A comparative study of the Berenger perfectly matched layer, the superabsorption technique and several higher-order ABC's for the FDTD algorithm in two and three dimensional problems

A new comparison of higher-order Engquist & Majda (1977), Higdon (1986), and Liao (1992) absorbing boundary conditions (ABCs) and the superabsorption method with the Berenger (see J. Comput. Physics, vol.114, p.185-200, 1994) perfectly matched layer (PML), is conducted. Reflection errors are calculated both globally and locally in 2-D and especially in new 3-D FDTD simulations in the presence or absence of a perfectly conducting scatterer. Numerical results indicate that the PML is by far superior to all other ABCs, especially when their layers, are implemented. It is also shown that the 5th-order Liao ABC incorporated in the superabsorption technique, yields a scheme which is almost equivalent to the 4-layer PML when referring to the induced local error. Absorption performance of the new boundary conditions obtained from the combination of the PML with the 2nd and 3rd-order Liao ABCs is, finally, evaluated.