PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 45 > pp. 1-20

COIFMAN WAVELETS IN ELECTROMAGNETIC WAVE SCATTERING BY A GROOVE IN CONDUCTING PLANE

By Y. Tretiakov and G. W. Pan

Full Article PDF (629 KB)

Abstract:
Scattering ofelectromagnetic waves from a groove in an infinite conducting plane is studied using the Coifman wavelets (Coiflets) under the integral equation formulation. The induced current is expressed in terms ofthe known Kirchhoff solution plus a localized correction current in the vicinity ofthe groove. The Galerkin procedure is implemented, employing the Coiflets as expansion and testing functions to find the correction current numerically. Owing to the vanishing moments, the Coiflets lead to a one-point quadrature formula in O(h5), which reduces the computational effort in filling the impedance matrix entries. The resulting matrix is sparse, which is desirable for iterative algorithms. Numerical results show that the new method is 2 to 5 times faster than the pulse based method of moments.

Citation:
Y. Tretiakov and G. W. Pan, "Coifman Wavelets in Electromagnetic Wave Scattering by a Groove in Conducting Plane," Progress In Electromagnetics Research, Vol. 45, 1-20, 2004.
doi:10.2528/PIER03091101
http://www.jpier.org/PIER/pier.php?paper=0309111

References:
1. Shifman, Y. and Y. Leviatan, "Scattering by a groove in a conducting plane: a PO-MoM hybrid formulation and wavelet analysis," IEEE Trans. Antennas Propagat., Vol. 49, 1807-1811, 2001.
doi:10.1109/8.982463

2. Harrington, R. F., Field Computation by Method of Moments, Macmillan, New York, 1968.

3. Pan, G., M. Toupikov, and B. Gilbert, "On the use of Coifman intervallic wavelets in the method of moments for fast construction of wavelet sparsified matrices," IEEE Trans. Antennas Propagat., Vol. 47, 1189-1999, 1999.
doi:10.1109/8.785751

4. Wang, G., "Application of wavelets on the interval to the analysis ofthin-wire antennas and scatterers," IEEE Trans. Antennas Prop., Vol. 45, 885-893, 1997.
doi:10.1109/8.575642

5. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, New York, 1989.

6. Kantorovich, L. V. and V. I. Krylov, Approximate Methods of Higher Analysis, 4th Ed., John Wiley & Sons, Inc., New York, 1959.

7. Daubechies, I., Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.

8. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, Cambridge University Press, 1992.

9. Van der Vorst, H. A., "Bi-CGSTAB: A fast and smoothly converging variant ofBi-CG for the solution ofnonsymmetric linear systems," SIAM J. Sci. Statist. Comput., Vol. 13, 631-644, 1992.
doi:10.1137/0913035

10. Chui, C. K., An Introduction to Wavelets, Academic Press, 1991.

11. Chui, C. K., Wavelets — A Tutorial in Theory and Applications, Academic Press, 1992.

12. Mallat, S. G., "Multiresolution approximations and wavelet orthonormal bases of L2(R)," Trans. Amer. Math. Soc., Vol. 315, 69-88, 1989.
doi:10.2307/2001373


© Copyright 2014 EMW Publishing. All Rights Reserved