  The efficient solution of sparse, linear systems resulting from the
discretization of partial differential equations is crucial to the performance
of many physics-based simulations. The algorithmic optimality of multilevel
approaches for common discretizations makes them a good candidate for an
efficient parallel solver. Yet, modern architectures for high-performance
computing systems continue to challenge the parallel scalability of multilevel
solvers. While algebraic multigrid methods are robust for solving a variety of
problems, the increasing importance of data locality and cost of data movement
in modern architectures motivates the need to carefully exploit structure in
the problem.
  Robust logically structured variational multigrid methods, such as Black Box
Multigrid (BoxMG), maintain structure throughout the multigrid hierarchy. This
avoids indirection and increased coarse-grid communication costs typical in
parallel algebraic multigrid. Nevertheless, the parallel scalability of
structured multigrid is challenged by coarse-grid problems where the overhead
in communication dominates computation. In this paper, an algorithm is
introduced for redistributing coarse-grid problems through incremental
agglomeration. Guided by a predictive performance model, this algorithm
provides robust redistribution decisions for structured multilevel solvers.
  A two-dimensional diffusion problem is used to demonstrate the significant
gain in performance of this algorithm over the previous approach that used
agglomeration to one processor. In addition, the parallel scalability of this
approach is demonstrated on two large-scale computing systems, with solves on
up to 500K+ cores.
