Performance Evaluation of Generalized Polynomial Chaos

Dongbin Xiu, Didier Lucor, C.-H. Su, George Em Karniadakis

Division of Applied Mathematics, Brown University, Providence, RI 02912, U.S.A.
gk@dam.brown.edu

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.

LNCS 2660, pp. 346-354.

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