A staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations

We consider a model explicit fourth-order staggered finite-difference metho d for the hyperbolic Maxwell's equations. Appropriate fourth-order accurate extrapolation and one-sided difference operators are derived in order to c omplete the scheme near metal boundaries and dielectric interfaces. An eige nvalue analysis of the overall scheme provides a necessary, but not suffici ent, stability condition and indicates longtime stability. Numerical result s verify both the stability analysis, and the scheme's fourth-order converg ence rate over complex domains that include dielectric interfaces and perfe ctly conducting surfaces. For a fixed error level, we find the fourth-order scheme is computationally cheaper in comparison to the Yee scheme by more than an order of magnitude. Some open problems encountered in the applicati on of such high-order schemes are also discussed. (C) 2001 Academic Press.