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annotate +time/Cdiff.m @ 1344:b4e5e45bd239 feature/D2_boundary_opt

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Remove round off zeros from D2Nonequidistant operators
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sat, 15 Oct 2022 15:48:20 +0200
parents 1a30dbe99c7c
children 7a5e770974ed
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 classdef Cdiff < time.Timestepper
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2 properties
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3 A, B, C
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4 AA, BB, CC
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5 G
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6 k
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7 t
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8 v, v_prev
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9 n
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10 end
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13 methods
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14 % Solves
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15 % A*v_tt + B*v_t + C*v = G(t)
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16 % v(t0) = v0
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17 % v_t(t0) = v0t
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18 % starting at time t0 with timestep k
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19 % Using
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20 % A*Dp*Dm*v_n + B*D0*v_n + C*v_n = G(t_n)
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21 function obj = Cdiff(A, B, C, G, v0, v0t, k, t0)
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22 m = length(v0);
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23 default_arg('A', speye(m));
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24 default_arg('B', sparse(m,m));
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25 default_arg('G', @(t) sparse(m,1));
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26 default_arg('t0', 0);
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28 obj.A = A;
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29 obj.B = B;
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30 obj.C = C;
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31 obj.G = G;
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32
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33 % Rewrite as AA*v_(n+1) + BB*v_n + CC*v_(n-1) = G(t_n)
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34 obj.AA = A/k^2 + B/(2*k);
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35 obj.BB = -2*A/k^2 + C;
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36 obj.CC = A/k^2 - B/(2*k);
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37
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38 obj.k = k;
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39 obj.v_prev = v0;
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40 obj.v = v0 + k*v0t;
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41 obj.t = t0+k;
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42 obj.n = 1;
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43 end
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44
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45 function [v,t] = getV(obj)
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46 v = obj.v;
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47 t = obj.t;
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48 end
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49
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50 function [vt,t] = getVt(obj)
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51 vt = (obj.v-obj.v_prev)/obj.k; % Could be improved using u_tt = f(u))
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52 t = obj.t;
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53 end
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55 function E = getEnergy(obj)
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56 v = obj.v;
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57 vp = obj.v_prev;
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58 vt = (obj.v - obj.v_prev)/obj.k;
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59
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60 E = vt'*obj.A*vt + v'*obj.C*vp;
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61 end
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62
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63 function obj = step(obj)
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64 v_next = obj.AA\(-obj.BB*obj.v - obj.CC*obj.v_prev + obj.G(obj.t));
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65
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66 obj.v_prev = obj.v;
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67 obj.v = v_next;
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68 obj.t = obj.t + obj.k;
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69 obj.n = obj.n + 1;
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70 end
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71 end
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72 end