Rigorous Approach to Analysis of Two-Dimensional Potential Problems, Wave Propagation and Scattering for Multi-conductor Systems

Abstract

The research described in this chapter analyses two-dimensional potential problems for the multi-body systems, transverse electromagnetic wave propagation along multi-conductor transmission lines and two-dimensional plane wave scattering by various arrays. All conductors may be of arbitrary cross-sections the only restriction on the system geometry is a smooth parameterization. These problems are mathematically modelled by Dirichlet boundary value problems for either the Laplace or the Helmholtz equation, with the classical integral representation of the solutions in the form of single-layer potential. The analytical-numerical algorithm presented here is based on the method of analytical regularization. The key idea behind this technique is an analytical transformation of the initial ill-posed integral equations to a well-conditioned Fredholm second kind matrix equation. The resulting system of infinite linear algebraic equations is effectively solved using the truncation method the solution of the truncated system converges to the solution of the infinite system with the guaranteed accuracy that only depends on the truncation number and thus may be pre-specified. The solution obtained is applied to the accurate analysis of -D electrostatic-and electrodynamic-field problems for multi-conductor systems with arbitrary profiled conductors. Examples of some conceptual shielded transmission lines incorporating various configurations of conductors and scattering problems for the arrays of thick strips establish the utility of our method and its reliability in various situations

Scattering of an obliquely incident E − polarised plane wave from ensembles of slotted cylindrical cavities: A rigorous approach

“…The rigorous Method of Analytical Regularisation (MAR) has previously been successfully applied to the analysis of two‐dimensional (2‐D) potential problems of multi‐conductor systems and of multiple wave scattering by ensembles of arbitrary closed cylinders (see [1, 2]). Here, we extend this approach to analyse the polarised plane wave scattering from an ensemble of slotted perfectly electrically conducting (PEC) cavities.…”

Asymptotic regularisation of the solution to the problem of electromagnetic field scattering from a set of small impedance particles

“…A specific kind of regularisation is applied when the geometry and physical properties of objects under investigation must be taken into account. For this goal, Martin and Ola used the combination of pairs of coupled integral equations in [28] and Safonova and Vinogradova adopted an analytical conversion of the initial ill‐posed integral equations into Fredholm’s well‐conditioned matrix equation of the second kind in [29]. Lucido with co‐authors used analytical regularisation, based on a combination of the Helmholtz decomposition and the Galerkin method, for the analysis of the EM wave scattering by a finite‐length PEC round, hollow cylinder in [30] and performed analytical preconditioning of the surface integral equation converted into the spectral domain with the subsequent discretisation using the Galerkin method with the analytically Fourier‐transformable expansion bases in [31].…”