Vol. 68

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2016-10-02

On Instabilities in Time Marching Methods

By Juan Becerra, Felix Vega, and Farhad Rachidi
Progress In Electromagnetics Research C, Vol. 68, 1-10, 2016
doi:10.2528/PIERC16062905

Abstract

We discuss in this paper the stability of the time marching (TM) method. We identify one cause of instability in the method associated with the calculation of variables involved in the convolution operation. We provide a solution to this problem, preventing the appearance of unstable poles in the Z-domain. This solution is fundamentally different from other previously presented approaches in the sense that it is not based on filtering or predictive techniques. Instead, it consists of preprocessing the known variable in the convolution equations.

Citation


Juan Becerra, Felix Vega, and Farhad Rachidi, "On Instabilities in Time Marching Methods," Progress In Electromagnetics Research C, Vol. 68, 1-10, 2016.
doi:10.2528/PIERC16062905
http://jpier.org/PIERC/pier.php?paper=16062905

References


    1. Tesche, F. M., "On the analysis of a transmission line with nonlinear terminations using the timedependent BLT equation," IEEE Transactions on Electromagnetic Compatibility, Vol. 49, No. 2, 427-433, May 2007.
    doi:10.1109/TEMC.2007.897141

    2. Rao, S. M., Time Domain Electromagnetics, Academic Press, 1999.

    3. Taflove, A., Computational Electrodynamics: The Finite-difference Time-domain Method, 1 Ed., Artech House, 1995.

    4. Tijhuis, A. G., "Toward a stable marching-on-in-time method for two-dimensional transient electromagnetic scattering problems," Radio Science, Vol. 19, No. 5, 1311-1317, Sep. 1984.
    doi:10.1029/RS019i005p01311

    5. Shi, Y., M.-Y. Xia, R. Chen, E. Michielssen, and M. Lu, "A stable marching-on-in-time solver for time domain surface electric field integral equations based on exact integration technique," 2010 IEEE Antennas and Propagation Society International Symposium (APSURSI), 1-4, 2010.
    doi:10.1109/APS.2010.5562167

    6. Bin Sayed, S., H. A. Ulku, and H. Bagci, "A stable marching on-in-time scheme for solving the time-domain electric field volume integral equation on high-contrast scatterers," IEEE Transactions on Antennas and Propagation, Vol. 63, No. 7, 3098-3110, Jul. 2015.
    doi:10.1109/TAP.2015.2429736

    7. Smith, P. D., "Instabilities in time marching methods for scattering: Cause and rectification," Electromagnetics, Vol. 10, No. 4, 439-451, Oct. 1990.
    doi:10.1080/02726349008908256

    8. Rynne, B. P. and P. D. Smith, "Stability of time marching algorithms for the electric field integral equation," Journal of Electromagnetic Waves and Applications, Vol. 4, No. 12, 1181-1205, Jan. 1990.
    doi:10.1163/156939390X00762

    9. Sadigh, A. and E. Arvas, "Treating the instabilities in marching-on-in-time method from a different perspective [electromagnetic scattering]," IEEE Transactions on Antennas and Propagation, Vol. 41, No. 12, 1695-1702, Dec. 1993.
    doi:10.1109/8.273314

    10. Lacik, J., Z. Lukes, and Z. Raida, "Signal processing techniques for stabilization of marching-onin- time method," International Conference on Electromagnetics in Advanced Applications, 2009, ICEAA’09, 670-673, 2009.
    doi:10.1109/ICEAA.2009.5297278

    11. Al-Jarro, A., M. A. Salem, H. Bagci, T. M. Benson, P. Sewell, and A. Vukovic, "Explicit solution of the time domain volume integral equation using a stable predictor-corrector scheme," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 11, 5203-5214, Nov. 2012.
    doi:10.1109/TAP.2012.2207691

    12. Ulku, H. A., H. Bagci, and E. Michielssen, "Marching on-in-time solution of the time domain magnetic field integral equation using a predictor-corrector scheme," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 8, 4120-4131, Aug. 2013.
    doi:10.1109/TAP.2013.2262016

    13. Proakis, J. G. and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications, Prentice Hall, 1996.

    14. Pupalaikis, P. J., "The relationship between discrete-frequency s-parameters and continuousfrequency responses," Design Con., 1-28, Santa Clara, CA, 2012.

    15. Bertholet, P. F. and F. M. Tesche, "The fast laplace transform,", Sep. 6, 2009.

    16. Priyanka, B., S. Panwar, and S. D. Joshi, "Finding zeros for linear phase FIR filters," 2013 IEEE 3rd International Advance Computing Conference (IACC), 1103-1107, 2013.
    doi:10.1109/IAdCC.2013.6514381

    17. Ahmadi, M., M. Azimi-Sadjadi, R. Gorgui-Naguib, R. King, and A. Kwabwe, Digital Filtering in One and Two Dimensions: Design and Applications, Springer Science & Business Media, 2013.