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

## TL;DR

This paper presents a parallel algebraic multigrid implementation that reduces communication costs by exploiting intra-node communication, significantly improving scalability for solving large sparse linear systems.

## Contribution

It introduces a node-aware communication strategy for AMG that decreases inter-node messages, enhancing scalability during setup and solve phases.

## Key findings

- Reduced inter-node communication leads to better scalability.
- Performance tests show improved efficiency in intra- and inter-node communication.
- The method maintains solver accuracy while decreasing communication overhead.

## Abstract

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.

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Source: https://tomesphere.com/paper/1904.05838