Recursively Convolutional CFS-PML in Three-dimensional Laguerre-FDTD Scheme for Arbitrary Media
This publication appears in: IEEE Transactions on Microwave Theory and Techniques
Authors: G. He, J. Stiens, W. Shao and B. Wang
Publication Date: Feb. 2018
Weighted Laguerre finite-difference time-domain (Laguerre-FDTD) method is an efficient and unconditionally stable time-domain numerical method. The complex frequency shifted perfectly matched layer (CFS-PML) is the main absorbing boundary condition (ABC) in the Laguerre-FDTD method. The implementations of CFS-PML in the Laguerre-FDTD method, which have been reported, include the use of auxiliary variables and auxiliary differential equations (ADEs). These implementations make CFS-PML sensitive to its parameters and time scale parameter s of weighted Laguerre polynomials and result in potential instability and poor absorption issues in numerical simulations. In this paper, we proposed an efficient and stable implementation of CFS-PML based on recursive convolution in the Laguerre-FDTD method. The accuracy of the proposed implementation is theoretically validated. Its numerical dispersion is theoretically derived for choosing the key parameters of CFS-PML in the Laguerre-FDTD scheme. The numerical dispersion demonstrates that the time scale factor s needs to match the simulated signal frequency and the CFS-PML parameter a is chosen as 0.5se0 to obtain the minimum dispersive error. Numerical examples validate the theoretical predictions and verify that the proposed implementation of CFS-PML is robust and retains the advantages of CFS-PML in classical FDTD method, such as effectively absorbing evanescent as well as guided waves. It requires non-splits of electromagnetic field components, no auxiliary variables, and no modifications when applying it to inhomogeneous, lossy, and dispersive media. The CFS-PML formulas can be directly converted into computer codes of the Laguerre-FDTD method.