Study On Impedance Matrix Sparsity Algorithm For Electromagnetic Scattering Calculation

The electromagnetic scattering of metal conductors has always been the focus of computational electromagnetic research,which has important research significance for radar communication and stealth aircraft and other military scenarios.Through the efforts of many experts and researchers in the field of computational electromagnetics,there are already many theoretically mature numerical methods used to study electromagnetic scattering problems.How to reduce the storage required for calculation and speed up the solving speed have always been the core issues to be considered by these numerical methods.Each of these numerical methods has its advantages and disadvantages,and it can be applied to different practical scenarios according to its own characteristics,Most of the algorithms decompose the matrix based on its mathematical properties,that is,compress the impedance matrix.Matrix sparsity algorithm is one of the most common matrix compression algorithms.Its core idea is to reduce the calculation amount and storage required by matrix dimensionality reduction decomposition,and speed up the solving speed during iteration.The framing decomposition algorithm studied in this paper is based on the mathematical principle of interpolation decomposition.After the target is stratified,because the far-field submatrix has the property of low rank,the far-field impedance matrix filled by the method of moment is decomposed by the framing algorithm.In this way,the storage capacity needed to store the impedance matrix is reduced and the speed of solving the matrix equation is improved.The main work of this paper is as follows:Firstly,this paper introduces the integral equation of electromagnetic field and the method of moment for studying the electromagnetic scattering of metal objects,and deduces the process of using the method of moment to discretize the integral equation and the related formulas in detail,and gives the method to deal with the singularity of the element of impedance matrix.Next,the framing decomposition algorithm of matrix sparsity is studied,its mathematical principle is introduced in detail,and the related formulas are deduced.In this chapter,several simple numerical examples are used to verify the accuracy and effectiveness of the framing decomposition algorithm,and the performance of the algorithm is compared with the traditional method of moments.The advantages of the framing decomposition algorithm are demonstrated.Then,in order to improve the performance of the framing decomposition algorithm and apply it to complex electromagnetic models,a new method combining the framing decomposition algorithm and the adaptive crossover approximation algorithm is proposed in the fourth chapter of this paper,the calculation scheme of the algorithm is given and its feasibility is analyzed.The basic idea of the new algorithm is as follows: Using octree structure to layer the targets,the framing algorithm is used to process the far-field impedance matrix of the thinnest layer,and the ACA algorithm is used to process the far field of the other layers,thus,the scattering problem of complex electromagnetic target can be solved effectively,and the storage capacity required for calculation can be reduced obviously,and the iteration speed can be accelerated.This chapter also tests the accuracy and effectiveness of the joint algorithm through the experimental results of several complex models.In order to further enhance the performance of the above algorithm,this paper optimizes and improves it in Chapter 5,and puts forward the improved algorithm combining the framing decomposition algorithm and the adaptive crossover approximation algorithm.Compared with the original algorithm,the improved joint algorithm has a higher solving speed and overall performance,and some complex examples are given to verify and analyze the improved joint algorithm.Finally,in chapter six,this paper makes a detailed summary of the work done,explains the areas to be improved in this paper,and looks forward to the future scientific research work.