Envelope ADI-FDTD method and its application in three-dimensional nonuniform meshes

Abstract—The envelope alternating-direction-implicit finite difference time domain (ADI–FDTD) method in 3-D nonuniform meshes was proposed and studied. The phase velocity error for the envelope ADI–FDTD and ADI–FDTD methods in uniform and nonuniform meshes and different temporal increments were studied. A cavity problem was studied using the envelope ADI–FDTD and ADI–FDTD methods in graded meshes and the conventional FDTD method in a uniform mesh. The simulation results show that the envelope ADI–FDTD performs better than the ADI–FDTD in numerical accuracy. Index Terms—Courant–Friedrich–Levy (CFL) stability condi-tion, envelope alternating-direction-implicit finite difference time domain (ADI–FDTD) method, phase velocity. I