Finite Element Method for Transient Electric Field by Using Indirect Laplace Transform with High Accuracy

This paper focuses on the finite element method in the complex frequency domain (CFD-FEM) for the transient electric field. First, the initial value and boundary value problem of the transient electric field under the electroquasistatic field in the complex frequency domain is given. In addition, the finite element equation and the constrained electric field equation on the boundary are derived. Secondly, the indirect algorithm of the numerical inverse Laplace transform is introduced. Based on it, the calculation procedures of the CFD-FEM are illustrated in detail. Thirdly, the step response, zero-state response under the positive periodic square waveform (PPSW) voltage, and the zero-input response by the CFD-FEM with direct algorithm and indirect algorithm are compared. Finally, the reason for the numerical oscillations of the zero-state response under the PPSW voltage is analyzed, and the method to reduce oscillations is proposed. The results show that the numerical accuracy of the indirect algorithm of the CFD-FEM is more than an order of magnitude higher than that of the direct algorithm when calculating the step response of the transient electric field. The proposed method can significantly reduce the numerical oscillations of the zero-state response under the PPSW voltage. The proposed method is helpful for the calculation of the transient electric field, especially in the case of frequency-dependent parameters.