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annotate +sbp/+implementations/d1_noneq_minimal_6.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
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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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_6(N,h)
261
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2
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3 % N: Number of grid points
266
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Martin Almquist <martin.almquist@it.uu.se>
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4 if(N<10)
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5 error('Operator requires at least 10 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 = 5;
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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 = 1.2740260779883e-01;
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15 P1 = 6.1820981002054e-01;
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16 P2 = 9.4308973897679e-01;
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17 P3 = 1.0093019060199e+00;
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18 P4 = 9.9884825610465e-01;
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19
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20 for i = 0:BP-1
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21 P(i+1) = eval(['P' num2str(i)]);
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22 end
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23
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24 H = ones(N,1);
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25 H(1:BP) = P;
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26 H(end-BP+1:end) = flip(P);
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27 H = spdiags(h*H,0,N,N);
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28 %%%%%%%%%%%%%%%%%%%%%%%%%
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29
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30 %%%% Q matrix %%%%%%%%%%%
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31 % interior stencil
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 267
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32 order = 6;
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33 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
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34 d = repmat(d,N,1);
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35 Q = spdiags(d,-order/2:order/2,N,N);
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36
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37 % Boundaries
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38 Q0_0 = -5.0000000000000e-01;
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39 Q0_1 = 6.3217364546846e-01;
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40 Q0_2 = -1.6411963429825e-01;
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41 Q0_3 = 3.6495407984639e-02;
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42 Q0_4 = -4.5494191548490e-03;
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43 Q0_5 = 0.0000000000000e+00;
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44 Q0_6 = 0.0000000000000e+00;
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45 Q0_7 = 0.0000000000000e+00;
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46 Q1_0 = -6.3217364546846e-01;
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47 Q1_1 = 0.0000000000000e+00;
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48 Q1_2 = 8.0515625504417e-01;
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49 Q1_3 = -2.0755653563249e-01;
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50 Q1_4 = 3.4573926056780e-02;
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51 Q1_5 = 0.0000000000000e+00;
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52 Q1_6 = 0.0000000000000e+00;
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53 Q1_7 = 0.0000000000000e+00;
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54 Q2_0 = 1.6411963429825e-01;
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55 Q2_1 = -8.0515625504417e-01;
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56 Q2_2 = 0.0000000000000e+00;
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57 Q2_3 = 7.9402676057785e-01;
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58 Q2_4 = -1.6965680649860e-01;
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59 Q2_5 = 1.6666666666667e-02;
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60 Q2_6 = 0.0000000000000e+00;
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61 Q2_7 = 0.0000000000000e+00;
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62 Q3_0 = -3.6495407984639e-02;
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63 Q3_1 = 2.0755653563249e-01;
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64 Q3_2 = -7.9402676057785e-01;
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65 Q3_3 = 0.0000000000000e+00;
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66 Q3_4 = 7.5629896626333e-01;
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67 Q3_5 = -1.5000000000000e-01;
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68 Q3_6 = 1.6666666666667e-02;
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69 Q3_7 = 0.0000000000000e+00;
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70 Q4_0 = 4.5494191548490e-03;
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71 Q4_1 = -3.4573926056780e-02;
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72 Q4_2 = 1.6965680649860e-01;
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73 Q4_3 = -7.5629896626333e-01;
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74 Q4_4 = 0.0000000000000e+00;
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75 Q4_5 = 7.5000000000000e-01;
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76 Q4_6 = -1.5000000000000e-01;
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77 Q4_7 = 1.6666666666667e-02;
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78 for i = 1:BP
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79 for j = 1:BP
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80 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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81 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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82 end
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83 end
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84 %%%%%%%%%%%%%%%%%%%%%%%%%%%
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85
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86 %%%% Difference operator %%
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87 D1 = H\Q;
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88 %%%%%%%%%%%%%%%%%%%%%%%%%%%