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comparison +sbp/+implementations/d1_noneq_minimal_12.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
comparison
equal deleted inserted replaced
260:b4116ce49ac4 261:6009f2712d13
1 function [D1,H,x,h] = d1_noneq_minimal_12(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 = 4;
14 order = 12;
15
16 %%%% Non-equidistant grid points %%%%%
17 x0 = 0.0000000000000e+00;
18 x1 = 4.6552112904489e-01;
19 x2 = 1.4647984306493e+00;
20 x3 = 2.7620429464763e+00;
21 x4 = 4.0000000000000e+00;
22 x5 = 5.0000000000000e+00;
23 x6 = 6.0000000000000e+00;
24 x7 = 7.0000000000000e+00;
25 x8 = 8.0000000000000e+00;
26 x9 = 9.0000000000000e+00;
27 x10 = 1.0000000000000e+01;
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 = 1.3013597111750e-01;
47 P1 = 7.6146045079020e-01;
48 P2 = 1.1984222247012e+00;
49 P3 = 1.3340123109301e+00;
50 P4 = 1.0951811473364e+00;
51 P5 = 9.7569096377130e-01;
52 P6 = 1.0061945410831e+00;
53 P7 = 9.9874339446564e-01;
54 P8 = 1.0001702615573e+00;
55 P9 = 9.9998873424721e-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 = 6.7603132599815e-01;
90 Q0_2 = -2.6781065957921e-01;
91 Q0_3 = 1.4050310470012e-01;
92 Q0_4 = -5.4072653004710e-02;
93 Q0_5 = -1.1876984028213e-02;
94 Q0_6 = 2.6300694680362e-02;
95 Q0_7 = -9.8077210531438e-03;
96 Q0_8 = 4.2848959311712e-04;
97 Q0_9 = 3.0440269352791e-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 Q0_15 = 0.0000000000000e+00;
104 Q1_0 = -6.7603132599815e-01;
105 Q1_1 = 0.0000000000000e+00;
106 Q1_2 = 9.5204118058043e-01;
107 Q1_3 = -4.1306598236120e-01;
108 Q1_4 = 1.5442577883533e-01;
109 Q1_5 = 2.6535212157067e-02;
110 Q1_6 = -6.7869317213141e-02;
111 Q1_7 = 2.6431850942376e-02;
112 Q1_8 = -1.8383496124689e-03;
113 Q1_9 = -6.2904733024363e-04;
114 Q1_10 = 0.0000000000000e+00;
115 Q1_11 = 0.0000000000000e+00;
116 Q1_12 = 0.0000000000000e+00;
117 Q1_13 = 0.0000000000000e+00;
118 Q1_14 = 0.0000000000000e+00;
119 Q1_15 = 0.0000000000000e+00;
120 Q2_0 = 2.6781065957921e-01;
121 Q2_1 = -9.5204118058043e-01;
122 Q2_2 = 0.0000000000000e+00;
123 Q2_3 = 9.4424869445124e-01;
124 Q2_4 = -3.0369922793820e-01;
125 Q2_5 = -1.7036409572828e-02;
126 Q2_6 = 9.7546158402857e-02;
127 Q2_7 = -4.2534720340735e-02;
128 Q2_8 = 5.3471186513813e-03;
129 Q2_9 = 3.5890734751923e-04;
130 Q2_10 = 0.0000000000000e+00;
131 Q2_11 = 0.0000000000000e+00;
132 Q2_12 = 0.0000000000000e+00;
133 Q2_13 = 0.0000000000000e+00;
134 Q2_14 = 0.0000000000000e+00;
135 Q2_15 = 0.0000000000000e+00;
136 Q3_0 = -1.4050310470012e-01;
137 Q3_1 = 4.1306598236120e-01;
138 Q3_2 = -9.4424869445124e-01;
139 Q3_3 = 0.0000000000000e+00;
140 Q3_4 = 8.1369662782755e-01;
141 Q3_5 = -8.4027084126181e-02;
142 Q3_6 = -1.0721180825279e-01;
143 Q3_7 = 6.1098180874949e-02;
144 Q3_8 = -1.2618762739267e-02;
145 Q3_9 = 7.4866320589496e-04;
146 Q3_10 = 0.0000000000000e+00;
147 Q3_11 = 0.0000000000000e+00;
148 Q3_12 = 0.0000000000000e+00;
149 Q3_13 = 0.0000000000000e+00;
150 Q3_14 = 0.0000000000000e+00;
151 Q3_15 = 0.0000000000000e+00;
152 Q4_0 = 5.4072653004710e-02;
153 Q4_1 = -1.5442577883533e-01;
154 Q4_2 = 3.0369922793820e-01;
155 Q4_3 = -8.1369662782755e-01;
156 Q4_4 = 0.0000000000000e+00;
157 Q4_5 = 6.8140317057259e-01;
158 Q4_6 = -5.0090848997730e-02;
159 Q4_7 = -3.2156238350691e-02;
160 Q4_8 = 1.2270208460707e-02;
161 Q4_9 = -8.9539078453821e-04;
162 Q4_10 = -1.8037518037522e-04;
163 Q4_11 = 0.0000000000000e+00;
164 Q4_12 = 0.0000000000000e+00;
165 Q4_13 = 0.0000000000000e+00;
166 Q4_14 = 0.0000000000000e+00;
167 Q4_15 = 0.0000000000000e+00;
168 Q5_0 = 1.1876984028213e-02;
169 Q5_1 = -2.6535212157067e-02;
170 Q5_2 = 1.7036409572828e-02;
171 Q5_3 = 8.4027084126181e-02;
172 Q5_4 = -6.8140317057259e-01;
173 Q5_5 = 0.0000000000000e+00;
174 Q5_6 = 7.3535220394540e-01;
175 Q5_7 = -1.7565390898074e-01;
176 Q5_8 = 4.5853976429252e-02;
177 Q5_9 = -1.2971393808506e-02;
178 Q5_10 = 2.5974025974031e-03;
179 Q5_11 = -1.8037518037522e-04;
180 Q5_12 = 0.0000000000000e+00;
181 Q5_13 = 0.0000000000000e+00;
182 Q5_14 = 0.0000000000000e+00;
183 Q5_15 = 0.0000000000000e+00;
184 Q6_0 = -2.6300694680362e-02;
185 Q6_1 = 6.7869317213141e-02;
186 Q6_2 = -9.7546158402857e-02;
187 Q6_3 = 1.0721180825279e-01;
188 Q6_4 = 5.0090848997730e-02;
189 Q6_5 = -7.3535220394540e-01;
190 Q6_6 = 0.0000000000000e+00;
191 Q6_7 = 8.2185236816776e-01;
192 Q6_8 = -2.4842386107781e-01;
193 Q6_9 = 7.6038690915127e-02;
194 Q6_10 = -1.7857142857146e-02;
195 Q6_11 = 2.5974025974031e-03;
196 Q6_12 = -1.8037518037522e-04;
197 Q6_13 = 0.0000000000000e+00;
198 Q6_14 = 0.0000000000000e+00;
199 Q6_15 = 0.0000000000000e+00;
200 Q7_0 = 9.8077210531438e-03;
201 Q7_1 = -2.6431850942376e-02;
202 Q7_2 = 4.2534720340735e-02;
203 Q7_3 = -6.1098180874949e-02;
204 Q7_4 = 3.2156238350691e-02;
205 Q7_5 = 1.7565390898074e-01;
206 Q7_6 = -8.2185236816776e-01;
207 Q7_7 = 0.0000000000000e+00;
208 Q7_8 = 8.5207110387533e-01;
209 Q7_9 = -2.6676625654053e-01;
210 Q7_10 = 7.9365079365093e-02;
211 Q7_11 = -1.7857142857146e-02;
212 Q7_12 = 2.5974025974031e-03;
213 Q7_13 = -1.8037518037522e-04;
214 Q7_14 = 0.0000000000000e+00;
215 Q7_15 = 0.0000000000000e+00;
216 Q8_0 = -4.2848959311712e-04;
217 Q8_1 = 1.8383496124689e-03;
218 Q8_2 = -5.3471186513813e-03;
219 Q8_3 = 1.2618762739267e-02;
220 Q8_4 = -1.2270208460707e-02;
221 Q8_5 = -4.5853976429252e-02;
222 Q8_6 = 2.4842386107781e-01;
223 Q8_7 = -8.5207110387533e-01;
224 Q8_8 = 0.0000000000000e+00;
225 Q8_9 = 8.5702210251244e-01;
226 Q8_10 = -2.6785714285718e-01;
227 Q8_11 = 7.9365079365093e-02;
228 Q8_12 = -1.7857142857146e-02;
229 Q8_13 = 2.5974025974031e-03;
230 Q8_14 = -1.8037518037522e-04;
231 Q8_15 = 0.0000000000000e+00;
232 Q9_0 = -3.0440269352791e-04;
233 Q9_1 = 6.2904733024363e-04;
234 Q9_2 = -3.5890734751923e-04;
235 Q9_3 = -7.4866320589496e-04;
236 Q9_4 = 8.9539078453821e-04;
237 Q9_5 = 1.2971393808506e-02;
238 Q9_6 = -7.6038690915127e-02;
239 Q9_7 = 2.6676625654053e-01;
240 Q9_8 = -8.5702210251244e-01;
241 Q9_9 = 0.0000000000000e+00;
242 Q9_10 = 8.5714285714289e-01;
243 Q9_11 = -2.6785714285718e-01;
244 Q9_12 = 7.9365079365093e-02;
245 Q9_13 = -1.7857142857146e-02;
246 Q9_14 = 2.5974025974031e-03;
247 Q9_15 = -1.8037518037522e-04;
248 for i = 1:BP
249 for j = 1:BP
250 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
251 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
252 end
253 end
254 %%%%%%%%%%%%%%%%%%%%%%%%%%%
255
256 %%%% Difference operator %%
257 D1 = H\Q;
258 %%%%%%%%%%%%%%%%%%%%%%%%%%%