Finite-element time-domain modelling of cylindrical structures with a modal non-reflecting boundary condition

This dissertation presents Galerkin weighted residual Finite-Element Time-Domain (FETD) formulations using a 2D cylindrical modal non-reflecting boundary condition (MNRBC) for the modelling of plane wave scattering from cylindrical structures of arbitrary cross-section surrounded by free space. Chapter 1 begins by presenting the motivation for this work. Key concepts regarding cylindrical geometries are introduced at this stage. The Galerkin weighted residual Finite-Element method is briefly outlined. Chapter 2 presents a novel scattered field FETD-MNRBC formulation for the transverse electric polarisation of a modal non-reflecting boundary condition for plane wave scattering from perfectly electrically conductive (PEC) cylindrical structures of arbitrary cross-section. The boundary condition is based on a Vector-Fitting (VF) approximation of the boundary kernel appearing in the time-domain formulation. The convolution integral appearing in the time-domain formulation of the boundary condition is calculated recursively using the Vector-Fitting coefficients. Accurate numerical results are shown for the bistatic scattering width (BSW) that validate the approach. Chapter 3 focuses on the VF approximation of the cylindrical boundary kernel. Two approaches are investigated; the so called Vector-Fitting G function approximation (VFG) and the Vector-Fitting U function approximation (VFU). Both approaches produce satisfactory finite-element results with the VFU being more versatile. Chapter 4 presents, for the first time, the total field FETD-MNRBC formulation for both transverse electric and transverse magnetic polarisations. The VFU approach is employed. The structures considered in this chapter are not only PEC cylinders but also dielectric ones of various cross-sections and various values of relative permittivity and permeability. The numerical results demonstrate the good accuracy of this formulation. Chapter 5 combines the cylindrical modal non-reflecting boundary condition with the Floquet theorem and extends this formulation, for the first time, to azimuthally periodic cylinders using scattered and total field time-domain formulations. The advantages and disadvantages of the periodic modal non-reflecting boundary condition approach are discussed and numerical results for the BSW are shown. Chapter 6 presents a novel sparse-matrix scattered field FETD-MNRBC formulation in which the fully dense submatrices associated with the boundary integral are avoided. Through numerical results the accuracy of the proposed formulation is investigated. Chapter 7 concludes the work by summarizing the main achievements and discussing its impact in electromagnetics