A Massively Parallel Algebraic Multigrid Preconditioner based on Aggregation for Elliptic Problems with Heterogeneous Coefficients

This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that detects changes in the coefficients and prevents aggregation across them. Using decoupled aggregation on each process with data agglomeration onto fewer processes on the coarse level, it weakly scales well in terms of both total time to solution and time per iteration to nearly 300,000 cores. Because of simple piecewise constant interpolation between the levels, its memory consumption is low and allows solving problems with more than 100,000,000,000 degrees of freedom.