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annotate +sbp/+implementations/d2_variable_hollow_2.m @ 1337:bf2554f1825d feature/D2_boundary_opt

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Add periodic D1 and D2 operators for orders 8,10,12
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 13 May 2022 13:28:10 +0200
parents b5907140c069
children
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49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet
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_hollow_2(m,h)
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2
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3 BP = 1;
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4 if(m<2*BP)
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5 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
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6 end
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8 % Norm
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9 Hv = ones(m,1);
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10 Hv(1) = 1/2;
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11 Hv(m:m) = 1/2;
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12 Hv = h*Hv;
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13 H = spdiag(Hv, 0);
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14 HI = spdiag(1./Hv, 0);
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17 % Boundary operators
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18 e_l = sparse(m,1);
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19 e_l(1) = 1;
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20 e_r = rot90(e_l, 2);
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21
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22 d1_l = sparse(m,1);
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23 d1_l(1:3) = 1/h*[-3/2 2 -1/2];
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24 d1_r = -rot90(d1_l, 2);
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25
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26 % D1 operator
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27 diags = -1:1;
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28 stencil = [-1/2 0 1/2];
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29 D1 = stripeMatrix(stencil, diags, m);
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31 D1(1,1)=-1;D1(1,2)=1;D1(m,m-1)=-1;D1(m,m)=1;
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32 D1(m,m-1)=-1;D1(m,m)=1;
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33 D1=D1/h;
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34 %Q=H*D1 + 1/2*(e_1*e_1') - 1/2*(e_m*e_m');
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37 nBP = 2;
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38 M = sparse(m,m);
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39 coeffs = load('sbplib/+sbp/+implementations/coeffs_d2_variable_2.mat');
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40
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41 function D2 = D2_fun(c)
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42 M_l = zeros(nBP, coeffs.nBPC);
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43 M_r = zeros(nBP, coeffs.nBPC);
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44
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45 for i=1:coeffs.nBPC
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46 M_l = M_l + coeffs.C_l{i}*c(i);
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47 M_r = M_r + coeffs.C_r{i}*c(m-coeffs.nBPC+i);
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48 end
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49
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50 M(1:nBP, 1:coeffs.nBPC) = M_l;
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51 M(m-nBP+1:m, m-coeffs.nBPC+1:m) = M_r;
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52
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53 D2 = M/h^2;
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54 end
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55 D2 = @D2_fun;
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56 end