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annotate +sbp/D1_minimal_4th_3BP_1shifts.m @ 255:df3cc9c5dffc operator_remake

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Added ordinary 12th order accurate, with D1*D1 as 2nd derivative.
author Martin Almquist <martin.almquist@it.uu.se>
date Wed, 07 Sep 2016 15:54:41 +0200
parents 07fa0d6a05bb
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
252
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
1 function [D1,H,x,h] = D1_minimal_4th_3BP_1shifts(N,L)
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
2
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
3 % L: Domain length
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
4 % N: Number of grid points
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
5 if(nargin < 2)
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
6 L = 1;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
7 end
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
8
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
9 % BP: Number of boundary points
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
10 % m: Number of nonequidistant spacings
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
11 % order: Accuracy of interior stencil
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
12 BP = 3;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
13 m = 1;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
14 order = 4;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
15
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
16 %%%% Non-equidistant grid points %%%%%
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
17 x0 = 0.0000000000000e+00;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
18 x1 = 7.7122987842562e-01;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
19 x2 = 1.7712298784256e+00;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
20 x3 = 2.7712298784256e+00;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
21
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
22 xb = zeros(m+1,1);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
23 for i = 0:m
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
24 xb(i+1) = eval(['x' num2str(i)]);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
25 end
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
26 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
27
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
28 %%%% Compute h %%%%%%%%%%
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
29 h = L/(2*xb(end) + N-1-2*m);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
30 %%%%%%%%%%%%%%%%%%%%%%%%%
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
31
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
32 %%%% Define grid %%%%%%%%
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
33 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
34 %%%%%%%%%%%%%%%%%%%%%%%%%
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
35
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
36 %%%% Norm matrix %%%%%%%%
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
37 P = zeros(BP,1);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
38 %#ok<*NASGU>
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
39 P0 = 2.6864248295847e-01;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
40 P1 = 1.0094667153500e+00;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
41 P2 = 9.9312068011715e-01;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
42
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
43 for i = 0:BP-1
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
44 P(i+1) = eval(['P' num2str(i)]);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
45 end
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
46
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
47 H = ones(N,1);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
48 H(1:BP) = P;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
49 H(end-BP+1:end) = flip(P);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
50 H = spdiags(h*H,0,N,N);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
51 %%%%%%%%%%%%%%%%%%%%%%%%%
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
52
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
53 %%%% Q matrix %%%%%%%%%%%
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
54
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
55 % interior stencil
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
56 switch order
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
57 case 2
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
58 d = [-1/2,0,1/2];
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
59 case 4
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
60 d = [1/12,-2/3,0,2/3,-1/12];
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
61 case 6
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
62 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
63 case 8
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
64 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
65 case 10
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
66 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
67 case 12
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
68 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];
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
69 end
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
70 d = repmat(d,N,1);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
71 Q = spdiags(d,-order/2:order/2,N,N);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
72
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
73 % Boundaries
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
74 Q0_0 = -5.0000000000000e-01;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
75 Q0_1 = 6.1697245625434e-01;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
76 Q0_2 = -1.1697245625434e-01;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
77 Q0_3 = 0.0000000000000e+00;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
78 Q0_4 = 0.0000000000000e+00;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
79 Q1_0 = -6.1697245625434e-01;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
80 Q1_1 = 0.0000000000000e+00;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
81 Q1_2 = 7.0030578958767e-01;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
82 Q1_3 = -8.3333333333333e-02;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
83 Q1_4 = 0.0000000000000e+00;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
84 Q2_0 = 1.1697245625434e-01;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
85 Q2_1 = -7.0030578958767e-01;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
86 Q2_2 = 0.0000000000000e+00;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
87 Q2_3 = 6.6666666666667e-01;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
88 Q2_4 = -8.3333333333333e-02;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
89 for i = 1:BP
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
90 for j = 1:BP
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
91 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
92 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
93 end
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
94 end
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
95 %%%%%%%%%%%%%%%%%%%%%%%%%%%
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
96
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
97 %%%% Difference operator %%
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
98 D1 = H\Q;
07fa0d6a05bb Renamned class files and added nonequidistant operators.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
99 %%%%%%%%%%%%%%%%%%%%%%%%%%%