E. D. Vinogradova

Scattering of an E-Polarized Plane Wave by Two-Dimensional Airfoils

Abstract This article presents the implementation of the rigorous method of regularization to the scattering of an E-polarized plane wave by the classical airfoil described by the Zhukovski transform. The accurate computation of the scattering patterns and the radar cross-section are performed in a wide frequency band for different incident angles.

Regularization of the Dirichlet Problem for Laplace's Equation: Surfaces of Revolution

Abstract Based on the idea of analytical regularization, a mathematically rigorous and numerically efficient method to solve the Laplace equation with a Dirichlet boundary condition on an open or closed arbitrarily shaped surface of revolution is described. To improve the convergence of the series for the single-layer density, we extracted and evaluated in an explicit form the singularity of the density at the surface edge. Numerical investigations of canonical structures, such as the open prolate spheroid and the open surface obtained by the rotation of “Pascals Limaçon” or the “Cassini Oval,” exhibit the high accuracy and wide applicability of the method.

Analytical regularization based analysis of a spherical reflector symmetrically illuminated by an acoustic beam

A mathematically accurate and numerically efficient method of analysis of a spherical reflector, fed by a scalar beam produced by a complex source-point feed, is presented. Two cases, soft and hard reflector surface, are considered. In each case the solution of the full-wave integral equation is reduced to dual series equations and then further to a regularized infinite-matrix equation. The latter procedure is based on the analytical inversion of the static part of the problem. Sample numerical results for 50-lambda reflectors demonstrate features that escape a high-frequency asymptotic analysis.

Rigorous Analysis of Extremely Large Spherical Reflector Antennas: EM Case

The transmitting spherical reflector antenna (SRA) has a well-known rigorous solution form as a second kind Fredholm system that is well conditioned when truncated to a finite system. The size of such systems for extremely large SRAs require specially designed highly efficient numerical algorithms to make their analysis feasible. Two significant features of the system are that its convolution format admits a computationally rapid implementation of the bi-conjugate gradient method, and at high frequencies, a certain decoupling occurs. These features allow an effective numerical treatment of apertures some thousands of wavelengths.

Scalar diffraction problem for N arbitrarily shaped surfaces of revolution: Rigorous approach

This paper describes the application of the analytical regularization method to the solution of scalar diffraction problems. Reflectors composed from several coaxial surfaces of revolution are considered. The surfaces are arbitrarily shaped and may be closed or open. The initial problem is transformed to an infinite linear algebraic system of second kind in l2 space. Numerical solutions to such systems with a guaranteed pre-specified accuracy are readily obtained.

On eigenfrequences of an open resonator: Rigorous approach

This paper describes the application of the analytical regularization method to the solution of the scalar diffraction problem for N coaxial arbitrary shaped bodies (or cavities) of revolution. The developed approach is applied to the accurate analysis of the spectrum of open resonators widely used in the design of microwave sources.

Diffraction of H-polarized Plane Wave by Cylindrical Cavities of Arbitrary Shape

The diffraction problem for an arbitrary shaped cylindrical cavity excited by a H-polarized plane wave is rigorously solved by the Method of Regularization. Along with the previously solved analogous problem for E-polarization this rigorous solution completes the construction of a reliable and highly efficient analytic-numerical technique for the analysis of diffraction problems for metallic cylinders of an arbitrary cross-section. Both problems are reduced to the numerical solution of a well-conditioned infinite system of linear algebraic equations of Fredholm type. Its numerical solution is effected by a truncation method. The computational accuracy only depends on truncation number. The effectiveness of this approach is demonstrated by examples of wave scattering problems for two-dimensional airfoils and engine intakes of various shapes. The combination of well-known approximate techniques with the developed approach has been exploited for studies of wave scattering problems for elongated cylinders of arbitrary cross-section.

Resonance scattering: Spectrum of quasi-eigenmodes of Two-Dimensional arbitrary open cavities

Complex resonances of open 2D arbitrary cavities are comprehensively investigated by the rigorous Method of Regularization. The quasi-eigenvalues for TM-modes are calculated with high accuracy for rectangular and elliptic cavities with longitudinal slot of various widths. In addition, these values are also calculated for one specially shaped duct-like structure. For cavities of rectangular and elliptic shape the effect of a slot location on the bounding contour is examined: the certain slot position dramatically impacts the existence of some TM-modes in the spectrum. Problems related to higher modes competition are also highlighted.

On detection of shadowed targets in axisymmetric configurations

Objects in the shadow zone of a larger body are generally difficult to detect and identify. In some scenarios, however, the number of multiple scatterers can be deduced. We use an accurate solver to examine the wide-band response of some symmetric configurations of bodies lying in the shadow of the illuminated front body. The Q-factor of the configuration as well as that of the individual scatterers is an important factor in determining the number of scatterers.

Analytical Grounds for Modern Theory of Two- Dimensionally Periodic Gratings

Rigorous models of one-dimensionally periodic diffraction gratings made their appearance in the 1970s, when the corresponding theoretical problems had been considered in the con‐ text of classical mathematical disciplines such as mathematical physics, computational mathematics, and the theory of differential and integral equations. Periodic structures are currently the objects of undiminishing attention. They are among the most called-for disper‐ sive elements providing efficient polarization, frequency and spatial signal selection. Fresh insights into the physics of wave processes in diffraction gratings are being implemented in‐ to radically new devices operating in gigahertz, terahertz, and optical ranges, into new ma‐ terials with inclusions ranging in size from microto nanometers, and into novel circuits for in-situ man-made and natural material measurements.