juSFEM: A Julia-based open-source package of parallel Smoothed Finite Element Method (S-FEM) for elastic problems

• Published in: Computers & mathematics with applications (1987) 2021-01, Vol.81 (1), p.459-477
• Main Authors: Huo, Zenan, Mei, Gang, Xu, Nengxiong
• Format: Article
• Language: English
• Subjects: Benchmarks; Cantilever beams; Computational accuracy; Computational efficiency; Finite element analysis; Finite element method; Julia language; Mathematical models; Open source software; Packages; Parallel algorithm; Programming languages; Smoothed Finite Element Method (S-FEM); Software; Software development; Source code
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2020.01.027

The Smoothed Finite Element Method (S-FEM) proposed by Liu G.R. can achieve more accurate results than the conventional FEM. Currently, much commercial software and many open-source packages have been developed to analyze various science and engineering problems using the FEM. However, there is little work focusing on designing and developing software or packages for the S-FEM. In this paper, we design and implement an open-source package of the parallel S-FEM for elastic problems by utilizing the Julia language on multi-core CPU. The Julia language is a fast, easy-to-use, and open-source programming language that was originally designed for high-performance computing. We term our package as juSFEM. To the best of the authors’ knowledge, juSFEM is the first package of parallel S-FEM developed with the Julia language. To verify the correctness and evaluate the efficiency of juSFEM, two groups of benchmark tests are conducted. The benchmark results show that (1) juSFEM can achieve accurate results when compared to commercial FEM software ABAQUS, and (2) juSFEM only requires 543 s to calculate the displacements of a 3D elastic cantilever beam model which is composed of approximately 2 million tetrahedral elements, while in contrast the commercial FEM software needs 930 s for the same calculation model; (3) the parallel juSFEM executed on the 24-core CPU is approximately 20× faster than the corresponding serial version. Moreover, the structure and function of juSFEM are easily modularized, and the code in juSFEM is clear and readable, which is convenient for further development.