Lee, KookjinElman, Howard C.Sousedik, Bedrich2021-10-222021-10-222019-10-31Lee, 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/10.1137/17M1151912https://doi.org/10.1137/17M1151912http://hdl.handle.net/11603/23155We 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.26 pagesen-USThis 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.© 2019, Society for Industrial and Applied Mathematics and American Statistical Association.A Low-Rank Solver for the Navier--Stokes Equations with Uncertain ViscosityText