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comparison +sbp/+implementations/d1_noneq_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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equal deleted inserted replaced
260:b4116ce49ac4 261:6009f2712d13
1 function [D1,H,x,h] = d1_noneq_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 = 8;
13 m = 4;
14 order = 8;
15
16 %%%% Non-equidistant grid points %%%%%
17 x0 = 0.0000000000000e+00;
18 x1 = 3.8118550247622e-01;
19 x2 = 1.1899550868338e+00;
20 x3 = 2.2476300175641e+00;
21 x4 = 3.3192851303204e+00;
22 x5 = 4.3192851303204e+00;
23 x6 = 5.3192851303204e+00;
24 x7 = 6.3192851303204e+00;
25 x8 = 7.3192851303204e+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 = 1.0758368078310e-01;
45 P1 = 6.1909685107891e-01;
46 P2 = 9.6971176519117e-01;
47 P3 = 1.1023441350947e+00;
48 P4 = 1.0244688965833e+00;
49 P5 = 9.9533550116831e-01;
50 P6 = 1.0008236941028e+00;
51 P7 = 9.9992060631812e-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 = 6.7284756079369e-01;
86 Q0_2 = -2.5969732837062e-01;
87 Q0_3 = 1.3519390385721e-01;
88 Q0_4 = -6.9678474730984e-02;
89 Q0_5 = 2.6434024071371e-02;
90 Q0_6 = -5.5992311465618e-03;
91 Q0_7 = 4.9954552590464e-04;
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 Q1_0 = -6.7284756079369e-01;
97 Q1_1 = 0.0000000000000e+00;
98 Q1_2 = 9.4074021172233e-01;
99 Q1_3 = -4.0511642426516e-01;
100 Q1_4 = 1.9369192209331e-01;
101 Q1_5 = -6.8638079843479e-02;
102 Q1_6 = 1.3146457241484e-02;
103 Q1_7 = -9.7652615479254e-04;
104 Q1_8 = 0.0000000000000e+00;
105 Q1_9 = 0.0000000000000e+00;
106 Q1_10 = 0.0000000000000e+00;
107 Q1_11 = 0.0000000000000e+00;
108 Q2_0 = 2.5969732837062e-01;
109 Q2_1 = -9.4074021172233e-01;
110 Q2_2 = 0.0000000000000e+00;
111 Q2_3 = 9.4316393361096e-01;
112 Q2_4 = -3.5728039257451e-01;
113 Q2_5 = 1.1266686855013e-01;
114 Q2_6 = -1.8334941452280e-02;
115 Q2_7 = 8.2741521740941e-04;
116 Q2_8 = 0.0000000000000e+00;
117 Q2_9 = 0.0000000000000e+00;
118 Q2_10 = 0.0000000000000e+00;
119 Q2_11 = 0.0000000000000e+00;
120 Q3_0 = -1.3519390385721e-01;
121 Q3_1 = 4.0511642426516e-01;
122 Q3_2 = -9.4316393361096e-01;
123 Q3_3 = 0.0000000000000e+00;
124 Q3_4 = 8.7694387866575e-01;
125 Q3_5 = -2.4698058719506e-01;
126 Q3_6 = 4.7291642094198e-02;
127 Q3_7 = -4.0135203618880e-03;
128 Q3_8 = 0.0000000000000e+00;
129 Q3_9 = 0.0000000000000e+00;
130 Q3_10 = 0.0000000000000e+00;
131 Q3_11 = 0.0000000000000e+00;
132 Q4_0 = 6.9678474730984e-02;
133 Q4_1 = -1.9369192209331e-01;
134 Q4_2 = 3.5728039257451e-01;
135 Q4_3 = -8.7694387866575e-01;
136 Q4_4 = 0.0000000000000e+00;
137 Q4_5 = 8.1123946853807e-01;
138 Q4_6 = -2.0267150541446e-01;
139 Q4_7 = 3.8680398901392e-02;
140 Q4_8 = -3.5714285714286e-03;
141 Q4_9 = 0.0000000000000e+00;
142 Q4_10 = 0.0000000000000e+00;
143 Q4_11 = 0.0000000000000e+00;
144 Q5_0 = -2.6434024071371e-02;
145 Q5_1 = 6.8638079843479e-02;
146 Q5_2 = -1.1266686855013e-01;
147 Q5_3 = 2.4698058719506e-01;
148 Q5_4 = -8.1123946853807e-01;
149 Q5_5 = 0.0000000000000e+00;
150 Q5_6 = 8.0108544742793e-01;
151 Q5_7 = -2.0088756283071e-01;
152 Q5_8 = 3.8095238095238e-02;
153 Q5_9 = -3.5714285714286e-03;
154 Q5_10 = 0.0000000000000e+00;
155 Q5_11 = 0.0000000000000e+00;
156 Q6_0 = 5.5992311465618e-03;
157 Q6_1 = -1.3146457241484e-02;
158 Q6_2 = 1.8334941452280e-02;
159 Q6_3 = -4.7291642094198e-02;
160 Q6_4 = 2.0267150541446e-01;
161 Q6_5 = -8.0108544742793e-01;
162 Q6_6 = 0.0000000000000e+00;
163 Q6_7 = 8.0039405922650e-01;
164 Q6_8 = -2.0000000000000e-01;
165 Q6_9 = 3.8095238095238e-02;
166 Q6_10 = -3.5714285714286e-03;
167 Q6_11 = 0.0000000000000e+00;
168 Q7_0 = -4.9954552590464e-04;
169 Q7_1 = 9.7652615479254e-04;
170 Q7_2 = -8.2741521740941e-04;
171 Q7_3 = 4.0135203618880e-03;
172 Q7_4 = -3.8680398901392e-02;
173 Q7_5 = 2.0088756283071e-01;
174 Q7_6 = -8.0039405922650e-01;
175 Q7_7 = 0.0000000000000e+00;
176 Q7_8 = 8.0000000000000e-01;
177 Q7_9 = -2.0000000000000e-01;
178 Q7_10 = 3.8095238095238e-02;
179 Q7_11 = -3.5714285714286e-03;
180 for i = 1:BP
181 for j = 1:BP
182 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
183 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
184 end
185 end
186 %%%%%%%%%%%%%%%%%%%%%%%%%%%
187
188 %%%% Difference operator %%
189 D1 = H\Q;
190 %%%%%%%%%%%%%%%%%%%%%%%%%%%