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comparison +sbp/D1_minimal_10th_8BP_3shifts.m @ 252:07fa0d6a05bb operator_remake

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Renamned class files and added nonequidistant operators.
author Martin Almquist <martin.almquist@it.uu.se>
date Wed, 07 Sep 2016 13:40:41 +0200
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251:6a5e94bb5e13 252:07fa0d6a05bb
1 function [D1,H,x,h] = D1_minimal_10th_8BP_3shifts(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 = 8;
13 m = 3;
14 order = 10;
15
16 %%%% Non-equidistant grid points %%%%%
17 x0 = 0.0000000000000e+00;
18 x1 = 5.8556160757529e-01;
19 x2 = 1.7473267488572e+00;
20 x3 = 3.0000000000000e+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
27 xb = zeros(m+1,1);
28 for i = 0:m
29 xb(i+1) = eval(['x' num2str(i)]);
30 end
31 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
32
33 %%%% Compute h %%%%%%%%%%
34 h = L/(2*xb(end) + N-1-2*m);
35 %%%%%%%%%%%%%%%%%%%%%%%%%
36
37 %%%% Define grid %%%%%%%%
38 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
39 %%%%%%%%%%%%%%%%%%%%%%%%%
40
41 %%%% Norm matrix %%%%%%%%
42 P = zeros(BP,1);
43 %#ok<*NASGU>
44 P0 = 1.6717213975289e-01;
45 P1 = 9.3675739171278e-01;
46 P2 = 1.3035532379753e+00;
47 P3 = 1.1188461804303e+00;
48 P4 = 9.6664345922660e-01;
49 P5 = 1.0083235564392e+00;
50 P6 = 9.9858767377362e-01;
51 P7 = 1.0001163606893e+00;
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 = 6.7349296966214e-01;
86 Q0_2 = -2.5186401896559e-01;
87 Q0_3 = 8.3431385420901e-02;
88 Q0_4 = 2.5480326895984e-02;
89 Q0_5 = -4.5992420658252e-02;
90 Q0_6 = 1.7526412909003e-02;
91 Q0_7 = -2.0746552641799e-03;
92 Q0_8 = 0.0000000000000e+00;
93 Q0_9 = 0.0000000000000e+00;
94 Q0_10 = 0.0000000000000e+00;
95 Q0_11 = 0.0000000000000e+00;
96 Q0_12 = 0.0000000000000e+00;
97 Q1_0 = -6.7349296966214e-01;
98 Q1_1 = 0.0000000000000e+00;
99 Q1_2 = 9.1982892384044e-01;
100 Q1_3 = -2.7262271754043e-01;
101 Q1_4 = -5.0992113348238e-02;
102 Q1_5 = 1.1814647281129e-01;
103 Q1_6 = -4.6693123378079e-02;
104 Q1_7 = 5.8255272771571e-03;
105 Q1_8 = 0.0000000000000e+00;
106 Q1_9 = 0.0000000000000e+00;
107 Q1_10 = 0.0000000000000e+00;
108 Q1_11 = 0.0000000000000e+00;
109 Q1_12 = 0.0000000000000e+00;
110 Q2_0 = 2.5186401896559e-01;
111 Q2_1 = -9.1982892384044e-01;
112 Q2_2 = 0.0000000000000e+00;
113 Q2_3 = 7.8566746772741e-01;
114 Q2_4 = -2.4097806629929e-02;
115 Q2_5 = -1.5312168858669e-01;
116 Q2_6 = 6.9451518963875e-02;
117 Q2_7 = -9.9345865998262e-03;
118 Q2_8 = 0.0000000000000e+00;
119 Q2_9 = 0.0000000000000e+00;
120 Q2_10 = 0.0000000000000e+00;
121 Q2_11 = 0.0000000000000e+00;
122 Q2_12 = 0.0000000000000e+00;
123 Q3_0 = -8.3431385420901e-02;
124 Q3_1 = 2.7262271754043e-01;
125 Q3_2 = -7.8566746772741e-01;
126 Q3_3 = 0.0000000000000e+00;
127 Q3_4 = 6.2047871210535e-01;
128 Q3_5 = 1.4776775176509e-02;
129 Q3_6 = -4.6889652372990e-02;
130 Q3_7 = 7.3166499053672e-03;
131 Q3_8 = 7.9365079365079e-04;
132 Q3_9 = 0.0000000000000e+00;
133 Q3_10 = 0.0000000000000e+00;
134 Q3_11 = 0.0000000000000e+00;
135 Q3_12 = 0.0000000000000e+00;
136 Q4_0 = -2.5480326895984e-02;
137 Q4_1 = 5.0992113348238e-02;
138 Q4_2 = 2.4097806629929e-02;
139 Q4_3 = -6.2047871210535e-01;
140 Q4_4 = 0.0000000000000e+00;
141 Q4_5 = 6.9425006383507e-01;
142 Q4_6 = -1.5686345740485e-01;
143 Q4_7 = 4.2609496719925e-02;
144 Q4_8 = -9.9206349206349e-03;
145 Q4_9 = 7.9365079365079e-04;
146 Q4_10 = 0.0000000000000e+00;
147 Q4_11 = 0.0000000000000e+00;
148 Q4_12 = 0.0000000000000e+00;
149 Q5_0 = 4.5992420658252e-02;
150 Q5_1 = -1.1814647281129e-01;
151 Q5_2 = 1.5312168858669e-01;
152 Q5_3 = -1.4776775176509e-02;
153 Q5_4 = -6.9425006383507e-01;
154 Q5_5 = 0.0000000000000e+00;
155 Q5_6 = 8.0719535654891e-01;
156 Q5_7 = -2.2953297936781e-01;
157 Q5_8 = 5.9523809523809e-02;
158 Q5_9 = -9.9206349206349e-03;
159 Q5_10 = 7.9365079365079e-04;
160 Q5_11 = 0.0000000000000e+00;
161 Q5_12 = 0.0000000000000e+00;
162 Q6_0 = -1.7526412909003e-02;
163 Q6_1 = 4.6693123378079e-02;
164 Q6_2 = -6.9451518963875e-02;
165 Q6_3 = 4.6889652372990e-02;
166 Q6_4 = 1.5686345740485e-01;
167 Q6_5 = -8.0719535654891e-01;
168 Q6_6 = 0.0000000000000e+00;
169 Q6_7 = 8.3142546796428e-01;
170 Q6_8 = -2.3809523809524e-01;
171 Q6_9 = 5.9523809523809e-02;
172 Q6_10 = -9.9206349206349e-03;
173 Q6_11 = 7.9365079365079e-04;
174 Q6_12 = 0.0000000000000e+00;
175 Q7_0 = 2.0746552641799e-03;
176 Q7_1 = -5.8255272771571e-03;
177 Q7_2 = 9.9345865998262e-03;
178 Q7_3 = -7.3166499053672e-03;
179 Q7_4 = -4.2609496719925e-02;
180 Q7_5 = 2.2953297936781e-01;
181 Q7_6 = -8.3142546796428e-01;
182 Q7_7 = 0.0000000000000e+00;
183 Q7_8 = 8.3333333333333e-01;
184 Q7_9 = -2.3809523809524e-01;
185 Q7_10 = 5.9523809523809e-02;
186 Q7_11 = -9.9206349206349e-03;
187 Q7_12 = 7.9365079365079e-04;
188 for i = 1:BP
189 for j = 1:BP
190 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
191 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
192 end
193 end
194 %%%%%%%%%%%%%%%%%%%%%%%%%%%
195
196 %%%% Difference operator %%
197 D1 = H\Q;
198 %%%%%%%%%%%%%%%%%%%%%%%%%%%