15. Metoda konÄnih elementov in reÅ¡evanje BDE in PDE v Matlabu
15. Metoda konÄnih elementov in reÅ¡evanje BDE in PDE v Matlabu
15. Metoda konÄnih elementov in reÅ¡evanje BDE in PDE v Matlabu
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L<strong>in</strong>earni sistem<br />
Iz enačb ∂I<br />
∂γ k<br />
(φ) = 0 za k = 1, . . . , n dobimo l<strong>in</strong>earni sistem<br />
kjer je<br />
za elemente A = [α ij ] <strong>in</strong> b = [β i ] pa velja<br />
α ij =<br />
∫∫<br />
Ω<br />
Ac = b,<br />
c = [γ 1 · · · γ n ] T ,<br />
[<br />
p(x, y) ∂φ i<br />
∂x (x, y)∂φ j<br />
∂x (x, y) + q(x, y)∂φ i<br />
∂y (x, y)∂φ j<br />
∂y<br />
(x, y)<br />
] ∫<br />
−r(x, y)φ i (x, y)φ j (x, y) dxdy + g 1 (x, y)φ i (x, y)φ j (x, y)dS<br />
S 2<br />
za i, j = 1, . . . , n <strong>in</strong><br />
∫∫<br />
β i = −<br />
Ω<br />
f(x, y)φ i (x, y)dxdy +<br />
∫<br />
S 2<br />
g 2 (x, y)φ i (x, y)dS −<br />
m∑<br />
k=n+1<br />
α ik γ k .<br />
Bor Plestenjak - Numerična analiza 2005/06
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