Time Domain Plane Wave Algorithm

With the increase of the engineering applications of broadband signals and non-linear systems, the study of time domain integral equation (TDIE) methods for analysis of transient electromagnetic scattering and radiation phenomena is more and more active. But the cost of analyzing electrically large objects using a classical MOT (marching-on in-time) scheme is highly expensive, which has limited the applications of TDIE methods. In this dissertation, a fast algorithm---plane wave time-domain (PWTD) algorithm, for reducing the cost of analyzing electrically large objects, is introduced. This algorithm is more suitable for practical applications. The dissertation is arranged as follows.At first, the time-domain electric field, magnetic field, and combined field integral equation used to analyze arbitrarily 3-D PEC are described. The method of moments and its relative details used to solve the TDIE are simply introduced.Then, the marching-on-in-time algorithm (MOT) is shown. The singular integrals of TDIE are dealt with the transformations of the parametric coordinates and Duffy coordinates. So the currents can be evaluated stability and accuracy. Two new memory modes are presented to solve memory problems of electrically large objects. And these two modes can be also used in PWTD algorithm. The cost of MOT schemes is analyzed using numerical results. The conclusion that the MOT scheme efficiency can be improved by reducing the cost of evaluating impedances and the vector sum is obtained. Next, the principle of PWTD algorithm used for solving scalar quantity fields is analyzed in details. The implementation and the numerical realization are also discussed. This part is the theoretical foundation of PWTD algorithm.At last, the principle and the implementation of PWTD algorithm used for solving TDIE are analyzed in details. And the computational complexity of PWTD algorithm is also analyzed. The optimums of the important parameters of PWTD algorithm are given according to the analyses. In the end, the correctness of two-level PWTD algorithm realized in this dissertation is validated according to the numerical results. The late-time stability of two-level PWTD algorithm is also presented. The research work presented in this dissertation provides an efficient approach to analyze the electrically large objects, as well as a solid foundation for engineering applications of TDIE methods.