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annotate +sbp/D2VariablePeriodic.m @ 1037:2d7ba44340d0 feature/burgers1d

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Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 18 Jan 2019 09:02:02 +0100
parents 5ccf6aaf6d6b
children bf2554f1825d
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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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31 case 6
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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_6(m,obj.h);
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35 obj.borrowing.M.d1 = 0.1878;
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36 obj.borrowing.R.delta_D = 0.3696;
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37 % Borrowing e^T*D1 - d1 from R
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38
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39 case 4
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40 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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41 obj.e_r, obj.d1_l, obj.d1_r] = ...
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42 sbp.implementations.d2_variable_periodic_4(m,obj.h);
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43 obj.borrowing.M.d1 = 0.2505765857;
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44
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45 obj.borrowing.R.delta_D = 0.577587500088313;
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46 % Borrowing e^T*D1 - d1 from R
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47 case 2
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48 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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49 obj.e_r, obj.d1_l, obj.d1_r] = ...
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50 sbp.implementations.d2_variable_periodic_2(m,obj.h);
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51 obj.borrowing.M.d1 = 0.3636363636;
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52 % Borrowing const taken from Virta 2014
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53
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54 obj.borrowing.R.delta_D = 1.000000538455350;
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55 % Borrowing e^T*D1 - d1 from R
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56
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57 otherwise
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58 error('Invalid operator order %d.',order);
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59 end
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60 obj.borrowing.H11 = obj.H(1,1)/obj.h; % First element in H/h,
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61
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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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70
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71 end