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annotate +sbp/+util/minimalBoundaryOptimizedGrid.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] = minimalBoundaryOptimizedGrid(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));
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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7
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
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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 %%%%%%%%%%%%%%%%%%%%%%%%%
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11
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
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12 %%%% Define grid %%%%%%%%
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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) ];
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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14 %%%%%%%%%%%%%%%%%%%%%%%%%
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15 end
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
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16
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 function xb = boundaryPoints(order)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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18 switch order
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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19 case 4
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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20 x0 = 0.0000000000000e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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21 x1 = 7.7122987842562e-01;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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22 xb = [x0 x1]';
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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 = 4.0842950991998e-01;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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26 x2 = 1.1968523189207e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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27 xb = [x0 x1 x2]';
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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28 case 8
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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29 x0 = 0.0000000000000e+00;
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30 x1 = 4.9439570885261e-01;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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31 x2 = 1.4051531374839e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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32 xb = [x0 x1 x2]';
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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33 case 10
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34 x0 = 0.0000000000000e+00;
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35 x1 = 5.8556160757529e-01;
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36 x2 = 1.7473267488572e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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37 x3 = 3.0000000000000e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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38 xb = [x0 x1 x2 x3]';
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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39 case 12
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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40 x0 = 0.0000000000000e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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41 x1 = 4.6552112904489e-01;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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42 x2 = 1.4647984306493e+00;
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43 x3 = 2.7620429464763e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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44 x4 = 4.0000000000000e+00;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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45 xb = [x0 x1 x2 x3 x4]';
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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46 otherwise
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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47 error('Invalid operator order %d.',order);
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48 end
6b68f939d023 Add utility functions for constructing the grids used by the boundary optimized D1Nonequidistant opsets
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49 end