Klawonn, Axel; Widlund, O.B.:

FETI and Neumann-Neumann Iterative Substructuring Methods: Connections and New Results

In: Communications on Pure and Applied Mathematics, Jg. 54 (2001) ; Nr. 1, S. 57-90
ISSN: 0010-3640
Zeitschriftenaufsatz / Fach: Mathematik
Abstract:
The FETI and Neumann-Neumann families of algorithms are among the best
known and most severely tested domain decomposition methods for elliptic partial
differential equations. They are iterative substructuring methods and have
many algorithmic components in common, but there are also differences. The
purpose of this paper is to further unify the theory for these two families of
methods and to introduce a new family of FETI algorithms. Bounds on the rate
of convergence, which are uniform with respect to the coefficients of a family of
elliptic problems with heterogeneous coefficients, are established for these new
algorithms. The theory for a variant of the Neumann-Neumann algorithm is also
redeveloped stressing similarities to that for the FETI methods. 
c 2001 John
Wiley & Sons, Inc.