Abstract
The Domain Decomposition Method (DDM) is a powerful approach to solving many types of PDE's. DDM is especially suitable for massively parallel computers. In the past, most research on DDM has focused on the domain splitting technique. In this paper, we focus our attention on use of a combination of techniques to solve each subproblem. The central question with DDM is that of how to deal with the pseudoboundary conditions. Here, we introduce a set of operators which act on the pseudo-boundaries in the solution process, referring to this new procedure as the “Generalized Domain Decomposition Method (GDDM).” We have already obtained convergence factors for GDDM with certain classes of PDE's. These convergence factors show that we can derive exact solutions of the whole problem for certain types of PDE's, and can get superior speed of convergence for other types.
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