| In recent years, a fast, accurate and stable method for analyzing transient electromagnetic is demanded in order to meet the growing need for non-linear systems and ultra-wideband signals. Time domain integral equation methods(TDIE) caters to this need, and growing number of researchers began to study it. In this paper, we focus on exploring proper space basis functions and the temporal basis functions to improve the computing efficiency of marching-on-in-time(MOT) which is based on time-domain integral equation. The main content is divided into the following four parts:In the first part of this paper, the basic theory of TDIE-based MOT scheme is reviewed. Starting from the time domain Maxwell equ ations, derived time-domain integral equation(TDIE). Matrix equations for solving the time-domain integral equations are established. Several common temporal basis functions and Gaussian pulse waveform are introduced. The far field function in time domain is derived and the definition of RCS is given.In the second part of this paper, Higher Order Hierarchical Vector Basis Functions and its application in the time domain integral equation methods are researched. Then higher order geometric modeling based on surface quadrilateral elements and the definition of Higher Order Hierarchical Vector Basis Functions are presented. A brief introduction about direct methods and iterative methods for solving current coefficient matrix of TDIE-based marching-on-in-time(MOT) algorithms is also given. The results of different orders of higher order hierarchical vector basis functions are compared with each other. The advantages of higher order hierarchical vector basis functions for solving equations in the time domain are illustrated by numerical examples.In the third part of this paper, the order adaptive selection of higher order hierarchical vector basis functions in marching-on-in-time(MOT) algorithms are proposed. The relevant theoretical basis about the order adaptive selection are given. Reduced-order process and the extraction of relevant parameters are presented. The reason of the improvement in computation time and memory consumption when using order adaptive selection of higher order hierarchical vector basis functions in marching-on-in-time(MOT) algorithms is analyzed through numerical examples.In the Fourth part of this paper, a new space-delayed temporal basis functions in the time domain integral equation methods is studied. Definition of space-delayed temporal basis functions are introduced. Time domain integral equation forms of using space-delayed temporal basis functions are derived. Advantages of using space-delayed temporal basis functions and Roof-top basis functions in marching on-in-time(MOT) algorithms are analyzed. Moreover, the influence in mesh size, number of unknowns, memory consumption and computation time are also shown. |
