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annotate +sbp/+grid/accurateBoundaryOptimizedGrid.m @ 1298:0ffb5bfa65e4 feature/boundary_optimized_grids

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author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Tue, 07 Jul 2020 16:23:44 +0200
parents e53b1e25970a
children
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1298
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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1 % Computes the grid points x and grid spacing h used by the boundary optimized SBP operators
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2 % with improved boundary accuracy, presented in
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3 % 'Boundary optimized diagonal-norm SBP operators - Mattsson, Almquist, van der Weide 2018'.
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4 %
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5 % lim - cell array with domain limits
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6 % N - Number of grid points
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7 % order - order of accuracy of sbp operator.
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8 function [x,h] = accurateBoundaryOptimizedGrid(lim,N,order)
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9 assert(iscell(lim) && numel(lim) == 2,'The limit should be cell array with 2 elements.');
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10 L = lim{2} - lim{1};
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11 assert(L>0,'Limits must be given in increasing order.');
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12 %%%% Non-equidistant grid points %%%%%
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13 xb = boundaryPoints(order);
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14 m = length(xb)-1; % Number of non-equidistant points
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15 assert(N-2*(m+1)>=0,'Not enough grid points to contain the boundary region. Requires at least %d points.',2*(m+1));
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16 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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17
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18 %%%% Compute h %%%%%%%%%%
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19 h = L/(2*xb(end) + N-1-2*m);
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20 %%%%%%%%%%%%%%%%%%%%%%%%%
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21
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22 %%%% Define grid %%%%%%%%
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23 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
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24 x = x + lim{1};
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25 %%%%%%%%%%%%%%%%%%%%%%%%%
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26 end
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27 function xb = boundaryPoints(order)
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28 switch order
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29 case 4
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30 x0 = 0.0000000000000e+00;
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31 x1 = 6.8764546205559e-01;
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32 x2 = 1.8022115125776e+00;
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33 xb = [x0 x1 x2]';
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34 case 6
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35 x0 = 0.0000000000000e+00;
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36 x1 = 4.4090263368623e-01;
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37 x2 = 1.2855984345073e+00;
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38 x3 = 2.2638953951239e+00;
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39 xb = [x0 x1 x2 x3]';
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40 case 8
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41 x0 = 0.0000000000000e+00;
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42 x1 = 3.8118550247622e-01;
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43 x2 = 1.1899550868338e+00;
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44 x3 = 2.2476300175641e+00;
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45 x4 = 3.3192851303204e+00;
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46 xb = [x0 x1 x2 x3 x4]';
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47 case 10
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48 x0 = 0.0000000000000e+00;
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49 x1 = 3.5902433622052e-01;
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50 x2 = 1.1436659188355e+00;
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51 x3 = 2.2144895894456e+00;
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52 x4 = 3.3682742337736e+00;
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53 x5 = 4.4309689056870e+00;
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54 xb = [x0 x1 x2 x3 x4 x5]';
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55 case 12
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56 x0 = 0.0000000000000e+00;
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57 x1 = 3.6098032343909e-01;
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58 x2 = 1.1634317168086e+00;
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59 x3 = 2.2975905356987e+00;
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60 x4 = 3.6057529790929e+00;
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61 x5 = 4.8918275675510e+00;
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62 x6 = 6.0000000000000e+00;
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63 xb = [x0 x1 x2 x3 x4 x5 x6]';
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64 otherwise
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65 error('Invalid operator order %d.',order);
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66 end
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67 end