Asymptotic and absorbing boundary conditions for finite element analysis of digital circuit and scattering problems

The finite element method (FEM) is very appealing for solving open regional digital circuit and scattering problems due to its simplicity in modeling complex-shaped structures and inhomogeneous dielectric scatterers. However, it must deal with the practical problems of mesh truncation and the introduction of an artificial outer boundary in order to limit the number of node points to a manageable size. Therefore, the major difficulty encountered when using FEM is how to find a boundary condition operator which when applied on the artificial outer boundary mimics the asymptotic behavior of the field at infinity and yields reasonably accurate results in the interior region without the need of an exorbitantly large number of mesh points.This thesis is an effort to provide some techniques to deal with the FEM mesh truncation, in an efficient manner, through the introduction of three new boundary condition concepts, viz., the boundary conditions for arbitrary outer boundaries, the asymptotic boundary condition for digital circuit applications, and the higher-order asymptotic and absorbing boundary conditions. The use of generalized boundary conditions or the boundary conditions for arbitrary outer boundaries enables one to reduce the number of node points significantly and to solve larger sized problems than had been possible in the past. The asymptotic boundary condition for digital circuit applications does not suffer from the complications associated with the infinite elements, and yet enables one to bring the outer boundary much closer to the structure than would be possible with a p.e.c. artificial outer boundary. The higher-order asymptotic and absorbing boundary conditions, unlike the available ABCs, e.g., the Bayliss, Gunzburger, and Turkel (BGT), which assume that in the far region the solution can adequately be represented by the first few terms of the series, require that the asymptotic representation be a combination of the lower- and higher-order terms. The higher-order boundary conditions help reduce the error in the finite element solution caused by the neglecting of the higher-order terms in other available ABC assumptions.Various investigations of scattering as well as two- and three-dimensional digital circuit problems are presented. Numerical examples are shown for a variety of scatterers and transmission line configurations. Results show that the boundary condition concepts introduced in this work yield good agreement with work published elsewhere and significant improvements in computation time and storage compared to other available methods.U of I OnlyETDs are only available to UIUC Users without author permissio