Complex Envelope Approximate Crank-Nicolson Method and Its Open Boundary Implementation for Bandpass Problem

Abstract

To efficiently simulate the bandpass electromagnetic problems by employing the finite-difference time-domain (FDTD) algorithm, unconditionally stable implementation is proposed based upon the complex envelope method and the Crank-Nicolson Direct-Splitting (CNDS) algorithm. To further absorb outgoing waves and reduce wave reflections in open region problems, absorbing boundary condition with improved absorption is proposed by incorporating the proposed scheme with the higher order perfectly matched layer (PML) formulation. The proposed scheme takes advantage of the complex envelope method, the CNDS algorithm and the higher order PML formulation in terms of simulating bandpass signals and enhancing absorption and improving computational efficiency. Numerical examples are carried out to further demonstrate the effectiveness and efficiency. Through the resultants, it can be illustrated that the proposed scheme can not only obtain considerable accuracy, favorable absorbing performance, outstanding efficiency in the simulation of bandpass open region problems but also maintain the stability of the algorithm when the time step surpasses far beyond the Courant-Friedrich-Levy condition.

Keywords

• Complex envelope (CE)
• Crank-Nicolson direct-splitting
• finite-difference time-domain (FDTD)
• perfectly matched layer (PML)