Singular boundary method

A review and computer implementation aspects

authored by: Zhuojia Fu, Qiang Xi, Yan Gu, Junpu Li, Wenzhen Qu, Linlin Sun, Xing Wei, Fajie Wang, Ji Lin, Weiwei Li, Wenzhi Xu, Chuanzeng Zhang
Abstract: This paper presents an overview of the singular boundary method (SBM) and its various engineering applications. The basic concepts of the singular boundary method are first introduced, such as the collocation scheme, fundamental solutions and origin intensity factors (OIFs). In the SBM implementation, the OIF-determination approaches are then classified into three categories, namely, the inverse interpolation technique (IIT), the subtracting and adding-back technique (SABT) and the integral mean value (IMV). Several additional schemes are introduced to resolve the non-uniqueness issue encountered in the SBM, and enable the application of the SBM to large-scale engineering and scientific computing, nonhomogeneous partial differential equations (PDEs), non-isotropic problems and initial-boundary value problems. Several selected numerical examples are presented and discussed to show the recent developments and applications of the SBM to the solution of some typical boundary value problems, such as anomalous heat conduction, high wavenumber acoustic wave propagation, water wave-structure interaction, elastic wave propagation and structural vibration induced underwater acoustic radiation in the shallow ocean environment and so on. Besides, some efficient techniques, such as moment condition and modified combined Helmholtz integral equation formulation (CHIEF), are introduced into the SBM to enhance its performance. Finally, the essential conclusions of the SBM are summarized and some future trends in this interesting research field are highlighted.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Hohai University
Qingdao University
Zhengzhou University
Nantong University
East China Jiaotong University
Shandong University of Technology
University of Siegen
Type: Review article
Journal: Engineering Analysis with Boundary Elements
Volume: 147
Pages: 231-266
No. of pages: 36
ISSN: 0955-7997
Publication date: 02.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Analysis, Engineering(all), Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.enganabound.2022.12.004 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{6d8522659122467dafb8450442f1290f,
title = "Singular boundary method: A review and computer implementation aspects",
abstract = "This paper presents an overview of the singular boundary method (SBM) and its various engineering applications. The basic concepts of the singular boundary method are first introduced, such as the collocation scheme, fundamental solutions and origin intensity factors (OIFs). In the SBM implementation, the OIF-determination approaches are then classified into three categories, namely, the inverse interpolation technique (IIT), the subtracting and adding-back technique (SABT) and the integral mean value (IMV). Several additional schemes are introduced to resolve the non-uniqueness issue encountered in the SBM, and enable the application of the SBM to large-scale engineering and scientific computing, nonhomogeneous partial differential equations (PDEs), non-isotropic problems and initial-boundary value problems. Several selected numerical examples are presented and discussed to show the recent developments and applications of the SBM to the solution of some typical boundary value problems, such as anomalous heat conduction, high wavenumber acoustic wave propagation, water wave-structure interaction, elastic wave propagation and structural vibration induced underwater acoustic radiation in the shallow ocean environment and so on. Besides, some efficient techniques, such as moment condition and modified combined Helmholtz integral equation formulation (CHIEF), are introduced into the SBM to enhance its performance. Finally, the essential conclusions of the SBM are summarized and some future trends in this interesting research field are highlighted.",
keywords = "Engineering and scientific computing, Fundamental solutions, Origin intensity factors, Singular boundary method",
author = "Zhuojia Fu and Qiang Xi and Yan Gu and Junpu Li and Wenzhen Qu and Linlin Sun and Xing Wei and Fajie Wang and Ji Lin and Weiwei Li and Wenzhi Xu and Chuanzeng Zhang",
note = "Funding Information: The first ten authors would like to dedicate this review paper to their venerated supervisor, the late Prof. Wen Chen (1967–2018) of Hohai University, China, for his education and guidance. Prof. Wen Chen was an Alexander von Humboldt Research Fellow and visited Chuanzeng Zhang as his host many times. Chuanzeng Zhang would like to dedicate his contribution to Prof. Wen Chen for pleasant collaboration and friendship over many years. The work described in this paper was supported by the National Science Fund of China (Grant Nos. 12122205, 11772119), Alexander von Humboldt Research Fellowship (ID: 1195938) and the Six Talent Peaks Project in Jiangsu Province of China (Grant No. 2019-KTHY-009). ",
year = "2023",
month = feb,
doi = "10.1016/j.enganabound.2022.12.004",
language = "English",
volume = "147",
pages = "231--266",
journal = "Engineering Analysis with Boundary Elements",
issn = "0955-7997",
publisher = "Elsevier Ltd.",
}