A Fourth-Order Accurate Numerical Boundary Scheme for the Planar Dielectric Interface: a 2-D TM Case

Hwang, Kyu-Pyung

doi:2011.11.1.11

J. Electromagn. Eng. Sci > Volume 11(1); 2011 > Article

Journal of the Korean Institute of Electromagnetic and Science 2011;11(1):11-15.
DOI: https://doi.org/10.5515/JKIEES.2011.11.1.011

A Fourth-Order Accurate Numerical Boundary Scheme for the Planar Dielectric Interface: a 2-D TM Case

Kyu-Pyung Hwang

Samsung Electro-Mechanics Co., Ltd.

Abstract

Preserving high-order accuracy in high-order FDTD solutions across dielectric interfaces is very important for practical time-domain electromagnetic simulations. This paper presents a fourth-order accurate numerical boundary scheme for the planar dielectric interface to be used in the fourth-order FDTD method proposed earlier by the author. The interface scheme for the two-dimensional (2-D) transverse magnetic (TM) polarization case is derived and validated by monitoring the $L_2$ norm errors in the numerical solutions of a partially-filled cavity demonstrating its fourth-order convergence and long-time numerical stability in the presence of the planar dielectric interface.

Key words: Finite-Difference Time-Domain (FDTD) Methods, Convergence of Numerical Methods, High-Order Method, Numerical Stability