Two-Step Preconditioner of Multilevel Simple Sparse Method for Electromagnetic Scattering Problems

Authors

  • Xiaoqing Hu Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China
  • Rushan Chen Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China
  • Dazhi Ding Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China
  • Zhenhong Fan Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China
  • Yuan Xu Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China

Keywords:

Two-Step Preconditioner of Multilevel Simple Sparse Method for Electromagnetic Scattering Problems

Abstract

In order to efficiently solve the dense complex linear systems arising from electric field integral equations (EFIE) formulation of electromagnetic scattering problems, the multilevel simple sparse method (MLSSM) is used to accelerate the matrix-vector product operations. Because of the nature of EFIE, the resulting linear systems from EFIE formulation are challenging to solve by iterative methods. In this paper, the twostep preconditioner is used to alleviate the low convergence of Krylov subspace solvers, which combine the modified complex shifted preconditioner and sparse approximate inversion (SAI) preconditioner. Numerical examples demonstrate that the two-step preconditioner can greatly improve the convergence of the generalized minimal residual method (GMRES) for the dense complex linear systems and reduce the computationnal time significantly.

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Author Biographies

Xiaoqing Hu, Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China

Xiaoqing Hu was born in Hubei
province, China. He received the
B.S. and M.S. degree in Applied
Mathematics from Jilin University,
Changchun, China, in 2004 and
2007, respectively. He is currently
working toward the Ph.D. degree at
Nanjing University of Science and
Technology. His research interests include integral
equation and its fast methods.

Rushan Chen, Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China

Rushan Chen was born in Jiang-su,
China. He received his B.S. and
M.S. degrees from the Dept. of
Radio Engineering, Southeast
University, in 1987 and in 1990,
respectively, and his Ph.D. from the
Dept. of Electronic Engin-eering,
City University of Hong Kong in
2001. Since September 1996, he has
been a Visiting Scholar with Department of Electronic
Engineering, City University of Hong Kong, first as
Research Associate, then as a Senior Research
Associate in July 1997, a Research Fellow in April
1998, and a Senior Research Fellow in 1999. From June
to September 1999, he was also a Visiting Scholar at
Montreal University, Canada. In September 1999, he
was promoted to Full Professor and Associate Director
of the Microwave & Communication Research Center
in NJUST and in 2007, he was appointedHead of the
Dept of Communication Engineering, University of Science & Technology. His research
interests mainly include microwave/millimeter-wave
systems, measurements, antenna, RF-integrated circuits,
and computational electro-magnetics. He is aSenior
Member of the Chinese Institute of Electronics (CIE).
He received the 1992 third-class science and
technology advance prize given by the National
Military Industry Department of China, the 1993 third
class science and technology advance prize given by the
National Education Committee of China, the 1996
second-class science and technology advance prize
given by the National Education Committee of China,
and the 1999 first-class science and technology advance
prize given by JiangSu Province as well asthe 2001
second-class science and technology advance prize. At
NUST, he was awarded the Excellent Honor Prize for
academic achievement in 1994, 1996, 1997, 1999,
2000, 2001, 2002, and 2003. He has authored or co-
authored more than 200 papers, including over 140
papers in international journals. He is the recipient of
the Foundation for China Distinguished Young
Investigators presented by the National Science
Foundation (NSF) of China in 2003. In 2008, he
became a Chang-Jiang Professor under the Cheung
Kong Scholar Program awarded by the Ministry of
Education, China.

Dazhi Ding, Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China

Dazhi Ding was born in Jiangsu,
China. He receivedthe B.S. and
Ph.D. degrees in electro-magnetic
field and microwave technique
from Nanjing Univer-sity of
Science and Technology (NJUST),
Nanjing, China, in 2002 and 2007,
respectively. During 2005, he was
with the Center of wirelessCommunication in the City
University of HongKong, Kowloon, as a Research
Assistant. He is currently a Lecturer with the Electronic
Engi-neering of NJUST. He is the author or coauthor of
over 20 technical papers. His current research interests
include computational electromagnetics,
electromagnetic scattering and radiation.

Zhenhong Fan, Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China

Zhenhong Fan was born in Jiangsu,
China, in 1978. He receivedthe
M.Sc and Ph.D degrees in
electromagnetic field and
microwave technique from Nanjing
University of Science and
Technology (NJUST), Nan-jing,
China, in 2003 and 2007,
respectively. During 2006, he was with the Center of
wireless Communication in the City University of Hong
Kong, Kowloon, as a Research Assistant. He is
currently a Lecturer with the Electronic Engineering of
NJUST. He is the author or coauthor of over 20
technical papers. His current research interests include
computational electromagnetics, electromagnetic
scattering and radiation.

Yuan Xu, Department of Communication Engineering Nanjing University of Science and Technology, Nanjing, 210094, China

Yuan Xu received the B.S. and
M.S. degrees in mathematics from
Suzhou University, Suzhou, China,
in 1988 and 1991, respectively, and
the Ph.D. degree in electrical
engineering from Nanjing
University of Science and
Technology, China, in 2001.He is
currently working as a Postdoctoral Scholar at the
University of Kentucky, Lexington. His research
interest includes computational electromagnetics,
integral equation methods, and the analysis of large-
scale electromagnetic problems.

References

S. Rao, D.Wilton, and A. Glisson, “Electro-

magnetic Scattering by Surfaces of Arbitrary

Shape,” IEEE Trans. Antennas and Propag., vol.

, no. 3, pp. 409-418, May 1982.

K. A. Michalskiand D. L. Zheng, “Electro-

magnetic Scattering and Radiation by Surfaces of

Arbitrary Shape in Layered Media, Part I: Theory,”

IEEE Trans. Antennas and Propag., vol. 38, no. 3,

pp. 335-344, March 1990.

K. A. Michalskiand D. L. Zheng, “Electro-

magnetic Scattering and Radiation by Surfaces of

Arbitrary Shape in Layered Media, Part II:

Implementation and Results for Contiguous Half-

Spaces,” IEEE Trans. Antennas and Propag., vol.

, no. 3, pp. 345-352, 1990.

D. Ding, J. Ge,and R. Chen, “Well-Conditioned

CFIE for Scattering from Dielectric Coated

Conducting Bodies above a Half-Space,” Applied

Computational Electromagnetic Society (ACES)

Journal, vol. 25, no. 11, pp. 936- 946, November

W. C. Chew, J. M. Jin, E. Michielssen, and J.

Song, Fast Efficient Algorithms in Computa-tional

Electromagnetics, Boston, MA,Artech House,

J. M. Song, C. C. Lu, and W. C. Chew, “Multilevel

Fast Multipole Algorithm for Electromagnetic

Scattering by Large Complex Objects,” IEEE

Trans. Antennas Propagat., vol. 45,no. 10, pp.

-1493, 1997.

L. Rossi, P.J. Cullen, and C. Brennan,

“Implementation of aMultilevel Fast Far-Field

Algorithm for Solving Electric-Field Integral

Equations,” IEE Proc., Microw. Antennas Propag.,

vol. 147, iss. 1, pp. 19-24, 2000.

M. Bebendorf, “Approximation of Boundary

Element Matrices,” Numer. Math., vol. 86, no. 4,

pp. 565–589, 2000.

K. L. Lai, L. Tsang, and C. -J. Ong, “Application

of the Multilevel UV Method to Analyze Large

Microstrip Patch Structures,” IEEE Antennas

Wireless Propag. Lett., vol. 4, no. 1, pp. 471-474,

F. X. Canning and K. Rogovin,“A Universal

Matrix Solver for Integral-Equation Based

Problems,” IEEE Antennas and Propagation

Magazine, vol. 45, iss. 1, pp. 16-19, Feb. 2003.

A. Zhu, R. J. Adams, and F. X. Canning:

“Modified Simply Sparse Method for

Electromagnetic Scattering by PEC,” IEEE

Antennas and Propagation Society Internatio-nal

Symposium, Washington, DC, pp. 427-430, 2005.

R. J. Adams, A. Zhu, and F.X. Canning, “Sparse

Factorization of the TMz Impedance Matrix in an

Overlapped Localizing Basis, Progress in Electromagnet Research, vol. 61, pp. 291-322,

Y. Xu, X. Xin, R.J. Adams, S. D. Gedney, and

F.X. Canning, “Sparse Direct Solution of the

Electric Field Integral Equation using

Nonoverlapped Localizing LOGOS Modes,”

Micro. Opt. Tech. Lett., vol. 2, pp. 303-307, Feb.

Y. Xu, X. Xin,and R. J. Adams, “A Sparse

Factorization for Fast Computation ofLocalizing

Modes,” IEEE Trans. Antennas Propagat., vol.

, no. 9, pp. 3044-3049, 20120.

X. Q. Hu, Y. Xu,and R. S. Chen, “Fast Iterative

Solution of Integral Equation with Matrix

Decomposition Algorithm and Multilevel Simple

Sparse Method,” IET Microwaves, Antennas, and

Propagation, vol. 5, no. 13, pp. 1583-1588, Oct.

J. M. Song, C. C. Lu, and W. C. Chew,

“Multilevel Fast Multipole Algorithm for

Electromagnetic Scattering by Large Complex

Objects,” IEEE Trans. Antennas Propagat., vol.

, no. 10, pp. 1488-1493, 1997.

K. Sertel and J. L. Volakis, “Incomplete LU

Preconditioner for FMMImplementation,”

Microwave and Optical Technology Letters,

(7):265–267, 2000.

T. Wan, R. S. Chen, and X. Q. Hu, “Data-Sparse

LU-Decomposition Preconditioning Combined

with MLFMM for Electromagnetic Scattering

Problems,” IET Microwaves, Antennas &

Propagation, vol. 5, no. 11, pp.1288-1296, Aug.

B. Carpentieri, I. S. Duff, L. Griud, and G. Alleon,

“Combing Fast Multipole Techniques and an

Approximate Inverse Preconditioner for Large

Electromagnetism Calculations,” SIAM J. Sci.

Comput., 27(3):774–792, 2005.

Y. Xie, J. He, A. Sulllvan, and L. Carin, “A

Simple Preconditioner for Electric-Field Integral

Equations,” Micro. Opt. Tech. Lett., vol. 30(1), pp.

-54, 2001.

J. Lee, J. Zhang, and C. –C. Lu, “Sparse Inverse

Preconditioning of Multilevel Fast Multipole

Algorithm for Hybrid Integral Equations in

Electromagnetics,” IEEE Transactions on

Antennas and Propagat., vol. 52(9), pp. 2277-

, 2004.

P. L. Rui, R. S. Chen,D. X. Wang, and E.K. N.

Yung, “Spectral Two-step Preconditioning of

Multilevel Fast Multipole Algorithm for the Fast

Monostatic RCS Calculation,” vol. 55, no. 8,

IEEE Transactions on Antennas and Propagation,

August 2007.

P. L. Rui and R. S. Chen, “A Spectral Multigrid

Method Combined with MLFMA for Sol Electromagnetic Wave Scattering Problems,”

IEEE Transactions on Antennas and Propagation,

September 2007.

D. Z. Ding, R. S. Chen, Z. H. Fan, and P. L. Rui,

“AA Novel Hierarchical Two-Level Spectral

Preconditioning Technique for Electromag-netic

Wave Scattering,” IEEE Transactions on

Antennas and Propagation, vol. 56, no. 4, April

X. Q. Hu, M. Chen, D.Z. Ding, and R. S. Chen,

“A Modified Complex Shifted Preconditiner

Combined with Sparse Approximate Inversion

Preconditiner for Electromagnetic Scattering,”

Micro. Opt. Tech. Lett., vol. 53, no. 1, pp. 55-58,

January 2011.

Y. Saad and M. Schultz, “GMRES: A Generalized

Minimal Residual Algorithm for Solving

Nonsymmetric Linear Systems,” SIAM J. Sci. Stat.

Comput., vol. 7, no. 3, pp. 856-869, 1986.

J. Cheng, S. A. Maloney, R. J. Adams, and F.X.

Canning, “Efficient Fill of a Nested Re-

presentation of the EFIE at Low Frequencies,”

IEEE AP-S International Symposium San Diego,

CA, 2008.

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Published

2022-05-02

How to Cite

[1]
X. . Hu, R. . Chen, D. . Ding, Z. . Fan, and Y. . Xu, “Two-Step Preconditioner of Multilevel Simple Sparse Method for Electromagnetic Scattering Problems”, ACES Journal, vol. 27, no. 1, pp. 9–21, May 2022.

Issue

2012: Vol 27 Iss 1

Section

General Submission