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AN EFFICIENT MULTICORE IMPLEMENTATION OF A NOVEL HSS-STRUCTURED MULTIFRONTAL SOLVER USING RANDOMIZED SAMPLING.

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Title: AN EFFICIENT MULTICORE IMPLEMENTATION OF A NOVEL HSS-STRUCTURED MULTIFRONTAL SOLVER USING RANDOMIZED SAMPLING.
Authors: GHYSELS, PIETER1 pghysels@lbl.gov, LI, XIAOYE S.1 xsli@lbl.gov, ROUET, FRANÇOIS-HENRY1 fhrouet@lbl.gov, WILLIAMS, SAMUEL1 swwilliams@lbl.gov, NAPOV, ARTEM2 anapov@ulb.ac.be
Source: SIAM Journal on Scientific Computing. 2016, Vol. 38 Issue 5, pS358-S384. 27p.
Subjects: Linear systems, Semiseparable matrices, Algorithms, Partial differential equations, Finite element method
Abstract: 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-ofthe-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. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract: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-ofthe-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. [ABSTRACT FROM AUTHOR]
ISSN:10648275
DOI:10.1137/15M1010117