Efficient Laguerre-Based BOR–FDTD Method

What is it about?

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 is calculated for comparisons with Mur’s absorbing boundary condition.

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Photo by Austin Neill on Unsplash

Photo by Austin Neill on Unsplash

Why is it important?

In this work, an improved ADI iterative algorithm with a two-step Gauss–Seidel procedure for an efficient Laguerre-based BOR–FDTD method is proposed. Through applying the two-step Gauss–Seidel procedure in the entire iteration and adding the correction term, the proposed algorithm not only becomes more efficient but also has faster convergence. Meanwhile, the proposed algorithm can weaken the perturbation effect, which results in fewer iterations for maintaining a result with equal accuracy to that of the existing algorithm. Three scattered numerical examples indicate that the proposed algorithm is superior in accuracy and efficiency to the existing algorithm for the BOR structure, especially for a fine one.

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