Restricted Additive Schwarz Method for Nonlinear Complementarity Problem with an M-Function

Abstract

Nonlinear complementarily problem (NCP) is a kind of very important problem. This kind of problem can be arisen from some complicated free boundary problem and other mathematical programming problem. In this paper, numerical solution of NCP with an M-function is considered. A new variant Schwarz method called restricted additive Schwarz method (RAS) is presented. Compared to classical additive Schwarz method, this method has many advantages, such as it reduces communication time while maintaining the most desirable used in practice. Some preliminary numerical results are reported. As we can see from the preliminary numerical results, the restricted additive Schwarz method spends less CPU time and needs fewer iteration numbers then classical additive Schwarz method and PSOR.