Abstract
It is well known that Green's function can be expressed by multipole expansion, plane-wave expansion, and exponential expansion (spectral representation). These three expansions constitute of the foundations of the fast multipole algorithm (FMA). The plane-wave expansion has the low-frequency breakdown issue due to its failure in capturing the evanescent spectra, while the multipole expansion is inefficient at high frequencies. The spectral representation usually involves in direction-dependent issue. In this communication, the 2-D FMA is interpreted as Parseval's theorem in Fourier transform. To achieve a stable and accurate transition between the multipole expansion and the plane-wave expansion, a novel diagonalization in the 2-D FMA is proposed with scaled special functions based on a discrete Fourier transform. A wideband fast algorithm with high accuracies can be achieved efficiently.
Recommended Citation
L. L. Meng et al., "A Wideband 2-D Fast Multipole Algorithm With A Novel Diagonalization Form," IEEE Transactions on Antennas and Propagation, vol. 66, no. 12, pp. 7477 - 7482, article no. 8472206, Institute of Electrical and Electronics Engineers, Dec 2018.
The definitive version is available at https://doi.org/10.1109/TAP.2018.2872167
Department(s)
Electrical and Computer Engineering
Keywords and Phrases
Discrete Fourier transform (DFT); multipole expansion; Parseval's theorem; plane-wave expansion
International Standard Serial Number (ISSN)
0018-926X
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Institute of Electrical and Electronics Engineers, All rights reserved.
Publication Date
01 Dec 2018
Comments
National Science Foundation, Grant EECS 1609195