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comparison +sbp/+implementations/d1_noneq_minimal_4.m @ 423:a2cb0d4f4a02 feature/grids

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Merge in default.
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 07 Feb 2017 15:47:51 +0100
parents f7ac3cd6eeaa
children 4cb627c7fb90
comparison
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218:da058ce66876 423:a2cb0d4f4a02
1 function [D1,H,x,h] = d1_noneq_minimal_4(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<6)
10 error('Operator requires at least 6 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 = 3;
17 m = 1;
18 order = 4;
19
20 %%%% Non-equidistant grid points %%%%%
21 x0 = 0.0000000000000e+00;
22 x1 = 7.7122987842562e-01;
23 x2 = 1.7712298784256e+00;
24 x3 = 2.7712298784256e+00;
25
26 xb = sparse(m+1,1);
27 for i = 0:m
28 xb(i+1) = eval(['x' num2str(i)]);
29 end
30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
31
32 %%%% Compute h %%%%%%%%%%
33 h = L/(2*xb(end) + N-1-2*m);
34 %%%%%%%%%%%%%%%%%%%%%%%%%
35
36 %%%% Define grid %%%%%%%%
37 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
38 %%%%%%%%%%%%%%%%%%%%%%%%%
39
40 %%%% Norm matrix %%%%%%%%
41 P = sparse(BP,1);
42 %#ok<*NASGU>
43 P0 = 2.6864248295847e-01;
44 P1 = 1.0094667153500e+00;
45 P2 = 9.9312068011715e-01;
46
47 for i = 0:BP-1
48 P(i+1) = eval(['P' num2str(i)]);
49 end
50
51 H = ones(N,1);
52 H(1:BP) = P;
53 H(end-BP+1:end) = flip(P);
54 H = spdiags(h*H,0,N,N);
55 %%%%%%%%%%%%%%%%%%%%%%%%%
56
57 %%%% Q matrix %%%%%%%%%%%
58
59 % interior stencil
60 switch order
61 case 2
62 d = [-1/2,0,1/2];
63 case 4
64 d = [1/12,-2/3,0,2/3,-1/12];
65 case 6
66 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
67 case 8
68 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
69 case 10
70 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
71 case 12
72 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];
73 end
74 d = repmat(d,N,1);
75 Q = spdiags(d,-order/2:order/2,N,N);
76
77 % Boundaries
78 Q0_0 = -5.0000000000000e-01;
79 Q0_1 = 6.1697245625434e-01;
80 Q0_2 = -1.1697245625434e-01;
81 Q0_3 = 0.0000000000000e+00;
82 Q0_4 = 0.0000000000000e+00;
83 Q1_0 = -6.1697245625434e-01;
84 Q1_1 = 0.0000000000000e+00;
85 Q1_2 = 7.0030578958767e-01;
86 Q1_3 = -8.3333333333333e-02;
87 Q1_4 = 0.0000000000000e+00;
88 Q2_0 = 1.1697245625434e-01;
89 Q2_1 = -7.0030578958767e-01;
90 Q2_2 = 0.0000000000000e+00;
91 Q2_3 = 6.6666666666667e-01;
92 Q2_4 = -8.3333333333333e-02;
93 for i = 1:BP
94 for j = 1:BP
95 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
96 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
97 end
98 end
99 %%%%%%%%%%%%%%%%%%%%%%%%%%%
100
101 %%%% Difference operator %%
102 D1 = H\Q;
103 %%%%%%%%%%%%%%%%%%%%%%%%%%%