Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification
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3. basis HUQ.pdf
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Author(s)
El-Moselhy, Tarek A.
Elfadel, Ibrahim M.
Zhang, Zheng
Daniel, Luca
Alternative Title
Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification
Date Issued
April 2014
Journal
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Zheng Zhang; El-Moselhy, Tarek A.; Elfadel, Ibrahim M. and Daniel, Luca. "Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 33, no. 5 (May 2014): 728-740. © 2013 Institute of Electrical and Electronics Engineers (IEEE)
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
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DOI of Published Version
https://doi.org/10.1109/TCAD.2013.2295818
