Comparison of Wavelet Packet and Wavelet in Solving Arbitrary Array of Parallel Wires Integral Equations in Electromagnetics

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M. Bayjja
G. Alsharahi
M. Aghoutane
N. A. Touhami

Abstract

In this paper, wavelets transformation (WT) and wavelet packet transformation (WPT) are used in solving, by the method of moments, a semicircular array of parallel wires electric field integral equation.  First, the integral equation is solved by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix.  Therefore, wavelet transformation and wavelet packet transformation are used to sparsify the impedance matrix, using two categories of wavelets functions, Biorthogonal (bior2.2) and Orthogonal (db4) wavelets.  The far-field scattering patterns and the comparison between wavelets transformation and wavelet packet transformation in term number of zeros in impedance matrix and CPU Time reduction are presented. Numerical results are presented to identify which technique is best suited to solve such scattering electromagnetic problems and compared with published results.

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How to Cite
Bayjja, M., Alsharahi, G., Aghoutane, M., & Touhami, N. A. (2020). Comparison of Wavelet Packet and Wavelet in Solving Arbitrary Array of Parallel Wires Integral Equations in Electromagnetics. Advanced Electromagnetics, 9(3), 8-14. https://doi.org/10.7716/aem.v9i3.1487
Section
Research Articles

References


  1. Stéphane Mallat, "A Wavelet Tour of Signal Processing the Sparse Way", Third Edition. Copyright (2009) by Elsevier Inc.
    View Article

  2. Matthew N. O. Sadiku, Ph.D., "Numerical techniques in electromagnetics", 2nd Ed, ©2001 by CRC Press LLC, Boca Raton London New York Washington, D.C.

  3. J.H. Richmond, "Scattering by an arbitrary array of parallel wires," IEEE Trans. Micro. Theo. Tech., vol. MTT-13, no. 4, July 1965, pp. 408-412.
    View Article

  4. Walton C. Gibson, "The Method of Moments in Electromagnetics", Second Edition, © (2015) by Taylor & Francis Group, LLC.

  5. R. F. Harrington, Field computation by Moment Methods, Editorial Board William Perkins, Editor in Chief 1992.
    View Article

  6. N. Khanna, V. Kumar and S. K. Kaushik, "Wavelet packets and their vanishing moments", Poincare Journal of Analysis & Applications, Vol. 2017(2), 95-105.
    View Article

  7. J. C. Goswami, A. K. Chan, ʺFundamentals Wavelets Theory, Algorithms, and Applicationsʺ, Copyright © (2011) by John Wiley & Sons, Inc. All rights reserved.

  8. G. W. Pan, ʺWavelets in Electromagnetics and Device Modelingʺ, Copyright © (2003) by John Wiley & Sons, Inc. All rights reserved.

  9. Mohammad Yazdi And Nader Komjani, "Polarizability calculation of arbitrary individual scatterers, scatterers in arrays, and substrated scatterers", Journal of the Optical Society of America B, Vol. 33, No. 3 / March 2016.
    View Article

  10. Mohamed Bayjja and al, ʺModeling a Planar Coupled Microstrip Lines using various Wavelets and Method of Momentsʺ, Advanced Electromagnetics, Vol. 9, No. 1, March 2019.
    View Article

  11. P. Papakanellos, "Study of Two Arbitrarily Located Parallel Cylindrical Dipoles Based on an Auxiliary Sources Technique", Electromagnetics, 2003, 23:5, 399-416.
    View Article

  12. Wojciech L. Golik, "Wavelet Packets for Fast Solution of Electromagnetic Integral Equations", IEEE Trans. on Antennas and Propagat., Vol. 46, No. 5, May 1998.
    View Article

  13. Dorsaf Omri, Mourad Aidi · Taoufk Aguili, "A comparison of three temporal basis functions for the time domain method of moments (TD MoM)", Journal of Computational Electronics, March 2020.
    View Article

  14. mir Geranmayeh, Rouzbeh Moini, and S. H. Hesam Sadeghi, Numerical Simulation of Electromagnetic Fields Radiated by Lightning Return Stroke Channels: A Wavelet-Based Approach, IEEE Trans. on Electromag. Compatibility., Vol. 48, No. 1, Feb. 2006.
    View Article

  15. E. Ashpazzadeh, B. Han, M. Lakestani, Biorthogonal multiwavelets on the interval for numerical solutions of Burgers' equation, Journal of Computational and Applied Mathematics, 2016.
    View Article

  16. Mohamed Bayjja, A.K. Belbachir, M. Boussouis, and Naima Amar Touhami, ''Orthogonal and biorthogonal compactly supported wavelets in modeling the circular loop antenna'', International Journal of Microwave and Optical Technology, Vol. 12, NO. 5, September 2017.

  17. D.B. Davidson, ''Computational Electromagnetics for Rf and Microwave Engineering'', Published in the United States of America by Cambridge University Press, New York, 2005.
    View Article

  18. M. Lerer, A.B. Kleshchenkov, O.S. Labunko, "Time-Domain Scattering from Arbitrary Array of Parallel Electric Dipoles", 11 Int. Conf. on Mathematical Methods in Electromagnetic Theory. Kharkiv, Ukraine, June 26-29, 2006.

  19. Guido Ala, and al, "An Advanced Numerical Model in Solving Thin-Wire Integral Equations by Using Semi-Orthogonal Compactly Supported Spline Wavelets", IEEE Trans. on Electromag. Compatibility, Vol. 45, No. 2, May 2003.
    View Article