Time-Domain Finite-Element Method for Near-Field Applications With Magnetic Metamaterials

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.