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annotate +sbp/D2VariablePeriodic.m @ 681:7368affc8f78 feature/poroelastic

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Add D2 variable periodic for second order.
author Martin Almquist <malmquist@stanford.edu>
date Wed, 07 Feb 2018 15:42:50 -0800
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children 5ccf6aaf6d6b
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7368affc8f78 Add D2 variable periodic for second order.
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 error('Not impl')
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33
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34 [obj.H, obj.HI, obj.D1, obj.D2, ...
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35 ~, obj.e_l, obj.e_r, ~, ~, ~, ~, ~,...
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36 obj.d1_l, obj.d1_r] = ...
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37 sbp.implementations.d4_variable_periodic_6(m, obj.h);
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38 obj.borrowing.M.d1 = 0.1878;
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39 obj.borrowing.R.delta_D = 0.3696;
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40 % Borrowing e^T*D1 - d1 from R
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41
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42 case 4
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43 error('Not impl')
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44
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45 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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46 obj.e_r, obj.d1_l, obj.d1_r] = ...
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47 sbp.implementations.d2_variable_periodic_4(m,obj.h);
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48 obj.borrowing.M.d1 = 0.2505765857;
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49
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50 obj.borrowing.R.delta_D = 0.577587500088313;
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51 % Borrowing e^T*D1 - d1 from R
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52 case 2
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53 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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54 obj.e_r, obj.d1_l, obj.d1_r] = ...
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55 sbp.implementations.d2_variable_periodic_2(m,obj.h);
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56 obj.borrowing.M.d1 = 0.3636363636;
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57 % Borrowing const taken from Virta 2014
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58
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59 obj.borrowing.R.delta_D = 1.000000538455350;
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60 % Borrowing e^T*D1 - d1 from R
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61
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62 otherwise
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63 error('Invalid operator order %d.',order);
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64 end
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65 obj.borrowing.H11 = obj.H(1,1)/obj.h; % First element in H/h,
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66 obj.m = m;
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67 obj.M = [];
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68 end
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69 function str = string(obj)
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70 str = [class(obj) '_' num2str(obj.order)];
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71 end
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72 end
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73
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74
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75 end