volume | PIER Journals

Abstract

A rigorous solution in L₂ to the EFIE for 2-D screens is developed and proposed as a reference solution for testing the convergence rate and scattering amplitude error of any MoM algorithm in L₂. The proposed reference solution permits to choose judiciously an appropriate mesh density for a MoM algorithm instead of using the ten-points-rule in all cases. Additionally, using the reference solution it is demonstrated that the discrepancy should not be used as a performance value of the scattering amplitude error while solving the EFIE with the MoM in L₂. Both the E- and H-cases are considered.

1. Hsiao, G. C., R. E. Kleinman, R. X. Li, and P. M. van den Berg, "Residual error â€”a simple and sufficient estimate of actual error in solutions of boundary integral equations," Computational Engineering with Boundary Elements, Vol. 1: Fluid and Potential Problems, 73-83, 1990.

2. Hsiao, G. C. and R. E. Kleinman, "Feasible error estimates in boundary element methods," Boundary Element Technology VII, 875-886, 1991.

3. Van den Berg, P. M., A. P. M. Zwamborn, G. C. Hsiao, and R. E. Kleinman, "Iterative solutions of first kind integral equations," Direct and Inverse Boundary Value Problems, 213-232, 1991.

4. Hsiao, G. C. and R. E. Kleinman, "Error analysis in numerical solution of acoustic integral equation," Int. J. Numer. Meth. Eng., Vol. 37, 2921-2933, 1994.
doi:10.1002/nme.1620371705

5. Feistauer, M., G. C. Hsiao, and R. E. Kleinman, "Asymptotic and a posteriori estimates for boundary element solutions of hypersingular integral equations," SIAM J. Numer. Anal., Vol. 33, No. 4, 666-685, 1996.
doi:10.1137/0733034

6. Warnick, K. F. and W. C. Chew, "Accuracy and conditioning of the method of moments for the 2D EFIE," Proceedings of the Annual Review of Progress in Applied Computational Electromagnetics, 15-20, 1999.

7. Warnick, K. F. and W. C. Chew, "Convergence of moment method solutions of the EFIE for a 2D open cavity," Microw. Opt. Tech. Lett., Vol. 23, No. 11, 212-218, 1999.
doi:10.1002/(SICI)1098-2760(19991120)23:4<212::AID-MOP7>3.0.CO;2-K

8. Warnick, K. F. and W. C. Chew, "Accuracy of the method of moments for scattering by a cylinder," IEEE Transactions on Microwave Theory and Techniques, Vol. 48, No. 10, 1652-1660, 2000.
doi:10.1109/22.873892

9. Warnick, K. F. and W. C. Chew, "Error analysis of the moment method," IEEE Antennas and Propagation Magazine, Vol. 46, No. 12, 38-52, 2004.
doi:10.1109/MAP.2004.1396735

10. Davis, C. P. and K. F. Warnick, "Error analysis of 2-D MoM for MFIE/EFIE/CFIE based on the circular cylinder," IEEE Trans. Antennas and Propag., Vol. 53, No. 1, 321-331, 2005.
doi:10.1109/TAP.2004.838791

11. Tyzhnenko, A. G., "Two-dimensional TE-plane wave scattering by a dielectric loaded semicircular trough in a ground plane," Electromagnetics, Vol. 24, No. 6, 357-368, 2004.
doi:10.1080/02726340490458042

12. Tyzhnenko, A. G., "A unique solution to the 2-D H-scattering problem for a semicircular trough in a PEC ground plane," Progress In Electromagnetics Research, Vol. 54, 303-319, 2005.
doi:10.2528/PIER05011803

13. Hongo, K. and Q. A. Naqvi, "Diffraction of electromagnetic wave by disk and circular hole in a perfectly conducting plane," Progress In Electromagnetics Research, Vol. 68, 113-150, 2007.

14. Anastassiu, H. T., "Error estimation of the Method of Auxiliary Sources (MAS) for scattering from an impedance circular cylinder," Progress In Electromagnetics Research, Vol. 52, 109-128, 2005.
doi:10.2528/PIER04072101

15. Hussein, K. A., "Fast computational algorithm for EFIE applied to arbitrarily shaped conducting surface," Progress In Electromagnetics Research, Vol. 68, 339-357, 2007.

16. Tyzhnenko, A. G., "Convergent Galerkin MoM solver for the EFIE in two dimensions," Electromagnetics, Vol. 25, No. 4, 217-229, 2005.
doi:10.1080/02726340590915601

17. Tyzhnenko, A. G. and Y. V. Ryeznik, "Convergent Galerkin MoM solution to the hypersingular 1st kind integral equation for 2-D Neumann problem," Journal of Applied Electromagnetism, Vol. 6, No. 2, 37-51, 2004.

18. Tyzhnenko, A. G. and Y. V. Ryeznik, "Convergent Galerkin MoM solution for 2-D H-scattering from screens," Electromagnetics, Vol. 25, No. 5, 329-341, 2005.

19. Colak, D., A. I. Nosich, and A. Altinas, "Radar cross-section study of cylindrical cavity-backed apertures with outer or inner material coating: The case of E-polarization," IEEE Trans. Antennas and Propag., Vol. 41, No. 11, 1551-1559, 1993.
doi:10.1109/8.267355

20. Yan, Y. and I. H. Sloan, "On integral equations of the first kind with logarithmic kernels," J. Integral Eq. and Appl., Vol. 1, No. 4, 549-579, 1988.

21. Atkinson, K. E., "A discrete galerkin method for first kind integral equations with logarithmic kernel," J. Integral Eq. and Appl., Vol. 1, No. 3, 343-363, 1988.

22. Von Koch, H., "Sur un theoreme de hilbert," Mathem. Ann., Vol. 69, 266-283, 1910.
doi:10.1007/BF01456875

23. Mikhlin, S. G., Direct Methods in Mathematical Physics, Moscow, 1950.

24. Il'iinskiy, A. S. and Y. G. Smirnov, "Integral equations for problems of wave diffraction at screens," Sov. J. Communicat. Tech. Elect., Vol. 39, No. 4, 129-136, 1994.

25. Koshikawa, S., D. Colak, A. Altintas, K. Kobayashi, and A. I. Nosich, "A comparative study of RCS predictions of canonical rectangular and circular cavities with double-layer material loading," IEICE Trans. Electron., Vol. E80-C, No. 11, 1457-1466, 1997.

26. Sladek, V. and J. Sladek (eds.), Singular Integrals in Boundary Element Method, Computational Mechanics Publications, Southampton, U.K., 1998.

27. Morita, N., N. Kumagai, and J. R. Mautz, Integral Equations Methods for Electromagnetics, Artech House, London, 1990.

Dr. Alexander Tyzhnenko

Dr. Yevgen Ryeznik