = 0.0000000000000e+00;
131 Q2_13 = 0.0000000000000e+00;
132 Q2_14 = 0.0000000000000e+00;
133 Q3_0 = -1.4438714982130e-01;
134 Q3_1 = 4.2442349882626e-01;
135 Q3_2 = -9.6073770842387e-01;
136 Q3_3 = 0.0000000000000e+00;
137 Q3_4 = 9.1551097634196e-01;
138 Q3_5 = -2.8541713079648e-01;
139 Q3_6 = 4.1398809121293e-02;
140 Q3_7 = 1.7256059167927e-02;
141 Q3_8 = -9.4349194803610e-03;
142 Q3_9 = 1.3875650645663e-03;
143 Q3_10 = 0.0000000000000e+00;
144 Q3_11 = 0.0000000000000e+00;
145 Q3_12 = 0.0000000000000e+00;
146 Q3_13 = 0.0000000000000e+00;
147 Q3_14 = 0.0000000000000e+00;
148 Q4_0 = 7.7273673750760e-02;
149 Q4_1 = -2.1538865145190e-01;
150 Q4_2 = 3.9378595264609e-01;
151 Q4_3 = -9.1551097634196e-01;
152 Q4_4 = 0.0000000000000e+00;
153 Q4_5 = 8.3519401865051e-01;
154 Q4_6 = -2.0586492924974e-01;
155 Q4_7 = 3.1230261235901e-02;
156 Q4_8 = -2.0969453466651e-04;
157 Q4_9 = -5.0965470499782e-04;
158 Q4_10 = 0.0000000000000e+00;
159 Q4_11 = 0.0000000000000e+00;
160 Q4_12 = 0.0000000000000e+00;
161 Q4_13 = 0.0000000000000e+00;
162 Q4_14 = 0.0000000000000e+00;
163 Q5_0 = -2.5570078343005e-02;
164 Q5_1 = 7.1939778160350e-02;
165 Q5_2 = -1.3302097358959e-01;
166 Q5_3 = 2.8541713079648e-01;
167 Q5_4 = -8.3519401865051e-01;
168 Q5_5 = 0.0000000000000e+00;
169 Q5_6 = 8.1046389580138e-01;
170 Q5_7 = -2.1879194972141e-01;
171 Q5_8 = 5.2977237804899e-02;
172 Q5_9 = -9.0146730522360e-03;
173 Q5_10 = 7.9365079365079e-04;
174 Q5_11 = 0.0000000000000e+00;
175 Q5_12 = 0.0000000000000e+00;
176 Q5_13 = 0.0000000000000e+00;
177 Q5_14 = 0.0000000000000e+00;
178 Q6_0 = -4.2808774693299e-03;
179 Q6_1 = 8.2539187832840e-03;
180 Q6_2 = -8.1200458151489e-05;
181 Q6_3 = -4.1398809121293e-02;
182 Q6_4 = 2.0586492924974e-01;
183 Q6_5 = -8.1046389580138e-01;
184 Q6_6 = 0.0000000000000e+00;
185 Q6_7 = 8.2787884456005e-01;
186 Q6_8 = -2.3582460382545e-01;
187 Q6_9 = 5.9178678209520e-02;
188 Q6_10 = -9.9206349206349e-03;
189 Q6_11 = 7.9365079365079e-04;
190 Q6_12 = 0.0000000000000e+00;
191 Q6_13 = 0.0000000000000e+00;
192 Q6_14 = 0.0000000000000e+00;
193 Q7_0 = 8.2902108933389e-03;
194 Q7_1 = -1.9930661669090e-02;
195 Q7_2 = 2.3849770528789e-02;
196 Q7_3 = -1.7256059167927e-02;
197 Q7_4 = -3.1230261235901e-02;
198 Q7_5 = 2.1879194972141e-01;
199 Q7_6 = -8.2787884456005e-01;
200 Q7_7 = 0.0000000000000e+00;
201 Q7_8 = 8.3301028859275e-01;
202 Q7_9 = -2.3804321850015e-01;
203 Q7_10 = 5.9523809523809e-02;
204 Q7_11 = -9.9206349206349e-03;
205 Q7_12 = 7.9365079365079e-04;
206 Q7_13 = 0.0000000000000e+00;
207 Q7_14 = 0.0000000000000e+00;
208 Q8_0 = -3.2031176427908e-03;
209 Q8_1 = 7.7433256989613e-03;
210 Q8_2 = -9.6600442856829e-03;
211 Q8_3 = 9.4349194803610e-03;
212 Q8_4 = 2.0969453466651e-04;
213 Q8_5 = -5.2977237804899e-02;
214 Q8_6 = 2.3582460382545e-01;
215 Q8_7 = -8.3301028859275e-01;
216 Q8_8 = 0.0000000000000e+00;
217 Q8_9 = 8.3333655748509e-01;
218 Q8_10 = -2.3809523809524e-01;
219 Q8_11 = 5.9523809523809e-02;
220 Q8_12 = -9.9206349206349e-03;
221 Q8_13 = 7.9365079365079e-04;
222 Q8_14 = 0.0000000000000e+00;
223 Q9_0 = 4.4502749689556e-04;
224 Q9_1 = -1.0681515760869e-03;
225 Q9_2 = 1.3234579460680e-03;
226 Q9_3 = -1.3875650645663e-03;
227 Q9_4 = 5.0965470499782e-04;
228 Q9_5 = 9.0146730522360e-03;
229 Q9_6 = -5.9178678209520e-02;
230 Q9_7 = 2.3804321850015e-01;
231 Q9_8 = -8.3333655748509e-01;
232 Q9_9 = 0.0000000000000e+00;
233 Q9_10 = 8.3333333333333e-01;
234 Q9_11 = -2.3809523809524e-01;
235 Q9_12 = 5.9523809523809e-02;
236 Q9_13 = -9.9206349206349e-03;
237 Q9_14 = 7.9365079365079e-04;
238 for i = 1:BP
239 for j = 1:BP
240 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
241 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
242 end
243 end
244 %%%%%%%%%%%%%%%%%%%%%%%%%%%
245
246 %%%% Difference operator %%
247 D1 = H\Q;
248 %%%%%%%%%%%%%%%%%%%%%%%%%%%