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annotate +sbp/+implementations/d2_variable_periodic_2.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents bbf303c1f0cf
children
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7368affc8f78 Add D2 variable periodic for second order.
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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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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14
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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