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annotate +sbp/D4Variable.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 42c89b5eedc0
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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c0cbffcf6513 Created new operator class for lonely D4 operators. Removed some output parameters of implementations.
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1 classdef D4Variable < sbp.OpSet
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2 properties
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3 m % Number of grid points.
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4 h % Step size
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5 x % grid
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31d6698c1edf Clean up and fixing of new operators
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6 H % Norm matrix
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7 HI % H^-1
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8 D1 % SBP operator approximating first derivative
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9 D2 % SBP operator for second derivative
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10 D4 % SBP operator for fourth derivative
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11 Q % Skew-symmetric matrix
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12 M % Norm matrix, second derivative
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13 M4 % Norm matrix, fourth derivative
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14 e_l, e_r % Left and right boundary operator
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15 d1_l, d1_r % Left and right boundary first derivative
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16 d2_l, d2_r % Left and right boundary second derivative
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17 d3_l, d3_r % Left and right boundary third derivative
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21a180acbd49 Renamed standard class to D2Standard etc, Rewrote class properties.
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18 borrowing % Struct with borrowing limits for different norm matrices
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19 order
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20 end
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21
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22 methods
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23 function obj = D4Variable(m, lim, order)
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8a625c5a3633 Changed input parameter L (domain length) to lim (cell with domain boundaries)
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24 x_l = lim{1};
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25 x_r = lim{2};
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26 L = x_r-x_l;
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27 obj.h = L/(m-1);
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28 obj.x = linspace(x_l, x_r,m)';
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29
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30 if order == 2
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9230c056a574 Fixed formatting.
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31 [H, HI, D1, D2, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = ...
310
ffa5d557942b Moved operator implementations and fixed some naming.
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32 sbp.implementations.d4_variable_2(m, obj.h);
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33 obj.borrowing.M.d1 = 0.4000;
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34 obj.borrowing.N.S2 = 1.2500;
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35 obj.borrowing.N.S3 = 0.4000;
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36 elseif order == 4
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37 [H, HI, D1, D2, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = ...
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38 sbp.implementations.d4_variable_4(m, obj.h);
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39 obj.borrowing.M.d1 = 0.2508;
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40 obj.borrowing.N.S2 = 0.5055;
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41 obj.borrowing.N.S3 = 0.9290;
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42 elseif order == 6
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43 [H, HI, D1, D2, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = ...
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parents: 312
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44 sbp.implementations.d4_variable_6(m, obj.h);
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45 obj.borrowing.M.d1 = 0.1878;
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46 obj.borrowing.N.S2 = 0.3259;
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47 obj.borrowing.N.S3 = 0.1580;
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48 else
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49 error('Invalid operator order.');
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50 end
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51
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52 obj.m = m;
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53 obj.order = order;
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54
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55 obj.H = H;
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56 obj.HI = HI;
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57 obj.D1 = D1;
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58 obj.D2 = D2;
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59 obj.D4 = D4;
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60 obj.M4 = M4;
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61 obj.e_l = e_l;
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62 obj.e_r = e_r;
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63 obj.d1_l = d1_l;
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64 obj.d1_r = d1_r;
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65 obj.d2_l = d2_l;
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66 obj.d2_r = d2_r;
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67 obj.d3_l = d3_l;
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68 obj.d3_r = d3_r;
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69 end
330
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70
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71 function str = string(obj)
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72 str = [class(obj) '_' num2str(obj.order)];
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73 end
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74 end
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75 end