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annotate +sbp/D2VariableCompatible.m @ 1217:a3d9567d9004 feature/d2_compatible

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Improve efficiency of construction of D2(b) by precomputing as much as possible
author Martin Almquist <malmquist@stanford.edu>
date Wed, 13 Nov 2019 14:54:22 -0800
parents 2924b3a9b921
children 60c875c18de3
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2924b3a9b921 Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
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1 classdef D2VariableCompatible < sbp.OpSet
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2 properties
2924b3a9b921 Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
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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
2924b3a9b921 Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
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15 x % grid
2924b3a9b921 Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
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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
2924b3a9b921 Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
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20 function obj = D2VariableCompatible(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-1);
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26 obj.x = linspace(x_l,x_r,m)';
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27
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28 switch order
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29
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30 case 6
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31
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32 [obj.H, obj.HI, obj.D1, D2, ...
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33 ~, obj.e_l, obj.e_r, ~, ~, ~, ~, ~,...
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34 d1_l, d1_r] = ...
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35 sbp.implementations.d4_variable_6(m, obj.h);
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36
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37 case 4
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38 [obj.H, obj.HI, obj.D1, D2, obj.e_l,...
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39 obj.e_r, d1_l, d1_r] = ...
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40 sbp.implementations.d2_variable_4(m,obj.h);
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41 case 2
2924b3a9b921 Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
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42 [obj.H, obj.HI, obj.D1, D2, obj.e_l,...
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43 obj.e_r, d1_l, d1_r] = ...
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44 sbp.implementations.d2_variable_2(m,obj.h);
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45
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46 otherwise
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47 error('Invalid operator order %d.',order);
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48 end
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49 obj.borrowing.H11 = obj.H(1,1)/obj.h; % First element in H/h,
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50 obj.borrowing.M.d1 = obj.H(1,1)/obj.h; % First element in H/h is borrowing also for M
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51 obj.borrowing.R.delta_D = inf;
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52 obj.m = m;
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53 obj.M = [];
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56 D1 = obj.D1;
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57 e_r = obj.e_r;
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58 e_l = obj.e_l;
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60 % D2 = Hinv * (-M + br*er*d1r^T - bl*el*d1l^T);
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61 % Replace d1' by e'*D1 in D2.
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62 correction_l = obj.HI*(e_l*d1_l' - e_l*e_l'*D1);
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63 correction_r = - obj.HI*(e_r*d1_r' - e_r*e_r'*D1);
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64
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65 D2_compatible = @(b) D2(b) + b(1)*correction_l + b(m)*correction_r;
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67 obj.D2 = D2_compatible;
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68 obj.d1_l = (e_l'*D1)';
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69 obj.d1_r = (e_r'*D1)';
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71 end
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72 function str = string(obj)
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73 str = [class(obj) '_' num2str(obj.order)];
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74 end
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75 end
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78 end
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