Solution of wave diffraction problems by the method of continued boundary conditions

Numerical solution of three-dimensional diffraction problems by the method of continued boundary conditions, which is known to be effective in the case of two-dimensional problems, is discussed. The basic idea of the method is that the boundary condition is imposed at a certain sufficiently small distance from the impedance surface that produces the diffraction field. This procedure reduces the boundary-value problem to the Fredholm integral equation of the first or second kind with a smooth kernel. Results are reported that show how to apply the MCBC most efficiently, depending on particular requirements regarding the accuracy of the solution and number of calculations. Examples illustrating the high efficiency of the approach are presented.     

One method of solving rough surface wave diffraction problems

The problems of wave diffraction on a rough surface is considered by reducing surface scattering to volume scattering and then using methods for study of multiple scattering developed in the theory of wave propagation in random-inhomogeneous media. Using this approach, the Dyson equation is solved in the Bourret approximation as is the Bethe-Salpeter equation in the ladder approximation for the correlation function of the scalar field scattered on an infinite ideally reflective statistically homogeneous surface. Solutions of these equations automatically consider shadowing of some portions of the surface by others.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 27, No. 1, pp. 65–70, January, 1984.The author is greatly indebted to A. B. Shmelev and A. G. Vinogradov for their valuable remarks and evaluation of the study.     

Efficient method for solving the problems of wave diffraction by scatterers with broken boundaries

The pattern equations method is extended to solving the problems of wave scattering by bodies with piecewise smooth boundaries. The method is based on the reduction of the initial boundary-value problem to an integro-operator equation of the second kind in the scattering pattern of a body. With the use of the series expansion of the scattering pattern in angular spherical harmonics, the problem is ultimately reduced to solving an infinite algebraic system of equations in the expansion coefficients of the scattering pattern. The conditions at which this system can be solved by the method of reduction are formulated. Examples of solving the problems of wave scattering by bodies with impedance boundaries are considered. Essential advantages of the proposed method over other known methods are demonstrated.     

Near-field computation using the null-field method

In this paper we analyze three methods for computing the total field in the near-zone region. These methods use the expansion of the scattered field outside the minimum circumscribing sphere, an integral representation of the scattered field and a vector spherical wave expansion of the near-zone field. Calculations of the total field within the circumscribing sphere are presented for dielectric prolate spheroids to compare the different methods.     

Solution of the three-dimensional problem of wave diffraction by an ensemble of objects

The pattern equations method is extended to solving three-dimensional problems of wave diffraction by an ensemble of bodies. The method is based on the reduction of the initial problem to a system of N (N is the number of scatterers in the ensemble) integro-operator equations of the second kind for the scattering patterns of scatterers. With the use of the series expansions of the scattering patterns in angular spherical harmonics, the problem is reduced to an algebraic system of equations in the expansion coefficients. An explicit (asymptotic) solution to the problems is obtained in the case when the scattering bodies are separated by sufficiently long distances. It is shown that the method can be used to model the characteristics of wave scattering by complex-shaped bodies.     

Solution of the three-dimensional problem of plane wave diffraction by a two-period plane grating

Using the discrete source method, we develop an algorithm for solving the three-dimensional problem of wave scattering by a plane grating consisting of acoustically soft or acoustically stiff bodies. An efficient algorithm is proposed for determining the periodic Green’s function of the grating. Numerical results are obtained for different geometries of the grating elements. The fulfillment of the energy conservation law is verified along with the fulfillment of the boundary condition at the surface of the central grating element.     

Effective-dielectric-constant method for the problem of wave diffraction by a close-spaced dielectric grating

A simple method for determination of effective dielectric constants is proposed that allows a close-spaced two-dimensionally periodic dielectric layer with rectangular elements to be replaced by a homogeneous and anisotropic layer of the same thickness. The method makes it unnecessary to solve the complicated problem of determination of the fields within the elements for calculation of the plane-wave reflection and transmission coefficients in a long-wave approximation, which considerably simplifies the calculations. Comparison with known solutions obtained by rigorous methods for one-dimensionally periodic gratings shows exact agreement of the results. The method is easily extended to magnetodielectric media as well as to multicomponent media, including those whose dielectric constants are functions of the coordinate perpendicular to the layer.Academician A. L. Mints Radio-Engineering Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 3-4, pp. 286–294, March–April, 1993.     

Regularization of boundary integral equations in the problems of wave field diffraction by curved boundaries

A regularization of the exact Fredholm integral equations for the field or its derivative on a scattering surface is proposed. This approach allows one to calculate the scattering or diffraction of pulsed wave fields by curved surfaces of arbitrary geometry. Mathematically, the method is based on the replacement of the exact Fredholm integral equations by their truncated analogs, in which the contributions of the geometrically shadowed regions are cancelled. This approach has a clear physical meaning and provides stable solutions even when the direct numerical solution of mathematically exact initial integral equations leads to unstable results. The method is mathematically substantiated and tested using the problem of plane-wave scattering by a cylinder as an example.     

Determination of the error of approximate solutions of problems in wave diffraction by metal septa in rectangular waveguides by the method of singular integral equations

Electrical Engineering Institute of Communications, Kuibyshev. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 31, No. 10, pp. 1241–1245, October, 1988.     

Solution of two-dimensional problems of diffraction at piecewise-smooth cylindrical surfaces

Radiophysics and Quantum Electronics -     

The method of the boundary diffraction wave for impedance surfaces

The line integral of the boundary diffraction wave theory is extended for the diffraction process of waves by the impedance surfaces with edge discontinuities. With this aim, the exact diffraction field expression of Maliuzhinets is transformed into a line integral. The method is applied to the scattering problems of waves by a spherical reflector with edge discontinuity and the diffracted fields are evaluated asymptotically. The resultant expressions of the waves are examined numerically.     

Analysis of mutiple-shepers radiation and scattering problems by using a null-field integral equation approach

A systematic approach using the null-field integral equation in conjunction with the degenerate kernel is employed to solve the multiple radiation and scattering problems. Our approach can avoid calculating the principal values of singular and hypersingular integrals. Although we use the idea of null-field integral equation, we can locate the point on the real boundary thanks to the degenerate kernel. The proposed approach is seen as one kind of semi-analytical methods, since the error is attributed from the truncation of spherical harmonics. Finally, the numerical examples including one and two spheres are given to verify the validity of proposed approach.     

Solution of problem of electromagnetic-wave diffraction by multiangle dielectric cylinder using regions-product method

A method is developed for solution of the problem of diffraction of E- and H-polarized waves by a dielectric body with a multiangle cross section. In each of the regions formed by the interfaces of the media, the field is sought as a sum of functions that pertain to individual elements of the contour and are represented by series in Mathieu functions. The results of solutions of model problems are discussed. The possibility of using a triangular dielectric prism as a decelerating lens is shown.Zaporozh'ye Mechanical-Engineering Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 798–805, July, 1991.     

A hybrid Maliuzhinets/PO method for diffraction problems by impedance wedges

The solution of Maliuzhinets of the diffraction problem of waves by an impedance wedge is transformed into a physical optics integral. The resultant expression is suitable for the investigation of various diffraction problems having impedance wedges. The method is applied to the scattering of waves by an impedance spherical reflector with wedge structure at its discontinuity. The results are examined numerically.