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annotate +time/SBPInTimeSecondOrderFormImplicit.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 66eb4a2bbb72
children 8894e9c49e40
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1 classdef SBPInTimeSecondOrderFormImplicit < time.Timestepper
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2 properties
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3 A, B, C, f
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4 AA, BB, ff
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5
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6 n
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7 t
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8 k
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9
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10 firstOrderTimeStepper
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11 end
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12
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13 methods
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14 % Solves A*u_tt + B*u_t + C*u = f(t)
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15 % A, B can either both be constants or both be function handles,
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16 % They can also be omitted by setting them equal to the empty matrix.
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17 function obj = SBPInTimeSecondOrderFormImplicit(A, B, C, f, k, t0, v0, v0t, do_scaling, TYPE, order, blockSize)
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18 default_arg('f', []);
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19 default_arg('TYPE', []);
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20 default_arg('order', []);
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21 default_arg('blockSize',[]);
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22 default_arg('do_scaling', false);
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24 m = length(v0);
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26 default_arg('A', speye(m, m));
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27 default_arg('B', sparse(m, m));
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28 default_arg('C', sparse(m, m));
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30 I = speye(m);
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31 O = sparse(m,m);
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33 % Rewrite to
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34 % AA*w_t = BB*w + ff(t);
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36 obj.AA = [
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37 I, O;
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38 O, A;
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39 ];
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40 obj.BB = [
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41 O, I;
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42 -C, -B;
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43 ];
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45 if ~isempty(f)
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46 obj.ff = @(t)[
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47 sparse(m,1);
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48 f(t);
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49 ];
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50 else
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51 obj.ff = @(t) sparse(2*m,1);
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52 end
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53
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54 w0 = [v0; v0t];
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55
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56 obj.k = k;
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57 obj.t = t0;
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58 obj.n = 0;
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59
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60 if do_scaling
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61 scaling = [ones(m,1); sqrt(diag(C))];
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62 obj.firstOrderTimeStepper = time.SBPInTimeScaled(obj.AA, obj.BB, obj.ff, obj.k, obj.t, w0, scaling, TYPE, order, blockSize);
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63 else
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64 obj.firstOrderTimeStepper = time.SBPInTimeImplicitFormulation(obj.AA, obj.BB, obj.ff, obj.k, obj.t, w0, TYPE, order, blockSize);
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65 end
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66 end
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67
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68 function [v,t] = getV(obj)
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69 w = obj.firstOrderTimeStepper.getV();
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70 v = w(1:end/2);
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71 t = obj.t;
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72 end
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73
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74 function [vt,t] = getVt(obj)
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75 w = obj.firstOrderTimeStepper.getV();
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76 vt = w(end/2+1:end);
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77 t = obj.t;
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78 end
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79
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80 function obj = step(obj)
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81 obj.firstOrderTimeStepper.step();
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82 obj.t = obj.firstOrderTimeStepper.t;
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83 obj.n = obj.firstOrderTimeStepper.n;
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84 end
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85 end
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86 end