A Finite Element Time-Domain Algorithm Based on the Alternating-Direction Implicit Method

We present an implicit finite element time-domain (FETD) solution of the Maxwell equations. The time-dependent formulation employes a time-integration method based on the alternating-direction implicit (ADI) method. The ADI method is directly applied to the Maxwell equations in order to obtain an unconditionally stable FETD approach. The method uses edge elements for electric field and facet elements for magnetic flux density. The advantage of this formulation based on the ADI scheme is that the time step is no longer governed by the spatial discretization of the mesh, but rather by the spectral content of the time-dependent signal. Numerical formulations are presented and simulation results are compared to those using the conventional FETD method

I. Introduction

In the past few years, numerical methods have been extensively used to solve the Maxwell equations in the time domain for the analysis of transient problems. Moreover, it is often important to analyze systems in a large frequency band. Time-domain methods are well suited to achieve this target, because they can obtain broadband information from a single computation. In electromagnetic compatibility (EMC) studies or antenna analysis, for instance, we can obtain the response of a system over a wide frequency band by using a large-band transient signal as excitation and by applying the Fourier transform on the results. This can give a significant reduction of the computational cost compared to frequency domain calculations.