B. Katsenelenbaum, G. Matviyiv, N. Voitovich. How to find the shape of the body, then its several scattering patterns are known. Proc. of 1995 URSI Int. Symp. on Electromagn. Theory, St.Petersburg, 1995, p.133-135.

Abstract. The patterns of the field scattered on a body are orthogonal to some function of angles by any illumination, when the frequency is an eigen frequency of inner volume of this body. The function depends only on the body shape and its position. This fact is used to find the shape of scattering body when several scattering patterns are given but the illuminated fields are not known. The scalar two-dimensional problems are discussed in the paper. The results of two numerical experiments are given. To find not very complicated body it is enough to know from 5 to 7 patterns.

B. Z. Katsenelenbaum, N. N. Voitovich, G. M. Matviyiv. Determination of moving body shape by several patterns of field scattered by it. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-95), Lviv, 1995, p. 56-57 (In Russian).

B. Z. Katsenelenbaum, G. M. Matviyiv, N. N. Voitovich. Finding the shape of the moving body according to several scattering patterns. 11th Int. Microwave Conf. MIKON-96, Warsaw, 1996, v.2, p. 391-395.

Abstract. The method proposed above for finding shape of a fixed body is developed and applied for case if the body is moving. Method's idea and numerical results are presented.

A. Golubyatnikov, B. Katsenelenbaum, G. Matviyiv, N. Voitovich. Finding the body shape according to several scattering patterns. Int. Conf. on Operator Theory and its Applications to Science and Industrial Problems (Abstracts), Winnipeg, 1998, p. 47.

Анотація. Розвинуто метод відновлення форми тіла оснований на властивостях діаграм розсіяння на власній частоті його внутрішньої області. Описано різні підходи до задачі мінімізації відповідного функціонала, проведено числові експерименти на модельних прикладах та проаналізовано їх результати.

Abstract. A method of body shape reconstruction based on properties of scattering patterns measured at resonant frequency of inner domain is developed for the case of uniformly moving body. Numerical results for a two-dimensional model problem concerning the kite-shaped body are presented.

Abstract. A method for reconstructing the shape of irregular waveguide is proposed. The method uses amplitudes of the normal modes excited by the point source moving along the irregular part of the waveguide and measured at its output. Mean-square residual of the measured and calculated mode amplitudes integrated over the source path is minimized. Direct problem is solved by the cross-section method. Numerical results concerning a 2D model problem are presented.

Abstract. The paper develops a method of body shape reconstruction based on the property that a set of scattering patterns, measured at a resonant frequency of inner domain, is noncomplete. The method consists in numerical determination of the orthogonal complement function which generates some auxiliary real field, one of zero lines of which is the sought body contour. The variational technique is used. The method is transferred onto the case of uniformly moving body. Numerical results for two-dimensional model problems concerning the pencil- and kite-shaped bodies are presented. They show, in particular, that for reconstruction of complicated shapes the measurements should be made at higher resonant frequencies.

Abstract.

Abstract. A method for decreasing the back scattering from bodies having complex impedance boundaries is developed. A system of nonlinear integral equations is given for determining the impedance distribution which provides minimal back scattering. Numerical results for a model problem of scattering on the infinite circular cylinder are given. Frequency dependencies of scattering at obtained impedance distributions are shown.

Abstract. Method for body reconstruction at its resonant frequencies is further investigated. Applicability of the method is numerically confirmed for some cases when the classical Herglotz functions with kernels being orthogonal complement functions to a set of patterns scattered on the body at a resonant frequency of its interior domain, do not exist.

Abstract. Подано метод розв"язування задачі виизначення форми тіла на власних частотах його внутрішньої області. Метод полягає в побудові апроксимуючих функцій Герглотца, таких що їхні нульові лінії наближаються до шуканого контуру тіла.

Abstract. Method proposed earlier for body reconstruction at its resonant frequencies is further developed. An attempt is made to establish the connection between the method applicability and existence of the Herglotz functions approximating the eigenoscillation field inside the body. Two propositions are given concerning convergence of the method for two cases when a Herglotz function coinciding with this field exists or not. Numerical results shoving the fast decreasing of the appropriate functional with increasing the number of measured patterns, are presented. Two ways of computer modeling of the input data are numerically compared.

Abstract. A method for decreasing the back scattering from bodies having complex impedance boundaries is developed. A system of nonlinear integral equations is given for determining the impedance distribution which provides minimal back scattering. Numerical results for a model problem of scattering on the infinite circular cylinder are given. Frequency dependencies of scattering at obtained impedance distributions are shown.