Chapter

Recent Advances in Boundary Element Methods

pp 287-303

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

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Abstract

In this chapter, we review some recent development of the fast multipole boundary element method (BEM) for solving large-scale acoustic wave problems in both 2-D and 3-D domains. First, we review the boundary integral equation (BIE) formulations for acoustic wave problems. The Burton-Miller 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 2-D and 3-D problems. Several numerical examples are presented to demonstrate the effectiveness and efficiency of the developed fast multipole BEM for solving large-scale acoustic wave problems, including scattering and radiation problems, and half-space problems.