Non - linear additive Schwarz preconditioners and application in computational uid dynamics 3

The focus of this paper is on the numerical solution of large sparse non-linear systems of algebraic 9 equations on parallel computers. Such non-linear systems often arise from the discretization of non-linear partial di erential equations, such as the Navier–Stokes equations for uid ows, using nite element 11 or nite di erence methods. A traditional inexact Newton method, applied directly to the discretized system, does not work well when the non-linearities in the algebraic system become unbalanced. In 13 this paper, we study some preconditioned inexact Newton algorithms, including the single-level and multilevel non-linear additive Schwarz preconditioners. Some results for solving the high Reynolds 15 number incompressible Navier–Stokes equations are reported. Copyright ? 2002 John Wiley & Sons, Ltd. 17