A Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwellʹs Equations

We consider a model explicit fourth-order staggered finite-difference method for the hyperbolic Maxwellʹs equations. Appropriate fourth-order accurate extrapolation and one-sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces. An eigenvalue analysis of the overall scheme provides a necessary, but not sufficient, stability condition and indicates long-time stability. Numerical results verify both the stability analysis, and the schemeʹs fourth-order convergence rate over complex domains that include dielectric interfaces and perfectly 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 application of such high-order schemes are also discussed.