A Memory-Efficient Formulation of the Unconditionally Stable FDTD Method for Solving Maxwell´s Equations

An unconditionally stable finite-difference time-domain (FDTD) method based on the weighted Laguerre polynomials (WLP) for solving Maxwell´s equations had been proposed. In this paper, a memory efficient modification to the proposed methodology is described. In this novel modification, the divergence theorem is introduced in the WLP-FDTD method, in which Maxwell´s divergence equation replaces one of the curl equations. This leads to a more memory-efficient matrix equation and a more rapid computational speed. A numerical example considering a two dimensional (2-D) TE case is present to validate the efficiency of the proposed algorithm.