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annotate +time/CdiffNonlin.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
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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19
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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
5ae4f23d9130 Added CdiffNonlin timestepper. Probably fixed a bug with Cdiff. Added default arguments to Rk4SecondOrderNonlin.
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28
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