Abstract
It is shown that to determine approximately (in the L 2-metric) the polar diagram of a scattered field of sources contained inside a certain smooth nonresonance boundary with a given variable transparency from a known polar diagram for these sources in a vacuum it is possible to use finite segments of the expansion of the field in divergent waves. The proof is carried out for the two-dimensional scalar problem. The inverse problem is stated as a variational problem. The results of numerical computation are given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
V. F. Apel'tsin, “The method of nonorthogonal series and the Rayleigh conjecture in internal diffraction problems,”Izv. Vuzov. Radiofizika 25, No. 3, 339–347 (1982).
N. N. Voitovich and O. F. Zamorskaya, “Use of expansion in divergent waves in determining the scattering diagram on a closed semitransparent boundary,” in:Waves and Diffraction-90 [in Russian], Vol. 1, Physical Society, Moscow (1990), pp. 234–237.
N. N. Voitovich, B. Z. Katsenelenbaum, E. N. Korshunova, et al.,Electrodynamics of Antennas with Semitransparent Surfaces: Methods of Constructive Synthesis [in Russian], Nauka, Moscow (1989).
N. N. Voitovich, O. F. Zamorskaya, and E. N. Korshunova, “Synthesis of the distribution of transparency of a conformal antenna with a given perturbation,”Radioelektronika,35, No. 10, 2046–2052 (1989).
N. N. Voitovich, B. Z. Katsenelenbaum, and A. N. Sivov,The Generalized Method of Singular Oscillations in the Theory of Diffraction. With an Appendix by M. S. Agranovich [in Russian], Nauka, Moscow (1977).
N. N. Voitovich, B. Z. Katsenelenbaum, and A. N. Sivov,The Generalized Method of Oscillations in the Theory of Diffraction. With an Appendix by M. S. Agranovich: Spectral Properties of Diffraction Problems [in Russian], Nauka, Moscow (1977).
B. Z. Katsenelenbaum, “Constructive Synthesis of a Nonresonance Antenna with a Semitransparent Surface,”Dokl. Akad. Nauk SSSR,283, No. 1, 109–113 (1985).
M. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, et al.,Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).
A. G. Kyurkchan, “The Rayleigh and Sommerfeld representations for diffracted fields and their regions of convergence,”Radiotekh. i Elektrotekh.,27, No. 2, 233–240 (1982).
A. N. Tikhonov and V. Ya. Arsenin,Methods of Solving Ill-posed Problems, Interscience, New York (1983).
M. Yu. Shalukhin, “Contour currents with minimal norm that guarantee an approximate synthesis of given fields,” Kand. Diss., Moscow (1989).
Additional information
Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 138–142.
Rights and permissions
About this article
Cite this article
Voitovich, N.N., Zamorskaya, O.F. Application of Galerkin's method in the problem of synthesis of an antenna with semitransparent boundary. J Math Sci 67, 2950–2954 (1993). https://doi.org/10.1007/BF01095875
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01095875