The Complementary Derivatives Method for High-Accuracy Finite-Difference Time-Domain Simulations

Non-uniform grid in FDTD-based methods, which is typically used to resolve fine structures or improve the accuracy of the electric or magnetic fields with large gradients within a limited volume, can reduce the computational domain and therefore lead to a reduction of the computational cost. However, for high-accuracy problems, such as resonators, or microwave integrated circuits, using different grid size increases the truncation error at the boundary of domains having different grid size. To address this problem, in this work, we introduce the complementary derivatives method (CDM). Theoretical discussion and numerical results are presented to show that the CDM can maintain second-order accuracy throughout the computational domain