Study On Higher Order Nystr (?) M Method For Time - Domain Integral Equations Of Electromagnetic Scattering From Dispersive Media

It is of great importance to study the transient electromagnetic characteristics of dispersive media owing to its promotive effects in many fields of engineering interest. However, due to the complexity of the dispersion of media is always the difficulty of electromagnetic, time domain integral equation (TDIE), as one of the main research direction in the field of computational electromagnetics, plays an important role to resolve the problem. In addition, how to solve the equation quickly and accurately, minimizing time and memory consumption are the fundamental indicators of measure the algorithm superiority.Firstly, this paper introduces a high-order Nystrom scheme for solving TDIE based on marching-on-in-time (MOT). In space, this method takes the high-order mesh size, constructs the high-order vector interpolation basis function and takes the point matching method, fully improving the solving efficiency. On the time dimension, we study the shifted Lagrange time basis function, and give a detailed derivation of the realization of the time basis function. Through numerical analysis, we compare the advantages and disadvantages between the different orders of time basis functions. It provides a good reference for the choice of time basis function in TDIE via high-order Nystrom scheme.Subsequently, this paper researches and analyses the transient electromagnetic scattering characteristics of dispersive media using TDIE of high-order Nystrom scheme. It adopts the idea of recursive convolution method and combines with the unique advantage of Nystrom scheme, compared with the traditional TDIE based on SWG basis function effectively reduces the computing time and memory consumption, and has good stability.Frequency domain integral equation makes an important step in solving electromagnetic problems by introducing the multilevel fast multipole algorithm (MLFMA). Plane wave time domain (PWTD) algorithm is a fast method based on the development of MLFMA, with a strict mathematical foundation in TDIE-based MOT scheme. Finally, PWTD accelerator is applied in TDIE, effectively extends the practical ability of the proposed method to analyze the electromagnetic scattering characteristics of dispersive media.