Critical analysis of Yee and matched layers absorbing boundary conditions for 2-D and 3-D applications of the FDTD method

Since Yee defined the basic cell for the finite difference time domain (FDTD) technique in 1966, applications of FDTD have been adopted widely, which provide not only insights of the wave behavior in time domain but also wide band frequency domain information using Fourier transforms. The FDTD technique is based on the finite difference approximations of Maxwell´s differential equations in both spatial field arrangements and time difference. Since the storage space available for computed fields in computers is finite, there is a need to truncate the problem space using absorbing boundary conditions (ABCs) that simulate continuous wave propagation on the truncation interfaces. Many ABCs have been introduced in the last few years; however, there is no reflectionless absorbing boundary. Two and three dimensional numerical absorbers, matched layers (ML) similar to those presented by Holland and Williams (1983) and by Reineix and Jecko (1989), and Yee´s tapered damping function ABC are presented and critically evaluated.