Alternating-Direction Implicit Formulation of the Finite-Element Time-Domain Method

In this paper, two implicit finite-element time-domain (FETD) solutions of the Maxwell equations are presented. The first time-dependent formulation employs a time-integration method based on the alternating-direction implicit (ADI) method. The ADI method is directly applied to the time-dependent Maxwell curl equations in order to obtain an unconditionally stable FETD approach, unlike the conventional FETD method, which is conditionally stable. A numerical formulation for the 3-D ADI-FETD method is presented. For stability analysis of the proposed method, the amplification matrix is derived. Investigation of the proposed method formulation shows that it does not generally lead to a tri-diagonal system of equations. Therefore, the Crank-Nicolson FETD method is introduced as another alternative in order to obtain an unconditionally stable method. Numerical results are presented to demonstrate the effectiveness of the proposed methods and are compared to those obtained using the conventional FETD method.