Higher-order finite-difference schemes for electromagnetic radiation, scattering, and penetration .1. Theory

Abstract

Higher-order schemes for the finite-difference time-domain (FDTD) method are presented, in particular, a second-order-in-time, fourth-order-in-space method: FDTD(2,4). This method is compared to the original Yee (1966) FDTD scheme. One-dimensional update equations are presented, and the characteristics of the FDTD(2,4) scheme are investigated. Theoretical results for numerical stability and dispersion are presented, with numerical results for the latter, as well. The use of the perfectly matched layer for the FDTD(2,4) scheme is discussed, and numerical results are shown.