Recent Advances in Boundary Element Methods
pp 287303
Development of the Fast Multipole Boundary Element Method for Acoustic Wave Problems
 Yijun LiuAffiliated withDepartment of Mechanical Engineering, University of Cincinnati Email author
 , Liang ShenAffiliated withDepartment of Mechanical Engineering, University of Cincinnati
 , Milind BapatAffiliated withDepartment of Mechanical Engineering, University of Cincinnati
Abstract
In this chapter, we review some recent development of the fast multipole boundary element method (BEM) for solving largescale acoustic wave problems in both 2D and 3D domains. First, we review the boundary integral equation (BIE) formulations for acoustic wave problems. The BurtonMiller BIE formulation is emphasized, which uses a linear combination of the conventional BIE and hypersingular BIE. Next, the fast multipole formulations for solving the BEM equations are provided for both 2D and 3D problems. Several numerical examples are presented to demonstrate the effectiveness and efficiency of the developed fast multipole BEM for solving largescale acoustic wave problems, including scattering and radiation problems, and halfspace problems.
 Title
 Development of the Fast Multipole Boundary Element Method for Acoustic Wave Problems
 Book Title
 Recent Advances in Boundary Element Methods
 Book Subtitle
 A Volume to Honor Professor Dimitri Beskos
 Pages
 pp 287303
 Copyright
 2009
 DOI
 10.1007/9781402097102_19
 Print ISBN
 9781402097096
 Online ISBN
 9781402097102
 Publisher
 Springer Netherlands
 Copyright Holder
 Springer Science+Business Media B.V.
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 Editors

 George D. Manolis ^{(1)}
 Dr D. Polyzos ^{(2)}
 Editor Affiliations

 1. Department of Civil Engineering, Aristotle University
 2. Department of Mechanical Engineering and Institute of Chemical Engineering&High Temperature Processes, University of Patras
 Authors

 Yijun Liu ^{(3)}
 Liang Shen ^{(3)}
 Milind Bapat ^{(3)}
 Author Affiliations

 3. Department of Mechanical Engineering, University of Cincinnati, 452210072, Cincinnati, Ohio, USA
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