Researches On Fast Method Of Moment Based On Rank-structured Matrix

The numerical calculation method of modern electromagnetic field plays an important role in target stealth technology research,target character recognition and radar system design.With the demand of electromagnetic characteristic analysis of the electrical large-scale target,the acceleration method of numerical algorithm is widely concerned.The Method of Moment(MoM)is an integral equation method,which has the advantage of small number of unknowns and automatically satisfies the boundary conditions of infinity.Therefore,it is especially suitable for the calculation of target scattering and radiation characteristics.In addition,as the rank-structured matrix has received wide attention in recent years,(39)-matrix,(39)~2-matrix and HSS matrix have great applications in solving integral equations and differential equation problems.In this paper,based on the Method of Moment and the research on the Fast Multi-pole Method(FMM)and Multilevel Fast Multi-pole Method(MLFMA),understand the basic principle of matrix accelerate algorithm,and then by studying the development of rank-structured matrix,acceleration method is presented based on rank-structured matrix.The paper mainly includes the following three contents:Firstly,the basic theory of Moment of Method is introduced,including the derivation of integral equation,the RWG basis function and the weighted residual method.Then,the basic mathematical form of FMM is derived by using the addition theorem and the plane wave of Green function,and the radiation,reception and transfer equations are obtained by combining the integral equation of MoM.Based on the one-level FMM theory,the theoretical basis and algorithm of MLFMA are derived.Finally,the effectiveness of MFLMA algorithm is verified by comparing with simulation results of MoM.Secondly,the basic theory of the rank structure matrix is introduced,including the basic form of structure matrix and the basic principle of low rank approximation.Based on the ULV decomposition algorithm,this paper proposes how to solve the matrix equation of MoM by using the single-level rank structure matrix,and gives the specific flow of the algorithm and analyzes the complexity of memory reduction.Finally,the effectiveness of the algorithm is verified by numerical simulation.Finally,the hierarchical semiseparable matrix(HSS)in multiple rank-structured matrix is introduced,and the basic theory and structure of HSS matrix are introduced.Through the analysis of the low rank characteristic of matrix,the effective compression of the matrix nondiagonal block is proposed through the RWG base function space grouping.This paper introduces the latest randomized sampling algorithm based on ID(Interpolative Decomposition)and applies it to MoM solution with HSS matrix.Finally,an example is given to demonstrate the advantage of the algorithm to improve the computing efficiency and reduce the memory consumption.It was believed that the matrix obtained by the basic method of moments is dense generally dense,but the rank structure matrix theory point of view,this kind of matrix can seem as sparse structure based on the low rank characteristics of the diagonal blocks,which constitutes the theoretical basis of the algorithm in this paper.