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comparison +sbp/+implementations/d1_noneq_12.m @ 1286:4cb627c7fb90 feature/boundary_optimized_grids

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Make D1Nonequidistant use the grid generation functions accurate/minimalBoundaryOptimizedGrid and remove grid generation from +implementations
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 01 Jul 2020 13:43:32 +0200
parents f7ac3cd6eeaa
children
comparison
equal deleted inserted replaced
1285:6b68f939d023 1286:4cb627c7fb90
1 function [D1,H,x,h] = d1_noneq_12(N,L) 1 function [D1,H] = d1_noneq_12(N,h)
2 2
3 % L: Domain length
4 % N: Number of grid points 3 % N: Number of grid points
5 if(nargin < 2)
6 L = 1;
7 end
8
9 if(N<24) 4 if(N<24)
10 error('Operator requires at least 24 grid points'); 5 error('Operator requires at least 24 grid points');
11 end 6 end
12 7
13 % BP: Number of boundary points 8 % BP: Number of boundary points
14 % m: Number of nonequidistant spacings
15 % order: Accuracy of interior stencil
16 BP = 12; 9 BP = 12;
17 m = 6;
18 order = 12;
19
20 %%%% Non-equidistant grid points %%%%%
21 x0 = 0.0000000000000e+00;
22 x1 = 3.6098032343909e-01;
23 x2 = 1.1634317168086e+00;
24 x3 = 2.2975905356987e+00;
25 x4 = 3.6057529790929e+00;
26 x5 = 4.8918275675510e+00;
27 x6 = 6.0000000000000e+00;
28 x7 = 7.0000000000000e+00;
29 x8 = 8.0000000000000e+00;
30 x9 = 9.0000000000000e+00;
31 x10 = 1.0000000000000e+01;
32 x11 = 1.1000000000000e+01;
33 x12 = 1.2000000000000e+01;
34
35 xb = sparse(m+1,1);
36 for i = 0:m
37 xb(i+1) = eval(['x' num2str(i)]);
38 end
39 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
40
41 %%%% Compute h %%%%%%%%%%
42 h = L/(2*xb(end) + N-1-2*m);
43 %%%%%%%%%%%%%%%%%%%%%%%%%
44
45 %%%% Define grid %%%%%%%%
46 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
47 %%%%%%%%%%%%%%%%%%%%%%%%%
48 10
49 %%%% Norm matrix %%%%%%%% 11 %%%% Norm matrix %%%%%%%%
50 P = sparse(BP,1); 12 P = sparse(BP,1);
51 %#ok<*NASGU> 13 %#ok<*NASGU>
52 P0 = 1.0000000000011e-01; 14 P0 = 1.0000000000011e-01;
71 H(end-BP+1:end) = flip(P); 33 H(end-BP+1:end) = flip(P);
72 H = spdiags(h*H,0,N,N); 34 H = spdiags(h*H,0,N,N);
73 %%%%%%%%%%%%%%%%%%%%%%%%% 35 %%%%%%%%%%%%%%%%%%%%%%%%%
74 36
75 %%%% Q matrix %%%%%%%%%%% 37 %%%% Q matrix %%%%%%%%%%%
76
77 % interior stencil 38 % interior stencil
78 switch order 39 order = 12;
79 case 2 40 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];
80 d = [-1/2,0,1/2];
81 case 4
82 d = [1/12,-2/3,0,2/3,-1/12];
83 case 6
84 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
85 case 8
86 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
87 case 10
88 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
89 case 12
90 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];
91 end
92 d = repmat(d,N,1); 41 d = repmat(d,N,1);
93 Q = spdiags(d,-order/2:order/2,N,N); 42 Q = spdiags(d,-order/2:order/2,N,N);
94 43
95 % Boundaries 44 % Boundaries
96 Q0_0 = -5.0000000000000e-01; 45 Q0_0 = -5.0000000000000e-01;