کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
523019 | 867897 | 2006 | 23 صفحه PDF | دانلود رایگان |

KL approximation of a possibly instationary random field a(ω, x) ∈ L2(Ω, dP; L∞(D )) subject to prescribed meanfield Ea(x)=∫Ωa(ω,x)dP(ω) and covariance Va(x,x′)=∫Ω(a(ω,x)-Ea(x))(a(ω,x′)-Ea(x′))dP(ω) in a polyhedral domain D⊂RdD⊂Rd is analyzed. We show how for stationary covariances Va(x, x′) = ga(|x − x′|) with ga(z) analytic outside of z = 0, an M-term approximate KL-expansion aM(ω, x) of a(ω, x) can be computed in log-linear complexity. The approach applies in arbitrary domains D and for nonseparable covariances Ca. It involves Galerkin approximation of the KL eigenvalue problem by discontinuous finite elements of degree p ⩾ 0 on a quasiuniform, possibly unstructured mesh of width h in D, plus a generalized fast multipole accelerated Krylov-Eigensolver. The approximate KL-expansion aM(x, ω) of a(x, ω) has accuracy O(exp(−bM1/d)) if ga is analytic at z = 0 and accuracy O(M−k/d) if ga is Ck at zero. It is obtained in O(MN(log N)b) operations where N = O(h−d).
Journal: Journal of Computational Physics - Volume 217, Issue 1, 1 September 2006, Pages 100–122