A NEW FAMILY OF PRECONDITIONERS FOR DOMAIN DECOMPOSITION

This paper presents a new approach to construct preconditioners for th e domain decomposition-based preconditioned conjugate gradient methods . The idea is to approximate the spectrum of the Schur complement by s imple functions, such as rational approximations, which leads to solvi ng an easy, lower dimension interface problem. Examples are given for nonuniform grids on interfaces; this is a common situation for which n o effective preconditioners now exist. Theory and experimental data ar e given to illustrate the effectiveness of the author's approach in th is application.