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Beyond Wiener-Askey expansions: handling arbitrary PDFs (2006)
| Venue: | J. Sci. Comput |
| Citations: | 26 - 1 self |
BibTeX
@ARTICLE{Wan06beyondwiener-askey,
author = {Xiaoliang Wan and George Em Karniadakis},
title = {Beyond Wiener-Askey expansions: handling arbitrary PDFs},
journal = {J. Sci. Comput},
year = {2006}
}
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Abstract
In this paper we present a Multi-Element generalized Polynomial Chaos (ME-gPC) method to deal with stochastic inputs with arbitrary probability measures. Based on the decomposition of the random space of the stochastic inputs, we construct numerically a set of orthogonal polynomials with respect to a con-ditional probability density function (PDF) in each element and subsequently implement generalized Polynomial Chaos (gPC) locally. Numerical examples show that ME-gPC exhibits both p- and h-convergence for arbitrary probabil-ity measures. KEY WORDS: Uncertainty; polynomial chaos; stochastic differential equation. 1.
Keyphrases
arbitrary pdfs wiener-askey expansion stochastic input polynomial chaos stochastic differential equation numerical example random space arbitrary probability measure con-ditional probability density function orthogonal polynomial multi-element generalized polynomial chaos key word arbitrary probabil-ity measure
