  We study an element agglomeration coarsening strategy that requires data
redistribution at coarse levels when the number of coarse elements becomes
smaller than the used computational units (cores). The overall procedure
generates coarse elements (general unstructured unions of fine grid elements)
within the framework of element-based algebraic multigrid methods (or AMGe)
studied previously. The AMGe generated coarse spaces have the ability to
exhibit approximation properties of the same order as the fine-level ones since
by construction they contain the piecewise polynomials of the same order as the
fine level ones. These approximation properties are key for the successful use
of AMGe in multilevel solvers for nonlinear partial differential equations as
well as for multilevel Monte Carlo (MLMC) simulations. The ability to coarsen
without being constrained by the number of available cores, as described in the
present paper, allows to improve the scalability of these solvers as well as in
the overall MLMC method. The paper illustrates this latter fact with detailed
scalability study of MLMC simulations applied to model Darcy equations with a
stochastic log-normal permeability field.
