A NONLINEAR ELIMINATION PRECONDITIONED INEXACT NEWTON ALGORITHM

Lulu Liu, Feng Nan Hwang, Li Luo, Xiao Chuan Cai, David E. Keyes

研究成果: 雜誌貢獻期刊論文同行評審

摘要

A nonlinear elimination preconditioned inexact Newton (NEPIN) algorithm is proposed for problems with localized strong nonlinearities. Due to unbalanced nonlinearities ("nonlinear stiffness"), the traditional inexact Newton method often exhibits a long plateau in the norm of the nonlinear residual or even fails to converge. NEPIN implicitly removes the components causing trouble for the global convergence through a correction based on nonlinear elimination within a subspace that provides a modified direction for the global Newton iteration. Numerical experiments show that NEPIN can be more robust than global inexact Newton algorithms and maintain fast convergence even for challenging problems, such as full potential transonic flows. NEPIN complements several previously studied nonlinear preconditioners with which it compares favorably experimentally on a classic shocked duct flow problem considered herein. NEPIN is shown to be fairly insensitive to mesh resolution and "bad" subproblem identification based on the local Mach number or the local nonlinear residual for transonic flow over a wing.

原文???core.languages.en_GB???
頁(從 - 到)A1579-A1605
期刊SIAM Journal on Scientific Computing
44
發行號3
DOIs
出版狀態已出版 - 2022

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