High stability symplectic filtered finite-difference time-domain method

Abstract

As the most standard algorithm, the traditional finite-difference time-domain (FDTD) method, which is explicit second-order accurate in both space and time, has been widely applied to electromagnetic computation and simulation. One of the primary drawbacks associated with the FDTD method is significant accumulated errors from numerical instability, dispersion, anisotropy. To overcome the shortcoming, some high-order space strategies have been put forward. For example, High-order FDTD (4, 4) method is propose. Yet, the method is difficult to handle material interface for modeling the three-dimensional complex objects. Based on the assumption that Maxwell's equations can be written as infinite-dimensional Hamiltonian system, the energy-preserving explicit symplectic integration scheme has been introduced to the computational electromagnetics. Although it is nondissipative and saves memory, the symplectic FDTD (SFDTD) scheme proposed needs at least four iterations with every time step compared with one iteration for the traditional FDTD method. As a result, the SFDTD scheme with higher stability and lower dispersion does not seem acquire lower computational complexity. However, the SFDTD must follow the Courant-Friedrichs-Lewy (CFL) number to obtain numerical precision. It is shown that the well-known Courant stability limit of the finite-difference time domain (FDTD) method can be controlled and extended by filtering out unstable spatial harmonics that develop when the time-step is chosen to exceed this limit. Therefore, The CFL of SFDTD can be extended by filtering out unstable spatial harmonics. SFDTD achieves the controllable stability beyond the stability limit. The formulation of a spatially filtered SFDTD algorithm is accompanied by a numerical benchmarking study that includes cavity resonator and backward wave media simulation