FETI and Neumann-Neumann iterative substructuring methods: Connections andnew results

The FETI and Neumann-Neumann families of algorithms are among the best know n and most severely tested domain decomposition methods for elliptic partia l differential equations. They are iterative substructuring methods and hav e many algorithmic components in common, but there are also differences. Th e purpose of this paper is to further unify the theory for these two famili es of methods and to introduce a new family of FETI algorithms. Bounds on t he rate of convergence, which are uniform with respect to the coefficients of a family of elliptic problems with heterogeneous coefficients, are estab lished for these new algorithms. The theory for a variant of the Neumann-Ne umann algorithm is also redeveloped stressing similarities to that for the FETI methods. (C) 2001 John Wiley & Sons, Inc.