A Low-Rank Solver for the Navier--Stokes Equations with Uncertain Viscosity
| dc.contributor.author | Lee, Kookjin | |
| dc.contributor.author | Elman, Howard C. | |
| dc.contributor.author | Sousedik, Bedrich | |
| dc.date.accessioned | 2021-10-22T17:26:19Z | |
| dc.date.available | 2021-10-22T17:26:19Z | |
| dc.date.issued | 2019-10-31 | |
| dc.description.abstract | We study an iterative low-rank approximation method for the solution of the steady-state stochastic Navier--Stokes equations with uncertain viscosity. The method is based on linearization schemes using Picard and Newton iterations and stochastic finite element discretizations of the linearized problems. For computing the low-rank approximate solution, we adapt the nonlinear iterations to an inexact and low-rank variant, where the solution of the linear system at each nonlinear step is approximated by a quantity of low rank. This is achieved by using a tensor variant of the GMRES method as a solver for the linear systems. We explore the inexact low-rank nonlinear iteration with a set of benchmark problems, using a model of flow over an obstacle, under various configurations characterizing the statistical features of the uncertain viscosity, and we demonstrate its effectiveness by extensive numerical experiments. | en_US |
| dc.description.sponsorship | The work of the authors was supported by the U.S. Department of Energy Office of Advanced Scientific Computing Research, Applied Mathematics program under award DEC-SC0009301 and by the National Science Foundation under grants DMS-1819115 and DMS-1521563. | en_US |
| dc.description.uri | https://epubs.siam.org/doi/abs/10.1137/17M1151912?journalCode=sjuqa3& | en_US |
| dc.format.extent | 26 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.identifier | doi:10.13016/m2cvsy-ynuj | |
| dc.identifier.citation | Lee, Kookjin; Elman, Howard C.; Sousedik, Bedrich; A Low-Rank Solver for the Navier--Stokes Equations with Uncertain Viscosity; SIAM/ASA Journal on Uncertainty Quantification, 7(4), 1275-1300, 31 October, 2019; https://doi.org/10.1137/17M1151912 | en_US |
| dc.identifier.uri | https://doi.org/10.1137/17M1151912 | |
| dc.identifier.uri | http://hdl.handle.net/11603/23155 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Society for Industrial and Applied Mathematics | en_US |
| 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 | This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author. | en_US |
| dc.rights | © 2019, Society for Industrial and Applied Mathematics and American Statistical Association. | |
| dc.title | A Low-Rank Solver for the Navier--Stokes Equations with Uncertain Viscosity | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0002-8053-8956 | en_US |