Mathematical and Information Technologies, MIT-2016 Mathematical modeling

Transcription

1 Mathematical and Information Technologies, MIT-26 Mathematical modeling 496

2 Mathematical and Information Technologies, MIT-26 Mathematical modeling 497

3 Mathematical and Information Technologies, MIT-26 Mathematical modeling Ω Ω Φ Π Π Φ Π Γ {z = } η(x, y, t) η t + g (hv ) = V t + g η = η t= = φ(x, y), V t= = ; V n = Π cη yt η tt + c2 2 η xx y= = ; cη yt η tt + c2 2 η xx y=y = ; cη xt η tt + c2 2 η yy x=x = cη xt η tt + c2 2 η yy x= = ; V = (v x, v y ) x y v x v y h(x, y) g c(x, y) = gh(x, y) n φ(x, y) Ω 498

4 Mathematical and Information Technologies, MIT-26 Mathematical modeling φ(x, y) R = {(x i y i i = P } η (x i, y i, t) = η (x i, y i, t), (x i, y i ) R. SV D φ(x, y) Ω φ(x, y) = M N m= n= c mn sin mπ x sin nπ y l l 2 (x, y) [, l ] [, l 2 ] c = {c mn } marigrams η = (η, η 2,..., η Nt, η 2,..., η 2Nt, η P,..., η P Nt ) T η pj = η(x p, y p, t j ) (x p, y p ), p =,..., P t j, j =,..., N t η η = Ac, A φ mn (x, y) = sin mπ l x sin nπ l 2 y α k c c = MN j= α je j α j = (η,lj) s j l j e j A s j c [r] = φ(x, y) r j= α j e j φ [r] (x, y) = r M α j j= m= n= N βmnφ j mn (x, y), e j = (β j, βj 2..., βj MN )T r A cond r = max{k : 499

5 Mathematical and Information Technologies, MIT-26 Mathematical modeling s k /s /cond} A φ(x, y) A (.738 S, E) Π = {(x; y) : 4 E x 85 E; 7 S y 3 N} (4 E, 7 S) Ox Oy Ω = { E x E;.238 S y.238 S} P = 6 DART R ( ) 4sec N t = 2 M N M = 5; N = 5 A (225 (2 p)) 27 8 Π 6 6 Ω (59, 376) A A A {c mn } φ [r] (x, y) 5

6 Mathematical and Information Technologies, MIT-26 Mathematical modeling Π ( ) A A r > 2 5

7 Mathematical and Information Technologies, MIT-26 Mathematical modeling lg(s i /s ) lg(s i /s ) numbers of singular values r= numbers of singular values {4, 5, 6} {, 3, 5} {, 5, 6} {, 2, 3, 5, 6} {, 2, 3, 4, 5, 6}.24S.74S r=49; φ max =2.9m; φ min =.6m S 64.64W 65.4W 65.64W 2.74S 2.24S r=2; φ max =.9m; φ min =.46m S 64.64W 65.4W 65.64W, 2, 3, 4, 5, 6 r

8 Mathematical and Information Technologies, MIT-26 Mathematical modeling (,2,5);r=2; φ max =.64m; φ min =.4m.24S.74S S 64.64W 65.4W 65.64W (4,5,6);r=3;φ max =.95m;φ min =.43m.24S.5.74S S 64.64W 65.4W 65.64W (,2,5,6);r=2; φ =.56m;φ =.25m max min.24s.74s S 64.64W 65.4W 65.64W 2 (,3,5); r=2; φ max =.89m; φ min =.6m.24S.74S S W 65.4W 65.64W (,4,5,6); r=2;φ =.58m; φ =.65m max min.24s.74s S 64.64W 65.4W 65.64W 2 (,2,3,5,6); r=2; φ max =.88; φ min =.6; (m).24s.74s s 64.64W 65.4W 65.64W

9 Mathematical and Information Technologies, MIT-26 Mathematical modeling cond φ(x, y) 54

10 Mathematical and Information Technologies, MIT-26 Mathematical modeling Amplitude (cm) min. Amplitude (cm) min min min. 5 3 min min. Amplitude (cm) Amplitude (cm) 5 3 min min. 5 3 min min. Amplitude (cm) 5 5 Amplitude (cm) 5 5 3min 3 min DART s R A 55

11 Mathematical and Information Technologies, MIT-26 Mathematical modeling 56

12 Mathematical and Information Technologies, MIT-26 Mathematical modeling 57