2017/06/14 by Michael J. Jenkinson, Jenkinson, Michael J., Jeffrey W. Banks +1 · 1 citation
Engineering · Physics and Astronomy · #35L05 #35Q60 #35Q61 #65M06 #65M12 #65Z05 #78A40 #78M20 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1706.04585
openalex publication_date 2017/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a novel finite-difference time-domain (FDTD) scheme for the\nsolution of the Maxwell's equations in which linear dispersive effects are\npresent. The method uses high-order accurate approximations in space and time\nfor the dispersive Maxwell's equations written as a second-order vector wave\nequation with a time-history convolution term. The modified equation approach\nis combined with the recursive convolution (RC) method to develop high-order\napproximations accurate to any desired order in space and time.\nHigh-order-accurate centered approximations of the physical Maxwell interface\nconditions are derived for the dispersive setting in order to fully restore\naccuracy at discontinuous material interfaces. Second- and fourth-order\naccurate versions of the scheme are presented and implemented in two spatial\ndimensions for the case of the Drude linear dispersion model. The stability of\nthese schemes is analyzed. Finally, our approach is also amenable to\ncurvilinear numerical grids if used with appropriate generalized Laplace\noperator.\n