Increasing the performance of the Jacobi-Davidson method by blocking

Journal article
(Original article)

Publication Details

Author(s): Röhrig-Zöllner M, Thies J, Kreutzer M, Alvermann A, Pieper A, Basermann A, Hager G, Wellein G, Fehske H
Journal: SIAM Journal on Scientific Computing
Publisher: Society for Industrial and Applied Mathematics Publications
Publication year: 2015
Volume: DLR Portal ISSN 1064-8275
Pages range: 1-27
ISSN: 1064-8275


Block variants of the Jacobi-Davidson method for computing a few eigenpairs of a large sparse matrix are known to improve the robustness of the standard algorithm when it comes to computing multiple or clustered eigenvalues. In practice, however, they are typically avoided because the total number of matrix-vector operations increases. In this paper we present the implementation of a block Jacobi-Davidson solver. By detailed performance engineering and numerical experiments we demonstrate that the increase in operations is typically more than compensated by performance gains through better cache usage on modern CPUs, resulting in a method that is both more efficient and robust than its single vector counterpart. The steps to be taken to achieve a block speedup involve both kernel optimizations for sparse matrix and block vector operations, and algorithmic choices to allow using blocked operations in most parts of the computation. We discuss the aspect of avoiding synchronization in the algorithm and show by numerical experiments with our hybrid parallel implementation that a significant speedup through blocking can be achieved for a variety of matrices on up to 5 120 CPU cores as long as at least about 20 eigenpairs are sought.

FAU Authors / FAU Editors

Hager, Georg Dr.
Regionales Rechenzentrum Erlangen (RRZE)
Kreutzer, Moritz
Regionales Rechenzentrum Erlangen (RRZE)
Wellein, Gerhard Prof. Dr.
Professur für Höchstleistungsrechnen

External institutions with authors

Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)
Universität Greifswald

How to cite

Röhrig-Zöllner, M., Thies, J., Kreutzer, M., Alvermann, A., Pieper, A., Basermann, A.,... Fehske, H. (2015). Increasing the performance of the Jacobi-Davidson method by blocking. SIAM Journal on Scientific Computing, DLR Portal ISSN 1064-8275, 1-27.

Röhrig-Zöllner, Melven, et al. "Increasing the performance of the Jacobi-Davidson method by blocking." SIAM Journal on Scientific Computing DLR Portal ISSN 1064-8275 (2015): 1-27.


Last updated on 2018-10-08 at 05:55