Abstract
The iterative Domain Decomposition Method (DDM) is one of the most effective parallel algorithm for large scale problems due to its excellent parallelism and variety of researches have already been done. As the iterative DDM satisfies continuity among subdomains through the iterative calculations, it is indispensable to reduce the number of iterations with a preconditioning technique especially for speed-up for computing. Thus, we have chosen the Balancing Domain Decomposition (BDD) proposed by J. Mandel. The BDD is a Neumann-Neumann type preconditioner with a coarse grid correction, and then its convergence estimates are independent of the number of subdomains. In this research, we introduce the BDD algorithm and how to apply it for elastic problems, then we develop a parallel BDD based on the Hierarchical DDM (HDDM) and apply it to some numerical examples on parallel computers.
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