开口腔体高波数情况下电磁散射的高阶快速算法研究

Electromagnetic scattering from open cavities with high wave number has been considered as a hot challenging issue in the fields of computational mathematics and electromagnetism. Due to the highly oscillatory nature of the fields, it is difficult to obtain meaningful numerical solution of scattered fields. The project aims at the study of fast high order algorithm for electromagnetic scattering from open cavity filled with homogeneous or inhomogeneous media and with arbitrary shape in the situation of high wave number. The main innovative points are listed as follows. .Firstly, a fast high order algorithm is presented for solving electromagnetic scattering from open cavities filled with homogeneous medium embedded in an infinite ground plane. Compact high order scheme is constructed in cavities domain and for the transparent boundary condition. The fast algorithm is developed for the resulting discrete system with the help of the fast Fourier transform in the horizontal direction, and a Gaussian elimination in the vertical direction, which reduces the equations in the cavity domain to a small aperture system..Secondly, the scattering for open cavities filled with inhomogeneous media is studied. In the discontinuous interface of various media, in terms of the immersed interface method, high order accuracy can be obtained. In view of the characteristics of the inhomogeneous media, we propose a fast preconditioned iterative algorithm to solve the discrete linear system. . Thirdly, a fast high order algorithm for electromagnetic scattering from open cavity with arbitrary geometry shape is developed. We embed the cavity within a large area with regular shape, in which fast iterative solver will be used to solve the scattering model. The cavity boundary will be treated as a discontinuous interface between two different media. Then the immersed interface method is used to construct a high order method to solve the problem in the whole domain.. The research work will be helpful to promote the multidisciplinary integration of computational mathematics and computational electromagnetics, and the presented algorithms can be easily extended to solve general scattering problems.

开口腔体在高波数情况时的电磁散射特性分析在计算电磁学与计算数学领域都是极具挑战性的热点问题。这种情况下散射场振荡剧烈，传统方法难以得到有意义的数值解。本项目旨在研究高波数时填充各种介质以及任意形状开口腔体电磁散射的高阶快速算法。创新之处在于：针对填充均匀介质的开口腔体的电磁散射方程建立高阶离散方法，并使用Fourier分析与Gauss消去法将腔内方程归结到腔体口径面处进行求解，极大地简化了计算；建立基于浸入界面方法的计算填充非均匀介质的开口腔体散射的高阶算法，结合腔体物理特性和几何特征构造基于Krylov子空间的预处理迭代算法来快速求解线性系统；研究复杂形状的开口腔体电磁散射特性，将其嵌入较大的规则区域，利用浸入界面方法与水平集方法构造相应的高阶快速算法。本项目的研究将促进计算数学与计算电磁学的交叉融合，相关的算法对于一般的散射问题亦有较高的推广和应用价值。

腔体结构电磁散射特性的分析在航空航天、水下探测、军事安全等方面有着重要的应用。高波数情况下腔体的散射具有强烈的震荡特性，应用传统方法难以得到有意义的数值解，在计算电磁学与计算数学领域都是极具挑战性的课题。本项目针对高波数情况下的腔体电磁散射问题进行了深入细致的探索，主要围绕腔体填充各种介质以及复杂外形展开。针对高波数情况下填充均匀介质和非均匀介质的腔体、部分覆盖腔体、复杂形状腔体以及多腔体模型的电磁散射问题建立了一系列的高效数值算法。对非局部边界条件Hadamard超奇异积分的高精度近似、腔体内非均匀介质交界面的高阶离散、高波数腔体散射问题数值离散形成大规模线性系统的预处理和快速求解、复杂腔体外形的准确刻画与处理等关键科学问题进行了认真的研究，完成了拟定的研究目标。所提出的算法集合了数学、物理学和电磁学等多学科的知识和背景，大大缩减了高波数情况下腔体散射的计算量，应用前景广泛且深刻，有利于提高军事与工业应用中腔体目标的隐身性能，并促进各种军用目标的优化设计。