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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)
 

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