基于逆算子自恰算法的积分方程区域分解法研究

Complex multi-scale time-harmonic electromagnetic problem is one of hot topics in modern electronic information filed which exists broadly but is hard to achieve accurate and efficient numerical solution, for example, optimal design of antenna on complex platform with electrically large sizes, signal integrity and EMC problems in high-speed IC, electromagnetic modeling of nano structures. Because electrically large structures and electrically small, fine structures exist together, traditional numerical methods for partially differential equations are difficult to deal with large scale matrix from electrically large sizes and ill-conditioned property due to fine structures, they can not converge into correct solutions in general. So analysis of the complex multi-scale time-harmonic electromagnetic problem becomes an important computation issue to solve. To solve the above problem, we plan to research the integral equation domain decomposition methods (IE-DDM) based reverse operation self-consistent evaluation (ROSE) and its applications in this proposal. The contents will cover the novel IE-DDM scheme, new transmission conditions and filling technology for non-conformal mesh case and iterative technique with high convergence and high stability for the above IE-DDM. The goal of this proposal is to build robust, efficient numerical tools available for analysis of typical multi-scale time-harmonic electromagnetic problems, It has important academic significance and engineering value.

复杂多尺度时谐电磁问题是现代电子信息领域广泛存在但却难以实现精确高效数值求解的热点问题，诸如复杂电大平台上的天线优化设计、集成电路中的信号完整性和电磁兼容性问题、纳米电子结构电磁建模问题等等。由于电大宏观结构和电小精细结构并存，传统求解偏微分方程的数值方法难以兼顾电大结构带来的大规模矩阵和精细结构带来的病态特性，难以正常收敛到正确解，因此复杂多尺度时谐电磁问题成为了急待解决的重要计算难题。为解决这一难题，本项目拟针对多尺度时谐电磁问题开展基于逆算子自恰算法的新型积分方程方法区域分解方法理论及应用研究，包括新型积分方程区域分解法理论、逆算子自恰算法中的插值和映射技术、非共形网格新型传输条件及填充技术、高收敛性和高稳健性的迭代技术和预条件技术等方面。通过算法研究，最终形成可资典型复杂多尺度时谐电磁问题利用的可靠高效数值分析工具，具有重要的学术意义和工程价值。

复杂目标电磁特性建模研究及应用在现实电子工程领域扮演着越来越重要的角色，不断发展的工程需求期待着计算结果更为准确、计算效率更高、内存需求更低的高效电磁建模方法。本项目主要研究基于逆算子自洽算法的积分方程区域分解算法及其工程应用。通过分而治之，区域分解方法将复杂的大问题转变为更易求解的小问题进行求解。通过研究，针对各类复杂多尺度目标，本项目建立了复杂目标电磁特性问题高效数值分析的新型积分方程区域分解方法框架。深入探究了表面积分方程区域分解法、体积分方程区域分解算法，及其混合方法的区域分解方法；形成了直接求解器和迭代求解器两套计算框架；成功用于复杂多尺度目标电磁散射特性快速数值计算；深入研究了混合2D/3D的时域不连续伽略金方法及时域问题的高效计算。最终研发出适合于远近场建模的高效电磁模块。本项目研发的数值代码在国内率先成功实现了电大尺寸多尺度高逼真度复杂整机的电磁散射计算。本项目成果已经用于隐身飞机等重要目标电磁特性预估与分析，在电磁散射建模理论和目标特性工程上都具有重要的学术和应用价值