The Exact Absorbing Conditions Method in the Analysis of Open Electrodynamic Structures

Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 91)


The authors expound the method of exact absorbing boundary conditions, which solves one of the most important theoretical problems in computational electrodynamics, namely, the problem of equivalent replacement of an open (with infinite domain of analysis) initial boundary value problem by a closed (with bounded computation domain) one. This method, being mathematically strict, allows proper formulation and numerical study of transient and steady-state processes in various open resonant systems. The authors present local (in space and time) and non-local exact absorbing conditions for virtual boundaries located in cross-sections of regular waveguides or in free space. The elaborated concept of the so-called virtual feeding waveguides allows to solve many practically interesting radiation problems. The approach outlined in this chapter was implemented in software for solving both scalar (plane and axially symmetric) and vector problems.


  1. 1.
    Maikov, A.R., Sveshnikov, A.G., Yakunin, S.A.: A difference scheme for the non-stationary Maxwell equations in waveguide systems. USSR Comput. Math. Math. Phys. 26(3), 130–138 (1986)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Sirenko, K.Y., Sirenko, Y.K.: Exact ‘absorbing’ conditions in the initial boundary value problems of the theory of open waveguide resonators. Comput. Math. Math. Phys. 45(3), 490–506 (2005)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Sirenko, Y.K., Strom, S., Yashina, N.P.: Modeling and Analysis of Transient Processes in Open Resonant Structures. New Methods and Techniques. Springer, New York (2007)zbMATHGoogle Scholar
  4. 4.
    Sirenko, K.Y., Sirenko, Y.K., Yashina, N.P.: Modeling and analysis of transients in periodic gratings. I. Fully absorbing boundaries for 2-D open problems. J. Opt. Soc. Am. A 27(3), 532–543 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    Sirenko, Y.K., Strom, S. (eds.): Modern Theory of Gratings. Resonant Scattering: Analysis Techniques and Phenomena. Springer, New York (2010)Google Scholar
  6. 6.
    Sirenko, K., Pazynin, V., Sirenko, Y., Bagci, H.: An FFT-accelerated FDTD scheme with exact absorbing conditions for characterizing axially symmetric resonant structures. Prog. Electromagnet. Res. 111, 331–364 (2011)CrossRefGoogle Scholar
  7. 7.
    Shafalyuk, O., Sirenko, Y., Smith, P.: Simulation and analysis of transient processes in open axially-symmetrical structures: method of exact absorbing boundary conditions. In: Zhurbenko, V. (ed.) Electromagnetic Waves, pp. 99–116. InTech, Rijeka (2011)Google Scholar
  8. 8.
    Kravchenko, V.F., Sirenko, Y.K., Sirenko, K.Y.: Electromagnetic Wave Transformation and Radiation by the Open Resonant Structures. Modelling and Analysis of Transient and Steady-State Processes. Fizmathlit, Moscow (2011) (in Russian)Google Scholar
  9. 9.
    Shafalyuk, O., Smith, P., Velychko, L.: Rigorous substantiation of the method of exact absorbing conditions in time-domain analysis of open electrodynamic structures. Prog. Electromagnet. Res. B 41, 231–249 (2012)CrossRefGoogle Scholar
  10. 10.
    Engquist, B., Majda, A.: Absorbing boundary conditions for the numerical simulation of waves. Math. Comput. 31(139), 629–651 (1977)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Mur, G.: Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations. IEEE Trans. Electromagnet. Capab. 23(4), 377–382 (1981)CrossRefGoogle Scholar
  12. 12.
    Tirkas, P.A., Balanis, C.A., Renaut, R.A.: Higher order absorbing boundary conditions for FDTD-method. IEEE Trans. Antennas Propag. 40(10), 1215–1222 (1992)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Mei, K.K., Fang, J.: Superabsorbtion—a method to improve absorbing boundary conditions. IEEE Trans. Antennas Propag. 40(9), 1001–1010 (1992)ADSCrossRefGoogle Scholar
  14. 14.
    Berenger, J.-P.: A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114(1), 185–200 (1994)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Berenger, J.-P.: Three-dimensional perfectly matched layer for absorption of electromagnetic waves. J. Comput. Phys. 127(2), 363–379 (1996)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Sacks, Z.S., Kingsland, D.M., Lee, R., Lee, J.F.: A perfectly matched anisotropic absorber for use as an absorbing boundary condition. IEEE Trans. Antennas Propag. 43(12), 1460–1463 (1995)Google Scholar
  17. 17.
    Perov, A.O., Sirenko, Y.K., Yashina, N.P.: Explicit conditions for virtual boundaries in initial boundary value problems in the theory of wave scattering. J. Electromagnet. Waves Appl. 13(10), 1343–1371 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Sirenko, Y.K., Velychko, L.G., Erden, F.: Time-domain and frequency-domain methods combined in the study of open resonance structures of complex geometry. Prog. Electromagnet. Res. 44, 57–79 (2004)CrossRefGoogle Scholar
  19. 19.
    Sirenko, K.Y., Pazynin, V.L.: Axially-symmetrical radiators of pulsed and monochromatic TE 0n- and TM 0n-waves. Uspehi Sovremennoy Radioelektroniki 4, 52–69 (2006) (in Russian)Google Scholar
  20. 20.
    Velychko, L.G., Sirenko, Y.K., Velychko, O.S.: Time-domain analysis of open resonators. Analytical grounds. Prog. Electromagnet. Res. 61, 1–26 (2006)CrossRefGoogle Scholar
  21. 21.
    Sirenko, K.Y.: Slot resonances in axially symmetric radiators of pulse-modulated and monochromatic TM 0n-modes. Telecommun. Radio Eng. 66(1), 9–21 (2007)CrossRefGoogle Scholar
  22. 22.
    Sirenko, K.Y.: Splitting of super-broadband pulses by simple inhomogeneities of circular and coaxial waveguide. Telecommun. Radio Eng. 67(16), 1415–1428 (2008)CrossRefGoogle Scholar
  23. 23.
    Kuzmitchev, I.K., Melezhyk, P.M., Pazynin, V.L., Sirenko, K.Y., Sirenko, Y.K., Shafalyuk, O.S., Velychko, L.G.: Model synthesis of energy compressors. Radiofizika I Elektronika 13(2), 166–172 (2008)Google Scholar
  24. 24.
    Velychko, L.G., Sirenko, Y.K.: Controlled changes in spectra of open quasi-optical resonators. Prog. Electromagnet. Res. B 16, 85–105 (2009)CrossRefGoogle Scholar
  25. 25.
    Sirenko, K.Y., Sirenko, Y.K., Yashina, N.P.: Modeling and analysis of transients in periodic gratings. II. Resonant wave scattering. J. Opt. Soc. Am. A 27(3), 544–552 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    Sirenko, K., Pazynin, V., Sirenko, Y., Bagci, H.: Compression and radiation of high-power short radio pulses. I. Energy accumulation in direct-flow waveguide compressors. Progress In Electromagnetics Research 116, 239–270 (2011)CrossRefGoogle Scholar
  27. 27.
    Sirenko, K., Pazynin, V., Sirenko, Y., Bagci, H.: Compression and radiation of high-power short radio pulses. II. A novel antenna array design with combined compressor/radiator elements. Prog. Electromagnet. Res. 116, 271–296 (2011)CrossRefGoogle Scholar
  28. 28.
    Taflove, A., Hagness, S.C.: Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House, Boston (2000)zbMATHGoogle Scholar
  29. 29.
    Rao, S.M. (ed.): Time Domain Electromagnetics. Academic Press, San Diego (1999)Google Scholar
  30. 30.
    Sirenko, K.Y.: Transport operators in the axially-symmetrical problems of the electrodynamics of pulsed waves. Elektromagnitnye Volny I Elektronnye Sistemy 11(11), 15–26 (2006) (in Russian)Google Scholar
  31. 31.
    Kravchenko, V.F., Sirenko, K.Y., Sirenko, Y.K.: Transport operators and exact absorbing conditions in the plane problems of the electrodynamics of pulsed waves for compact open resonators with the waveguide feeder line. Elektromagnitnye Volny I Elektronnye Sistemy 14(1), 4–19 (2009) (in Russian)Google Scholar
  32. 32.
    Borisov, V.V.: Electromagnetic Fields of Transient Currents. St. Petersburg University Press, St. Petersburg (1996) (in Russian)Google Scholar
  33. 33.
    Ladyzhenskaya, O.A.: The Boundary Value Problems of Mathematical Physics. Springer, New York (1985)CrossRefzbMATHGoogle Scholar
  34. 34.
    Korn, G.A., Korn, T.M.: Mathematical Handbook for Scientists and Engineers. McGraw-Hill, New York (1961)zbMATHGoogle Scholar
  35. 35.
    Vladimirov, V.S.: Equations of Mathematical Physics. Dekker, New York (1971)zbMATHGoogle Scholar
  36. 36.
    Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions. Dover, New York (1972)zbMATHGoogle Scholar
  37. 37.
    Bateman, H., Erdelyi, A.: Tables of Integral Transforms, vol. 1. McGraw-Hill, New York (1954)Google Scholar
  38. 38.
    Waynberg, B.R.: Asymptotic Methods in the Equations of Mathematical Physics. Moscow State University Press, Moscow (1982) (in Russian)Google Scholar
  39. 39.
    Sirenko, Y.K., Shestopalov, V.P., Yashina, N.P.: Free oscillations in coaxial-waveguide resonator. Soviet J. Commun. Technol. Electron. 32(7), 60–67 (1987)Google Scholar
  40. 40.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic Press, San Diego, London (2000)zbMATHGoogle Scholar
  41. 41.
    Mikhailov, V.P.: Partial Differential Equations. Mir Publishers, Moscow (1978)Google Scholar
  42. 42.
    Jackson, J.D.: Classical Electrodynamics. Wiley, New York (1975)zbMATHGoogle Scholar
  43. 43.
    Bateman, H., Erdelyi, A.: Higher Transcendental Functions. McGraw-Hill, New York (1953)zbMATHGoogle Scholar
  44. 44.
    Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I.: Integrals and Series, vol. 2. Gordon & Breach, New York (1986)zbMATHGoogle Scholar
  45. 45.
    von Hurwitz, A.: Allgemeine Funktionentheorie und Elliptische Funktionen. In: von Courant, R. (ed.) Geometrische Funktionentheorie. Springer, Berlin (1964) (in German)Google Scholar
  46. 46.
    Maloney, J.G., Smith, G.S., Scott, W.R.: Accurate computation of the radiation from simple antennas using the finite-difference time-domain method. IEEE Trans. Antennas Propag. 38(7), 1059–1068 (1990)Google Scholar
  47. 47.
    Montoya, T.P., Smith, G.S.: A study of pulse radiation from several broad-band monopoles. IEEE Trans. Antennas Propag. 44(8), 1172–1182 (1996)Google Scholar
  48. 48.
    Shestopalov, V.P., Tuchkin, Y.A., Poyedinchuk, A.Y., Sirenko, Y.K.: New solution methods for direct and inverse problems of the diffraction theory. In: Analytical Regularization of the Boundary Value Problems in Electromagnetic Theory. Osnova, Kharkov (1997) (in Russian)Google Scholar
  49. 49.
    Colton, D., Kress, R.: Integral Equation Methods in Scattering Theory. Wiley-Interscience, New York (1983)zbMATHGoogle Scholar
  50. 50.
    Reed, M., Simon, B.: Methods of Modern Mathematical Physics. Analysis of Operators. Academic Press, New York, IV (1978)zbMATHGoogle Scholar
  51. 51.
    Keldysh, M.V.: On the completeness of eigenfunctions of some classes of non-selfadjoint linear operators. Russian Math. Surv. 26(4), 15–44 (1971)ADSCrossRefzbMATHGoogle Scholar
  52. 52.
    Bamberger, A., Joly, P., Roberts, J.E.: Second order absorbing boundary conditions for the wave equation: a solution for the corner problem. SIAM J. Numer. Anal. 27(2), 323–352 (1990)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  53. 53.
    Collino, F.: Conditions Absorbantes D’ordre Eleve Pour des Modeles de Propagation D’onde Dans des Domaines Rectangulaires. Rocquencourt, France: Report I.N.R.I.A. No.1790 (1993) (in French)Google Scholar
  54. 54.
    Levin, L.: Theory of Waveguides: Techniques for Solution of Waveguide Problems. Newnes-Butterworths, London (1975)Google Scholar
  55. 55.
    Balanis, C.A.: Antenna Theory: Analysis and Design. Wiley, New York (1982)Google Scholar
  56. 56.
    Velychko, L.G., Sirenko, Y.K., Vinogradova, E.D.: Analytical grounds for modern theory of two-dimensionally periodic gratings. In: Kishk, A. (ed.) Solutions and Applications of Scattering, Propagation, Radiation and Emission of Electromagnetic Waves, pp. 123–158. InTech, Rijeka (2012)Google Scholar
  57. 57.
    Kantartzis, N.V., Tsiboukis, T.D.: High Order FDTD Schemes for Waveguide and Antenna Structures. Morgan & Claypool, San Rafael, CA (2006)Google Scholar
  58. 58.
    Gerald, C.F., Wheatley, P.O.: Applied Numerical Analysis. Addison-Welsley, Boston (1999)zbMATHGoogle Scholar
  59. 59.
    Bagci, H., Yilmaz, A.E., Lomakin, V., Michielssen, E.: Fast solution of mixed-potential time-domain integral equations for half-space environments. IEEE Trans. Geosci. Remote Sens. 43(2), 269–279 (2005)ADSCrossRefGoogle Scholar
  60. 60.
    Bagci, H., Yilmaz, A.E., Jin, J.-M., Michielssen, E.: Fast and rigorous analysis of EMC/EMI phenomena on electrically large and complex structures loaded with coaxial cables. IEEE Trans. Electromagnet. Capab. 49(2), 361–381 (2007)CrossRefGoogle Scholar
  61. 61.
    Bagci, H., Yilmaz, A.E., Michielssen, E.: An FFT-accelerated time-domain multiconductor transmission line simulator. IEEE Trans. Electromagnet. Capab. 52(1), 199–214 (2010)CrossRefGoogle Scholar
  62. 62.
    Oppenheim, A.V., Schafer, R.W., Buck, J.R.: Discrete-Time Signal Processing. Prentice-Hall, Englewood Cliffs, NJ (1999)Google Scholar
  63. 63.
    Pazynin, V.L.: Compression of frequency-modulated electromagnetic pulses in sections of regular waveguides. Telecommun. Radio Eng. 71(20), 1833–1857 (2012)CrossRefGoogle Scholar
  64. 64.
    Shestopalov, V.P., Kirilenko, A.A., Rud’, L.A.: Resonance Wave Scattering. Waveguide Discontinuities, vol. 2. Naukova Dumka, Kiev (1986) (in Russian)Google Scholar
  65. 65.
    Shestopalov, V.P., Kirilenko, A.A., Masalov, S.A.: Matrix Convolution-Type Equations in the Diffraction Theory. Naukova Dumka, Kiev (1984) (in Russian)Google Scholar
  66. 66.
    Pochanina, I.E., Yashina, N.P.: Electromagnetic properties of open waveguide resonator. Electromagnetics 13(3), 289–300 (1993)CrossRefGoogle Scholar
  67. 67.
    Yashina, N.P.: Accurate analysis of coaxial slot bridge. Microwave Opt. Technol. Lett. 20(5), 345–349 (1999)CrossRefGoogle Scholar
  68. 68.
    Maloney, J.G., Smith, G.S.: A study of transient radiation from the Wu-King resistive monopole—FDTD analysis and experimental measurements. IEEE Trans. Antennas Propag. 41(5), 668–676 (1993)Google Scholar
  69. 69.
    Shirman, Ya.D.: Radio Ducts and Resonant Cavities. Svyaz’izdat, Moscow (1959) (in Russian)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.King Abdullah University of Science and TechnologyThuwalSaudi Arabia
  2. 2.O.Ya. Usikov Institute for Radiophysics and Electronics, National Academy of SciencesKharkivUkraine
  3. 3.L.N. Gumilyov Eurasian National UniversityAstanaRepublic of Kazakhstan

Personalised recommendations