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annotate +sbp/D2VariablePeriodic.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 5ccf6aaf6d6b
children
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7368affc8f78 Add D2 variable periodic for second order.
Martin Almquist <malmquist@stanford.edu>
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1 classdef D2VariablePeriodic < sbp.OpSet
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2 properties
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3 D1 % SBP operator approximating first derivative
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4 H % Norm matrix
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5 HI % H^-1
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6 Q % Skew-symmetric matrix
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7 e_l % Left boundary operator
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8 e_r % Right boundary operator
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9 D2 % SBP operator for second derivative
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10 M % Norm matrix, second derivative
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11 d1_l % Left boundary first derivative
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12 d1_r % Right boundary first derivative
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13 m % Number of grid points.
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14 h % Step size
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15 x % grid
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16 borrowing % Struct with borrowing limits for different norm matrices
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17 end
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18
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19 methods
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20 function obj = D2VariablePeriodic(m,lim,order)
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21
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22 x_l = lim{1};
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23 x_r = lim{2};
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24 L = x_r-x_l;
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25 obj.h = L/m;
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26 x = linspace(x_l,x_r,m+1)';
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27 obj.x = x(1:end-1);
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28
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29 switch order
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30
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bf2554f1825d Add periodic D1 and D2 operators for orders 8,10,12
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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31 case 12
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32 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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33 obj.e_r, obj.d1_l, obj.d1_r] = ...
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34 sbp.implementations.d2_variable_periodic_12(m,obj.h);
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35 obj.borrowing.M.d1 = obj.H(1, 1) / obj.h; % First element in H/h is borrowing also for M
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36 obj.borrowing.R.delta_D = inf;
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37
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38 case 10
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39 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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40 obj.e_r, obj.d1_l, obj.d1_r] = ...
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41 sbp.implementations.d2_variable_periodic_10(m,obj.h);
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42 obj.borrowing.M.d1 = obj.H(1, 1) / obj.h; % First element in H/h is borrowing also for M
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43 obj.borrowing.R.delta_D = inf;
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44
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45 case 8
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46 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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47 obj.e_r, obj.d1_l, obj.d1_r] = ...
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48 sbp.implementations.d2_variable_periodic_8(m,obj.h);
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49 obj.borrowing.M.d1 = obj.H(1, 1) / obj.h; % First element in H/h is borrowing also for M
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50 obj.borrowing.R.delta_D = inf;
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51
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52 case 6
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53 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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54 obj.e_r, obj.d1_l, obj.d1_r] = ...
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55 sbp.implementations.d2_variable_periodic_6(m,obj.h);
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56 obj.borrowing.M.d1 = 0.1878;
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57 obj.borrowing.R.delta_D = 0.3696;
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58 % Borrowing e^T*D1 - d1 from R
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59
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60 case 4
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61 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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62 obj.e_r, obj.d1_l, obj.d1_r] = ...
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63 sbp.implementations.d2_variable_periodic_4(m,obj.h);
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64 obj.borrowing.M.d1 = 0.2505765857;
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65
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66 obj.borrowing.R.delta_D = 0.577587500088313;
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67 % Borrowing e^T*D1 - d1 from R
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68 case 2
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69 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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70 obj.e_r, obj.d1_l, obj.d1_r] = ...
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71 sbp.implementations.d2_variable_periodic_2(m,obj.h);
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72 obj.borrowing.M.d1 = 0.3636363636;
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73 % Borrowing const taken from Virta 2014
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74
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75 obj.borrowing.R.delta_D = 1.000000538455350;
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76 % Borrowing e^T*D1 - d1 from R
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77
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78 otherwise
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79 error('Invalid operator order %d.',order);
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80 end
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81 obj.borrowing.H11 = obj.H(1,1)/obj.h; % First element in H/h,
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82
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83 obj.m = m;
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84 obj.M = [];
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85 end
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86 function str = string(obj)
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87 str = [class(obj) '_' num2str(obj.order)];
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88 end
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89 end
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90
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91
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92 end