An adaptive nonlinear elimination preconditioned inexact Newton algorithm for highly local nonlinear multicomponent PDE systems

Haijian Yang, Feng Nan Hwang

研究成果: 雜誌貢獻期刊論文同行評審

9 引文 斯高帕斯(Scopus)

摘要

This work aims to develop an adaptive nonlinear elimination preconditioned inexact Newton method as the numerical solution of large sparse multi-component partial differential equation systems with highly local nonlinearity. A nonlinear elimination algorithm used as a nonlinear preconditioner has been shown to be a practical technique for enhancing the robustness and improving the efficiency of an inexact Newton method for some challenging problems, such as the transonic full potential problems. The basic idea of our method is to remove some components causing troubles in order to decrease the impact of local nonlinearity on the global system. The two key elements of the method are the valid identification of the to-be-eliminated components and the choice of subspace correction systems, respectively. In the method, we employ the point-wise residual component of nonlinear systems as an indicator for selecting these to-be-eliminated components adaptively and build a subspace nonlinear system consisting of the components corresponding to the bad region and an auxiliary linearized subsystem to reduce the interfacial jump pollution. The numerical results demonstrate that the new approach significantly improves performance for incompressible fluid flow and heat transfer problems with highly local nonlinearity when compared to the classical inexact Newton method.

原文???core.languages.en_GB???
頁(從 - 到)100-115
頁數16
期刊Applied Numerical Mathematics
133
DOIs
出版狀態已出版 - 11月 2018

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