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annotate +sbp/+implementations/d2_variable_periodic_4.m @ 1037:2d7ba44340d0 feature/burgers1d

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Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 18 Jan 2019 09:02:02 +0100
parents bbf303c1f0cf
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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5ccf6aaf6d6b Add D2VariablePeriodic orders 4 and 6.
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_4(m,h)
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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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4 if(m<5)
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5 error(['Operator requires at least ' num2str(5) ' grid points']);
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6 end
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7
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Martin Almquist <malmquist@stanford.edu>
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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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Martin Almquist <malmquist@stanford.edu>
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10 Hv = h*Hv;
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Martin Almquist <malmquist@stanford.edu>
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11 H = spdiag(Hv, 0);
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Martin Almquist <malmquist@stanford.edu>
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12 HI = spdiag(1./Hv, 0);
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13
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14
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Martin Almquist <malmquist@stanford.edu>
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15 % Dummy boundary operators
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Martin Almquist <malmquist@stanford.edu>
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16 e_l = sparse(m,1);
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Martin Almquist <malmquist@stanford.edu>
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17 e_r = rot90(e_l, 2);
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18
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Martin Almquist <malmquist@stanford.edu>
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19 d1_l = sparse(m,1);
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Martin Almquist <malmquist@stanford.edu>
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20 d1_r = -rot90(d1_l, 2);
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21
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Martin Almquist <malmquist@stanford.edu>
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22 S = d1_l*d1_l' + d1_r*d1_r';
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23
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Martin Almquist <malmquist@stanford.edu>
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24 % D1 operator
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Martin Almquist <malmquist@stanford.edu>
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25 stencil = [1/12 -2/3 0 2/3 -1/12];
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Martin Almquist <malmquist@stanford.edu>
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26 diags = -2:2;
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Martin Almquist <malmquist@stanford.edu>
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27 Q = stripeMatrixPeriodic(stencil, diags, m);
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Martin Almquist <malmquist@stanford.edu>
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28 D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r');
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29
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30
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Martin Almquist <malmquist@stanford.edu>
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31 scheme_width = 5;
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Martin Almquist <malmquist@stanford.edu>
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32 scheme_radius = (scheme_width-1)/2;
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Jonatan Werpers <jonatan@werpers.com>
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33
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34 r = 1:m;
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Martin Almquist <malmquist@stanford.edu>
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35 offset = scheme_width;
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36 r = r + offset;
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37
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38 function D2 = D2_fun(c)
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39 c = [c(end-scheme_width+1:end); c; c(1:scheme_width) ];
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40
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Martin Almquist <malmquist@stanford.edu>
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41 % Note: these coefficients are for -M.
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Martin Almquist <malmquist@stanford.edu>
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42 Mm2 = -1/8*c(r-2) + 1/6*c(r-1) - 1/8*c(r);
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Martin Almquist <malmquist@stanford.edu>
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43 Mm1 = 1/6 *c(r-2) + 1/2*c(r-1) + 1/2*c(r) + 1/6*c(r+1);
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Martin Almquist <malmquist@stanford.edu>
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44 M0 = -1/24*c(r-2)- 5/6*c(r-1) - 3/4*c(r) - 5/6*c(r+1) - 1/24*c(r+2);
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45 Mp1 = 0 * c(r-2) + 1/6*c(r-1) + 1/2*c(r) + 1/2*c(r+1) + 1/6 *c(r+2);
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46 Mp2 = 0 * c(r-2) + 0 * c(r-1) - 1/8*c(r) + 1/6*c(r+1) - 1/8 *c(r+2);
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47
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48 vals = -[Mm2,Mm1,M0,Mp1,Mp2];
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49 diags = -scheme_radius : scheme_radius;
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50 M = spdiagsPeriodic(vals,diags);
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51
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52 M=M/h;
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53 D2=HI*(-M );
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54
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55 end
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Martin Almquist <malmquist@stanford.edu>
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56 D2 = @D2_fun;
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57 end