Performance evaluation of generalized polynomial chaos

Authors:
Dongbin Xiu;Didier Lucor;C.-H. Su;George Em Karniadakis
Affiliations:
Division of Applied Mathematics, Brown University, Providence, RI;Division of Applied Mathematics, Brown University, Providence, RI;Division of Applied Mathematics, Brown University, Providence, RI;Division of Applied Mathematics, Brown University, Providence, RI
Venue:
ICCS'03 Proceedings of the 2003 international conference on Computational science
Year:
2003

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Abstract

In this paper we review some applications of generalized polynomial chaos expansion for uncertainty quantification. The mathematical framework is presented and the convergence of the method is demonstrated for model problems. In particular, we solve the first-order and second-order ordinary differential equations with random parameters, and examine the efficiency of generalized polynomial chaos compared to Monte Carlo simulations. It is shown that the generalized polynomial chaos can be orders of magnitude more efficient than Monte Carlo simulations when the dimensionality of random input is low, e.g. for correlated noise.