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Multilevel Fast Multipole Algorithm For Solving Combined Field Integral Equation Of Electromagnetic Scattering

Authors:
Jiming Song at Iowa State University
Jiming Song
W.C. Chew at University of Illinois, Urbana-Champaign
W.C. Chew
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Abstract

The fast multipole method (FMM) has been implemented to speed up the matrixvector multiply when an iterative method is used to solve combined field integral equation (CFIE). FMM reduces the complexity from O(N 2 ) to O(N 1:5 ). With a multilevel fast multipole algorithm (MLFMA), it is further reduced to O(NlogN ). A 110,592 unknown problem can be solved within 24 hours on a SUN Sparc10. 1. Introduction The electromagnetic (EM) field scattering by three-dimensional (3D) arbitrarily shaped conductor can be obtained by finding the solution of an integral equation where the unknown function is the induced current distribution. The integral equation is discretized into a matrix equation by the method of moments (MOM). The resultant matrix equation y The authors would like to thank L. Hernquist, J.E. Barnes and P. Hut for providing us with copies of their codes, and thank M.B. Woodworth, M.G. Cot'e, and A.D. Yaghjian for providing us with their numerical and experimental data. This wor...
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1e-05
0.0001
0.001
0.01
0.1
1
0 50 100 150 200 250 300 350
Normalized Residual Norm
No. of Iterations
r=1m sphere, f=0.72GHz, 294 patches, 9408 unkws
EFIE
MFIE
CFIE
-15
-10
-5
0
5
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20
25
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Normalized Bistatic RCS (dB)
r=1m sphere, f=0.72GHz, 294 patches, 9,408 unkws
Mie series
EFIE with FMM
MFIE with FMM
CFIE with FMM
θ (Degrees)
10
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1000 10000 100000
CPU Time Per Iteration (sec)
Unknowns
Without using disk
With using disk
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Unknowns
Core
Total
-15
-10
-5
0
5
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35
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Normalized Bistatic RCS (dB)
θ (Degrees)
r=1m sphere, f=2.4GHz, N=110,592, 6 levels
Mie Series
CFIE with MLFMA
-30
-20
-10
0
10
20
30
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RCS (dBsw)
θ (Degrees)
2.5 X 2.5 X 3.75 open cavity
LUD
MLFMA
Measurement
z
y
x
θ
λ
3
-30
-20
-10
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θ (Degrees)
2.5 X 2.5 X 3.75 λ open cavity
LUD
MLFMA
Measurement
3
z
y
x
θ
-10
0
10
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Bistatic RCS (dBsw)
MLFMA
High Freq.
DMFIE
k
E
θ
θ (Degrees)
10
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Bistatic RCS (dBsw)
MLFMA
High Freq.
DMFIE
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H
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θ (Degrees)
... Many real-world electromagnetic (EM) problems require multiscale discretization [1][2][3][4]. When the method of moments (MoM) [5], along with classical fast algorithms, is used to model the multi-scale problems, a single fast algorithm [6][7][8][9][10][11][12] is often insufficient to achieve satisfactory computational performance. Instead, due to capturing both the circuit physics and wave physics [1], hybrid fast algorithms [19][20][21][22] generally provide a more practical path to efficiently solve EM multiscale problems. ...
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... Since 1988, he has been with the State Key Laboratory of Millimeter Waves and serves for the director of the lab, since . In 1993, 1995, 1996, and 1998, he was a short-term visiting scholar with the University of California at Berkeley and at Santa Cruz, respectively. He is currently a professor with the School of Information Science and Engineering, Southeast University. ...
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