避免通信的块式低并行多前沿三角解法与多右边解法

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-01-12 DOI:10.1137/23m1568600

Patrick Amestoy, Olivier Boiteau, Alfredo Buttari, Matthieu Gerest, Fabienne Jézéquel, Jean-Yves L’Excellent, Theo Mary

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引用次数: 0

摘要

SIAM 矩阵分析与应用期刊》，第 45 卷，第 1 期，第 148-166 页，2024 年 3 月。摘要块低秩 (BLR) 压缩可以显著降低并行稀疏直接求解器的内存和时间成本。在本文中，我们研究了 BLR 三角求解阶段的性能，我们观察到在处理许多右边（RHS）时，BLR 三角求解阶段的性能不尽如人意。我们解释说，这是因为三角求解的瓶颈不在于访问 BLR LU 因子，而在于访问未压缩的 RHS。受这一发现的启发，我们提出了几种新的混合变体，它们结合了右视和左视通信模式，最大限度地减少了访问 RHS 的次数。我们通过理论分析证实，这些新变体可以显著减少总通信量。我们使用 MUMPS 求解器评估了这种减少对一系列实际应用的时间性能的影响，结果发现时间最多可减少 20%。

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Communication Avoiding Block Low-Rank Parallel Multifrontal Triangular Solve with Many Right-Hand Sides

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 148-166, March 2024.
Abstract. Block low-rank (BLR) compression can significantly reduce the memory and time costs of parallel sparse direct solvers. In this paper, we investigate the performance of the BLR triangular solve phase, which we observe to be underwhelming when dealing with many right-hand sides (RHS). We explain that this is because the bottleneck of the triangular solve is not in accessing the BLR LU factors, but rather in accessing the RHS, which are uncompressed. Motivated by this finding, we propose several new hybrid variants, which combine the right-looking and left-looking communication patterns to minimize the number of accesses to the RHS. We confirm via a theoretical analysis that these new variants can significantly reduce the total communication volume. We assess the impact of this reduction on the time performance on a range of real-life applications using the MUMPS solver, obtaining up to 20% time reduction.

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来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.