A finite difference delay estimation approach to the discretization of the time domain integral equations of electromagnetics

In this paper, we introduce a method of temporal discretization based on finite differences, or, more generally, a mapping from the Laplace (s) domain to the z- transform domain. The idea is very old, and goes by the name "convolution quadrature" in the math literature [3], and "filter design by approximation of derivatives," or "the bilinear transformation" in the signal processing literature [4]. Assuming the spatial discretization does not give rise to unstable eigenvalues, this new finite difference delay estimation (FDDE) method has completely predictable stability and accuracy properties. First- and second-order unconditionally stable methods can be derived, and since no basis functions are involved, no shadow region arises. While FDDE has important efficiency disadvantages relative to MOT, these can be mitigated by fast methods.