Application of the wavelets in 2D and 3D scattering or radiation problems

Abstract

Ahstract: -Wavelets technique is applied for solving of 2D and 3D Dirichlet, Neumann and mix boundary problems. The developed method utilizes Haar or linear Battle-Lemarie wavelets functions and Fredholni integral equations (-or a system of the Fredholm integral equations) of fist kind with smooth or singular kernels and developed new method of "prolonged" boundary conditions. The results of the wavelet technique's using are illustrated by calculations of the scattering pattern by dielectric (-or perfect conducting) cylinder with complicated cross sections, ellipsoid of revolution, perfect conducting screens, single and dual-reflector antennas (both kD E 1 and kD >> 1 regions). The problems of accuracy, choosing auxiliary surfaces are discussed.

Calculation of the near field for concave and convex-concave screens with a variable curvature in the presence of whispering-gallery modes

“…We use the following parameters of scattering contour (12) and of the position of cylindrical wave source Q: kR 0 = 78, ϕ 0 =-π/2, ka = 80, ϕ b = -π/256, and ϕ e = π/2; the total number of basis functions is N = 256; and the dis placement of the auxiliary contour is δ = 0.001 here and below. Figure 2a shows the calculated spatial distribution of the absolute value of field amplitude in the neighborhood of the concave segment of cylindrical contour (12). It is seen from the figure that the field structure inside such a contour is characterized by the presence of two regions.…”

“…This method is referred to as the method of extended boundary conditions. Its high efficiency has been demonstrated for a series of prob lems [10][11][12][13][14][15]. Recall that the method of extended boundary conditions is based on two ideas.…”

“…Studies [12][13][14][15] are an exclusion, but, in these studies, only the field in the far zone of such screens (scattering pat tern) is investigated. Therefore, solution of such prob lems in a rigorous formulation and analysis of the near scattered field obtained on the basis of these solutions are of practical and theoretical interests.…”

MMDS and 2D scattering problem by cylindrical structure with piece-wise smooth boundary

“…If r i (ϕ) is arbitrary analytical function then value ϕ qi could be found by numerically [9,10]. We would like to remind that total auxiliary contour Σ have to enclose all principal singularities and only in this case we will have a unique solution of scattering problem [2][3][4].…”

“…The influence of the imaginary source's location and singular points (11) on accuracy was investigated in [7][8][9][10]. In this paper we explored the influence of the type of breakpoints for total original contour's function ρ(ϕ) on accuracy problem.…”