面向电大复杂平台上天线优化设计的高效混合全波数值方法研究

The design and optimization of antennas on a electrically large and complex platform is one of key issues in the complex electronic and information system. Since the above problem involves the solution of large-scale, multi-scale, and multi-media Maxwell equation, it is an essential topic of accurate and fast simulation analysis for antenna and platform integration. In recent years, scholars in computational electromagnetics have conducted a series of studies and achieved certain progress on this issue. However, recent studies are mainly from the aspect of efficient analysis to design general algorithms, and little is from the aspect of optimization to develop advanced algorithms. Not only for the analysis of antenna and platform integration but also simultaneously consider the optimization of antennas’ shape and location which is actual concern in current projects, this project first presents a novel hybrid full-wave numerical method based on surface domain decomposition. This method use nonconformal domain decomposition of hybrid finite element-boundary integral method to deal with antennas region while nonoverlapping domain decomposition method of boundary integral equation to deal with PEC platform region, which is flexible, accurate, and general. Subsequently, taking advantage of antenna design and optimization only relating with modification of finite element matrix in the proposed method, we further reduce the problem of optimization to the repeated solution of small-scale matrix equation only relating with the antenna area through using the Schur complement operation and the interpolative decomposition based low-rank matrix compressing technique. In this way, the efficiency of analysis for optimization of antennas on electrically large platform can be improved significantly.

电大复杂平台上天线的设计与优化是复杂电子信息系统研究的一个关键性问题。由于该问题涉及电大、多尺度、多媒质的麦克斯韦方程求解，对其进行准确快速的仿真分析面临重大挑战。近年来，计算电磁学者针对该问题已取得一定的研究进展，但大多是从分析计算角度进行的一般意义下的算法设计，很少针对平台上天线的优化研究更高效的算法。本项目不仅针对天线与平台一体化仿真分析，同时考虑工程中关心的天线形状与位置的优化设计，首先提出一种新型的基于面区域分解的混合全波数值方法，采用非共形区域分解有限元-边界积分方法模拟天线区域、非重叠型区域分解边界积分方法模拟金属平台区域，具有灵活、精确、通用的优势。其次，利用优化只涉及方法中天线区域有限元矩阵改变的优点，采用Schur补运算和低秩矩阵插值分解压缩技术，进一步将优化问题转降为仅与天线区域相关的小规模矩阵方程的重复求解，能够显著提高电大平台上天线优化分析的效率。

天线作为武器装备（飞机、导弹、舰船等）重要的电磁收发装置，发挥着极其重要的作用。为保证天线的电磁性能，天线与平台的一体化建模分析非常重要。本项目针对该问题，基于有限元方法、边界积分方法和区域分解技术，发展了一种模块化的区域分解混合全波算法，实现天线与载体平台一体化电磁辐射问题的高置信度建模分析。基于该模块化混合全波算法，利用平台的不变性与有限元-边界元非共形区域分解算法的灵活性，提出一种数值格林函数来准确代替平台对局部天线的影响，借助于该平台格林函数，获得一个只与局部天线区域相关的降阶计算模型。该降阶计算模型与传统混合全波模型的精度相当，但由于规模很小计算速度比传统模型提高至少一个数量级，非常适用于复杂电大金属平台上局部部件优化时电磁辐射和散射特性的快速评估。该降阶方法采用线上与线下的计算策略：线下计算平台格林函数、线上求解降阶模型，满足电磁工程师在优化设计时对评估结果快速获取的需求。该方法是对局部优化性能评估的一次少有的尝试，效果非常好，具有很高的应用价值。此外，针对复杂涂覆平台电磁建模问题，提出一种新型的自对偶边界积分方法，在保证高精度的同时比现有方法的收敛性显著提高。基于进程-线程混合并行的策略，面向该自对偶边界积分方法开发了高效的并行计算程序，可用于电大尺度复杂薄涂覆平台电磁辐射和散射特性的快速计算，在装备隐身性能设计与评估方面具有很大的应用价值。