An accurate and stable fourth order finite difference time domain method

A long-stencil fourth order finite difference method over a Yee-grid is developed to solve Maxwell’s equations. The different variables are located at staggered mesh points, and a symmetric image formula is introduced near the boundary. The introduction of these symmetric ghost grid points assures the stability of the boundary extrapolation, and in turn a complete set of purely imaginary eigenvalues are given for the fourth-order discrete curl operators for both electric and magnetic fields. Subsequently, the four-stage Jameson method integrator constrained by a pre-determined time step is utilized to produce a stable full fourth order accuracy in both time and space. The accuracy of the developed numerical scheme has been validated by comparing its results to the closed form solutions for a rectangular cavity.