  Multiscale methods for second order elliptic equations based on
non-overlapping domain decomposition schemes have great potential to take
advantage of multi-core, state-of-the-art parallel computers. These methods
typically involve solving local boundary value problems followed by the
solution of a global interface problem. Known iterative procedures for the
solution of the interface problem have typically slow convergence, increasing
the overall cost of the multiscale solver. To overcome this problem we develop
a scalable recursive solution method for such interface problem that replaces
the global problem by a family of small interface systems associated with
adjacent subdomains, in a hierarchy of nested subdomains. Then, we propose a
novel parallel algorithm to implement our recursive formulation in multi-core
devices using the Multiscale Robin Coupled Method by Guiraldello et al. (2018),
that can be seen as a generalization of several multiscale mixed methods.
Through several numerical studies we show that the new algorithm is very fast
and exhibits excellent strong and weak scalability. We consider very large
problems, that can have billions of discretization cells, motivated by the
numerical simulation of subsurface flows.
