Journal of Scientific Computing

, Volume 27, Issue 1–3, pp 455–464 | Cite as

Beyond Wiener–Askey Expansions: Handling Arbitrary PDFs

  • Xiaoliang Wan
  • George Em Karniadakis


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


Uncertainty polynomial chaos stochastic differential equation 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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