共形单步交替方向隐式时域有限差分方法及其改进

王文兵; 周辉; 马良; 程引会; 刘逸飞; 郭景海; 赵墨

doi:doi:10.11884/hplpb201830.170475

强激光与粒子束, 2018, 30 (7): 073205, 网络出版: 2018-08-21

共形单步交替方向隐式时域有限差分方法及其改进

Stability analysis and improvement of conformal leapfrog alternating direction implicit finite-difference time-domain method

论文大纲

王文兵 ^*周辉马良程引会刘逸飞郭景海赵墨

作者单位

西北核技术研究所强脉冲辐射环境模拟与效应国家重点实验室, 西安 710024

摘要

提出了一种基于共形网格技术的共形单步交替方向隐式时域有限差分(CLeapfrog ADI-FDTD)方法。与常规FDTD方法相比，此方法能够减小由于目标边界不契合网格划分而引入的阶梯近似误差，提高算法计算不规则目标时的精度；同时算法稳定性更强，计算效率更高。由于引入共形技术后显著降低了原差分法的无条件稳定性，本文利用增长矩阵本征值方法理论分析了算法的稳定性，然后采用了一种改进的共形面积计算方法，在此基础上提出了一种稳定性更高的改进的共形单步交替方向隐式时域有限差分(ICLeapfrog ADI-FDTD)方法。数值算例验证了ICLeapfrog ADI-FDTD是一种具有高稳定性和高精度的高效算法。

Abstract

A conformal leapfrog alternating direction implicit finite-difference time-domain (CLeapfrog ADI-FDTD) method based on conformal technique was proposed in the article. Compared with the conventional FDTD method, the proposed method decreased the step approximation error, it was used to simulate the irregular object whose boundary couldn’t match the orthogonal grid; at the same time, this method could have a high efficiency because leapfrog alternating direction implicit finite-difference time-domain (Leapfrog ADI-FDTD) is a method with unconditional stability. However, CLeapfrog ADI-FDTD method may lose the stability expected with the Leapfrog ADI-FDTD schemes, and instability factor in CLeapfrog ADI-FDTD was analyzed through eigenvalue of the growth matrix, then a new method named improved conformal leapfrog alternating direction implicit finite-difference time-domain (ICLeapfrog ADI-FDTD) with a modified conformal technique was proposed, which could improve the stability without losing the calculation accuracy. The accuracy and efficiency of the proposed ICLeapfrog ADI-FDTD method were verified by numerical results.

参考文献

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王文兵, 周辉, 马良, 程引会, 刘逸飞, 郭景海, 赵墨. 共形单步交替方向隐式时域有限差分方法及其改进[J]. 强激光与粒子束, 2018, 30(7): 073205. Wang Wenbing, Zhou Hui, Ma Liang, Cheng Yinhui, Liu Yifei, Guo Jinghai, Zhao Mo. Stability analysis and improvement of conformal leapfrog alternating direction implicit finite-difference time-domain method[J]. High Power Laser and Particle Beams, 2018, 30(7): 073205.

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