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Singular boundary method: A review and computer implementation aspects
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DOI：10.1016/j.enganabound.2022.12.004.png)
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Abstract
En 中文
This paper presents an overview of the singular boundary method (SBM) and its various engineering applica-tions. 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:
Singular boundary method
Fundamental solutions
Origin intensity factors
Engineering and scientific computing
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