Comments on “Efficient Implementations of SC-PML for Arbitrary Media Using DSP Techniques”

In the above letter, the matched
z
-transform (MZT) and bilinear
z
-transform implementations of the stretched coordinate perfectly matched layer (PML) are presented. In this article, numerical experiments demonstrate numerical instability of the MZT method. Efficient exponential time differencing implementation of the stretched coordinate PML is proposed. It is found that the MZT method is a low-order approximation of the exponential time differencing formulation. The calculations indicate that neglecting higher order terms leads to the numerical instability. In addition, Von Neumann stability analysis shows that the MZT method is unstable. The MZT method is invalid.