NDLI: Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Content Provider	IEEE Xplore Digital Library
Author	Zheng Zhang El-Moselhy, T.A. Elfadel, I.M. Daniel, L.
Copyright Year	1982
Abstract	Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input a-priori. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.
Sponsorship	IEEE Council on Electronic Design Automation IEEE Circuits and Systems Society
Starting Page	728
Ending Page	740
Page Count	13
File Size	10014808
File Format	PDF
ISSN	02780070
Volume Number	33
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Density functional theory Stochastic processes Polynomials Probability density function Interpolation Integrated circuit modeling Uncertainty uncertainty quantification Density estimation Gauss quadrature generalized polynomial chaos stochastic circuit simulation surrogate model
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Electrical and Electronic Engineering Software

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