کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
523019 867897 2006 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Karhunen–Loève approximation of random fields by generalized fast multipole methods
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Karhunen–Loève approximation of random fields by generalized fast multipole methods
چکیده انگلیسی

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).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 217, Issue 1, 1 September 2006, Pages 100–122
نویسندگان
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