Low Frequency Problems In Computational Electromagnetics, Integral Equation Methods

The development of a number of engineering applications has called for the solution of complex and fine structures when the structures are small compared to wavelength, and yet the complexity of these structures cannot be ignored. As a kind of accurate numerical method, the integral equation has the capability to reliably predict the electromagnetic performance, which has been proved in wide application of scattering problem. When it comes to the complex sub-wavelength structures, however, the low frequency breakdown problem has been observed in the integral equation based method.This thesis is aimed to analysis the low frequency problems in term of the integral equation based method. There are several sections as the following.First of all, the Loop-Tree bases decomposition technology is applied in Electric Field Integral Equation (EFIE) to overcome the low frequency problem. The thesis discusses the reason of low frequency breakdown in EFIE and the algorithm for finding the Loop-Tree bases. Moreover, the basis rearrangement precondition method is studied, which could dramatically improve the iteration speed.At the second place, the fast multipole algorithm (FMA) based the spectral representation of the Green function is introduced. It has been verified that the fast multipole algorithm is highly efficient to solve large-scale electromagnetic scattering problems. But when the discretization is small compared with the wavelength, FMA suffers from the problem of sub-wavelength breakdown. One way to overcome the sub-wavelength breakdown of the traditional fast multipole algorithm is to use the spectral representation of the Green function. Furthermore, a new scheme of integral rule to reduce the memory consumption and the computing cost is proposed in this section.Third, a novel integral method called Augmented Electric Field Integral Equation (Augmented EFIE) is used to solve low frequency problem. Through the process of separating the currents and charges, the Separated Currents and Charges EFIE is free of low frequency breakdown. The Augmented EFIE includes charges as extra unknowns to separate the contribution of the vector and scalar potentials. Furthermore, the Block LU method is applied in the Augmented EFIE to accelerate solving procedure. Finally, the method is used in the solution of extracting the input inductance parameter for some application models successfully.