Finite Step Conjugate Gradients Methods for the Solution of an Impedance Operator Equation Arising in Electromagnetics
Haifa belhadj, Taoufik Aguili
DOI: 10.4236/jemaa.2011.310066   PDF    HTML     4,290 Downloads   7,005 Views  


A class of finite step iterative methods, conjugate gradients, for the solution of an operator equation, is presented on this paper to solve electromagnetic scattering. The method of generalized equivalent circuit is used to model the problem and then deduce an electromagnetic equation based on the impedance operator. Four versions of the conjugate gradient method are presented and numerical results for an iris structure are given, to illustrate convergence properties of each version. Computational efficiency of these methods has been compared to the moment method.

Share and Cite:

H. belhadj and T. Aguili, "Finite Step Conjugate Gradients Methods for the Solution of an Impedance Operator Equation Arising in Electromagnetics," Journal of Electromagnetic Analysis and Applications, Vol. 3 No. 10, 2011, pp. 416-422. doi: 10.4236/jemaa.2011.310066.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. R. Hestenes and E. Stiefel, “Methods of Conjugate Gradients for Solving Linear Systems,” Journal of Research of the National Bureau of Standards, Vol. 49, No. 6, 1952, pp. 409-436.
[2] T. K. Sarkar, “The Conjugate Gradient Method as Applied to Electromagnetic Field Problems,” IEEE Antennas and Propagation Society Newsletter, Vol. 28, No. 4, 1986, pp. 4-14.
[3] A. F. Peterson and R. Mittra, “Convergence of the Conju- Gate Gradient Method When Applied to Matrix Equations Representing Electromagnetic Scattering Problems,” IEEE Transactions on Antennas and Propagation, Vol. 34, No. 12, 1986, pp.1447-1454. doi:10.1109/TAP.1986.1143780
[4] K. Barkeshli and J. L. Volakis, “Improving the Converge-Nce Rate of the Conjugate Gradient FFT Using Subdomain Basis Functions,” IEEE Transactions on Antennas and Propagation, Vol. 37, No. 7, 1989, pp. 893-900. doi:10.1109/8.29384
[5] T. A. Cwik and R. Mittra, “Scattering from a Periodic Array of Free-Standing Arbitrarily Shaped Perfectly Conducting or Resistive Patches,” IEEE Transactions on Antennas and Propagation, Vol. 35, No. 11, 1987, pp. 1226-1234. doi:10.1109/TAP.1987.1143999
[6] T. K. Sarkar, E. Arvas and S. M. Rao, “Application of FFT and the Conjugate Gradient Method for the Solution of Electromagnetic Radiation from Electrically Large and Small Conducting Bodies,” IEEE Transactions on Antennas and Propagation, Vol. 34, No. 5, 1986, pp. 635-640. doi:10.1109/TAP.1986.1143871
[7] R. F. Harrington and T. K. Sarkar, “Boundary Elements and the Method of Moments,” 5th International Conference of Boundary Elements, Hiroshima, 8-11 November 1983, pp. 31-40.
[8] H. Belhadj, S. Mili and T. Aguili, “New Implementation of the Conjugate Gradient Based on the Impedance Operator to Analyze Electromagnetic Scattering,” Progress in Electromagnetic Research B, Vol. 27, 2011, pp. 21-36.
[9] H. Baudrand, “Representation by Equivalent Circuit of the Integrals Methods in Microwave Passive Elements,” European Microwave Conference, Budapest, 10-13 Sepetember 1990, Vol. 2, pp. 1359-1364.
[10] T. Aguili, “Modélisation des Composantes SFH Planaires par la Méthode des Circuits équivalents Généralisés”, Ph.D.Thesis, National Engineering School of Tunis, Tunis, 2000.
[11] H. Baudrand and D. Bajon, “Equivalent Circuit Representation for Integral Formulations of Electromagnetic Problems,” International Journal of Numerical Modelling Electronic Networks Devices and Fields, Vol. 15, No. 1, 2002, pp. 23-57. doi:10.1002/jnm.430
[12] H. Aubert and H. Baudrand, “L’Electromagnétisme par les Schémas Equivalents, ” in Fran?ais, Cepaduès, 2003.
[13] T. K. Sarkar and E. Arvas, “On a Class of Finite Step Iterative Methods (Conjugate Directions) for the Solution of an Operator Equation Arising in Electromagnetics,” IEEE Antennas and Propagation, Vol. 33, No. 10, 1985, pp. 1058-1066.
[14] C. Lanczos, “Solution of Systems of Linear Equtions by Minimized Iterations,” Journal of research of the National Bureau of Standards, Vol. 49, 1952, pp. 33-53.
[15] D. R. Wilton and C. M. Butler, “Efficient Numerical Techniques for Solving Pocklington’s Equation and Their Relationship to Other Methods”, IEEE Transactions on Antennas and Propagation, Vol. 24, No. 1, 1976, pp. 83-86. doi:10.1109/TAP.1976.1141286

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.