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Abstract 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 Iog2 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.
Qing Liu (1994) studied this question.