NDLI: PSelInv—A Distributed Memory Parallel Algorithm for Selected Inversion: The Symmetric Case

Content Provider	ACM Digital Library
Author	Lin, Lin Yang, Chao Jacquelin, Mathias
Copyright Year	2016
Description	Author Affiliation: Lawrence Berkeley National Laboratory, Berkeley CA USA(University of california, Berkeley and Lawrence Berkeley National Laboratory, Berkeley CA (Lin, Lin; Yang, Chao); Jacquelin, Mathias)
Abstract	We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call PSelInv. The PSelInv method computes selected elements of a general sparse matrix $\textit{A}$ that can be decomposed as $\textit{A}$ = $\textit{LU},$ where $\textit{L}$ is lower triangular and $\textit{U}$ is upper triangular. The implementation described in this article focuses on the case of sparse symmetric matrices. It contains an interface that is compatible with the distributed memory parallel sparse direct factorization SuperLU_DIST. However, the underlying data structure and design of PSelInv allows it to be easily combined with other factorization routines, such as PARDISO. We discuss general parallelization strategies such as data and task distribution schemes. In particular, we describe how to exploit the concurrency exposed by the elimination tree associated with the $\textit{LU}$ factorization of $\textit{A}.$ We demonstrate the efficiency and accuracy of PSelInv by presenting several numerical experiments. In particular, we show that PSelInv can run efficiently on more than 4,000 cores for a modestly sized matrix. We also demonstrate how PSelInv can be used to accelerate large-scale electronic structure calculations.
Starting Page	1
Ending Page	28
Page Count	28
File Format	PDF
ISSN	00983500
e-ISSN	15577295
DOI	10.1145/2786977
Volume Number	43
Issue Number	3
Journal	ACM Transactions on Mathematical Software (TOMS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2016-12-21
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Selected inversion Distributed memory parallel algorithm Electronic structure theory High-performance computation Sparse direct method
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Software

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