| Abstract: | In this paper an explicit finite-difference time-domain scheme for solving
the Maxwell's equations in non-staggered grids is presented. The proposed scheme
for solving the Faraday's and Ampère's equations in a theoretical manner is aimed to
preserve discrete zero-divergence for the electric and magnetic fields. The inherent local conservation laws in Maxwell's equations are also preserved discretely all the time
using the explicit second-order accurate symplectic partitioned Runge-Kutta scheme.
The remaining spatial derivative terms in the semi-discretized Faraday's and Ampère's
equations are then discretized to provide an accurate mathematical dispersion relation
equation that governs the numerical angular frequency and the wavenumbers in two
space dimensions. To achieve the goal of getting the best dispersive characteristics, we
propose a fourth-order accurate space centered scheme which minimizes the difference
between the exact and numerical dispersion relation equations. Through the computational exercises, the proposed dual-preserving solver is computationally demonstrated
to be efficient for use to predict the long-term accurate Maxwell's solutions. |
