Time-domain Finite Element Method for Transient Electric Field and Transient Charge Density on Dielectric Interface

This paper is devoted to solving the transient electric field and transient charge density on the dielectric interface under the electroquasistatic (EQS) field conditions with high accuracy. The proposed method is suitable for both 2-D and 3-D applications. Firstly, the governing equations represented by scalar electric potential are discretized by the nodal finite element method (FEM) in space and the finite difference method in time. Secondly, the transient constrained electric field equation on the boundary (TCEFEB) is derived to calculate the normal component of the transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface. Finally, a 2-D numerical example is employed to demonstrate the validity of the proposed method. Furthermore, the comparisons of the numerical accuracy of the proposed method in this paper with the existing FEMs for electric field intensity and charge density on the dielectric interface are conducted. The results show that the numerical accuracy of the proposed method for calculating the normal component of transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface is close to that of nodal electric potential and an order of magnitude higher than those of existing FEMs.

Automated summary

This paper proposes a method to solve the transient electric field and charge density on the dielectric interface with high accuracy, using nodal finite element method in space and finite difference method in time. The proposed method is validated through a 2-D numerical example and compared with existing methods, showing a comparable or higher numerical accuracy.