THE BOUNDARY ELEMENT METHOD

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 comp...

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Published inInternational journal of computational methods Vol. 10; no. 6; pp. 1350037 - 1350091
Main Authors MUKHERJEE, SUBRATA, LIU, YIJUN
Format Journal Article
LanguageEnglish
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
Online AccessGet full text
ISSN0219-8762
1793-6969
DOI10.1142/S0219876213500370

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Abstract 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.
AbstractList 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.
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-electromechanical 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.
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.
Author MUKHERJEE, SUBRATA
LIU, YIJUN
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Keywords boundary element method
Boundary integral equation
elasticity
boundary node method
acoustics
fast multipole method
boundary contour method
potential theory
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Snippet 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...
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SubjectTerms 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
Title THE BOUNDARY ELEMENT METHOD
URI http://www.worldscientific.com/doi/abs/10.1142/S0219876213500370
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https://www.proquest.com/docview/1448707051
Volume 10
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