Performance Enhanced Crank-Nicolson Boundary Conditions for EM Problems.

Based upon the approximate Crank–Nicolson (CN) algorithms and the higher order (HO) concept, unconditionally stable perfectly matched layer (PML) implementations are proposed for electromagnetic problems in the finite-difference time-domain (FDTD) lattice. The approximate CN algorithms include the CN direct-splitting (CNDS) and CN approximate-factorization-splitting (CNAFS). The proposed schemes take advantage of the approximate CN algorithms in terms of eliminating the Courant–Friedrichs–Levy stability condition and maintaining the computational accuracy. By introducing the HO concept to the PML formulation, the absorbing performance can be enhanced during the simulation. Furthermore, to cope with the existence of half-time-step problems in simulating the anisotropic magnetized plasma, a modified ADE method is proposed at the integer time step. Thus, the modified ADE method can be directly employed in the approximate CN algorithms. Numerical examples and experiments are carried out to demonstrate the effectiveness, efficiency, and performance. Through the results, it can be observed that the computational efficiency and absorbing performance can be significantly improved. Meanwhile, it can be concluded that the CNAFS-PML and CNDS-PML algorithms show higher accuracy and considerable efficiency, respectively, when the time step surpasses far beyond the CFL condition. [ABSTRACT FROM AUTHOR]