On the relationship between the multiscale finite volume method and
domain decomposition preconditioners
In this talk we review the classical non-overlapping domain decomposition
(NODD) preconditioners, together with the newly developed multi-scale control
volume (MSCV) method. By comparing the formulations, we observe that the MSCV
method is a limited special case of a NODD preconditioner. We go on to suggest
how the more general framework of NODD can be applied in the multi-scale
context to obtain improved multi-scale estimates.
These results are placed in the setting of a more general comment on the
development of multi-scale method.