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annotate +sbp/+implementations/d1_noneq_6.m @ 1286:4cb627c7fb90 feature/boundary_optimized_grids

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Make D1Nonequidistant use the grid generation functions accurate/minimalBoundaryOptimizedGrid and remove grid generation from +implementations
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 01 Jul 2020 13:43:32 +0200
parents f7ac3cd6eeaa
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_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<12)
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5 error('Operator requires at least 12 grid points');
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6 end
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7
261
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8 % BP: Number of boundary points
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9 BP = 6;
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10
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11 %%%% Norm matrix %%%%%%%%
267
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Martin Almquist <martin.almquist@it.uu.se>
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12 P = sparse(BP,1);
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13 %#ok<*NASGU>
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14 P0 = 1.3030223027124e-01;
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15 P1 = 6.8851501587715e-01;
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16 P2 = 9.5166202564389e-01;
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17 P3 = 9.9103890475697e-01;
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18 P4 = 1.0028757074552e+00;
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19 P5 = 9.9950151111941e-01;
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20
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21 for i = 0:BP-1
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22 P(i+1) = eval(['P' num2str(i)]);
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23 end
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24
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25 H = ones(N,1);
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26 H(1:BP) = P;
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27 H(end-BP+1:end) = flip(P);
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28 H = spdiags(h*H,0,N,N);
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29 %%%%%%%%%%%%%%%%%%%%%%%%%
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30
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31 %%%% Q matrix %%%%%%%%%%%
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32 % interior stencil
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 267
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33 order = 6;
4cb627c7fb90 Make D1Nonequidistant use the grid generation functions accurate/minimalBoundaryOptimizedGrid and remove grid generation from +implementations
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34 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
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35 d = repmat(d,N,1);
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36 Q = spdiags(d,-order/2:order/2,N,N);
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37
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38 % Boundaries
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39 Q0_0 = -5.0000000000000e-01;
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40 Q0_1 = 6.6042071945824e-01;
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41 Q0_2 = -2.2104152954203e-01;
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42 Q0_3 = 7.6243679810093e-02;
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43 Q0_4 = -1.7298206716724e-02;
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44 Q0_5 = 1.6753369904210e-03;
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45 Q0_6 = 0.0000000000000e+00;
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46 Q0_7 = 0.0000000000000e+00;
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47 Q0_8 = 0.0000000000000e+00;
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48 Q1_0 = -6.6042071945824e-01;
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49 Q1_1 = 0.0000000000000e+00;
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50 Q1_2 = 8.7352798702787e-01;
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51 Q1_3 = -2.6581719253084e-01;
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52 Q1_4 = 5.7458484948314e-02;
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53 Q1_5 = -4.7485599871040e-03;
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54 Q1_6 = 0.0000000000000e+00;
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55 Q1_7 = 0.0000000000000e+00;
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56 Q1_8 = 0.0000000000000e+00;
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57 Q2_0 = 2.2104152954203e-01;
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58 Q2_1 = -8.7352798702787e-01;
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59 Q2_2 = 0.0000000000000e+00;
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60 Q2_3 = 8.1707122038457e-01;
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61 Q2_4 = -1.8881125503769e-01;
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62 Q2_5 = 2.4226492138960e-02;
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63 Q2_6 = 0.0000000000000e+00;
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64 Q2_7 = 0.0000000000000e+00;
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65 Q2_8 = 0.0000000000000e+00;
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66 Q3_0 = -7.6243679810093e-02;
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67 Q3_1 = 2.6581719253084e-01;
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68 Q3_2 = -8.1707122038457e-01;
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69 Q3_3 = 0.0000000000000e+00;
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70 Q3_4 = 7.6798636652679e-01;
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71 Q3_5 = -1.5715532552963e-01;
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72 Q3_6 = 1.6666666666667e-02;
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73 Q3_7 = 0.0000000000000e+00;
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74 Q3_8 = 0.0000000000000e+00;
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75 Q4_0 = 1.7298206716724e-02;
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76 Q4_1 = -5.7458484948314e-02;
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77 Q4_2 = 1.8881125503769e-01;
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78 Q4_3 = -7.6798636652679e-01;
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79 Q4_4 = 0.0000000000000e+00;
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80 Q4_5 = 7.5266872305402e-01;
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81 Q4_6 = -1.5000000000000e-01;
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82 Q4_7 = 1.6666666666667e-02;
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83 Q4_8 = 0.0000000000000e+00;
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84 Q5_0 = -1.6753369904210e-03;
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85 Q5_1 = 4.7485599871040e-03;
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86 Q5_2 = -2.4226492138960e-02;
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87 Q5_3 = 1.5715532552963e-01;
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88 Q5_4 = -7.5266872305402e-01;
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89 Q5_5 = 0.0000000000000e+00;
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90 Q5_6 = 7.5000000000000e-01;
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91 Q5_7 = -1.5000000000000e-01;
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92 Q5_8 = 1.6666666666667e-02;
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93 for i = 1:BP
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94 for j = 1:BP
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95 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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96 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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97 end
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98 end
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99 %%%%%%%%%%%%%%%%%%%%%%%%%%%
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100
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101 %%%% Difference operator %%
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102 D1 = H\Q;
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103 %%%%%%%%%%%%%%%%%%%%%%%%%%%