Model-order reduction techniques for the numerical solution of electromagnetic wave scattering problems

Abstract

It is the aim of this work to contribute to the development of model-order reduction (MOR) techniques for the field of computational electromagnetics in relation to the electric field integral equation (EFIE) formulation. The ultimate goal is to enable a fast-sweep analysis. In a fast-sweep problem, some parameter on which the original problem depends is varying and the problem must be solved as the parameter changes over a desired parameter range. The complexity of the original model prohibits its direct use in simulation to compute the results at every required point. However, one can use MOR techniques to generate reduced-order models (ROMs), which can be rapidly solved to characterise the parameter-dependent behaviour of the system over the entire parameter range. This thesis focus is to implement robust, fast and accurate MOR techniques with strict error controls, for application with varying parameters, using the EFIE formulations. While these formulations result in matrices that are significantly smaller relative to differential equation-based formulations, the matrices resulting from discretising integral equations are very dense. Consequently, EFIEs pose a difficult proposition in the generation of low-order accurate reduced order models. The MOR techniques presented in this thesis are based on the theory of Krylov projections. They are widely accepted as being the most flexible and computationally efficient approaches in the generation of ROMs. There are three main contributions attributed to this work. ² The formulation of an approximate extension of the Arnoldi algorithm to produce a ROM for an inhomogeneous contrast-sweep and source-sweep analysis. ² Investigation of the application of the Well-Conditioned Asymptotic Waveform Evaluation (WCAWE) technique to problems in which the system matrix has a nonlinear parameter dependence for EFIE formulations. ² The development of a fast full-wave frequency sweep analysis using the WCAWE technique for materials with frequency-dependent dielectric properties