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annotate +time/CdiffNonlin.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 d1f9dd55a2b0
children b5e5b195da1e
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1
5ae4f23d9130 Added CdiffNonlin timestepper. Probably fixed a bug with Cdiff. Added default arguments to Rk4SecondOrderNonlin.
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1 classdef CdiffNonlin < time.Timestepper
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2 properties
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3 D
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4 E
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5 S
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6 k
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7 t
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8 v
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9 v_prev
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10 n
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11 end
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12
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14 methods
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15 function obj = CdiffNonlin(D, E, S, k, t0,n0, v, v_prev)
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16 m = size(D(v),1);
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17 default_arg('E',0);
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18 default_arg('S',0);
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20 if isnumeric(S)
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21 S = @(v,t)S;
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22 end
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23
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24 if isnumeric(E)
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25 E = @(v)E;
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26 end
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27
1
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28
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29 % m = size(D,1);
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30 % default_arg('E',sparse(m,m));
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31 % default_arg('S',sparse(m,1));
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32
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33 obj.D = D;
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34 obj.E = E;
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35 obj.S = S;
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36 obj.k = k;
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37 obj.t = t0;
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38 obj.n = n0;
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39 obj.v = v;
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40 obj.v_prev = v_prev;
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41 end
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42
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43 function [v,t] = getV(obj)
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44 v = obj.v;
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45 t = obj.t;
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46 end
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47
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48 function [vt,t] = getVt(obj)
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49 vt = (obj.v-obj.v_prev)/obj.k; % Could be improved using u_tt = f(u))
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50 t = obj.t;
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51 end
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52
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53 function obj = step(obj)
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54 D = obj.D(obj.v);
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55 E = obj.E(obj.v);
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56 S = obj.S(obj.v,obj.t);
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57
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58 m = size(D,1);
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59 I = speye(m);
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60
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61 %% Calculate for which indices we need to solve system of equations
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62 [rows,cols] = find(E);
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63 j = union(rows,cols);
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64 i = setdiff(1:m,j);
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65
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66
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67 %% Calculate matrices need for the timestep
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68 % Before optimization: A = 1/k^2 * I - 1/(2*k)*E;
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69 k = obj.k;
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70
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71 Aj = 1/k^2 * I(j,j) - 1/(2*k)*E(j,j);
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72 B = 2/k^2 * I + D;
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73 C = -1/k^2 * I - 1/(2*k)*E;
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74
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75 %% Take the timestep
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76 v = obj.v;
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77 v_prev = obj.v_prev;
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78
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79 % Want to solve the seq A*v_next = b where
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80 b = (B*v + C*v_prev + S);
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81
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82 % Before optimization: obj.v = A\b;
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83
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84 obj.v(i) = k^2*b(i);
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85 obj.v(j) = Aj\b(j);
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86
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87 obj.v_prev = v;
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88
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89 %% Update state of the timestepper
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90 obj.t = obj.t + obj.k;
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91 obj.n = obj.n + 1;
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92 end
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93 end
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94 end