An Iterative Substructuring Algorithm for Problems in Three Dimensions

In domain decomposition algorithms with more than a few subdomains, there is a crucial need for a mechanism to provide for global communication of information at each step of the iterative process. The convergence rate will decay rapidly with an increasing number of subdomains if communication is only between neighboring subdomains. For iterative substructuring algorithms (those domain decomposition algorithms that use nonoverlapping subdomains), the method that provides for good global communication in two dimensions does not work well for problems in three dimensions. In this paper we present an alternative approach for providing global communication that works well in three dimensions. Sample theoretical and numerical results are presented.