Efficient technique in low-frequency fast multipole boundary element method for plane-symmetric acoustic problems

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• 作者：Yosuke Yasuda^a ; ^{yyasuda@kanagawa-u.ac.jp} ; Kazutaka Higuchi^a ; Takuya Oshima^b ; Tetsuya Sakuma^c
• 关键词：Helmholtz equation ; Acoustic problems ; Fast multipole method (FMM) ; Plane-symmetric problems
• 刊名：Engineering Analysis with Boundary Elements
• 出版年：2012
• 期刊代码：51_09557997
• 类别：et
• 出版时间：October, 2012
• 卷：36
• 期：10
• 页码：1493-1501
• 文件大小：409 K

摘要

The fast multipole boundary element method (FMBEM) has been well known as a highly efficient BEM with the use of the fast multipole method (FMM). In the present paper, an efficient technique for plane-symmetric acoustic problems is proposed in the framework of an FMBEM based on the original multipole expansion theory (FMBEM for low-frequency problems: LF-FMBEM). Presented here are concrete computational procedures, which are based on the symmetries among multipole expansion coefficients for a plane-symmetric sound field produced by monopole or dipole sources. The proposed technique is straightforwardly applicable to a variety of formulations for the BEM, such as hypersingular, Burton-Miller, and indirect formulations. Numerical results show an ideal improvement of computational efficiency, with the proposed technique reducing both the computation time and required memory to about of those using the standard LF-FMBEM, where is the number of planes of symmetry.