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dc.contributor.authorLuo, Li
dc.contributor.authorCai, Xiao Chuan
dc.contributor.authorYan, Zhengzheng
dc.contributor.authorXu, Lei
dc.contributor.authorKeyes, David E.
dc.date.accessioned2020-11-25T11:32:12Z
dc.date.available2020-11-25T11:32:12Z
dc.date.issued2020-11-24
dc.date.submitted2019-12-16
dc.identifier.citationLuo, L., Cai, X.-C., Yan, Z., Xu, L., & Keyes, D. E. (2020). A Multilayer Nonlinear Elimination Preconditioned Inexact Newton Method for Steady-State Incompressible Flow Problems in Three Dimensions. SIAM Journal on Scientific Computing, 42(6), B1404–B1428. doi:10.1137/19m1307184
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/19m1307184
dc.identifier.urihttp://hdl.handle.net/10754/666105
dc.description.abstractWe develop a multilayer nonlinear elimination preconditioned inexact Newton method for a nonlinear algebraic system of equations, and a target application is the three-dimensional steady-state incompressible Navier--Stokes equations at high Reynolds numbers. Nonlinear steadystate problems are often more difficult to solve than time-dependent problems because the Jacobian matrix is less diagonally dominant, and a good initial guess from the previous time step is not available. For such problems, Newton-like methods may suffer from slow convergence or stagnation even with globalization techniques such as line search. In this paper, we introduce a cascadic multilayer nonlinear elimination approach based on feedback from intermediate solutions to improve the convergence of Newton iteration. Numerical experiments show that the proposed algorithm is superior to the classical inexact Newton method and other single layer nonlinear elimination approaches in terms of the robustness and efficiency. Using the proposed nonlinear preconditioner with a highly parallel domain decomposition framework, we demonstrate that steady solutions of the Navier--Stokes equations with Reynolds numbers as large as 7,500 can be obtained for the lid-driven cavity flow problem in three dimensions without the use of any continuation methods.
dc.description.sponsorshipThe first author is supported in part by NSFC 11701547. The third author is supported in part by NSFC 11901559.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttps://epubs.siam.org/doi/10.1137/19M1307184
dc.rightsArchived with thanks to SIAM Journal on Scientific Computing
dc.rights.uriRedistribution subject to SIAM license or copyright.
dc.titleA Multilayer Nonlinear Elimination Preconditioned Inexact Newton Method for Steady-State Incompressible Flow Problems in Three Dimensions
dc.typeArticle
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentOffice of the President
dc.identifier.journalSIAM Journal on Scientific Computing
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionDepartment of Mathematics, University of Macau, Macau, China.
dc.contributor.institutionShenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China.
dc.identifier.volume42
dc.identifier.issue6
dc.identifier.pagesB1404-B1428
kaust.personLuo, Li
kaust.personKeyes, David E.
dc.date.accepted2020-03-03
refterms.dateFOA2020-11-25T11:34:40Z
dc.date.published-online2020-11-24
dc.date.published-print2020-01


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