A fast Fourier transform on multipoles (FFTM) algorithm for solving Helmholtz equation in acoustics analysis.
This article presents a fast algorithm for the efficient solution of the Helmholtz equation. The method is based on the translation theory of the multipole expansions. Here, the speedup comes from the convolution nature of the translation operators, which can be evaluated rapidly using fast Fourier transform algorithms. Also, the computations of the translation operators are accelerated by using the recursive formulas developed recently by Gumerov and Duraiswami [SIAM J. Sci. Comput. 25, 1344-1381(2003)]. It is demonstrated that the algorithm can produce good accuracy with a relatively low order of expansion. Efficiency analyses of the algorithm reveal that it has computational complexities of O(Na), where a ranges from 1.05 to 1.24. However, this method requires substantially more memory to store the translation operators as compared to the fast multipole method. Hence, despite its simplicity in implementation, this memory requirement issue may limit the application of this algorithm to solving very large-scale problems.
Ong
Eng Teo
ET
Institute of High Performance Computing, Science Park II, Singapore 117528. onget@ihpc.a-star.edu.sg
Lee
Heow Pueh
HP
Lim
Kian Meng
KM
D000161:Acoustic Stimulation; D000162:Acoustics; D000465:Algorithms; D001307:Auditory Perception / Q000502:physiology*; D005583:Fourier Analysis; D006801:Humans