An unconditionally stable 3-D ADI-MRTD method free of the CFL stability condition

In this paper, an alternating direction implicit (ADI) technique is applied to the recently developed multiresolution time-domain (MRTD) method, resulting in an unconditionally stable ADI-MRTD scheme free of the Courant-Friedich-Lecy (CFL) stability condition. The unconditional stability is theoretically proved, and preliminary numerical results are presented to validate the scheme. Because the scheme is now free of the stability condition, its time step is determined only by modeling accuracy. The price for having the unconditional stability is, however, that the required computation memory becomes almost twice of that for the original MRTD.

I. Introduction

FDTD is a powerful numerical method for solving electromagnetic problems where field components are computed in a time recursive fashion. An extensive review of the state-of-the-art was presented in [1] and [2]. Nevertheless, FDTD is very computationally intensive due to its two inherent physical constraints, one being the numerical dispersion and another being the numerical stability. To make the numerical dispersion small, the spatial step of FDTD must be small, normally smaller than one-tenth of wavelength. To make the time-recursion stable, the time step must also be small, smaller than the so-called Courant–Friedich–Lecy (CFL) stability condition. As a result, a large numerical mesh and a long simulation time may be required for solving electrically large structures.