• Chinese Science Citation Database(CSCD)
  • Chinese Scientific and Technological Paper and Citation Database (CSTPCD)
  • China National Knowledge Infrastructure(CNKI)
  • Chinese Science Abstracts Database(CSAD)
  • JST China
  • SCOPUS
Advanced Search

Latest Notice

Latest Notice
WeChat Official Account

WeChat Official Account

Volume 35 Issue 2
Apr.  2020
Turn off MathJax
Article Contents
Abstract
References
WU Yumao, JIN Yaqiu. The modern high frequency methods for solving electromagnetic scattering problems[J]. CHINESE JOURNAL OF RADIO SCIENCE, 2020, 35(2): 192-204. doi: 10.13443/j.cjors.2019090205
Reference format: WU Yumao, JIN Yaqiu. The modern high frequency methods for solving electromagnetic scattering problems[J]. CHINESE JOURNAL OF RADIO SCIENCE, 2020, 35(2): 192-204. doi: 10.13443/j.cjors.2019090205
shu

The modern high frequency methods for solving electromagnetic scattering problems

  • School of Information Science and Technology, Fudan University, Key Laboratory for Information Science of Electromagnetic Waves(MoE), Shanghai 200433, China

More Information
  • Received Date: September 01, 2019
  • Available Online: December 30, 2020
  • Published Date: April 29, 2020
    Graphical Abstract
    • Abstract
  • The high frequency scattering problems of electromagnetic fields scattered from electrically large scatterers are important and challenging. On the calculation of the reflected and diffracted wave fields, the high frequency methods could be classified into the current based method and the ray based method. In this paper, first, the author gives a review on the progress of the modern high frequency methods for solving the electromagnetic scattering problems. Next, due to the highly oscillatory property of the high frequency electromagnetic scattered fields, the author proposes the numerical steepest descent path method. Finally, the author comprehensively addresses the high frequency wave physics, including the high frequency critical point contributions, the Keller's cone, the shadow and reflection boundaries and the creeping wave fields.
    • FullText(HTML)
    • References (68)
  • [1]
    MAXWELL J C. A dynamical theory of the electromagnetic field[J]. Philosophical transactions of the Royal Society of London, 1865:459-512. http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_math-ph%2f0311034
    [2]
    HEAVISIDE O. Electromagnetic theory[M]. Cosimo, Inc., 2008.
    [3]
    CHEW W C. Waves and fields in inhomogeneous media[M]. New York:IEEE Press, 1995.
    [4]
    KONG J A. Electromagnetic wave theory[M]. New York:Wiley-Interscience, 1990.
    [5]
    KNOTT E F, SHAEFFER J F, TULEY M T. Radar cross section[M]. Norwood:Artech House, 1993.
    [6]
    BALANIS C A. Antenna theory:analysis and design[M]. 3rd ed. New York:John Wiley and Sons, 2012.
    [7]
    DATTA S. Quantum transport:atom to transistor[M]. Cambridge University Press, 2005.
    [8]
    CAI W. Computational methods for electromagnetic phenomena:electrostatics in solvation, scattering, and electron transport[M]. Cambridge:Cambridge University Press, 2013.
    [9]
    GARRISON J, CHIAO R. Quantum optics[M]. Oxford University Press, 2014.
    [10]
    TANG L, KONG J A, SHIN B. Theory of microwave remote sensing[M]. New York:John Wiley, 1985.
    [11]
    JIN Y Q. Electromagnetic scattering modelling for quantitative remote sensing[M]. Singapore:World Science Press, 2000.
    [12]
    HARRINGTON R F. Field computation by moment method[M]. New York:Macmillan, 1968.
    [13]
    JIN J M. The finite element method in electromagnetics[M]. 3rd ed. Hoboken:Wiley-IEEE Press, 2014.
    [14]
    TAFLOVE A, HAGNESS S C. Computational electrodynamics:the finite-difference time-domain method[M]. 3rd ed. Boston:Artech House, 2015.
    [15]
    SONG J M, LU C C, CHEW W C. Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects[J]. IEEE transactions on antennas and propagation, 1997, 45(10):1488-1493. doi: 10.1109/8.633855
    [16]
    CHEW W C, JIN J M, MICHIELSSEN E, et al. Fast and efficient algorithms incomputational electromagnetics[M]. Boston:Artech House, 2001.
    [17]
    MACDONALD H M. The effect produced by an obstacle on a train of electric waves[J]. Philosophical transactions of the Royal Society of London, series A, Math. Phys. Sci., 1913, 212:299-337. http://cn.bing.com/academic/profile?id=370c12fa010249cc9b17e55694e7da02&encoded=0&v=paper_preview&mkt=zh-cn
    [18]
    UFIMTSEV P Y. Backscatter[M]. New York:John Wiley and Sons, 2005.
    [19]
    UFIMTSEV P Y. Fundamentals of the physical theory of diffraction[M]. New York:John Wiley and Sons, 2007.
    [20]
    MITZNER K M. Incremental length diffraction coefficients[R]. Tech. Rep. No. AFAL-TR-73-296, 1974.
    [21]
    SHORE R A, YAGHJIAN A D. Incremental diffraction coefficients for planar surfaces[J]. IEEE transactions on antennas and propagation, 1988, 36(1):55-70. doi: 10.1109/8.1075
    [22]
    HANSEN T B, SHORE R A. Incremental length diffraction coefficients for the shadow boundary of a convex cylinder[J]. IEEE transactions on antennas propagation, 1998, 46(10):1458-1466. doi: 10.1109/8.725277
    [23]
    YAGHJIAN A D, SHORE R A, WOODWORTH M B. Shadow boundary incremental length diffraction coefficients for perfectly conducting smooth, convex surfaces[J]. Radio science, 1996, 31(12):1681-1695. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=8aad00b51fb39ab0a377e60b634d6539
    [24]
    KELLER J B. Geometrical theory of diffraction[J]. Journal of the Optical Society of America, 1962, 52(2):116-130. doi: 10.1364/JOSA.52.000116
    [25]
    JAMES G L. Geometrical theory of diffraction for electromagnetic waves[M]. Stevenage:Peregrinus, 1980.
    [26]
    KOUYOUMJIAN R G, PATHAK P H. A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface[J]. Proceedings of IEEE, 1974, 62(11):1448-1461. doi: 10.1109-PROC.1974.9651/
    [27]
    LEE S W, DESCHAMPS G A. A uniform asymptotic theory of electromagnetic diffraction by a curved wedge[J]. IEEE transactions on antennas and propagation, 1976, 24(1):25-34. doi: 10.1109/TAP.1976.1141283
    [28]
    KOUYOUMJIAN R G. Asymptotic high-frequency methods[J]. Proceedings of IEEE, 1965, 53(8):864-876. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ0220998117/
    [29]
    PATHAK P H. High-frequency techniques for antenna analysis[J]. Proceedings of IEEE, 1992, 80(1):44-65. http://cn.bing.com/academic/profile?id=d2faaea55c29cc5e50c3c19541264ed2&encoded=0&v=paper_preview&mkt=zh-cn
    [30]
    BOROVIKOV V A. Uniform stationary phase method[M]. London:Institution of Electrical Engineers, 1994.
    [31]
    CONDE O M, P'EREZ J, C'ATEDRA M F. Stationary phase method application for the analysis of radiation of complex 3-D conducting structures[J]. IEEE transactions on antennas and propagation, 2001, 49(5):724-731. doi: 10.1109/8.929626
    [32]
    CARLUCCIO G, ALBANI M, PATHAK P H. Uniform asymptotic evaluation of surface integrals with polygonal integration domains in terms of UTD transition functions[J]. IEEE transactions on antennas propagation, 2010, 58(4):1155-1163. doi: 10.1109/TAP.2010.2041171
    [33]
    SOMMERFELD A. Mathematische theorie der diffraction[J]. Mathematische annalen, 1896, 47(319):317-374.(in German) http://cn.bing.com/academic/profile?id=ad8bc9e3daf6ef80f5251229fe780949&encoded=0&v=paper_preview&mkt=zh-cn
    [34]
    FOCK V A. The distributions of currents induced by a plane wave on the surface of a conductor[J]. Acad. Sci. USSR. J. Phys., 1946, 10:130-136. https://mathscinet.ams.org/mathscinet-getitem?mr=17661
    [35]
    KLINE M. Mathematical theory of optics[J]. Brown University Notes, Providence, RI, 1944.
    [36]
    LING H, CHOU R C, LEE S W. Shooting and bouncing rays:calculating the RCS of anarbitrarily shaped cavity[J]. IEEE transactions on antennas and propagation, 1989, 37(2):194-205. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=18706
    [37]
    LEE S W, MITTRA R. Fourier transform of a polygonal shape function and its application in electromagnetics[J]. IEEE transactions on antennas and propagation, 1983, 31(1):99-103. doi: 10.1109/TAP.1983.1142981
    [38]
    GORDON W B. High-frequency approximations to the physical optics scattering integral[J]. IEEE transactions on antennas and propagation, 1994, 42(3):427-432. doi: 10.1109/8.280733
    [39]
    ENGQUIST B, FATEMI E, OSHER S. Numerical solution of the high frequency asymptotic expansion for the scalar wave equation[J]. Journal of computational physics, 1995, 120(1):145-155. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=ZSbbOPTIOEpHBn13PNFHvflS3LiuEMVa1JodA49BDH4=
    [40]
    ENGQUIST B, RUNBORG O. Computational high frequency wave propagation[J]. Acta numerica, 2003, 12:181-266. doi: 10.1017/S0962492902000119
    [41]
    WONG R. Asymptotic approximations of integrals[J]. New York:SIAM, 2001. http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_math%2f9310223
    [42]
    ABRAMOWITZ M, STEGUN I A. Handbook of mathematical functions[M]. New York:Dover Publications, 1972.
    [43]
    JOSEF S, ROLAND B. Introduction to numerical analysis[M]. New York:Springer-Verlag, 1980.
    [44]
    ASHEIM A, HUYBRECHS D. Asymptotic analysis of numerical steepest descent with path approximations[J]. Foundations of computational mathematics, 2010, 10(6):647-671. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=99b870f93cd143b6ab4058b1619aa237
    [45]
    BONDIA F V, FERRANDO-BATALLER M, VALERO-NOGUEIRA A. A new fast physical optics for smooth surfaces by means of a numerical theory of diffraction[J]. IEEE transactions on antennas and propagation, 2010, 58(3):773-789. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=08c582bebba159b6aa788a34d5f619b4
    [46]
    ZHANG J, XU B, CUI T J. An alternative treatment of saddle stationary phase points in physical optics for smooth surfaces[J]. IEEE transactions on antennas propagation, 2014, 62(2):986-991. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=8c3633dc8d5f40640019ba7d1289bec8
    [47]
    WU Y L, JIANG J, CHEW W C. An efficient method for computing highly oscillatory physical optics integral[J]. Progress in electromagnetics research, 2012, 127:211-257. doi: 10.2528/PIER12022308
    [48]
    WU Y M, JIANG L J, CHEW W C. An efficient method for highly oscillatory physical optics integrals[C]//IEEE International Symposium on Antennas and Propagation, 2012.
    [49]
    WU Y M, JIANG L J, SHA W, et al. The numerical steepest descent path method for calculating physical optics integrals on smooth conducting surfaces[J]. IEEE transactions on antennas propagation, 2013, 61(8):4183-4193. doi: 10.1109/TAP.2013.2259788
    [50]
    WU Y M, JIANG L J, CHEW W C. Computing highly oscillatory physical optics integral on the polygonal domain by an efficient numerical steepest descent path method[J]. Journal of computational physics, 2013, 236:408-425. doi: 10.1016/j.jcp.2012.10.052
    [51]
    WU Y M, JIANG L, CHEW W C. The contour deformation method for calculating the high frequency scattered fields by the Fock current on the surface of the 3-D convex cylinder[C]//2014 IEEE Antennas and Propagation Society International Symposium (APSURSI). Memphis, July 6-11, 2014.
    [52]
    WU Y M, JIANG L J, CHEW W C, et al. The contour deformation method for calculating the high frequency scattered field by the Fock current on the surface of the 3-D convex cylinder[J]. IEEE transactions on antennas and propagation, 2015, 63(5):2180-2190. doi: 10.1109/TAP.2015.2407411
    [53]
    PERREY-DEBAIN E, TREVELYAN J, BETTESS P. Wave boundary elements:a theoretical overview presenting applications in scattering of short waves[J]. Engineering analysis with boundary elements, 2004, 28(2):131-141. http://cn.bing.com/academic/profile?id=033dd67e780835a944175ebaf97c4421&encoded=0&v=paper_preview&mkt=zh-cn
    [54]
    ENGQUIST B, FOKAS A, HAIRER E, et al. Highly oscillatory problems[R]. London Mathematical Society Lecture Note Series, Cambridge University Press, 2009.
    [55]
    CHANDLER S N, LANGDON S. Acoustic scattering: high frequency boundary element methods and unified transform methods[M]//FOKAS A S, PELLONI B. Unified transform for boundary value problems: applications and advances. New York: SIAM, 2015.
    [56]
    CHENG H, CRUTCHFIELD W Y, GIMBUTAS Z, et al. A wideband fast multipole method for the Helmholtz equation in three dimensions[J]. Journal of computational physics, 2006, 216(1):300-325. http://cn.bing.com/academic/profile?id=b8a1efa98c45c4faafe5fb97716f402b&encoded=0&v=paper_preview&mkt=zh-cn
    [57]
    BRUNO O P. Fast, high-order, high-frequency integral methods for computational acoustics and electromagnetics[M]. Berlin:Springer, 2003.
    [58]
    UMUL Y Z. Rigorous expressions for the equivalent edge currents[J]. Progress in electromagnetics research B, 2009, 15:77-94. doi: 10.2528/PIERB09040104
    [59]
    MICHAELI A. Equivalent edge currents for arbitrary aspects of observation[J]. IEEE transactions on antennas and propagation, 1984, 32:252-258. doi: 10.1109/TAP.1984.1143303
    [60]
    CHOU H T, PATHAK P H, ROUSSEAU P R. TD-UTD solutions for the transient radiation and surface fields of pulsed antennas placed on PEC smooth convex surfaces[J]. IEEE transactions on antennas and propagation, 2011, 59(5):1626-1637. doi: 10.1109/TAP.2011.2122235
    [61]
    JOHANSEN P M. Time-domain version of the physical theory of diffraction[J]. IEEE transaction on antennas and propagation, 1999, 47:261-270. http://cn.bing.com/academic/profile?id=2f928878c69bc2729532e8db27dcd557&encoded=0&v=paper_preview&mkt=zh-cn
    [62]
    陈曦.任意光滑凸曲面电磁波绕射建模方法研究[D].武汉: 武汉大学, 2013. http://cdmd.cnki.com.cn/Article/CDMD-10486-1013210929.htm

    CHEN X. Simulation method for electromagnetic diffraction by arbitrarily shaped convex surfaces[D]. Wuhan: Wuhan University, 2013.(in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-10486-1013210929.htm
    [63]
    付松.介质涂覆目标表面爬行波寻迹及其电磁绕射建模方法研究[D].武汉: 武汉大学, 2015. http://cdmd.cnki.com.cn/Article/CDMD-10486-1016016060.htm

    FU S. Research on creeping wave tracing and modeling algorithms of electromagnetic diffraction on dielectric-coated target surfaces[D]. Wuhan: Wuhan University, 2015.(in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-10486-1016016060.htm
    [64]
    CHEN X, HE S Y, YU D F, et al. Ray-tracing method for creeping waves on arbitrarily shaped nonuniform rational B-splines surfaces[J]. JOSA A, 2013, 30(4):663-670. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=285c46c7ffafa446da4b939cb8d4f141
    [65]
    ZHOU X, ZHU J Y, YU W M, et al. time-domain shooting and bouncing rays method based on beam tracing technique[J]. IEEE transactions on antennas and propagation, 2015, 63(9):4037-4048. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=c24176e45acef0bab2eac309cf5bed8e
    [66]
    ZHANG J, YU W M, ZHOU X Yet al.Efficient Evaluation of the physical-optics integrals for conducting surfaces using the uniform stationary phase method[J]. IEEE transactions on antennas and propagation, 2012, 60(5):2398-2408. doi: 10.1109/TAP.2012.2189737
    [67]
    YAN H, YIN H, LI S, et al.3-D rotation representation of multiple reflections and parametric model for bistatic scattering from arbitrary multiplate structure[J]. IEEE transactions on antennas and propagation, 2019, 67(7):4777-4791. doi: 10.1109/TAP.2019.2911268
    [68]
    ZHANG F, ZHANG Y H, HE S Y, et al. Numerical simulation of scattering by a wedge with periodic anisotropic impedance faces[J]. IEEE transactions on antennas and propagation, 2014, 62(12):6091-6101. doi: 10.1109/TAP.2014.2364054
    • Related Articles

Catalog

    Get Citation
    PDF
    XML
    Article views (302) PDF downloads (143) Cited by()
    Related

    Copyright © China Research Institute of Radiowave Propagation 豫ICP备16036117号

    Address：No.84 Jianshe East Rd., Muye District, Xinxiang, Henan（453000） Tel：0373-3712411 Fax：0373-3052232 E-mail: dbkxxb@126.com

    Supported by: Beijing Renhe Information Technology Co., Ltd.  Baidu Analytics

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return