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A wideband fast multipole algorithm for two‐dimensional volume integral equations
Author(s) -
Nakashima N.,
Tateiba M.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2409
Subject(s) - computation , discretization , diagonal , integral equation , multipole expansion , wideband , fast fourier transform , mathematics , algorithm , fast multipole method , interpolation (computer graphics) , volume integral , cylinder , mathematical analysis , computer science , geometry , optics , physics , telecommunications , quantum mechanics , frame (networking)
This paper describes a wideband fast multipole algorithm (FMA) for the computation of two‐dimensional volume integral equations. Our previous paper presented the wideband FMA by switching between the diagonal and non‐diagonal forms according to cell size and required accuracy. In order to improve the efficiency of the algorithm, we use interpolation and filtering techniques. Moreover, we introduce a simple and efficient way to store sequences of the special functions and their discrete Fourier transforms. Numerical examples show that the computational and memory complexities are reduced from O ( N 2 ) to O ( N ), where N is the number of square elements followed by the discretization of the volume integral equations. The computation results show very good agreement with the analytical solutions. We present some numerical results for the computation of scattering from a cylindrical object with sharp edges and a Gaussian‐like inhomogeneous cylinder. Copyright © 2008 John Wiley & Sons, Ltd.