Improved Absorbing Boundary Conditions for Time-Domain Methods in Elecromagnetics

Abstract

<p>This thesis contributes to the development of novel absorbing boundary conditions (ABCs) for two finite-difference time-domain (FDTD) methods in computational electromagnetics; the well-known FDTD method to the solution of Maxwell's equations and the wave equation in the time-domain (WTD) method. The conventional approach to create a perfectly matched layer (PML) ABC for the FDTD solution to Maxell's equations is reviewed, as well several other state-of-the-art techniques to define a PML medium. The novel WETD technique is described for applications in numerical algorithms both for optical waveguides and structures, and in the microwave and millimetre-wave structure analysis. The new algorithm requires a reliabe efficient ABC, which can handle both open problems (i.e., radiation and scattering) and problems involving port terminations (such as high-frequency circuit problems and optical guiding structures). A new degree of freedom is introduced in the definition of the PML variable profiles and thus improved algorithms for PML ABCs are formulated and developed both for the WETD method and for the FDTD solution to Maxwell's equations. The proposed modified PML profiles handle equally well both port terminations in guide-wave problems and truncations of the computational domain of open problems. The performance of the proposed PML absorber is further improved by new types of PML termination walls using single-layer ABCs. For that, a lossy version of Mur's second order ABC and a lossy version of the second order dispersive boundary condition (DBC) have been developed on orthogonal non-uniform grids. It handles inhomogeneous dielectrics intersecting the PML boundaries. Various numerical simulations have been carried out to validate the theoretical models at microwave and optical frequencies, as well as in depth detailed comparison with commonly used PML ABCs is presented. Suggestions for further research are provided.</p>