Efficient 3-D Laguerre-Based FDTD Method Using a New Temporal Basis

Due to the finite expanding order in an actual numerical simulation, the finite-difference time-domain method based on weighted Laguerre polynomials (Laguerre-FDTD) often has a large error near t = 0. In this communication, a new temporal basis is proposed to solve this problem, which is composed of three weighted Laguerre polynomials in adjacent orders. Based on this new temporal basis, the matrix equation for three-dimensional (3-D) FDTD method is derived in which the accumulation term is eliminated. By introducing a perturbation term and an iterative procedure to the matrix equation, an efficient 3-D FDTD method is obtained. To verify the accuracy and efficiency of the proposed FDTD method, two structures are calculated as examples. Numerical results show that the solution of the proposed method has no error at t = 0 and the efficiency of the proposed method is superior to the conventional FDTD method, the alternating direction implicit (ADI) FDTD method, and the original efficient Laguerre-FDTD method using a single Laguerre polynomial at a comparable accuracy.