Computational electromagnetic approaches for the analysis of rough surface scattering and artificial composite materials

With the rapid development of high performance computers, numerical techniques play a more important role in many electromagnetic problems. My research is focused on developing computational algorithms for problems for which analytical analysis is limited or unavailable. In this dissertation, two problems are considered in the light of computational electromagnetic (CEM) approaches.; The first problem is the analysis of wave scattering by rough surfaces with and without objects. Significant amounts of research have been devoted to investigating of this problem due to its practical applications in diverse areas. The efficient and rigorous implementation of the finite-difference time-domain (FDTD) method for the rough surface scattering problem is discussed. Several examples of practical rough surface problems are explored using the FDTD method such as, (i) Zenneck wave propagation over a finitely conducting one-dimensional rough surface, (ii) scattering by randomly distributed wedges, and (iii) scattering by an object in the presence of a rough interface.; The second problem is the characterization of artificial composite materials. The development of artificial materials which have new material properties that are not found in natural materials is a topic of continuing interest. I present two different techniques for the characterization of composite materials which consist of a host medium and electrically small inclusions. The first method utilizes whole structure simulations using the FDTD method, and is applied for the analysis of conductor-loaded dielectric materials which are developed to obtain high permittivity and low-loss dielectric materials. More general complex bi-anisotropic materials are examined with the second method which employs an analytical formula that is based on the quasi-static Lorentz theory and requires numerical simulations of a single inclusion rather than a whole structure. A chiral medium composed of an array of helices and a metamaterial consisting of an array of split-ring resonators (SRRs) are analyzed to illustrate the usefulness of the proposed method.