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We present a method for linear stability analysis of systems with parametricuncertainty formulated in the stochastic Galerkin framework. Specifically, weassume that for a model partial differential equation, the parameter is givenin the form of generalized polynomial chaos expansion. The stability analysisleads to the solution of a stochastic eigenvalue problem, and we wish tocharacterize the rightmost eigenvalue. We focus, in particular, on problemswith nonsymmetric matrix operators, for which the eigenvalue of interest may bea complex conjugate pair, and we develop methods for their efficient solution.These methods are based on inexact, line-search Newton iteration, which entailsuse of preconditioned GMRES. The method is applied to linear stability analysisof Navier-Stokes equation with stochastic viscosity, its accuracy is comparedto that of Monte Carlo and stochastic collocation, and the efficiency isillustrated by numerical experiments.

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