[P-EM17] Space Plasma Science

[PEM17-P04] Improving the Finite-Difference Time-Domain (FDTD) method: Suppressing numerical errors from current densities in higher-order methods

*Xinyu Ge^1,2, Harune Sekido^1,2, Takayuki Umeda³, Yoshizumi Miyoshi² (1.Graduate School of Engineering, Nagoya University, 2.Institute for Space-Earth Environmental Research, Nagoya University, 3.Information Initiative Center, Hokkaido University)

Keywords:FDTD, Courant condition, phase velocity, dispersion relation

The objective of the present study is to suppress numerical errors arising from current densities in higher-order FDTD (Finite-Difference Time-Domain) methonds. The FDTD method is a numerical approach for solving time-development of electromagnetic fields by approximating Maxwell's equations with finite differences of second-order accuracy in both time and space (Yee 1966), which is referred to as FDTD(2,2). FDTD(2,2) has problems such as numerical oscillations in continuous waveforms. Consequently, numerical methods with higher-order finite differences were developed. However, FDTD(2,4) (Fang 1989; Petropoulos 1994) and FDTD(2,6), which uses fourth and sixth-order spatial differences, respectively, have certain issues such that the Courant conditions are more restricted and that numerical errors arise in the time-development equations including current sources. In this study, FDTD(2,6) is improved by introducing higher-degree spatial difference terms including Laplacian operators (Sekido+ 2024). This present method successfully relaxes Courant conditions and reduces numerical oscillations. Furthermore, numerical errors from current densities in FDTD(2,6) are suppressing by introducing correction terms to the time-development equations.