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annotate +sbp/+implementations/d1_noneq_minimal_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 4cb627c7fb90
children
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1286
4cb627c7fb90 Make D1Nonequidistant use the grid generation functions accurate/minimalBoundaryOptimizedGrid and remove grid generation from +implementations
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 267
diff changeset
1 function [D1,H] = d1_noneq_minimal_4(N,h)
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2
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3 % N: Number of grid points
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4 if(N<6)
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5 error('Operator requires at least 6 grid points');
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6 end
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7
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8 % BP: Number of boundary points
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9 BP = 3;
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10
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11 %%%% Norm matrix %%%%%%%%
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12 P = sparse(BP,1);
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13 %#ok<*NASGU>
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14 P0 = 2.6864248295847e-01;
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15 P1 = 1.0094667153500e+00;
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16 P2 = 9.9312068011715e-01;
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17
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18 for i = 0:BP-1
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19 P(i+1) = eval(['P' num2str(i)]);
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20 end
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21
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22 H = ones(N,1);
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23 H(1:BP) = P;
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24 H(end-BP+1:end) = flip(P);
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25 H = spdiags(h*H,0,N,N);
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26 %%%%%%%%%%%%%%%%%%%%%%%%%
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27
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28 %%%% Q matrix %%%%%%%%%%%
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29 % interior stencil
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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30 order = 4;
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31 d = [1/12,-2/3,0,2/3,-1/12];
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32 d = repmat(d,N,1);
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33 Q = spdiags(d,-order/2:order/2,N,N);
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34
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35 % Boundaries
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36 Q0_0 = -5.0000000000000e-01;
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37 Q0_1 = 6.1697245625434e-01;
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38 Q0_2 = -1.1697245625434e-01;
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39 Q0_3 = 0.0000000000000e+00;
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40 Q0_4 = 0.0000000000000e+00;
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41 Q1_0 = -6.1697245625434e-01;
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42 Q1_1 = 0.0000000000000e+00;
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43 Q1_2 = 7.0030578958767e-01;
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44 Q1_3 = -8.3333333333333e-02;
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45 Q1_4 = 0.0000000000000e+00;
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46 Q2_0 = 1.1697245625434e-01;
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47 Q2_1 = -7.0030578958767e-01;
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48 Q2_2 = 0.0000000000000e+00;
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49 Q2_3 = 6.6666666666667e-01;
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50 Q2_4 = -8.3333333333333e-02;
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51 for i = 1:BP
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52 for j = 1:BP
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53 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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54 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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55 end
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56 end
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57 %%%%%%%%%%%%%%%%%%%%%%%%%%%
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58
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59 %%%% Difference operator %%
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60 D1 = H\Q;
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61 %%%%%%%%%%%%%%%%%%%%%%%%%%%