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In this paper, we revisit the nonoverlapping domain decomposition methods forsolving elliptic problems with high contrast coefficients. Some interestingresults are discovered. We find that the Dirichlet-Neumann algorithm andRobin-Robin algorithms may make full use of the ratio of coefficients.Actually, in the case of two subdomains, we show that their convergence ratesare $O(\epsilon)$, if $\nu_1\ll\nu_2$, where $\epsilon = \nu_1/\nu_2$ and$\nu_1,\nu_2$ are coefficients of two subdomains. Moreover, in the case of manysubdomains, the condition number bounds of Dirichlet-Neumann algorithm andRobin-Robin algorithm are $1+\epsilon(1+\log(H/h))^2$ and$C+\epsilon(1+\log(H/h))^2$, respectively, where $\epsilon$ may be a very smallnumber in the high contrast coefficients case. Besides, the convergencebehaviours of the Neumann-Neumann algorithm and Dirichlet-Dirichlet algorithmmay be independent of coefficients while they could not benefit from thediscontinuous coefficients. Numerical experiments are preformed to confirm ourtheoretical findings.

Domain Decomposition Methods for Elliptic Problems with High Contrast Coefficients Revisited