Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

An accelerated boundary element method using fast Fourier transform on multipoles

Kian-Meng Lima,*, Eng-Teo Ongb, Heow-Pueh Leea,b
aMechanical Engineering, National University of Singapore, Singapore 117576  bInstitute of High Performance Computing, Singapore 117528

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We present a fast algorithm, called the fast Fourier transform on multipoles (FFTM) method, for accelerating the boundary element method. The algorithm employs the multipole and local expansions to approximate far-field potentials and exploits the discrete convolution nature of the multipole to local translation operator to accelerate the potential evaluation process. The method is illustrated with a three-dimensional acoustics scattering problem governed by the Helmholtz equation. It is shown that the method has approximately linear computational complexity and it achieves accurate results with a relatively low order of expansion.

Keywords:  Boundary element method; Multipole; Fast Fourier transform; Acoustics scattering

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