Study On Interpolation Decomposition Algorithm For RCS Calculation From Heterogeneous Medium Target

With the rapid development of science and technology,in various fields of society,especially satellite communications,remote sensing detection,and military fields,metallic media and homogeneous media can no longer meet the needs of modern equipment.The research of heterogeneous media has been put on the agenda.The method of moments is a relatively classic method of studying electromagnetic problems.It can be used to solve the electromagnetic problems of heterogeneous media.However,it has the disadvantages of large memory consumption and low calculation efficiency.So it is necessary to compress and decompose the impedance matrix of the method of moments.This paper uses Interpolative Decomposition(ID)to carry out this compression and decomposition process.This paper is mainly based on the Volume Integral Equation(VIE)to study the interpolation decomposition algorithm for RCS calculation of heterogeneous media.Firstly,the application of PCV(Piecewise Constant Vector)basis function in RCS calculation of heterogeneous media target is studied,and then ID algorithm is combined with the method of moments based on PCV basis function,and the ID-PCV joint algorithm is proposed.The calculation results of the joint algorithm are in good agreement with the calculation results of finite element.Compared with the method of moments based on PCV basis functions,the storage capacity of the joint algorithm is significantly reduced,and the iteration time of each step in the process of solving the matrix equation is also significantly reduced.In order to improve the computational efficiency of the ID-PCV joint algorithm,this paper further proposes an improved ID-PCV joint algorithm.Compared with the ID-PCV joint algorithm,the accuracy of the calculation result of this algorithm is basically the same,but the calculation speed is significantly improved.Both of the above-mentioned algorithms have been verified by the example model to ensure the correctness and effectiveness of algorithms.The main content of this paper is as follows:First,this paper introduces the principle of the method of moments,analyzes the selection rules of test functions and basis functions,then derives the volume fraction equation and related formulas in detail.The processing of tetrahedral elements and the solution of radar cross section are introduced,and related formulas are derived.Next,this paper first studied the SWG basis function,but when solving the electromagnetic scattering problem of inhomogeneous dielectric body through the SWG basis function,it is more troublesome to deal with the non-conformal problem at the interface.So the PCV basis function was chosen to solve this problem.This paper studies the principle of the PCV basis function,derives the relevant formulas,and derives the process of applying it to the method of moments in detail,and verifies the calculation results of the method of moments through an example model.The results show that: the method of moments based on PCV basis functions has a high accuracy in calculating the RCS of inhomogeneous dielectric bodies.Then,this paper combines the interpolation decomposition algorithm with the method of moments based on PCV basis functions,and proposes a joint ID-PCV algorithm.The joint algorithm is mainly to solve the problem of excessive storage consumption when the method of moments based on PCV basis function calculates complex heterogeneous media objects.This paper studies the principle of the joint algorithm,derives its basic formula,analyzes its feasibility,and derives its implementation process in detail.The algorithm uses ID to compress and decompose the original impedance matrix,which greatly reduces the amount of storage required and improves the iteration speed of each step in the process of solving the matrix equation.Then,the algorithm was verified by numerical example models to ensure the effectiveness and accuracy of the algorithm.Finally,in order to further improve the computational efficiency of the ID-PCV joint algorithm,this paper proposes an improved ID-PCV joint algorithm.The main idea is to change the method of layered calculation and compression of the far-field impedance matrix of the ID-PCV joint algorithm to the method of centralized calculation in the last layer,to balance the storage capacity and the calculation efficiency,so that while reducing storage consumption,the calculation time is also greatly reduced.Finally,the effectiveness and accuracy of the algorithm are verified by example models.