Study Questions Low-frequency Electric Field Integral Equation Method Crash

With the development of electromagnetism and the technology for engineering, the accurate and efficient analysis of the electromagnetic characteristics of complex targets becomes more and more important. Electric field integral equation (EFIE). as a kind of accurate integral equations method, has been widely used in the analysis of the extraction of circuit parameters and the electromagnetic scattering characteristic. When electric field integral equation (EFIE) are applied to very low frequency scattering computation or the targets subdivision size is far less than the wavelength, there will be a low-frequency breakdown problem.The low frequency breakdown problem in electric field integral equation (EFIE) has been well recognized and extensively studied. The root cause of the low frequency breakdown is finite machine precision and it leads to the loss of the vector potential term. And the rest of the scalar potential information can’t fully describe the surface current distribution which results in low-frequency breakdown. State of the art methods for solving this problem either reformulate the integral equations or introduce a different set of basis functions, including the loop-tree and loop-star basis functions.The low frequency breakdown for the original full-wave EFIE with the Rao-Wilton-Glisson (RWG)-basis functions is analyzed in this thesis firstly. Different from existing methods that tackle the low-frequency breakdown from the perspective of how to change the original matrix,this thesis first to solve a generalized eigenvalue problem of the matrix generated by the vector potential and the scalar potential. By analyzing the contribution to EFIE solution from the eigenvectors and eigenvalues, we found that due to the finite machine precision which is the root cause of the low-frequency breakdown, the smaller eigenvalues are not distinguishable.We also overcome the low-frequency breakdown caused by the loss of the frequency dependence of the right hand side vector in scattering analysis and the same loss in Green’s function in RCS computation. Based on the idea of the generalized eigenvalue, this thesis puts forward a kind of low frequency rapid analysis scheme that the solution at low frequency can be quickly figured out by obtaining a solution vector from the traditional EFIE solver. Numerical experiments in inductance, capacitance, and RCS extraction at very low frequencies including DC have demonstrated both accuracy and efficiency of the proposed method.Secondly, it can be found that the low frequency problem also exists in the analysis of scattering problem from a metallic target for Nystrom method.Using the method mentioned in this thesis to overcome the low frequency problem for Nystrom method, the idea of which is that solving the system matrix equation was transformed into solving the generalized eigenvalue problem. Numerical example results of low frequency scattering problem show that this method is accurate.At the end of this thesis, it is discussed when the volume-surfaced integral equation method is used to calculate the scattering problem from the metallic and dielectric targets whether there is a low frequency breakdown phenomenon. Generalized eigenvalue method is also applied to the volume-surfaced integral equation method. It can be found that the proposed method is efficient to overcome the low frequency problem of the volume-surfaced integral equation method.