Daniel S. Katz*1, Christopher E. Reuter2, Eric T. Thiele3, Rose M. Joseph4, Allen Taflove4
1Cray Research, Inc., 222 N. Sepulveda Blvd., Ste. 1406,
El Segundo, CA 90245
2Rome Laboratory/ERST, 525 Brooks Road, Griffis AFB, NY 13441-4505
3University of Colorado, ECE Department, Boulder, CO 80309
4Northwestern University, EECS Department, Evanston, IL 60208
In 1994 Berenger published a novel absorbing boundary condition (ABC) for FDTD meshes in two dimensions with substantially improved performance relative to any earlier technique (J. P. Berenger, Jour. Comp. Phys. 114, 185-200, 1994). This method is based on a decomposition of fields in the boundary region into split fields, in order to assign differing losses to individual directional components of the finite difference used to update these fields. Following this paper many extensions have been studied, including three dimensional applications (D. S. Katz, et al., IEEE MGWL 4, 268-270, 1994, J. P. Berenger, Annales des Telecom., 1994), the use of the ABC for waveguide termination (C. E. Reuter, et al., IEEE MGWL 4, 344-346, 1994), etc. Many groups are now trying to apply the concepts of the Perfectly Matched Layer (PML) ABC to finite element techniques. The majority of the work to date has been on extending this ABC or examining the parameters of the ABC in order to further reduce the reflection beyond the -40 to -70 dB of the first papers.
The primary focus of this paper will be on results that have been obtained by use of the PML ABC, with comparison to results obtained from similar problems using the Mur RBC. We will show how the PML ABC enables both more accurate solutions of some problems that have been attempted using other ABCs and solution of problems that were not possible without the PML ABC. Examples will include radar cross section calculations for the NASA Almond and microstrip analysis. Additionally, we will briefly highlight some recent attempts at extension of the PML ABC to problems such as waveguiding structures. We will also include a discussion of the relationship between the conductivity profile in the PML, the thickness of the PML, and the amount of reflection.