Development of the SBP-SAT FDTD(2,4) Method With Nonuniform Grids for Electromagnetic Analysis

A three-dimensional, finite-difference time-domain (FDTD) method with second-order temporal and fourth-order spatial accuracy (FDTD(2,4)), combined with the summation-by-parts simultaneous approximation term (SBP-SAT) technique, is proposed in this article to guarantee the theoretical stability and reduce numerical dispersion errors. The proposed method remains theoretically stable in long-time simulations and accurate at low spatial sampling rates, thereby improving the stability and accuracy for complicated structures. This article mainly focuses on its three-dimensional implementation, numerical dispersion characteristics, and comparisons to the FDTD(2,2) method, the FDTD(2,4) method and the SBP-SAT FDTD(2,2) method. The effectiveness of the proposed method is verified through several numerical examples. Results show that the proposed SBP-SAT FDTD(2,4) method is theoretically stable and exhibits good accuracy.