Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures

Patrick Amestoy (1, 2) , Alfredo Buttari (3, 2) , Jean-Yves L'Excellent (4, 5) , Théo Mary (6, 2)

1 Toulouse INP - Institut National Polytechnique (Toulouse)
2 IRIT-APO - Algorithmes Parallèles et Optimisation
3 CNRS - Centre National de la Recherche Scientifique
4 ROMA - Optimisation des ressources : modèles, algorithmes et ordonnancement
5 LIP - Laboratoire de l'Informatique du Parallélisme
6 UT3 - Université Toulouse III - Paul Sabatier

Matrices coming from elliptic Partial Differential Equations have been shown to have a low-rank property which can be efficiently exploited in multifrontal solvers to provide a substantial reduction of their complexity. Among the possible low-rank formats, the Block Low-Rank format (BLR) is easy to use in a general purpose multifrontal solver and its potential compared to standard (full-rank) solvers has been demonstrated. Recently, new variants have been introduced and it was proved that they can further reduce the complexity but their performance has never been analyzed. In this paper, we present a multithreaded BLR factorization, and analyze its efficiency and scalability in shared-memory multicore environments. We identify the challenges posed by the use of BLR approximations in multifrontal solvers and put forward several algorithmic variants of the BLR factorization that overcome these challenges by improving its efficiency and scalability. We illustrate the performance analysis of the BLR multifrontal factorization with numerical experiments on a large set of problems coming from a variety of real-life applications.

Mots clés: multicore architectures; sparse linear algebra; Block Low-Rank; multifrontal factorization

Domaines: Mathématiques [math]; Informatique [cs]

Patrick Amestoy, Alfredo Buttari, Jean-Yves L'Excellent, Théo Mary. Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures. ACM Transactions on Mathematical Software, 2019, 45 (1), pp.1-23. ⟨10.1145/3242094⟩. ⟨hal-01955766v2⟩