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arXiv · 2202.12485

Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty

Bedřich Sousedík·Kookjin Lee
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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.

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Bedřich Sousedík, Kookjin Lee. 2022-02-25. Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty. https://doi.org/10.1137/21m1415595

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