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2010-12-15
An FFT-Accelerated FDTD Scheme with Exact Absorbing Conditions for Characterizing Axially Symmetric Resonant Structures
By
Progress In Electromagnetics Research, Vol. 111, 331-364, 2011
Abstract
An accurate and efficient finite-difference time-domain (FDTD) method for characterizing transient waves interactions on axially symmetric structures is presented. The method achieves its accuracy and efficiency by employing localized and/or fast Fourier transform (FFT) accelerated exact absorbing conditions (EACs). The paper details the derivation of the EACs, discusses their implementation and discretization in an FDTD method, and proposes utilization of a blocked-FFT based algorithm for accelerating the computation of temporal convolutions present in nonlocal EACs. The proposed method allows transient analyses to be carried for long time intervals without any loss of accuracy and provides reliable numerical data pertinent to physical processes under resonant conditions. This renders the method highly useful in characterization of high-Q microwave radiators and energy compressors. Numerical results that demonstrate the accuracy and efficiency of the method are presented.
Citation
Kostyantyn Sirenko, Vadim Pazynin, Yuriy K. Sirenko, and Hakan Bagci, "An FFT-Accelerated FDTD Scheme with Exact Absorbing Conditions for Characterizing Axially Symmetric Resonant Structures," Progress In Electromagnetics Research, Vol. 111, 331-364, 2011.
doi:10.2528/PIER10102707
References

1. Kuzmitchev, I. K., P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, "Model synthesis of energy compressors," Radiophysics and Electronics: Sci. Works Collection, Vol. 13, No. 2, 166-172, NAS of Ukraine, A. Usikov Institute of Radiophysics and Electronics, Kharkiv, 2008.

2. Tantawi, S. G., R. D. Ruth, A. E. Vlieks, and M. Zolotorev, "Active high-power RF pulse compression using optically switched resonant delay lines," IEEE Trans. Microwave Theory Tech., Vol. 45, No. 8, 1486-1492, 1997.
doi:10.1109/22.618460

3. Vikharev, A. L., A. M. Gorbachev, O. A. Ivanov, V. A. Isaev, S. V. Kuzikov, B. Z. Movshevich, J. Hirshfield, and S. H. Gold, "Active Bragg compressor of 3-cm wavelength microwave pulses," Radiophys. Quantum Electron., Vol. 51, No. 7, 539-555, 2008.
doi:10.1007/s11141-008-9053-3

4. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, Boston, 2005.

5. Keller, J. B., "Exact non-reflecting boundary conditions," J. Comput. Phys., Vol. 82, 179-192, 1989.

6. Hagstrom, T., "Radiation boundary conditions for the numerical simulation of waves," Acta Numerica, Vol. 8, 47-106, 1999.
doi:10.1017/S0962492900002890

7. Olivier, J. C., "On the synthesis of exact free space absorbing boundary conditions for the finite-difference time-domain method," IEEE Trans. Antennas Propag., Vol. 40, No. 4, 456-460, 1992.
doi:10.1109/8.138832

8. De Moerloose, J. and D. De Zutter, "Surface integral representation radiation boundary condition for the FDTD method," IEEE Trans. Antennas Propag., Vol. 41, No. 7, 890-896, 1993.
doi:10.1109/8.237619

9. Ziolkowski, R. W., N. K. Madsen, and R. C. Carpenter, "Three-dimensional computer modeling of electromagnetic fields: A global lookback lattice truncation scheme," J. Comput. Phys., Vol. 50, 360-408, 1983.
doi:10.1016/0021-9991(83)90103-1

10. Hagstrom, T. and H. B. Keller, "Exact boundary conditions at an artificial boundary for partial differential equations in cylinders," SIAM J. Math. Anal., Vol. 17, No. 2, 322-341, 1986.
doi:10.1137/0517026

11. Grote, M. J. and J. B. Keller, "Nonreflecting boundary conditions for Maxwell's equations," J. Comput. Phys., Vol. 139, 327-342, 1998.
doi:10.1006/jcph.1997.5881

12. Lubich, C. and A. Shadle, "Fast convolution for nonreflecting boundary conditions," SIAM J. Sci. Comput., Vol. 24, No. 1, 161-182, 2002.
doi:10.1137/S1064827501388741

13. Alpert, B., L. Greengard, and T. Hagstrom, "Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation," SIAM J. Numer. Anal., Vol. 37, No. 4, 1138-1164, 2000.
doi:10.1137/S0036142998336916

14. Sirenko, Y. K., S. Strom, and N. P. Yashina, Modeling and Analysis of Transient Processes in Open Resonant Structures --- New Methods and Techniques, Springer, Berlin, 2007.

15. Sirenko, K. Y. and Y. K. Sirenko, "Exact "absorbing" conditions in the initial boundary-value problems of the theory of open waveguide resonators," Comput. Math. Math. Phys., Vol. 45, No. 3, 490-506, 2005.

16. Hairer, E., C. H. Lubich, and M. Schlichte, "Fast numerical solution of nonlinear Volterra convolution equations," SIAM J. Sci. Stat. Comput., Vol. 6, No. 3, 532-541, 1985.
doi:10.1137/0906037

17. Yilmaz, A. E., D. S. Weile, B. Shanker, J.-M. Jin, and E. Michielssen, "Fast analysis of transient scattering in lossy media," IEEE Antennas Wireless Propag. Lett., Vol. 1, No. 1, 14-17, 2002.
doi:10.1109/LAWP.2002.802577

18. Bagci, H., A. E. Yilmaz, and E. Michielssen, "A fast hybrid TDIE-FDTD-MNA scheme for analyzing cable-induced transient coupling into shielding enclosures," Proc. IEEE Int. Symp. Electromagn. Compat., Vol. 3, 828-833, 2005.

19. Bagci, H., A. E. Yilmaz, V. Lomakin, and E. Michielssen, "Fast solution of mixed-potential time-domain integral equations for half-space environments," IEEE Trans. Geosci. Remote Sensing, Vol. 43, No. 2, 269-279, 2005.
doi:10.1109/TGRS.2004.841489

20. Bagci, H., A. E. Yilmaz, and E. Michielssen, "FFT-accelerated MOT-based solution of time-domain BLT equations," Proc. IEEE Int. Antennas Propagat. Symp., 1175-1178, 2006.
doi:10.1109/APS.2006.1710748

21. Bagci, H., A. E. Yilmaz, J.-M. Jin, and E. Michielssen, "Fast and rigorous analysis of EMC/EMI phenomena on electrically large and complex structures loaded with coaxial cables," IEEE Trans. Electromagn. Compat., Vol. 49, No. 2, 361-381, 2007.
doi:10.1109/TEMC.2007.897159

22. Bagci, H., A. E. Yilmaz, and E. Michielssen, "An FFT-accelerated time-domain multiconductor transmission line simulator," IEEE Trans. Electromagn. Compat., Vol. 52, No. 1, 199-214, 2010.
doi:10.1109/TEMC.2009.2036602

23. Sirenko, Y. K., L. G. Velychko, and F. Erden, "Time-domain and frequency-domain methods combined in the study of open resonance structures of complex geometry," Progress In Electromagnetics Research, Vol. 44, 57-79, 2004.
doi:10.2528/PIER03030601

24. Velychko, L. G., Y. K. Sirenko, and O. S. Shafalyuk, "Time-domain analysis of open resonators. Analytical grounds," Progress In Electromagnetics Research, Vol. 61, 1-26, 2006.
doi:10.2528/PIER06020701

25. Velychko, L. G. and Y. K. Sirenko, "Controlled changes in spectra of open quasi-optical resonators," Progress In Electromagnetics Research B, Vol. 16, 85-105, 2009.
doi:10.2528/PIERB09060202

26. Ladyzhenskaya, O. A., The Boundary Value Problems of Mathematical Physics, Springer-Verlag, New York, 1985.

27. Vladimirov, V. S., Equations of Mathematical Physics, Dekker, New York, 1971.

28. Korn, G. A. and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York, 1961.

29. Bateman, H. and A. Erdelyi, Higher Transcendental Functions,, Vol. 2, McGraw-Hill, New York, 1953.

30. Prudnikov, A. P., Y. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2, Gordon and Breach, New York, 1986.

31. Von Hurwitz, A., Allgemeine Funktionentheorie und Elliptische Funktionen, Von Courant, R., Geometrische Funktionentheorie, Springer-Verlag, Berlin, 1964 (in German).

32. Abramowitz, M. and I. A. Stegun Ed., Handbook of Mathematical Functions, Dover, New York, 1972.

33. Kantartzis, N. V. and T. D. Tsiboukis, High Order FDTD schemes for Waveguide and Antenna Structures, Morgan&Claypool, San Rafael, CA, 2006.

34. Gerald, C. F. and P. O. Wheatley, Applied Numerical Analysis, Addison-Welsley, Boston, 1999.

35. Oppenheim, A. V., R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1999.