## Abstract

Inexact Newton algorithms are commonly used for solving large sparse nonlinear system of equations F(u*) = 0 arising, for example, from the discretization of partial differential equations. Even with global strategies such as linesearch or trust region, the methods often stagnate at local minima of ∥F∥, especially for problems with unbalanced nonlinearities, because the methods do not have built-in machinery to deal with the unbalanced nonlinearities. To find the same solution u*, one may want to solve instead and equivalent nonlinearly preconditioned system F(u*) = 0 whose nonlinearities are more balanced. In this paper, we propose and study a nonlinear additive Schwarz-based parallel nonlinear preconditioner and show numerically that the new method converges well even for some difficult problems, such as high Reynolds number flows, where a traditional inexact Newton method fails.

Original language | English (US) |
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Pages (from-to) | 183-200 |

Number of pages | 18 |

Journal | SIAM Journal on Scientific Computing |

Volume | 24 |

Issue number | 1 |

DOIs | |

State | Published - Apr 15 2003 |

## Keywords

- Domain decomposition
- Incompressible flows
- Inexact Newton methods
- Krylov subspace methods
- Nonlinear additive Schwarz
- Nonlinear equations
- Nonlinear preconditioning
- Parallel computing

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics