项目名称： 复杂电磁环境下相控阵天线电磁仿真的低秩分解技术研究

项目编号： No.61501159

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 无线电电子学、电信技术

项目作者： 姜兆能

作者单位： 合肥工业大学

项目金额： 19万元

中文摘要： 随着现代军事技术的发展，对相控阵天线电磁特性的快速分析研究越来越受到关注和重视。得益于计算机技术的快速发展，电磁场数值技术逐渐成为相控阵天线电磁特性研究的重要手段。课题根据数据的稀疏特性，研究几种基于QR分解算法的快速低秩分解技术。矩阵低秩分解算法作为电磁学中日益重要的数值方法，具有模拟复杂结构通用性强、计算精度可控等优点。传统QR分解算法在分析电大尺寸问题时，占有的资源比较大，且计算时间比较长，不利于快速分析大型相控阵天线电磁特性问题。为此，研究几种低秩分解技术用于改进QR分解算法。主要有：基于QR分解的新型再压缩技术、基于树形结构层层嵌套形式QR分解算法、基于嵌套形式QR分解的快速直接解法及混合方法等。该类方法主要利用树形结构中远场矩阵具有很好的低秩特性原理，对QR分解形成的子矩阵进行再压缩，可以显著地降低内存消耗及计算时间，为复杂电磁环境下相控阵天线电磁特性研究提供重要的分析途径。

中文关键词： 低秩分解算法；矩量法；相控阵天线；全波分析

英文摘要： With the development of modern military technology, rapid analysis of the electromagnetic characteristics of phased array antenna gets more and more attention. Due to the rapid development of computer technology, the numerical technique has gradually become an important mean for analyzing the electromagnetic characteristics of phased array antenna. According to the sparse characteristic of data, this project studies several fast low-rank decomposition techniques based on QR decomposition algorithm. As an increasingly important numerical method in electromagnetic, the matrix low-rank decomposition method with the simulation of complex structure versatility and the precision of calculation is controllable. For the electrically large problems, the traditional QR decomposition algorithm consumes a lot of computer resources and the computation time is very long, not conducive to the rapid analysis of electromagnetic characteristics of the large-scale phased array antenna problems. Therefore, several low-rank decomposition techniques are researched to improve the QR decomposition algorithm. The main research contents include a new post-compression technique based on QR decomposition algorithm, the nested form of QR decomposition algorithm, fast direct solution method based on the nested form of QR decomposition algorithm and hybrid method etc. This kind of methods utilize the low-rank of the far-field matrix to compress the matrices of QR decomposition algorithm, so as to obtain the sparse form of impedance matrix, can significantly reduce the memory consumption and computation time, provides an important way for the analysis of electromagnetic of the phased array antenna in complex electromagnetic environment.

英文关键词： low-rank decomposition algorithm;method of moments;phased array antenna;full wave analysis