AbstractsMathematics

The principal objective of this dissertation is to develop, test, and optimize accurate, efficient, and robust computational methodology and tools for modeling of general antennas and scatterers based on solutions of electromagnetic integral equation formulations using the method of moments (MoM) and diakoptics. The approaches and implementations include the volume integral equation (VIE) method and its hybridization with the surface integral equation (SIE) method, in two ways. The first way combines the VIE method for dielectric parts and the SIE method for metallic parts of the structure. The second way performs subdivision of the entire structure into SIE domains of different constant permittivities, while modeling the inhomogeneity within each domain by the VIE method and employing different Green's functions, with describing the inhomogeneity within each domain in terms of a perturbation with respect to the background permittivity. The first approach is very suitable for analysis of composite wire-plate-dielectric radiation/scattering structures. The second approach provides a particularly efficient solution to problems involving inhomogineities embedded within high-contrast homogeneous dielectric scatterers. The efficiency of computation is enhanced by applying the diakoptic domain decomposition. In the VIE-SIE diakoptic method, the interior diakoptic subsystems containing inhomogeneous dielectric materials are analyzed completely independently applying the VIE-SIE MoM solver, and the solution to the original problem is obtained from linear relations between electric and magnetic surface-current diakoptic coefficients on diakoptic surfaces, written in the form of matrices. The techniques implement Lagrange-type generalized curved parametric hexahedral MoM-VIE volume elements and quadrilateral MoM-SIE and diakoptic patches of arbitrary geometrical-mapping orders, and divergence-conforming hierarchical polynomial vector basis functions of arbitrary current expansion orders. The hexahedra can be filled with inhomogeneous dielectric materials with continuous spatial variations of the permittivity described by Lagrange interpolation polynomials of arbitrary material-representation orders. Numerical computation is further accelerated by MPI parallelization to enable analysis of large electromagnetic problems. Advisors/Committee Members: Notaros, Branislav M. (advisor), Reising, Steven (committee member), Oprea, Iuliana (committee member), Chandrasekar, V. (committee member), Pezeshki, Ali (committee member).