用于复杂多尺度电磁问题的新型非共形积分方程方法研究

Accurate and efficient numerical modeling of electromagnetic scattering from a target is an important and fundamental research topic in the area of stealth and anti-stealth design. Due to the increasing complexity of modern stealth combat system, the target under analysis usually possesses electrically-large structures and fine components simultaneously. Traditional computation methods usually cannot handle large-scale matrix from electrically-large structures and ill-conditioned matrix due to fine components, and the iterative solvers cannot converge correctly. What is worse, due to this multiscale feature, uniform geometrical modeling is extremely difficult, which may lead to a failure of the traditional computation methods that rely on uniform conformal mesh. Therefore, geometrical modeling is gradually becoming the bottleneck in the theoretical prediction of electromagnetic characteristics. To address this problem, we study the theory and application of a novel non-conformal integral equation method. The main contents include: (1) non-conformal geometrical modeling method based on surface decomposition and mixed elements; (2) definition of a novel square-integrable basis function and its dual testing in integral operators; (3) treatment of the hyper-singular integral with the methodology of reverse operation self-consistent evaluation; (4) domain decomposition preconditioning method based on non-conformal integral equation. Based on the innovative research, we aim to realize accurate and efficient numerical modeling of typical complex multiscale electromagnetic problems.

目标电磁散射的精确高效数值建模是隐身与反隐身设计领域的重要基础研究课题。由于现代隐身作战系统的日益复杂化，待求解目标通常具备电大结构和精细部件并存的特点。传统计算方法常常难以兼顾电大结构带来的矩阵大规模性和精细部件带来的矩阵病态性，造成迭代算法难以收敛到正确解。更为严重的是，由于该多尺度特性，一体化的几何建模极为困难，导致依赖于一体化共形网格的传统计算方法几乎失效。因此，几何建模正逐渐成为电磁特性理论预估的瓶颈。为解决上述问题，本项目拟开展新型的非共形积分方程方法理论及应用研究。主要研究内容包括：(1)基于目标表面几何特征分区及混合单元的非共形几何建模方法；(2)新型平方可积基函数的定义及其在积分算子中的对偶测试；(3)基于逆向操作自洽推演算法的超奇异性积分方法；(4)基于非共形积分方程的区域分解预条件方法。通过上述创新研究，实现典型复杂多尺度电磁问题的精确高效数值模拟。

目标电磁散射特性的精确高效建模在雷达系统设计、隐身与反隐身等领域发挥着重要作用。随着技术的不断发展，各类目标的外形结构、组成材料日趋复杂，使得传统基于积分方程的电磁建模方法变得越发困难。目标电大平台与精细结构并存的多尺度特性使得一体化几何建模极为困难，生成的网格往往质量低下、非均匀特性显著。网格的多尺度特性直接导致电磁建模得到的矩阵极为病态，严重影响迭代求解器的迭代效率与求解精度。同时，大量复杂介质材料的运用进一步增大了电磁分析的难度。针对上述问题，本项目开展了针对复杂多尺度目标的非共形积分方程方法研究。项目首先研究了基于目标几何特征分区和混合网格的非共形几何建模方法，对网格质量剖分和质量优化进行了深入研究；其次，针对平面网格，发展了一种零阶平方可积基函数，使基函数定义更为灵活，针对曲面网格，研究了高阶叠层矢量基函数，使得建模未知量显著下降；第三，针对两类网格和基函数，分别研究了基于逆向操作自洽推演算法和改进型双正切变化技术，解决了积分方程并矢格林函数导致的超奇异性积分难题；第四，针对大型病态矩阵迭代求解不收敛难题，发展了基于叠层矩阵的快速直接求解方法，避免了矩阵迭代，结合高阶技术，使直接求解的计算能力得到大幅提升；第五，针对分层介质材料建模，发展了基于局部耦合的区域分解方法，使系统矩阵稀疏化，并构造了性态优良的全局预条件矩阵，同时，针对多层背景介质中的目标，研究了基于分层介质格林函数的特征模分析方法，重点研究了低频情形下数值崩溃现象与改善措施。本项目研究为复杂电磁分析提供了新的思路，解决了多尺度电磁散射建模中的若干重要问题，为相关电磁预估工具的研发与工程应用的深入开展打下了坚实的基础。