Improving Robustness and Parallel Scalability of Newton Method Through Nonlinear Preconditioning

  • Feng-Nan Hwang
  • Xiao-Chuan Cai
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)


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.


Newton Method High Reynolds Number Inexact Newton Method Newton Direction Steep Descent Direction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Feng-Nan Hwang
    • 1
  • Xiao-Chuan Cai
    • 2
  1. 1.Department of Applied MathematicsUniversity of Colorado at BoulderBoulderUSA
  2. 2.Department of Computer ScienceUniversity of Colorado at BoulderBoulderUSA

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