Improving robustness and parallel scalability of Newton method through nonlinear preconditioning

Feng Nan Hwang, Xiao Chuan Cai

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

17 Scopus citations


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.

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Scienceand Engineering
PublisherSpringer Verlag
Number of pages8
ISBN (Print)3540225234, 9783540225232
StatePublished - 2005

Publication series

NameLecture Notes in Computational Science and Engineering
ISSN (Print)1439-7358


Dive into the research topics of 'Improving robustness and parallel scalability of Newton method through nonlinear preconditioning'. Together they form a unique fingerprint.

Cite this