Stochastic Galerkin Methods for Linear Stability Analysis of Systems with Parametric Uncertainty

We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that model partial differential equation, parameter is given form generalized polynomial chaos expansion. The leads to solution eigenvalue problem, and wish characterize rightmost eigenvalue. focus, particular, on problems nonsymmetric matrix operators, which interest may be complex conjugate pair, develop methods their efficient solution. These are based inexact, line-search Newton iteration, entails use preconditioned GMRES. applied Navier–Stokes equations viscosity, its accuracy compared Monte Carlo collocation, efficiency illustrated by numerical experiments.