Derivation of equivalent boundary conditions using the homogenization method and their implementation in time-domain electromagnetics techniques

Equivalent Boundary Conditions are important in disciplines where boundary conditions are involved like, acoustics, hydrodynamics and electromagnetics. In electromagnetics they are used in scattering, propagation, and waveguide analysis to simulate material and geometric properties of surface involved. These boundary conditions provide an approximate relation of the Electric and Magnetic fields in the complex medium under consideration by replacing the entire medium with just a layer of newly derived electric and magnetic field. In other words, Approximate Boundary Condition converts a two (or more) media problem into a single medium problem.; In my thesis the method of homogenization is applied to the derivation of the equivalent boundary condition for a thin layer of dielectric and/or magnetic material. Homogenization is an asymptotic method for the analysis of physical phenomena possessing variations on widely differing scales. The details of the method is presented in the thesis. Different boundary conditions for various geometries are derived.; The objective of the derivation of these boundary conditions is to reduce the computational expense while retaining sufficient solution accuracy. The boundary conditions will be implemented in S22-FDTD technique. Numerical results are compared with those from the numerical model without the boundary condition.; The run time of a finite-difference time-domain (FDTD) simulation is proportional to the required simulated time, and the chosen time step, Δ t run time∝simulatedtimeD t 1 ; A major limitation of existing FDTD schemes is the conditionally stable nature of the technique, which sets an upper bound on Δt. The bound on Δt leads to undesirable and often unattainable run times. This thesis investigates the alternating direction implicit method for FDTD (ADI-FDTD) schemes. ADI-FDTD is unconditionally stable, allowing Δ t to be increased and the resulting run time decreased. For highly resolved FDTD models, ADI-FDTD's ability to allow larger time steps increases modeling capabilities. There is a memory overhead associated with using ADI-FDTD, however the decrease in run time makes it a desired technique for many industrial applications.; A comprehensive comparative study is conducted for ADI-FDTD vs. Yee's traditional FDTD scheme. Classes of appropriate ADI-FDTD type problems are then identified. Then, dispersive material properties are developed and implemented into ADI-FDTD. Finally, the boundary conditions are implemented in to ADI-FDTD. (Abstract shortened by UMI.)...