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annotate +sbp/+implementations/d2_noneq_variable_8.m @ 1332:8e9df030a0a5 feature/D2_boundary_opt

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author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 04 May 2022 08:42:13 +0200
parents 855871e0b852
children b4e5e45bd239
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1325
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
1 function [H, HI, D1, D2, DI] = d2_noneq_variable_8(N, h, options)
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
2 % N: Number of grid points
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
3 % h: grid spacing
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
4 % options: struct containing options for constructing the operator
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
5 % current options are:
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
6 % options.stencil_type ('minimal','nonminimal','wide')
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
7 % options.AD ('upwind', 'op')
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
8
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
9 % BP: Number of boundary points
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
10 % order: Accuracy of interior stencil
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
11 BP = 8;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
12 order = 8;
1330
855871e0b852 Add size checks to the operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1326
diff changeset
13 if(N<2*BP)
855871e0b852 Add size checks to the operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1326
diff changeset
14 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
855871e0b852 Add size checks to the operators
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1326
diff changeset
15 end
1325
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
16
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
17 %%%% Norm matrix %%%%%%%%
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
18 P = zeros(BP, 1);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
19 P0 = 1.0758368078310e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
20 P1 = 6.1909685107891e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
21 P2 = 9.6971176519117e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
22 P3 = 1.1023441350947e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
23 P4 = 1.0244688965833e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
24 P5 = 9.9533550116831e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
25 P6 = 1.0008236941028e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
26 P7 = 9.9992060631812e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
27
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
28 for i = 0:BP - 1
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
29 P(i + 1) = eval(['P' num2str(i)]);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
30 end
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
31
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
32 Hv = ones(N, 1);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
33 Hv(1:BP) = P;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
34 Hv(end - BP + 1:end) = flip(P);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
35 Hv = h * Hv;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
36 H = spdiags(Hv, 0, N, N);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
37 HI = spdiags(1 ./ Hv, 0, N, N);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
38 %%%%%%%%%%%%%%%%%%%%%%%%%
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
39
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
40 %%%% Q matrix %%%%%%%%%%%
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
41
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
42 % interior stencil
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
43 d = [1/280, -4/105, 1/5, -4/5, 0, 4/5, -1/5, 4/105, -1/280];
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
44 d = repmat(d, N, 1);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
45 Q = spdiags(d, -order / 2:order / 2, N, N);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
46
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
47 % Boundaries
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
48 Q0_0 = -5.0000000000000e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
49 Q0_1 = 6.7284756079369e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
50 Q0_2 = -2.5969732837062e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
51 Q0_3 = 1.3519390385721e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
52 Q0_4 = -6.9678474730984e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
53 Q0_5 = 2.6434024071371e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
54 Q0_6 = -5.5992311465618e-03;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
55 Q0_7 = 4.9954552590464e-04;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
56 Q0_8 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
57 Q0_9 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
58 Q0_10 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
59 Q0_11 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
60 Q1_0 = -6.7284756079369e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
61 Q1_1 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
62 Q1_2 = 9.4074021172233e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
63 Q1_3 = -4.0511642426516e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
64 Q1_4 = 1.9369192209331e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
65 Q1_5 = -6.8638079843479e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
66 Q1_6 = 1.3146457241484e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
67 Q1_7 = -9.7652615479254e-04;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
68 Q1_8 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
69 Q1_9 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
70 Q1_10 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
71 Q1_11 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
72 Q2_0 = 2.5969732837062e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
73 Q2_1 = -9.4074021172233e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
74 Q2_2 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
75 Q2_3 = 9.4316393361096e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
76 Q2_4 = -3.5728039257451e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
77 Q2_5 = 1.1266686855013e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
78 Q2_6 = -1.8334941452280e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
79 Q2_7 = 8.2741521740941e-04;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
80 Q2_8 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
81 Q2_9 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
82 Q2_10 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
83 Q2_11 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
84 Q3_0 = -1.3519390385721e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
85 Q3_1 = 4.0511642426516e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
86 Q3_2 = -9.4316393361096e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
87 Q3_3 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
88 Q3_4 = 8.7694387866575e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
89 Q3_5 = -2.4698058719506e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
90 Q3_6 = 4.7291642094198e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
91 Q3_7 = -4.0135203618880e-03;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
92 Q3_8 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
93 Q3_9 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
94 Q3_10 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
95 Q3_11 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
96 Q4_0 = 6.9678474730984e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
97 Q4_1 = -1.9369192209331e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
98 Q4_2 = 3.5728039257451e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
99 Q4_3 = -8.7694387866575e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
100 Q4_4 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
101 Q4_5 = 8.1123946853807e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
102 Q4_6 = -2.0267150541446e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
103 Q4_7 = 3.8680398901392e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
104 Q4_8 = -3.5714285714286e-03;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
105 Q4_9 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
106 Q4_10 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
107 Q4_11 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
108 Q5_0 = -2.6434024071371e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
109 Q5_1 = 6.8638079843479e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
110 Q5_2 = -1.1266686855013e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
111 Q5_3 = 2.4698058719506e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
112 Q5_4 = -8.1123946853807e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
113 Q5_5 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
114 Q5_6 = 8.0108544742793e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
115 Q5_7 = -2.0088756283071e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
116 Q5_8 = 3.8095238095238e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
117 Q5_9 = -3.5714285714286e-03;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
118 Q5_10 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
119 Q5_11 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
120 Q6_0 = 5.5992311465618e-03;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
121 Q6_1 = -1.3146457241484e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
122 Q6_2 = 1.8334941452280e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
123 Q6_3 = -4.7291642094198e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
124 Q6_4 = 2.0267150541446e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
125 Q6_5 = -8.0108544742793e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
126 Q6_6 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
127 Q6_7 = 8.0039405922650e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
128 Q6_8 = -2.0000000000000e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
129 Q6_9 = 3.8095238095238e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
130 Q6_10 = -3.5714285714286e-03;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
131 Q6_11 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
132 Q7_0 = -4.9954552590464e-04;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
133 Q7_1 = 9.7652615479254e-04;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
134 Q7_2 = -8.2741521740941e-04;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
135 Q7_3 = 4.0135203618880e-03;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
136 Q7_4 = -3.8680398901392e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
137 Q7_5 = 2.0088756283071e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
138 Q7_6 = -8.0039405922650e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
139 Q7_7 = 0.0000000000000e+00;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
140 Q7_8 = 8.0000000000000e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
141 Q7_9 = -2.0000000000000e-01;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
142 Q7_10 = 3.8095238095238e-02;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
143 Q7_11 = -3.5714285714286e-03;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
144
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
145 for i = 1:BP
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
146
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
147 for j = 1:BP
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
148 Q(i, j) = eval(['Q' num2str(i - 1) '_' num2str(j - 1)]);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
149 Q(N + 1 - i, N + 1 - j) = -eval(['Q' num2str(i - 1) '_' num2str(j - 1)]);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
150 end
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
151
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
152 end
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
153
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
154 %%%%%%%%%%%%%%%%%%%%%%%%%%%
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
155
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
156 %%% Undivided difference operators %%%%
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
157 % Closed with zeros at the first boundary nodes.
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
158 m = N;
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
159
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
160 DD_4 = (diag(ones(m - 2, 1), 2) - 4 * diag(ones(m - 1, 1), 1) + 6 * diag(ones(m, 1), 0) - 4 * diag(ones(m - 1, 1), -1) + diag(ones(m - 2, 1), -2));
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
161 DD_4(1:6, 1:8) = [0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; 0.70921010190504348684e1 -0.14196080536361841322e2 0.11072881931325435634e2 -0.50473576941871051066e1 0.10784552801730759259e1 0 0 0; 0 0.13740993382151221352e1 -0.42105600869792757010e1 0.54761010136211975317e1 -0.35797005751940657417e1 0.94006031033702177578e0 0 0; 0 0 0.82467928104463767301e0 -0.33274694995849432461e1 0.52587584638857303123e1 -0.37020511582893568152e1 0.94608291294393207601e0 0; 0 0 0 0.86436129166612654748e0 -0.37325441295306179390e1 0.57924699560798105338e1 -0.39066885960487908497e1 0.98240147783347170744e0; ];
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
162 DD_4(m - 5:m, m - 7:m) = [0.98240147783347170744e0 -0.39066885960487908497e1 0.57924699560798105338e1 -0.37325441295306179390e1 0.86436129166612654748e0 0 0 0; 0 0.94608291294393207601e0 -0.37020511582893568152e1 0.52587584638857303123e1 -0.33274694995849432461e1 0.82467928104463767301e0 0 0; 0 0 0.94006031033702177578e0 -0.35797005751940657417e1 0.54761010136211975317e1 -0.42105600869792757010e1 0.13740993382151221352e1 0; 0 0 0 0.10784552801730759259e1 -0.50473576941871051066e1 0.11072881931325435634e2 -0.14196080536361841322e2 0.70921010190504348684e1; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0; ];
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
163 DD_4 = sparse(DD_4);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
164
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
165 DD_5 = (-diag(ones(m - 3, 1), -3) + 5 * diag(ones(m - 2, 1), -2) - 10 * diag(ones(m - 1, 1), -1) + 10 * diag(ones(m, 1), 0) - 5 * diag(ones(m - 1, 1), 1) + diag(ones(m - 2, 1), 2));
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
166 DD_5(1:7, 1:9) = [0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0; -0.82098088052411907132e1 0.18024024120655590699e2 -0.17692096674769448317e2 0.12181944917152947702e2 -0.53922764008653796295e1 0.10882128430674802600e1 0 0 0; 0 -0.13913240333052950751e1 0.50983574122643719988e1 -0.89139255753021486176e1 0.89492514379851643542e1 -0.47003015516851088789e1 0.95794231004301621873e0 0 0; 0 0 -0.80388595981635823711e0 0.40861386922975635215e1 -0.87645974398095505205e1 0.92551278957233920380e1 -0.47304145647196603800e1 0.95763137632461357808e0 0; 0 0 0 -0.85214912336218661144e0 0.46656801619132724238e1 -0.96541165934663508896e1 0.97667214901219771242e1 -0.49120073891673585372e1 0.98587145396064649030e0; ];
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
167 DD_5(m - 5:m, m - 8:m) = [-0.98587145396064649030e0 0.49120073891673585372e1 -0.97667214901219771242e1 0.96541165934663508896e1 -0.46656801619132724238e1 0.85214912336218661144e0 0 0 0; 0 -0.95763137632461357808e0 0.47304145647196603800e1 -0.92551278957233920380e1 0.87645974398095505205e1 -0.40861386922975635215e1 0.80388595981635823711e0 0 0; 0 0 -0.95794231004301621873e0 0.47003015516851088789e1 -0.89492514379851643542e1 0.89139255753021486176e1 -0.50983574122643719988e1 0.13913240333052950751e1 0; 0 0 0 -0.10882128430674802600e1 0.53922764008653796295e1 -0.12181944917152947702e2 0.17692096674769448317e2 -0.18024024120655590699e2 0.82098088052411907132e1; 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0; ];
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
168 DD_5 = sparse(DD_5);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
169
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
170 DD_6 = (diag(ones(m - 3, 1), 3) - 6 * diag(ones(m - 2, 1), 2) + 15 * diag(ones(m - 1, 1), 1) - 20 * diag(ones(m, 1), 0) + 15 * diag(ones(m - 1, 1), -1) - 6 * diag(ones(m - 2, 1), -2) + diag(ones(m - 3, 1), -3));
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
171 DD_6(1:7, 1:10) = [0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0; 0.92604272237009487731e1 -0.21899951980342041757e2 0.25706973995952182034e2 -0.23795532642767976509e2 0.16176829202596138889e2 -0.65292770584048815597e1 0.10805312592656301300e1 0 0 0; 0 0.14058275749850312569e1 -0.59637699688344396810e1 0.13135580487711615439e2 -0.17898502875970328708e2 0.14100904655055326637e2 -0.57476538602580973124e1 0.96761398731089236944e0 0 0; 0 0 0.78692381135906040550e0 -0.48340889923923043812e1 0.13146896159714325781e2 -0.18510255791446784076e2 0.14191243694158981140e2 -0.57457882579476814685e1 0.96506937655440259938e0 0; 0 0 0 0.84209241882516286974e0 -0.55988161942959269085e1 0.14481174890199526334e2 -0.19533442980243954248e2 0.14736022167502075612e2 -0.59152287237638789418e1 0.98819842177699528293e0; ];
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
172 DD_6(m - 6:m, m - 9:m) = [0.98819842177699528293e0 -0.59152287237638789418e1 0.14736022167502075612e2 -0.19533442980243954248e2 0.14481174890199526334e2 -0.55988161942959269085e1 0.84209241882516286974e0 0 0 0; 0 0.96506937655440259938e0 -0.57457882579476814685e1 0.14191243694158981140e2 -0.18510255791446784076e2 0.13146896159714325781e2 -0.48340889923923043812e1 0.78692381135906040550e0 0 0; 0 0 0.96761398731089236944e0 -0.57476538602580973124e1 0.14100904655055326637e2 -0.17898502875970328708e2 0.13135580487711615439e2 -0.59637699688344396810e1 0.14058275749850312569e1 0; 0 0 0 0.10805312592656301300e1 -0.65292770584048815597e1 0.16176829202596138889e2 -0.23795532642767976509e2 0.25706973995952182034e2 -0.21899951980342041757e2 0.92604272237009487731e1; 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0; ];
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
173 DD_6 = sparse(DD_6);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
174
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
175 DD_7 = (-diag(ones(m - 4, 1), -4) + 7 * diag(ones(m - 3, 1), -3) - 21 * diag(ones(m - 2, 1), -2) + 35 * diag(ones(m - 1, 1), -1) - 35 * diag(ones(m, 1), 0) + 21 * diag(ones(m - 1, 1), 1) - 7 * diag(ones(m - 2, 1), 2) + diag(ones(m - 3, 1), 3));
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
176 DD_7(1:8, 1:11) = [0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0; -0.10257962606384161889e2 0.25816283570514673553e2 -0.35082323899232605336e2 0.40909341259657284245e2 -0.37745934806057657407e2 0.22852469704417085459e2 -0.75637188148594109098e1 0.10718455919447922848e1 0 0 0; 0 -0.14183700945143243060e1 0.68109221539151178574e1 -0.18129991367652287552e2 0.31322380032948075240e2 -0.32902110861795762152e2 0.20116788510903340593e2 -0.67732979111762465861e1 0.97367953737208690559e0 0 0; 0 0 -0.77264857229409862775e0 0.55732122985135573041e1 -0.18405654623600056093e2 0.32392947635031872133e2 -0.33112901953037622660e2 0.20110258902816885140e2 -0.67554856358808181957e1 0.97027194845028099974e0 0; 0 0 0 -0.83355973075426177031e0 0.65319522266785813933e1 -0.20273644846279336868e2 0.34183525215426919935e2 -0.34384051724171509761e2 0.20703300533173576296e2 -0.69173889524389669805e1 0.98986727836499775519e0; ];
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
177 DD_7(m - 6:m, m - 10:m) = [-0.98986727836499775519e0 0.69173889524389669805e1 -0.20703300533173576296e2 0.34384051724171509761e2 -0.34183525215426919935e2 0.20273644846279336868e2 -0.65319522266785813933e1 0.83355973075426177031e0 0 0 0; 0 -0.97027194845028099974e0 0.67554856358808181957e1 -0.20110258902816885140e2 0.33112901953037622660e2 -0.32392947635031872133e2 0.18405654623600056093e2 -0.55732122985135573041e1 0.77264857229409862775e0 0 0; 0 0 -0.97367953737208690559e0 0.67732979111762465861e1 -0.20116788510903340593e2 0.32902110861795762152e2 -0.31322380032948075240e2 0.18129991367652287552e2 -0.68109221539151178574e1 0.14183700945143243060e1 0; 0 0 0 -0.10718455919447922848e1 0.75637188148594109098e1 -0.22852469704417085459e2 0.37745934806057657407e2 -0.40909341259657284245e2 0.35082323899232605336e2 -0.25816283570514673553e2 0.10257962606384161889e2; 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0; ];
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
178 DD_7 = sparse(DD_7);
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
179
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
180 DD_8 = (diag(ones(m - 4, 1), 4) - 8 * diag(ones(m - 3, 1), 3) + 28 * diag(ones(m - 2, 1), 2) - 56 * diag(ones(m - 1, 1), 1) + 70 * diag(ones(m, 1), 0) - 56 * diag(ones(m - 1, 1), -1) + 28 * diag(ones(m - 2, 1), -2) - 8 * diag(ones(m - 3, 1), -3) + diag(ones(m - 4, 1), -4));
1b0f2415237f Add variable coefficient boundary-optimized second derivatives.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
181 DD_8(1:8, 1:12) = [0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0; 0.11211983054345146839e2 -0.29767555907566203748e2 0.45789440151310044599e2 -0.64530162797168947524e2 0.75491869612115314813e2 -0.60939919211778894557e2 0.30254875259437643639e2 -0.85747647355583382784e1 0.10642345748642342173e1 0 0 0; 0 0.14294303785648149613e1 -0.76427065234692260122e1 0.23888038475126051744e2 -0.50115808052716920383e2 0.65804221723591524304e2 -0.53644769362408908249e2 0.27093191644704986344e2 -0.77894362989766952447e1 0.97783801558437253538e0 0 0; 0 0 0.76035645561041265933e0 -0.63048462739199410204e1 0.24540872831466741457e2 -0.51828716216050995413e2 0.66225803906075245320e2 -0.53627357074178360373e2 0.27021942543523272783e2 -0.77621755876022479980e1 0.97411941507587258409e0 0; 0 0 0 0.82615990808320718845e0 -0.74650882590612358780e1 0.27031526461705782491e2 -0.54693640344683071895e2 0.68768103448343019521e2 -0.55208801421796203457e2 0.27669555809755867922e2 -0.79189382269199820415e1 0.99112262457261614959e0; ];
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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182 DD_8(m - 7:m, m - 11:m) = [0.99112262457261614959e0 -0.79189382269199820415e1 0.27669555809755867922e2 -0.55208801421796203457e2 0.68768103448343019521e2 -0.54693640344683071895e2 0.27031526461705782491e2 -0.74650882590612358780e1 0.82615990808320718845e0 0 0 0; 0 0.97411941507587258409e0 -0.77621755876022479980e1 0.27021942543523272783e2 -0.53627357074178360373e2 0.66225803906075245320e2 -0.51828716216050995413e2 0.24540872831466741457e2 -0.63048462739199410204e1 0.76035645561041265933e0 0 0; 0 0 0.97783801558437253538e0 -0.77894362989766952447e1 0.27093191644704986344e2 -0.53644769362408908249e2 0.65804221723591524304e2 -0.50115808052716920383e2 0.23888038475126051744e2 -0.76427065234692260122e1 0.14294303785648149613e1 0; 0 0 0 0.10642345748642342173e1 -0.85747647355583382784e1 0.30254875259437643639e2 -0.60939919211778894557e2 0.75491869612115314813e2 -0.64530162797168947524e2 0.45789440151310044599e2 -0.29767555907566203748e2 0.11211983054345146839e2; 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0; ];
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183 DD_8 = sparse(DD_8);
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184
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185 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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186
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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187 %%%% Difference operators %%
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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188 D1 = H \ Q;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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189
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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190 % Helper functions for constructing D2(c)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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191 % TODO: Consider changing sparse(diag(...)) to spdiags(....)
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192
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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193 % Minimal 9 point stencil width
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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194 function D2 = D2_fun_minimal(c)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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195 % Here we add variable diffusion
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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196 C1 = sparse(diag(c));
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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197 C2 = 1/2 * diag(ones(m - 1, 1), -1) + 1/2 * diag(ones(m, 1), 0); C2(1, 2) = 1/2;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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198 C3 = 3/10 * diag(ones(m - 1, 1), -1) + 3/10 * diag(ones(m - 1, 1), 1) + 2/5 * diag(ones(m, 1), 0); C3(1, 3) = 3/10; C3(m, m - 2) = 3/10;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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199 C4 = 1/4 * diag(ones(m - 2, 1), -2) + 1/4 * diag(ones(m - 1, 1), -1) + 1/4 * diag(ones(m - 1, 1), 1) + 1/4 * diag(ones(m, 1), 0); C4(2, 4) = 1/4; C4(1, 3) = 1/4; C4(1, 4) = 1/4; C4(m, m - 2) = 1/4; C4(m, m - 3) = 1/4;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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200
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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201 C2 = sparse(diag(C2 * c));
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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202 C3 = sparse(diag(C3 * c));
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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203 C4 = sparse(diag(C4 * c));
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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204
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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205 % Remainder term added to wide second derivative operator
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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206 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;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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207
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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208 D2 = D1 * C1 * D1 - H \ R;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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209 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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210
1332
8e9df030a0a5 Clarify comments
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1330
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211 % Non-minimal 11 point stencil width
1325
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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212 function D2 = D2_fun_nonminimal(c)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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213 % Here we add variable diffusion
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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214 C1 = sparse(diag(c));
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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215 C2 = 1/2 * diag(ones(m - 1, 1), -1) + 1/2 * diag(ones(m, 1), 0); C2(1, 2) = 1/2;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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216 C3 = 3/10 * diag(ones(m - 1, 1), -1) + 3/10 * diag(ones(m - 1, 1), 1) + 2/5 * diag(ones(m, 1), 0); C3(1, 3) = 3/10; C3(m, m - 2) = 3/10;
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217
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218 C2 = sparse(diag(C2 * c));
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219 C3 = sparse(diag(C3 * c));
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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220
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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221 % Remainder term added to wide second derivative operator
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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222 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;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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223 D2 = D1 * C1 * D1 - H \ R;
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224 end
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225
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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226 % Wide stencil
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c2d716c4f1ed Fix bug when using wide stencils
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1325
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227 function D2 = D2_fun_wide(c)
1325
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228 % Here we add variable diffusion
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229 C1 = sparse(diag(c));
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230 D2 = D1 * C1 * D1;
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231 end
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232
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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233 switch options.stencil_width
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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234 case 'minimal'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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235 D2 = @D2_fun_minimal;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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236 case 'nonminimal'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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237 D2 = @D2_fun_nonminimal;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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238 case 'wide'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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239 D2 = @D2_fun_wide;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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240 otherwise
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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241 error('No option %s for stencil width', options.stencil_width)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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242 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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243
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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244 %%%%%%%%%%%%%%%%%%%%%%%%%%%
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
245
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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246 %%%% Artificial dissipation operator %%%
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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247 switch options.AD
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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248 case 'upwind'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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249 % This is the choice that yield 7th order Upwind
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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250 DI = H \ (transpose(DD_4) * DD_4) * (-1/280);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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251 case 'op'
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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252 % This choice will preserve the order of the underlying
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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253 % Non-dissipative D1 SBP operator
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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254 DI = H \ (transpose(DD_5) * DD_5) * (-1 / (5 * 280));
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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255 % Notice that you can use any negative number instead of (-1/(5*280))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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256 otherwise
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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257 error("Artificial dissipation options '%s' not implemented.", option.AD)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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258 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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259
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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260 %%%%%%%%%%%%%%%%%%%%%%%%%%%
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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261 end