Fast Multipole Method Accelerated by Lifting Wavelet Transform Scheme
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Fast Multipole Method Accelerated by Lifting Wavelet Transform SchemeAbstract
The lifting wavelet like transform (LWLT) is applied to the fast multipole method (FMM) to complete the scattering analysis of three-dimensional (3D) objects. The aggregation matrix and disaggregation matrix are sparsified by the LWLT scheme in time. Numerical results for different shaped three-dimensional objects are considered. It is shown that the proposed method can speed up FMM with lower memory required.
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References
V. Rokhlin, “Rapid solution of integral
equations of scattering theory in two
dimensions,” J. of Comput. Phys., vol. 86, no.
, pp. 414-439, 1990.
N. Engheta, W. D. Murphy, V. Rokhlin, and
M. S. Vassiliou, “The fast multipole method
(FMM) for electromagnetic scattering
problems,” IEEE Trans. Antennas Propagat .,
vol. 40, no. 6, pp. 634-641, 1992.
R.Coifman and V.Rokhlin, “The fast
multipole method for the wave equation:a
pedestrian prescription,” IEEE Antennas
Propagat. Mag., vol. 35, no. 3, pp. 7-12,
J. M. Song and W. C. Chew, “Multilevel
fast-multipole algorithm for solving
combined field integral equations of
electromagnetic scattering,” Micro. Opt.
Tech. Lett., vol. 10, no. 1, pp. 14-19, 1995.
T. F. Eibert, “A diagonalized multilevel fast
multipole method with spherical harmonics
expansion of the k-space integrals,” IEEE
Trans. Antennas Propag. , vol. 53, no. 2, pp.
-817, 2005.
R. L. Wagner and W. C. Chew, “A Study of
Wavelets for the Solution of Electromagnetic
Integral-Equations,” IEEE Transactions on
Antennas and Propagation, vol. 43, no. 8, pp.
-810, 1995.
Z. G. Xiang and Y. L. Lu, “A study of the
fast wavelet transform method in
computational electromagnetics”, IEEE
Trans. Magnetics, vol. 34, no. 5, pp. 3323-
, 1998.
H. Deng and H. Ling, “Preconditioning of
electromagnetic integral equations using pre-
defined wavelet packet basis,” Elect. Lett .,
vol. 35, no. 14, pp. 1144-1145, 1999.
J. Yu and A. A. Kishk, “Use of wavelet
transform to the method-of-moments matrix
arising from electromagnetic scattering
problems of 2D objects due to oblique plane-
wave incidence,” Micro. Opt. Tech. Lett., vol.
, no. 2, pp. 130-134, 2002.
D. Huybrechs and S. Vandewalle, “A two-
dimensional wavelet-packet transform for
matrix compression of integral equations
with highly oscillatory kernel,” J. Comput.
App. Math., vol. 197, no. 1, pp. 218-232,
I. Daubechies and W. Sweldens, “Factoring
wavelet transforms into lifting steps,” J. of
Fourier Analysis and App ., vol. 4, no. 3, pp.
-269, 1998.
R. L. Wagner, and W. C. Chew, “A ray-
propagation fast multipole algorithm,” Micro.
Opt. Tech. Lett., vol. 7, no. 10, pp. 435-438,
F. P. Andriulli, G. Vecchi, F. Vipiana, P.
Pirinoli, and A. Tabacco, “Optimal A priori
clipping estimation for wavelet-based
method of moments matrices,” IEEE Trans.
Antennas Prop., vol. 53, no. 11, pp. 3726-
, 2005
