Explicit finite-difference time-domain method with perfectly matched layers for transient low-frequency eddy-current analysis

The finite-difference time-domain (FDTD) method is a robust algorithm for the solution of high-frequency electromagnetic problems, but, unfortunately, the method has no counterpart in eddy-current analysis. Hence, the extension of FDTD to power frequencies is an attractive theoretical problem that could give rise to an entirely new methodology for low-frequency electromagnetics. In this paper, we introduce a general explicit FDTD algorithm for transient eddy-current problems. We perform a theoretical investigation of a nonstandard difference scheme, including the issues of stability and consistency. The study provides a class of explicit methods with varying properties and computational complexity. From these, we chose the DuFort-Frankel algorithm for its simplicity and efficiency. However, the most intricate issue for the application of an explicit scheme is the solution of the open boundary problem. Unlike conventional integral equation or forced truncation approaches, the free-space problem is successfully treated by using a specially designed perfectly matched layer (PML) for eddy currents. The explicit scheme within the conductors is, finally, efficiently combined with the free space-PML equations via the interface conditions.