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comparison +time/CdiffImplicit.m @ 1197:433c89bf19e0 feature/rv

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Merge with default
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 07 Aug 2019 15:23:42 +0200
parents 1a30dbe99c7c
children 47e86b5270ad
comparison
equal deleted inserted replaced
1196:f6c571d8f22f 1197:433c89bf19e0
1 classdef CdiffImplicit < time.Timestepper 1 classdef CdiffImplicit < time.Timestepper
2 properties 2 properties
3 A, B, C, G 3 A, B, C
4 AA, BB, CC 4 AA, BB, CC
5 G
5 k 6 k
6 t 7 t
7 v, v_prev 8 v, v_prev
8 n 9 n
9 10
11 L,U,p,q 12 L,U,p,q
12 end 13 end
13 14
14 methods 15 methods
15 % Solves 16 % Solves
16 % A*u_tt + B*u + C*v_t = G(t) 17 % A*v_tt + B*v_t + C*v = G(t)
17 % u(t0) = f1 18 % v(t0) = v0
18 % u_t(t0) = f2 19 % v_t(t0) = v0t
19 % starting at time t0 with timestep k 20 % starting at time t0 with timestep
20 function obj = CdiffImplicit(A, B, C, G, f1, f2, k, t0) 21 % Using
21 default_arg('A', []); 22 % A*Dp*Dm*v_n + B*D0*v_n + C*I0*v_n = G(t_n)
22 default_arg('C', []); 23 function obj = CdiffImplicit(A, B, C, G, v0, v0t, k, t0)
23 default_arg('G', []); 24 m = length(v0);
24 default_arg('f1', 0); 25 default_arg('A', speye(m));
25 default_arg('f2', 0); 26 default_arg('B', sparse(m,m));
27 default_arg('G', @(t) sparse(m,1));
26 default_arg('t0', 0); 28 default_arg('t0', 0);
27
28 m = size(B,1);
29
30 if isempty(A)
31 A = speye(m);
32 end
33
34 if isempty(C)
35 C = sparse(m,m);
36 end
37
38 if isempty(G)
39 G = @(t) sparse(m,1);
40 end
41
42 if isempty(f1)
43 f1 = sparse(m,1);
44 end
45
46 if isempty(f2)
47 f2 = sparse(m,1);
48 end
49 29
50 obj.A = A; 30 obj.A = A;
51 obj.B = B; 31 obj.B = B;
52 obj.C = C; 32 obj.C = C;
53 obj.G = G; 33 obj.G = G;
54 34
55 AA = 1/k^2*A + 1/2*B + 1/(2*k)*C; 35 % Rewrite as AA*v_(n+1) + BB*v_n + CC*v_(n-1) = G(t_n)
56 BB = -2/k^2*A; 36 AA = A/k^2 + B/(2*k) + C/2;
57 CC = 1/k^2*A + 1/2*B - 1/(2*k)*C; 37 BB = -2*A/k^2;
58 % AA*v_next + BB*v + CC*v_prev == G(t_n) 38 CC = A/k^2 - B/(2*k) + C/2;
59 39
60 obj.AA = AA; 40 obj.AA = AA;
61 obj.BB = BB; 41 obj.BB = BB;
62 obj.CC = CC; 42 obj.CC = CC;
63 43
64 v_prev = f1; 44 v_prev = v0;
65 I = speye(m); 45 I = speye(m);
66 % v = (1/k^2*A)\((1/k^2*A - 1/2*B)*f1 + (1/k*I - 1/2*C)*f2 + 1/2*G(0)); 46 v = v0 + k*v0t;
67 v = f1 + k*f2;
68
69 47
70 if ~issparse(A) || ~issparse(B) || ~issparse(C) 48 if ~issparse(A) || ~issparse(B) || ~issparse(C)
71 error('LU factorization with full pivoting only works for sparse matrices.') 49 error('LU factorization with full pivoting only works for sparse matrices.')
72 end 50 end
73 51
75 53
76 obj.L = L; 54 obj.L = L;
77 obj.U = U; 55 obj.U = U;
78 obj.p = p; 56 obj.p = p;
79 obj.q = q; 57 obj.q = q;
80
81 58
82 obj.k = k; 59 obj.k = k;
83 obj.t = t0+k; 60 obj.t = t0+k;
84 obj.n = 1; 61 obj.n = 1;
85 obj.v = v; 62 obj.v = v;
90 v = obj.v; 67 v = obj.v;
91 t = obj.t; 68 t = obj.t;
92 end 69 end
93 70
94 function [vt,t] = getVt(obj) 71 function [vt,t] = getVt(obj)
95 % Calculate next time step to be able to do centered diff. 72 vt = (obj.v-obj.v_prev)/obj.k; % Could be improved using u_tt = f(u))
96 v_next = zeros(size(obj.v)); 73 t = obj.t;
97 b = obj.G(obj.t) - obj.BB*obj.v - obj.CC*obj.v_prev; 74 end
98 75
99 y = obj.L\b(obj.p); 76 % Calculate the conserved energy (Dm*v_n)^2_A + Im*v_n^2_B
100 z = obj.U\y; 77 function E = getEnergy(obj)
101 v_next(obj.q) = z; 78 v = obj.v;
79 vp = obj.v_prev;
80 vt = (obj.v - obj.v_prev)/obj.k;
102 81
103 82 E = vt'*obj.A*vt + 1/2*(v'*obj.C*v + vp'*obj.C*vp);
104 vt = (v_next-obj.v_prev)/(2*obj.k);
105 t = obj.t;
106 end 83 end
107 84
108 function obj = step(obj) 85 function obj = step(obj)
109 b = obj.G(obj.t) - obj.BB*obj.v - obj.CC*obj.v_prev; 86 b = obj.G(obj.t) - obj.BB*obj.v - obj.CC*obj.v_prev;
110 obj.v_prev = obj.v; 87 obj.v_prev = obj.v;
121 obj.t = obj.t + obj.k; 98 obj.t = obj.t + obj.k;
122 obj.n = obj.n + 1; 99 obj.n = obj.n + 1;
123 end 100 end
124 end 101 end
125 end 102 end
126
127
128
129
130
131 %%% Derivation
132 % syms A B C G
133 % syms n k
134 % syms f1 f2
135
136 % v = symfun(sym('v(n)'),n);
137
138
139 % d = A/k^2 * (v(n+1) - 2*v(n) +v(n-1)) + B/2*(v(n+1)+v(n-1)) + C/(2*k)*(v(n+1) - v(n-1)) == G
140 % ic1 = v(0) == f1
141 % ic2 = A/k*(v(1)-f1) + k/2*(B*f1 + C*f2 - G) - f2 == 0
142
143 % c = collect(d, [v(n) v(n-1) v(n+1)]) % (-(2*A)/k^2)*v(n) + (B/2 + A/k^2 - C/(2*k))*v(n - 1) + (B/2 + A/k^2 + C/(2*k))*v(n + 1) == G
144 % syms AA BB CC
145 % % AA = B/2 + A/k^2 + C/(2*k)
146 % % BB = -(2*A)/k^2
147 % % CC = B/2 + A/k^2 - C/(2*k)
148 % s = subs(c, [B/2 + A/k^2 + C/(2*k), -(2*A)/k^2, B/2 + A/k^2 - C/(2*k)], [AA, BB, CC])
149
150
151 % ic2_a = collect(ic2, [v(1) f1 f2]) % (A/k)*v(1) + ((B*k)/2 - A/k)*f1 + ((C*k)/2 - 1)*f2 - (G*k)/2 == 0
152