不连续伽略金电磁场面积分方程方法关键技术及其应用研究

It is still a very challenging task to accurately analyze with full wave method the electromagnetic environment of a complex object such as cabins of planes. The surface electromagnetic integral equation method is an important method for solving these problems. In analyzing these objects, it is usually required to combine together many sub-blocks that are connected with metals. In order to get high computational efficiency, proper mesh structure and basis functions have to be chosen for sub-blocks according to their structures and materials. In these situations, how to guarantee the continuity of currents in the connection metals is a big difficulty for conventional continuous Galerkin surface integral equation methods. However, discontinuous Galerkin surface integral equation method has loosen the condition of current continuity, and can flexibly combine sub-blocks with different kind of meshes. Meanwhile, by introducing an interior penalty term, the computation accuracy can be kept satisfactorily. In this application, we plan to investigate the intuitive formulation of discontinuous Galerkin electromagnetic surface integral equations, and solve the key scientific problems such as the choice criterion of the stabilizing function associate with the interior penalty term, the convergence property (or the conditioning property of the coefficient matrix), and the control strategy of computation accuracy, and finally establish an applicable discontinuous Galerkin electromagnetic surface integral equations method that can be used for analyzing the electromagnetic problems in complex objects containing many blocks connected with metals.

对飞机舱室等复杂结构内部电磁环境进行精确全波分析仍然是极具挑战性的问题，电磁场面积分方程方法是解决这类问题的重要方法之一。对这类系统进行电磁场分析时，通常需要把多个由金属导体连接的子模块整合在一起。为了提高计算效率，每个子模块需要根据其材料、结构特性采用不同的网格剖分和基函数形式。这种情况下，如何保证子模块之间金属分界面上电流的连续性就成了传统连续伽略金面积分方程方法的一个难点。不连续伽略金电磁场面积分方程方法适当放宽了电流连续性限制，可以将采用不同网格的子模块灵活地连接起来，同时利用内罚函数来实现分界面上电流的弱连续性，以保证计算精度。本项目研究直观形式不连续伽略金电磁场面积分方程方法，解决算法的稳定函数选择、收敛特性分析、精度控制等关键科学问题，拟建立比较完善的直观形式不连续伽略金电磁场面积分方程方法，用于分析包含由金属结构连接的大量子模块的复杂结构电磁场问题。

不连续伽略金法的主要优点是对于复杂目标可以采用区域分块方法求解，每一块可独立进行网格剖分，用不连续伽略金法能够灵活地处理非共形网格。本项目按照研究计划，研究了低阶矢量基函数和阶数步进（marching on in degree，MOD）时域不连续伽略金电磁场面积分方程方法；研究了不连续伽略金面积分方程法计算散射体特征模的方法；研究了应用高阶、分层矢量基函数的不连续伽略金电磁场面积分方程方法；研究了不连续伽略金法与分层基函数相结合的实现方法；研究了不连续伽略金电磁场面积分方程方法的收敛特性与计算精度评估方法。通过研究，提出了一种MOD不连续伽略金算法、不连续伽略金与分层矢量函数相结合的方法，提出了直接忽略直观形式不连续伽略金法中惩罚项的方法。发表了8篇论文，1次国际会议workshop的特邀学术报告。按计划完成了相应FORTRAN程序编写与调试。.本项目研究成果可以用于一般散射体的电磁散射特性分析。特别是带有移动结构的物体如直升机旋翼结构，利用不连续伽略金法可以处理非共形网格计算不同旋转状态下的电磁散射特性；研究成果可以用于分析计算一般散射体、超表面单元、相控天线阵单元及阵列的特征模结构，实现优化设计；可用于对含有大型金属平板结构的系统进行区域分解、然后进行电磁特性分析。

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