Study On Matrix Compression Algorithm For Electromagnetic Scattering Calculation

Electromagnetic scattering calculation has very important significance in the communication,remote sensing detection and the construction of national defense.Therefore,the study on the fast electromagnetic scattering calculation has always been a hot topic.Up to now,there are a lot of excellent numerical methods to solve the electromagnetic scattering problems,both of them have their own application scenarios and advantages,but classical algorithms are difficult to quickly solve the large electromagnetic scattering problem.In order to quickly solve large electromagnetic scattering problems,this paper mainly studies the matrix compression algorithm for electromagnetic scattering calculation,which is a fast algorithm to solve the impedance matrix or matrix equation established by the method of moment.It can be roughly divided into two categories: the first type is the algorithm that decomposes the matrix by taking advantage of the low-rank property of the far-filed matrix to reduce the storage space and speed up the solution speed,such as the adaptive cross approximation algorithm(ACA);The second type is a fast algorithm for dimension reduction of large matrix equation by using characteristic basic function,such as the characteristic basis function method(CBFM).This paper focuses on matrix dimension reduction compression algorithm and proposes a joint algorithm which realizes the compression and quickly solution for larger dimension matrix equation by combine Krylov subspace iterative domain decomposition algorithm(called Krylov subspace dimension reduction algorithm)and adaptive cross approximation algorithm.This algorithm divides the surface of the target model into server subdomain and constructs Krylov subspace dimension reduction matrix on each subdomain.Through this dimension reduction matrix,the large matrix equation which is difficult to be solved can be reduced to a small matrix equation which can be solved by the direct method,this algorithm avoids the iterative solving process of the large matrix equation,which not only reduces the memory required by the algorithm,but also reduces the computation required by the algorithm.The main contents of this paper are as follow:Firstly,the method of moment in computational electromagnetics is introduced in detail,and the formula of surface integral equation is derived,and the method of discretization of surface integral equation by the method of moment is emphasized.Secondly,this paper mainly focuses on Krylov subspace dimension reduction algorithm,briefly introduces the theory,deduces its mathematical principle in detail,and expounds its implementation process.Comparing with the numerical example of the method of moment,the results show that the Krylov subspace dimensionality reduction algorithm has obvious advantagesHowever,Krylov subspace dimension reduction algorithm still inevitably exsit the problem that demand for computer storage is too large,the computation time is too long.In order to solve the above problems,and further improve the efficiency of the analysis of electromagnetic scattering problems,this paper puts forward the ACA-Krylov subspace dimension reduction joint algorithm in the fourth chapter,deduces the implementation method and mathematical formula of the joint algorithm in detail,demonstrates the feasibility of the joint algorithm from the principle.This algorithm uses ACA to decompose the original impedance matrix into two low rank matrix's production,which reduce the storage space needed for the algorithm,accelerate the speed of matrix equation to establish,improve the efficiency of the Krylov subspace dimension reduction algorithm,so that the whole algorithm of storage and computation than the original Krylov subspace dimension reduction algorithm has obvious advantages.Then,in order to further promote the efficiency of ACA-Krylov subspace dimension reduction joint algorithm,this paper proposed RACA-Krylov subspace dimension reduction in the fifth chapter,its main idea is to use QR decomposition and singular value decomposition(SVD)to orthogonality compression the low rank matrix compression of ACA,delete the redundant data,thereby further reducing the storage capacity,improve the efficiency of the matrix equation solution.