Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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By M.-S. Tong

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Electromagnetic scattering by electrically large scatterers usually requires a large number of unknowns. To reduce the matrix size, one expects to choose a small sampling rate for the unknown function. In the method of moments (MoM) scheme, this rate is about 10 unknowns per wavelength for electrically small or medium scatterers. However, this rate may not work well for electrically large scatterers with a concave surface. The concave area on the scatter is observed to be the oscillatory part in the solution domain. The oscillation property requires more samplings to eliminate the numerical noises. The multiscalets with a multiplicity of two are higher-order bases. It is shown that the multiscalets are more suitable to represent the unknown function with oscillatory characteristic. Furthermore, the testing scheme under the discrete Sobolev-type inner product allows the MoM have the derivative sampling which enhances the tracking quality of the multiscalets further. Numerical Examples of scattering by 1000 and 1024 wavelength 2D scatterers demonstrate that the use of multiscalets in the MoM can keep the same discretization size for electrically large scatterers as for electrically small scatterers without losing the accuracy of the solution. In contrast, the traditional MoM and Nyström method require the finer discretization scheme if achieving a stable solution.

Citation: (See works that cites this article)
M.-S. Tong, "A stable integral equation solver for electromagnetic scattering by large scatterers with concave surface," Progress In Electromagnetics Research, Vol. 74, 113-130, 2007.

1. Harrington, R. F., Field Computation by Moment Methods, IEEE Press, New York, 1993.

2. Al Sharkawy, M. H., V. Demir, and A. Z. Elsherbeni, "The iterative multi-region algorithm using a hybrid finite difference frequency domain and method of moment techniques," Progress In Electromagnetics Research, Vol. 57, 19-32, 2006.

3. Wang, S., X. Guan, D. Wang, X. Ma, and Y. Su, "Electromagnetic scattering by mixed conducting/dielectric objects using higherorder MOM," Progress In Electromagnetics Research, Vol. 66, 51-63, 2006.

4. Chew, W. C., J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Boston, 2001.

5. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Ant. Propag. Mag., Vol. 35, No. 3, 7-12, 1993.

6. Song, J. M. and W. C. Chew, "Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering," Micro. Opt. Tech. Lett., Vol. 10, No. 1, 14-19, 1995.

7. Song, J. M. and W. C. Chew, "Large scale computations using FISC," IEEE Antennas Propag. Soc. Int. Symp., Vol. 4, 1856-1859, 2000.

8. Pan, X. M. and X. Q. Sheng, "A highly efficient parallel approach of multi-level fast multipole algorithm," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 8, 1081-1092, 2006.

9. Bucci, O. M., G. D'Elia, and M. Santojanni, "A fast multipole approach to 2D scattering evaluation based on a non redundant implementation of the method of auxiliary sources," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1715-1723, 2006.

10. Canino, L. S., J. J. Ottusch, M. A. Stalzer, J. L. Visher, and S. Wandzura, "Numerical solution of the Helmholtz equation in 2D and 3D using a high-order Nyström discretization," J. Comput. Phys., Vol. 146, No. 2, 627-663, 1998.

11. Gedney, S. D., "On deriving a locally corrected Nyström scheme from a quadrature sampled moment method," IEEE Trans. Antennas Propagat., Vol. 51, No. 9, 2402-2412, 2003.

12. Burghignoli, P., C. Di Nallo, F. Frezza, and A. Galli, "A simple Nyström approach for the analysis of 3D arbitrarily shaped conducting and dielectric bodies," Int. J. Numer. Model. El., Vol. 16, No. 2, 179-194, 2003.

13. Pan, G., Wavelets in Electromagnetics and Device Modeling, John Wiley & Sons, Hoboken, 2003.

14. Pan, G., M. Tong, and B. Gilbert, "Multiwavelet based moment method under discrete Sobolev-type norm," Micro. Opt. Tech. Lett., Vol. 40, No. 1, 47-50, 2004.

15. Tong, M., G. Pan, and G. Lei, "Full-wave analysis of coupled lossy transmission lines using multiwavelet-based method of moments," IEEE Trans. Microw. Theory Tech., Vol. 53, No. 7, 2362-2370, 2005.

16. Zunoubi, M. R. and A. A. Kishk, "A combined Bi-Cgstab (1) and wavelet transform method for EM problems using method of moments," Progress In Electromagnetics Research, Vol. 52, 205-224, 2005.

17. Alyt, O. M., A. S. Omar, and A. Z. Elsherbeni, "Detection and localization of RF radar pulses in noise environments using wavelet packet transform and higher order statistics," Progress In Electromagnetics Research, Vol. 58, 301-317, 2006.

18. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons, New York, 1989.

19. Adams, L. and J. L. Nazareth, Linear and Nonlinear Conjugate Gradient-related Methods, Society for Industrial and Applied Mathematics, Philadelphia, 1996.

20. Kolm, P. and V. Rokhlin, "Numerical quadratures for singular and hypersingular integrals," Comput. Math. Appl., Vol. 41, No. 3, 327-352, 2001.

21. Wagner, R. L. and W. C. Chew, "A study of wavelets for the solution of electromagnetic integral equation," IEEE Trans. Antennas Propagat., Vol. 43, No. 8, 802-810, 1995.

22. Pan, G., Y. V. Tretiakov, and B. Gilbert, "Smooth local cosine based Galerkin method for scattering problems," IEEE Trans. Antennas Propagat., Vol. 51, No. 6, 1177-1184, 2003.

23. Deng, H. and H. Ling, "Fast solution of electromagnetic integral equations using adaptive wavelet packet transform," IEEE Trans. Antennas Propagat., Vol. 47, No. 4, 674-682, 1999.

24. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: the art of scientific computing, 2nd edition, Cambridge University Press, New York, 1992.

25. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, New York, 1970.

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