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annotate +sbp/+implementations/d1_noneq_minimal_8.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:
rev   line source
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_8(N,h)
261
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parents:
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2
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Martin Almquist <martin.almquist@it.uu.se>
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3 % N: Number of grid points
266
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Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
4 if(N<12)
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Martin Almquist <martin.almquist@it.uu.se>
parents: 261
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5 error('Operator requires at least 12 grid points');
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Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
6 end
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parents: 261
diff changeset
7
261
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diff changeset
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
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
12 P = sparse(BP,1);
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13 %#ok<*NASGU>
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14 P0 = 1.4523997892351e-01;
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15 P1 = 7.6864793350174e-01;
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16 P2 = 9.9116487068535e-01;
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17 P3 = 9.9992473335107e-01;
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18 P4 = 1.0002097054636e+00;
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19 P5 = 9.9996591555866e-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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parents:
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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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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
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33 order = 8;
4cb627c7fb90 Make D1Nonequidistant use the grid generation functions accurate/minimalBoundaryOptimizedGrid and remove grid generation from +implementations
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parents: 267
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34 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
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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 = 6.6697342753834e-01;
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41 Q0_2 = -2.2919342278749e-01;
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42 Q0_3 = 7.4283116457276e-02;
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43 Q0_4 = -1.2020661178873e-02;
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44 Q0_5 = -4.2460029252999e-05;
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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 Q0_9 = 0.0000000000000e+00;
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49 Q1_0 = -6.6697342753834e-01;
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50 Q1_1 = 0.0000000000000e+00;
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51 Q1_2 = 8.8241196934163e-01;
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52 Q1_3 = -2.6653314104602e-01;
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53 Q1_4 = 5.5302527504316e-02;
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54 Q1_5 = -4.2079282615860e-03;
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55 Q1_6 = 0.0000000000000e+00;
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56 Q1_7 = 0.0000000000000e+00;
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57 Q1_8 = 0.0000000000000e+00;
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58 Q1_9 = 0.0000000000000e+00;
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59 Q2_0 = 2.2919342278749e-01;
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60 Q2_1 = -8.8241196934163e-01;
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61 Q2_2 = 0.0000000000000e+00;
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62 Q2_3 = 8.2904844081126e-01;
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63 Q2_4 = -2.1156614214635e-01;
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64 Q2_5 = 3.9307676460659e-02;
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65 Q2_6 = -3.5714285714286e-03;
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66 Q2_7 = 0.0000000000000e+00;
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67 Q2_8 = 0.0000000000000e+00;
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68 Q2_9 = 0.0000000000000e+00;
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69 Q3_0 = -7.4283116457276e-02;
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70 Q3_1 = 2.6653314104602e-01;
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71 Q3_2 = -8.2904844081126e-01;
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72 Q3_3 = 0.0000000000000e+00;
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73 Q3_4 = 8.0305501223679e-01;
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74 Q3_5 = -2.0078040553808e-01;
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75 Q3_6 = 3.8095238095238e-02;
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76 Q3_7 = -3.5714285714286e-03;
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77 Q3_8 = 0.0000000000000e+00;
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78 Q3_9 = 0.0000000000000e+00;
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79 Q4_0 = 1.2020661178873e-02;
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80 Q4_1 = -5.5302527504316e-02;
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81 Q4_2 = 2.1156614214635e-01;
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82 Q4_3 = -8.0305501223679e-01;
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83 Q4_4 = 0.0000000000000e+00;
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84 Q4_5 = 8.0024692689207e-01;
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85 Q4_6 = -2.0000000000000e-01;
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86 Q4_7 = 3.8095238095238e-02;
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87 Q4_8 = -3.5714285714286e-03;
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88 Q4_9 = 0.0000000000000e+00;
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89 Q5_0 = 4.2460029252999e-05;
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90 Q5_1 = 4.2079282615860e-03;
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91 Q5_2 = -3.9307676460659e-02;
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92 Q5_3 = 2.0078040553808e-01;
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93 Q5_4 = -8.0024692689207e-01;
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94 Q5_5 = 0.0000000000000e+00;
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95 Q5_6 = 8.0000000000000e-01;
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96 Q5_7 = -2.0000000000000e-01;
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97 Q5_8 = 3.8095238095238e-02;
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98 Q5_9 = -3.5714285714286e-03;
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99 for i = 1:BP
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100 for j = 1:BP
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101 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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102 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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103 end
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104 end
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105 %%%%%%%%%%%%%%%%%%%%%%%%%%%
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106
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107 %%%% Difference operator %%
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108 D1 = H\Q;
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109 %%%%%%%%%%%%%%%%%%%%%%%%%%%