Journal of the
Korean Mathematical Society JKMS

We pay attention to a coupled problem by a penalty term which is induced from non-overlapping domain decomposition methods based on augmented Lagrangian methodology. The coupled problem is composed by two parts mainly; one is a problem associated with local problems in non-overlapping subdomains and the other is a coupled part over all subdomains due to the penalty term. For the speedup of iterative solvers for the coupled problem, we propose two different types of preconditioners: a block-diagonal preconditioner and an additive Schwarz preconditioner as overlapping domain decomposition methods. We analyze the coupled problem and the preconditioned problems in terms of their condition numbers. Finally we present numerical results which show the performance of the proposed methods.

Keywords: Coupled problem, penalty term, domain decomposition, preconditioners, additive Schwarz

MSC numbers: 65F10, 65N30, 65N55

Supported by: The work of the rst author was supported by the National Research Foundation of Korea (NRF) grant funded by Ministry of Science and ICT (MSIT) (NRF-2017R1A2B4011627). The work of the second author was supported in part by the NRF grant funded by MSIT (NRF-2019R1F1A1060746) and the 2017 Research Grant from Kangwon National University(No. 620170078).