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Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic
author Martin Almquist <malmquist@stanford.edu>
date Thu, 05 Sep 2019 14:13:00 -0700
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children 60c875c18de3
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1 classdef D2VariableCompatible < 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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19 methods
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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
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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 D2_compatible = @(b) D2(b) - obj.HI*(b(m)*e_r*d1_r' - b(m)*e_r*e_r'*D1) ...
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63 + obj.HI*(b(1)*e_l*d1_l' - b(1)*e_l*e_l'*D1);
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64
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65 obj.D2 = D2_compatible;
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66 obj.d1_l = (e_l'*D1)';
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67 obj.d1_r = (e_r'*D1)';
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68
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69 end
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70 function str = string(obj)
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71 str = [class(obj) '_' num2str(obj.order)];
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72 end
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76 end
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