Theory And Application Research On Synthetic Basis Functions Method

Accurate analysis of targets' electromagnetic properties is always a research hotspot in the field of electromagnetism,and it has been widely applied into such cases as antenna design,stealthy design,target recognition,and electromagnetic compatibility analysis of electronic systems.Compared to measured methods,numerical simulating methods are more frequently used in the analysis of electromagnetic problems due to a series of advantages: low cost,high efficiency,controllable accuracy,and etc.This work begins with a classic numerical approach: method of moment(MoM),and a high order MoM called synthetic basis functions method(SBFM)is studied here.In contrast to traditional MoM,SBFM uses a series of high order synthetic functions to discretize surface currents and to make inner products.Thus,a high compressed matrix equation will be yielded which greatly decreases the number of unknowns.So,SBFM makes it possible to analyze large scale problems in a personal computer.Besides,for periodic structures,synthetic functions defined on different sub-blocks can be reused for the sake of geometrical similarity and this greatly improves SBFM's efficiency in the analysis of large scale arrays.Based on the current theory,this work conducts a further research on SBFM and the work can be generally classified into two categories: theory research and application research.For the theory research part,we first analyze the surface integral equations(SIE)for bodies composed of perfect electric conductors(PEC),homogeneous dielectrics,and composite metallic and dielectric mediums.Then,MoM is used to solve these SIEs,and based on this,electromagnetic analysis of complex 3D models is achieved.After that,SBFM is also adopted to solve SIEs.Based on the relationship between MoM and SBFM,we develop the code of MoM yielding the code of SBFM.Finally,intrinsic features of SBFM are discussed: 1)We analyze the influence of truncation error on the stability of SBFM.Then,based on the singular values of synthetic functions' solution space,an index called capability of description(CoD)of solution space is defined and used to determined the number of synthetic functions which is helpful to improve SBFM's stability.2)We analyze the influence of matrix decomposition on accuracy and efficiency of SBFM and find the phenomenon that,only one synthetic function is enough to get a satisfying accuracy.Then,through theoretical analysis,we give a sound explanation on the phenomenon.For the application research part,we first introduce the application of SBFM in the analysis of periodic structures composed of three kinds of mediums: perfect electric conductors,homogeneous dielectrics,and composite metallic and dielectrics.Then,an improved SBFM is proposed for the quasi-periodic structures-I whose sub-blocks merely share identical/similar contour features but spatial attitudes,spatial positions,and geometrical sizes can be arbitrary.And for the improved SBFM,synthetic functions defined on different sub-blocks can be reused.Apart from that,a multi-level domain decomposition scheme is also proposed for the quasi-periodic structures-II whose sub-blocks possess different geometries.This scheme makes SBFM has the ability to analyze multi-type,multiscale arrays.Finally,in the application of complex large scale targets,the concept of global auxiliary sources is defined.Based on global auxiliary sources,we simplify the calculation of mutual impedance matrix between targets and auxiliary exciting sources in the construction of synthetic functions and an automatic scheme for domain decomposition is also proposed for the process of preprocessing.This automatic scheme can greatly decrease the manual interventions and improve autonomy of SBFM in the analysis of complex large scale targets.Finally,based on SBFM,a novel approach called stepwise MoM and a matched iterative process are proposed which can be used to analyze large scale array problems.Compared to SBFM,stepwise MoM is more efficient as it does not need to construct synthetic functions.And compared to classic iterative solvers,suach as biconjugate gradient stabilized method(BiCGSTAB),the proposed iterative process converges more quickly.