Paper Info
Title
Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures
Abstract
Matrices coming from elliptic Partial Differential Equations have been shown to have a low-rank property that 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 article, 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.
Year
DOI
Venue
2019
10.1145/3242094
ACM Transactions on Mathematical Software (TOMS)
Keywords
Field
DocType
Block Low-Rank, Sparse linear algebra, multicore architectures, multifrontal factorization
Mathematical optimization,General purpose,Matrix (mathematics),Computer science,Parallel computing,Theoretical computer science,Factorization,Solver,Elliptic partial differential equation,Multi-core processor,Scalability
Journal
Volume
Issue
ISSN
45
1
0098-3500
Citations 
PageRank 
References 
1
0.36
15
Authors
4
Name
Order
Citations
PageRank
Patrick R. Amestoy144644.24
Alfredo Buttari264753.60
Jean-Yves L'Excellent334836.02
Mary, T.4184.24