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

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

Abstract

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.

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References

  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)

    MathSciNet  CrossRef  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  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)

    ADS  CrossRef  Google Scholar 

  5. Sirenko, Y.K., Strom, S. (eds.): Modern Theory of Gratings. Resonant Scattering: Analysis Techniques and Phenomena. Springer, New York (2010)

    Google Scholar 

  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)

    CrossRef  Google Scholar 

  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. 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. 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)

    CrossRef  Google Scholar 

  10. Engquist, B., Majda, A.: Absorbing boundary conditions for the numerical simulation of waves. Math. Comput. 31(139), 629–651 (1977)

    ADS  MathSciNet  CrossRef  MATH  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    ADS  MathSciNet  CrossRef  MATH  Google Scholar 

  13. Mei, K.K., Fang, J.: Superabsorbtion—a method to improve absorbing boundary conditions. IEEE Trans. Antennas Propag. 40(9), 1001–1010 (1992)

    ADS  CrossRef  Google Scholar 

  14. Berenger, J.-P.: A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114(1), 185–200 (1994)

    ADS  MathSciNet  CrossRef  MATH  Google Scholar 

  15. Berenger, J.-P.: Three-dimensional perfectly matched layer for absorption of electromagnetic waves. J. Comput. Phys. 127(2), 363–379 (1996)

    ADS  MathSciNet  CrossRef  MATH  Google Scholar 

  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. 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)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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. Velychko, L.G., Sirenko, Y.K., Velychko, O.S.: Time-domain analysis of open resonators. Analytical grounds. Prog. Electromagnet. Res. 61, 1–26 (2006)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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. Velychko, L.G., Sirenko, Y.K.: Controlled changes in spectra of open quasi-optical resonators. Prog. Electromagnet. Res. B 16, 85–105 (2009)

    CrossRef  Google Scholar 

  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)

    ADS  CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  28. Taflove, A., Hagness, S.C.: Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House, Boston (2000)

    MATH  Google Scholar 

  29. Rao, S.M. (ed.): Time Domain Electromagnetics. Academic Press, San Diego (1999)

    Google Scholar 

  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. 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. Borisov, V.V.: Electromagnetic Fields of Transient Currents. St. Petersburg University Press, St. Petersburg (1996) (in Russian)

    Google Scholar 

  33. Ladyzhenskaya, O.A.: The Boundary Value Problems of Mathematical Physics. Springer, New York (1985)

    CrossRef  MATH  Google Scholar 

  34. Korn, G.A., Korn, T.M.: Mathematical Handbook for Scientists and Engineers. McGraw-Hill, New York (1961)

    MATH  Google Scholar 

  35. Vladimirov, V.S.: Equations of Mathematical Physics. Dekker, New York (1971)

    MATH  Google Scholar 

  36. Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions. Dover, New York (1972)

    MATH  Google Scholar 

  37. Bateman, H., Erdelyi, A.: Tables of Integral Transforms, vol. 1. McGraw-Hill, New York (1954)

    Google Scholar 

  38. Waynberg, B.R.: Asymptotic Methods in the Equations of Mathematical Physics. Moscow State University Press, Moscow (1982) (in Russian)

    Google Scholar 

  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. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic Press, San Diego, London (2000)

    MATH  Google Scholar 

  41. Mikhailov, V.P.: Partial Differential Equations. Mir Publishers, Moscow (1978)

    Google Scholar 

  42. Jackson, J.D.: Classical Electrodynamics. Wiley, New York (1975)

    MATH  Google Scholar 

  43. Bateman, H., Erdelyi, A.: Higher Transcendental Functions. McGraw-Hill, New York (1953)

    MATH  Google Scholar 

  44. Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I.: Integrals and Series, vol. 2. Gordon & Breach, New York (1986)

    MATH  Google Scholar 

  45. von Hurwitz, A.: Allgemeine Funktionentheorie und Elliptische Funktionen. In: von Courant, R. (ed.) Geometrische Funktionentheorie. Springer, Berlin (1964) (in German)

    Google Scholar 

  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. 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. 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. Colton, D., Kress, R.: Integral Equation Methods in Scattering Theory. Wiley-Interscience, New York (1983)

    MATH  Google Scholar 

  50. Reed, M., Simon, B.: Methods of Modern Mathematical Physics. Analysis of Operators. Academic Press, New York, IV (1978)

    MATH  Google Scholar 

  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)

    ADS  CrossRef  MATH  Google Scholar 

  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)

    ADS  MathSciNet  CrossRef  MATH  Google Scholar 

  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. Levin, L.: Theory of Waveguides: Techniques for Solution of Waveguide Problems. Newnes-Butterworths, London (1975)

    Google Scholar 

  55. Balanis, C.A.: Antenna Theory: Analysis and Design. Wiley, New York (1982)

    Google Scholar 

  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. Kantartzis, N.V., Tsiboukis, T.D.: High Order FDTD Schemes for Waveguide and Antenna Structures. Morgan & Claypool, San Rafael, CA (2006)

    Google Scholar 

  58. Gerald, C.F., Wheatley, P.O.: Applied Numerical Analysis. Addison-Welsley, Boston (1999)

    MATH  Google Scholar 

  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)

    ADS  CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  62. Oppenheim, A.V., Schafer, R.W., Buck, J.R.: Discrete-Time Signal Processing. Prentice-Hall, Englewood Cliffs, NJ (1999)

    Google Scholar 

  63. Pazynin, V.L.: Compression of frequency-modulated electromagnetic pulses in sections of regular waveguides. Telecommun. Radio Eng. 71(20), 1833–1857 (2012)

    CrossRef  Google Scholar 

  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. 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. Pochanina, I.E., Yashina, N.P.: Electromagnetic properties of open waveguide resonator. Electromagnetics 13(3), 289–300 (1993)

    CrossRef  Google Scholar 

  67. Yashina, N.P.: Accurate analysis of coaxial slot bridge. Microwave Opt. Technol. Lett. 20(5), 345–349 (1999)

    CrossRef  Google Scholar 

  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. Shirman, Ya.D.: Radio Ducts and Resonant Cavities. Svyaz’izdat, Moscow (1959) (in Russian)

    Google Scholar 

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Sirenko, K., Sirenko, Y. (2016). The Exact Absorbing Conditions Method in the Analysis of Open Electrodynamic Structures. In: Sirenko, Y., Velychko, L. (eds) Electromagnetic Waves in Complex Systems. Springer Series on Atomic, Optical, and Plasma Physics, vol 91. Springer, Cham. https://doi.org/10.1007/978-3-319-31631-4_5

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