Elongated 3D FDTD modeling using PML

The method of perfectly matched layers (PML) has been proposed by Berenger (1994) for the finite-difference time-domain (FDTD) method. The new method aroused an enthusiastic response in the electromagnetics community. Many papers have been published on the subject, but the PML has never been tested for modeling a large elongated region which is often the case when we are interested in the propagation properties in a preferred direction (such as in the geophysical modeling of a borehole structure). In this situation, a good absorbing boundary condition (ABC) becomes critical, because such a structure involves wave absorption of incident angles from 0 to near 90 degrees. In this paper, we apply the PML method to a large elongated 3D FDTD modeling of a dipole source in both lossless and lossy media. Good agreement has been achieved between the FDTD results and the analytical results for lossless and lossy media. Since most of the existing ABC methods do not work well at large incident angles except for the Lindman ABC (Chen and Liu, 1995) which is for homogeneous media only, the PML offers an excellent ABC tool for the modeling of such an elongated structure. However, a large number of PML layers are needed at the side boundaries in order to get rid of the reflections at large incident angle.