Yu. A. Tuchkin

New numerical-analytical methods in diffraction theory

This paper is aimed at presenting analytical and numerical-analytical methods developed by the authors to be employed in solving boundary value problems in mathematical physics and finding their application in diffraction theory. It was consistently realized that the idea of analytical regularization of ill-conditioned integral, integral-differential, and series equations of the first kind resulted in the efficient techniques and numerical algorithms which made it possible to solve these equations on the computer. The presented regularization techniques are successfully used in studies of two- and three-dimensional wavy scattering by closed and unclosed screens, compact and periodic, dielectric and perfectly conducting scatterers.

Analytical Regularization Method for Wave Diffraction by Bowl-Shaped Screen of Revolution

Analytical Regularization Method is generalized on the case of three dimensional diffraction BVP for bowl-shaped screen of revolution. Both Dirichlet and Neumann BVP are solved, i.e. they are reduced to corresponding infinite linear algebraic systems (I+H)x=b, x,b∈l2 of the second kind in space l2 with compact operator in space l2 H. These systems can be used for construction of numerically efficient algorithms that gives solutions with arbitrary necessary accuracy

MATHEMATICAL MODELING OF ELECTROMAGNETIC WAVE SCATTERING BY WAVY PERIODIC BOUNDARY BETWEEN TWO MEDIA

The extension of C method, combined with idea of Tikhonov’s regularization is proposed. The regularizing algorithm for numerical solution of electromagnetic wave diffraction by the boundary of dielectric media is developed. This algorithm is based on the solution of the system linear algebraic equations of C method as subject of regularizing method of A. N. Tikhonov. The numerical calculations of scattered field in the case of E-polarization are presented. The efficiency and reliability of the method for the solution of the problems of boundary shape reconstruction have been proved and demonstrated numerically for several situations.

Two-dimensional scattering from thin screens of arbitrary cross section

A generalization of the Riemann-Hilbert problem approach, which gives good results in constructing highly efficient numerical methods in electromagnetic scattering theory, is presented. The derivation of this generalized method and the solution of two-dimensional diffraction wave problems on thin perfectly conductive screens having arbitrary cross-sections are presented. It is shown that the radar cross-section value of a number of circular cylinders may be increased considerably by an appropriate choice of cylinder locations, when the dimensions of the structure are comparable to the wavelength. The characteristics of excitation of an open resonator at the eigenfrequencies and near the eigenfrequencies by line sources are discussed.<<ETX>>

Scalar wave diffraction from infinitely thin perfectly conducting circular ring

A new strong mathematically rigorous and numerically efficient method for solving the boundary value problem of scalar wave diffraction by an infinitely thin circular ring screen is proposed. The method is based on the combination of the orthogonal polynomials approach and the ideas of the methods of analytical regularization. As a result of the suggested regularization procedure, the initial boundary value problems was equivalently reduced to the infinite system of the linear algebraic equations of the second kind, i.e., to an equation of the type (I+H)x=b, x, b/spl isin/l/sub 2/ in the space l/sub 2/ of square summable sequences. This equation was solved numerically by means of a truncation method with, in principle, any required accuracy.

Arbitrary shaped hollow resonators and waveguides modeling. Analytical regularization method

Mathematically strong and efficient approach for simulation of resonators and waveguides of arbitrary profile is suggested. The approach is based on new implementation of Analytical Regularization Method. Numerical results of E-polarized wave diffraction by waveguide resonant structures demonstrate the method efficiency and reliability.

ELECTROMAGNETIC WAVE SCATTERING BY SMOOTH IMPERFECTLY CONDUCTIVE CYLINDRICAL OBSTACLE

The problem of wave diffraction by impedance cylindrical smooth surface is solved. The initial boundary value problem is reduced to a few different algebraic systems in l2 of the kind (I+H)x=b, x,b∈l2 This gives relevant basis for efficient numerical algorithm construction for most part of possible physical and engineering applications. The constructed method includes the most complicated case of imperfectly but well conductive cylinder.

Millimeter Wave Band Cavity Resonators for Magnetoresonance Experiments

Electrodynamical features of rectangular cavity resonators as experimental cells of Electron Spin Resonance spectrometer for the millimeter frequency band have been investigated. Measurements and analytical estimations of features of three types of resonators (film-wall type, diffraction grating-wall type, double-wall type) are presented. The advantages and imperfections of each design as well as recommendations for their applications in millimeter wave magnetospectroscopy are given.

Axially Symmetric Compact Range Reflectors: Application of the Analytic Regularization Method

An axially symmetric compact range reflector with a blended rolled edge was analyzed and optimized in a rigorous formulation of the diffraction problem. The corresponding boundary-value diffraction problem is solved with the analytic regularization method, which reduces the problem to an operator equation of the second kind, thus guaranteeing a numerically stable and effective solution. The distribution of the surface density and the fields at the aperture and in the near-field zone were obtained and analyzed for different types of the reflector-edge curvature. In addition, a “blending function” was used that esures an infinitely smooth contour across the junction between the paraboloid part of the reflector and its rolled edge. The procedure for determining the optimal edge is carried out in the rigorous formulation of the diffraction problem by minimizing the deviation from a plane wave.

Analytical Regularization Method for axially symmetrical antennae and compact range applications

This paper is devoted to finding out the most influential qualitative and quantitative factors affecting compact range construction with properly chosen radiators and reflector antennae. The results were obtained utilizing the Analytical Regularization Method. It reduces the problem to an infinite system of linear algebraic equations of the second kind that guarantees a mathematically rigorous and numerically efficient solution.