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comparison +sbp/+implementations/d2_variable_periodic_8.m @ 1337:bf2554f1825d feature/D2_boundary_opt

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Add periodic D1 and D2 operators for orders 8,10,12
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 13 May 2022 13:28:10 +0200
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1336:0666629aa183 1337:bf2554f1825d
1 function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_periodic_8(m,h)
2 % m = number of unique grid points, i.e. h = L/m;
3
4 if(m<9)
5 error(['Operator requires at least ' num2str(8) ' grid points']);
6 end
7
8 % Norm
9 Hv = ones(m,1);
10 Hv = h*Hv;
11 H = spdiag(Hv, 0);
12 HI = spdiag(1./Hv, 0);
13
14
15 % Dummy boundary operators
16 e_l = sparse(m,1);
17 e_r = rot90(e_l, 2);
18
19 d1_l = sparse(m,1);
20 d1_r = -rot90(d1_l, 2);
21
22
23 % D1 operator
24 diags = -4:4;
25 stencil = [1/280, -4/105, 1/5, -4/5, 0, 4/5, -1/5, 4/105, -1/280];
26 D1 = stripeMatrixPeriodic(stencil, diags, m);
27 D1 = D1/h;
28
29 % Undivided differences
30 diags = -3:2;
31 stencil = [-1 5 -10 10 -5 1];
32 DD_5 = stripeMatrixPeriodic(stencil, diags, m);
33
34 diags = -3:3;
35 stencil = [1 -6 15 -20 15 -6 1];
36 DD_6 = stripeMatrixPeriodic(stencil, diags, m);
37
38 diags = -4:3;
39 stencil = [-1 7 -21 35 -35 21 -7 1];
40 DD_7 = stripeMatrixPeriodic(stencil, diags, m);
41
42 diags = -4:4;
43 stencil = [1 -8 28 -56 70 -56 28 -8 1];
44 DD_8 = stripeMatrixPeriodic(stencil, diags, m);
45
46 % D2 operator
47 function D2 = D2_fun(c)
48
49 C1 = sparse(diag(c));
50
51 diags = -1:0;
52 stencil = [1/2, 1/2];
53 C2 = stripeMatrixPeriodic(stencil, diags, m);
54
55 diags = -1:1;
56 stencil = [3/10, 2/5, 3/10];
57 C3 = stripeMatrixPeriodic(stencil, diags, m);
58
59 diags = -2:1;
60 stencil = [1/4, 1/4, 1/4, 1/4];
61 C4 = stripeMatrixPeriodic(stencil, diags, m);
62
63 C2 = sparse(diag(C2 * c));
64 C3 = sparse(diag(C3 * c));
65 C4 = sparse(diag(C4 * c));
66
67 % Remainder term added to wide second derivative operator
68 R = (1/78400 / h) * transpose(DD_8) * C1 * DD_8 + (1/14700 / h) * transpose(DD_7) * C2 * DD_7 + (1/2520 / h) * transpose(DD_6) * C3 * DD_6 + (1/350 / h) * transpose(DD_5) * C4 * DD_5;
69
70 D2 = D1 * C1 * D1 - H \ R;
71 end
72 D2 = @D2_fun;
73
74
75 end