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annotate +time/CdiffNonlin.m @ 4:8e14b5a577a6

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Attempt att optimization of CdiffNonlin.
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 18 Sep 2015 15:12:44 +0200
parents 5ae4f23d9130
children b18d3d201a71
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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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5ae4f23d9130 Added CdiffNonlin timestepper. Probably fixed a bug with Cdiff. Added default arguments to Rk4SecondOrderNonlin.
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15 function obj = CdiffNonlin(D, E, S, k, t0, v, v_prev)
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16 m = size(D(v),1);
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17 default_arg('E',@(v)sparse(m,m));
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18 default_arg('S',@(v,t)sparse(m,1));
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19
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20
5ae4f23d9130 Added CdiffNonlin timestepper. Probably fixed a bug with Cdiff. Added default arguments to Rk4SecondOrderNonlin.
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21 % m = size(D,1);
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22 % default_arg('E',sparse(m,m));
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23 % default_arg('S',sparse(m,1));
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24
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25 obj.D = D;
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26 obj.E = E;
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27 obj.S = S;
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28 obj.k = k;
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29 obj.t = t0;
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30 obj.v = v;
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31 obj.v_prev = v_prev;
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32 end
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33
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34 function [v,t] = getV(obj)
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35 v = obj.v;
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36 t = obj.t;
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37 end
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38
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39 function [vt,t] = getVt(obj)
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40 vt = (obj.v-obj.v_prev)/obj.k; % Could be improved using u_tt = f(u))
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41 t = obj.t;
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42 end
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44 function obj = step(obj)
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45 D = obj.D(obj.v);
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46 E = obj.E(obj.v);
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47 S = obj.S(obj.v);
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48
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49 m = size(D,1);
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50 I = speye(m);
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51
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52 %% Calculate for which indices we need to solve system of equations
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53 [rows,cols] = find(E);
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54 j = union(rows,cols);
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55 i = setdiff(1:m,j);
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56
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57
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58 %% Calculate matrices need for the timestep
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59 % Before optimization: A = 1/k^2 * I - 1/(2*k)*E;
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60 k = obj.k;
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61 Aj = 1/k^2 * I(j,j) - 1/(2*k)*E(j,j);
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62 B = 2/k^2 * I + D;
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63 C = -1/k^2 * I - 1/(2*k)*E;
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64
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65 %% Take the timestep
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66 v = obj.v;
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67
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68 % Before optimization: obj.v = A\(B*v + C*v_prev + S);
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69 obj.v(i) = k^2*(B(i,i)*v(i) -1/k^2*obj.v_prev(i) + S(i));
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70 obj.v(j) = Aj\(B(j,j)*v(j) + C(j,j)*obj.v_prev(j) + S(j));
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71 obj.v_prev = v;
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72
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73 %% Update state of the timestepper
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74 obj.t = obj.t + obj.k;
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75 obj.n = obj.n + 1;
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76 end
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77 end
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78 end