Absorbing Boundary Conditions on Circular and Elliptical Boundaries

Abstract

Finite difference methods are becoming increasingly popular in the computational electromagnetics community. A major issue in applying these methods to electromagnetic wave scattering is to limit the computational domain to a finite size, which is accomplished by selecting an outer boundary and imposing absorbing boundary conditions to simulate free space. In this paper, the pseudo-differential operator approach is employed to derive absorbing boundary conditions for both circular and elliptical outer boundaries. The pseudo-differential operator approach employed by Engquist and Majda is modified to derive improved absorbing boundary conditions. In the case of the circular outer boundary, the modified pseudo-differential operator approach leads to a condition equivalent to that of Bayliss and Turkel's second-order condition. The modified pseudo-differential operator is then used to derive the second-order absorbing boundary condition for the elliptical outer boundary. The effectiveness of the second-order absorbing boundary condition on the elliptical outer boundary is illustrated by calculating scattered fields from various objects. It is shown that for elongated scatterers, the elliptical outer boundary can be used to reduce the size of the computational domain.