Numerical challenges in the use of polynomial chaos representations for stochastic processes


Journal Article

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. © 2004 Society for Industrial and Applied Mathematics.

Full Text

Duke Authors

Cited Authors

  • Debusschere, BJ; Najm, HN; Pébayt, PP; Knio, OM; Ghanem, RG; Le Maître, OP

Published Date

  • April 15, 2005

Published In

Volume / Issue

  • 26 / 2

Start / End Page

  • 698 - 719

International Standard Serial Number (ISSN)

  • 1064-8275

Digital Object Identifier (DOI)

  • 10.1137/S1064827503427741

Citation Source

  • Scopus