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annotate +sbp/+implementations/d2_variable_periodic_2.m @ 1289:2fd2e2337b77 feature/boundary_optimized_grids

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Add utility function for constructing a (possibly multidimensional) grid based on the grid points used by the boundary optimized SBP operators
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 01 Jul 2020 15:15:30 +0200
parents bbf303c1f0cf
children
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Martin Almquist <malmquist@stanford.edu>
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1 function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_periodic_2(m,h)
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2 % m = number of unique grid points, i.e. h = L/m;
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3
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4 if(m<3)
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5 error(['Operator requires at least ' num2str(3) ' grid points']);
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6 end
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7
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8 % Norm
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Martin Almquist <malmquist@stanford.edu>
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9 Hv = ones(m,1);
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10 Hv = h*Hv;
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11 H = spdiag(Hv, 0);
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12 HI = spdiag(1./Hv, 0);
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13
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15 % Dummy boundary operators
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16 e_l = sparse(m,1);
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17 e_r = rot90(e_l, 2);
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18
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19 d1_l = sparse(m,1);
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20 d1_r = -rot90(d1_l, 2);
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21
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22 % D1 operator
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23 diags = -1:1;
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24 stencil = [-1/2 0 1/2];
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25 D1 = stripeMatrixPeriodic(stencil, diags, m);
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26 D1 = D1/h;
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27
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28 scheme_width = 3;
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29 scheme_radius = (scheme_width-1)/2;
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30
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31 r = 1:m;
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32 offset = scheme_width;
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33 r = r + offset;
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34
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35 function D2 = D2_fun(c)
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36 c = [c(end-scheme_width+1:end); c; c(1:scheme_width) ];
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37
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38 Mm1 = -c(r-1)/2 - c(r)/2;
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39 M0 = c(r-1)/2 + c(r) + c(r+1)/2;
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40 Mp1 = -c(r)/2 - c(r+1)/2;
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41
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42 vals = [Mm1,M0,Mp1];
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43 diags = -scheme_radius : scheme_radius;
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44 M = spdiagsPeriodic(vals,diags);
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45
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46 M=M/h;
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47 D2=HI*(-M );
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48 end
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49 D2 = @D2_fun;
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50 end