麦克斯韦方程组四阶精度时域有限差分法的能量分析

IF 1.8 3区数学 Q1 MATHEMATICS

AIMS Mathematics Pub Date : 2023-01-01 DOI:10.3934/math.2023012

Li Zhang, Maohua Ran, Han Zhang

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引用次数: 0

摘要

本文提出了求解无源无电荷二维麦克斯韦方程组的四阶时域精度ADI-FDTD方法。本文主要对所提出的ADI-FDTD方法进行了能量分析。利用能量法推导了ADI-FDTD方法的数值能量恒等式，并证明了ADI-FDTD方法是近似能量守恒的。与理论能量相比，数值能量有两个摄动项，可以在计算中使用，以保持其近似保能。数值实验验证了所提出的ADI-FDTD方法的性能，验证了理论结果。

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Energy analysis of the ADI-FDTD method with fourth-order accuracy in time for Maxwell's equations

In this work, the ADI-FDTD method with fourth-order accuracy in time for the 2-D Maxwell's equations without sources and charges is proposed. We mainly focus on energy analysis of the proposed ADI-FDTD method. By using the energy method, we derive the numerical energy identity of the ADI-FDTD method and show that the ADI-FDTD method is approximately energy-preserving. In comparison with the energy in theory, the numerical one has two perturbation terms and can be used in computation in order to keep it approximately energy-preserving. Numerical experiments are given to show the performance of the proposed ADI-FDTD method which confirm the theoretical results.

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来源期刊

AIMS Mathematics Mathematics-General Mathematics

CiteScore

3.40

自引率

13.60%

发文量

769

审稿时长

90 days

期刊介绍： AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.