复杂金属-(高对比度/各向异性)介质体混合目标宽带电磁散辐射问题的高阶矩量法及其快速算法研究

The efficient and accurate modeling method for wide-band domain electromagnetic scattering and radiation from the multicale composite metallic and (high contrast/anisotropy) dielectric targets has been the key research subject in the fields of electromagnetic numerical analysis and target detection. However, the existing methods are generally deficient in the accuracy, efficiency and flexibility. Therefore, a more accurate and efficient numerical modeling method is urgently needed in academic and engineering fields. Based on the higher order geometric modeling and higher order hierarchical vector basis functions, this project firstly foucs on the study of the nonconformal volume surface integral equation with higher order method of moments, and its developed version, i.e., integrated with the domain decomposition algorithm and the MLFMA-MLACEA hybrid algorithm, is adopted to highly reduce the computational complexity for the electric-large size target involving in fine structure and high contrast/anisotropy dielectric. Secondly, based on the integral equation with higher order method of moments, and the fast algorithms, the reduction basis function method integrated with Taylor series expansion algorithm is investigated for the analysis of wide-band electromagnetic problems, further for the achievement of the fast interpolation algorithm with controllable accuracy which is developed for the wide-band and wide-angle electromagnetic analysis. Finally, this proposed new hybrid wideband algorithm above combined with the genetic algorithm integrated is utilized to develop RCS reduction and enhancement optimization strategy for anisotropic material coating targets. The developed theory and the implementation of accurate and efficient algorithm are highly valuable for scientific significance，academic research and engineering application prospect.

具有多尺度结构的复杂金属-(高对比度/各向异性)介质体混合目标宽带电磁散辐射的高效精确数值建模方法一直是电磁数值分析及目标特性领域亟待深入研究的重要课题，但现有方法普遍存在精度、效率和灵活性较低等缺陷，学术和工程上迫切需要一种更为精确高效的数值建模方法。本项目拟首先研究基于高阶几何建模和高阶叠层矢量基函数的非共形体面积分方程高阶矩量法，并结合区域分解算法和MLFMA-MLACEA混合算法以实现大幅降低含有精细结构、高对比度/各向异性介质体的电大尺寸目标的计算复杂度。然后，研究基于积分方程高阶矩量法及快速算法的缩减基函数法和泰勒级数展开算法分析宽带电磁问题，以实现宽频带及宽角域电磁特性分析的精度可控的的快速插值算法。最后，将上述新型混合宽带算法与遗传算法相结合，实现各向异性材料涂敷模型的宽带RCS缩减和增强优化策略。相关理论研究及精确高效算法的实现具有重要的科学意义、学术价值和工程应用前景。

本项目采用高阶体面积分方程(VSIE)算法结合区域分解算法(DDM)、多层快速多极子算法-多层笛卡尔展开算法(MLFMA-MLACEA)混合算法以及缩减基函数法(RBM)和泰勒级数展开(TSE)算法来分析具有频率多尺度和结构多尺度的金属-各向异性介质体混合目标的宽带电磁散辐射特性。从研究内容上看，主要完成了以下4部分工作：（1）针对电大尺寸多尺度金属目标的电磁散射问题，研究了基于面型高阶叠层矢量基函数的MLACE-MLFMA，此快速算法仅通过改变叠层矢量基函数的阶数而非剖分网格便可逐点计算出较宽频段内的电磁散射特性；（2）针对复杂各向异性介质体-金属混合结构目标的电磁仿真，提出了基于体和面型高阶叠层矢量基函数的MLACE-MLFMA，此快速算法仍可通过改变叠层矢量基函数的阶数而非剖分网格逐点计算出较宽频段内的电磁散射特性；（3）基于体面积分方程的MLACE-MLFMA提出了精确快速的VSIE-RBM插值算法。同时，将VSIE-RBM与自适应分段策略（ASS）结合，提出了自适应分段插值方法（VSIE-ASRBM）。与VSIE-RBM相比，VSIE-ASRBM具有更高的宽频带插值计算效率。另外，基于高阶体面积分方程的MLACE-MLFMA提出了精确快速的HOVSIE-RBM插值算法。与VSIE-RBM和VSIE-ASRBM相比，HOVSIE-RBM进一步降低了插值消耗内存，且获得了更高的宽频带插值计算效率；（4）将混合快速算法与简单重叠型区域分解算法结合，提出了基于高阶叠层矢量基函数的快速区域分解算法，即SODDM-HOVSIE。SODDM-HOVSIE有效地改善了高阶体面积分方程混合快速算法的迭代收敛性，同时降低了计算机消耗内存，为计算复杂目标的RBM采样样本提供了技术支撑。从研究成果上看，发表了期刊论文10篇、会议论文29篇，培养了2名博士研究生和5名硕士研究生(另外还有4名硕士研究生在培)。总之，超额完成了项目预期的研究成果。