Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
권호 표지
DOI QR코드

DOI QR Code

Convergence rates of the TE EFIE scattering solutions from a PEC cylinder

PEC 원통을 TE EFIE 방법으로 산란 해석한 결과의 수렴율

  • 홍진수 (순천향대학교 물리학과) ;
  • 배형철 (순천향대학교 물리학과)
  • Received : 2015.06.30
  • Accepted : 2015.10.08
  • Published : 2015.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

The method of moments (MoM) is implemented to simulate scattering from a PEC (perfectly electric conductor) cylinder in the TE(transversw electric) EFIE (Electric Field Integral Equation) approach. The procedure expresses the singularity integral and the hypersingularity integral in terms of an analytic function and employs a singularity isolation process coupled with numerical technique along the discretized segment to evaluate the self terms. It is known that, in the MoM technique, the choice of base functions and test functions is very important for the accuracy and convergence of the numerical analysis. Thus, in this paper, three conditions, obtained from the combination of basis functions and test functions, are adopted to get the induced currents on the PEC surface. These currents are compared to the analytical one in the relative rms current error to get the condition that shows fast convergence rate. The fast order of convergence of the current error, 2.528, is obtained under the combination of pulse basis function/delta test function.

모멘트법(MoM)인 TE(transversw electric) 전장 적분 방정식(EFIE)으로 완전 전기도체(PEC) 원통을 산란 해석하였다. 이 과정에서 나타나는 특이점(singlarity)과 과대 특이점(hypersingularity)을 포함한 적분 계산은 어렵기 때문에 수치해석 방법으로 특이점을 고립시켜 자체항(self-term)을 얻었다. 모멘트법에서 base 함수와 test 함수의 선택은 수치해석 결과의 정확도와 수렴에 있어 매우 중요한 요인이됨은 알려져 있는 사실이다. basis 함수와 test함수를 달리하여 세 가지 방법으로 PEC 원통에 유도된 전류를 구하였다. 이렇게 구한 결과를 해석학적 방법과 모멘트법에서 얻은 전류와 비교하여 상대 효율 전류 오차를 구하였으며 어떤 결합 방법이 효율적인지 확인하였다. 또한 각 결합방법에 따른 상대 효율 전류 오차의 수렴율을 구하여 가장 정확한 결과를 얻을 조건을 찾았다. 전류 오차의 가장 빠른 수렴오더(order of convergence) 2.528은 펄스 base 함수/델타 test 함수 결함 조건에서 얻었다.

Keywords

References

  1. Cecilia Marasini, "Efficient computation techniques for Galerkin MoM antenna design" PhD thesis, Technische universiteit Eindhoven (2008).
  2. Chengyou Yin and mengzhong Hu, "An efficient analysis method for cylindrical conformal microstrip antenna fed by microstripline", Int. J. Anten. Propag. 2012, 629748 (2012).
  3. Ahmed A. Sakr, Ezzeldin A. Soliman, and Alaa K. Abdelmageed, "An integral equation formulation for TM scattering by a conducting cylinder coated with an inhomogeneous dielectric/magnetic material", PIER B 60, pp 49-62 (2014). DOI: http://dx.doi.org/10.2528/PIERB14031502
  4. D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alu, "Experimental verification of three-dimensional plasmonic cloaking in free space", New J. Phys. 14, 013054 (2012). DOI: http://dx.doi.org/10.1088/1367-2630/14/1/013054
  5. Constantinos A. Valagiannopoulos, and Pekka Alitalo, "Electromagnetic cloaking of cylindrical objects by multilayer or uniform dielectric claddings", Phys. Rev. B 85, 115402 (2012). DOI: http://dx.doi.org/10.1103/PhysRevB.85.115402
  6. G. Selcuk and S. S. Koc, "Evaluatio of hypersingular integrals on non-planar surfaces", 2014 International Conference on NEMO pp 1-4 (2014).
  7. Usman Saeed, "Adaptive numerical techniques for the solution of electromagnetic integral equations", PhD thesis, Georgia Institute of Technology (2011).
  8. Secil Kilinc, "Solution of electromagnetic scattering problems with the locally corrected Nystrom method", Master thesis, Bilkent University (2010).
  9. Alexader Herschlein, Jurgen v. Hagen, and Werner Wiesbeck, "Methods for the evaluation of regular, weakly singular and strongly singular surface reaction integrals arising in method of moments", Aces J. 17, pp 63-73 (2002).
  10. Smain Amari and Jens Bornemann, "Efficient numerical computation of singular integrals with applications to electromagnetics", IEEE Trans. Antenna Propagat. 43, pp 1343-1348 (1995). DOI: http://dx.doi.org/10.1109/8.475113
  11. Ursula C. Resende, Maicon V. Moreira, and Marcio M. Afonso, "Evaluation of singular integral equation in MoM analysis of arbitrary thin wire structures", IEEE Trans. Magnetics 50, 7011204 (2014). DOI: http://dx.doi.org/10.1109/TMAG.2013.2281315
  12. M. S. Tong, "A stable integral equation solver for electromagnetic scattering by large scatterers with concave surface", PIER 74, pp 113-130 (2007). DOI: http://dx.doi.org/10.2528/PIER07041506
  13. Giovanni Monegato, "Numerical evaluation of hypersingular integrals", J. Comput. Appl. Mathem. 50, pp 9-31 (1994). DOI: http://dx.doi.org/10.1016/0377-0427(94)90287-9
  14. Rainer Kress, "On the numerical solution of a hypersingular integral equation in scattering theory", J. Comput. Appl. Mathem. 61, pp 345-360 (1995). DOI: http://dx.doi.org/10.1016/0377-0427(94)00073-7
  15. Karl F. Warnick "Numerical analysis for electromagnetic integral equations" (Artech House, 2008) section 3-4.
  16. Andrew F. Peterson, Scott L. Ray, and Raj Mittra, "Computational Methods for Electromagnetics" (IEEE press, New York, 1998). Sect. 2-4.
  17. Al-Majdi Kadhum, "An enhanced solution for the axial current using electromagnetic wire scattering analysis", J. Engin. Develop. 18, 37-44 (2014). https://doi.org/10.4186/ej.2014.18.3.37
  18. A. Ike Mowete and A. ogunsola, "Plane wave scattering by a coated thin wire", PIERS Proceedings pp 743-749, Xi'an, China, March 22-26 (2010).
  19. S. hatamzdeh-Varmazyar and M. Naser-Moghadasi, "New numerical method for determining the scattered electromagnetic fields from thin wires", PIER B 3, pp 207-218 (2008). DOI: http://dx.doi.org/10.2528/PIERB07121303
  20. Paul Tsuji, Kristen Parrish, and Chicheng Xu, "Scattering from PEC cylinders by a normally incident plane wave" EE 383V Computational Electromagnetics: MoM project 1-7.
  21. K. F. Warnick and W. C. Chew, "Accuracy of the method of moments for scattering by a cylinder", IEEE Trans. Micr. Th. Tech. 48, pp 1652-1660 (2000). DOI: http://dx.doi.org/10.1109/22.873892
  22. Yun-Sheng Xu and Kan Wang, "Moment method solution of the EFIE for TE-wave scattering by conducting cylinders using basis and testing functions lacking in sufficient degrees of differentiability" 2009 3rd IEEE Internaltional symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communctions, pp. 917-920 (2009). DOI: http://dx.doi.org/10.1109/mape.2009.5355779
  23. Gokhun Selcuk and S. Sencer Koc, "Evaluation of hypersingular integrals on non-planar surfaces" 2014 International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO), pp 1-4 (2014). DOI: http://dx.doi.org/10.1109/nemo.2014.6995683
  24. Mei Song Tong and Weng Cho Chew, "A novel approach for evaluating hypersingular and strongly singular surface integrals in electromagnetics" IEEE Transc. Antennas Propag. 58, pp 3593-3601 (2010). DOI: http://dx.doi.org/10.1109/TAP.2010.2071370
  25. read.pudn.com/downloads93/ebook/365471/MOM2.ppt
  26. J. Wettergren and P. Slattman, "Electric field integral equation for cylindrical structures" IEE Proc. Microw. Antennas Propag. 143, pp 147-151 (1996). DOI: http://dx.doi.org/10.1049/ip-map:19960234
  27. Nobby Stevens and Luc Martens, "An efficient method to calculate surface currents on a PEC cylinder with flat end caps" Radio Science 38, 6 (2003). DOI: http://dx.doi.org/10.1029/2002RS002768
  28. Walton C. Gibson, "The Method of Moments in Electromagnetics" Eq. (5-108).(Taylor & Francis, 2008).
  29. Karl F. Warnick, "Numerical analysis for electromagnetic integral equations" Eq. (2-51).(Artech House, Boston, 2008).
  30. Clayton Paul Davis, "Understanding and improving moment method scattering solutions", Master thesis, Brigham Young University (2004).
  31. Karl F. Warnick and Weng Cho Chew, "Error analysis of the moment method", IEEE Antenna Propagat. Magazine 46, pp 38-53 (2004). DOI: http://dx.doi.org/10.1109/MAP.2004.1396735