Algorithm Studies And Application Of Integral Equations In Time Domain On Analyzing The Dielectric Bodies

The scattering and radiation of dielectric bodies in time domain are thoroughly studied in this paper. Compared with finite-difference time-domain (FDTD) method, when utilizing the boundary integral equation (BIE) and marching-on in-time (MOT) scheme to solve these questions, it has the advantage over computer memory, computer time and accuracy of results. Also, there is a new algorithm to enhance the speed of the marching-on in-time scheme. So the studies in this paper surround the MOT scheme.Several integral equations of electromagnetic field in time domain, which express the scattering of homogeneous dielectric bodies in free space, are formulated in this paper using the equivalence electric currents and magnetic currents according to the symmetry Maxwell equations in time domain, the equivalence principle and boundary condition. These integral equations include the electric field integral equation in time domain, the magnetic field integral equation in time domain and the coupled integral equations in time domain ( the PMCHW equations and the Müller equations). These are the important bases in theory of this paper.It's researched how to resolve the Müller equations in time domain using the marching-on in-time scheme. The procedure includes the model building, data extraction, some mathematical formulations in realizing the algorithm, resolving the matrix elements, the parameter extraction and the post process after the simulation, etc. The formulations of the matrix elements are deduced in this paper. An improved method to resolving the singular integrals in the MOT scheme is presented, which gives the new formulations on the approximate resolving to the time parts in the normal method and can improve the accuracy of results. The new method is better to analyzing the sensitive questions on accuracy such as electromagnetic interference (EMI).The MOT scheme is also studied based on the Laguerre polynomials as the temporal basis function in this paper. The procedure on Galerkin testing is deduced when using the Laguerre polynomials, and some examples are given. Some optimize method in the computation are supplied. When realizing the algorithm, the Galerkin testing is done in time domain, so the late-time instabilities existing previously are eliminated in the procedure. Based on the Laguerre polynomials as the temporal basis function, there has not only the Galerkin testing to the spatial basis function but also to the temporal basis function, therefore the time variable is separated from the space variable completely in this method. For the integral of Galerkin testing on the source, the Gauss-Laguerre method is chose after the comparing of several integral methods.The dielectric rod antenna, which end changes gradually, is analyzed using the MOT scheme. The wave shapes in near space, radiation patterns and the antenna characteristic changed with the changeable structure parameter are given. The MOT method is more reliable than the approximate analytical method.The plane-wave time-domain (PWTD) algorithm is researched, which can enhance the speed of the MOT method. We deduce the key formulation in PWTD algorithm, expatiate the idea and the three steps in the procedure of PWTD algorithm, formulate the idea of two-level PWTD enhanced MOT method and analyze how to resolve Müller coupled integral equation in time domain using PWTD enhanced MOT method in theory.