A Nonlinear Elimination Preconditioned Inexact Newton Algorithm

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

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish (US)
Pages (from-to)A1579-A1605
Number of pages1
JournalSIAM Journal on Scientific Computing
Volume44
Issue number3
DOIs
StatePublished - Jun 21 2022

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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