Towards a parallel algebraic multigrid solver using PGAS

Abstract

The Algebraic Multigrid (AMG) method has over the years developed into an efficient tool for solving unstructured linear systems. The need to solve large industrial problems discretized on unstructured meshes, has been a key motivation for devising a parallel AMG method. Despite some success, the key part of the AMG algorithm; the coarsening step, is far from trivial to parallelize efficiently. We here introduce a novel parallelization of the inherently sequential Ruge-Stüben coarsening algorithm, that retains most of the good interpolation properties of the original method. Our parallelization is based on the Partitioned Global Address Space (PGAS) abstraction, which greatly simplifies the parallelization as compared to traditional message passing based implementations. The coarsening algorithm and solver is described in detail and a performance study on a Cray XC40 is presented.