Reducing Communication in Algebraic Multigrid with Multi-step Node Aware Communication.

Algebraic multigrid (AMG) is often viewed as a scalable $\mathcal{O}(n)$ solver for sparse linear systems. Yet, parallel AMG lacks scalability due to increasingly large costs associated with communication, both in the initial construction of a multigrid hierarchy as well as the iterative solve phase. This work introduces a parallel implementation of AMG to reduce the cost of communication, yielding an increase in scalability. Standard inter-process communication consists of sending data regardless of the send and receive process locations. Performance tests show notable differences in the cost of intra- and inter-node communication, motivating a restructuring of communication. In this case, the communication schedule takes advantage of the less costly intra-node communication, reducing both the number and size of inter-node messages. Node-centric communication extends to the range of components in both the setup and solve phase of AMG, yielding an increase in the weak and strong scalability of the entire method.