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ISSN 2753-3239
ISSN 2753-3239
CCC: 14
PROCEEDINGS OF THE SIXTEENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
PROCEEDINGS OF THE SIXTEENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: P. Iványi, J. Kruis and B.H.V. Topping
Paper 2.3
Investigating Heavy-Ball Method as a Synchronization-Free Alternative to Conjugate Gradients
D. Hrbáč1, D. Horák2,3 and J. Kružík2,3
1Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VSB - Technical University of Ostrava, Czechia
2Department of Applied Mathematics, Faculty of Electrical Engineering and Computer Science, VSB - Technical University of Ostrava, Czechia
3Institute of Geonics, Czech Academy of Sciences, Ostrava, Czechia
Full Bibliographic Reference for this paper
D. Hrbáč, D. Horák, J. Kružík, "Investigating Heavy-Ball Method as a Synchronization-Free Alternative to Conjugate Gradients", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Sixteenth International Conference on
Computational Structures Technology", Civil-Comp Press, Edinburgh, UK,
Online volume: CCC 14, Paper 2.3, 2026, doi:10.4203/ccc.14.2.3
Keywords: heavy ball method, communication reduction, conjugate gradient, parallel computing, high-performance computing, iterative solvers, synchronisation-free.
Abstract
This paper investigates the heavy ball method as a synchronisation-free iterative solver for symmetric positive definite linear systems arising in finite element computations. Unlike conjugate gradient methods, heavy ball avoids global dot products and therefore removes global reductions from the iteration. We compare heavy ball with classical conjugate gradient and pipelined conjugate gradient on sparse matrices from structural mechanics, and we examine the effect of spectral parameter estimation using software-based eigenvalue estimates and Gershgorin bounds. The results show that heavy ball consistently eliminates global synchronisation but typically requires more iterations than conjugate-gradient-based methods. Its practical efficiency depends strongly on the quality and cost of spectral estimates. These findings suggest that heavy ball is not a universal replacement for conjugate gradient, but a promising alternative in communication-limited regimes where synchronisation dominates time to solution.
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