[天线]Efficient MLFMA, RPFMA, and FAFFA algorithms for EM scattering by very large structures

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 3, MARCH 2004 759 *m`KY)b=l  
Efficient MLFMA, RPFMA, and FAFFA Algorithms s(M8 Y  
for EM Scattering by Very Large Structures x)!NB99(tC  
Tie Jun Cui, Senior Member, IEEE, Weng Cho Chew, Fellow, IEEE, Guang Chen, and NRZ>03w  
Jiming Song, Senior Member, IEEE a%)-iL X8&  
Abstract—Based on the addition theorem, the principle of a VH5Vg We  
multilevel ray-propagation fast multipole algorithm (RPFMA) L\y>WR%s  
and fast far-field approximation (FAFFA) has been demonstrated or..e  
for three-dimensional (3-D) electromagnetic scattering problems. i*Ee(m]I  
From a rigorous mathematical derivation, the relation among l/@t>%  
RPFMA, FAFFA, and a conventional multilevel fast multipole $_NP4V8|z/  
algorithm (MLFMA) has been clearly stated. For very large-scale PH3#\ v.   
problems, the translation between groups in the conventional -<.b3Mh  
MLFMA is expensive because the translator is defined on an jwZBWt )5  
Ewald sphere with many sampling ^ directions. When two ]BBL=$*  
groups are well separated, the translation can be simplified using psZ #^@>mJ  
RPFMA, where only a few sampling ^ directions are required "+:~#&r  
within a cone zone on the Ewald sphere. When two groups are in FT.;}!"l  
the far-field region, the translation can be further simplified by )gP0+W!u  
using FAFFA where only a single ^ is involved in the translator ET}Dh3A  
along the ray-propagation direction. Combining RPFMA and  QKtTy>5  
FAFFA with MLFMA, three algorithms RPFMA-MLFMA, 7cMSJM(]G  
FAFFA-MLFMA, and RPFMA-FAFFA-MLFMA have been developed, BjIKs~CT  
which are more efficient than the conventional MLFMA x1{gw 5:  
in 3-D electromagnetic scattering and radiation for very large 9?#L/  
structures. Numerical results are given to verify the efficiency of 4]3(Vyh`  
the algorithms. cG~-OHU  
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