The concurrent complementary operators method for FDTD mesh truncation

The complementary operators were developed for the purpose of truncating the computational domain of finite-difference time-domain (FDTD) open-region simulations. In the original implementation of the complementary operators method, two independent simulations were performed. The solutions from these two simulations were then averaged to obtain a solution devoid of first-order reflections. The complementary operators are implemented in a concurrent fashion. This new implementation, referred to as the concurrent complementary operators method (C-COM), requires only one simulation, thus reducing the operation count by approximately one half. The implementation for two-dimensional (2-D) space is outlined first with emphasis on reducing reflections from corner regions; then the extension to three dimensions is developed. Numerical results are provided in addition to an analysis of the source of error that arises from this new implementation.