Some Nonoverlapping Domain Decomposition Methods

The purpose of this paper is to give a unified investigation of a class of nonoverlapping domain decomposition methods for solving second-order elliptic problems in two and three dimensions. The methods under scrutiny fall into two major categories: the substructuring--type methods and the Neumann--Neumann-type methods. The basic framework used for analysis is the parallel subspace correction method or additive Schwarz method, and other technical tools include local-global and global-local techniques. The analyses for both two- and three-dimensional cases are carried out simultaneously. Some internal relationships between various algorithms are observed and several new variants of the algorithms are also derived.