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annotate +sbp/D1Staggered.m @ 636:476b7e411ce3 feature/d1_staggered

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Add staggered operators
author Martin Almquist <malmquist@stanford.edu>
date Tue, 07 Nov 2017 20:44:13 -0800
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children eead18a8964d
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1 classdef D1Staggered < sbp.OpSet
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2 properties
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3 % xp: "plus" grid with m points
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4 % xm: "minus" grid with m+1 points
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5
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6 D1p % SBP operator approximating first derivative
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7 D1m % SBP operator approximating first derivative
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8 Hp % Norm matrix
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9 Hm % Norm matrix
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10 HpI % H^-1
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11 HmI % H^-1
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12 ep_l % Left boundary operator
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13 em_l % Left boundary operator
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14 ep_r % Right boundary operator
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15 em_r % Right boundary operator
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16 m % Number of grid points.
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17 mp % Number of grid points.
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18 mm % Number of grid points.
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19 h % Step size
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20 xp % grid
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21 xm % grid
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22 x
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23 borrowing % Struct with borrowing limits for different norm matrices
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24 end
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25
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26 methods
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27 function obj = D1Staggered(m,lim,order)
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28
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29 x_l = lim{1};
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30 x_r = lim{2};
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31 L = x_r-x_l;
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32
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33 mp = m;
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34 mm = m+1;
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35
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36 switch order
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37 case 2
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38 [xp, xm, Pp, Pm, Qp, Qm] = sbp.implementations.d1_staggered_2(m, L);
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39 case 4
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40 [xp, xm, Pp, Pm, Qp, Qm] = sbp.implementations.d1_staggered_4(m, L);
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41 case 6
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42 [xp, xm, Pp, Pm, Qp, Qm] = sbp.implementations.d1_staggered_6(m, L);
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43 otherwise
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44 error('Invalid operator order %d.',order);
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45 end
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46
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47 obj.m = m;
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48 obj.mp = mp;
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49 obj.mm = mm;
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50 obj.xp = x_l + xp';
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51 obj.xm = x_l + xm';
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52
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53 D1p = Pp\Qp;
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54 D1m = Pm\Qm;
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55
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56 obj.D1p = D1p;
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57 obj.D1m = D1m;
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58 pbj.Hp = Pp;
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59 obj.Hm = Pm;
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60
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61 obj.ep_l = sparse(mp,1);
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62 obj.ep_r = sparse(mp,1);
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63 obj.ep_l(1) = 1;
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64 obj.ep_r(mp) = 1;
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65
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66 obj.em_l = sparse(mm,1);
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67 obj.em_r = sparse(mm,1);
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68 obj.em_l(1) = 1;
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69 obj.em_r(mm) = 1;
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70
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71 obj.HpI = inv(obj.Hp);
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72 obj.HmI = inv(obj.Hm);
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73
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74 obj.borrowing = [];
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75 obj.x = [];
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76
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77 end
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78
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79 function str = string(obj)
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80 str = [class(obj) '_' num2str(obj.order)];
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81 end
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82 end
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83 end