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高阶矢量有限元方法及其在三维电磁散射与辐射问题中的应用
Higher Order Vector Finite Element Method for Three-Dimensional Electromagnetic Scattering and Radiation Analysis
【作者】 班永灵；
【导师】 聂在平；
【作者基本信息】 电子科技大学 ， 电磁场与微波技术， 2006， 博士
【摘要】 由于工程电磁场应用的需求，长期以来精确高效的数值分析方法一直是计算电磁学领域的研究重点。本文的研究工作是以高阶矢量基函数核心的高阶矢量有限元方法及其混合方法——高阶矢量有限元／边界积分(FE-BI)方法，主要包括三个部分：高阶矢量有限元／边界积分混合方法的研究、加速高阶矢量有限元／边界积分矩阵系统方程迭代求解技术的研究、实现宽频带电磁参数精确快速仿真方法的研究。在第一部分中，本文发展了一种基于六面体单元高阶矢量基函数的高阶矢量有限元／边界积分混合方法(FE-BI)，并将其用于三维腔体散射和贴片天线辐射问题的分析中。在第二部分，提出了两种有效的新型预条件技术，用于加速高阶矢量FE-BI矩阵方程迭代收敛的速度，其有效性通过腔体散射的算例进行了数值验证，并对其中涉及到的不完全LU分解(ILU分解)对预条件技术的影响进行了讨论。最后一部分发展了几种结合模式阶缩减技术(Model Order Reduction，MORe)的高阶矢量FE-BI方法，包括AWE(渐近波形估计技术)、伽略金渐近波形估计(Galerkin AWE，GAWE)、PVA(Proiection via Arnoldi)、良态渐近波形估计(Well-Conditoned AWE，WCAWE)，用于宽频带电磁参数的快速仿真，实现了一段频带内贴片天线输入阻抗的快速精确计算。 本文对当前计算电磁学领域研究的热点方向——基于高阶矢量基函数的高阶矢量有限元方法进行了比较系统深入的研究，并以其在三维电磁散射和辐射问题应用中的优异表现证明了高阶方法的优势。本文的工作表明高阶矢量有限元方法具有解决工程电磁场问题的优势和潜力，是一种极具发展前景的电磁学数值分析方法。
【Abstract】 In recent years the fields of computational electromagnetics have been seen a considerable surge in research on efficient accurate numerical methods, which have been stimulated by the demands for electromagnetic targets simulations. The emphases of this paper are concentrating on investigating of higher order vector finite element methods and its applications to three-dimensional electromagnetic scattering and radiation. First, higher order vector basis functions corresponding to three finite elements including tetrahedral elements, prism elements and hexahedral elements are studied. Second, a higher order vector finite element-boundary integral method (FE-BI) based on hexahedral elements is developed and employed to compute RCS of cavities and input-impedance of cavity-backed patch antennas. Third, two novel reliable preconditoners are introduced to accelerate the solutions of higher order vector FE-BI matrix equations. The effects of the incomplete LU decomposition involved on the preconditoners are investigated. Numerical results from RCS of cavities demonstrate the efficiency of the presented preconditioners. Finally, combined with model order reduction techniques (MORe) including asymptotic waveform evaluation (AWE), Galerkin AWE (GAWE), projection via Arnoldi, and well-conditioned AWE (WCAWE), several higher order vector FE-BI methods are developed and are capable of producing fast accurate robust wide-band simulations with just one expansion point. The studies of this paper demonstrate high accuracy and efficiency of higher order vector finite element methods and show tremendous potential for the solutions of electromagnetic engineering problems.