Balancing Domain Decomposition: Theory and Performance in Two and Three Dimensions

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

Abstract

The Balancing Domain Decomposition method uses in each iteration the solution of a local problem on each subdomain that is used to propogate the error globally and to guarantee that the possibly singular local problems are consistent. The abstract theory introduced in [19] is used to develop condition number bounds for conforming linear elements in two and three dimensions. The bounds are independent of arbitrary coefficient jumps between subdomains and the number of subdomains and only grow as the squared logarithm of the mesh size h. Computational experiments for the two and three-dimensional problems confirm the theory and in addition show that the method is remarkably resilent and performs very well for strongly discontinuous coefficients as well as unstructured subdomains.


Contributed December 16, 1992.