Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
Abstract
This paper gives an overview of the use of polynomial chaos (PC) expansions to represent stochastic processes in numerical simulations. Several methods are presented for performing arithmetic on, as well as for evaluating polynomial and nonpolynomial functions of variables represented by PC expansions. These methods include {Taylor} series, a newly developed integration method, as well as a sampling-based spectral projection method for nonpolynomial function evaluations. A detailed analysis of the accuracy of the PC representations, and of the different methods for nonpolynomial function evaluations, is performed. It is found that the integration method offers a robust and accurate approach for evaluating nonpolynomial functions, even when very high-order information is present in the PC expansions.
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Published In
SIAM Journal on Scientific Computing
Pages: 698 - 719
ISSN (online): 1095-7197
Copyright
Copyright © 2004 Society for Industrial and Applied Mathematics.
History
Published online: 26 July 2006
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