Phase Error Control for FD-TD Methods

Abstract

Researchers in computational electromagnetics have recently become aware of an important property1 of finite element methods for elliptic boundary-value problems relevant to the frequency-domain Maxwell’s equations. This property relates the number of points per wavelength, N _ppwto frequency, ω, through a non-linear relationship. The theoretical results are for a fixed physical domain size and relate a scaled time-frequency, k = ω/c, to the quantity kΔ = 2π/N _ppw, where c is the speed of light in vacuum and Δ is the characteristic spatial scale of the discretization. Herein, we derive a property of the phase error for finite difference approximations to the time-domain Maxwell’s equations that is appropriately conjugate to that for the conjugate, frequency-domain, problem¹.