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annotate +sbp/+util/accurateBoundaryOptimizedGrid.m @ 1285:6b68f939d023 feature/boundary_optimized_grids

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Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 01 Jul 2020 11:15:57 +0200
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children 38653d26225c
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1285
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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1 function [x,h] = accurateBoundaryOptimizedGrid(L,N,order)
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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2 %%%% Non-equidistant grid points %%%%%
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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3 xb = boundaryPoints(order);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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4 m = length(xb)-1; % Number of non-equidistant points
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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5 assert(N-2*(m+1)>=0,'Not enough grid points to contain the boundary region. Requires at least %d points.',2*(m+1));
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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7
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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8 %%%% Compute h %%%%%%%%%%
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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9 h = L/(2*xb(end) + N-1-2*m);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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10 %%%%%%%%%%%%%%%%%%%%%%%%%
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
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11
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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12 %%%% Define grid %%%%%%%%
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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13 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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14 %%%%%%%%%%%%%%%%%%%%%%%%%
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
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15 end
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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16 function xb = boundaryPoints(order)
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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17 switch order
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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18 case 4
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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19 x0 = 0.0000000000000e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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20 x1 = 6.8764546205559e-01;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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21 x2 = 1.8022115125776e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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22 xb = [x0 x1 x2]';
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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23 case 6
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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24 x0 = 0.0000000000000e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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25 x1 = 4.4090263368623e-01;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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26 x2 = 1.2855984345073e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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27 x3 = 2.2638953951239e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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28 xb = [x0 x1 x2 x3]';
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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29 case 8
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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30 x0 = 0.0000000000000e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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31 x1 = 3.8118550247622e-01;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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32 x2 = 1.1899550868338e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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33 x3 = 2.2476300175641e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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34 x4 = 3.3192851303204e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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35 xb = [x0 x1 x2 x3 x4]';
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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36 case 10
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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37 x0 = 0.0000000000000e+00;
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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38 x1 = 3.5902433622052e-01;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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39 x2 = 1.1436659188355e+00;
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40 x3 = 2.2144895894456e+00;
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41 x4 = 3.3682742337736e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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42 x5 = 4.4309689056870e+00;
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43 xb = [x0 x1 x2 x3 x4 x5]';
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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44 case 12
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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45 x0 = 0.0000000000000e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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46 x1 = 3.6098032343909e-01;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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47 x2 = 1.1634317168086e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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48 x3 = 2.2975905356987e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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49 x4 = 3.6057529790929e+00;
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50 x5 = 4.8918275675510e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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51 x6 = 6.0000000000000e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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52 xb = [x0 x1 x2 x3 x4 x5 x6]';
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53 otherwise
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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54 error('Invalid operator order %d.',order);
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55 end
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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56 end