Two-level extension of the hierarchical domain decomposition method

Abstract

For post peta-scale supercomputers that have tens of thousands of cores, efficient parallel algorithms for finite element analysis (FEA) have been in great demand. The domain decomposition method (DDM) is a well-known technique for parallel FEA and the hierarchical DDM (HDDM) is an efficient implementation of the DDM on massively parallel computers. The HDDM has two-level parallelization and is expected to achieve highly parallel efficiency. However, the HDDM is essentially the same as the original DDM. Therefore, the number of subdomains may increase with an increase in the problem size, and then the DDM and HDDM would suffer from an increase in the number of iterations and reduction in parallel efficiency. In this study, for huge-scale FEA in the post peta-scale era, a two-level extension of the HDDM is proposed. The proposed method adopts the DDM for solving a linear equation in the interior of a subdomain, that is, a recursive algorithm.