The Study Of High Efficient And Fast Algorithms For The Solution Of Volume Integral Equations In Electromagnetics

The electromagnetic scattering analysis from dielectric objects is one of the important subjects in computational electromagnetics(CEM).In this dissertation,the electromagnetic scattering from dielectric objects is solved by the volume integral equation method of moments(VIE-MoM).The principle,the implementation procedure as well as the numerical characteristics of the VIE-MoM are studied.Several high efficient and fast algorithms to solve VIE are proposed in this dissertation.This dissertation firstly gives a review for the development of CEM and MoM briefly.Then,the following aspects of the VIE-MoM are studied in depth:(1)the numerical characteristics of the VIE-MoM using the SWG basis function;(2)the domain decomposition algorithms for volume integral equation;(3)the direct solution algorithms based on the hierarchical matrix(H-Matrix)for VIE.In this dissertation,the VIE-MoM and several commonly used basis functions are firstly introduced.Then,the formulation and the techniques dealing with the singular integrals for the impedance matrix elements are derived in detail when discretizing VIE using the SWG basis function.In consideration of the associated numerical results,the accuracy and the iterative characteristics of VIE are studied.According to the physical characteristic of the equivalent volume currents,we propose to use the Full-and Half-SWG basis functions to deal with the problems involving the piecewise homogenous dielectric objects.Compared with the scheme using the constant vector basis functions,the number of unknowns of the VIE has been decreased.As VIE is commonly used to deal with the inhomogeneous dielectric object problems involving multi-materials,we propose to solve the VIE using the domain decomposition algorithm.By the use of this algorithm,the efficiency of the modelling and discretization process has been improved,and at the same time avoiding the increase of the number of unknowns which is caused by the traditionally used conformal meshes.The piecewise constant vector basis function and the SWG basis function have been used in this algorithm.The details of the associated formulation and the techniques dealing with the hypersingularity have been presented.The numerical results show that by the use of the proposed domain decomposition algorithm,the number of unknowns of VIE-MoM has been decreased greatly when dealing with the multi-scale problems.The solution efficiency of the VIE-MoM has also been improved accordingly.When solving the corresponding matrix equations resulted from the VIE-MoM by iterative algorithm,the number of iterations for iterative algorithm will be increased rapidly with the increase of the permittivity.And for those problems associated with the multi right-hand sides,the solution efficiency of the iterative algorithm is relatively low.To overcome these difficulties,the direct solution method for VIE based on the H-Matrix has been applied.The influencing factors on the accuracy and efficiency of the direct solution method as well as the complexity of the algorithm have been studied.Moreover,this direct solution method has been used to solve VIE efficiently for the problems associated with the high-permittivity and multi right-hand sides.This avoids the poor solution efficiency of iterative algorithms when solving these kinds of problems.