An Isotropic Algorithm for Solving Maxwell's Equations in 2D

Abstract

A popular time evolution algorithm for solving Maxwell's equations for electromagnetic problems is the Yee's finite difference time domain (FDTD) algorithm. This algorithm introduces a non physical algorithmic anisotropic dispersion error and limited stability range. A new improved algorithm with isotropic dispersion error, better stability and faster execution is introduced in this paper. In this study, we compared the results of our improved isotropic algorithm, for simple and well-known problems, to that of the exact solution and that of the Yee algorithm. These comparisons show more accurate results for our improved isotropic algorithm compared to that for the Yee Algorithm. For practical application problems where solutions are too complicated to be solved analytically, we compared our algorithm to that of Yee and found that our algorithm simulate such problems faster and with smaller error.

Evolution of Transient Electromagnetic Fields in Radially Inhomogeneous Nonstationary Medium

“…The sampling step is chosen reasoning from the quickest change of medium characteristics on r and time dependence of exciting current to avoid numerical instability [31,32].…”