Improved ADI iterative algorithm with two-step Gauss–Seidel procedure for efficient Laguerre-based BOR–FDTD method

An improved alternating-direction-implicit (ADI) algorithm for an efficient Laguerre-based body-of-revolution finite-difference time-domain (BOR–FDTD) method is presented. A new correction equation for Eρ * q is added to the linear equations to speed up the convergence, and the two-step Gauss–Seidel procedure instead of the one-step procedure in the existing algorithm is introduced in the entire iterative algorithm. To validate the accuracy and efficiency of the proposed algorithm, which is applied to the BOR structure, two scattering examples are provided to demonstrate the algorithm. At the same time, the relative reflection error of the perfectly matched layer (PML) is calculated for comparisons with Mur's absorbing boundary condition.