Two-level Nonlinear Additive Schwarz Preconditioned Inexact Newton Algorithms and Applications

Xiao-Chuan Cai

Department of Computer Science, University of Colorado, Boulder, CO 80309-0430,

David E. Keyes

Department of Mathematics, Old Dominion University, Norfolk, VA 23529-0077

Leszek Marcinkowski

Department of Computer Science, University of Colorado, Boulder, CO 80309-0430


Abstract

A one-level nonlinear additive Schwarz preconditioned inexact Newton method (ASPIN) was introduced recently for solving large sparse nonlinear systems of equations obtained from the discretization of nonlinear partial differential equations, and the method has proved to be much more robust than the traditional inexact Newton methods, especially for problems with unbalanced nonlinearities. However, the algorithm is not scalable with respect to the number of processors. In this talk, we present a parallel two-level version of ASPIN and show numerically that it is scalable both linearly and nonlinearly. Numerical results for some fluid dynamics problems will be reported.