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comparison +sbp/+grid/accurateBoundaryOptimizedGrid.m @ 1300:196123459178

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Merge in feature/boundary_optimized_grids
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 08 Jul 2020 18:22:54 +0200
parents 0ffb5bfa65e4
children
comparison
equal deleted inserted replaced
1250:8ec777fb473e 1300:196123459178
1 % Computes the grid points x and grid spacing h used by the boundary optimized SBP operators
2 % with improved boundary accuracy, presented in
3 % 'Boundary optimized diagonal-norm SBP operators - Mattsson, Almquist, van der Weide 2018'.
4 %
5 % lim - cell array with domain limits
6 % N - Number of grid points
7 % order - order of accuracy of sbp operator.
8 function [x,h] = accurateBoundaryOptimizedGrid(lim,N,order)
9 assert(iscell(lim) && numel(lim) == 2,'The limit should be cell array with 2 elements.');
10 L = lim{2} - lim{1};
11 assert(L>0,'Limits must be given in increasing order.');
12 %%%% Non-equidistant grid points %%%%%
13 xb = boundaryPoints(order);
14 m = length(xb)-1; % Number of non-equidistant points
15 assert(N-2*(m+1)>=0,'Not enough grid points to contain the boundary region. Requires at least %d points.',2*(m+1));
16 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
17
18 %%%% Compute h %%%%%%%%%%
19 h = L/(2*xb(end) + N-1-2*m);
20 %%%%%%%%%%%%%%%%%%%%%%%%%
21
22 %%%% Define grid %%%%%%%%
23 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
24 x = x + lim{1};
25 %%%%%%%%%%%%%%%%%%%%%%%%%
26 end
27 function xb = boundaryPoints(order)
28 switch order
29 case 4
30 x0 = 0.0000000000000e+00;
31 x1 = 6.8764546205559e-01;
32 x2 = 1.8022115125776e+00;
33 xb = [x0 x1 x2]';
34 case 6
35 x0 = 0.0000000000000e+00;
36 x1 = 4.4090263368623e-01;
37 x2 = 1.2855984345073e+00;
38 x3 = 2.2638953951239e+00;
39 xb = [x0 x1 x2 x3]';
40 case 8
41 x0 = 0.0000000000000e+00;
42 x1 = 3.8118550247622e-01;
43 x2 = 1.1899550868338e+00;
44 x3 = 2.2476300175641e+00;
45 x4 = 3.3192851303204e+00;
46 xb = [x0 x1 x2 x3 x4]';
47 case 10
48 x0 = 0.0000000000000e+00;
49 x1 = 3.5902433622052e-01;
50 x2 = 1.1436659188355e+00;
51 x3 = 2.2144895894456e+00;
52 x4 = 3.3682742337736e+00;
53 x5 = 4.4309689056870e+00;
54 xb = [x0 x1 x2 x3 x4 x5]';
55 case 12
56 x0 = 0.0000000000000e+00;
57 x1 = 3.6098032343909e-01;
58 x2 = 1.1634317168086e+00;
59 x3 = 2.2975905356987e+00;
60 x4 = 3.6057529790929e+00;
61 x5 = 4.8918275675510e+00;
62 x6 = 6.0000000000000e+00;
63 xb = [x0 x1 x2 x3 x4 x5 x6]';
64 otherwise
65 error('Invalid operator order %d.',order);
66 end
67 end