Rigorous approach to analysis of two-dimensional potential problems, wave propagation and scattering for multi-conductor systems

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 2-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
Keywords: Scattering, propagation, analytical regularization, Laplace equation, Helmholtz equation