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annotate +time/CdiffNonlin.m @ 774:66eb4a2bbb72 feature/grids

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Remove default scaling of the system. The scaling doens't seem to help actual solutions. One example that fails in the flexural code. With large timesteps the solutions seems to blow up. One particular example is profilePresentation on the tdb_presentation_figures branch with k = 0.0005
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 18 Jul 2018 15:42:52 -0700
parents d1f9dd55a2b0
children b5e5b195da1e
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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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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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24 if isnumeric(E)
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25 E = @(v)E;
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26 end
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5ae4f23d9130 Added CdiffNonlin timestepper. Probably fixed a bug with Cdiff. Added default arguments to Rk4SecondOrderNonlin.
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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