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comparison +sbp/+implementations/d1_noneq_4.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_4(N,L) 1 function [D1,H] = d1_noneq_4(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<8) 4 if(N<8)
10 error('Operator requires at least 8 grid points'); 5 error('Operator requires at least 8 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 = 4; 9 BP = 4;
17 m = 2;
18 order = 4;
19
20 %%%% Non-equidistant grid points %%%%%
21 x0 = 0.0000000000000e+00;
22 x1 = 6.8764546205559e-01;
23 x2 = 1.8022115125776e+00;
24 x3 = 2.8022115125776e+00;
25 x4 = 3.8022115125776e+00;
26
27 xb = sparse(m+1,1);
28 for i = 0:m
29 xb(i+1) = eval(['x' num2str(i)]);
30 end
31 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
32
33 %%%% Compute h %%%%%%%%%%
34 h = L/(2*xb(end) + N-1-2*m);
35 %%%%%%%%%%%%%%%%%%%%%%%%%
36
37 %%%% Define grid %%%%%%%%
38 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
39 %%%%%%%%%%%%%%%%%%%%%%%%%
40 10
41 %%%% Norm matrix %%%%%%%% 11 %%%% Norm matrix %%%%%%%%
42 P = sparse(BP,1); 12 P = sparse(BP,1);
43 %#ok<*NASGU> 13 %#ok<*NASGU>
44 P0 = 2.1259737557798e-01; 14 P0 = 2.1259737557798e-01;
55 H(end-BP+1:end) = flip(P); 25 H(end-BP+1:end) = flip(P);
56 H = spdiags(h*H,0,N,N); 26 H = spdiags(h*H,0,N,N);
57 %%%%%%%%%%%%%%%%%%%%%%%%% 27 %%%%%%%%%%%%%%%%%%%%%%%%%
58 28
59 %%%% Q matrix %%%%%%%%%%% 29 %%%% Q matrix %%%%%%%%%%%
60
61 % interior stencil 30 % interior stencil
62 switch order 31 order = 4;
63 case 2 32 d = [1/12,-2/3,0,2/3,-1/12];
64 d = [-1/2,0,1/2];
65 case 4
66 d = [1/12,-2/3,0,2/3,-1/12];
67 case 6
68 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
69 case 8
70 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
71 case 10
72 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
73 case 12
74 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];
75 end
76 d = repmat(d,N,1); 33 d = repmat(d,N,1);
77 Q = spdiags(d,-order/2:order/2,N,N); 34 Q = spdiags(d,-order/2:order/2,N,N);
78 35
79 % Boundaries 36 % Boundaries
80 Q0_0 = -5.0000000000000e-01; 37 Q0_0 = -5.0000000000000e-01;