In the previous chapters the PML ABC has been derived in Cartesian coordinates for solving the Maxwell equations, and the only numerical method that has been considered in detail is the Yee FDTD method. In the following, some extensions of the PML concept to other coordinates and other numerical techniques are briefly reviewed.
The finite-difference time-domain method (FDTD) [40] is probably the most used numerical technique in electromagnetics. The basic FDTD scheme introduced by K. S. Yee in 1966 [2] is simple and versatile. It has been extended to most existing physical media, such as anisotropic, dispersive, chiral, and even nonlinear media. The original Yee scheme is a second-order approximation of the Maxwell equations, both in time and space.
This lecture presents the perfectly matched layer (PML) absorbing boundary condition (ABC) used to simulate free space when solving the Maxwell equations with such finite methods as the finite differe
In this chapter, the perfectly matched layer absorbing boundary condition is introduced in the two-dimensional (2D) case. The 2D case is simple and important because the absorption of plane waves by a PML or any other ABC is essentially a 2D problem. With a 3D computational domain, the interaction of a plane wave with a PML is a true 3D problem in the edge and corner regions, but it remains a 2D problem in the walls that form most of the outer boundary of the domain.
