Time domain finite element method for metamaterial-based low frequency near field systems

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.

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.

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.

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.