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Progress In Electromagnetics Research
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USE OF SEMI-INVERSION METHOD FOR THE DIRICHLET PROBLEM IN ROUGH SURFACE SCATTERING

By V. I. Tatarskii

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Abstract:
The scattering problem from the random interface with the Dirichlet boundary condition can be formulated as an integral equation x = K̂y with respect to surface sources y (here, K̂ is the integral operator). Starting with an approximate operator K̂0, for which the inverse operator M̂=K̂−10 is known, the series in powers of the operator Ẑ=M̂(K̂0−K̂) is derived. As an approximate kernel, we consider the kernel depending only on the difference of arguments: K0=K0(r-r´), for which the kernel of the operator M̂ can be found in terms of generalized functions. The norm of the difference operator ||Ẑ|| is found; the conditions of convergency ||Ẑ||≤ 1 were obtained.

Citation:
V. I. Tatarskii, "Use of Semi-Inversion Method for the Dirichlet Problem in Rough Surface Scattering," Progress In Electromagnetics Research, Vol. 54, 109-135, 2005.
doi:10.2528/PIER04110802
http://www.jpier.org/PIER/pier.php?paper=0411082

References:
1. Charnotskii, M. I. and V. I. Tatarskii, WRM, Vol. 5, 361-380, Vol. 5, 361-380, 1995.

2. Gelfand, I. M. and G. E. Shilov, Generalized Functions, Vol. 1. Properties and operations, Vol. 1. Properties and operations.

3. Kapp, D. A. and G. S. Brown, IEEE Transactions AP, Vol. 44, 711-721, Vol. 44, 711-721, 1996.

4. Kreyszig, E., Advanced Engineering Mathematics, Seventh edition, Section 19.3, Formula 11, John Wiley & Sons, Inc., New York, 1993.

5. Kreyszig, E., Introductory Functional Analysis with Applications, John Wiley & Sons, Inc., New York, 1989.

6. Lerer, A. M. and A. G. Schuchinsky, IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-41, 2002-2009, Vol. MTT-41, 11, 2002-2009, 1993.

7. Lerer, A., I. Donets, and S. Bryzgalo, J. of Electromagnetic Waves and Application, Vol. 10, No. 6, 765-790, Vol. 10, No. 6, 765-790, 1996., 1996.

8. Liszka, E. G., J. J. McCoyJ. Acoust. Soc. Am., and Vol. 71, 1093-1100, Vol. 71, 1093-1100, 1982., 1982.

9. Lysanov, Yu. P. and Zh. AkustVol. 2, 182-187, Vol. 2, 182-187, 1956 (in Russian)., 1956.

10. McDaniel, S. T., WRM, Vol. 8, 3-14, Vol. 8, 3-14, 1998.

11. McDaniel, S. T., WRM, Vol. 9, 401-413, Vol. 9, 401-413, 1999.

12. Meecham W. C., J. Acoust. Soc. Am. and Vol. 28, 370-377, Vol. 28, 370-377, 1956., 1956.

13. Milder, D. M., J. Acoust. Soc. Am., and Vol. 89, 529-541, Vol. 89, 529-541, 1991., 1991.

14. Morse, P. M. and H. Feshbach, Methods of Theoretical Physics, Part I, Chapt. 8, McGraw-Hill, New York, 1953.

15. Nosich, A. I., IEEE Antenna and Propagation Magazine, Vol. 41, No. 3, 34-49, Vol. 41, No. 3, 34-49, 1999.

16. Polyanin, A. D. and A. V. Manzhirov, Handbook of Integral Equations, CRC Press, Boca Raton, Boston, London, New York, Washington DC, 1998.

17. Tatarskii, V. I., "The effects of the turbulent atmosphere on wave propagation," Translated from the Russian by the Israel Program for Scientific Translations, 2215.

18. Tatarskii, V. I., WRM, Vol. 3, 127-146, Vol. 3, 127-146, 1993.

19. Voronovich, A. G., Wave Scattering from Rough Surfaces, Second edition, Springer, Berlin, 1999.

20. Wolf, E., "A generalized extinction theorem and its role in scattering theory," Coherence and Quantum Optics, 1973.


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