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Transient electromagnetic modeling with the generalized K ‐space (GkS) method
Author(s) -
Liu QingHuo
Publication year - 1994
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.4650071809
Subject(s) - discretization , domain (mathematical analysis) , transient (computer programming) , mathematical analysis , fast fourier transform , mathematics , fourier transform , algebraic equation , finite element method , frequency domain , space (punctuation) , integral equation , algorithm , computer science , physics , quantum mechanics , nonlinear system , thermodynamics , operating system
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.