Based On Time Domain Integral Equation Of The Metal Target Time-domain Electromagnetic Scattering Value

Electromagnetic in time domain has been paid great attention and studied extensively since 1960s. In recent years, the urgent need for the simulation of ultra wideband signal and nonlinear circuit demands an efficient algorithm that can deal with time domain electromagnetic problems efficiently, accurately and stably. Apparently, numerical methods based on the time domain integral equation can well meet these requirements. Particularly, most studies in time domain integral equation are focused on the stable and accurate simulation of scattering and radiation problems of electrically large object. Therefore, the work in this paper is aimed at the stability and accuracy in the solving of time domain integral equation.This paper begins with the derivation of time domain electric field integral equation (TDEFIE), time domain magnetic field integral equation (TDMFIE), and time domain combined field integral equation (TDCFIE) from the well known Maxwell's equation in time domain. Numerical methods such as method of moment (MoM) and marching-on-in-time (MOT) algorithm are also described to illustrate their effectiveness in the solution of time domain integral equation. Subsequently, several kinds of commonly used temporal and space basis functions are introduced. Due to the fact that the basis function chosen will have a strong influence on the solving efficiency and accuracy, the selection rule of various temporal and space basis function are presented based on the analysis. Finally, limitations and advantages of the two MOT methods, i.e., explicit and inexplicit MOT, are analyzed and demonstrated. Solving methods for matrix equation are also presented.One of the fatal problems in time domain integral equation is the late-time instability. The main ingredient can be due to the inaccurate numerical computation method and inexact approximation introduced in the discretization process of the time domain integral equation, thus we expect that an accurate impedance matrix computation method will significantly improve the accuracy of the time domain integral equation and effectively avoid the late-time instability. In this paper, a hybrid method based on the Duffy Coordinate Transformations method (for singularity terms) and adaptive integration method (for nonsingularity terms) are proposed to accurately compute impedance matrix. The second section describes a method of solving time-domain integral equation though analytizing a part of retarded-time potential integrals. This method can well eliminate the difficulties in the accurate computation of the singularity terms, which will improve the stability in late-time. Finally, the convolution of the time basis functions with the vector and scalar potential are derived to an analytical expression.