Comparison of Wavelet Packet and Wavelet in Solving Arbitrary Array of Parallel Wires Integral Equations in Electromagnetics
Main Article Content
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.
Downloads
Article Details
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
References
Stéphane Mallat, "A Wavelet Tour of Signal Processing the Sparse Way", Third Edition. Copyright (2009) by Elsevier Inc.
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.
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.
Walton C. Gibson, "The Method of Moments in Electromagnetics", Second Edition, © (2015) by Taylor & Francis Group, LLC.
R. F. Harrington, Field computation by Moment Methods, Editorial Board William Perkins, Editor in Chief 1992.
N. Khanna, V. Kumar and S. K. Kaushik, "Wavelet packets and their vanishing moments", Poincare Journal of Analysis & Applications, Vol. 2017(2), 95-105.
J. C. Goswami, A. K. Chan, ʺFundamentals Wavelets Theory, Algorithms, and Applicationsʺ, Copyright © (2011) by John Wiley & Sons, Inc. All rights reserved.
G. W. Pan, ʺWavelets in Electromagnetics and Device Modelingʺ, Copyright © (2003) by John Wiley & Sons, Inc. All rights reserved.
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.
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.
P. Papakanellos, "Study of Two Arbitrarily Located Parallel Cylindrical Dipoles Based on an Auxiliary Sources Technique", Electromagnetics, 2003, 23:5, 399-416.
Wojciech L. Golik, "Wavelet Packets for Fast Solution of Electromagnetic Integral Equations", IEEE Trans. on Antennas and Propagat., Vol. 46, No. 5, May 1998.
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.
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.
E. Ashpazzadeh, B. Han, M. Lakestani, Biorthogonal multiwavelets on the interval for numerical solutions of Burgers' equation, Journal of Computational and Applied Mathematics, 2016.
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.
D.B. Davidson, ''Computational Electromagnetics for Rf and Microwave Engineering'', Published in the United States of America by Cambridge University Press, New York, 2005.
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.
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.