Balancing Domain Decomposition

J. Mandel
Center for Computational Mathematics
University of Colorado at Denver
Denver, CO 80217-3364


The Newumann-Neumann algorithm is known to be an efficient domain decomposition preconditioner with unstructured subdomains for iterative solution of finite element discretizations of difficult problems with highly discontinuous coefficients [6]. However, this algorithm suffers from the need to solve in each iteration an inconsistent singular problem for every subdomain, and the convergence deteriorates with increasing number of subdomains due to the lack of a coarse problem to propagate the error globally. We show that the equilibrium conditions for the singular problems on subdomains lead to a simple and natural construction of a coarse problem. The construction is purely algebraic and applies also to systems, such as those that arise in elasticity. A convergence bound independent of the number of subdomains is proved and results of computational tests are reported.

Contributed December 16, 1992.