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

License
Redistribution subject to SIAM license or copyright.

Type
Article

Authors
Luo, Li
Cai, Xiao Chuan
Yan, Zhengzheng
Xu, Lei
Keyes, David E.

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

Online Publication Date
2020-11-24

Print Publication Date
2020-01

Date
2020-11-24

Submitted Date
2019-12-16

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

Acknowledgements
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

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