Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty
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2022-03-03
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Sousedík, Bedřich, and Kookjin Lee. "Stochastic Galerkin Methods for Linear Stability Analysis of Systems with Parametric Uncertainty." SIAM/ASA Journal on Uncertainty Quantification 10, no. 3 (2022): 1101-1129. https://doi.org/10.1137/21M1415595.
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Copyright©by SIAM and ASA. Unauthorized reproduction of this article is prohibited.
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Abstract
We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that for a model partial differential equation, the parameter is given in the form of generalized polynomial chaos expansion. The stability analysis leads to the solution of a stochastic eigenvalue problem, and we wish
to characterize the rightmost eigenvalue. We focus, in particular, on problems with nonsymmetric
matrix operators, for which the eigenvalue of interest may be a complex conjugate pair, and we
develop methods for their efficient solution. These methods are based on inexact, line-search Newton
iteration, which entails use of preconditioned GMRES. The method is applied to linear stability analysis of Navier–Stokes equation with stochastic viscosity, its accuracy is compared to that of Monte
Carlo and stochastic collocation, and the efficiency is illustrated by numerical experiments.