Second-Order Temporal-Accurate Scheme for 3-D LOD-FDTD Method With Three Split Matrices

Abstract

This letter presents a second-order temporal-accurate scheme for three-dimensional (3-D) locally one-dimensional finite-difference time-domain (LOD-FDTD) method with three split matrices. The main iterations of the proposed scheme comprise only one more procedure in addition to the existing three procedures. Using proper (initial only) input and (often infrequent, field-point only) output processings, the second-order temporal accuracy is achieved and verified analytically. To further enhance the efficiency, the proposed scheme is implemented based on the principle of fundamental schemes for unconditionally-stable FDTD methods, which feature a matrix-operator-free right-hand side. Stability analysis is provided to ascertain the unconditional stability of the proposed scheme and numerical results are demonstrated to justify its higher accuracy.