Magnetic metamaterials exhibit extraordinary electromagnetic properties and have shown great potential in low-frequency near-field electromagnetic applications. A near-field device or system is consisted of different natural media and low-frequency metamaterials, and it is essential to develop a numerical methodology to compute the transient response of such a device or system. However, most existing works are dedicated to high-frequency metamaterials and wave propagation problems, whereas the study of numerical methodology for low-frequency metamaterials in magnetoquasistatic (MQS) fields is still blank and challenging. In this regard, a time-domain finite-element method (TDFEM) is first derived for MQS field applications of low-frequency metamaterials. The metamaterials are modeled as continuous media and approximated by a nonstandard Lorentz dispersion equation. The formulas to handle dispersive media in near field are derived based on the auxiliary equation method. The proposed method is validated in a 2-D axisymmetric case study by comparing its results with those of frequency-domain computations.

中文翻译：

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磁性超材料的近场应用的时域有限元方法

磁性超材料展现出非凡的电磁性能，并在低频近场电磁应用中显示出巨大的潜力。近场设备或系统由不同的自然介质和低频超材料组成，因此开发一种数值方法来计算此类设备或系统的瞬态响应至关重要。然而，大多数现有的工作致力于高频超材料和波传播问题，而在磁准静态（MQS）领域中对低频超材料的数值方法的研究仍然是空白且具有挑战性。在这方面，首先针对低频超材料的MQS现场应用推导了时域有限元方法（TDFEM）。将超材料建模为连续介质，并通过非标准Lorentz色散方程进行近似。基于辅助方程法，推导了处理近场色散介质的公式。通过将其结果与频域计算结果进行比较，该方法在二维轴对称案例研究中得到了验证。