Development of a 3D staggered FDTD scheme for solving Maxwell’s equations in Drude medium

• Published in: Computers & mathematics with applications (1987) Vol. 71; no. 6; pp. 1198 - 1226
• Main Authors: Sheu, Tony W.H., Wang, Y.C., Li, J.H.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2016
• Subjects: Dispersions; Errors; Exact and numerical phase velocities; Fourth-order; Mathematical analysis; Mathematical models; Maxwell's equations; Phase velocity; Runge-Kutta method; Staggered grids; Symplectic partitioned Runge–Kutta; Three dimensional; Zero-divergence; Fourth-order; Staggered grids; Exact and numerical phase velocities; Zero-divergence; Symplectic partitioned Runge–Kutta; Maxwell’s equations
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2016.01.025

An explicit finite-difference scheme is developed to solve the three-dimensional Maxwell’s equations in Drude medium. Our aim of developing this scheme in time domain is to compute solutions in staggered grids from the Faraday’s and Ampère’s equations. The electric and magnetic field solutions are sought subject to the discrete zero-divergence condition (Gauss’s law). The local conservation laws in ideal Maxwell’s equations are also numerically preserved all the time using the explicit second-order accurate symplectic partitioned Runge–Kutta temporal scheme. The spatial derivative terms in the Faraday’s and Ampère’s equations are discretized to obtain fourth-order accuracy using the developed scheme underlying the concept of minimizing the discrepancy between the exact and the derived numerical phase velocities. Dispersion and anisotropy errors have been much reduced through the procedure of minimizing phase velocity error. In addition to performing the fundamental analysis on the proposed scheme, the computational efficiency and long-term accurate properties embedded in the proposed symplectic dispersion-error reduction centered scheme are numerically demonstrated through several test problems investigated in ideal and Drude media.