Experiments with high-accuracy finite-difference schemes for the time-domain Maxwell equations

maximum order of accuracy possible, they can be High-accuracy finite-difference schemes for the time-domain Maxwell equations are investigated through numerical experiments. The finite-difference schemes combine a seven-point spatial operator with an explicit six-stage Runge-Kutta time-march method. The maximum-order scheme is comparcd with several schcmcs which are optimized to provide reduced errors over a specific wavenumber range. A fourth-order scheme is also included in the comparisons. The schcmes arc compared for a one-dimensional test case consisting of waves propagating through a dielectric slab surrounded by free space. The results show that the high-accuracy schcmcs are much more accurate than the fourth-ordcr schemc used for comparison. Although the optimizcd schemes can produce reduced errors for specific cases, the maximum-order scheme is superior for most of the simulations considered. W Introduction In the pas few ycars, intcrest has grown in timedomain numerical simulations of wave phenomena using finite-diffcrcncc or related methods. Of particular intcrest in the aerospace community are clcctromagnctic and acoustic waves. It is gcnerally rccognizcd that in ordcr to avoid excessively fine meshes for many practical problems, high-order discrctizations are required. Consequently, many highordcr diffcrcncing methods have been developed for problems involving wave phenomena. Furthermore, optimized, or specual-like, finite-difference schemes have been proposed which can provide improvements in accuracy over high-order schemes with the same computational cffort. In an optimized scheme, the phase and amplitude errors (gcncrally obtained from Fourier analysis) are minimizcd over a finite range of spatial wavenumbcrs. Although such schemes do not have the I