Linear solvers for power grid optimization problems: A review of GPU-accelerated linear solvers

IF 2 4区计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Parallel Computing Pub Date : 2022-07-01 DOI:10.1016/j.parco.2021.102870

Kasia Świrydowicz , Eric Darve , Wesley Jones , Jonathan Maack , Shaked Regev , Michael A. Saunders , Stephen J. Thomas , Slaven Peleš

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引用次数: 19

Abstract

The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite, and they become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or ${LDL}^{T}$ decompositions. We benchmark five well known direct linear solver packages on CPU- and GPU-based hardware, using matrices extracted from power grid optimization problems. The achieved solution accuracy varies greatly among the packages. None of the tested packages delivers significant GPU acceleration for our test cases. For completeness of the comparison we include results for MA57, which is one of the most efficient and reliable CPU solvers for this class of problem.

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电网优化问题的线性求解器:gpu加速线性求解器综述

约束优化的内部方法所产生的线性方程是稀疏对称不定的，并且随着内部方法的收敛而变得极其病态。这些线性系统对现有的基于稀疏LU或LDLT分解的求解器框架提出了挑战。我们使用从电网优化问题中提取的矩阵，在基于CPU和gpu的硬件上对五个众所周知的直接线性求解器包进行基准测试。不同的封装所获得的解的精度差别很大。在我们的测试用例中，没有一个测试包提供显著的GPU加速。为了完整地比较，我们包括了MA57的结果，它是这类问题中最有效和最可靠的CPU求解器之一。

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来源期刊

Parallel Computing 工程技术-计算机：理论方法

CiteScore

3.50

自引率

7.10%

发文量

审稿时长

4.5 months

期刊介绍： Parallel Computing is an international journal presenting the practical use of parallel computer systems, including high performance architecture, system software, programming systems and tools, and applications. Within this context the journal covers all aspects of high-end parallel computing from single homogeneous or heterogenous computing nodes to large-scale multi-node systems. Parallel Computing features original research work and review articles as well as novel or illustrative accounts of application experience with (and techniques for) the use of parallel computers. We also welcome studies reproducing prior publications that either confirm or disprove prior published results. Particular technical areas of interest include, but are not limited to: -System software for parallel computer systems including programming languages (new languages as well as compilation techniques), operating systems (including middleware), and resource management (scheduling and load-balancing). -Enabling software including debuggers, performance tools, and system and numeric libraries. -General hardware (architecture) concepts, new technologies enabling the realization of such new concepts, and details of commercially available systems -Software engineering and productivity as it relates to parallel computing -Applications (including scientific computing, deep learning, machine learning) or tool case studies demonstrating novel ways to achieve parallelism -Performance measurement results on state-of-the-art systems -Approaches to effectively utilize large-scale parallel computing including new algorithms or algorithm analysis with demonstrated relevance to real applications using existing or next generation parallel computer architectures. -Parallel I/O systems both hardware and software -Networking technology for support of high-speed computing demonstrating the impact of high-speed computation on parallel applications

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