The last several decades have experienced an extraordinarily focused effort on developing general-purpose numerical methods in computational electromagnetics (CEM) that can accurately model a wide variety of electromagnetic systems. In turn, this has led to a number of techniques, such as the Method of Moments (MoM), the Finite Element Method (FEM), and the Finite-Difference-Time-Domain (FDTD), each of which exhibits their own advantages and disadvantages. In particular, the FDTD has become a widely used tool for modeling electromagnetic systems, and since it solves Maxwell's equations directly---without having to derive Green's Functions or to solve a matrix equation or---it experiences little or no difficulties when handling complex inhomogeneous media. Furthermore, the FDTD has the additional advantage that it can be easily parallelized; and, hence, it can model large systems using supercomputing clusters. However, the FDTD method is not without its disadvantages when used on platforms with limited computational resources. For many problems, the domain size can be extremely large in terms of the operating wavelengths, whereas many of the objects have fine features (e.g., Body Area Networks). Since FDTD requires a meshing of the entire computational domain, presence of these fine features can significantly increase the computational burden; in fact, in many cases, it can render the problem either too time-consuming or altogether impractical to solve. This has served as the primary motivation in this thesis for developing multi-scale techniques that can circumvent many of the problems associated with CEM, and in particular with time domain methods, such as the FDTD.;Numerous multi-scale problems that frequently arise in CEM have been investigated in this work. These include: (1) The coupling problem between two conformal antennas systems on complex platforms; (2) Rigorous modeling of Body Area Networks (BANs), and some approximate human phantom models for path loss characterization; (3) Efficient modeling of fine features in the FDTD method and the introduction of the dipole moment method for finite methods; and, (4) Time domain scattering by thin wire structures using a novel Time-Domain-Electric-Field-Integral-Equation (TD-EFIE) formulation. Furthermore, it is illustrated, via several examples, that each problem requires a unique approach. Finally, the results obtained by each technique have been compared with other existing numerical methods for the purpose of validation.
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