PSelInv – A distributed memory parallel algorithm for selected inversion: The non-symmetric case

•Parallel selected inversion for non-symmetric sparse matrices.•High performance implementation on distributed memory platforms.•Experiments demonstrate excellent strong and weak scalability. This paper generalizes the parallel selected inversion algorithm called PSelInv to sparse non-symmetric matr...

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Vydané v:Parallel computing Ročník 74; číslo C; s. 84 - 98
Hlavní autori: Jacquelin, Mathias, Lin, Lin, Yang, Chao
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: United States Elsevier B.V 01.05.2018
Elsevier
Predmet:
High performance computation
MATHEMATICS AND COMPUTING
Non-symmetric
Parallel algorithm
Selected inversion
Parallel algorithm
High performance computation
Non-symmetric
Selected inversion
ISSN:0167-8191, 1872-7336
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Popis
Shrnutí:•Parallel selected inversion for non-symmetric sparse matrices.•High performance implementation on distributed memory platforms.•Experiments demonstrate excellent strong and weak scalability. This paper generalizes the parallel selected inversion algorithm called PSelInv to sparse non-symmetric matrices. We assume a general sparse matrix A has been decomposed as PAQ=LU on a distributed memory parallel machine, where L, U are lower and upper triangular matrices, and P, Q are permutation matrices, respectively. The PSelInvmethod computes selected elements of A−1. The selection is confined by the sparsity pattern of the matrix AT. Our algorithm does not assume any symmetry properties of A, and our parallel implementation is memory efficient, in the sense that the computed elements of A−T overwrites the sparse matrix L+Uin situ. PSelInv involves a large number of collective data communication activities within different processor groups of various sizes. In order to minimize idle time and improve load balancing, tree-based asynchronous communication is used to coordinate all such collective communication. Numerical results demonstrate that PSelInv can scale efficiently to 6,400 cores for a variety of matrices.
Bibliografia:AC02-05CH11231; 1450372
National Science Foundation (NSF)
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
USDOE Office of Science (SC), Basic Energy Sciences (BES)
ISSN:0167-8191
1872-7336
DOI:10.1016/j.parco.2017.11.009