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    A Multilayer Nonlinear Elimination Preconditioned Inexact Newton Method for Steady-State Incompressible Flow Problems in Three Dimensions

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    Type
    Article
    Authors
    Luo, Li cc
    Cai, Xiao Chuan cc
    Yan, Zhengzheng
    Xu, Lei
    Keyes, David E. cc
    KAUST Department
    Extreme Computing Research Center
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Office of the President
    Date
    2020-11-24
    Online Publication Date
    2020-11-24
    Print Publication Date
    2020-01
    Submitted Date
    2019-12-16
    Permanent link to this record
    http://hdl.handle.net/10754/666105
    
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    Abstract
    We 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.
    Citation
    Luo, 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
    Sponsors
    The first author is supported in part by NSFC 11701547. The third author is supported in part by NSFC 11901559.
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Scientific Computing
    DOI
    10.1137/19m1307184
    Additional Links
    https://epubs.siam.org/doi/10.1137/19M1307184
    ae974a485f413a2113503eed53cd6c53
    10.1137/19m1307184
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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