Affiliation:
1. University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
2. University of New Mexico, Albuquerque, New Mexico, USA
Abstract
Krylov methods are a key way of solving large sparse linear systems of equations but suffer from poor strong scalability on distributed memory machines. This is due to high synchronization costs from large numbers of collective communication calls alongside a low computational workload. Enlarged Krylov methods address this issue by decreasing the total iterations to convergence, an artifact of splitting the initial residual and resulting in operations on block vectors. In this article, we present a performance study of an enlarged Krylov method, Enlarged Conjugate Gradients (ECG), noting the impact of block vectors on parallel performance at scale. Most notably, we observe the increased overhead of point-to-point communication as a result of denser messages in the sparse matrix-block vector multiplication kernel. Additionally, we present models to analyze expected performance of ECG, as well as motivate design decisions. Most importantly, we introduce a new point-to-point communication approach based on node-aware communication techniques that increases efficiency of the method at scale.
Funder
Department of Energy, National Nuclear Security Administration
National Science Foundation
National Center for Supercomputing Applications
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Computer Science Applications,Hardware and Architecture,Modeling and Simulation,Software
Reference35 articles.
1. Tarun Agarwal, Amit Sharma, A. Laxmikant, and Laxmikant V. Kalé. 2006. Topology-aware task mapping for reducing communication contention on large parallel machines. In Proceedings of the 20th IEEE International Parallel & Distributed Processing Symposium. IEEE, 10.
2. Improving the scalability of a symmetric iterative eigensolver for multi-core platforms
3. LogGP: Incorporating Long Messages into the LogP Model for Parallel Computation
4. MFEM: A modular finite element methods library
5. Allison H. Baker, Martin Schulz, and Ulrike M. Yang. 2010. On the performance of an algebraic multigrid solver on multicore clusters. In International Conference on High Performance Computing for Computational Science. Springer, 102–115.
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