Compact System-Combined-Based FDTD Implementations With Approximate Crank–Nicolson Scheme and Electromagnetic Scattering

In this article, we develop the efficacious system-combined-based approximate Crank–Nicolson finite-difference time-domain (SC-ACN-FDTD) method which can be applied to electromagnetic scattering. After being processed by the matrix form with the discrete time, the electric and magnetic fields from Maxwell’s equations are both unified as the unique vector at the same time step. By means of the vector transformation, iterative procedures in the time domain of both electric and magnetic fields can be obtained in the Crank–Nicolson format. To model an open-domain problem, we apply convolutional perfectly matched layer (CPML) to truncate the finite computational region. To guarantee the numerical accuracy of the SC-ACN-FDTD method, we employ the empirical formula to forecast the maximum Courant–Friedrichs–Lewy (CFL) factor based on the spatial sampling density. Compared with the conventional finite-difference time-domain (FDTD) methods, the proposed SC-ACN-FDTD method can be well demonstrated and further validated by adopting electromagnetic scattering in the near and far fields. To further validate our results, the commercial software COMSOL is also adopted for the far field’s pattern in the single frequency.