TY - JOUR

T1 - Singular boundary method

T2 - A review and computer implementation aspects

AU - Fu, Zhuojia

AU - Xi, Qiang

AU - Gu, Yan

AU - Li, Junpu

AU - Qu, Wenzhen

AU - Sun, Linlin

AU - Wei, Xing

AU - Wang, Fajie

AU - Lin, Ji

AU - Li, Weiwei

AU - Xu, Wenzhi

AU - Zhang, Chuanzeng

N1 - 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).

PY - 2023/2

Y1 - 2023/2

N2 - 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.

AB - 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.

KW - Engineering and scientific computing

KW - Fundamental solutions

KW - Origin intensity factors

KW - Singular boundary method

UR - http://www.scopus.com/inward/record.url?scp=85144468669&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2022.12.004

DO - 10.1016/j.enganabound.2022.12.004

M3 - Review article

AN - SCOPUS:85144468669

VL - 147

SP - 231

EP - 266

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

SN - 0955-7997

ER -