The stability analysis of the one-step leapfrog periodic ADI-FDTD

摘要

In this paper, the stability analysis of the unconditionally stable one-step leapfrog alternating direction implicit (ADI) finite-difference time-domain (FDTD) method for periodic structures is presented. The amplification matrix of the proposed leap-frog ADI-FDTD method is obtained through the spatial domain with Fourier method and eigenvalues of the Fourier amplification matrix are obtained analytically to prove the unconditional stability of the periodic leapfrog ADI-FDTD method. Numerical verification is proposed to confirm the theoretical result.