Numerical performance and applications of the envelope ADI-FDTD method

The numerical performance of the envelope alternating-direction-implicit-finite-difference time-domain (ADI-FDTD) method and its applications are studied in this paper. The ADI-FDTD method is independent of the Courant-Friedrich-Levy stability condition, but its numerical dispersion grows with the increase of the time-step size. By introducing the envelope technique in the ADI-FDTD method, the numerical accuracy can be improved efficiently. In this paper, the phase velocity error of a propagating Gaussian pulse was studied for the envelope ADI-FDTD and ADI-FDTD and conventional FDTD methods with different cell size and time-step increment, then two waveguide problems and a scattering problem were simulated with the envelope ADI-FDTD and ADI-FDTD methods in graded meshes and the conventional FDTD method in a uniform mesh. The simulation results show the superior performance of the envelope ADI-FDTD over the ADI-FDTD in numerical accuracy.