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comparison +sbp/+implementations/d1_noneq_minimal_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_minimal_4(N,L) 1 function [D1,H] = d1_noneq_minimal_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<6) 4 if(N<6)
10 error('Operator requires at least 6 grid points'); 5 error('Operator requires at least 6 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 = 3; 9 BP = 3;
17 m = 1;
18 order = 4;
19
20 %%%% Non-equidistant grid points %%%%%
21 x0 = 0.0000000000000e+00;
22 x1 = 7.7122987842562e-01;
23 x2 = 1.7712298784256e+00;
24 x3 = 2.7712298784256e+00;
25
26 xb = sparse(m+1,1);
27 for i = 0:m
28 xb(i+1) = eval(['x' num2str(i)]);
29 end
30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
31
32 %%%% Compute h %%%%%%%%%%
33 h = L/(2*xb(end) + N-1-2*m);
34 %%%%%%%%%%%%%%%%%%%%%%%%%
35
36 %%%% Define grid %%%%%%%%
37 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
38 %%%%%%%%%%%%%%%%%%%%%%%%%
39 10
40 %%%% Norm matrix %%%%%%%% 11 %%%% Norm matrix %%%%%%%%
41 P = sparse(BP,1); 12 P = sparse(BP,1);
42 %#ok<*NASGU> 13 %#ok<*NASGU>
43 P0 = 2.6864248295847e-01; 14 P0 = 2.6864248295847e-01;
53 H(end-BP+1:end) = flip(P); 24 H(end-BP+1:end) = flip(P);
54 H = spdiags(h*H,0,N,N); 25 H = spdiags(h*H,0,N,N);
55 %%%%%%%%%%%%%%%%%%%%%%%%% 26 %%%%%%%%%%%%%%%%%%%%%%%%%
56 27
57 %%%% Q matrix %%%%%%%%%%% 28 %%%% Q matrix %%%%%%%%%%%
58
59 % interior stencil 29 % interior stencil
60 switch order 30 order = 4;
61 case 2 31 d = [1/12,-2/3,0,2/3,-1/12];
62 d = [-1/2,0,1/2];
63 case 4
64 d = [1/12,-2/3,0,2/3,-1/12];
65 case 6
66 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
67 case 8
68 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
69 case 10
70 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
71 case 12
72 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];
73 end
74 d = repmat(d,N,1); 32 d = repmat(d,N,1);
75 Q = spdiags(d,-order/2:order/2,N,N); 33 Q = spdiags(d,-order/2:order/2,N,N);
76 34
77 % Boundaries 35 % Boundaries
78 Q0_0 = -5.0000000000000e-01; 36 Q0_0 = -5.0000000000000e-01;