Asynchronous One-Level and Two-Level Domain Decomposition Solvers

TL;DR

This paper investigates asynchronous communication techniques in domain decomposition solvers, demonstrating significant speed-ups and scalability improvements on supercomputers, especially for large and heterogeneous systems.

Contribution

It introduces a scalable asynchronous two-level domain decomposition method utilizing MPI one-sided primitives, addressing load balancing and communication bottlenecks.

Findings

Achieved up to 4x speed-up over synchronous methods.

Demonstrated scalability on state-of-the-art supercomputers.

Improved performance in load imbalanced scenarios.

Abstract

Parallel implementations of linear iterative solvers generally alternate between phases of data exchange and phases of local computation. Increasingly large problem sizes on more heterogeneous systems make load balancing and network layout very challenging tasks. In particular, global communication patterns such as inner products become increasingly limiting at scale. We explore the use of asynchronous communication based on one-sided MPI primitives in a multitude of domain decomposition solvers. In particular, a scalable asynchronous two-level method is presented. We discuss practical issues encountered in the development of a scalable solver and show experimental results obtained on state-of-the-art supercomputer systems that illustrate the benefits of asynchronous solvers in load balanced as well as load imbalanced scenarios. Using the novel method, we can observe speed-ups of up to 4x over its classical synchronous equivalent.