A one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method for lossy media is presented. Different from the method provided by others, the proposed method is originated from the conventional ADI-FDTD method instead of considering the leapfrog ADI-FDTD method as a perturbation of the conventional explicit FDTD method. Its unconditional stability is analytically proven through a method that combines the von Neumann method with the Jury criterion. In addition, its unconditional stability and computational efficiency are verified through numerical experiments.
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