复杂金属-介质体混合结构宽带电磁散射/辐射问题的高效算法研究

Despite the frequency domain volume-surface integral equation (VSIE) based on method of moment(MOM) is versatile and suitable for processing the electromagnetic scattering and radiation problems, implementation of the algorithm is still difficult for its high computational complexity and memory requirements, VSIE based on method of moment and its fast algorithm are involved little, and it needs to be improved for its less computational efficiency. The project intends to study the high-order VSIE-MOM based on hierarchical vector basis functions and its fast algorithm of the electrically large composite metallic and anisotropic material with the fine structure. First, using Multi-Level Fast Multipole Algorithm (MLFMA) to significantly reduce the computational complexity of the electrically large structure and combining MLFMA with Multi-Level Accelerated Cartesian Expansion Algorithm (MLACEA) to avoid the dramatic increase in the computational amount and memory requirements of the MLFMA in processing the objects containing fine structure and dielectric. Second, using a impedance-matrix-normalized basis functions and the matrix preconditioning technique to efficiently accelerate the convergence of theiterative method. Finally, studying the interpolation and extrapolation techniques in the angular and frequency domain. This theoretical research and its accurate and efficient algorithm not only have important academic value, but also have broad application prospects in analyzing and designing a scale of integrated circuits, geo-physical exploring, military projects and other practical engineering fields.

尽管频域体面积分方程(VSIE)矩量法通用性强且适用范围广，但因算法及程序实现困难、计算量及内存需求大，国内外对VSIE矩量法及其快速算法研究较少且计算效率亟待提高. 本项目拟利用基于高阶叠层矢量基函数的体面积分方程高阶矩量法及其快速算法模拟含有精细结构的电大尺寸复杂金属-介质体混合结构的宽带电磁散射/辐射问题. 利用多层快速多级子算法(MLFMA)大幅降低电大尺寸结构的计算复杂度，同时采用MLFMA-MLACEA混合快速算法以避免因含有精细结构、介质体等所导致的MLFMA算法计算量及内存需求的急剧增加，然后采用基于阻抗矩阵归一化基函数的矩阵预条件技术提高阻抗矩阵方程迭代解法的收敛速度，最后研究用于角域及频域扫描的内插外推技术. 相关理论研究及其精确高效通用算法的实现不但具有重要的学术价值，而且在集成电路分析与设计、地球物理勘探及军事应用等实际工程领域具有广泛的应用前景.

项目研究并首次实现了基于曲三角形/曲四面体和高阶叠层矢量基函数的体面积分方程高阶矩量法，大幅度降低了求解复杂金属-介质体混合结构的宽带电磁散射/辐射问题的未知量数目、计算量和内存需求；采用MLFMA-MLACEA混合快速算法有效地降低了含有精细结构目标和介质体目标的计算复杂度；与基于低阶矩量法的快速算法相比，基于积分方程高阶矩量法的快速算法具有更低计算量和内存需求，对于高对比度介质体目标尤为明显；采用基于阻抗矩阵归一化基函数的矩阵预条件技术提高了阻抗矩阵方程迭代解法的收敛速度；最后，利用缩减基法(RBM)初步研究了目标的宽角域及宽频带电磁散射问题，实现了精度可控的宽频带和宽角域电磁散射分析的快速插值算法. 相关理论研究及其精确高效通用算法的实现不但具有重要的学术价值，而且在集成电路分析与设计、地球物理勘探及军事应用等实际工程领域具有广泛的应用前景.