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An efficient exact numerical solution for scattering by a circular cylinder
Author(s) -
Zhu Chunhui,
Liu Lijun,
Song Zhengyong,
Liu Yanhui,
Liu Qing Huo
Publication year - 2016
Publication title -
ieej transactions on electrical and electronic engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.254
H-Index - 30
eISSN - 1931-4981
pISSN - 1931-4973
DOI - 10.1002/tee.22319
Subject(s) - fast fourier transform , cylinder , mathematics , convolution theorem , sampling (signal processing) , convolution (computer science) , convergence (economics) , scattering , mathematical analysis , boundary value problem , algorithm , harmonic , fourier transform , integral equation , wavelength , boundary (topology) , wavenumber , nyquist–shannon sampling theorem , computational complexity theory , geometry , computer science , optics , acoustics , fourier analysis , physics , filter (signal processing) , fractional fourier transform , machine learning , artificial neural network , economics , computer vision , economic growth
An efficient and exact spectral integral method (SIM) for the general problems of scattering by a circular cylinder is presented, both for acoustic and electromagnetic cases. Fast Fourier transform (FFT) and convolution theorem help us to execute the algorithm efficiently with O ( N log ( N ) ) computational complexity. The Fourier coefficients of the integral kernels are computed in a semianalytical way to accomplish a fast convergence rate with spectral accuracy. Compared with the method not using the semianalytical forms, without the increase of the computing and memory abundance, it saves more than 90 % sampling points to achieve about the same accuracy, and with the same number of sampling points, several to more than ten orders of magnitude more accuracy can be achieved. For example, for the tested large wavenumber case with 2 × 10 6 wavelengths on the boundary, only two sampling points per wavelength are required to achieve a relative error of less than 0.001 % . More than 90 % computational time is saved compared with the normal summation formula of harmonic cylinder expansions. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.