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annotate +sbp/+implementations/d2_variable_hollow_4.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_4(m,h)
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2
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3 BP = 6;
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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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11 % Norm
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12 Hv = ones(m,1);
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13 Hv(1:4) = [17/48 59/48 43/48 49/48];
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14 Hv(m-3:m) = rot90(Hv(1:4),2);
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15 Hv = h*Hv;
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16 H = spdiag(Hv, 0);
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17 HI = spdiag(1./Hv, 0);
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19
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20 % Boundary operators
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21 e_l = sparse(m,1);
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22 e_l(1) = 1;
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23 e_r = rot90(e_l, 2);
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24
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25 d1_l = sparse(m,1);
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26 d1_l(1:4) = 1/h*[-11/6 3 -3/2 1/3];
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27 d1_r = -rot90(d1_l, 2);
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32 S = d1_l*d1_l' + d1_r*d1_r';
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33
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34 stencil = [1/12 -2/3 0 2/3 -1/12];
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35 diags = -2:2;
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36
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37 Q_U = [
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38 0 0.59e2/0.96e2 -0.1e1/0.12e2 -0.1e1/0.32e2;
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39 -0.59e2/0.96e2 0 0.59e2/0.96e2 0;
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40 0.1e1/0.12e2 -0.59e2/0.96e2 0 0.59e2/0.96e2;
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41 0.1e1/0.32e2 0 -0.59e2/0.96e2 0;
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42 ];
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43
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44 Q = stripeMatrix(stencil, diags, m);
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45 Q(1:4,1:4) = Q_U;
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46 Q(m-3:m,m-3:m) = -rot90(Q_U, 2);
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47
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48 D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r');
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50
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51 % Second derivative
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52 nBP = 6;
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53 M = sparse(m,m);
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54 coeffs = load('sbplib/+sbp/+implementations/coeffs_d2_variable_4.mat');
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55
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56 function D2 = D2_fun(c)
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57 M_l = zeros(nBP, coeffs.nBPC);
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58 M_r = zeros(nBP, coeffs.nBPC);
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60 for i=1:coeffs.nBPC
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61 M_l = M_l + coeffs.C_l{i}*c(i);
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62 M_r = M_r + coeffs.C_r{i}*c(m-coeffs.nBPC+i);
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63 end
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65 M(1:nBP, 1:coeffs.nBPC) = M_l;
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66 M(m-nBP+1:m, m-coeffs.nBPC+1:m) = M_r;
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67
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68 D2 = M/h^2;
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69 end
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70 D2 = @D2_fun;
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72 end