Purpose

The purpose of this work is to develop a computational paradigm for performance analysis of low-frequency electromagnetic devices containing both magnetic metamaterials (MTMs) and natural media.

Design/methodology/approach

A time domain finite element method (TDFEM) is proposed. The electromagnetic properties of the MTMs are modeled by a nonstandard Lorentz model. The time domain governing equation is derived by converting the one from the frequency domain into the time domain based on the Laplace transform and convolution. The backward difference is used for the temporal discretization. An auxiliary variable is introduced to derive the recursive formula.

Findings

The numerical results show good agreements between the time domain solutions and the frequency domain solutions. The error convergence trajectory of the proposed TDFEM conforms to the first-order accuracy.

Originality/value

To the best knowledge of the authors, the presented work is the first one focusing on TDFEMs for low-frequency near fields computations of MTMs. Consequently, the proposed TDFEM greatly benefits the future explorations and performance evaluations of MTM-based near field devices and systems in low-frequency electrical and electronic engineering.

中文翻译：

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基于超材料的低频近场系统的时域有限元方法

目的

这项工作的目的是开发一种计算范例，用于同时包含磁性超材料（MTM）和自然介质的低频电磁设备的性能分析。

设计/方法/方法

提出了一种时域有限元方法。MTM的电磁特性通过非标准的Lorentz模型建模。通过基于Laplace变换和卷积将频域中的一个从频域转换为时域，可以得出时域控制方程。向后差异用于时间离散化。引入辅助变量以导出递归公式。

发现

数值结果表明时域解和频域解之间具有良好的一致性。提出的TDFEM的误差收敛轨迹符合一阶精度。

创意/价值

据作者所知，本文是针对TDFEM进行MTM低频近场计算的第一篇论文。因此，提出的TDFEM极大地有利于低频电气和电子工程中基于MTM的近场设备和系统的未来探索和性能评估。