Abstract
In this paper, the Newmark-Beta algorithm is introduced into the finite-difference time-domain (FDTD) method to eliminate the Courant–Friedrich–Levy constraint. A time-marching FDTD formulation involving the calculation of a banded-sparse matrix equation is derived while the spatial and temporal derivatives are discretized by the central difference technique and Newmark-Beta algorithm, respectively. Since the coefficient matrix keeps unchanged during the time-marching process, the lower–upper decomposition needs to be performed only once at the beginning of the calculation. Moreover, the reverse Cuthill–Mckee technique, an effective preconditional processing technique in bandwidth compression of sparse matrices, is used to improve computational efficiency. The 3-D stability proof and numerical dispersion analysis of the proposed method are given. Two 3-D numerical examples are presented to validate the accuracy and efficiency of the proposed method.
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