电磁辐射数值模拟中Atkinson-Wilcox定理的推广及新型比例边界有限元格式的发展
Generalization of the Atkinson-Wilcox Theorem and the Development of a Novel Scaled Boundary Finite Element Formulation for the Numerical Simulation of Electromagnetic Radiation
摘要：
比例边界有限元法是由宋崇敏和John P Wolf联合开发的一种新型半分析方法，用于解决弹性动力学问题和土木工程中的相关问题。这种新的方法最近已重新制定了以下几类问题的电磁学：（1）金属腔结构的本征值的确定，2）全波分析的屏蔽微带传输线结构，超大规模集成电路（VLSI）互连，和3）全波分析的周期性结构。本文提出了一种新的比例边界有限元法，用于数值模拟自由空间中任意形状金属结构的时谐电磁辐射。新配方的发展需要推广熟悉的阿特金森-威尔科克斯辐射级数展开，以便适用于任意边界外接的辐射源。
英文摘要：
The Scaled Boundary Finite Element Method is a novel semi-analytical method jointly developed by Chongmin Song and John P Wolf to solve problems in elastodynamics and allied problems in civil engineering. This novel method has been recently reformulated for the following categories of problems in electromagnetics: (1) Determination of Eigen values of metallic cavity structures, 2) Full wave analysis of Shielded micro-strip transmission line structures, and Very Large Scale Integrated Circuit (VLSI) interconnects, and 3) Full wave analysis of periodic structures. In this paper, a novel Scaled Boundary Finite Element formulation is developed for the numerical simulation of the time harmonic electromagnetic radiation in free space from metallic structures of arbitrary shape. The development of the novel formulation necessitates the generalization of the familiar Atkinson-Wilcox radiation series expansion so as to be applicable for arbitrary boundary circumscribing the source of radiation.
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