A 3-D Weakly Conditionally Stable Single-Field Finite-Difference Time-Domain Method

Abstract

A novel finite-difference solution of the time-domain three-dimensional wave equation with a stability criterion relaxed from the discretization space steps in two directions is presented. This method is particularly useful and efficient for electromagnetic simulation of structures having fine details in two Cartesian directions. During the algorithm iteration process, updating of only the electric field is required. In comparison to other weakly conditional finite-difference time-domain (WCS-FDTD) algorithms, the proposed method is shown to be computationally more efficient in terms of runtime because the implicit updating equations can be solved simultaneously (in parallel) by applying multithreading, while in the earlier WCS-FDTD methods, a simultaneous solution of the implicit updating equations was not feasible. The high computational efficiency and accuracy of the proposed method is demonstrated by producing several numerical examples and providing comparison to the results obtained using methods available in the literature.