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. © Springer-Verlag Berlin Heidelberg 2003.
CITATION STYLE
Xiu, D., Lucor, D., Su, C. H., & Karniadakis, G. E. (2003). Performance evaluation of generalized polynomial chaos. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. https://doi.org/10.1007/3-540-44864-0_36
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