New reduced matrix construction accelerated iterative solution of characteristic basis function method

Wang Zhong-Gen; Mu Jun-Wen; Lin Han; Nie Wen-Yan

doi:10.7498/aps.68.20190572

Abstract

The characteristic basis function method is known as an effective method to solve the electromagnetic scattering problems, but the convergence of the iterative solution of the reduced matrix equation is slow when the characteristic basis function method is used to analyze the electromagnetic scattering characteristics of the electrically large target. In order to mitigate this problem, a new reduced matrix construction method is proposed to improve the iterative solution efficiency of characteristic basis function method in this paper. Firstly, the singular value decomposition technique is used to compress the incident excitations, and the characteristic basis functions of each sub-domain under the new excitations are solved. Then, the new excitations and the characteristic basis functions are defied as the testing and basis functions to construct the reduced matrix. The diagonal sub-matrices of the reduced matrix constructed by the new testing and basis functions are all identity matrices, thereby improving the condition of reduced matrix. Thus, the total number of iterations to achieve reasonable results is significantly reduced. Numerical simulations are conducted to validate the performance of the proposed method. The results demonstrate that the efficiency of the iterative solution of the reduced matrix equation constructed by the new method is significantly improved. Furthermore, the characteristic basis functions’ generation time required by the proposed method is noticeably less than that by the traditional characteristic basis function method due to the reduced number of matrix equation solutions.

Keywords:

Authors and contacts

1.
College of Electrical and Information Engineering, Anhui University of Science and Technology, Huainan 232001, China
2.
College of Mechanical and Electrical Engineering, Huainan Normal University, Huainan 232001, China

Corresponding author: Wang Zhong-Gen, zgwang@ahu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61401003), the Natural Science Foundation of Anhui Province, China (Grant Nos. 1808085MF166, 1808085QF197), the Postdoctoral Science Foundation of Anhui Province, China (Grant No. 2017B214), and the Outstanding Young Talents of Anhui Province, China (Grant No. gxgwfx2018025).

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References

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[2]	Coifman R, Rokhlin V, Wandzura S 1993 IEEE Antennas Propagat. Mag. 35 7
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[11]	Chen Y, Wang C F 2015 IEEE Trans. Antenn. Propag. 63 1004 Google Scholar
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[20]	Fenni I, Roussel H, Darces M 2016 IEEE Trans. Antenn. Propag. 64 4539 Google Scholar
[21]	王仲根, 孙玉发, 王国华 2013 物理学报 62 204102 Google Scholar Wang Z G, Sun Y F, Wang G H 2013 Acta Phys. Sin. 62 204102 Google Scholar
[22]	Fang X X, Cao Q S, Zhou Y 2019 IEEE Trans. Electromagn. Compat. 61 191 Google Scholar
[23]	Chen X L, Niu Z Y, Li Z Gu C Q 2011 J. Electromagn. Waves Appl. 25 1940 Google Scholar
[24]	Garcia E, Delgado C, Diego I G, Catedra M F 2008 IEEE Trans. Antenn. Propag. 56 2363 Google Scholar
[25]	Hu J, Lu W, Shao H, Nie Z 2012 IEEE Trans. Antenn. Propag. 60 5709 Google Scholar
[26]	Hu L, Li W L, Mittra R 2010 IEEE Trans. Antenn. Propag. 58 3086 Google Scholar
[27]	García E, Delgado C, Cátedra F 2019 IEEE Trans. Antenn. Propag. 67 3241 Google Scholar
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图 1 (a)不同SVD门限下2种方法的计算误差及CBFs数目; (b)左半球面4个子域的奇异值分布曲线; (c)导体球双站RCS

Figure 1. (a) Calculation error and numbers of CBFs under different SVD thresholds of two methods; (b) singular value distribution curve in four sub-domains of the left hemisphere; (c) bistatic RCS of PEC sphere.

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图 2 锥球带缝体双站RCS

Figure 2. Bistatic RCS of cone-sphere with gap.

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图 3 杏仁体HH极化单站RCS

Figure 3. Monostatic RCS in HH polarization of NASA almond.

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表 1 计算时间比较

Table 1. Comparison of computation time.

目标及未知量个数	方法	阻抗矩阵填充/s	基函数构造/s	缩减矩阵构造/s	缩减矩阵方程求解/s	计算时间/s
导体球(17278)	CBFM	239.9	1081.4	41.7	0.44	1375.6
导体球(17278)	NCBFM	239.1	979.4	40.8	0.31	1267.9
锥球带缝体(124685)	CBFM	3297.5	27736.4	1535.7	104.5	32740.1
锥球带缝体(124685)	NCBFM	3289.2	26985.1	1506.6	57.3	31889.7
杏仁体(153690)	CBFM	4097.8	33173.5	3553.7	237.8	83936.8
杏仁体(153690)	NCBFM	4098.4	31832.3	3524.1	121.2	61437.9

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[1]	Harrington R F 1993 Field Computation by Moment Methods (New York: Wiley-IEEE Press) pp5−7
[2]	Coifman R, Rokhlin V, Wandzura S 1993 IEEE Antennas Propagat. Mag. 35 7
[3]	Song J M, Lu C C, Chew W C 1997 IEEE Trans. Antenn. Propag. 45 1488 Google Scholar
[4]	王晓冰, 梁子长, 吴振森 2012 物理学报 61 124104 Google Scholar Wang X B, Liang Z C, Wu Z S 2012 Acta Phys. Sin. 61 124104 Google Scholar
[5]	Ma J, Guo L X, Wang A Q 2009 Chin. Phys. B 18 3431 Google Scholar
[6]	Nie X C, Yuan N, Li L W 2008 IEEE Trans. Antenn. Propag. 56 3526 Google Scholar
[7]	Lu W B, Cui T J, Zhao H 2007 IEEE Trans. Antenn. Propag. 55 414 Google Scholar
[8]	Freni A, Vita D P, Pirinoli P, Matekovits L, Vecchi G 2011 IEEE Trans. Antenn. Propag. 59 4588 Google Scholar
[9]	Suter E, Mosing J R 2000 Microw. Opt. Technol. Lett. 26 270 Google Scholar
[10]	Guan L, He Z, Ding D Z, Chen R S 2019 IEEE Trans. Antenn. Propag. 67 199 Google Scholar
[11]	Chen Y, Wang C F 2015 IEEE Trans. Antenn. Propag. 63 1004 Google Scholar
[12]	Prakash V V S, Mittra R 2003 Microw. Opt. Technol. Lett. 36 95 Google Scholar
[13]	Sun Y F, Chan C H, Mittra R 2003 IEEE Antennas and Propagation Society International Symposium Columbus, June 22−27, 2003 p1068
[14]	Lucente E, Monorchio A, Mittra R 2008 IEEE Trans. Antenn. Propag. 56 999 Google Scholar
[15]	侯兆国, 王超, 董纯柱, 殷红成 2011 系统工程与电子技术 33 1458 Google Scholar Hou Z G, Wang C, Dong C Z, Yin H C 2011 Syst. Engineer. Electron. 33 1458 Google Scholar
[16]	Ding J, Li J F, Zhang T 2016 IEICE Electron. Expr. 13 1
[17]	Zhu J Y, Sun Y F, Fang H Y 2018 Prog. Electromag. Res. M 68 173 Google Scholar
[18]	Tanaka T, Inasawa Y, Yoneda N, Miyashita H 2018 IEICE Trans. Electron. E101.C 96
[19]	王仲根, 唐晓菀, 汪强 2018 电子与信息学报 40 573 Google Scholar Wang Z G, Tang X W, Wang Q 2018 J. Electron. Inf. Tech. 40 573 Google Scholar
[20]	Fenni I, Roussel H, Darces M 2016 IEEE Trans. Antenn. Propag. 64 4539 Google Scholar
[21]	王仲根, 孙玉发, 王国华 2013 物理学报 62 204102 Google Scholar Wang Z G, Sun Y F, Wang G H 2013 Acta Phys. Sin. 62 204102 Google Scholar
[22]	Fang X X, Cao Q S, Zhou Y 2019 IEEE Trans. Electromagn. Compat. 61 191 Google Scholar
[23]	Chen X L, Niu Z Y, Li Z Gu C Q 2011 J. Electromagn. Waves Appl. 25 1940 Google Scholar
[24]	Garcia E, Delgado C, Diego I G, Catedra M F 2008 IEEE Trans. Antenn. Propag. 56 2363 Google Scholar
[25]	Hu J, Lu W, Shao H, Nie Z 2012 IEEE Trans. Antenn. Propag. 60 5709 Google Scholar
[26]	Hu L, Li W L, Mittra R 2010 IEEE Trans. Antenn. Propag. 58 3086 Google Scholar
[27]	García E, Delgado C, Cátedra F 2019 IEEE Trans. Antenn. Propag. 67 3241 Google Scholar
[28]	Woo A C, Wang H T G, Schuh M J 1993 IEEE Antennas Propagat. Mag. 35 84 Google Scholar

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Vol. 68, Issue 17 - 2019-09-05

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