Optimized (2, 4) Stencil Runge–Kutta ADE-ADI FDTD With Application to Plasma

Abstract

This paper discusses the improvement of the numerical dispersion characteristics of alternating direction implicit (ADI) finite-difference time-domain (FDTD) aimed at acquiring more accurate electromagnetic information of plasma. Through adding the optimization method, which is based on the optimization of spatial derivative to the (2, 4) stencil ADI FDTD, the optimized (2, 4) stencil ADI FDTD is proposed, and its unconditional stability is proved theoretically. The phase velocity error of the optimized (2, 4) stencil ADI FDTD versus propagation angle and grid density is investigated. In addition, the Runge–Kutta auxiliary differential equation (RKADE) scheme for tackling the constitutive relation equation of plasma is deduced, which is without additional storage occupation and computational burden compared with ADE scheme. Its numerical conductivity error is analyzed under different incident frequencies and electron collision frequencies. Through incorporating the RKADE scheme into the optimized (2, 4) stencil ADI FDTD, the optimized (2, 4) stencil RKADE-ADI FDTD is presented. The accuracy and relatively wideband capability of the proposed method is validated by two numerical experiments.