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Sparse supernodal solver using block low-rank compression: Design, performance and analysis

Abstract : In this work, we present two approaches using a Block Low-Rank (BLR) compression technique to reduce the memory footprint and/or the time-to-solution of the sparse supernodal solver PaStiX. This flat, non-hierarchical, compression method allows to take advantage of the low-rank property of the blocks appearing during the factorization of sparse linear systems, which come from the discretization of partial differential equations. The proposed solver can be used either as a direct solver at a lower precision or as a very robust preconditioner. The first approach, called Minimal Memory, illustrates the maximum memory gain that can be obtained with the BLR compression method, while the second approach, called Just-In-Time, mainly focuses on reducing the computational complexity and thus the time-to-solution. Singular Value Decomposition (SVD), Rank-Revealing QR (RRQR), and other variants using randomized compression kernels, are compared in terms of factorization time, memory consumption, as well as numerical properties. On a set of matrices from real-life problems, we demonstrate a memory footprint reduction of up to 4 times using the Minimal Memory strategy and a computational time speedup of up to 3.5 times with the Just-In-Time strategy.
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https://hal.inria.fr/hal-02326407
Contributor : Pierre Ramet <>
Submitted on : Tuesday, October 22, 2019 - 5:08:45 PM
Last modification on : Friday, February 26, 2021 - 12:10:04 PM
Long-term archiving on: : Thursday, January 23, 2020 - 7:10:13 PM

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Grégoire Pichon, Eric Darve, Mathieu Faverge, Esragul Korkmaz, Pierre Ramet, et al.. Sparse supernodal solver using block low-rank compression: Design, performance and analysis. JOREK development meeting, Nov 2019, Cadarache, France. ⟨hal-02326407⟩

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