Christopher E. Reuter*1, Rose M. Joseph2, Daniel S. Katz3, Eric T. Thiele4, Allen Taflove2
1Rome Laboratory/ERST, 525 Brooks Road, Griffis AFB, NY 13441-4505
2Northwestern University, EECS Department, Evanston, IL 60208
3Cray Research, Inc., 222 N. Sepulveda Blvd., Ste. 1406,
El Segundo, CA 90245
4University of Colorado, ECE Department, Boulder, CO 80309
Berenger (J. P. Berenger, Jour. Comp. Phys., pp. 185-200, 1994) recently introduced a novel absorbing boundary condition (ABC) for the FD-TD electromagnetic simulation technique. This ABC called the perfectly matched layer (PML) has shown dramatic improvement over the traditional analytic ABCs similar to that presented by Mur (G. Mur, IEEE EMC, pp. 377-382, 1981). In fact, we have shown a reduction in the local error caused by the PML of more that 40 dB as compared to standard second-order MUR ABCs (D. S. Katz, et al., IEEE MGWL, pp. 268-270, 1994).
It is desirable to obtain the minimum reflection possible from the PML. Three parameters control the magnitude of the numerical reflection at grid-PML interfaces; 1) the PML thickness, 2) the theoretical reflection at normal incidence, R(0), as defined by Berenger, and 3) the spatial profile of the conductivity within the PML. Berenger reported limited results for conductivity profiles having constant, linear, and parabolic distributions. Furthermore, since computer resources are limited, the above three parameters must be optimized to meet the required model fidelity and to enable solution of the problem within limits of the available computer system. A thicker PML generally reduces reflections but requires larger memory and longer cpu run time. Modification of the remaining two parameters has insignificant effect on the required memory and run time. However, the relationship between these two parameters and the magnitude of the reflection is not obvious and warrants investigation.
We have performed numerical experiments to determine the optimal values for these parameters while limiting computational requirements. This paper will discuss the results of these experiments for both 2-D and 3-D FD-TD simulations. All computations were performed on either a Cray Research Y-MP or C-90.