ANALYTIC SOLUTIONS FOR THE FINITE-DIFFERENCE TIME-DOMAIN AND TRANSMISSION-LINE-MATRIX METHODS

Eigenmodal decomposition formulations are given for numerical solutions of the finite-difference time-domain (FDTD) and the transmission-line-matrix (TLM) methods. Instead of direct simulation with these time-recursive schemes, the analysis involves two steps: (1) solving an eigenvalue problem, and (2) analytically constructing the numerical solutions in terms of the eigenvalues and eigenvectors. The numerical solution at any time step can be obtained with only O(N) computation once the corresponding eigenvalue problem has been solved. The main advantage of this technique is that the eigenvalues and eigenvectors for a problem can be stored, the numerical solutions then quickly processed with the stored data. In addition, high-frequency numerical noise can be reduced simply by discarding the related high-frequency modes. (C) 1994 John Wiley & Sons, Inc.