Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty
| dc.contributor.author | Sousedík, Bedřich | |
| dc.contributor.author | Lee, Kookjin | |
| dc.date.accessioned | 2022-03-30T13:40:01Z | |
| dc.date.available | 2022-03-30T13:40:01Z | |
| dc.date.issued | 2022-03-03 | |
| dc.description.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. | en_US |
| dc.description.sponsorship | We would like to thank the anonymous reviewers for their insightful suggestions. Bedˇrich Soused´ık would also like to thank Professors Pavel Burda, Howard Elman, Vladim´ır Janovsk´y and Jaroslav Novotn´y for many discussions about bifurcation analysis and Navier–Stokes equations that inspired this work. | en_US |
| dc.description.uri | https://epubs.siam.org/doi/abs/10.1137/21M1415595 | en_US |
| dc.format.extent | 29 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.identifier | doi:10.13016/m2mqzj-wp9c | |
| dc.identifier.citation | 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. | |
| dc.identifier.uri | https://doi.org/10.1137/21M1415595 | |
| dc.identifier.uri | http://hdl.handle.net/11603/24466 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | SIAM | |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.rights | Copyright©by SIAM and ASA. Unauthorized reproduction of this article is prohibited. | en_US |
| dc.title | Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0002-8053-8956 | en_US |