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

The Balancing Domain Decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate 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 coeecient jumps between subdomains and of the number of subdomains, and grow only as the squared logarithm of the mesh size h. Computational experiments for two and three-dimensional problems connrm the theory and, in addition, show that the method is remarkably resilient and performs very well for strongly discontinuous coeecients as well as unstructured subdomains.