Toward the construction of a fourth-order difference scheme for transient EM wave simulation: staggered grid approach

A compact central-difference approximation in conjunction with the Yee (1966) grid is used to compute the spatial derivatives in Maxwell's equations. To advance the semi-discrete equations, the four-stage Runge-Kutta (RK) integrator is invoked. This combination of spatial and temporal differencing leads to a scheme that is fourth-order accurate, conditionally stable, and highly efficient. Moreover, the use of compact differencing allows one to apply the compact operator in the vicinity of a perfect conductor-an attribute not found in other higher order methods. Results are provided that quantify the spectral properties of the method. Simulations are conducted on problem spaces that span one and three dimensions and whose domains are of the open and closed type. Results from these simulations are compared with exact closed-form solutions; the agreement between these results is consistent with numerical analysis.