Journal of the
Korean Mathematical Society JKMS

A dual substructuring method with a penalty term was introduced in the previous works by the authors, which is a variant of the \fetidp \ method. The proposed method imposes the continuity not only by using Lagrange multipliers but also by adding a penalty term which consists of a positive penalty parameter $\eta$ and a measure of the jump across the interface. Due to the penalty term, the proposed iterative method has a better convergence property than the standard \fetidp \ method in the sense that the condition number of the resulting dual problem is bounded by a constant independent of the subdomain size and the mesh size. In this paper, a further study for a dual iterative substructuring method with a penalty term is discussed in terms of its convergence analysis. We provide an improved estimate of the condition number which shows the relationship between the condition number and $\eta$ as well as a close spectral connection of the proposed method with the \fetidp \ method. As a result, a choice of a moderately small penalty parameter is guaranteed.

Keywords: augmented Lagrangian, domain decomposition, dual substructuring, FETI-DP, penalty parameter

MSC numbers: 65F10, 65N30, 65N55