A new reflection-free truncation in finite methods: transparent absorbing technique (TAT)

The PML boundary condition proposed by Berenger [1994] involves two parts: splitting the field components and enforcing the matching condition /spl sigma//(/spl epsi/0)=/spl sigma/*//spl mu//sub 0/. Such a technique results in 40 dB improvement in truncation errors over the second Mur radiation boundary condition. The trade-off is that twelve, instead of six, field components have to be stored in a three dimensional problem. An alternative PML approach was proposed which uses anisotropic permittivity and permeability so that no additional storage is needed [Sacks, 1995]. However, it only works in the regions where the fields attenuate only in one direction. A splitting formulation is still needed in other regions, such as corners where attenuation is required in all three directions. In addition to the storage trade-off, the PML boundary condition has a few more problems. These shortcomings not only make the PML computationally inefficient, especially storage-wise, but also limit its applications. In this paper, we propose a new technique that can 1) absorb the fields without requiring an additional computational domain, 2) yield a non-splitting formulation, and 3) result in a homogeneous boundary condition at the outer boundaries of the computation domain. We also discuss numerical schemes to solve redefined problems, and show some results.