A flexible sparse matrix data format and parallel algorithms for the assembly of finite element matrices on shared memory systems

IF 2 4区计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Parallel Computing Pub Date : 2023-09-01 DOI:10.1016/j.parco.2023.103039

Adam Sky , César Polindara , Ingo Muench , Carolin Birk

引用次数: 0

Abstract

Finite element methods require the composition of the global stiffness matrix from local finite element contributions. The composition process combines the computation of element stiffness matrices and their assembly into the global stiffness matrix, which is commonly sparse. In this paper we focus on the assembly process of the global stiffness matrix and explore different algorithms and their efficiency on shared memory systems using C++. A key aspect of our investigation is the use of atomic synchronization primitives for the derivation of data-race free algorithms and data structures. Furthermore, we propose a new flexible storage format for sparse matrices and compare its performance with the compressed row storage format using abstract benchmarks based on common characteristics of finite element problems.

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一种灵活的稀疏矩阵数据格式及其在共享存储系统上有限元矩阵装配的并行算法

有限元方法要求由局部有限元贡献组成整体刚度矩阵。组合过程将单元刚度矩阵的计算及其组装成全局刚度矩阵，该矩阵通常是稀疏的。本文以全局刚度矩阵的装配过程为研究对象，探讨了不同的装配算法及其在共享存储系统上的效率。我们研究的一个关键方面是使用原子同步原语来派生无数据竞争的算法和数据结构。此外，我们提出了一种新的稀疏矩阵的灵活存储格式，并使用基于有限元问题共同特征的抽象基准将其性能与压缩行存储格式进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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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