A New Analytically Regularizing Method for the Analysis of the Scattering by a Hollow Finite-Length Pec Circular Cylinder

Abstract

Abstract-In this paper, a new analytically regularizing method, based on Helmholtz decomposition and Galerkin method, for the analysis of the electromagnetic scattering by a hollow finite-length perfectly electrically conducting (PEC) circular cylinder is presented. After expanding the involved functions in cylindrical harmonics, the problem is formulated as an electric field integral equation (EFIE) in a suitable vector transform (VT) domain such that the VT of the surface curl-free and divergence-free contributions of the surface current density, adopted as new unknowns, are scalar functions. A fast convergent secondkind Fredholm infinite matrix-operator equation is obtained by means of Galerkin method with suitable expansion functions reconstructing the expected physical behaviour of the unknowns. Moreover, the elements of the scattering matrix are efficiently evaluated by means of analytical asymptotic acceleration technique.

Efficient Evaluation of Slowly Converging Integrals Arising from MAP Application to a Spectral-Domain Integral Equation

“…it was simple to conclude that functions in Formula (17) were bounded around z = 0 and decayed asymptotically as 1/z 2 for l = 1 and 0 ≤ arg(z) < π, and for l = 2 and −π < arg(z) ≤ 0. Therefore, Jordan lemma [45] allowed us to rewrite Formula (18) for l = 1 and l = 2, respectively, as follows:…”

“…We achieved this by analytically inverting the most singular part of the integral operator and obtaining a Fredholm second-kind integral equation that could be solved via any direct discretization that keeps Fredholm's nature [12,13]. On the other hand, an analytically regularized matrix equation can be obtained in a single step through the suitable choice of a discretization scheme [14][15][16][17]. This is what happened when we used a complete set of orthogonal eigenfunctions of a suitable operator containing the most singular part of the original integral operator as the expansion basis of a Galerkin scheme.…”

“…In the literature devoted to applications of the method of analytical preconditioning (MAP) to integral equation formulations, it has been widely shown that the choice of expansion functions reconstructing the physical behavior of unknowns guarantees fast convergence, i.e., fewer expansion functions are needed to achieve highly accurate results provided that a suitable accurate evaluation of matrix coefficients has been made [14][15][16][17][18][19][20][21][22][23][24]. Moreover, spectral-domain formulations were preferred in the quoted papers, as convolution integrals resulting from the Galerkin projection technique could be reduced to algebraic products by selecting expansion functions with closed-form spectral-domain counterparts.…”

Scattering of the plane acoustic wave from a finite hollow rigid cone at oblique incidence

“…In the known scientific literature, a lot of attention has been focused on the study of the diffraction characteristics of both acoustic and electromagnetic fields scattered by discs, hollow cylinders and structures created by combinations of these structures, such as cylindrical cavities and rods . The Wiener‐Hopf method or the analytic regularization technique are usually used to obtain the mathematically rigorous solutions of these problems.…”

Gaussian Beam Electromagnetic Scattering From Pec Polygonal Cross-Section Cylinders

“…The proposed method is efficient even in terms of computation time since the elements of the coefficient matrix, which are improper integrals of oscillating functions with a slow asymptotic decay in the worst case, are efficiently evaluated by means of an analytical asymptotic acceleration technique. This approach has been successfully applied in propagation, radiation and scattering problems involving PEC/dielectric 2D/3D structures in homogeneous and layered media [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”