THE BOUNDARY ELEMENT METHOD

• Published in: International journal of computational methods Vol. 10; no. 6; pp. 1350037 - 1350091
• Main Authors: MUKHERJEE, SUBRATA, LIU, YIJUN
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 01.12.2013; World Scientific Publishing Co. Pte., Ltd
• Subjects: Acoustics; Boundaries; Boundary element method; Computation; Computer simulation; Elasticity; Finite difference method; Finite element method; Integral equations; Mathematical analysis; Mathematical models; Mechanical systems; Methods; Nonlinear programming; Potential theory; Software; boundary element method; Boundary integral equation; elasticity; boundary node method; acoustics; fast multipole method; boundary contour method; potential theory
• ISSN: 0219-8762; 1793-6969
• DOI: 10.1142/S0219876213500370

The boundary element method (BEM), along with the finite element and finite difference methods, is commonly used to carry out numerical simulations in a wide variety of subjects in science and engineering. The BEM, rooted in classical mathematics of integral equations, started becoming a useful computational tool around 50 years ago. Many researchers have worked on computational aspects of this method during this time. This paper presents an overview of the BEM and related methods. It has three sections. The first, relatively short section, presents the governing equations for classical applications of the BEM in potential theory, linear elasticity and acoustics. The second describes specialized applications in bodies with thin features including micro-electro-mechanical systems (MEMS). The final section addresses current research. It has three subsections that present the boundary contour, boundary node and fast multipole methods (BCM, BNM and FMM), respectively. Several numerical examples are included in the second and third sections of this paper.