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annotate +sbp/D2Variable.m @ 1198:2924b3a9b921 feature/d2_compatible

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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.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 16 Aug 2019 14:30:28 -0700
parents 52a9dedb9171
children 738de3a4058b
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1 classdef D2Variable < 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 = D2Variable(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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30 case 6
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32 [obj.H, obj.HI, obj.D1, obj.D2, ...
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33 ~, obj.e_l, obj.e_r, ~, ~, ~, ~, ~,...
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34 obj.d1_l, obj.d1_r] = ...
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35 sbp.implementations.d4_variable_6(m, obj.h);
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36 obj.borrowing.M.d1 = 0.1878;
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37 obj.borrowing.R.delta_D = 0.3696;
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38 % Borrowing e^T*D1 - d1 from R
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39
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40 case 4
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41 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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42 obj.e_r, obj.d1_l, obj.d1_r] = ...
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43 sbp.implementations.d2_variable_4(m,obj.h);
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44 obj.borrowing.M.d1 = 0.2505765857;
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46 obj.borrowing.R.delta_D = 0.577587500088313;
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47 % Borrowing e^T*D1 - d1 from R
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48 case 2
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49 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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50 obj.e_r, obj.d1_l, obj.d1_r] = ...
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51 sbp.implementations.d2_variable_2(m,obj.h);
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52 obj.borrowing.M.d1 = 0.3636363636;
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53 % Borrowing const taken from Virta 2014
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55 obj.borrowing.R.delta_D = 1.000000538455350;
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56 % Borrowing e^T*D1 - d1 from R
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58 otherwise
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59 error('Invalid operator order %d.',order);
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60 end
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61 obj.borrowing.H11 = obj.H(1,1)/obj.h; % First element in H/h,
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62 obj.m = m;
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63 obj.M = [];
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64 end
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65 function str = string(obj)
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66 str = [class(obj) '_' num2str(obj.order)];
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67 end
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68 end
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71 end
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