Reducing Truncation Error of Non-Uniform Grid Size in FDTD Methods using the Complementary Derivatives Method (CDM)

The finite-difference time-domain (FDTD) method and its variants such as the ADI-FDTD, are very versatile and general numerical schemes suitable for efficient solution of a wide class of electromagnetic problems. Using non-uniform grid size in FDTD-based methods to resolve fine structures can reduce the computational domain and therefore lead to a reduction of the computational cost (time and computer memory). However, for high-accuracy problems, using different grid size increases the truncation error at the boundary domains having different grid size. To address this problem, in this work, we introduce the complementary derivatives method, henceforth referred to as CDM. The method is essentially an interpolation scheme enforced at the boundary. Numerical results will be presented to show that the CDM can maintain second-order accuracy throughout the computational domain