Domain Decomposition Methods for a Complementarity Problem*

Abstract

We introduce a family of parallel Newton-Krylov-Schwarz methods for solving complementarity problems. The methods are based on a smoothed grid sequencing method, a semismooth inexact Newton method, and a two-grid restricted overlapping Schwarz preconditioner. We show numerically that such an approach is highly scalable in the sense that the number of Newton iterations and the number of linear iterations are both nearly independent of the grid size and the number of processors. In addition, the method is not sensitive to the sharp discontinuity that is often associated with obstacle problems. We present numerical results for some large scale calculations obtained on machines with hundreds of processors.