DEVELOPMENT OF A SYMPLECTIC SCHEME WITH OPTIMIZED NUMERICAL DISPERSION-RELATION EQUATION TO SOLVE MAXWELLʹS EQUATIONS IN DISPERSIVE MEDIA

In this paper an explicit finite-difference scheme is developed in staggered grids for solving the Maxwellʹs equations in time domain. We are aimed to preserve the discrete zero-divergence condition in the electrical and magnetic fields and conserve the inherent laws in non-dispersive simple media all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta temporal scheme for the time derivative terms. The spatial derivative terms in the semi-discretized Faradayʹs and Ampereʹs equations are then approximated to get an accurate numerical dispersion relation equation that governs the numerical angular frequency and the wavenumbers for the Maxwellʹs equations defined in two space dimensions. To achieve the goal of getting the best dispersive characteristics in the chosen grid stencil, a fourth-order accurate space centered scheme with the ability of minimizing the difference between the exact and numerical dispersion relation equations is proposed. Our emphasis is placed on the accurate modeling of EM waves in the dispersive media of the Debye, Lorentz and Drude types. Through the computational exercises, the proposed dual-preserving Maxwellʹs equation solver is computationally demonstrated to be efficient for use to predict the long-term accurate wave solutions in a medium belonging either to a frequency independent or to a dependent type.