Error-optimized finite-difference modeling of wave propagation problems with Lorentz material dispersion

Abstract

In the context of finite-different time-domain (FDTD) methods, errors associated with numerical dispersion can be reduced by introducing high-order or error-optimized derivative approximations. Although there exist various accuracy-enhanced FDTD techniques for modeling wave propagation within non-dispersive media, the equally interesting case of dispersive materials is commonly neglected. In this paper, we present a suitable design procedure that derives FDTD algorithms based on the (2,4) stencil, which accomplish reduced errors levels in problems featuring Lorentz dispersion. In essence, novel finite-difference formulae for spatial derivatives are defined, based on two different treatments of a suitable error estimator, aiming at either single-frequency or wide-frequency optimization. Theoretical studies and numerical tests verify the expected performance improvement, and validate the desirable accuracy amendment of the (2,4) FDTD scheme in cases where dispersive materials need to be considered.