边界局部变化的高效电磁场积分方程方法研究

It is of great theoretical significance and engineering application value to study the accurate and efficient electromagnetic integral equation methods for solving boundary value problems with local boundary changes, because such problems are widespread in areas such as electromagnetic optimization. For this kind of problems, this project divides the target under analysis into two parts: variable local free structure and invariable electrically large mother structure, and study the fast methods based on the partitioned inverse formula and the Sherman-Morrison-Woodbury (SMW) formula for solving electromagnetic integral equations in two frameworks: mesh and meshless. In order to further improve the computational efficiency and the reliability of the proposed method, the fast calculation of the inverse matrix of the self-impedance matrix of the electrically large mother structure is studied by using the characteristic basis function method, the multilevel fast adaptive cross approximation algorithm and the SMW formula-based fast direct solver. Furthermore, combined with the intelligent optimization algorithm, the proposed method is employed to solve electromagnetic optimization problems, such as aircraft shape and coating stealth; combined with the quasi static method, the proposed method is employed to solve electromagnetic local boundary time-varying problems, such as the helicopter modulation effect on antenna and the field uniformity of reverberation chamber for a moving mechanical stirring. Research achievements can not only promote the development of the electromagnetic fast direct method, and also can be applied to fast solve a variety of electromagnetic engineering electromagnetic optimization problems and local boundary time-varying problems.

针对电磁优化设计等领域广泛存在的形状局部变化的边值问题，研究精确高效的电磁场积分方程方法具有重要的理论意义和工程应用价值。本项目在有网格和无网格两种框架下展开研究，将待研究目标分成局部变化的自由结构和不发生变化的电大母体结构两部分，利用部分逆公式和Sherman-Morrison-Woodbury (SMW)公式研究电磁场积分方程快速直接求解方法。为了进一步提高计算效率和方法的可靠性，采用特征基函数法、多层快速自适应交叉近似算法以及SMW公式研究电大母体结构自阻抗矩阵的逆矩阵的快速计算。在此基础上，结合智能优化算法，研究飞行器的外形隐身和涂敷隐身等电磁优化设计问题；结合准静态方法，研究直升机天线调制效应和机械搅拌混响室场均匀性等边界局部时变电磁问题。研究成果不仅可以促进电磁场快速直接求解方法的发展，而且可以应用于快速求解电磁工程实际中各种电磁优化设计问题和边界局部时变问题。

在电磁工程问题中，大量存在着边界局部变化的边值问题，针对此类问题的算法研究具有重要的理论意义和工程价值。本项目研究求解此类问题的精确高效积分方法，取得若干有价值的研究成果。主要研究成果和进展包括：(1)在算法方面：提出一种精确高效的局部变化算法(PMA)。该算法将任意一种形式的局部变化转化成先减去一个小结构，再加上一个小结构，具有很好的普适性。提出利用网格修改算法(MMA)和积分方程不连续伽略金(IEDG)技术提高局部变化算法的灵活性，使其允许原始结构和变化结构网格不匹配，二者可以独立剖分。使用SMWA快速直接求解算法和特征基函数法(CBFM)提高局部变化算法的计算效率。(2)在应用方法：将局部变化算法拓展应该到腔体内散射的局部变化问题。与阻抗边界条件(IBC)结合，将其拓展应用到腔体局部涂覆吸波材料的电磁散射问题中。与薄介质算法结合，将其拓展应用到一般目标局部涂覆吸波材料的电磁散射问题中。除此之外，还对其它的高效积分方法方法进行了研究。本项目共发表期刊和会议论文13篇，其中有6篇期刊论文发表在计算电磁学领域具有影响力的IEEE和IET系列期刊上。