Beyond Wiener---Askey Expansions: Handling Arbitrary PDFs

Authors:
Xiaoliang Wan;George Em Karniadakis
Affiliations:
Division of Applied Mathematics, Brown University, Providence, USA 02912;Division of Applied Mathematics, Brown University, Providence, USA 02912
Venue:
Journal of Scientific Computing
Year:
2006

Citing 6
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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