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

•Introduction of block low-rank compression in PaStiX sparse supernodal solver.•Development of a Minimal Memory strategy reducing the memory footprint of the solver.•Development of a Just-In-Time strategy focusing on reducing time-to-solution.•Analysis of performance, complexity, scalability and imp...

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Vydáno v:	Journal of computational science Ročník 27; s. 255 - 270
Hlavní autoři:	Pichon, Grégoire, Darve, Eric, Faverge, Mathieu, Ramet, Pierre, Roman, Jean
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier B.V 01.07.2018
Témata:	Block low-rank compression Multi-threaded architectures PaStiX sparse direct solver Sparse linear solver Multi-threaded architectures PaStiX sparse direct solver Sparse linear solver Block low-rank compression
ISSN:	1877-7503, 1877-7511
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Popis
Shrnutí:	•Introduction of block low-rank compression in PaStiX sparse supernodal solver.•Development of a Minimal Memory strategy reducing the memory footprint of the solver.•Development of a Just-In-Time strategy focusing on reducing time-to-solution.•Analysis of performance, complexity, scalability and impact of several parameters. This paper presents 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) and Rank-Revealing QR (RRQR), as compression kernels, are both compared in terms of factorization time, memory consumption, as well as numerical properties. Experiments on a shared memory node with 24 threads and 128 GB of memory are performed to evaluate the potential of both strategies. 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. Then, we study the impact of configuration parameters of the BLR solver that allowed us to solve a 3D laplacian of 36 million unknowns a single node, while the full-rank solver stopped at 8 million due to memory limitation.
ISSN:	1877-7503 1877-7511
DOI:	10.1016/j.jocs.2018.06.007