The idea of using a material-based absorbing boundary condition has existed for some time [8]. However, early material ABC's did not provide a sufficiently low level of boundary reflection, since the characteristic impedance of the material boundary was matched to the characteristic impedance of free space only at normal incidence. In the early 1990's, Rappaport et al. [19,20] proposed a new ABC termed the sawtooth anechoic chamber ABC. This ABC employs pyramidally-shaped absorber material similar to that which is often found in anechoic chambers. The most recent advance in material-based ABC's was put forward by Berenger [21]. His ABC, termed the perfectly matched layer (PML) absorbing boundary condition, appears to yield a major improvement in the reduction of boundary reflections compared to any ABC proposed previously. Although the ABC is new it has enjoyed enormous attention already [22,23,24,25,26,27,28].