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IEEE Transactions on Antennas and Propagation
Volume 47 Number 4, April 1999

Table of Contents for this issue

Complete paper in PDF format

Stability of Absorbing Boundary Conditions

Omar M. Ramahi, Member, IEEE

Page 593.

Abstract:

Higher order absorbing boundary conditions (ABC's) exhibit instabilities that can be detrimental to a wide class of finite-difference time-domain (FDTD) open-region simulations. Earlier works attributed the cause of instabilities to the intrinsic construction or makeup of the ABC's, and consequently to the pole-zero distribution of the transfer function that characterizes the boundary condition. In this work, we investigate the cause of instability. We focus on axial boundary conditions such as Higdon, Bayliss-Turkel, and Liao, and show through an empirical study that these ABC's are not intrinsically unstable in their original unmodified forms. Furthermore, we show that the instability typically observed in FDTD open-region simulations is caused by an artifact of the rectangular computational domain, contrary to previously conjectured hypotheses or theories. These findings will have strong implications that can aid in the construction of stable FDTD schemes.

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