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comparison +sbp/+implementations/d2_variable_periodic_6.m @ 686:5ccf6aaf6d6b feature/poroelastic

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Add D2VariablePeriodic orders 4 and 6.
author Martin Almquist <malmquist@stanford.edu>
date Thu, 08 Feb 2018 16:44:46 -0800
parents
children bbf303c1f0cf
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685:b035902869a8 686:5ccf6aaf6d6b
1 function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_periodic_6(m,h)
2 % m = number of unique grid points, i.e. h = L/m;
3
4 if(m<7)
5 error(['Operator requires at least ' num2str(7) ' 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 = -3:3;
25 stencil = [-1/60 9/60 -45/60 0 45/60 -9/60 1/60];
26 D1 = stripeMatrixPeriodic(stencil, diags, m);
27 D1 = D1/h;
28
29 % D2 operator
30 scheme_width = 7;
31 scheme_radius = (scheme_width-1)/2;
32
33 r = 1:m;
34 offset = scheme_width;
35 r = r + offset;
36
37 function D2 = D2_fun(c)
38 c = [c(end-scheme_width+1:end); c; c(1:scheme_width) ];
39
40 Mm3 = c(r-2)/0.40e2 + c(r-1)/0.40e2 - 0.11e2/0.360e3 * c(r-3) - 0.11e2/0.360e3 * c(r);
41 Mm2 = c(r-3)/0.20e2 - 0.3e1/0.10e2 * c(r-1) + c(r+1)/0.20e2 + 0.7e1/0.40e2 * c(r) + 0.7e1/0.40e2 * c(r-2);
42 Mm1 = -c(r-3)/0.40e2 - 0.3e1/0.10e2 * c(r-2) - 0.3e1/0.10e2 * c(r+1) - c(r+2)/0.40e2 - 0.17e2/0.40e2 * c(r) - 0.17e2/0.40e2 * c(r-1);
43 M0 = c(r-3)/0.180e3 + c(r-2)/0.8e1 + 0.19e2/0.20e2 * c(r-1) + 0.19e2/0.20e2 * c(r+1) + c(r+2)/0.8e1 + c(r+3)/0.180e3 + 0.101e3/0.180e3 * c(r);
44 Mp1 = -c(r-2)/0.40e2 - 0.3e1/0.10e2 * c(r-1) - 0.3e1/0.10e2 * c(r+2) - c(r+3)/0.40e2 - 0.17e2/0.40e2 * c(r) - 0.17e2/0.40e2 * c(r+1);
45 Mp2 = c(r-1)/0.20e2 - 0.3e1/0.10e2 * c(r+1) + c(r+3)/0.20e2 + 0.7e1/0.40e2 * c(r) + 0.7e1/0.40e2 * c(r+2);
46 Mp3 = c(r+1)/0.40e2 + c(r+2)/0.40e2 - 0.11e2/0.360e3 * c(r) - 0.11e2/0.360e3 * c(r+3);
47
48 vals = [Mm3,Mm2,Mm1,M0,Mp1,Mp2,Mp3];
49 diags = -scheme_radius : scheme_radius;
50 M = spdiagsVariablePeriodic(vals,diags);
51
52 M=M/h;
53 D2=HI*(-M );
54 end
55 D2 = @D2_fun;
56
57
58 end