Research On Problem Of Low Frequency Breakdown By EFIE

Full-wave electromagnetic modeling for multiscale structures with high efficiency is urgently needed for engineering application. This is a great challenge for all computational electromagnetics methods. The electric field integral equation (EFIE) solved by the method of moments (MoM) using the Rao-Wilton-Glisson (RWG) expansion functions is one of the most popular full-wave methods, and has been applied to almost all electromagnetics problems. However, it is still very challenging to apply the method to low frequency problems or multiscale structures because of their complex geometries. When a portion or all of the mesh elements are of small electrical size, the vector potential is much smaller than the scalar potential in the conventional EFIE. Since the vector potential matrix is loss, the matrix system is ill-conditioned and even breaks down due to finite machine precision. This low-frequency characteristic issue is well-known as low-frequency break down.This thesis firstly analyzes the reason of the low-frequency breakdown problem, and introduces the most popular remedy, called the Loop-tree or Loop-star decomposition. But the Loop-tree based method is always burdened by the need to search for loops, which is especially difficult for complicated geometries which have many entangled long loops. In addition, the method will be fail at higher frequencies.In this thesis, a kind of connection matrix based on the relationship between triangle meshes and RWG basis functions is presented to build an augmented electric field integral equation (A-EFIE), which is used to modify the tradition EFIE through the equation of charge continuity. In order to avoid the imbalance between the vector potential and the scalar potential in the conventional EFIE, the potentials are separated to be individual matrix elements in the A-EFIE, which includes both the charge and the current as unknowns. This method can be a full-wave solver to analyze low frequency problems effectively as well as high frequency problems. Several examples are presented to demonstrate the effectiveness of this method.