Nonlinearly Preconditioned Inexact Newton Algorithms 论文

详细信息

发表期刊/会议

SIAM Journal on Scientific Computing

发表日期

2002-01-01

发表年份

2002

摘要

. 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 di#erential equations. Even with global strategies such as line search 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, an equivalent nonlinearly preconditioned system G(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 di#cult problems, such as high Reynolds number flows, when a traditional inexact Newton method fails. Key words. Nonlinear preconditioning, inexact Newton methods, Krylov subspace methods, nonlinear additive Schwarz, domain decomposition, nonlinear equations, parallel computing, incompressible flows 1.