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Beyond Wiener–Askey Expansions: Handling Arbitrary PDFs

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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 conditional 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 probability measures

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Xiaoliang Wan & George Em Karniadakis

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  1. Xiaoliang Wan
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  2. George Em Karniadakis
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Correspondence to Xiaoliang Wan.

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Wan, X., Karniadakis, G.E. Beyond Wiener–Askey Expansions: Handling Arbitrary PDFs. J Sci Comput 27, 455–464 (2006). https://doi.org/10.1007/s10915-005-9038-8

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  • DOI: https://doi.org/10.1007/s10915-005-9038-8

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