Performance Modeling of Algebraic Multigrid on Blue Gene/Q: Lessons Learned

The IBM Blue Gene/Q represents a large step in the evolution of massively parallel machines. It features 16-core compute nodes, with additional parallelism in the form of four simultaneous hardware threads per core, connected together by a five-dimensional torus network. Machines are being built with core counts in the hundreds of thousands, with the largest, Sequoia, featuring over 1.5 million cores. In this paper, we develop a performance model for the solve cycle of algebraic multigrid on Blue Gene/Q to help us understand the issues this popular linear solver for large, sparse linear systems faces on this architecture. We validate the model on a Blue Gene/Q at IBM, and conclude with a discussion of the implications of our results.