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Stability and dispersion analysis for the three-dimensional (3-D) leapfrog alternate direction implicit flnite difierence time domain (ADI-FDTD) method is presented in this paper. The leapfrog ADI- FDTD method is reformulated in the form similar to conventional explicit FDTD method by introducing two auxiliary variables. The auxiliary variables serve as perturbations of the main flelds variables. The stability of the leapfrog ADI-FDTD method is analyzed using the Fourier method and the eigenvalues of the Fourier ampliflcation matrix are obtained analytically to prove the unconditional stability of the leapfrog ADI-FDTD method. The dispersion relation of the leapfrog ADI-FDTD method is also presented.

STABILITY AND DISPERSION ANALYSIS FOR THREE-DIMENSIONAL (3-D) LEAPFROG ADI-FDTD METHOD