Transient electromagnetic modeling with the generalized K ‐space (GkS) method

A centralized k‐space (GkS) method is developed for transient electromagnetic modeling. This method consists of the solution of two equations: (1) the scattering equation in the spectral‐time < k − t) domain, and (2) the constitutive equation in the spatial‐time (r − t) domain. Both are derived as local algebraic equations, and therefore can be solved with O(N) operations. The connection between the r − t domain and k − t domain is obtained by the spatial FFT algorithm. Therefore, in each time step, the number of complex multiply‐add operations is O(N Iog 2 N), and the storage requirement is O(N). Because it treats the spatial derivatives by Fourier transform, the k‐space method, compared to the finite‐difference method, provides a high‐order accuracy for the same discretization. It is shown that with the same accuracy requirement, the GkS method requires much fewer unknowns than the conventional finite‐difference method. © 1994 John Wiley & Sons, Inc.