Asymptotic and Absorbing Boundary Conditions for Finite Element Analysis of Digital Circuit and Scattering Problems

Abstract

Abstract : The finite element method (FEM) is very appealing for solving open region 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 report 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.