特異応力問題における大規模並列有限要素法の収束性評価

概要

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In this study, a parallel Finite Element Method was applied to large-scale singular stress problems and its applicability was investigated in the following three aspects ; 1. The influence of stress singularity on the parallel performance. 2. The relationship between the scale of analysis and its accuracy. 3. The influence of domain decomposition pattern that it has on the convergence behavior of linear equation solvers. A dissimilar material, which has a V-notch at the end of its interface, was analyzed as an example of stress singular problem. Obtained results are : 1. The speed-up ratio obtained is 93% or higher at the smallest model, which has the smallest granularity. 2. The accuracy of the result was compared with the Bogy's theoretical accuracy, and it has been observed that the accuracy increases as the analysis scale becomes large. 3. In the case of no preconditioning or the diagonal preconditioning, the number of iteration needed to attain the convergence was not influenced by the domain decomposition patterns, while using the SSOR preconditioning, the convergence became faster when the singular area was contained in one subdomain, since the condition number was decreased.
日本シミュレーション学会の論文
2003-03-15