Improving robustness and parallel scalability of Newton method through nonlinear preconditioning

Feng Nan Hwang, Xiao Chuan Cai

研究成果: 書貢獻/報告類型篇章同行評審

16 引文 斯高帕斯(Scopus)

摘要

Inexact Newton method with backtracking is one of the most popular techniques for solving large sparse nonlinear systems of equations. The method is easy to implement, and converges well for many practical problems. However, the method is not robust. More precisely speaking, the convergence may stagnate for no obvious reason. In this paper, we extend the recent work of Tuminaro, Walker and Shadid [2002] on detecting the stagnation of Newton method using the angle between the Newton direction and the steepest descent direction. We also study a nonlinear additive Schwarz preconditioned inexact Newton method, and show that it is numerically more robust. Our discussion will be based on parallel numerical experiments on solving some high Reynolds numbers steady-state incompressible Navier-Stokes equations in the velocity-pressure formulation.

原文???core.languages.en_GB???
主出版物標題Domain Decomposition Methods in Scienceand Engineering
發行者Springer Verlag
頁面201-208
頁數8
ISBN(列印)3540225234, 9783540225232
DOIs
出版狀態已出版 - 2005

出版系列

名字Lecture Notes in Computational Science and Engineering
40
ISSN(列印)1439-7358

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