  A three dimensional parallel implementation of Multiscale Mixed Methods based
on non-overlapping domain decomposition techniques is proposed for multi-core
computers and its computational performance is assessed by means of numerical
experimentation. As a prototypical method, from which many others can be
derived, the Multiscale Robin Coupled Method is chosen and its implementation
explained in detail. Numerical results for problems ranging from millions up to
more than 2 billion computational cells in highly heterogeneous anisotropic
rock formations based on the SPE10 benchmark are shown. The proposed
implementation relies on direct solvers for both local problems and the
interface coupling system. We find good weak and strong scalalability as
compared against a state-of-the-art global fine grid solver based on Algebric
Multigrid preconditioning in single and two-phase flow problems.
