Nystr (?) Application Of M Method In Electromagnetic Scattering Analysis

Before the digital computer was developed, the analysis and design of electromagnetic devices and structures were largely experimental. Once the computer and numerical languages such as FORTRAN came along, researchers immediately began using them to tackle electromagnetic problems that could not be solved analytically. This led to a flurry of development in a field now referred to as computational electromagnetic (CEM). Many powerful numerical techniques have been developed in this area in the last50years. As the power of the computer continues to grow, so do the nature of the algorithms applied as well as the complexity and size of the problems that can be solved.The extremely wide range of electromagnetic problems has led to the development of many different CEM algorithms, each with its own benefits and limitations. These algorithms are typically classified as so-called "exact" or "low-frequency" and "approximate" or "high-frequency" methods and further sub-classified into time-or frequency-domain methods. Low-frequency (LF) methods include Finite Difference Time Domain Method (FDTD), Finite Element Method (FEM), Method of Moments (MoM); high-frequency Methods include Geometrical Optics (GO), Physical Optics (PO), Geometrical Theory of Diffraction (GTD), Physical Theory of Diffraction (PTD), Shooting and Bouncing Rays (SBR), etc.High-order methods are numerical methods characterized by their ability to obtain higher precision with comparatively small additional effort. We are able to significantly accelerate the part of the precomputation phase devoted to computing near-interaction matrix elements by using high-order regulated kernels, and when a point-based (Nystrom) scheme is used, most matrix elements in the impedance matrix fill step consist of nothing more than a kernel evaluation. And this paper studies higher-order Nystrom methods.A higher-order Nystro-m scheme is presented for the analysis of electromagnetic scattering problems by solving integral equation in this paper. The conventional Nystrom method is a simple and efficient mechanism for discretization of integral equations with nonsingular kernels.Firstly, the development of numerical methods in computational electromagnetic was described, also the principle of the MoM is introduced. Then, the higher-order Nystrom scheme and the higher-order element modeling are demonstrated in detail. Duffy transformation is introduced to remove1/R singularity in this paper. Finally, the basic principle of the Fast Multipole Method (Fast Multipole Method, FMM) and the definition of Radar Cross-Section (RCS) are briefly described.In this paper, the higher-order Nystrom method based on the metal surface integral equation is introduced, which is used to analyze the electromagnetic scattering from three dimensional (3D) conducting objects. Furthermore, this higher-order Nystrom method based on dielectric surface integral equation is introduced, which is used to analyze3D electromagnetic scattering from homogeneous medium.Subsequently, the implementation of the higher-order Nystrom method of volume integral equation process is introduced in detail:formula derivation, matrix evaluation and singularity processing, etc. The Fast Multipole Method is applied to analyze the electromagnetic scattering problems of targets with large electrical size. And finally some numerical results are given to validate the performance of the proposed medthod.This article mainly discusses the application of the higher-order Nystrom method for solving integral equation, and has carried on a preliminary study and laid a solid foundation in order to continue to study the higher-order Nystrom method in the field of computational electromagnetic in the future.