An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Ghysels, Pieter; Li, Xiaoye S.; Rouet, Francois -Henry; Williams, Samuel; Napov, Artem

doi:10.1137/15M1010117

Title: An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Journal Article · Thu Oct 27 00:00:00 EDT 2016 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/15M1010117· OSTI ID:1378736

Ghysels, Pieter ^[1]; Li, Xiaoye S. ^[1]; Rouet, Francois -Henry ^[1]; Williams, Samuel ^[1]; Napov, Artem ^[2]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Univ. Libre de Bruxelles, Brussels (Belgium)

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factorization leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to sevenfold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK (STRUctured Matrices PACKage), which also has a distributed memory component for dense rank-structured matrices.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1378736

Alternate ID(s):: OSTI ID: 1439185

Journal Information:: SIAM Journal on Scientific Computing, Vol. 38, Issue 5; ISSN 1064-8275

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 68 works

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Geometry-oblivious FMM for compressing dense SPD matrices Yu, Chenhan D.; Levitt, James; Reiz, Severin Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis on - SC '17 https://doi.org/10.1145/3126908.3126921	conference	January 2017
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97 MATHEMATICS AND COMPUTING
sparse Gaussian elimination
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parallel algorithm

Title: An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

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