Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908760427986944 |
|---|---|
| author | Sousedík, Bedřich Lee, Kookjin |
| author_facet | Sousedík, Bedřich Lee, Kookjin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_12485 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty Sousedík, Bedřich Lee, Kookjin Numerical Analysis Probability 35R60, 60H15, 65F15, 65L07, 65N22, 65N25 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. |
| title | Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty |
| topic | Numerical Analysis Probability 35R60, 60H15, 65F15, 65L07, 65N22, 65N25 |
| url | https://arxiv.org/abs/2202.12485 |