On the relationship between the multiscale finite-volume method and domain decomposition preconditioners

In this paper, we review the classical nonoverlapping domain decomposition (NODD) preconditioners, together with the newly developed multiscale control volume (MSCV) method. By comparing the formulations, we observe that the MSCV method is a special case of a NODD preconditioner. We go on to suggest how the more general framework of NODD can be applied in the multiscale context to obtain improved multiscale estimates.